#### Transcript Lorentz violating field theories and nonperturbative physics

Testing Relativity Theory With Neutrinos Brett Altschul University of South Carolina May 15, 2008 Overview Lorentz invariance is extremely well tested. Yet many candidate theories of quantum gravity “predict” Lorentz violation in certain regimes, especially at very high speeds. Neutrino physics offers interesting ways to test whether relativity still holds very close to the speed of light. Outline • • • • Introduction The Standard Model Extension (SME) Tests of Relativity with Neutrinos Conclusion Introduction In the last fifteen years, there has been growing interest in the possibility that Lorentz symmetry may not be exact. There are two broad reasons for this interest: Reason One: Many theories that have been put forward as candidates to explain quantum gravity involve LV in some regime. (For example, string theory, non-commutative geometry, loop quantum gravity…) Reason Two: Lorentz symmetry is a basic building block of both quantum field theory and the General Theory of Relativity, which together describe all observed phenomena. Anything this fundamental should be tested. Much of the story of modern theoretical physics is how important symmetries do not hold exactly. There is no excellent beauty that hath not some strangeness in the proportion. — Francis Bacon Standard Model Extension (SME) Idea: Look for all operators that can contribute to Lorentz violation. Then one usually adds restrictions: • locality • superficial renormalizability •SU(3)C SU(2) L U(1)Y gauge invariance • etc... With those restrictions, the Lagrange density for a free fermion looks like: L i M 1 M m a b 5 H 2 c d 5 A separate set of coefficients will exist for every elementary particle in the theory. One important effect of these Lorentz-violating terms is to modify the velocity. For example, with c present: 1 vk pk ckj p j c jk p j c j kc jl pl E c0k From this expression, we can see when the effective field theory breaks down. The velocity may become superluminal when E m c . If c m M P , this is E mMP . More generally, momentum eigenstates may not be eigenstates of velocity. Most Lorentz-violating effects at high relativistic energies depend on a particle’s maximum achievable velocity (MAV). v max 1 ( pˆ ) 1 c jk pˆ j pˆ k c 0 j pˆ j The corresponding energy-momentum relation is E m 1 2( pˆ )p 2 2 The photon sector contains more superficially renormalizable couplings. 1 1 1 L F F kF F F kAF A F 4 4 2 Most of these couplings are easy to constrain with astrophysical polarimetry. However, some will require more complicated measurements (e.g. with Doppler shifts or electromagnetostatics). Measurement Type System Coefficients log Sensitivity Source oscillations K (averaged) a (d, s) —20 E773 Kostelecký K (sidereal) a (d, s) —21 KTeV D (averaged) a (u, c) —16 FOCUS D (sidereal) a (u, c) —16 FOCUS B (averaged) a (d, b) —16 BaBar, BELLE, DELPHI, OPAL neutrinos a, b, c, d —19 to —26 SuperK Kostelecký, Mewes photon kAF (CPT odd) —42 Carroll, Field, Jackiw kF (CPT even) —32 to —37 Kostelecký, Mewes birefringence resonant cavity photon kF (CPT even) —7 to —16 Lipa et al. Muller et al. Schiller et al. Wolf et al. anomaly frequency e-/e+ b (e) —23 Dehmelt et al. e- (sidereal) b, c, d (e) —23 Mittleman et al. mu/anti-mu b (mu) —22 Bluhm, Kostelecký, Lane cyclotron frequency H-/anti-p c (e, p) —26 Gabrielse et al. hyperfine structure H (sidereal) b, d (e, p) —27 Walsworth et al. muonium (sid.) b, d (mu) —23 Hughes et al. various b, c, d (e, p, n) —22 to —30 Kostelecký, Lane He-Xe b, d (n) —31 Bear et al. Cane et al. spin-polarized solid b, d (e) —29 Heckel et al. Hou et al. clock comparison torsion pend. The coefficients need not be diagonal in flavor space either. Like neutrino masses, they may mix different species. In fact, three-parameter Lorentz-violating models can explain all observed neutrino oscillations (including LSND). However, many possible parameters have not been probed. The “full” neutrino sector has 102 Lorentzviolating parameters. Neutrino Tests of Relativity Since neutrinos are always relativistic, they are an interesting laboratory for looking for changes to special relativity. Constraints on ( pˆ ) can be set in two ways: • time of flight measurements, and • energy-momentum measurements. It’s well known that SN1987A neutrinos traveled to Earth with a speed that differed 9 2 10 from c 1by a fraction . However, this bound applies only to electron neutrinos moving in one direction. We can get better bounds by looking at energetic constraints. We now feel confident that ultrahigh-energy cosmic rays are primarily protons, with en9 ergies up to 6 10 GeV. The protons have to live long enough to travel tens of Mpc to reach Earth. Normally, that would be no problem, but relativity violations might cause fast-moving protons to decay, even if they’re stable at rest. If the protons has speeds greater than 1, they would emit vacuum Cerenkov radiation. The primary cosmic rays must also be immune to -decay, p n e e . This is where the neutrinos come in. This decay is disallowed only if mn ( pˆ ) 2 1011 ECR This is only a one-sided bound if the neutrino MAV is isotropic. However, an anistropic MAV is bounded on both sides at the 10 10 level. The bounds are the same for the . Just swap the positron for a . The constraints on the MAV for are worse by a factor of 3, since in a decay, the contribution. mass makes a significant Most other particles that a proton could decay into are also subject to similar or better bounds. Conclusion Lorentz violation is an interesting possibility to be part of the “Theory of Everything.” Lorentz tests for ultrarelativistic particles like neutrinos are parameterized by the MAV. The fact that primary cosmic ray protons don’t decay into neutrons sets stronger limits on the neutrino MAV than time-of-flight measurements. Thanks to V. A. Kostelecký and E. Altschul. That’s all, folks!