Dispatches From Turtle Island

Tuesday, December 22, 2020

Pages

Deur's Work On Gravity

Posted by andrew

517

Physics Literature Regarding Theoretical Post-Diction Of SM Constants

Posted by andrew

148

Apparent Lepton Universality Violations Are Probably Measurement And Statistical Errors

[Rescued from a September 2020 draft]:

In a post entitled "How Big Are The Lepton Universality Violation Tensions With The Standard Model?" I reviewed the evidence that there were lepton universality violations in B meson decays. After reviewing that evidence, I've become convinced that the anomalies observed are some combination of statistical error, measurement error and analysis error. The really key data points are that these anomalies have only appeared in b quark decays, and that:

Lepton universality violations are not seen in W boson decays at the LHC, are not found in tau lepton decays or pion decays (also here), and are not found in anti-B meson and D* meson decays or in Z boson decays. There were still tensions in the data from B meson decays, but the deviations were smaller as of 2019 than they were in 2015 (also here).

The absence of violations in W boson decays is particularly critical. Because this phenomena is only seen "in the semileptonic decays of B mesons involving b → s l+ l− (l ∈ e, µ) neutral current and b → c l ν (l ∈ e/µ, τ ) charged current quark level transitions."

This is because a semi-leptonic decay of a b quark actually has intermediate steps. First, there is a b → c W- step. Then, the W- decays to l- v. This gives you b → c l ν.

There may next be a decay c → s W+ in which the W+ then decays to l+ v. This gives you b → s l+ l− v v with the neutrino and anti-neutrino produced either being virtual particles or invisible.

The critical point is that in a semileptonic decay of a b quark, the leptons arise from one or two subsequent leptonic W boson decays. So, if W boson decays don't display violations of lepton universality, then either the leptons observed in semileptonic b quark decays are produced by some means other than an intermediate W boson decay, exclusive to b meson decays, which decays preferentially to lighter leptons, or there is some error in the observation. The latter result is infinitely more likely.

Friday, December 18, 2020

Scimitar Cat Ancient DNA Provides New Insights

The Scimitar cat, Homotherium latidens (a.k.a. one of the species of sabertooth tigers) split from other big cat species about 22.5 million years ago and did not admix with other big cat species after that point, ancient DNA now tells us (along with information about other traits graphically described above).

The most recent example of one before they went extinct is from 28,000 years ago.

The Evidence For A Strong Equivalence Principle Violation Explained

Stacy McGaugh at his Triton Station blog explains a recent (previously blogged) paper showing convincingly that the External Field Effect predicted by MOND is real, even though it violates the Strong Equivalence Principle of General Relativity.

A weird consequence of the EFE in MOND is that a dwarf galaxy orbiting a large host will behave differently than it would if it were isolated in the depths of intergalactic space. MOND obeys the Weak Equivalence Principle but does not obey local position invariance. That means it violates the Strong Equivalence Principle while remaining consistent with the Einstein Equivalence Principle, a subtle but important distinction about how gravity self-gravitates.

Nothing like this happens conventionally, with or without dark matter. Gravity is local; it doesn’t matter what the rest of the universe is doing. Larger systems don’t impact smaller ones except in the extreme of tidal disruption, where the null geodesics diverge within the lesser object because it is no longer small compared to the gradient in the gravitational field. An amusing, if extreme, example is spaghettification. The EFE in MOND is a much subtler effect: when near a host, there is an extra source of acceleration, so a dwarf satellite is not as deep in the MOND regime as the equivalent isolated dwarf. Consequently, there is less of a boost from MOND: stars move a little slower, and conventionally one would infer a bit less dark matter.

The importance of the EFE in dwarf satellite galaxies is well documented. It was essential to the a priori prediction of the velocity dispersion in Crater 2 (where MOND correctly anticipated a velocity dispersion of just 2 km/s where the conventional expectation with dark matter was more like 17 km/s) and to the correct prediction of that for NGC 1052-DF2 (13 rather than 20 km/s). Indeed, one can see the difference between isolated and EFE cases in matched pairs of dwarfs satellites of Andromeda. Andromeda has enough satellites that one can pick out otherwise indistinguishable dwarfs where one happens to be subject to the EFE while its twin is practically isolated. The speeds of stars in the dwarfs affected by the EFE are consistently lower, as predicted. For example, the relatively isolated dwarf satellite of Andromeda known as And XXVIII has a velocity dispersion of 5 km/s, while its near twin And XVII (which has very nearly the same luminosity and size) is affected by the EFE and consequently has a velocity dispersion of only 3 km/s.

The case of dwarf satellites is the most obvious place where the EFE occurs. In principle, it applies everywhere all the time. It is most obvious in dwarf satellites because the external field can be comparable to or even greater than the internal field. In principle, the EFE also matters even when smaller than the internal field, albeit only a little bit: the extra acceleration causes an object to be not quite as deep in the MOND regime. . . .

