Experimental bounds on Lorentz violation in the neutrino sector and baryonic asymmetry

Experimental bounds on Lorentz violation in the neutrino sector and baryonic asymmetry E. Di Grezia (Dipartimento di Scienze Fisiche, Universit`a di Napoli “Federico II”) in collaboration with S. Esposito and G. Salesi. Contents Introduction  Neutron β Decay  Pion Leptonic Decay  Baryonic asymmetry  Conclusions Cosmo05 BONN University, 27Aug -01Sept 2005

Introduction In recent times ultra-high energy Lorentz symmetry violations have been investigated, both theoretically and experimentally, by means of different approaches. The most important consequence of a Lorentz violation (LV) is the modification of the ordinary momentum-energy dispersion law: at energy scales of order of the Planck mass., by means of additional terms which vanish in the low momentum limit

Lorentz violating effects might emerge from: GUT Superstring/M/Brane theories Canonical or Loop Quantum Gravity Noncommutative Spacetime Geometry Nontrivial Spacetime Topology Variable speed of light or physical constants Extensions of Standard Model (SME). There may be a preferred energy scale related to the Planck energy. Even if the fundamental theory is Lorentz-invariant, the effective low-energy theory may not be, because of either symmetry-breaking or quantum effects.

Extensions of the standard dispersion relation can be parametrizes as: where Mindicates a (large ) mass scale characterizing LV. By using series expansion for f we have: Different theories (String Theory, SME, QG) converge to similar expression of dispersion relation in the case n=1.

Different dispersion laws arise from canonical Loop Gravity, Supergravity, or String Theory, NCG. For examplein NCG (G. Amelino-Camelia and T. Piran, Phys.Rev. D64, 036005 (2001)) assuming the canonical commutation relation one finds:

Evidences of violation of the Lorentz symmetry seem to emerge from the observation of: a) ultra-high energy cosmic rays with energies beyond the Greisen-Zatsepin-Kuzmin (GZK) cut-off (of the order of ); (G.T. Zatsepin, V.A. Kuzmin, JETP Lett. 41, 78 (1966)) b) gamma rays with energies beyond 20 TeV from distant sources such as Markarian 421 and Markarian 501 blazars; (F. Krennrich et al., Astrophys.J. 560, L45 (2001)) c) longitudinal evolution of air showers produced by ultra-high energy hadronic particles which seem to suggest that pions are more stable than expected . (E.E. Antonov, et. al JETP Lett. 73, 446 (2001))

Theoretical implications of the modified dispersion relation do carry many threshold effects associated to: • asymmetric momenta in photoproduction, pair creation, photon stability, vacuum Cerenkov; (T.J. Konopka et al., New J.Phys. 4, 57 (2002); R. Lehnert et al. Phys.Rev.Lett. 93, 110402 (2004); Phys.Rev. D70, 125010 (2004); T. Jacobson, et al. arXiv:hep-ph/0209264) • long baseline dispersion and vacuum birefringence (signals from gamma ray bursts, active galactic nuclei, pulsars); (R.J. Gleiser and C.N. Kozameh, Phys.Rev. D64, 083007 (2001)) • dynamical effects of LV background fields (gravitational coupling and additional wave modes), different maximum speeds for different particles; (S. Coleman et al. Phys.Rev. D59, 116008 (1999); arXiv:hep-th/9812418; T. Jacobsonet al. arXiv:hep-ph/0407370)

Proposed or performed experiments, on Earth and in space, to test both Lorentz and CPT symmetries. (R.E. Allen and S. Yokoo, arXiv:hep-th/0402154) atomic experiments (penning trap experiments with electrons, protons and their respective antiparticles, clock comparison experiments exploiting Zeeman and hyperfine transitions, spin polarized torsion pendulum experiments); clock-based experiments to probe effects of variations in both orientation and velocity (employing H-masers, laser-cooled Cs and Rb clocks, dual nuclear Zeeman He-Xe masers, superconducting microwave cavity oscillators);

experiments involving neutrino and kaon oscillations; measurements of cosmological birefringence by interferometric searches of spacetime metric fluctuations. (R. Bluhm, V.A. Kosteleck´y, N. Russell, Phys.Rev. D57, 3932 (1998); S.M. Carroll, G.B. Field, and R. Jackiw, Phys.Rev. D41, 1231 (1990); G. Amelino-Camelia, Nature 98, 216, (1999); Phys.Rev. D2, 024015, (2000)).

