How Long Do Exotic Particles Last?

Exotic hadrons and higher generation leptons are very short lived, and most are not found in Nature, or anywhere outside extraordinarily expensive high energy physics laboratories.  Their lifetimes are summarized below.  

How Does The Standard Model Determine Mean Lifetimes For Hadrons?

In principle, all of these mean hadron lifetimes ought to be possible to calculate from first principles using Standard Model physics and its 26 or so experimentally measured constants (i.e. the four CKM matrix parameters, the four PMNS matrix elements, the three fundamental force coupling constants, and the fifteen experimentally measured fundamental particle masses, plus constants like the speed of light, Plank's constant, and pi which are not generally considered to be "Standard Model" parameters, in particular).

Generally, the essence of the way that this is done is by determining the potential strong and weak force decays available for each hadron considering the relevant conservation laws, then assigning a time estimate to each possible decay path that leads to decay products with lighter combined rest mass and expressing that number in the form of a decay width, and then adding up all of the available path specific decay widths in the correct way so that the total decay width can be determined and converted back to mean lifetime.  

In general, the more mass-energy conservation permitted decays are available, the faster a particle will decay.  The decay widths of each available strong force decay is generally about six or seven orders of magnitude larger than that of each available weak force decay, so the mix of available strong force and weak force decays that are available dramatically influence the rate at which decays take place.

To do this from first principles for any given particle would require you to first calculate the masses of each of the roughly 700 possible ground state hadrons and many more possible excited state hadrons to determine which decay paths were permitted by mass-energy conservation, but with the crutch of experimentally measured masses for all or almost all of the hadrons which could plausible be in the decay paths for heavier hadrons, this task becomes much more manageable.

In the case of an undiscovered particle, the physicist must first predict the mass of the particle itself, and then examine all decay channels fitting known potential decay products that are permitted by conservation laws, but must finally consider whether there are any other undiscovered particles which could plausible be a decay channel for the undiscovered particle being evaluated and if so, must estimate the masses of these particles as well.

Mass estimates for undiscovered particles can start with simple extrapolation of patterns from the masses of particles that have some similarities with the target particle, as Gell-Mann did back in 1964 with the Omega baryon, and then can be refined by first principles calculations using tools like lattice QCD, which are much harder to do, but provide a more rigorously supported justification for the predicted value if done with sufficient precision.

In practice, all of the values below are experimentally measured values, because it is currently easier to obtain experimental observables, like particle masses, than it is to calculate them with precision using QCD.

The Seven Stable and Metastable Particles (Lifetimes Greater Than 10^-5 s)

Only seven kinds of composite or fundamental subatomic particles have a mean lifetime of more than 10^-5 (i.e. one hundred thousandths) seconds.

The Two Stable Or Metastable Spin 1/2 Baryons

*The proton (stable). This is a spin 1/2 baryon made up of two up quarks and one down quark.  This is the lightest possible baryon because less binding energy is required to bind a spin 1/2 baryon than a spin 3/2 baryon, and because it has the lightest possible spin 1/2 quark content, since the Pauli exclusion principle makes it impossible to have a three up quark baryon with spin 1/2.  Furthermore, conservation of baryon number prohibits decays into lighter mesons with equivalent quark contents (something that is far less problematic for meson decays since mesons have zero baryon number).

*The neutron (which is stable when bound in a stable atomic nucleus, but has a mean lifetime of 880 seconds as a free particle).  This is a spin 1/2 baryon made up of one up quark and two down quarks.  Neutrons can decay to protons via beta decay, which involves the weak force, but not via the strong force, because neutrons are only slightly heavier than protons because the binding energy is very similar but the down quark is slightly heavier than the up quark (even though this difference is muddied by the translation of the constituent quarks with their masses into binding energy amounts) leaving no other available strong force decays that conserve baryon number.

The Five Stable Fundamental Particles

*The electron (stable). This is a fundamental particle in the Standard Model.  As the lightest charged lepton, it cannot decay into anything lighter while still conserving charge and lepton number.

*The three kinds of neutrinos (whose stability is limited as the three neutrino flavors, electron, muon and tau, oscillate between each other in a process that is not yet fully understood). This is a fundamental particle in the Standard Model.  Neutrino oscillations conserve charge, since all neutrinos have zero electric charge and conserve lepton number.  Oscillations from lighter neutrino mass states to heavier ones require a conversion of energy into mass, but because all three neutrino types are so light, it doesn't take much kinetic energy to make an oscillation possible and neutrinos often have high kinetic energy relative to their rest mass.

*The photon (stable until it hits a charged particle). This is a fundamental particle in the Standard Model.  Since it has zero mass to start with, it can't decay into anything else with less rest mass, although it can have significant electromagnetic energy that can be converted into charged particle-charged antiparticle pairs in the right circumstances.

The Four Most Stable Exotic Particles (Lifetimes Less Than 10^-5 s And Greater Than 10^-9 s)

The muon and three kinds of spin zero mesons (and their antiparticles) have mean lifetimes of more than 10^-9 (i.e. one billionth) of a second.

The Muon, A Fundamental Particle

The mean lifetime of a muon, the second generation electron, which is a fundamental particle in the Standard Model, is on the order of 10^-6 (i.e. a millionth) seconds. This is about 100 times as long as the three longest lived types of mesons discussed below.  It can decay only via the weak force.

The Three Most Stable Mesons

The charged pion made of an up quark and an antidown quark, the charged kaon made of an up quark and an antistrange quark, and the long form of the neutral kaon consisting of the linear sum of a down quark and an antistrange quark (which appears only in combination with the short neutal kaon linear combination of the difference between that particle with a much shorter mean lifetime), all have mean lifetimes on the order of 10^-8 seconds.

The Many More Ephemeral Exotic Particles (Lifetimes Less Than 10^-9 s And More Than 10^-25 s)

About a hundred other kinds of hadrons, tau leptons (i.e. third generation electrons), top quarks, W bosons and Z bosons all have mean lifetimes of less than a billionth of a second.  Gluons are also effectively very short lived.

The Six Most Ephemeral Fundamental Particles

A tau lepton (i.e. a third generation electron) has a mean lifetime on the order of 10^-13 seconds, which is similar to the longer lived B mesons, D mesons, and spin-3/2 baryons, and is about 100,000 shorter than that of the longest lived mesons.  It decays much faster than the muon because its higher rest mass relative to the muon makes many more decay channels available to it than are available for the muon.  For example, a tau is heavy enough to decay to a muon, an electron, or up to four pions (charged and neutral combined).  But, muons are already muons so they can't decay to muons, and are lighter than pions.  Decays involving muons and pions make up much of its branching fractions, and it is also heavy enough to have a significant minority of decays that involve decays to kaons, which are also heavier than muons.  Tau leptons are also much lighter than W bosons, so the mass of the virtual W boson in tau decay does not place an upper boundary on its decay products.

The Higgs boson's mean lifetime has not been measured experimentally, but is predicted in the Standard Model to have a mean lifetime of 10^-22 seconds - similar to that of many hadrons with aligned spins, and about 1000 times as long as that of the top quark, W boson and Z boson.

Gluons are in principle as long lived as photons, but in practice, are only exchanged between color charged objects at very short range while moving at the speed of light, so they are in existence for only a time period on the order of 10^-24 seconds and certainly far less than 10^-9 seconds.

The mean lifetime of a top quark (i.e. the third generation up type quark) is about 5*10^-25 seconds, which is about ten times shorter than the shortest lived hadron. And, since theory dictates that this time period is too short for hadronization to occur, all hadrons should have longer mean lifetimes than the top quark. 

The W boson and Z boson have mean lifetimes of about 3*10^-25 seconds, i.e. about 40% shorter than that of the top quark (which makes since because W bosons are what makes top quark decays possible).

Decays of heavy fundamental particles are sensitive to the existence of undiscovered fundamental particles which could provide decay paths for the heavy particles, but only if the undiscovered fundamental particles have some quantum number that is present in the original particle or can produce pairs of particles in the ends state that cancel each other out with respect to this quantum number.  For example, a quark with lepton number zero can produce leptons as decay products, so long as they come in lepton-antilepton pairs.  

Of course, examining particle decay widths as a means of detecting new particles only works if the the new particle's decay widths can be measured fairly accurately.  Often, relative decay width measurements are not adequate for this task because the existence of a new particle providing a new decay path doesn't necessarily materially change the relative frequencies of other available decay paths of the particle.  Also, this technique is less sensitive to low branching ratio decay paths which often have the most massive sets of particles and are often therefore hardest to detect.

