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Silvia Pascoli: CP Violation and Leptogenesis

March 5, 2015

The third question after the nature of dark matter and dark energy in cosmology is the following: where does baryon asymmetry in the universe come from ? Maybe there is some connection between the new physics of neutrino masses and the new physics implied by the baryon asymmetry in the universe.

The Sakharov’s conditions for baryogenesis and leptogenesis are the following:
– Baryon (B) or Lepton (L) violation;
– violation of charge-conjugation (C) and of its product with parity (CP);
– a departure from thermal equilibrium.

The above are not sufficient conditions, but they need to be satisfied to generate dynamically a baryon asymmetry in the universe.

You need some specific processes to generate B or L violation. In the standard model the combination B-L is conserved, while L is violated at the non-perturbative level. A lepton asymmetry is converted in a B asymmetry by sphaleron effects at T>100 GeV. If neutrinos are Majorana particles, L is violated.

You need also C and CP violation, because if you produce a particle which decays as X->lq (where l is a lepton and q a quark, e.g.), in the conjugate process you do not create an asymmetry. And you need to be out of equilibrium, otherwise the inverse process lq->X will also occur and cancel the asymmetry. The decay products do not have enough energy to produce back the gauge boson X in an expanding universe.

See-saw type-I models cn be embedded in Grand-Unified theories and explain the baryon asymmetryvia leptogenesis. You introduce a right-handed neutrino N, and couple it to the Higgs boson. For heavy masses of N, one can get values of the neutrino masses in the right ballpark of 0.1 eV. It explains light neutrinos very economically.

At temperatures higher than M, the right-handed neutrinos N are in equilibrium with the thermal bath. When the temperature falls below the process producing N stops. N is Majorana so it will produce both leptons and anti-leptons, so there must be a difference decay rate N->lq and N_c->l_c q_c. This is the basic picture of leptogenesis in this type of model.

To compute the resulting baryon asymmetry one needs to evaluate the CP asymmetry arising from the above decay reactions. A solution of the Boltzmann equations takes into account the wash-out of the asymmetry. Finally one needs to convert the lepton asymmetry into the baryon one.

Can we test leptogenesis ? No: it is physics at very high energy scales we cannot reach. But we can test the conditions under which it can happen. If the conditions are satisfied, this would be a strong indication that the model is correct.

Lepton number violation could be generated at low energy by neutrinoless double-beta decay. Lepton-number-violating tau and meson decays could also be searched for. It is in neutrinoless double-beta decay where we lay our greatest hopes for a signal of LNV.

The decay rate in 0v2B decay depends on the neutrino properties and on the effective Majorana mass parameter, which depends on mixing angles which are known, and CPV phases which are unknown. Masses are partially known and also enter the equation. When masses are nearly degenerate, the effective Majorana mass is only dependent on angles and phases.

The other key piece of information is CP violation. There are hints in favour of this from neutrino experiments, particularly T2K which looks at muon to electron neutrino experiments, and reactor neutrino data (Daya Bay, Reno). These hints will be tested in the coming generation of experiments. The CP asymmetry peaks for sin^2 theta_13 at 0.001, A large angle makes the searches possible but not ideal. CP violation effects are also more pronounced at low energy.

In the current generation experiments we will be able to get some further information on these hints on the value of delta. But we will have to wait for more: LBNE could get up to 5-sigma discovery, as could T2HK. To go further you need a true neutrino factory.

If the delta phase is the only source of CP violation, the maximal value for the baryon asymmetry can be in the right ballpark because it contains sin theta_13. If sin delta is close to 1, this could be a viable way to generate the baryon asymmetry.

Leptogenesis can thus be the origin of hte baryon asymmetry. It requires L violation, C and CP violation in the lepton sector, and departure from equilibrium. The latter is automatically true in an expanding universe, the other two can be tested by experiment.

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