The figure above shows the amplitude of the EFE that best fits each rotation curve along the x-axis. The median is 5% of a0. This is non-zero at 4.7σ, and our detection of the EFE is comparable in quality to that of the Baryon Acoustic Oscillation or the accelerated expansion of the universe when these were first accepted. Of course, these were widely anticipated effects, while the EFE is expected only in MOND. Personally, I think it is a mistake to obsess over the number of σ, which is not as robust as people like to think. I am more impressed that the peak of the color map (the darkest color in the data density map above) is positive definite and clearly non-zero.

Taken together, the data prefer a small but clearly non-zero EFE. That’s a statistical statement for the whole sample. Of course, the amplitude (e) of the EFE inferred for individual galaxies is uncertain, and is occasionally negative. This is unphysical: it shouldn’t happen. Nevertheless, it is statistically expected given the amount of uncertainty in the data: for error bars this size, some of the data should spill over to e < 0.

I didn’t initially think we could detect the EFE in this way because I expected that the error bars would wash out the effect. That is, I expected the colored blob above would be smeared out enough that the peak would encompass zero. That’s not what happened, me of little faith. I am also encouraged that the distribution skews positive: the error bars scatter points in both direction, and wind up positive more often than negative. That’s an indication that they started from an underlying distribution centered on e > 0, not e = 0.

This is huge. While it is model dependent, it is the strongest evidence of a violation of General Relativity shown to date anywhere.

Many quantum gravity theories predict equivalence principle violations, although not necessarily the one observed in this case that was predicted by MOND:

Modern quantum theories, however, often require that at some scale the EP must be violated. Usually, the scale is small, no more than a few centimeters.

What sorts of forces violate the equivalence principle? In a way, one type of EP violation is familiar: any vector field which couples to a mass must violate the equivalence principle. To see this, consider electromagnetism, which is a vector field. There are two electrical charges; a positive charge behaves quite differently from a negative charge in an electric field. The existance of a charge and an anticharge is a general feature of vector fields. Then, if a vector field coupled to mass, there would have to be a mass and an antimass which would behave oppositely in the same gravitational field and therefore violate the EP.

Scalar fields also produce EP violations. Scalar charges, unlike vector charges, are not conserved. The statement of charge conservation for a vector charge is Lorentz invariant. The charge of an object is the integral of the time component of its vector current density, which picks up a factor under Lorentz transformation, over a volume element, which picks up a factor 1/. Therefore, the integral as a whole is Lorentz invariant. For a scalar charge, the relevant integral is a charge density (a Lorentz scalar) integrated over a volume; only the volume picks up a factor under a Lorentz transformation, so scalar charges are not conserved and depend on .

Now, strange things can happen because of that factor. Quarks inside the protons and neutrons are highly relativistic; electrons surrounding the nucleus move more slowly (v/c ~ Z). We therefore expect scalar interactions to be composition dependent, since larger atoms' electrons are much farther away from the nucleus and move much more slowly.]

Indo-Iranian Origins

Davidski, at his Eurogenes blog, makes a good case that the members of the Fatayanovo culture (a Chalcolithic and early Bronze Age culture which flourished in the forests of Russia from c. 2900 BCE to 2050 BCE) were linguistically more likely to have spoken a proto-Indo-Iranian language (a major subfamily of the Indo-European language family that includes the Indo-Aryan languages derived from Sanskrit, the Iranian languages such as Persian, and Nuristani, a minor language family of Central Asia now spoken in part of Afghanistan by about 130,000 people), rather than the language of the Corded Ware civilization people with whom this culture is often lumped (whose people may have spoken a Balto-Slavic or Germanic language family language). As he explains:

Fatyanovo males were rich in Y-haplogroup R1a-Z93, which is found at very low frequencies in Balto-Slavic populations (see here). It's actually much more common nowadays in Central and South Asia, where it often reaches frequencies of over 50% in Indo-Iranian speaking groups.

Balts and Slavs are rich in R1a-Z282, which is a sister clade of R1a-Z93, and has been found in Corded Ware and Corded Ware related samples from west of Fatyanovo sites. That is, in present-day Poland and the Baltic states.

Therefore, the origins of the Balto-Slavs should be sought somewhere west of the Fatyanovo culture, probably in the Corded Ware derived populations from what is now the border zone between Poland, Belarus and Ukraine.

Indeed, in my view the Fatyanovo people are more likely to have spoken Proto-Indo-Iranian rather than anything ancestral to Baltic or Slavic (see here).

The Fatyanovo culture is geographically adjacent to the Andronovo culture (ca. 2000 BCE to 900 BCE) which is widely believed to have been Indo-Iranian linguistically. There has also been a notable new discovery about the Andronovo culture.

Deep in China's interior region there is an Andronovo cemetery contains bodies genetically (as judged by mtDNA K1b and a PCA and f3 analysis of the autosomal ancient DNA recovered from one individual in the cemetery) almost identical to Andronovo individuals from the Eurasian steppe, the furtherest East that West Eurasian remains have been seen.

Baigetuobie cemetery is located to the east of the region (yellow triangle "a" above). Archaeologists have unearthed 32 burials belonging to the Andronovo culture. The radiocarbon dating of some samples shows that this cemetery is dated between 1782 BCE and 1439 BCE.