General Trends For Hadrons (i.e. Mesons and Baryons)

In general, hadrons in which the all of the component quarks have aligned spins (spin 1 mesons and spin 3/2 baryons) are much less stable than hadrons whose component quarks have maximally unaligned spins (spin 0 mesons and spin 1/2 baryons).

In spin 0 mesons and spin 1/2 baryons, in general, the presence of charm and bottom quarks is associated with shorter mean lifetimes.  Likewise, higher generation charged leptons are shorter lived than lower generation charged leptons.  But, this simple trend does not even extend to the case of spin 1 and spin 3/2 hadrons.

Similarly, while some of the longest lived hadrons are also among the lightest, and some of the heavier hadrons are fairly short lived, and there is probably some modest correlation between mass and mean lifetime for hadrons, there is not really a consistent relationship between mass and mean lifetime for hadrons.  Hadrons with similar masses and similar quark contents can have dramatically different mean lifetimes.  

Hadrons can have mean lifetimes much greater than lighter hadrons.  For example, pions, one of the longest lived kinds of mesons, are seven times lighter than protons and neutrons, which are much more stable.

There is a roughly 16 order of magnitude range of mean lifetimes for exotic hadrons (i.e. excluding the proton and neutron), while there is only about a 2 order of magnitude range of exotic hadron masses (which includes the proton and neutron mass).

Exotic Baryons

The most stable exotic spin 1/2 baryons (i.e. spin 1/2 baryons other than the proton or neutron) have mean lifetimes on the order of 10^-10 seconds or less, which is about 100 times shorter than the mean lifetime of the longest lived mesons.

The most stable spin 3/2 baryon, the Omega baryon which consists of three strange quarks, has a mean lifetime on the order of 10^-11 seconds. The Omega baryon's mean lifetime is 1,000 times shorter than the longest lived mesons and 10 times shorter than the longest lived unstable spin 1/2 baryons, but 100,000,000,000 (i.e. 100 billion) times as long as any other spin 3/2 baryon.  It's long life is explained essentially by the fact that the only available decays require one of the strange quarks to decay via the weak force into an up quark (typically into a uss baryon and an pi minus meson made of an antiup quark and a down quark that are produced in the decay of a W- boson emitted by one of the strange quarks as it became an up quark).  Since all combinations of hadrons with exactly three strange quarks have higher masses combined than the Omega baryon, it cannot decay via the strong force.  

The prediction of the Omega baryon's existence and properties with the quark model by Gell-Mann which was confirmed in 1964 was a major confirmation of that model (the model looked at a pattern in spin 3/2 baryons observing that there were four kinds of Delta baryons comprised only of up and down quarks that each had about the same mass, three kinds of Sigma baryons comprised of one strange quark and two up or down quarks that each had a mass about 152 MeV higher than the Delta baryons, two with two strange quarks and one up or down quark with about the same mass about 150 MeV higher than the Sigma baryons, and no candidates with three strange quarks.  Gell-Mann followed the logical progression and guessed that the new sss baryon would have a mass 151 MeV higher than the previous layer of spin 3/2 baryons - in practice it turned out to be 152 MeV higher with the discrepancy being far less than margin of error in the measurement.  At each step, it turns out, this involves about 90-100 MeV of strange quark mass and 50-60 MeV of additional gluon binding energy, although the strange quark mass wasn't known at the time.

As Hyperphysics explains, another step in the Omega baryon decay which also occurs only via the weak force, the decay of sigma baryons (see here), while for example a Delta++ baryon (three up type quarks) can easily decay via the strong force because its mass is greater than the sum of the proton (uud) and positively charged pion (u anti-d) with the same quark flavor numbers allowing it to decay via the strong force but with three sets of the lightest of the quark flavors does not easily decay via the weak force.  This makes it possible to discern the strength of the weak force coupling constant relative to the strong force coupling constant:

The fact that the both the strong force and the weak force initiate decays of particles gives a way to compare their strength. The lifetime of a particle is proportional to the inverse square of the coupling constant of the force which causes the decay. From the example of the decays of the delta and sigma baryons, the weak coupling constant can be related to the strong force coupling constant. This application gives

.

Since the strong coupling constant has a value of about 1 in the energy range around 1 GeV, this suggests a value for the weak coupling constant in the range

.
Similarly, the slowness of charged pion and chaged kaon and long neutral kaon decay is attributable to the fact that all of these processes involve only weak force decays.  This is not unrelated to mass.  The charged pion is the lighest hadron, so its decays can only take place when the down quark or anti-down quark in the meson decays to an up quark of opposite matter-antimatter character to the other quark in the meson leaving no quark flavor numbers to conserve, because there are no lighter hadrons that preserve its quark content.  They slow kaon decays, similarly, require a change in strangeness because there are no other hadrons with strange quarks lighter than this already light meson.  But, the mass is relevant only in relation to other combinations of hadrons with the same amount of quark conservation, not in absolute terms.

All of the other spin 3/2 baryons (even those with only up and down quark content) have mean lifetimes on the order of 10^-22 seconds or less, which is 100,000,000,000,000 (i.e. 100 trillion) times shorter than the longest lived mesons.  This is surprising since the strange quark is the median mass hadronizing quark, rather than being at either the light or the heavy extreme.  Presumably, spin 3/2 baryons without triplets of the same quark type decay quickly via the strong force because they have spin 1/2 counterparts with the same quark content which take less binding energy since the spins are balanced rather than aligned (there are no experimentally measured values for the properties of the bbb and ccc spin 3/2 baryons or for many other of the heavier quark content spin 3/2 baryons).

Delta baryons (which have spin 3/2) contain only up and down quarks, are the shortest lived hadrons of all, with mean lifetimes of about 5.58*10^-24 seconds, while the other spin 3/2 baryons, which contain strange, charm and bottom quarks, have longer mean lifetimes for the reasons explained above.

Mesons

The longest lived spin zero B and D mesons have mean lifetimes on the order of 10^-12 seconds or less, which is about 10,000 times shorter than the mean lifetime of the longest lived mesons.  The other spin zero mesons (aka scalar and pseudoscalar mesons) that are not mentioned above (such as short neutral kaons, and various eta mesons) have mean lifetimes on the order of 10^-11 seconds or less, but are generally longer lived than spin 1 mesons.

The longest lived vector mesons (those with spin one) have mean lifetimes on the order of 10^-20 seconds or less, which is about 1,000,000,000,000 (i.e. a trillion) times shorter than the mean lifetime of the longest lived mesons.  Their greater mass, relative to quark content, makes strong force decay routes to lower spin mesons (for example) available in most cases.  For example, the charged rho and charged pion both have quark contents of an up quark and an antidown quark.  But, the charged rho has a mass of about 775 MeV while the charged pion has a mass of about 139.6 MeV.  Given that the quark mass in both cases is about 10 MeV, the charged rho has gluonic binding energy of about 765 MeV while the charged pion has gluonic binding energy about about 130 MeV, so the rho takes about 5.6 times as much energy to hold together as the pion.

The shortest lived vector mesons have mean lifetimes on the order of 10^-24 seconds for the charged and neutral rho mesons (made up of only up and down quarks), and of 10^-23 seconds for the Omega meson (which is the long form of the neutral rho meson); while vector mesons with heavier constituent quarks are longer lived.

General Considerations and Observations

Five Flavors Of Quarks Have No Mean Lifetimes In Isolation

None of the quarks, other than the top quark, has a mean lifetime that is a meaningful number.  Their mean lifetimes are very dependent upon the kind of hadron in which they are confined.  The more binding energy a hadron has, the more likely it is that it will have many options to decay into products that conserve quantum numbers while involving less mass.  The presence of heavy quarks in a hadron can also increase the amount of mass that can be present in an end state and thereby make more decay routes available, but only at the cost of making decay products that preserve quantum numbers without flavor changing weak force interactions which proceed more rapidly scarce.

For example, an up quark in a proton is perfectly stable, while an up quark in a three up quark Delta baryon, Rho Meson or Omega meson is highly unstable.  A down quark in a proton is perfectly stable, but a down quark in a free neutron has a mean lifetime of 880 seconds.  An Omega baryon, with three strange quarks, is much longer lived than some baryons with fewer strange quarks.

On the other hand, no hadron containing a second or third generation quark is stable, because mass reducing weak force decays are always possible in that situation, even though they are slower than strong force decays. No hadron containing even a single strange quark has a mean lifetime of more than 10^-8 seconds.  No hadron containing even a single charm or bottom quark has a mean lifetime of more than 10^-12 seconds.  Since the slowest hadron decays generally involve cases where only the weak force is available to bring about the decays, these times are reasonable proxies for the characteristic weak force decay time period for these heavy quarks.

