Coherency and incoherency in neutrino-nucleus elastic and inelastic scattering

Abstract

Neutrino-nucleus scattering νA → νA, in which the nucleus conserves its integrity, is considered. Our consideration follows a microscopic description of the nucleus as a bound state of its constituent nucleons described by a multi-particle wave-function of a general form.We show that elastic interactions keeping the nucleus in the same quantum state lead to a quadratic enhancement of the corresponding cross-section in terms of the number of nucleons. Meanwhile, the crosssection of inelastic processes in which the quantum state of the nucleus is changed, essentially has a linear dependence on the number of nucleons. These two classes of processes are referred to as coherent and incoherent, respectively.Accounting for all possible initial and final internal states of the nucleus leads to a general conclusion independent of the nuclear model. The coherent and incoherent cross-sections are driven by factors |F p/n | 2 and (1 − |F p/n | 2 ), where |F p/n | 2 is a proton/neutron form-factor of the nucleus, averaged over its initial states. Therefore, our assessment suggests a smooth transition between regimes of coherent and incoherent neutrinonucleus scattering. In general, both regimes contribute to experimental observables.The coherent cross-section formula used in the literature is revised and corrections depending on kinematics are estimated. Consideration of only those matrix elements which correspond to the same initial and final spin states of the nucleus and accounting for a non-zero momentum of the target nucleon are two main sources of the corrections.As an illustration of the importance of the incoherent channel we considered three experimental setups with different nuclei. As an example, for 133 Cs and neutrino energies of 30 − 50 MeV the incoherent cross-section is about 10-20% of the coherent contribution if experimental detection threshold is accounted for.Experiments attempting to measure coherent neutrino scattering by solely detecting the recoiling nucleus, as is typical, might be including an incoherent background that is indistinguishable from the signal if the excitation gamma eludes its detection. However, as is shown here, the incoherent component can be measured directly by searching for photons released by the excited nuclei inherent to the incoherent channel. For a beam experiment these gammas should be correlated in time with the beam, and their higher energies make the corresponding signal easily detectable at a rate governed by the ratio of incoherent to coherent cross-sections. The detection of signals due to the nuclear recoil and excitation γs provides a more sensitive instrument in studies of nuclear structure and possible signs of new physics. CONTENTS

Probing neutrino transition magnetic moments with coherent elastic neutrino-nucleus scattering

“…Within the SM, the interaction of a neutrino with energy E ν scattered coherently upon a nucleus (A, Z) is theoretically well studied [45,[61][62][63]. The CEνNS cross section is usually expressed in terms of the nuclear recoil energy T A , as [64] dσ…”

“…Very recently, it has been emphasized the need for taking into account also the incoherent channel of neutrino-nucleus scattering at momentum transfers (q) beyond the coherency frontier, e.g. qR A 1 [45] (R A is the nuclear radius), which are particularly relevant for neutrino floor studies at direct detection dark matter experiments [46][47][48].…”

On Coherent Neutrino and Antineutrino Scattering off Nuclei

“…In [66] the SM coupling values were used (with g A ≡ 1). As demonstrated in [66], the neutrino-nucleus scattering ν(k) + A → ν(k ) + A ( * ) cross-section is a sum of incoherent and coherent terms.…”

“…In our previous paper [66] a theoretical framework allowing for elastic and inelastic neutrino-nucleus scattering in the process νA → νA ( * ) was developed on the basis of calculations from first principles. The possibility that the internal quantum state of a nucleus can be modified after an interaction is labeled by the ( * ) superscript.…”

Recent Probes of Standard and Non-standard Neutrino Physics With Nuclei

“…At low-and intermediate-energies, the neutrino being a key input to understand open issues in physics within and beyond the SM (see below), necessitated a generation of neutrino experiments for exploring neutrino scattering processes with nucleons and nuclei for both charged-current (inelastic) and neutral-current (coherent elastic and incoherent scattering) processes. Theoretically, the neutral-current neutrino-nucleus scattering we are interested here, is a well studied process for both coherent [61] an incoherent channels [62,63]. The accurate evaluation of the required transition matrix elements describing the various interaction channels of the electroweak processes between an initial and a final (many-body) nuclear state, is obtained on the basis of reliable nuclear wavefunctions.…”