Coherent pion production in Neutrino (anti-neutrino)-Nucleus interaction Hariom Sogarwal, Prashant Shukla Nuclear Physics Division, BARC, Mumbai XXIV DAE-BRNS high energy physics symposium December 18, 2020 1 Outline ● Introduction ● PCAC - based model ● Glauber model ● Study of Neutrino and Anti-neutrino coherent (CC and NC) scattering and its comparison with experiments ● Summary and outlook ● References 17-12-20 2 Introduction ● The neutrinos generated in the atmospheric shower and accelerator experiments are important for studying the phenomena of neutrino oscillations. ● The detectors measure recoil muons which are produced by charged current interaction of neutrinos inside the detector medium. ● The neutrino interaction with matter in the few GeV energy range gets contributions from many processes. One such processes in the resonance production region is coherent pion production. ● In coherent pion production process, the nucleus interacts as a whole with the neutrino and remains in the same quantum state it happens when the four-momentum transfer |t| to the nucleus remains small. ● The scattering process of charge current (CC) coherent pion production is given as: 3 PCAC-based model ● The differential cross section for the CC coherent pion production scattering is Ref.[1,2,7]: −5 −2 GF = 1.16639 ×10 GeV Fermi coupling constant, CosθC = 0.9725 matrix element in the CKM-matrix, u,v = (Eν + Eμ ± |q|)/(2Eν) Kinematic factors, Fπ = 0.93mπ pion decay constant and dσ (πA → πA)/dt pion-nucleus differential elastic cross section. The high-energy approximation to the true minimal 2 2 2 Q is Q m = m μ ν/(Eν − ν). The axial vector form factor 2 2 2 GA = m A /(Q + m A ) with the axial vector meson mass mA = 1.05 GeV. Ref.[1] The ν integration range: Ref.[3] The calculation has been done for 4 Glauber model ● The scattering matrix in Glauber model is Ref.[4]: where the Glauber phase shift Here σπN is the average total pion-nucleon cross section and απN is the ratio of real to imaginary parts of the πN scattering. 5 Glauber model (continued) ● In momentum space, T(b) is defined as: Ref.[4,7] Here Jo(qb) is Bessel function and S(q) is the fourier transform of nuclear density function ρ(r) given as: Ref.[5] ● Differential elastic cross section: where 6 Study of Neutrino and Anti-neutrino coherent (CC and NC) scattering and its comparison with experiments Total and Differential cross section for experiments: Minerva[6,8], INO, Aachen-Padova[9], Gargamelle[10], CHARM[11], SKAT[12], NOMAD[13], MINOS[14], NOVA[15], 15’BC[16] and SciBooNE[17]. 7 Total cross section vs Energy for Minerva experiment (Carbon, Hydrocarbon and Lead) All 4 plots are for CC Model gives good agreement with the data of C,CH and Pb 17-12-20 8 Differential cross section vs Q2 for Minerva experiment (Carbon, Hydrocarbon and Lead) All 4 plots are for CC Differntial cross-section is averaged on flux using: Model gives good agreement with the data of C, CH and Pb 17-12-20 9 Total and differential cross-section (INO and Minerva) for CC and NC interactions (Iron) CC NC CC CC NC Model gives good agreement with the data for Iron in case of Minerva experiment For INO site Neutrino flux (Honda et. al.) for Solar min is 17-12-20 10 taken Total cross section vs Target Nucleus and Energy for various experiments (Neutral current) Cross-section for different experiments are 17-12-20 11 scaled with carbon (12/A)2/3. Results and conclusions ● The pion-nucleus elastic cross section is calculated using the Glauber model in terms of the pion-nucleon cross sections obtained by parametrizing the experimental data. ● The differential and integrated cross sections of coherent pion production were calculated in neutrino-carbon scattering using the formalism based on PCAC theorem. ● We study the behavior of the cross sections as a function of neutrino energy and with nucleus mass and compared with experiments. ● Cross-sections for Experiments Minerva, Aachen-Padova, Gargamelle, CHARM, SKAT, NOVA are in good agreement with the theory within their experimental error. 17-12-20 12 References [1] C. Berger and L. M. Sehgal, Phys. Rev. D 79, 053003 (2009) [2] B. Z. Kopeliovich and P. Marage, Int. J. Mod. Phys. A 8, 1513 (1993). [3] A. Kartavtsev, E. A. Paschos, and G. J. Gounaris, Phys. Rev. D 74, 054007 (2006). [4] P. Shukla, nucl-th/0112039. [5] C. W. De Jager, H. De Vries and C. De Vries, Atom. Data Nucl. 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