Presumably, the mean lifetimes of quarks other than the top quark when unconfined (e.g. at the instant that they come into being during Z boson decay) is longer than the time required for hadronization, but this number is basically counterfactual as all quarks other than top quarks are always observed in a confined state.

Impact of Hadronic Molecular Binding

As noted in the previous post, there are indications that "hadronic molecules" akin to atomic nuclei can form from pairs of B mesons and from pairs of D mesons.  Neither of these "hadronic molecules" is stable and it isn't clear if this form of bonding has an impact on mean meson lifetime, although the comparable phenomena in atomic nuclei, clearly does have the capacity to extend the mean lifetime of a neutrino in some circumstances.

Certainly, there is no theoretical expectation at this time that some otherwise unstable exotic meson or baryon could be even metastable with a mean lifetime as long as a muon by virtue of being part of such a "hadronic molecule", although this is in part because there is very little theoretical work that has been done on the subject.

Mean Lifetime Is An Inverse Function Of Total Decay Width

For those so inclined, mean lifetimes can be converted to total decay widths as follows: mean lifetime equals reduced Planck's constant h divided by total decay width gamma.

Particles With Identical Lifetimes Are Treated As One Particle For These Purposes

At least at the level of precision involved in this post, in the Standard Model, particles and antiparticles have the same mean lifetimes.  Therefore, particles and antiparticles are not counted as different particles for the purposes of this post and are not separately discussed.  Similarly, other particles which are indistinguishable for purposes of mean lifetime (such as different parity versions of fermions, and the eight different kinds of gluons) are treated as one kind of particle for these purposes.

An Aside On Proton Decay

As an aside, a very large share of all beyond the Standard Model theories, and grand unification theories (GUTs) in particular, call for the proton to be unstable, even though proton decay (for example, into a neutral pion and a positron, which have the same charge and spin and lower mass, but which would violate baryon number conservation and is therefore absent from the Standard Model).

Proton decay has never been observed. The experimental bound on the minimum mean lifetime of a proton is about 10³⁴ years. By comparison, the age of the universe is approximately 10¹⁰ years, so the number of protons that have decayed since they formed over the lifetime of the universe is not more than one in 10²⁴. By comparison, there are approximately 3.5*1079 protons in the universe (of which fewer than one in 10<sup>10 are antiprotons). The mean proton lifetime is at least 1036 times as long as the mean lifetime of a free neutron. The mean proton lifetimes is at least 1062 times as long as the shortest observed mean hadron lifetime, which is very close to the minimum theoretical minimum hadron lifetime due to the minimum time necessary for hadronization revealed by the top quark's inability to hadronize.

Personally, I have a low opinion of beyond the Standard Model theories that claim, as some do, that proton decay in a manner that does not conserve baryon number occurs at a very low, but non-zero rate just beyond current detection limits, such as 1036 years.</sup>

Meson Molecules (aka Deusons) Have Been Discovered, But Not Tetraquarks

Background

Composite particles made out of quark and/or antiquarks and bound together by gluons are called hadrons.

There are three possible color charges for quarks (called, e.g., red, green and blue), and three possible color charges for antiquarks (called, e.g., antired, antigreen and antiblue).  Gluons have two color charges (a quark color and an antiquark color), or a linear combination of such couplings (there are actually only eight rather than nine possible color combinations for gluons).

All hadrons are color neutral by virtue of having one quark with of each of the three colors or each of the three anticolors, or by virtue of having a quark with one of the three colors and an antiquark with the corresponding anticolor.

The need for all composite particles to be color charge neutral has a number of corollaries.  One is that all quarks are "confined" in a hadron (subject to the exception of the top quark which decays essentially the instant it is formed into a lighter down type quark, almost always a bottom quark).  The second is that all hadrons have integer electric charge (mesons can have a charge of -1, 0 or +1, baryons can have a charge of -2, -1, 0, +1 or +2).

Two kinds of hadrons have been observed experimentally.

Two quark particles called mesons are made out of a quark and an antiquark (in which the antiquark has the antiquark color charge corresponding the the color charge of the quark in the meson) bound directly by gluons and have spins of 0 or 1.  Due to the requirement of color charge neutrality, mesons always have an equal number of quarks and antiquarks, mesons always have a baryon number of zero.

 Three quark particles called baryons are made out of three quarks, (one with each of the three color charges, or three antiquarks, one with each of the three antiquark color charges) bound directly by gluons and have spins of 1/2 or 3/2.  Due to the requirement of color charge neutrality, baryons are always composed of entirely of quarks and have a baryon number of 1, or are composite entirely of antiquarks and have a baryon number of -1.

There are a finite number of possible meson and baryon  ground states, although this is complicated a bit by the fact that some neutral hadrons appear only in linear combinations of each other, and by the fact that hadrons can have "excited states" with the same quark content but higher masses that the ground state for a particular kind of meson or baryon. The vast majority of observed composite particles fit neatly into one of these boxes.

All but a couple of hadrons (the stable proton and the metastable neutron with a mean lifetime of 880 seconds in a free state) are ephemeral, with lifetimes of 10^-8 seconds or less.

The stable baryons, protons and neutrons respectively, of course, in turn bind together into atomic nuclei which are held together by a nuclear binding force. This nuclear binding force is derivative of the strong force that holds hadrons together with gluons which use a meson called the pion (the lighest of the mesons which is made only of up and/or down quarks) to carry the force between baryons in the nucleus. Each atom in nature has one electron associated with it for each proton in the nucleus in its unionized state. Atoms, in turn, are often bound to each other in molecules via the electromagnetic forces generated by the protons and electrons in the various atoms. The details of these interactions largely flow from the characteristic way that a particular number of electrons arrange themselves around an atom with the corresponding number of protons.

Quantum chromodynamics (QCD), the part of the Standard Model that explains the strong force that confines quarks together into hadrons, allows for a number of composite particles bound directly by gluons that have not yet been experimentally observed and are hence called "exotic." In principle, QCD allows for the formation of composite particles from any color charge neutral combination of quarks and gluons, subject to limitations that arise because the strong force is a short range force.

Theoretical analysis and experimental searches for exotic composite particles bound by the strong force have focused on three possibilities: Glueballs with zero quarks, tetraquarks made of four quarks, and pentaquarks made of five quarks, in each case, bound to each other directly by gluons and having a neutral color charge.

A more comprehensive review of "unconventional" hadrons can be foundhere.  It adds two more categories to my list.

First, mesons with J^PC quantum numbers* not allowed by the constituent quark model (which is not itself strictly a part of QCD proper). Examples of this include any mesons with spins other than 0 or 1, and electrically neutral mesons with J^PC quantum numbers of 0^--, 0^+-, and 1^-+.

There are by my calculations, in the ground state in the constituent quark model, 5 kinds of possible baryons with just one quark flavor (all spin 3/2), 80 kinds of baryons with two quark flavors (40 possible sets of constituent quarks with spin 1/2 and spin 3/2 versions of each) and 240 kinds of baryons with three quark flavors (60 possible sets of constituent quarks with one spin 3/2 and two spin 1/2 versions of each), for a total of 325 possible baryon ground states and an equal number of antibaryons. Naively, there ought to be 25 spin 0 mesons and 25 spin 1 mesons, for a total of fifty but due to linear combinations, group theory considerations and the like, this may not be precisely right. A more technical analysis is found here. There are a potentially infinite or near infinite set of excited states as well (including all scalar, axial vector and tensor mesons).

Second, experimentally detected resonances whose masses and quantum numbers are not easily fit to either theoretically predicted QCD hadrons or to excited states of those hadrons. For example, the paper identifies experimentally detected resonances of less than 2 GeV of mass that seem to have J^PC quantum numbers of 0⁺⁺ (i.e. true scalar mesons), but only four theoretical candidates (two ground states and two excited states) with those quantum numbers in that mass range in the "constituent quark model."

* Strictly speaking J which is often loosely called "spin" is total angular momentum. In this context, P is parity, and C is charge conjugation parity.

The Results

The good news is that recent wave of high energy physics experiments have observed a number of hadron-like particles that do not fit neatly into one of the ordinary meson and baryon boxes, and that these exotic particles seem to have at a minimum, a four quark content including a bottom quark, a bottom antiquark, a down type antiquark, and an up quark, with masses on the order of 10.6 GeV/c² and a width of 15 MeV (implying a mean lifetime of, for example, about a third of the hypothetical Standard Model Higgs boson).

The bad news is that these observations don't appear to be the long hypothesized "genuine tetraquarks" that theorists have been predicting for years. Instead, they seem to be "meson molecules" in which two ordinary mesons become associated with each other.