Jiangsong Zhu and his colleagues have just published a paper entitled: The Baigetuobie cemetery: New discovery and human genetic features of Andronovo community's diffusion to the Eastern Tianshan Mountains (1800–1500 BC).

The paper that Davidski is discussing (and differing with in the post linked above) is:

Nordqvist and Heyd, The Forgotten Child of the Wider Corded Ware Family: Russian Fatyanovo Culture in Context, Proceedings of the Prehistoric Society, online (November, 12 2020). DOI: https://doi.org/10.1017/ppr.2020.9

Wednesday, December 16, 2020

Punt Was In Africa

One of the trade partners of ancient Egypt was the ancient kingdom of Punt. The location of that kingdom is not entirely clear from the written historical record. To help resolve that question, scientists at Dartmouth College compared oxygen and strontium levels in samples of baboon tissue imported from Punt found in ancient Egyptian baboon mummies since those levels are distinctive based upon the geographic area where the baboon consumed water.

Bottom line: the Kingdom of Punt was someplace in modern Eritrea, Ethiopia or Somalia, rather than on the Arabian Peninsula as some scholars have suggested.

The paper that is the source of this report is:

Nathaniel J Dominy, et al., "Mummified baboons reveal the far reach of early Egyptian mariners." 9 eLife (2020). DOI: 10.7554/eLife.60860

Friday, December 11, 2020

African Latin in Moorish Spain

The video below (about 11 minutes long) is delightful and packed full of historic linguistic facts and conjectures about a lost Romance language, often known as African Latin that persisted for about seven hundred years after the fall of the Roman empire before becoming extinct. It pieces together the clues we have about this lost language and demonstrates its likely influence, during the Moorish era in Spain, on the modern Iberian languages.

In the 400s CE, the Western Roman Empire fell to East Germanic barbarian tribes such as the Vandals.

Prior to its fall, the Mediterranean Sea was basically a Roman lake, ruled by the Roman empire and with elites at least, and realistically, pretty much everyone, speaking some form of Latin. This included not just the Southern European coast, but the islands of the Aegean sea, Anatolia, the Levant and the North African coast. At its greatest extent, the Roman Empire also extended to include much of Southern Europe (as far north of Southern Britain). The North African province of the Roman Empire was called Africa and that is where the continent got its modern English name.

Prior to the Roman conquest of North Africa, which was a bread belt of the Roman Empire in antiquity, North Africa was inhabited by city states established and ruled by the pre-Hebrew, Semitic maritime peoples known as the Phoenicians and the closely related Punic people of Carthage (roughly speaking in modern Tunisia). Prior to that, and further inland, in lands that the Romans never conquered and weren't really bothered to because it wasn't suitable for Roman style agriculture, were the Berber peoples.

We know from the journal entries of Saint Augustine of Hippo, who died in his 70s in the immediate wake of the Vandal conquest of his North African city, that even before the Vandals conquered this Roman territory, a North African dialect of Latin had been developing.

We also know that while the Vandals took political control of the Northwest African coast of the Mediterranean, that post-conquest the Vandals came to speak the African Latin dialect of the people they conquered, even in official legal documents, rather than converting the people that they ruled to the East Germanic language of the Vandals.

But in the post-Roman Empire era of barbarian rule, North Africa's dialect of African Latin, like that of the other regions of Rome, in which Latin derived Romance languages arose, developed its own regional distinctiveness. The distinction between the letters b and v broke down in favor of using b across the board. The distinction between long and short vowels present in Roman Latin broke down. Consonants at the end of Roman suffix inflections and sometimes the suffixes entirely were dropped. African Latin remained distinct even after a brief reconquest by the Byzantines. The Byzantines were the successors to the Eastern Roman Empire who also failed to replace the local language of North Africa with the Greek language spoken in the Eastern Roman Empire continuously since the Roman Empire conquered it.

While this conclusion is more speculative, African Latin's distinctive features may owe something to a Phoenician/Punic substrate in first generation North African language learners as they began to speak Latin, and from language contact with Berber peoples.

Roughly four hundred years after the fall of the Roman empire in North Africa, Rome's successors were displaced by an expanding Islamic Empire, with lower Egypt and the Northeast Africa falling to it under the the Rashidun Caliphate (632–661), and Northwest Africa and Iberia falling to it completely by 711 CE, under the Umayyad Caliphate (661–750), commencing the Moorish Spain era. Islamic rulers would continue to rule parts of Iberian until 1492 when the Reconquista of Christian Europeans that pushed relentlessly to the South was finally completed and went no further.

These conquests all happened very fast, as these things go, in an age where horses, camels and sail boats were the fastest available means of transportation. Northwest Africa and Iberia were conquered in period of less than fifty years, starting after 661 CE and concluding by 711 CE.

While the invading forces in the Umayyad conquests are conventionally described as Arab-Berber ethnically, North Africans greatly outnumbered Arab elites in these forces. At that time they defeated Hispania, for the most part, they spoke not Arabic, or Berber languages of the hinterlands, but the emerging Romance language of African Latin spoken by the people of much more densely populated Northwest African coastal people.

While it is impossible to say definitively, it appears likely that many or most of the very distinctive features of Spanish, relative to other Romance languages like Italian and French, owes a lot to the influence of African Spanish in Moorish Spain.

