Neutral Current ν Induced Reactions in Nuclei at Supernova Neutrino Energies
aa r X i v : . [ nu c l - t h ] A ug Neutral Current ν Induced Reactions in Nuclei at Supernova Neutrino Energies
S. Chauhan, M. Sajjad Athar and S. K. Singh
Department of Physics, Aligarh Muslim University, Aligarh-202 002, India (Dated: November 10, 2018)We calculate cross sections for the neutral current induced neutrino/antineutrino reaction from
P b target and applied it to study Supernova neutrino event rates. The calculations are done inlocal density approximation taking into account Pauli blocking, Fermi motion effects and renormal-ization of weak transition strengths in the nuclear medium. The numerical results for the neutrinonucleus total cross sections have been averaged over the various Supernova neutrino/antineutrinofluxes available in literature.
PACS numbers: 25.30.Pt, 26.50.+x, 23.40.Bw, 21.60.CsKeywords: nuclear effects, neutrino-nucleus interactions, quasielastic scattering
I. INTRODUCTION
In the late phase of stellar evolution the gravitational collapse of the core of a massive star takes place in which ahuge amount of energy is released over a period of few tens of seconds. The energy carriers are mainly neutrinos andthus called supernova neutrinos. This constitutes almost equal proportion of all the flavor of neutrinos. The averageenergy for ν e : h E ν e i = 12 MeV, ¯ ν e : h E ¯ ν e i = 15 MeV and for all other flavors ν µ , ν τ , ¯ ν µ , ¯ ν τ : h E i = 25 MeV. It is expectedthat these neutrinos may provide valuable information about the stellar core, its equation of state and the dynamicsof core collapse and supernova explosion mechanism. These neutrino burst from a galactic supernova can be detectedin terrestrial detectors. There are presently various detectors like Super-K, MiniBooNE, IceCube which are capableof detecting supernova neutrinos. The various detectors[1] like HALO, Icarus, LBNE LAr, LBNE WC, MEMPHYS,Hyper-K, LENA, GLACIER are planned in future which will also be sensitive to supernova neutrino detection. Mostof these detectors are using nuclear targets like O , Ar and P b . In this paper we have calculated event rates forneutral current neutrino induced process ν l ( k ) + N ( p ) → ν l ( k ′ ) + N ( p ′ ); N = proton or neutron (1)for the reaction taking place in the P b target. These events are presented for 1kT of target material. When theabove process takes place inside the nucleus various nuclear medium effects comes into play. We have calculated thecross section in the Fermi gas model using the local density approximation and took into account Pauli blocking,Fermi motion, renormalization of the weak transition strength in the nuclear medium [2]. The effects of Fermi motionand Pauli blocking are taking into account through the imaginary part of the Lindhard function for the particlehole excitations in the nuclear medium. The renormalization of the weak transition strengths are calculated in therandom phase approximation(RPA) through the interaction of the p-h excitations as they propagate in the nuclearmedium using a nucleon-nucleon potential described by pion and rho exchanges. The expression of total scatteringcross section in the local density approximation inside the nucleus is given by [2] σ ( E ν ) = − G F Z r max r min r dr Z k ′ max k ′ min k ′ dk ′ Z Q max Q min dQ E ν l E l L µν J µν ImU N ( q , q ) (2)Here q = k − k ′ . L µν is the leptonic tensor = ¯ P P L µ L ν † where the leptonic current L µ = ¯ u ( k ′ ) γ µ (1 − γ ) u ( k ). J µν is the hadronic tensor = ¯ P P J µ J ν † where J µ is the hadronic current given by J µ = ¯ u ( p ′ )[ (cid:18) γ µ − 6 qq µ q (cid:19) ˜ F N + i M N σ µν q ν ˜ F N + γ µ γ ˜ F NA + q µ M N γ ˜ F NP ] u ( p ) (3)where ˜ F N , , ˜ F NA and ˜ F NP are the vector, axial and pseudoscalar form factors, respectively. These form factors arein turn defined in terms of the standard Dirac and Pauli form factors of the nucleon F p,n and F p,n and a strangecomponent F s , , in the following way˜ F p , = ( 12 − sin θ W ) F p , − F n , − F s , , ˜ F n , = ( 12 − sin θ W ) F n , − F p , − F s , where θ W as the weak mixing angle. E ν (MeV) σ ( - c m ) Free caseWithout RPA With RPA E ν (MeV) Free CaseWithout RPAWith RPA (a) Neutrino (b) AntiNeutrino
FIG. 1: ν + AZ X → ν + AZ X ∗ scattering cross section σ ( E ) vs E for P b nucleus. ν Flavor Duan[3] Kneller[4] Livermore[5]Without With RPA With RPA With RPARPA ν e
40 14 339 315¯ ν e
119 44 217 665 ν µ
202 71 337 990¯ ν µ
41 15 226 360 ν τ
165 57 337 990¯ ν τ
96 35 217 665TABLE I: Number of events for 1kT of lead target
For simplicity we have taken F s , (0)=0 in our calculation. Axial form factors ˜ F p,nA are given by˜ F p,nA = ± F A − F sA ; F sA ( q ) = ∆ s (1 + q M A ) where M A (=1.1GeV) is axial dipole mass, ∆ s denotes the strange contribution to the nucleon spin taken as ∆ s =-0.15. The expression for the F p , , F n , , F A and F P are taken from the Ref.[2]. The consideration of renormalizationof weak transition strengths in the nuclear medium leads to modified hadronic tensor J µνRP A , the expression for whichis given in Ref. [2]. II. RESULTS & DISCUSSIONS