During the last three years strong experimental evidence from B and charm factories has been accumulating for the existence of exotic hadronic quarkonia, narrow resonances which cannot be made from a quark and an antiquark. Their masses and decay modes show that they contain a heavy quark-antiquark pair, but their quantum numbers are such that they must also contain a light quark-antiquark pair. The theoretical challenge has been to determine the nature of these resonances. The main possibilities are that they are either "genuine tetraquarks", i.e. two quarks and two antiquarks within one confinement volume, or "hadronic molecules" of two heavy-light mesons. In the last few months there as been more and more evidence in favor of the latter.

From Marek Karliner, "Doubly Heavy Tetraquarks and Baryons" (Pre-Print Submitted January 16, 2014).

The body of the paper proposes the name <b>deuson</b> for a "hadronic molecule" made up of two mesons bound together by something very similar to the forces that bind together protons and neutrons in an atom.

Karliner's paper goes on to "provide fairly precise predictions for masses and quantum numbers of the additional exotic states which are naturally expected in the molecular picture but have yet to be observed." The paper also discusses what experimental signatures we should look for because they would reveal even more exotic hadrons beyond the meson molecule model including "genuine tetraquarks."

Discussion and Analysis

As I commented above, this result is the less exciting of the two possibilities, although it is still pretty remarkable in that it represents the first time that something like the nuclear binding force between protons and neutrons in an atom has been observed in a case of hadrons other than protons and neutrons.

The use of the term "molecule" in this context, while apt in conveying the distinction between a true tetraquark and a state in which two separate mesons are bound to each other in a composite particle of some type, clouds the question of whether the force believed to bind the two mesons together is analogous to the nuclear binding force in atomic nuclei, which is derivative of the QCD strong force, or is actually the electromagnetic force that binds atoms together just as it does in ordinary molecules.

The body of the paper, however, resolves this ambiguity and makes clear that the state observed is really analogous to the nucleus of a deuterium atom, in which a single proton and single neutron are bound by the nuclear binding force transmitted via pions, even though term "molecule" which ordinarily refers to two or more atoms which interact electromagnetically, rather than via the strong force or nuclear binding force. As the paper explains at page 2 (citation omitted, some mathematical symbols translated into words, underlining mine):

The most interesting theoretical question is what are these states?

Their quantum numbers are those of a bb ud tetraquark, but such quantum numbers can also be realized by a system consisting of B* anti- B andB*anti- B* "hadronic molecules" loosely bound by pion exchange. The diff erence between these two possibilities is subtle, because they have the same quantum numbers and therefore in principle they can can mix with each other. The extent of the mixing depends on the overlap between the respective wave functions. By a "tetraquark" I mean a state where all four quarks are within the same "bag" or con finement volume, while by "hadronic molecule" I mean a state where there are two color-singlet heavy-light mesons attracting each other by exchange of pions and possibly other light mesons.

The proximity of the two resonances to the B* -anti- B and B*-anti- B* thresholds strongly suggests a parallel with X(3872), whose mass is almost exactly at the D* -anti- D threshold.

It also provides strong support for the the possibility that these state indeed are deuteron-like "molecules" of two heavy mesons quasi-bound by pion exchange. This is because it is very unlikely that two "genuine" tetraquarks just happened to sit at the respective two-meson thresholds. 

The attraction due to exchange is 3 times weaker in the I=1 channel than in the I=0 channel. Consequently, in the charm system the I=1 state is expected to be well above the D* -anti- D threshold and the I=0 X(3872) is at the threshold. In the bottom system the attraction due to exchange is essentially the same, but the kinetic energy is much smaller by a factor of on about m(B)/m(D) approximately equal to 2.8. Therefore the net binding is much stronger than in the charm system.

[Note that, in the quoted material referenced, B is a reference to a B meson (which means that it contains a bottom quark or bottom anti-quark), B* to an excited state of a B meson, D to a D meson (which contains a charm quark or charm anti-quark, but not a bottom quark or bottom anti-quark), D* to an excited state of a D meson, and anti-B, anti-B*, anti-D and anti-D* refer respectively to the antiparticles of these mesons. "X(3872)" is a temporary name assigned to an experimentally observed particle with a mass of approximately 3.872 GeV whose quark components are not known.]

What the underlined language is referring to is that in all known mesons and baryons made up of quarks directly bound to each other by gluons, the mass of the composite particle is much greater than the mass of the component quarks and is highly dependent upon the overall spin of the composite particle, with more subtle variations that seem related to other characteristics of the particle like the electric charges involved.  Even mesons or baryons with the same quark flavor content can have very different masses.

In contrast, the difference in mass between sum of the masses of the number of protons and neutrons in a particular atomic nuclei and the mass of the entire atomic nucleus after adjusted for the impact of the nuclear binding force is slight (although measureable - the slight differences in the amount of mass attributable to the nuclear binding force between different atomic nuclei is what is converted into the energy that powers nuclear fission reactors).  It seems unlikely therefore that a true tetraquark would have almost exactly the same mass as the sum of the masses of two mesons with the same combined quark content.

The hypothetical nuclear binding force between the two mesons in these systems is about a third as strong as the force binding quarks directly via gluons within a hadron.

Conjectures Re Exotic Strong Force Composite Particles

Will we find genuine tetraquarks or pentaquarks?

My conjecture is that we will not, or at least that they will be many orders of magnitude more rare than hadronic molecules of mesons and baryons with each other.

While these composite particles aren't naively forbidden by QCD, there is a factor that may make deusons, and analogous particles made of a meson and a baryon bound to each other in a similar way, greatly preferred relative to "genuine" tetraquarks and pentaquarks.

This factor is that in any given QCD color charge neutral tetraquark, it is always possible to divide the four quarks in the "color confinement bag" into two independent systems, each with a quark of a particular color and an antiquark with a corresponding color charge.  These two-quark subsystems can maintain their color charge neutrality independently without any need for interaction between the two subsystems.   So, there is no need for the two subsystems to be confined to each other in order to maintain a color charge neutral particle.

Likewise, in the case of quarks that could form a color charge neutral pentaquark, it is always possible to break the whole into a two quark subsystem and a separate three quark subsystem, without a need for interaction between the two subsystems to maintain a color charge neutral particle.

If the subsystems that need to exchange gluons with each other are effectively independent of each other, can't confine each other, and don't really exchange gluons with the other particles in the system, how can they be said to ever be a "genuine" tetraquark or pentaquark.

In contrast, this is not true in the case of either mesons, or baryons.  There are no possible ways that their quark content could be broken up into color charge neutral subsystems.

Therefore, it seems plausible that "genuine" tetraquarks and pentaquarks either do not exist at all, or are so rare relative to much less energetic hadronic molecule states that they cannot be found in statistically significant numbers at existing experiments.

Does the plausibility of interactions between quarks in different subsystems of tetraquarks or pentaquarks defeat this reasoning?

Tentatively, my answer is no.

There is a subtle caveat to the analysis above, but I am not ultimately convinced that this defeats the argument above against the formation of genuine tetraquarks or pentaquarks (which can be applied with equal force to any composite particle system with even more quarks that can fit within the effective range of the strong force).

Suppose that you have a B-anti-B molecule.  If the quarks in the B meson have red and anti-red color charge, and the quarks in the anti-B meson have blue and anti-blue color charge, then there is really no reason that there would be direct gluon exchange between the two mesons at all.  On the other hand, if the quarks in the B meson have red and anti-red color charge, and the quarks in the anti-B meson have red and anti-red color charge, it would make more sense that the gluon exchanges between the four quarks in the system would become intermingled with each other.

In the single color tetraquark case, it still wouldn't be necessary to keep all four quarks in one bag to create a color charge neutral composite particle to confine the quarks, but one might expect about a third of all such four quark systems to have more cross-subsystem interactions than the other two-third would experience.

This subtle distinction is even more relevant in any possible pentaquark system.   The quarks comprising a color neutral pentaquark can always be decomposed into a meson subsystem and a baryon subsystem. Indeed, there are actually no fewer than one and no more than two ways that this can happen in any given color neutral pentaquark.  But, every decomposition of a color neutral pentaquark will involve a situation where one of the quarks in the baryon subsystem can participate in the same gluon exchanges with one of the quarks in the meson subsystem as the other quark in the meson subsystem.

Thus, in a pentaquark, the non-trival interactions between subsystems which we would naively think would be possible in about one-third of tetraquarks, would always be present.

Ultimately, however, the fact that tetraquarks and pentaquarks never need to have all of their components confined in one system, even if components in one subsystem can have non-trivial interactions with components of another subsystem, probably deprives them of the simultaneous unbreakable strong force bond to all of the other components of the system that gives rise to ordinary mesons and baryons.  Mere coincidence in space and interactions between component quarks, without true confinement, does not appear to give rise to a "genuine" hadron.