In the Middle East, in what is now Iran, in lower Egypt and in Northeast Africa, the Umayyad Caliphate was succeeded by the the Abbasid Caliphate in 750 CE whose capitol was Baghdad which endured in some form until 1258 CE, including the period of the Crusades, and was mostly succeeded by the Malmuk Caliphate based in Cairo commencing in 1261 CE, after a brief interregnum.

In the Northeast and Iberia, the rump Umayyads held on for a while, eventually reorganizing into the Fatimid Caliphate (909–1171) based in Tunis in Northwest Africa and the Umayyad Caliphate of Córdoba (929–1031) in Iberia. African Latin continued to be spoken in this era, with even the most educated people of the day, like Isidore of Seville, a leading encyclopedist of the Middle Ages, writing in a form of Latin heavily influenced by the emerging African Latin Romance language.

Full language shift away from Latin in North Africa wasn't really achieved until these Caliphates were replaced with the rise of the Berber Muslim Almohad Caliphate (1147–1269) (which, of course, never fully replaced the languages of Spain and Portugal which were successors to Latin in Iberia).

Two hundred and sixty years after the fall of the Almohad empire, the last hurrahs of the Moorish Spain era end as the Reconquista runs its course in 1492.

Tuesday, December 8, 2020

What We Know And Don't Know About Mesons And Baryons

Background

What are mesons?

Mesons are composite particles also known as "hadrons" that are distinguished by their integer total angular momentum J (often called simply "spin") (making them "bosons" which behave consistently with Bose-Einstein statistics which means that there is no restriction on the number of them that occupy the same quantum state).

Spatial extent

Mesons are about the same size (about 1.2 femtometer) as a proton or neutron.

Mean Lifetime

All known mesons (like all composite particles bound by the strong force, which are collectively called "hadrons", except protons and neutrons which are bound in atoms) are unstable. Those mesons that have not been detected experimentally are expected to be even less stable that those which have been experimentally observed.

The mesons with the longest mean lifetimes are the charged pions (with an up quark and a down quark, one of which is an antiquark, as valence quarks) and the charged kaons (with an up quark and strange quark, one of which is an antiquark as valence quarks), which have mean lifetimes on the order of 10^-8 seconds. All other known pseudoscalar mesons have mean lifetimes on the order of 10^-11 seconds or less. All other known vector mesons have mean lifetimes on the order of 10^-20 seconds or less.

Gluons, up quarks, down quarks, strange quarks, charm quarks and bottom quarks are always confined in hadrons, all of which, except for protons and neutrons which are bound in atoms, are unstable. No hadrons with valence quarks other than up quarks or down quarks are stable or even metastable like neutrons. Gluons are theoretically stable and massless, but gluons travel very short distances on the order of one femtometer within the hadrons in which they are confined, at the speed of light, between being emitted and absorbed, so they are very short lived in practice.

Free neutrons have a mean lifetime of about 880 seconds. All hadrons which are fermions rather than bosons (which are called "baryons" and have three valence quarks), other than protons and neutrons, have mean lifetimes on the order of 10^-10 seconds or less.

Hypothetical pure "glueballs" with no quark components, which are bosons which QCD naively predicts are possible, have never been observed, but would be unstable with similarly short lifetimes to unstable mesons if the existed.

Some fundamental particles in the Standard Model that are found outside of hadrons are also unstable, specifically, there are means lifetimes for the following fundamental particles on the order of the times shown and in the order shown from longest to shortest: muons (2*10^-6 seconds), tau leptons (3*10^-13 seconds), Higgs bosons (2*10^-22 seconds), top quarks (5*10^-25 seconds), W bosons (3*10^-25 seconds) and Z bosons (3*10^-25 seconds). A unit of Planck time (a potential theoretical minimum of time measurement precision equal to the speed of light times the Planck length) is on the order of 10^-43 seconds.

Photons and electrons are stable. Neutrinos oscillate but don't decay.

Thus, in Nature, we observe only five, free, fundamental particles that have mean lifetimes of 3*10^-6 seconds or more, and two hadrons with lifetimes that long. The two long lived hadrons and the electron, in turn, combine into only a modest number of atomic isotopes which are that long lived, 254 isotopes of 80 elements of which are classified as stable, and there are scores or hundreds more that are unstable but have longer mean lifetimes than 3*10^-6 seconds. (Neutrinos and photons do not become a part of bound composite particles.)

Mass

The least massive meson (the neutral pion) has a mass of about 135 MeV. The heaviest experimentally measured meson mass (for an upsilon mesons which is a vector meson made up of a bottom quark and an anti-bottom quark), which is expected to be the heaviest possible simple meson, is about 9,460 MeV. By comparison, a proton is about 938 MeV and a neutron is about 940 MeV.

There are no hadrons (i.e. composite particles bound by the strong force) that are remotely close to the masses of the W boson (about 80,400 MeV), Z boson (about 91,200 MeV), Higgs boson (about 125,000 MeV) or top quark (about 173,000 MeV), all of which are fundamental particles in the Standard Model (with mean lifetimes of 2*10^-22 seconds or less).

