Consensus Value For Theta 13 Emerging

As September 26, 2012 paper updates the experimental effort to determine the value of the least well known of the three theta angle parameters in the PMNS matrix that govern neutrino oscillation. In its conclusion, it states:

In the space of ten months five experiments have produced results consistent with a value of sin^2(2 theta13)~ 0.1. As a result it can now be considered "well established" that the Ue3 element of the PMNS matrix is non-zero, with a global level of significance well over the conventional 5 sigma discovery threshold. A summary of these measurements, plus the previous hints from global fits, is provided in FIG 4. With the exception of MINOS, all the experiments described in this talk are expecting to take more data, so the precision on the measured value will almost certainly improve significantly. The divergences between the long-baseline and reactor measurements will now come to the fore, with reactor experiments providing precise measures of [Ue3]^2, while improved measurements from T2K can be used to study CP violation, theta 23, and even the mass hierarchy (via matter effects). The field as a whole is therefore rapidly transitioning from theta13 as an unknown parameter, towards theta 13 as a well-measured input for investigating other parameters.

The experiments shown in Figure 4 are KamLand & Solar, MINOS, T2K, Double Chooz, Daya Bay, and RENO. All of the results have 0.09 within the error bars of as May 2012, which matches the central value of the Daya Bay result from last March, the most precise of the six measurements.

The other two theta parameters of the PMNS matrix (theta 12 and theta 23) are also known with some level of precision, so the only parameter of the PMNS matrix that is not known with any meaningful accuracy at this point is the CP violating parameter of the matrix (zero if there is no CP violation, and non-zero if the neutrino oscillation matrix value, for example, from electron neutrino to tau neutrino and from tau neutrino to electron neutrino are not identical. The corresponding value for the CP violating parameter in the CKM matrix which applies to quark weak force flavor transitions in non-zero.

For theorists this development signals an imminent transition from the period of time in which mere pro forma estimates of the PMNS parameters such as the tribimaximal values will be replaced with genuine experimental values for each of the parameters of the PMNS matrix.

Background

There are a number of parameters of the Standard Model.

Some Standard Model parameters are considered "exact" or not treated as "constants" at all, such as the spin-1/2 of Standard Model fermions, the spin-1 of photons, W bosons, Z bosons and gluons, the spin-0 (scalar rather than pseudo-scalar) of the Higgs boson, the charges of the fundamental particles (+/- 2/3 for up type quarks and anti-quarks, +/- 1/3 for down type quarks and antiquarks, +/- 1 for charged leptons and W bosons, and 0 for neutrinos, photons, Z bosons and gluons), the three QCD colors, the three generations of fermions, the precisely eight types of gluons, the existence of left handed and right handed version of all fermions except neutrinos (which come only in left handed particles and right handed antiparticles), the zero masses of photons and gluons, and the assumption that there are exactly four dimensions of space-time. Also in this category are the exact forms of the Standard Model equations and conservation laws (e.g. baryon and lepton number conservation, matter-energy conservation, charge conservation, etc.).

There are other constants in the Standard Model that are measured. Specifically, the masses of each of the twelve types of fermions (with their antiparticles having precisely the same masses), the mass of the W boson, the mass of the Z boson, the mass of the Higgs boson, the coupling constants for the electromagnetic, weak and strong forces, four parameters in the CKM matrix that applies to weak force mixing of quarks, the four parameters of the PMNS matrix that applies to the weak force mixing of leptons, and two "beta function" constants that describe the running of each of the three coupling constants. There is in addition, one constant which is experimentally indistinguishable from zero and generally assumed to be zero in the Standard Model, but not otherwise disruptive to the Standard Model if it is small but non-zero, which relates to CP violation in the strong force. (There are also theoretically expected values of the Higgs boson coupling constants in the Standard Model, but those have not yet been confirmed in detail experimentally.)

A relatively minor variant on the Standard Model in which neutrinos are Majorana, rather than Dirac, in nature, would add two constants to the PMNS matrix and up to three more mass constants for neutrinos (to reflect their Majorana and Dirac mass components respectively). This would also alter the form of one of the "exact" Standard Model conservation laws (from separate baryon number and lpeton conservation to B-L number conservation). Two other experimentally values assumed to be zero in the Standard Model and have measured values consistent with zero, are the proton decay rate and the neutrinoless double beta decay rate for select radioactive atomic isotypes (which is a measure of lepton number violation frequency).

One of the great unsolved mysteries of physics is to discern if there is some means by which the experimentally measured fifteen masses, nine coupling strength constants, and eight mixing matrix parameters can be derived from first principles using some smaller number of fundamental constants.

There is good reason to think that there is some unknown structure or formula that relates these quantitites in a manner that could also explain unsolved problems of fundamental physics like the hierarchy problem (which relates to the way that a large number of very large terms (some not known with precision) that go into calculating the Higgs boson mass from first principles mysteriously cancel out to produce the relatively modest observed value of the quantity.

One of the main barriers to this enterprise is that the accuracy of the estimates of quite a few of the parameters, such as the masses of the five quarks other than the top quark (which can be observed directly due to quark confinement and also have very theory dependent estimation protocols), the three neutrino masses (which are hard to measure because neutrinos interact only via the weak force and are tiny), the beta function constants (which are sensitive to thinny measured very high energy data points), the CP violating term of the PMNS matrix (lower case delta), and the three theta parameters of the PMNS matrix are not known to sufficient levels of precision to exclude a wide variety of possibly spurious, empirically observed numerological coincidences of the values that are consistent with experiment to within the existing margins of error in measuring them.

In contrast, the masses of the top quark, of the charged leptons, of the W boson, of the Z boson, and increasingly of the Higgs boson, as well as all four of the CKM matrix parameters, and the basic coupling constant values of the strong, weak, and electromagnetic forces before adjusting for the running with different energy levels, are all known to considerable precision, and the masses and other properties of many composite particles (e.g. protons, neutrons, atoms, and many classes of exotic mesons and baryons) have also been measured experimentally to a high level of precision. Likewise, Koide's rule provides a very precise empirical relationship between the masses of the charged leptons (although without any known basis for their relationship).

Within the realm of fundamental physics, but not stictly speaking part of the Standard Model, are several other fundamental physical constants known to some reasonable level of precision, most notably Planck's constant, the speed of light, the gravitational constant, the cosmological constant, Hubble's constant (and relatedly, the age of the universe), the measured proportions of "dark matter" in the universe, and Milgrom's MOND constant a0 which accurately describes the effective dark matter distribution at the galactic scale with a single parameter (something not achieved by any of the prevailing dark matter models).

Many quantum gravity theories that could be integrated with the Standard Model (without forming a true grand unified theory) have at least one or two more additional constants related to quantum gravity effects and modification of beta functions to reflect quantum gravity effects at high energies. For example, many such models have a minimal scale of space-time that is fundamental.