Will our discoveries about deusons and tetraquarks have more than theoretical relevance?

We live in a work with six quark flavors.

Only five of these quark flavors, however, have been observed experimentally to hadronize, although I remain unconvinced that mesons and baryons containing top quarks are theoretically impossible, as opposed to merely very rare, because the mean lifetime of a top quark is not too profoundly shorter than the time frame required for hadronization, so one would expect some small subset of top quarks (only a modest finite number of which have ever been synthesized in an observable situation at all) to have actual lifetimes long enough to permit them to briefly hadronize.

But, there are few conditions in Nature, or for that matter, in man-made contexts other than particle accelerators, in which energies are so great that the heavier quark flavors actually come into being or have meaningful physical consequences (apart, perhaps, from their potential impact, for example, on the values of the physical constants for the masses of the Higgs boson and weak force bosons in a theory beyond the Standard Model where these physical constants are not themselves truly fundamental).

A single exotic quark flavor (the strange quark) in addition to the up and down quarks, is more than sufficient to explain pretty much all observed natural phenomena and all man-made systems not specifically designed to produce heavier exotic quarks - with the possible exception of the cosmology of the early universe and the inner workings of quark stars, if such things, as distinct from mere neutron stars, really even exist at all - something for which there is not particularly strong evidence from astronomy at this point.

I certainly can't easily think of engineering applications that rely on the existence of D mesons, B mesons, and baryons that include charm and bottom quarks. These more exotic hadrons take often immense energies to create and are also exceedingly short lived, even compared to more ordinary mesons and exotic baryons, which makes their engineering applications extremely limited.

What about glueballs?

Theory and experiment are neck and neck in the race to discover, or come up with a reason why we cannot discover, glueballs.  Increasing experimental power is likely to provide a definitive resolution of this question.

The reasoning advanced above, with regard to tetraquarks and pentaquarks, also tends to disfavor glueballs with sufficiently large numbers of component gluons.  If my conjecture is sound, then any glueball capable of being decomposed into color neutral subsystems will indeed do so.  So, only simpler glueball systems are really possible (or at least really likely to form at a sufficient frequency to be experimentally observed and described).  It follows that experimental efforts to detect glueballs should continue to focus on these simpler cases.

There are other reasons that could be proposed for either the non-existence of glueballs entirely, or for them to be far more rare given the rules of QCD than one might naively expect without really conducting the right kind of analysis.  But, those conjectures are beyond the scope of this post.

Did a key mutation dramatically expand where humans could live?

The figure above from the PLOS One article shows the proportion of people able to obtain the key biochemical from plants in yellow and the proportion of the Eurasian variant that lacks that gene in blue.

A new study suggests that humans were able to spread out and take over the world because of a new DNA change (or mutation) that popped up in their DNA 85,000 or so years ago. . . . it let them get away with just eating plants for good brain development. . . .

Human brains are sort of like modern electronics – they need rare materials to have them work as well as they should. While an iPhone needs various rare Earth minerals, human brains need lots of something called long chain polyunsaturated fatty acids or LC-PUFAs. Humans are terrible at making these fatty acids on their own and so have to get them from their diet (sort of like vitamin C).  Unfortunately for our ancestors, humans aren’t very good at turning a plant’s fatty acids into the ones they need.  And even though we are good at getting them from animals, we didn’t start hunting in a big way until around 50,000 years ago. Human ancestors probably got these fatty acids from fish and other aquatic animals.  In fact, scientists have long hypothesized that our ancestors’ need for aquatic animals was a big reason humans were such stick-in-the-muds for almost 100,000 years.  Their inability to get the brain food they needed from plants kept them trapped by the water’s edge, unable to spread across the globe. And yet, humans did start to spread in earnest across Africa around 60-80,000 years ago. This is thousands of years before there is any evidence that they did a lot of hunting of land animals. Clearly something changed sometime just before these humans started moving away from the shore.

A group of researchers thinks that the answer might lie in a mutation that allowed ancient humans to better use plant fatty acids to make the LC-PUFAs they needed for their brains.  Now humans could eat plants to get enough nutrients and so could migrate and conquer the world. The evidence to support this idea is the fact that Africans have a certain DNA difference that Asians and Europeans do not.  This difference strengthens an enzyme (FADS1) that converts plant fatty acids into the ones humans need for their brains.  In other words, Africans have a mutation that allows them to get at least some of their brain fatty acids from plants. When the researchers looked at the DNA surrounding this enzyme in Africans, they saw fewer DNA differences than expected.  This is a telltale sign that once the mutation appeared, it quickly spread through the population (a “selective sweep” in genetics lingo).  So once a few people were able to use plants effectively, they were off and running and quickly populated the world. A close look at the DNA also allowed these scientists to estimate that the mutation first appeared around 85,000 years ago (which fits the story nicely). . . . The actual number from the paper is 85,000 +/- 84,000 years ago.

The researchers also think that this DNA difference doesn’t come without a cost.  They conclude this from the fact that the mutation is no longer than common in Asians and Europeans.  The idea is that once humans could hunt for land animals, they no longer needed to rely on plants and so the mutation was lost. Of course another possibility is that the humans that headed for Europe and Asia just happened not to have this DNA difference any more.

From here which cites Mathias, et al., Adaptive Evolution of the FADS Gene Cluster within Africa (PLOS One September 19, 2012) (open access).

The Controversial Evolutionary Breakthrough Theories

The hypothesis that a small number of key evolutionary mutation with behavioral impact provided a breakthrough that gave modern humans a distinct evolutionary fitness advantage culminating the dominance of modern humans in the Holocene era, and perhaps not actually occurring until a punctuated evolutionary advance at the dawn of the Upper Paleolithic era is a controversial one.  Critics look at the evidence on brain size and see instead a steady and gradual convergent evolution over the course of hominin evolution in all hominin species.

The term "anatomically modern humans" in human evolution and anthropology reflects the notion that "behaviorally modern humans" may have been the product of an Upper Paleolithic or similar behavioral evolutionary package of genetic mutations that took place tens of thousands of years after modern humans had bodies substantially similar to our own.

Indeed, critics question the assumption that gracile modern humans were really smarter in any meaningful way than Neanderthals.  Judged by standard proxies for intelligence like brain size relative to body size, they may actually have been slightly smarter than modern humans.  And, increasing evidence of modest levels of admixture on many occasions between different varieties of archaic homins and between archaic hominins and modern humans also casts doubt on the notion that "anatomically modern humans" are even truly a biological species, as opposed to a mere subspecies of a diverse single modern hominin species that may extend as far back as, perhaps, Homo Erectus. Compare the anatomical and behavioral diversity of domestic dogs, which are undoubtedly a single species.

Problems With The Narrative

1.  Was large scale terrestrial hunting really that rare until 50,000 years ago?

There are many problems with the narrative quoted above. The notion that modern humans were reliant upon fish as their primary source of meat until 50,000 years ago is certainly news to me.  The paper cites for this proposition: Flinn MV, Geary DC, Ward CV, "Ecological dominance, social competition, and coalitionary arms races: Why humans evolved extraordinary intelligence" (2005). Evolut Human Behav 26: 10–46. This source does assert that hunting of large game increased around this time, but offers no factual support or citations to other sources for this key assertion.  

From context, this vague assertion whose dating isn't very precisely pinned down seems to be a backhanded reference to the earliest evidence of megafauna extinctions, but those can also be explained by theories such as the co-evolution of African megafauna with modern humans that left them less vulnerable to the appearance of modern humans, and to the theory that modern humans were more ecologically dominant in arid plains than they were in jungles preventing mass megafauna extinctions before modern humans arrived in these niche ecological zones.

A recent study from Morocco showing that Mesolithic hunter-gatherer populations there that relied heavily on acorns and shellfish for their diet had high rates of tooth decay atypical of hunter-gather populations elsewhere also suggest that heavy reliance on cereals for food was atypical of pre-Neolithic forager populations.  This disfavors the notion that large scale terrestrial hunting was a late arrival in the modern human hunter-gatherer diet.

Flinn, et al., also argues in their 2005 paper in support of the "evolutionary breakthrough" hypothesis that there are no other extant hominin species, but increasingly, it looks as if as recently as 25,000-28,000 years ago there may have been as many as three to five other extant hominin species (the last of the Neanderthals, up to two archaic hominin species in Africa that admixed with modern humans as recently as 10,000 years ago, and at least one or two species from a greater Denisovan/H. Florensis hominin clade which may have persisted a long time on Flores at least and perhaps in relict populations elsewhere as well).  This conclusion tends to disfavor their overall conceptual scheme.