Hadrons including top quarks aren't completely forbidden in the Standard Model (because decay times and hadronization times are probabilistic averages and not fixed values), but require such high energies to produce, and are so unlikely to form even then because of the average time it takes for quarks to hadronize is less than it mean lifetime, and the fact that a single top quark-antiquark pair would normally involve the creation of a pair of particles rapidly moving away from each other, and would be extremely short lived even if they did form again due to the short mean lifetime of a top quark. So, they are usually considered impossible to form for all practical purposes and certainly have never been observed.

Structure

The most well understood mesons are well modeled as a single valence quark with a particular color charge, and a single valence anti-quark with the anti-color charge of the same type, bound by gluons carrying the strong force emitted by both of them and by the gluons themselves, in a sea of quarks.

The valence quarks can be different flavors (i.e. up, down, strange, charm, and bottom/beauty since top quarks are to short lived to form hadrons). If there are the same flavor, they are called "quarkonium".

These simple mesons can be either spin-0 with odd parity pseudoscalar mesons, or spin-1 with odd parity, which are called vector mesons. If the valence quarks are of the same flavor they are called quarkonium.

In theory there are naively 15 possible simple pseudoscalar meson ground state combinations and 15 possible vector meson ground state combinations.

So far 16 pseudoscalar mesons and 14 vector mesons of which have been experimentally observed in their ground states, in addition to many excited states of these mesons that have been observed, although they don't line up precisely with the naively expected states. Of the simple mesons that scientists expect exist, only one has not yet been observed, the charmed vector B meson which should have a mass in the ballpark of 6,344 MeV.

This is a lot of meson resonances over a 10 GeV mass range, spanning two orders of magnitude, even before considering myriad excited resonances.

Seven important lighter electrically neutral valence quark pseudoscalar and vector mesons, however, don't neatly fit into these simple states and present as blends of simple states and replace some of the possibilities that would be expected in a truly simple model.

Three have only up quark and down quark components.

* Pseudoscalar neutral pions, which are a blend of pseudoscalar up quark and down quark quarkonia, producing one type of pseudoscalar meson where two would be naively expected.

* Neutral rho vector mesons and omega vector mesons, which are a blend of vector up quark and down quark quarkonia, producing a different pair of vector mesons than the two vector mesons that would be naively expected, but leaving the total number of vector mesons equal to the expected number.

Four more are electrically neutral pseudoscalar mesons that have a strange quark component.

* Two are the short and long components of electrically neutral kaons with down quark and strange quark components that occur blended into the one naively expected meson giving it unexpected properties.

* Two of the others are electrically neutral pseudoscalar mesons with a up quark, down quark and strange quark components: eta mesons and eta prime mesons, producing a pair of mesons where one mesons with only strange quark components would naively be expected.

Counting the short and long components of the kaon as separate, there is one more pseudoscalar mesons than naively expected overall.

We observe mesons that are scalar mesons (i.e. spin-0 with even parity), or axial vector mesons a.k.a. pseudovector mesons (spin-1 with even parity) whose structure is less well understood. We don't have clear theoretical expectations for how many ground states of these kinds of mesons are possible and the experimental data regarding how many scalar meson resonances and axial vector meson resonances exist in inconclusive because the relevant resonances are not always highly statistically significant or replicated consistently by different experiments, and the structure giving rise to particular well established resonances isn't a matter upon which a consensus has been reached. See review articles at the Particle Data Group here such as this one discussing scalar meson candidates and potential component structures under 2,000 MeV. It notes that:

In the literature, many suggestions are discussed, such as conventional qq¯ mesons, compact (qq)(¯qq¯) structures (tetraquarks) or meson-meson bound states. In addition, one expects a scalar glueball in this mass range. In reality, there can be superpositions of these components, and one often depends on models to determine the dominant one. Although we have seen progress in recent years, this question remains open.

A spin-2 meson (generally limited to excited states) is called a tensor meson.

In addition to spin and parity, two key properties of mesons that have to be determined from experimentally measured constants are the meson's mass (usually expressed in electron-volts with an implied divisor of the speed of light squared) and its resonance width. The mean lifetime for a particle is equal to the reduced Planck's constant (h bar, i.e. ħ) divided by resonance width (usually denoted with the capital Greek letter gamma, i.e. Γ). So, the larger the width of a particle (which can be expressed in electron-volt units used for mass and energy at this scale), the more short lived it will be, on average. Width is a convenient form in which to consider this because overall decay width of a particle is equal to the sum of the width of each of its possible decay channels which can only computed theoretically, one by one.

Meson spectroscopy is the enterprise of trying to determine all possible mesons (including excite state of mesons) which could exist and their properties. It is similar to creating a periodic table and table of isotopes for atoms. This is done with a combination of particle collider experiments and quantum chromodynamics (QCD) calculations.

