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Home , X and Y bosons

CP violation in , possible explanation of the - antimatter asymmetry in the Universe. PMNS matrix and the DUNE experiment at Fermilab.

The PMNS matrix describing the oscilltions has similar form to the CKM matrix. The most general form of the neutrino mixing can be written in the standard form of (11.93):

a value of the phase δ other than 0 or π will give rise to CP violation and differences in the behavior of and antineutrinos. The experimental values of the mixing angles θ12, θ13 and θ23 are now reasonably well-determined by the neutrino oscillations experiments, as discussed at the beginning of this course. It will hopefully be measured in future long-baseline oscillation experiments such as DUNE using beams of neutrinos and antineutrinos produced in accelerators, and a value other than 0 or π will imply CP violation in the neutrino sector. Beyond the Grand unification of Interactions

“What is the path? There is no path. On into the unknown”. Goethe (quoted in M&S) It has been noted, that running interactions constants become closer with energy, and possibly on the end we will achieve the unification of constants. This is viewed as a possible basis of a GUT), already attempted, albeit not perfect yet. Later possibly the physic theory will be unified also with the theory of gravity, now separate and not discussed in this course. The strength of an interaction depends on the distance over which it acts, or more precisely on the magnitude of the associated energy scale μ2. The strong interaction coupling (as we saw) decreases with μ2, (see e.g in Figure 7.3 in M&S and in our lectures), while the electroweak couplings vary more slowly, and an extrapolation from their low-energy values suggests that the various couplings might become equal at a value (see Fig 12.1) Grand Unification (GUT) (2)

15 2 The unification mass MX is estimated to be of order of 10 GeV/c , and gs is related to the QCD coupling αs (Section 7.1 M&S) by:

The electroweak couplings in Fig 12.1 are defined in Sections 2.2 and 10.1.2 (M&S):

In grand unified theories (GUT) all three interactions are united into a single interaction, characterized by a single coupling constant gU, at the unification mass. Of course, this interpolation assumes that nothing totally unexpected will emerge between energies of order 10 2GeV and 1015GeV that could spoil these predictions, this assumption is central to grand unified theories Grand Unification (GUT) (3) The earliest GUT is proposed by Georgi and Glashow in 1974, and the known and leptons are common families. As in the standard model the three color states of the down , Grand Unification (GUT) (4)

Mases of both and Y “unification” are assumed to be of order od 1015 GeV/c2. At the unification mass, all the processes, listed in the previous slide, are characterized by the single ‘grand unified coupling constant’ gU , whose value is such that the analogue of the fine structure constant is

At energies E << MX, MY , processes involving the exchange of the X and Y are heavily suppressed because of their large masses, in the same way that W± exchange processes are suppressed relative to electromagnetic ones in the unified electroweak theory. Because of this, processes involving the exchange of X and Y particles are difficult, but not impossible, to observe at presently attainable energies, as we will see later.

First in the next slides, however, we briefly comment on two other striking predictions of this simplest this GUT theory. Grand Unification (GUT) (5) Quark and charges

An attractive feature of the Georgi–Glashow model is that it offers an explanation of one of the longest-standing mysteries in physics – the equal magnitudes of the electric charges of the and . In the standard model this equality is guaranteed by assigning electric charges 2e/3 and -e/3 to the u and d quarks, where -e is the charge of the electron, but no explanation is given for these empirical assignments. However, in the Georgi–Glashow model it can be shown that the sum of the electric charges of all the particles in any given family must be zero (quarks and leptons are in GUT in one family) , it gives

3Qd + e = 0, where Qd is the charge of the . Hence Qd is –e/3 in terms of the electron charge, and the factor of 3 is seen to be a consequence of the fact that the quarks have

three distinct color states. The charge of the Qu is shown to be 2e/3 by a similar argument, and the equality of the proton charge

Qp = 2Qu + Qd = e and the charge follows from the usual quark assignment in proton p = uud. Grand Unification (GUT) (6) The weak mixing angle

When the strong and electroweak interactions are extrapolated to the unification mass MX, they are characterized by a single coupling constant gU . As a result, the three effective low-energy couplings of the standard model can be expressed in terms of only the two parameters gU and MX . In other words, in grand unified theories one of the three low- energy coupling constants can be predicted, given the values of the other two. It is conventional to convert this result into a prediction of the weak mixing angle θW , which is related to the coupling constants (12.1b) by (10.8). In the Georgi–Glashow GUT model this can be shown to give the value 2 sin θW = 0.21 (12.5) This value is encouragingly close to the measured value, but is not in precise agreement. Grand Unification (GUT) (7). The The most striking prediction of grand unified theories is that the proton becomes in GUT unstable, and in the Georgi–Glashow model it can decay by a variety of processes involving the exchange of X and Y bosons and their X and Y . Two of the related basic vertices are shown in previously discussed Figures 12.2(c) and (d). The model predicts three more such vertices, which are shown in Figure 12.3, and there are also another five that can be obtained from Figures 12.2(c) and (d) and Figure 12.3 by replacing all particles by their antiparticles. They predict the proton decays such as by mechanisms like those shown in Figure 12.4 below. Grand Unification (GUT) (8). The proton decay In such processes of a proton decay, both the and lepton numbers are not conserved, but the combination B-L as below is conserved:

The predicted lifetime of the proton in GUTs is extremely long as the effective low-energy coupling G is very small, suppressed by a large mass of unified particles X and Y (see M&S for more details).

A simple dimensional estimate gives for the width of a proton decay:

E here is a characteristic energy of the proton decay, and we assume that E= mp Then we get for the lifetime of a proton:

It gives numerically: Grand Unification (GUT) (9). The proton decay This value of the proton lifetime in GUTs is, however, very sensitive to the value chosen for the unification mass In other grand unified theories in which the unification mass may be larger, the lifetime can be as long as τ = 1032 − 1033 years. For comparison, the age of the universe is believed to be of order 1010 years. Proton decays are very rare events. For example, 300 tons of iron would only yield about one proton decay per year if the lifetime were of order 1032 years. Several searches have been conducted: with the IMB water Cerenkov detector in the US and then with Camiocande and Super-Camiocande in Japan. The results of these searches are expressed as lower limits on the partial lifetimes (see in M&S). E.g if a p → π0 + e+ decay occurs, the positron would be detected as a cone of Cerenkov radiation whose radius depends on the velocity of the particle, while the particle energy can be inferred from the number of detected. The neutral would decay almost immediately into two photons, since the neutral pion lifetime is about 10−16s, and the photons would in turn interact to produce and two further cones of Cerenkov radiation, as indicated schematically in Figure 12.6 on the next slide. Grand Unification (GUT) (10). The proton decay

In the Georgi–Glashow model, the branching ratio B(p → π0e+) is predicted to be about 0.3, and the Super-Camiocande experimental results are incompatible with the predicted lifetime. However, other GUT models, predict longer proton lifetimes, and are compatible with the proton decay data. To improve significantly these results are difficult since we need very large mass detectors, there is no way around for studies of the proton decays.