2.  Why is the adaptation least fixed where it would seem to be most needed?

Access to fish as an important limitation on Out of Africa expansion seems an odd for a wave of migration that was predominantly coastal until well into the Upper Paleolithic, particular when the people who would seem to have the greatest need for the mutation in Eurasia don't have it in great numbers.

What do we know about early modern human hunter-gatherer subsistence?

There is certainly archaeological evidence from 70,000 years ago and before of modern human fishing activity from middens and from evidence of harpoon fishing in Africa.

There is also evidence that modern human Cro-Magnons in Europe tended to have more diverse diets favoring smaller game than the diets of contemporaneous Neanderthals who focused more on bringing down big game like mammoths.

There were what appear to be human driven (or at least correlated) mega-fauna extinctions close in time to the appearance of significant and expanding populations of modern humans in Europe, Siberia, Japan, Australia, Oceania, and the Americas (although this evidence is much less pronounced for more tropical areas in Africa, India and Southeast Asia) which demonstrate that these populations clearly did engage in significant terrestrial hunting.  

Supportable Aspects Of The Narrative

There is good evidence in uniparental genetics for a modern human dispersal within African at a date which is 60,000-80,000 years ago as measured by mutation rate dating in Y-DNA and mtDNA which is also close in time to the estimate time of an Out of Africa dispersal measured by the same kind of mutation rate dating.

Indeed, there is a fair argument that the Out of Africa expansion and the expansion of modern humans within Africa were really pretty much the same phenomena operating in different geographic directions.

The possibility that modern human meat consumption was largely confined to fish for the first half of its evolutionary history or so, also restores some viability to the observations associated with the largely discredited "aquatic ape" hypothesis for explaining anatomical differences between modern humans and our closest primate ancestors.

There Clearly Is a Fitness Based Selection Story To Be Told Related To This Gene

Mathias, et al. (2012) do make an unimpeachable case that the gene that allows chemicals critical to brain development to be obtained from plant as well as animal sources which has reached fixation in African modern humans is indeed the subject of a fitness driven selective sweep sometime at or after the time that modern humans arose and before the Out of Africa event.  And, they also are very convincing in their argument regarding the purpose that these gene serves in brain function and nutritional processing.

There are relatively few such clear examples of a distinct fitness based selection of a particular gene in modern humans, so this story has to be a significant one.  Any gene that was the subject of a fitness based selection that was fitness enhancing enough to reach fixation at some point very likely does tell the tale of an important evolutionary pressure that modern humans faced in their prehistory, although determining the exact nature of that evolutionary pressure is more challenging.  

Large numbers of people lived or died based upon whether or not they had this gene sometime in modern human prehistory in Africa.  Likewise, it is clear that something abated that selective pressure sometime after modern humans left Africa.  But, it is hard to say more than that from the scant archaeological evidence regarding the lives of anatomically modern humans in Africa during the 75,000 to 100,000 or more years prior to their expansion out of Africa.

Issues Related To Dating The African Plant Nutrition Processing Mutation and Its Eurasian Variant

The quoted mutation rate date from the Mathias paper in 2012 which is better expressed as 1,000-169,000 years before present is pretty much meaningless for a species whose oldest skeletal remains have been dated to around 195,000 years ago.  

Even a 195,000 years ago figure for its appearance would be less than 1.5 standard deviations from the mean, something with a p-value of 0.10 or more.  For example, it would not be at all implausible given the date generated from genetic date for this gene to associate the appearance of this gene not with the expansion of modern humans within Africa midway through their evolutionary history, and instead with the package of genetic mutations that make modern humans as a species distinct from earlier archaic hominins.  

But, the fact that it is present in Africans and progressively more rare in Europeans means that it probably arose before modern humans left Africa (around 85,000 years ago based upon autosomal mutation rate dating, but more likely around 120,000 years ago based upon archaeological evidence), and not later, even though the genetic evidence would allow for a more recent date.

In order words, the narrative behind the events that caused this gene to reach fixation in African modern humans is clearly a story that is part of our shared pre-Out of African African heritage.

Similarly, the subsequent mutation displacing it in many Eurasians (which has reached fixation only in the Americas and there probably only due to founder effects) may have arisen before West Eurasian-East Eurasian divide around the same time as Neanderthal admixture, as the advent of the mtDNA M and N clades, and as the divide between the B and CT Y-DNA clades.  The latest mutation rate data put these events at about 85,000 years before present, a date whose absolute calendar year accuracy is dubious but whose systemic error is shared pretty much proportionately by other mutation rate dates, particularly autosomal ones for Y-DNA.

This secondary mutation is clearly part of the early Out of Africa story.

Meta Point and Other Commentary

I covered this story when I first came across it and must have overlooked it at the time that it came out for some reason (I had a lot going on at the time).

Maju covered the story when it broke and shared many of the same skepticisms that I do.  Dienekes also had skeptical commentary when it came out.

Part of his confusion, however, follows from a misunderstanding of a key point when he states: "The same logic that applies in Africa should apply in Eurasia-plus but the fact is that Eurasians retain the ancestral allele and related genetic bloc without obvious damage to the brains." In fact, neither the African nor the Eurasian allelles are ancestral. The Eurasian allelle is a mutation that arises after the African one, which in turn replaced an ancestral allelle that no one carries any longer (a point that presumably could be confirmed now from primate or Neanderthal or Denisovan DNA).

The story I quote above also does a decent job of explaining the purpose of this gene which was a point that Maju had found confusing about the paper and its suggested narrative.

What Other Narratives Could Make Sense?

It is notable that the Eurasian version of the gene has not reached fixation anywhere except the Americas.

Could another narrative make sense of the facts?

Suppose that in Africa, modern humans experienced periodic episodes when hunting did not generate enough meat to make up a meaningful portion of the band's diet for some reason and the band instead relied on gathering plants as in the case of the acorn eaters of Mesolithic Morocco.  During these periods people who lacked the gene allowing them to obtain the right biochemicals from plants would suffer impaired brain development and soon enough selection would remove people without this gene from the population causing the gene to reach fixation in Africa.

This ability to live on plants when their ancestors were obligate meat eaters may even be an important reason why modern humans rather than other archaic hominins ultimately become the dominant hominin species in Africa.

But, then suppose that the Eurasian version of these gene appears in someone just before or just after the Out of Africa migration to Arabia.  Indeed, let us suppose that this gene appears in descendants of a tribal leader who is observant enough to notice that his descendants thrive when they grow up eating enough meat, but fair poorly when they grow up eating predominantly vegetables.

Then, this tribe is hit with an extended patch of bad hunting and has to make a choice: stay in the same general vicinity and subsist predominantly on vegetables or take a big risk by making a major migration into unknown territory in the hope of finding game to kill to get meat so his descendants can grow up healthy.

Facing this choice, the tribal leader takes the risky course unlike all of his ancestors, so that he can save his descendants.  He also has the good fortune to do so at a time when the gamble pays off and there is meat to be found in the great unknown territory that no modern human has hunted in before at the time.  Voila, some portion of the founding population of Eurasia has this mutation and develops norms that encourage further exploration when hunting is weak locally, and hence they conquer the world.

Random Physics Thoughts

This post contains some unsourced random musings on physics, some of which are trivial observations, others of which may illustrate my ignorance or constitute category errors, and none of which necessarily even deserve the status of conjectures, as that implies some confidence that a proposition is true, rather than merely throwing an idea "out there" to put it on paper for future consideration.

* In the Standard Model, baryon number (B) is conserved and lepton number (L) is separately conserved, and there is also on obscure kind of interaction which can't be illustrated in a Feynman diagram, in which only B-L is conserved.

* But, the number of fundamental bosons present in the universe is not conserved.  It is interesting that there is not conservation of fundamental boson number even though there is indirectly something akin to composite boson number via baryon number conservation.  Would mesons, which are baryons made of fermions, be a good place to look for possible violations of baryon number by analogy to non-conservation of fundamental bosons number?

* There is also not a fixed number of fermions (because baryon number assigned positive numbers to particles and negative numbers to antiparticles, and lepton number similarly assigns positive numbers to particles and negative numbers to antiparticles).

* Is there any process in which we can determine that we have assigned the correct charges to what we view as particles and antiparticles respectively? In other words, how do we know, that up type quarks with positive electric charge, down type quarks with negative electric charge, and charged leptons with negative electric charge are matter, while up type quarks with negative electric charge, down type quarks with positive electric charge, and charged leptons with positive electric charge are antimatter?