Some properties of a hypothetical meson can be determined in a straightforward manner with minimal calculations. All mesons have zero net QCD color charge. The electromagnetic charge, total angular momentum a.k.a. spin, and the parity of a meson, and a list of all types of decays of a meson that are possible in the Standard Model are elementary and trivial to determine for a simple meson from the valence quarks from which it arises and whether the mesons have identical or opposite directions of spin (which is assumed to happen both ways for purposes of determining what is possible). Sometimes, the valence quark structure of a meson clearly isn't something as simple as a quark and antiquark pair and has to be deduced with less settled and consensus interpretations that sometimes produce dozens or even hundreds of papers debating which interpretation is correct.

The key properties determined in the core guts of experimental and theoretical meson spectroscopy primarily consist of the mass and width of the meson, and the properties of its decay channels, which have to be measured or calculated, and depend upon the precise values of experimentally measured Standard Model constants.

The calculations are based mostly* on the QCD equations, the experimentally determined quark masses, and the experimentally determined value of the strong force coupling constant (represented by the lower case Greek letter alpha).

I say "mostly" because electroweak interactions tweak the predominant effect of the strong force interactions, both directly and by facilitating "loops" of interactions mediated through other particles by means other than the strong force to which the source particle can transform, that have to be considered in a complete and rigorous calculation.

Arguably hypothetical glueballs (which have no valence quarks and have not be observed in a pure state) and tetraquarks (which have four valence quarks and been observed in a handful of cases and have candidate masses from 2632 MeV to 6900 MeV) and hypothetical hexaquarks are also mesons sometimes known as "exotic mesons". There could also be "exotic mesons" that are "hybrid particles" which contain a valence quark-antiquark pair and one or more gluons in a bound composite particle.

Predicted and observed baryons.

Baryon spectroscopy exists as well, but has posed fewer mysteries.

All of the experimentally observed baryons fit in the 75 naively expected categories and 43 of those combinations have been observed, while 32 have not been observed: 24 of the combinations predicted to exist but not yet observed have at least one bottom quark, 1 has three charm quarks, and 5 have two charm quarks and no bottom quarks. But some baryons with valence bottom quarks have been observed, and some baryons with two charm quarks have been observed. Like mesons, baryons also have excited states, some of which have been observed.

Every predicted baryon with only up, down and strange valence quarks have been observed, as have all predicted baryons with one valence charm quark.

No predicted baryons with three charm quarks or two or more bottom quarks have been observed, and it is conceivable that it is impossible for that strong force to bind that much quark mass into a single composite hadron although no QCD calculations to date have reached that conclusion.

All of the baryons not observed experimentally have at least one bottom quark, at least two charm quarks, or both, and hence take very high energy collisions to produce and are produced in smaller numbers than other baryons even at high energies, as a result. Thus, the baryons we haven't yet observed are the ones we would expect not to have observed yet.

The proton at 938 MeV is the least massive baryon. The most massive observed baryon has a mass of about 6,071 MeV (a bottom omega baryon with two valance strange quarks and a valence bottom quark), but it is expected that baryons not yet observed will be more massive.

Wikipedia notes that the only observed exotic baryons are the pentaquarks P+c(4380) and P+c(4450), discovered in 2015 by the LHCb collaboration.

A hypothetical triple bottom omega baryon, with three valance bottom quarks, if it can exist, would be the heaviest possible baryon and would be expected to have a mass on the order of 15,000 MeV or so. No other kind baryon with three valance quarks permitted by QCD should have a mass of more than about 11,500 MeV, although some pentaquarks might be more massive.

The New Paper

A new review paper spells out the state of what we do and do not know about meson structure in mesons beyond the simple cases.

The importance of S-matrix unitarity in realistic meson spectroscopy is reviewed, both its historical development and more recent applications. First the effects of imposing S-matrix unitarity on meson resonances is demonstrated in both the elastic and the inelastic case. Then, the static quark model is revisited and its theoretical as well as phenomenological shortcomings are highlighted.

A detailed account is presented of the mesons in the tables of the Particle Data Group that cannot be explained at all or only poorly in models describing mesons as pure quark-antiquark bound states.

Next the earliest unitarised and coupled-channel models are revisited, followed by several examples of puzzling meson resonances and their understanding in a modern unitarised framework. Also, recent and fully unquenched lattice descriptions of such mesons are summarised. Finally, attention is paid to production processes, which require an unconventional yet related unitary approach. Proposals for further improvement are discussed.

Eef van Beveren, George Rupp, "Modern meson spectroscopy: the fundamental role of unitarity" arXiv (December 7, 2020) (review to be published in "Progress in Particle and Nuclear Physics" 2021).

