U. Sarkar

Test of the equivalence principle from neutrino oscillation experiments

We consider the hypothesis that neutrino oscillation data can be explained if the gravitational couplings of (massless or degenerate mass) neutrinos are flavor nondiagonal, in violation of the equivalence principle. We analyze the various neutrino oscillation laboratory experimental data including the recent LSND observations to constrain the relevant parameter space. We find (under the hypothesis that gravity couples to matter and antimatter in the same way) that there is no allowed region of parameter space which can explain the existing data, implying that the LSND result cannot be explained by oscillations of degenerate-mass neutrinos due to equivalence principle violations.

Effects of quantum space time foam in the neutrino sector

We discuss violations of CPT and quantum mechanics due to interactions of neutrinos with space-time quantum foam. Neutrinoless double beta decay and oscillations of neutrinos from astrophysical sources (supernovae, active galactic nuclei) are analysed. It is found that the propagation distance is the crucial quantity entering any bounds on EHNS parameters. Thus, while the bounds from neutrinoless double beta decay are not significant, the data of the supernova 1987a imply a bound being several orders of magnitude more stringent than the ones known from the literature. Even more stringent limits may be obtained from the investigation of neutrino oscillations from active galactic nuclei sources, which have an impressive potential for the search of quantum foam interactions in the neutrino sector.

Test of special relativity from K physics

Abstract A breakdown of the Local Lorentz Invariance and hence the special theory of relativity in the Kaon system can, in principle, induce oscillations between K 0 and K 0 . We construct a general formulation in which simultaneous pairwise diagonalization of mass, velocity or weak eigenstates is not assumed and the maximum attainable velocities of K 0 and K 0 are different. This mechanism permits Local Lorentz Invariance violation in a manner that need not violate CPT conservation. We show that such a CPT-conserved violation of special relativity could be clearly tested experimentally through the energy dependence of the K L − K S mass difference and discuss constraints imposed by present experiments.

Test of special relativity and equivalence principle from neutrinoless double beta decay

Abstract: We generalize the formalism for testing Lorentz invariance and the weak equivalence principle in the neutrino sector. While neutrino oscillation bounds constrain the region of large mixing of the the weak and gravitational eigenstates, we obtain new constraints on violations of Lorentz invariance and the equivalence principle from neutrinoless double beta decay. These bounds apply even in the case of no mixing and thus probe a totally unconstrained region in the parameter space.

Test of special relativity and equivalence principle from K physics

A violation of local Lorentz invariance (VLI) and hence the special theory of relativity or a violation of the equivalence principle (VEP) in the kaon system can, in principle, induce oscillations between K 0 and K 0 . We construct a general formulation in which simultaneous pairwise diagonalization of mass, momentum, weak or gravitational eigenstates is not assumed. We discuss this problem in a general way and point out that, as expected, the VEP and VLI contributions are indistinguishable. We then insist on the fact that VEP or VLI can occur even when CPT is conserved. Possible CP violation of the superweak type induced by VEP or VLI is introduced and discussed. We show that the general VEP mechanism (or the VLI mechanism, but not both simultaneously), with or without conserved CPT, could be clearly tested experimentally through the energy dependence of the K L -K S mass difference and of η +− , η 00 , δ. Constraints imposed by present experiments are calculated.

Confronting Dilaton-exchange gravity with experiments

We study the experimental constraints on theories, where the equivalence principle is violated by dilaton-exchange contributions to the usual graviton-exchange gravity. We point out that in this case it is not possible to have any CPT violation and hence there is no constraint from the CPT violating measurements in the K−system. The most stringent bound is obtained from the KL −KS mass difference. In contrast, neither neutrino oscillation experiments nor neutrinoless double beta decay imply significant constraints.

Effects of New Gravitational Interactions on Neutrinoless Double Beta Decay

It has recently been proposed that violations of Lorentz invariance or violations of the equivalence principle can be constrained from the non-observation of neutrinoless double beta decay. We generalize this analysis to all possible new gravitational interactions and discuss briefly the constraints for different cases.

Implications of supersymmetric SU(15) grand unification

We consider the supersymmetric version of the grand unification scheme based on SU(15). We apply the constraints on the coupling constants form the LEP data and require the coupling constants to be less than one. We find that the nice feature of low energy unification is lost in the supersymmetric framework, implying that any signal of supersymmety will rule out the possibility of low energy unification.

On the Yukawa couplings of N=2 superconformal theories

Abstract We identify the Calabi-Yau manifolds corresponding to the (2, 2) compactification of the heterotic string on N = 2 superconformal models of the type D2, D4, E10 and E28 with those of the types A2, A1⊗A1, A1⊗A2, and A1⊗A3 respectively. We also calculate the Yukawa couplings and discrete symmetries of these models and point out that they give rise to the same phenomenology as well. These identifications reduce the 1176 N = 2 minimal superconformal theories with modular invariants to 588 models.