Obviously, the decision to call one of these groups matter and the other antimatter is purely arbitrary, although the stylistic choice to call the kind of charged fermion that makes up 99.9999999999%ish percent of all charged fermions in the universe matter, and the kind of charged fermion that makes up one part in 10^-10ish of all charged fermions antimatter is the obvious and eminently sensible way to make that arbitrary decision.

But, is there any reason, for example, that up type with positive electric charge quarks could be matter, while down type quarks with negative electric charge could be antimatter?

Suppose that a down quark emits a W- boson and becomes an up quark, and the W- boson then decays to an electron and an electron anti-neutrino in simple beta decay.  If an up type quark with positive electric charge were matter, but a down type quark with negative electric charge were antimatter, then ordinary beta decay via the weak force would violate conservation of baryon number.  So, the matter-antimatter designations of quarks in the Standard Model have to be as they are to be consistent with each other.

What about the other side of the beta decay process, however?  Suppose that negatively charged leptons were antimatter and that positively charged leptons were matter.  In simple beta decay, you could get an anti-electron and an electron neutrino, which would still conserve lepton number, if the matter-antimatter assignments were reserved.  Indeed, separate lepton number conservation implies that matter-antimatter assignments for leptons, in general, are separable from matter-antimatter assignments in the baryon sector.

If the ordinary charged leptons were considered to be antimatter, and the ordinary quarks were considered to be matter, then there would be no matter-antimatter asymmetry in the universe in the charged particle sector.  The baryon number of the universe is equal, to a high degree of precision that could easily be perfect due to conservation of charge in baryogenesis and leptogenesis, to the number of charged leptons in the universe.  In that case, all of the matter-antimatter asymmetry in the universe would arise in the electrically neutral neutrino sector.

* The W+ boson and W- boson are antiparticles of each other.  Is there any principled way to state that one is matter while the other is antimatter, or is that a distinction that does not apply to fundamental bosons at all?

Both W+ bosons and W- bosons can be emitted by ordinary matter quarks.  A W+ boson will frequently decay into a charged lepton with positive electric charge which is ordinarily called antimatter, and a corresponding neutrino (as opposed to a corresponding antineutrino) in order to preserve lepton number.  A W- boson will frequently decay into a charged lepton with negative electric charge which is ordinarily called matter, and a corresponding antineutrino.

Since W and Z boson decays produce equal numbers of matter particles and antimatter particles, and since W and Z bosons can be emitted by both matter particles and antimatter particles, it is probably most appropriate to say that they are neither matter nor antimatter (something also true of photons).  There is an irrational part of me that is tempted to think of the charged lepton that is more important than the neutrino produced in a W boson decay, and hence to link of the W- boson as matter and the W+ boson as antimatter.  But, upon reflection, that view simply must be wrong.

* If there truly only one Z boson particle, or are there Z bosons and anti-Z bosons which we simply lack the capacity to distinguish from each other.  The photon analogy, and the fact that the W+ mass plus W- mass plus Z mass equals Higgs boson mass divided by two formula suggests that there are no anti-Z bosons, because otherwise the formula would be W+ mass plus W- mass plus two times the Z mass.  The absence of right handed neutrinos also suggests that there are no anti-Z bosons.

* How can a neutrino be its own anti-particle, and hence have Majorana mass, if its very existence was based upon its need to conserve lepton number in beta decays by balancing out the lepton number of the charged lepton created in those decays?  This is one of the reasons, rightly or wrongly, that I favor the view that neutrinos have Dirac mass, but not Majorana mass.

* The matter or antimatter status of a quark or charged lepton can be determined simply from its electric charge.  In neutrinos, of course, the only way to distinguish neutrinos from anti-neutrinos observationaly is their parity.  If it has left parity, it is matter.  If it has right parity, it is antimatter.

In order for a theory in which there are right handed neutrinos that are direct counterparts of the Standard Model neutrinos with identical masses in the same generations, a particles matter-antimatter status would have to be a completely hidden variable (testable only by seeing if it interacted with W or Z bosons, I suppose), rather than a property determinable by observation of some other property of the particle.

If, as I have supposed, massive fundamental particles acquire their mass through their weak force interactions, however, since all particle types which have no weak force interactions have no rest mass and all particle types which have weak force interactions have rest mass, then sterile neutrinos, if they are really sterile, ought to be massless.

* Do W bosons, Z bosons and/or gluon have the properties of helicity and polarization that photons do?

* How do quarks know how to produce gluons with the right color charges?  Alternately, what happens, for example, to a blue-antired gluon emitted by a blue quark, if there is no red quark around to receive it?

* Is color charge conserved?  I think that it is.  How would we test for that experimentally?

* Gluons carry color charges including anti-color charges.  Am I right that gluons always carry a color charge and an anti-color charge providing it a net balance of matter affiliated charge and antimatter affiliated charge?  If so, gluons are matter-antimatter neutral but in a rather more dynamic way than other bosons.  Maybe not matter-antimatter neutral so much as simultaneously matter and antimatter objects.

* One often thinks, lazily, of color charge as a thing, a particle of its own, that quarks carry around singly and that gluons carry around in pairs.  But, this is wrong, because if it was right, there would be nine kinds of gluons instead of eight.  This in turn makes one wonder if maybe color charge could be a topological feature in three dimensions of a quark or gluon.

* Would it be possible for one to make a W+ boson couple to an up type quark, or to make a W- boson couple to a down type quark?  Does anything but electromagnetic repulsion prevent this from happening?  Could very strong electromagnetic repulsion at very short ranges always prevent this from happening?

* Some days I'm still not entirely clear on why electrons don't spiral down into protons, although I guess conservation of momentum has something to do with it.

* Does gluon source rest mass in a composite particle behave any differently than Higgs boson source rest mass in a composite particle?  Apparently not, but why?

* Supposedly, a hypothetical proton made up of massless quarks would have a mass of 870 MeV or so, extrapolating from the QCD equations.  But, what if that's wrong.  What if gluons actually amplify the rest mass of individual quarks, but can't create rest mass in the absence of a particle that has Higgs boson source rest mass?  If gluons merely amplify the rest mass of individual quarks, then glueballs would have no rest mass.  But, if gluons really do create rest mass in composite objects via their binding energy without Higgs boson interactions, then glueballs would have mass, as predicted.  At some point, does a failure to observe massive glueballs imply that the accepted theory regarding how mass is generated in QCD is wrong?

* All fundamental bosons have some mass-energy, even those with no rest mass like photons and gluons. Each fundamental fermions of the same type (twelve possibilities) and the three kinds of massive fundamental bosons has an exact rest mass associated with it that always stays the exactly the same for all particles of that type (subject to running masses with energy scale).  Given matter-energy conservation, therefore, the only possible source of energy that a fermion can call upon to emit bosons like photons and gluons is kinetic energy or potential energy from its position in fields.  What if an electron is perfectly at rest with no kinetic energy?  How can it emit photons?  How can it have electric charge if it doesn't emit photons, however?  Does it follow that an electron or other charged particle is incapable of being perfectly at rest with no kinetic energy?  Do hot magnets have different amounts of electro-magnetic charge than cold ones as a result?

* I strongly suspect that the possible 1 eV-ish sterile neutrino predicted from reactor anomalies is eventually determined not to exist.

Is The Higgs Boson A Walking Technicolor Glueball?

I've quoted at some length below from the new pre-print on the subject of glueballs in lattice QCD (i.e. one of the main ways of making calculations in the Standard Model theory of the strong nuclear force) by Biagio Lucini.  This is because this fairly readable paper does a good job of discussing the practical limitations involved in the study of glueballs and QCD generally, both on the theoretical calculation side, and on the experimental side.

Lucini also provides a few interesting insights into ways that walking technicolor theory might remain relevant.  In particular, he raises the possibility that the observed Higgs boson could actually be a composite glueball in this beyond the Standard Model theory.

After the quoted material, I make a few observations of my own.

Abstract

Recent numerical calculations of the glueball spectrum in QCD, in SU(N) Yang-Mills theory in the large-N limit and in candidate theories of strongly interacting dynamics beyond the standard model (in which the lowest-lying scalar plays the role of the Higgs boson) are reviewed and their implications for our theoretical understanding of glueballs in QCD-like theories and in strongly coupled gauge theories with a (near-) conformal dynamics are discussed.

Kimchee and Other National Food History

A recent post at Language Log discussed a South Korean effort to change the ideograms used to represent Kimchee, the Korean national dish, in Chinese.

One of my comments, and follow up to it (some by people much more knowledgeable about the subject than I), discussed the history of this dish and other famous national dishes.  I recap the pertinent posts below:

1. John said,

   January 3, 2014 @ 1:06 am
   韓 was also the name of a Chinese kingdom towards the end of the BC years.