The introduction of the paper explains (in language only somewhat more technical than I usually use in blog posts, with citations and internal references omitted, bracketed comments and emphasis mine):

Knowledge of low-energy QCD is encoded in the observable properties of hadrons, that is, mesons and baryons. Most importantly, hadronic mass spectra should provide detailed information on the forces that keep the quarks and/or antiquarks in such systems permanently confined, inhibiting their observation as free particles. However, since QCD is not tractable through perturbative calculations at low energies, owing to a large running coupling in that regime, quark confinement is usually dealt with employing a confining potential in the context of some phenomenological quark model. The shape of this potential is largely empirical, though its short-distance behaviour can be reasonably determined from one-gluon exchange, resulting in a Coulomb-like interaction, usually endowed with an r-dependent coupling constant in order to simulate asymptotic freedom. At large distances, the potential is mostly supposed to grow linearly, on the basis of flux-tube considerations, which have been observed in lattice simulations of string formation for static quarks. The most cited quark model of mesons with such a Coulomb-plus-linear confining potential, sometimes also called “funnel potential”, is due to Godfrey & Isgur (GI), which also accounts for kinematically relativistic effects. The enormous popularity of the model is understandable, in view of its exhaustive description of practically all imaginable qq¯ systems, including those with one or two top quarks, which had not yet even been discovered then. Experimentalists as well as model builders often invoke GI predictions as a touchstone for their observations or results. However, the GI model does not reproduce the excitation spectra of mesons made of light quarks. . . . Its principal shortcoming is the prediction of much too large radial splittings for mesons in the range of roughly 1–2 GeV, resulting in several experimentally observed states that do not fit in the GI level scheme. Also the lowest-lying scalar mesons, below 1 GeV, are not at all reproduced in the GI model. . . .

Logically, there can be two reasons for the problems of the GI model in the mentioned energy region, namely possible deficiencies of the employed confining potential and/or certain approximations inherent in the model. Let us first consider the employed funnel-type confining potential

V(conf) = − (αs(r))/r + λr , (1)

where the constant parameter λ is the so-called string tension and αs(r) a configuration-space parametrisation of the running strong coupling. Ignoring for the moment the r-dependence of αs, we see that V(conf) is independent of (quark) mass and therefore also flavour-independent, in accordance with the QCD Lagrangian. Consequently, the mass spectrum of a Schr¨odinger or related relativistic equation with such a potential will inexorably be mass-dependent, that is, radial splittings will increase according as the quark mass decreases. This had already been realised by the Cornell group when developing their potential model of charmonium, in which the strength κ of the Coulombic part was fitted to the few then known charmonium observables (quote):

“The recent discovery of the µ +µ− enhancement Υ probably implies the existence of another QQ¯ family, where Q is a quark carrying a new flavor and having a mass of 4–5 GeV. The variation of the spectrum with quark mass mQ is very sensitive to the form of V(r), and present indications are that our ansatz (1.1) may not pass this test.” [ed. In other words, these experimenters modeling mesons made up of a charm quark and an anti-charm quark resolved differences between their theory and experiment by accurately predicting the existence of the soon to be discovered bottom quark.]

Two years later, with more data available, the same authors adjusted their model parameters so as to try to accommodate charmonium as well as bottomonium states, both in the static and the coupled channel version of the model, though resulting in a clearly too heavy 3 3(S(1)) state in the latter case. Also, one of the authors used a slightly smaller value of κ when applying the coupled-channel model only to bottomonium states, by indeed arguing on the basis of a running coupling in the Coulombic part. . . . An empirical way to account for a running strong coupling αs(r) in the context of the static quark model simultaneously applied to charmonium and bottomonium states was [developed] . . . .

Now, the mechanism that allows to reproduce the approximate equal radial spacings in charmonium and bottomonium for the funnel potential, despite the quark-mass independence of its confining part, is a very delicate balance between the Coulombic behaviour and running coupling at short distances, as well as the linear rising at larger distances. However, this is impossible to sustain for light quarkonia, resulting in considerably increased spacings in the energy region of 1–2 GeV, in conflict with experiment. A model proposed by us almost four decades ago, does reproduce the observed radial spacings for light, charm, and bottom quarks, being based on a flavour-dependent harmonic-oscillator confining potential, while also accounting for non-perturbative coupled-channel effects in a manifestly unitary S-matrix formalism. . . .

The other possible reason why the GI and related quark models often fail in light-meson spectroscopy is the usual neglect of unitarisation effects. By this we mean that, as most mesons are resonances and not stable or quasi-stable qq¯, they must strictly speaking be described as poles in some unitary S-matrix, and not as bound states in a static potential. This becomes all the more true if one realises that many mesonic resonances are broad or very broad, some of which having widths of the same order of magnitude as the observed radial spacings. Picking just one typical example from the PDG Meson Summary Tables, we see that the mass difference between the ground-state ss¯ tensor meson f'(2) (1525) and its first radial excitation f(2)(1950) is about 420 MeV, while the full width of the latter resonance is (464 ± 24) MeV. So it is clear that a reliable determination of radial splittings that originate exclusively in the underlying confining potential demands to account for unitarisation effects, which inevitably will give rise to both the observed decay widths and real mass shifts hidden in the spectrum. Note that the size of such a mass shift may very well depend on the specific radial (or angular) quantum number and/or the vicinity of some decay threshold.