Implications in the neutrino-sector • Consequences of a nonstandard dispersion law on neutrino oscillations; (S. Coleman and S.L. Glashow: Phys.Rev. D59, 116008 (1999)) • Striking effects on neutrino physics as a possible explanation of the arrival delays of neutrinos emitted from supernova SN1987A, as well as a possible kinematical stability of neutrons and pions of very high momentum. SN1987A might constitute an interesting laboratory for studying LV’s, because of the relatively high energy of the observed neutrinos (up to 100MeV), the relatively large distances travelled (about 104 light-years), and the short (of the order of second) duration of the bursts; (T. Jacobson, S. Liberati and D. Mattingly, arXiv:hep-ph/0209264; G. Amelino-Camelia et al. arXiv:hep-th/0109191.)

Explanation of the so-called “tritium beta-decay anomaly”, i.e., the anomalous excess of decay events near the endpoint of the electron energy spectrum (where nonrelativistic few-eV neutrinos are produced) which yields a characteristic “tail” in the Kurie plot. (J.M. Carmona et al., Phys.Lett. B494, 75, (2000).)

Upper bounds on the LV parameters (“Laboratory bounds on Lorentz symmetry violation in low energy neutrino.” by E. Di Grezia, S. Esposito, G. Salesi e-Print Archive: hep-ph/0504245) We have deduced upper bounds on the LV parameters ,  appearing in equations, We have used the available precision experimental data on the neutron lifetime and the decay rates of the charged  meson (two of laboratory experiments more sensible) for the first and second dispersion relation respectively. We assume that even if the kinematics of the decays is affected by the LV in the dispersion law, nevertheless the dynamics, at the low energy scales of laboratory experiments, is essentially the one given by the Standard Model.

Neutron β Decay Let us first consider modifications induced by a LV dispersion relation for neutrinos on the lifetime of the neutron. The relevant decay channel: As first case we consider a neutrino dispersion relation of the form: In the ultrarelativistic limit: Consider the differential decay rate:

We obtain the following total (corrected) neutron decay rate: where is the Standard Model rate while the second term represents the Lorentz-breaking term. The parameter l is then obtained from: The factor is approximately given by the relative uncertainty in the experimental determination of the neutron lifetime ; from the Particle Data Group (S. Eidelman et al., Phys. Lett. B 592, 1 (2004)) analysis we deduce:

We finally obtain the following rough limit on the LV  parameter for the electron-neutrino relation:

As second case we consider a neutrino dispersion relation of the form: Repeating the computations for the decay rate along the lines outlined above we obtain: The following order of magnitude constraint on the parameter is:

Pion Leptonic Decay Assuming that the dynamics of the considered decays is substantially described in the framework of the Standard Model, the following ratio can be useful to obtain constraints on the LV parameters in the neutrino dispersion relations. Considering the first dispersion relation, we obtain:

where is the standard value of the ratio. From the experimental values for the particle masses and the ratio we deduce the following constraint on the and Lorentz-violating parameter:

For the second dispersion relation we obtain By using the experimental data we have: In conclusion the energy scales relevant for these processes are usually extremely large, and the corresponding phenomenology is, consequently, not accessible by laboratory experiments, so that only very poor limits on LV parameters can be obtained.

