Quantum Gravity on Neutrino Oscillation Length
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Quantum Gravity on Neutrino Oscillation Length Bipin Singh Koranga · M. Narayan
Received: 27 October 2012 / Accepted: 15 January 2013 / Published online: 24 January 2013 © Springer Science+Business Media New York 2013
Abstract The oscillation length of neutrino oscillation could be discussed in the frame work of quantum gravity. Quantum gravity (Planck scale effects) leads to an effective SU(2)L × U (1) invariant dimension-5 Lagrangian involving, neutrino and Higgs fields. On symmetry breaking, this operator gives rise to correction to the neutrino masses and mixing. We compute the neutrino oscillation length due to Planck scale effects. The gravitational interaction (MX = Mpl ) demands that the element of this perturbation matrix should be independent of flavor indices. In this paper, we study the quantum gravity effects on neutrino oscillation length, namely modified dispersion relation for neutrino oscillation phases. Keywords Quantum gravity · Oscillation length
1 Introduction The phenomenology of quantum gravity [1] is based on the observation that, regardless of incompatibility and diversity in theoretical details. In recent year the subject of quantum gravity phenomenology has rapid growth [2] complementary theoretical work. One main feature of quantum gravity which has much attention in principle and antiparticle physics phenomenology in particle and antiparticle physics phenomenology is the breaking of CPT symmetry.Theoretical extension of the standard model of Particle Physics, which also was expected to explain the origin and the shape of small neutrino mass matrix. Neutrino oscillations allow the transition among the three type of flavor eigenstates. The quantum mechanical phenomenon of neutrinos, propagating in gravitational field has be discussed by many author [3, 4] The outline of the article is as follows. In Sect. 2, we briefly discuss neutrino oscillation parameter due to Planck scale effects. In Sect. 3, we discuss about oscillation
B.S. Koranga Department of Physics, Kirori Mal college, University of Delhi, Delhi 110007, India M. Narayan () Department of Physics, Institute of Chemical Technology, Mumbai University, Mumbai 400 019, India e-mail: [email protected]
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Int J Theor Phys (2013) 52:2209–2214
length due to Planck scale effects. In Sect. 4, numerical results. In Sect. 4, we present our conclusions.
2 Neutrino Oscillation Parameter Due to Planck Scale Effects The neutrino mass matrix is assumed to be generated by the see saw mechanism [7, 8]. The effective gravitational interaction of neutrino with Higgs field can be expressed as SU(2)L × U (1) invariant dimension-5 operator [6], Lgrav =
λαβ −1 (ψAα ψC )Cab (ψBβ BD ψD ) + h.c. Mpl
(1)
Here and every where we use Greek indices α, β for the flavour states and Latin indices i, j , k for the miniass states. In the above equation ψα = (να , lα ) is the lepton doublet, φ = (φ + , φ ◦ ) is the Higgs doublet and Mpl = 1.2 × 1019 GeV is the Planck mass λ is a 3 × 3 matrix in a flavour space with each elements O(1). The Lorentz in
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