The conclusion is as follows:

In this review we aimed at making the case for a systematic treatment of meson spectroscopy based on the quark model for qq¯ states only, yet imposing the requirements of S-matrix unitarity. Thus, in Sec. 1 we started with a brief introduction to mainstream quark models of mesons using a Coulomb-plus linear confining potential, and mentioned the inevitable problem with radial spacings in the spectra of especially mesons made of light and strange quarks. In Sec. 2 we employed a simple unitary single channel model for the S-matrix in order to show discrepancies that may arise when using standard Breit-Wigner parametrisations, in particular when applied to very broad resonances not far above the lowest threshold, like in the case of the light scalar mesons f0(500) and K? 0 (700). Section 3 was devoted to a detailed discussion of static quark models, in which the dynamical effects of strong decay or virtual meson loops on the spectra are ignored. The shortcomings of the relativised meson model of Godfrey and Isgur were illustrated with many examples from particularly light-meson spectra. Furthermore, two fully relativistic static quark models were reviewed as well and shown to have similar or even worse problems. In Sec. 4 we briefly reviewed the very disparate predictions for meson mass shifts, some of them really huge, due to unitarisation or coupled channels in a series of old and more recent models, discussing their differences. Section 5 treated a simple unitarised model in momentum space, called Resonance Spectrum Expansion (RSE) and inspired by the unitarised quark-meson model in coordinate space developed by the Nijmegen group. Its predictive power was demonstrated by successfully describing e.g. the K? 0 (700) resonance, the charmed scalar meson D? s0 (2317), the charmed J P = 1+ mesons, and — in a multichannel extension of the model — even the whole light scalar meson nonet. Furthermore, the most general RSE model, applicable to systems with various quark antiquark channels coupled to an arbitrary number of meson-meson channels, was shown to be exactly solvable, both algebraically and analytically, owing to the separability of the effective meson-meson interaction and the employed string-breaking mechanism. In Sec. 6 the latter general RSE model was used to analyse again the charmed J P = 1+ mesons, thus allowing to dynamically produce the physical states as orthogonal mixtures of the 3P1 and 1P1 quark-antiquark components. This gives rise to two quasi-bound states in the continuum and two strongly shifted states, thus reproducing the observed disparate pattern of masses and widths with remarkable accuracy. Moreover, the same full RSE model as well as its multichannel coordinate space version were employed to describe the axialvector charmonium state χc1(3872), modelling it as a unitarised 2 3P1 charmonium state. The resulting pole trajectories, wave function, and electromagnetic transitions support our interpretation of this very enigmatic meson. Section 7 was devoted to several recent lattice calculations of controversial meson resonances that include meson-meson interpolating fields in the simulations, in order to allow for the computation of phase shifts and extract the corresponding resonance or bound-state pole positions. The results for χc1(3872), D? s0 (2317), the charmed J P = 1+ mesons, and the light scalars largely confirm our description of these mesons. In Sec. 8 we presented a formalism for production processes that is strongly related to our RSE model and satisfies the extended-unitary condition =m(P) = T ? P, with T the RSE T-matrix. The general expression features a purely kinematical, non-resonant real lead 45 term, plus a combination of two-body T-matrix elements with also kinematical yet complex coefficients. Fully empirical applications of the formalism to the controversial vector charmonium states ψ(4260) and ψ(4660) as well as the established Υ(10580) bottomonium state allowed to fit all three resonance-like structures as non-resonant threshold enhancements.
Let us repeat that we did not aspire to carry out a comprehensive review of general meson spectroscopy. Therefore, several alternative descriptions of mesons with very interesting results, like e.g. unitarised chiral models, the generalised Nambu–Jona-Lasinio model, or the quark-level linear σ model, have not been dealt with here at all. Nevertheless, we believe that these approaches have a more restricted applicability to meson spectroscopy, being usually limited to specific resonances or ground states only. In order to be able to infer information on the confining potential, it is necessary to be able to calculate radially excited states without introducing new parameters. We have also not paid attention to truly exotic meson candidates, as e.g. the charmed charmonium-like and bottomonium-like states Z ± c (3900), Z ± c (4430), Zb(10610), and Zb(10650). . . . Nevertheless, in this context it is worthwhile to mention a very recent paper by the COMPASS Collaboration, in which for the first time a triangle-singularity model is fitted directly to partial-wave data, viz. for the controversial a(1)(1420) state reported by COMPASS itself five years ago. The conclusion of this fit is that including the triangle singularity allows for a better fit to the data with fewer parameters, so that after all there is no need to introduce the new a(1)(1420) resonance. This result may have far-reaching consequences for exotic spectroscopy, in view of the increasing number of observed enhancements in the data that cannot be accommodated as qq¯ mesons. Clearly, all such controversial states will have to be refitted in a similar fashion.
To conclude, we recall the mentioned email exchange with a co-spokesperson of the E791 Collaboration about the need for easy formulae to fit the data and a related discussion at the LHCb workshop ‘Multibody decays of D and B mesons”, in Rio de Janeiro, 2015. The latter meeting focused on alternatives to the usual Breit-Wigner (BW) and Flatt´e parametrisations that guarantee multichannel unitarity, even in the case of overlapping broad resonances. In that spirit, we proposed our general RSE formalism, yet with the bare HO energies replaced by a few to-be-fitted real energies and possibly also the Bessel and Hankel-1 functions by more flexible expressions, thus allowing much more accurate fits to the data. Apart from thus guaranteeing manifest multichannel unitarity, the usual two BW parameters for each resonance could then be replaced by only one real energy. Finally, a similar generalisation of our production formalism should also be possible.