LO QUE PERDURA DEL PENSAMIENTO DEL CHE

This thesis focuses on measurements of flavor oscillations via the disappearance of muon antineu- trinos at anL/E≈250 km/GeV. At this distance, the disappearance probability is governed, to a good approximation, by two-neutrino oscillation with ¯νµ→ν¯τ. With only two neutrinos, the mixing matrixU must be real and ‘standard’ neutrino CP-violation via the phase δ cannot influence the disappearance probabilities,PL(¯νµ→ν¯µ) andPL(νµ→νµ). Thus, as was shown in Equation 2.138, ifPL(¯νµ →ν¯µ)=6 PL(νµ→νµ) then either the neutrinos are notCPT invariant or some other new physics needs to be introduced.

2.5.1 Non-standard Interactions

Standard matter-effects do introduce differences between neutrinos and antineutrinos since the ad- ditional components of the Hamiltonian have opposite signs. However, they cannot influence the ¯

νµ →¯ντtransition which does not involveνe’s. However, some other physics process could introduce additional Hamiltonian terms in the same way. Generically, these processes are called ‘non-standard interactions’ (NSI). A number of models have been proposed which introduce effects that, like matter effects, have opposite signs for neutrinos and antineutrinos. Examples include a flavor-dependent potential introduced by very lightZ0 _{bosons from a gaugedL}

µ−Lτ symmetry [78]; a new charged- current coupling between ντ’s and leptons, constructed so that flavor-violating contributions to τ decays are sufficiently suppressed [79]; and inclusion of a sterile neutrino, making the neutral-current matter effects non-trivial and/or introducing a new U(1) gauge force coupled toB−L[80].

A generic, model-independent formalism for NSI can be found in [81]. Non-standard interactions, whatever their source, will add a term to the Lagrangian of the form

LNSI=−G_√F 2 X f=u,d,e a=±1 εf a αβ h ¯ ναγµ 1−γ5 νβ ih ¯ fγµ _{1 +a γ}5 fi (2.162)

where the variousεf a

αβcoefficients give the strengths of the NSI effects. Analogous to standard matter effects, this NSI Lagrangian will add an additional term to the effective Hamiltonian with the form

HNSI=V      εee εeµ εeτ ε∗ eµ εµµ εµτ ε∗ eτ ε∗µτ ετ τ      (2.163)

where V = √2GFNe is the MSW potential and the NSI parameters have been summed over the various fermion contributions,

εαβ= X f,a εf a αβ Nf Ne (2.164) whereNf is the number density of fermionf in the (unpolarized) medium.

There have been numerous analyses of the existing neutrino data searching for evidence of NSI. The existing constraints are summarized in [82]. The constraints are for neutrinos only, and the constraints get tighter (usually by an order of magnitude) when the NSI effects are included as part of a renormalizable theory and their effects on the charged leptons are accounted for. There has even been an analysis of the data presented in this thesis which finds a value forεµτ =−0.12±0.21 [83].

2.5.2

CPT

Violation

CPT is a fundamental symmetry in quantum field theory. CPT invariance is required in order to have Lorentz-invariant models, and consequently any theory that includesCPT violation also, auto- matically, includes Lorentz violation [84]. CPT invariance also requires that particles and antipar- ticles share certain properties, including charge and mass. If different mass-splittings are measured for neutrinos and antineutrinos, the naive interpretation that the neutrinos and antineutrinos have different masses thus requiresCPT violation [85].

CPT violation in the neutrino sector first came to the forefront as an explanation for the LSND anomaly. The Liquid Scintillator Neutrino Detector (LSND) at Los Alamos searched for ¯νµ → ¯

νe oscillations using ¯νµ’s from muon decays at rest. They reported evidence of a mass splitting ∆m2 _{≈ 1 eV}2_{, inconsistent with the three-neutrino model and the two mass-splittings, ∆m}2

atm and ∆m2

sol, that had been previously measured [86]. A number of CPT-violating theories were proposed to explain this discrepancy [87, 88, 89, 90], but the possibleCPT-violating effects become much more tightly constrained once effects outside the neutrino sector are taken into account [91, 92]. Some theories endeavor to simultaneously explain LSND and the MINOS antineutrino measurements (discussed in Chapter 5) [93]. However, no theory has yet proven compelling and predictive.

42 Physics of Neutrinos and Antineutrinos possible Lorentz/CPT-violating models in great detail, including their possible influence on neutrino experiments [94]. They even have a model that explains MINOS in particular [95], although for now the model is more proof-of-principle and has too many parameters to be predictive. Using the Kosteleck´y parameterization of possible Lorentz/CPT violation, numerous analyses have been performed on experiments in wide-ranging areas of physics including, for example, neutral meson oscillations [96, 97, 98], comparisons of clocks [99], muon spin precession [100], electron-positron g-2 [101], and many others. Searches have been performed in MINOS data for sidereal variations in the neutrino rate, another signature of Lorentz-violation in the Kosteleck´y model [102, 103]. There has been, to date, no convincing evidence ofCPT violation in any sector.