Baryonic asymmetry(“Baryon asymmetry in the Universe resulting from Lorentz violation.”by E. Di Grezia, S. Esposito, G. Salesi e-Print Archive: hep-th/0508212) Our Universe exhibits a different content of matter and antimatter. In the Big Bang Cosmology, the actual difference in the number densities of baryons and antibaryons is set by the primordial nucleosynthesis of light elements to be of order of relative to photons. A baryon asymmetric Universe, however, is difficult to explain in a minimal picture, assuming an initially baryon symmetric one in thermal equilibrium, as it should be according to known data on particle interactions governing the evolution of the Universe. In order to allow a dynamical generation of a baryon asymmetry starting from a symmetric scenario, Sakharov pointed out three necessary conditions to be fulfilled, namely:

Existence of baryon number B non conserving interactions; • Violation of C and CP symmetries; • Departure from thermal equilibrium.

We have proposed a very simple alternative toy model which accomodates an equilibrium baryogenesis, just assuming the Lorentz symmetry violation. In the cubic case we consider a quark-antiquark sea in the very early Universe at a Temperature when nucleons are not still formed. In this case the average energy and momentum of quarks/antiquarks is much larger then the particle mass m, so that an ultrarelativistic approximation can be used. Moreover, since is expected to be small, at first order in this parameter, calculating the number density at equilibrium of quarks and antiquarks, accounting the cubic dispersion relation, we have:

baryon asymmetry: Baryon asymmetry is usually characterized in terms of the baryon-to-entropy ratio since, as long as the expansion is isoentropic and B non-conserving interactions do not occur, it remains constant during the evolution of the Universe: baryon-to-entropy ratio:

When the temperature goes down to 300 ÷ 100 MeV, where the quark-hadron phase transition takes place and quarks come together to form nucleons, the nucleons start to form with an initial baryon asymmetry carried by quarks but, in a short period, the newly formed neutrons and protons reach a thermal equilibrium with the surrounding plasma, and the value of the baryon asymmetry is set by the equilibrium one ruled by the bath temperature. This continues until nucleons freeze out around and the nucleosynthesis of light elements starts: since from now on no other equilibrium conditions involving baryons will never occur, the actual value of the baryon asymmetry is set, in the present picture, by the nucleon-antinucleon one at the onset of nucleosynthesis.

In the non relativistic limit, since and the effective number of degrees of freedom we obtain an estimate of the Lorentz violating parameter entering in the nucleon dispersion relation able to explain the observed baryon asymmetry: In our scenario, the smallness of the baryon asymmetry of the Universe is related to the smallness of the Lorentz symmetry breakdown; and the value obtained for l points out that Lorentz violating phenomena can arise at energies of the GZK cut-off and of the recently observed UHECR`s!!!

So a particle-antiparticle asymmetry is present already in the quark-antiquark sea, which is in thermal equilibrium (maintained by strong and electromagnetic interactions) with the background primordial plasma at very high temperatures when these species are relativistic. In these conditions, the equilibrium asymmetry decreases linearly with the temperature till the quark-hadron phase transition (at T ~ 300 ÷ 100 MeV) takes place, and the resulting quark-antiquark asymmetry gives the initial value of the formed baryon asymmetry.

Just after that, nucleons reach thermal equilibrium(again due to rapid strong and electromagnetic interactions),but theequilibrium baryon asymmetry is independent of the nucleon freeze-out temperature, in first approximation, due to the fact that the involved species arenon-relativistic and the nucleon mass playsa significantrole. In this case the different dispersion relation between particle and antiparticle is at the root of the observed matter-antimatter asymmetry.

Conclusions • We have determined the actually most stringent limits on several Lorentz violating parameters in the neutrino sector coming from two more sensible laboratory experiments; • Although the expected parameter region should be, as deduced in the present work, only poorly constrained, nevertheless the bounds considered here for the first time indicate the sensitivity of terrestrial experiments to this kind of physical problem, and set the starting point for future experimental investigations on Lorentz symmetry violation; • Then, we have proposed an alternative picture to the standard GUT baryogenesis, assuming that Lorentz invariance is broken at some scale and, from a phenomenological point of view, we have analyzed the consequences of a modified energy-momentum dispersion relation.

Experimental bounds on Lorentz violation in the neutrino sector and baryonic asymmetry