Refining the Cross Section of the Gallium Neutrino Capture Reaction and the Contributions from Sterile Neutrinos for Int
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ning the Cross Section of the Gallium Neutrino Capture Reaction and the Contributions from Sterile Neutrinos for Interpreting Neutrino Data on the Gallium Anomaly V. V. Khruschova, *, S. V. Fomicheva, and S. V. Semenova aNational
Research Center “Kurchatov Institute,” Moscow, 123182 Russia *e-mail: [email protected]
Received March 2, 2020; revised April 15, 2020; accepted April 27, 2020
Abstract—Graphical dependencies are presented of the probability of electron neutrino preservation in a model with three active and three sterile neutrinos as a function of the neutrino distance from the source at energies, which neutrinos acquire in processes with the participation of 51Cr, 37Ar, and 65Zn nuclei. Refined values of the cross section of the reaction for neutrino capture by 71Ga nuclei are also given for interpretation and prediction of the results of experiments to verify the Gallium anomaly. DOI: 10.3103/S106287382008016X
INTRODUCTION To describe the Gallium anomaly [1–4], we propose extending the model with three active neutrinos (ANs) and one sterile neutrino (SN), and refining the values obtained in [5, 6] for the cross section of the gallium neutrino capture reaction. The calculated values of the probability of electron neutrino (νe) preservation in an extended model with three ANs and three SNs are compared to results from calculations in the approximation of mixing of two neutrino states in the model with three ANs and one SN [7]. Neutrino oscillations are explained by the presence of neutrino masses, and the mixing of mass states is described by the Pontecorvo–Maki–Nakagawa– Sakata matrix [8]: UPMNS ≡ U = V × P, i.e.,
ψaL = ΣiU ai ψiL, where ψaL,i are left chiral fields with flavor a or mass mi, a = {e, μ, τ} and i = {1, 2, 3}. For three ANs, matrix V is expressed in the standard parametrization [9] by mixing angles θij and the CP phase; i.e., phase δ = δCP associated with CP violation in the lepton sector for Dirac or Majorana neutrinos, P = diag{1, eiα, eiβ}, where α ≡ αCP and β ≡ βCP are phases associated with CP violation only for Majorana neutrinos. Values of the angles of mixing and differences of 2 2 squares of neutrino masses Δm21 and Δm31 are found 2 2 experimentally [9, 10] (where Δmij = mi – m2j ). Since 2 only the absolute value is known for Δm31 , the values of masses can be ordered either as m1 < m2 < m3 (the normal hierarchy), or as m3 < m1 < m2 (inverse hierar-
chy). Estimates of the CP phase δCP have been obtained (see, e.g., [10–13]). For the normal hierarchy of the AN mass spectrum, they lead to sin δCP < 0 and δCP ≈ −π/2. If we allow for the constraints on the sum of neutrino masses from cosmological observations [14] and the results of the T2K experiment [13], the normal hierarchy of the AN mass spectrum becomes preferable. We therefore limit ourselves to this case when δCP = −π/2 in the calculations below. At the same time, there are indications of anomalous values of neutrino fluxes in a number of processes at short distances from the source. These so-called short-baseline anoma
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