2. ohwilleke said,

   January 3, 2014 @ 2:58 am
   As a follow up to John's comment, it is interesting to note that Korea's national dish, Kimchee, is a post-Columbian invention. The spice-hot spice in Kimchee comes from a pepper that is native to Meso-America and probably arrived in Korea via trade sometime in the 17th century CE.
   Korea is not the only country with relatively late arrived signature foods. Kumra the sweet potato of the Maori in New Zealand is a pre-Columbian arrival from South America probably via Easter Island ca. 500-1000 CE. Ireland's famous potatoes are a post-Columbian New World plant, and all of the famous European chocolates are likewise post-Columbian New World transfers. The tea to which the English are addicted was imported by the Dutch India company from Southeast Asia starting around the 16th century. The coffee that Americans started drinking in droves in protest of the English tea trade, of course, originates in Ethiopia. And, the bananas that we envision African primates eating arrived in Africa via Austronesian seafarers probably from Borneo ca. 500 CE. Many of the staple foods of Southern India arrived from the African Sahel where they are native ca. 2500 BCE.

3. Sohbet said,

   January 3, 2014 @ 7:40 am
   Kimchee has found a place in the Hawaiian barbecue restaurants that are ubiquitous on the US West Coast, but perhaps not so much elsewhere. And of course in the Korean-Mexican fusion cuisine that is diffusing out of LA. In a few decades it will be as American as sushi.

4. Victor Mair said,

5. January 3, 2014 @ 11:23 am

6. From Eugene Anderson, renowned Chinese food maven:

7. Good grief, people are obsessed with this. Certainly the Koreans are obsessed with kimchi.
   Ohwilleke is only sort of right, however. Pickled cabbage and so forth is well attested as far back as anything complicated is in east Asia. Chiles just got added to an already-perfected thing. They probably substituted for more expensive stuff, possibly long pepper and/or brown pepper, as they did in most of east and southeast Asia (cf change of meaning of "lada" from long pepper to chile in Bahasa Malaysia/Indonesia).
   There is a traditional pickle in the Auvergne in France that is just like kimchi. No possibility of contact, so far as I know. Just independent invention. Pickled cabbage of one sort or another is all over Eurasia. It uses lactic acid fermentation, which is interesting in itself….

8. Bendrix said,

   January 3, 2014 @ 1:58 pm
   Victor Mair, I think what you're saying about the tradition of pickled vegetables could be said of lots of foods, like noodles, dumplings, breads, etc. But I don't think anyone would argue that makes a won ton any less Chinese.

9. Victor Mair said,

   January 3, 2014 @ 4:10 pm
   @Bendrix
   Quite the contrary, "won ton" is very much Chinese, and I think that even Julie Lee would approve of this name.
   The Mandarin pronunciation is húntún / húntun 馄饨 / 餛飩, but the Cantonese pronunciation, from which we borrowed the English form, is wan4 tan1.
   Along the right side of this article (http://en.wikipedia.org/wiki/Wonton), you can see some of the many different ways of writing the name of this stuffed pasta item, which I've sometimes heard referred to lamely as "dumplings" or "ravioli", but "won ton" has definitely become a solid borrowing in English, so everyone can feel confident in using it.
   Húntún / wan4 tan1 is a very old Chinese word that is cognate with hùndùn 混沌 ("chaos"), which John Lagerwey long ago when we were graduate students together at Harvard used to refer to cleverly as "Humpty Dumpty".
   http://en.wikipedia.org/wiki/Hundun
   See especially the section on Daoist texts. But compare the translation of Zhuang Zi, chapter 7, section 7 (the last section of that chapter) by Mair in his Wandering on the Way, which may be found here (on p. xxxix) and on p. 71 of the same book (available here):
   =======
   The emperor of the Southern Sea was Lickety, the emperor of the Northern Sea was Split, and the emperor of the Center was Wonton. Lickety and Split often met each other in the land of Wonton, and Wonton treated them very well. Wanting to repay Wonton’s kindness, Lickety and Split said, “All people have seven holes for seeing, hearing, eating, and breathing. Wonton alone lacks them. Let’s try boring some holes for him.” So every day they bored one hole, and on the seventh day Wonton died.
   =======
   See p. 16 of the following for a brief paragraph on this subject:
   Mair, Victor H. 1994. "Introduction and Notes for a Complete Translation of the Chuang Tzu." Sino-Platonic Papers 48. (pdf available free here:http://www.sino-platonic.org/)
   For decades I've wanted to write a paper on the cognation of the disyllabic words / morphemes húntún / húntun 馄饨 / 餛飩 ("won ton") and hùndùn 混沌 ("chaos"), together with a study of their origin, which I strongly suspect (am virtually certain) is not Sinitic, but I haven't gotten around to it yet. One of these days I will, since I already have lots of notes assembled for that purpose.

10. Chris Waugh said,

    January 3, 2014 @ 6:35 pm
    @ohwilleke: The sweet potato is kumara, you were missing an a. And it was my understanding that the modern day kumara arrived after Eurpean contact and the pre-European kumara was considerably smaller. Nevertheless, it's a good example of how awesome the ancient Polynesian navigators were, ranging right across the Pacific as far as South America, then back as far southwest as New Zealand. And yes, it's a comparatively late-arriving "signature food" – later, even, than your 500 – 1000 CE. But then again, human settlement of New Zealand was really quite late, happening in the 13th century according to Michael King's "Penguin History of New Zealand".

11. Bendrix said,

    January 3, 2014 @ 8:01 pm
    Victor Mair,
    No, I agree completely that won tons are Chinese. The impression I got from your earlier posts was that you were implying the Koreans' cultural claim to kimchee is iffy because pickled vegetable dishes exist throughout Asia. But I was saying the same could be said of many similar foods – that does not mean, however, that a country's claim to its food culture is invalid.

12. Ferrer said,

    January 5, 2014 @ 8:39 am
    Interesting to note that speaking of lactic acid fermentation of cabbage many dishes have been mentioned, even some from Auvergne in France, and yet nobody has written of Sauerkraut or choucrout. True, Sauerkraut is not spicy, but also highly iconic for Germans and Alsatian French. Actually, Germans are sometimes called Krauts by some foreigners across the Channel.

13. Jongseong Park said,

    January 5, 2014 @ 1:32 pm
    @ohwilleke: As a follow up to John's comment, it is interesting to note that Korea's national dish, Kimchee, is a post-Columbian invention. The spice-hot spice in Kimchee comes from a pepper that is native to Meso-America and probably arrived in Korea via trade sometime in the 17th century CE.
    Chili pepper probably came to Korea slightly earlier, in the late 16th century. The Japanese who invaded Korea in 1592 and 1597 supposedly found chili pepper growing in Korea. The island of Kyushu in Japan had acquired chili pepper from Portuguese traders earlier, and thence it was introduced to Korea through trade. But chili pepper remained unknown to other parts of Japan, so ironically it was from Korea that it was introduced to the rest of Japan.
    Chili pepper was not actually used in Korean cuisine until much later on, around the 18th century. Before that, it was mainly considered an ornamental plant. Even when it began to be used in Korean cuisine, it was used sparingly because it was an expensive spice. Powdered chili pepper became an essential ingredient in kimchi only after the end of Japanese colonial rule in 1945.
    The most common type of kimchi today is made of napa cabbage, but this only became a popular ingredient of kimchi in the late 19th century. It was not easy to grow cabbages in Korea and it was only when napa cabbage was introduced from North China probably around the middle of the 19th century that it began to be used in kimchi. Recipes from the early 19th century mention several different types of kimchi, but none made from cabbages.
    So the kimchi we know today is a product of globalization, quite different from the kimchi of a hundred years ago, let alone that of a thousand years ago. The two essential ingredients, chili pepper and napa cabbage, are both relatively recent imports to Korea.

14. Milan said,

    January 6, 2014 @ 4:01 pm
    @ohwillike: It's not unusual for a national dish, and indeed whole national cuisines, to be rather young compared to the history of a people. The potato for example, an integral part of virtually every German meal, wasn't accepted in Germany until the late 18th century, when Frederick the Great promoted its cultivation in order to fight famines.

Kumara probably left South American a century or more before it arrived in New Zealand.

Of course, not all signature foods are recent.  For example, curry has been eaten in the Indus River Valley since the pre-Indo-Aryan Harappan era.

Also, vaguely on point, the pre-historic hunter-gatherer population of Morocco had very high rates of tooth decay, probably due to a very carb-heavy diet of sweet acorns and snails.  The acorns were likely boiled and also likely made into flours, a good reminder of the fact that flour is much, much older than grain domestication.