Recent status of the understanding of neutrino-nucleus cross section

TL;DR

This paper reviews the current understanding of neutrino-nucleus cross sections in the few GeV energy range, crucial for neutrino oscillation experiments, covering various interaction processes and their implications.

Contribution

It provides a comprehensive overview of the diverse neutrino interaction processes relevant for precise neutrino oscillation measurements.

Findings

Summarizes the status of neutrino-nucleus cross section knowledge

Highlights the importance of various interaction channels

Discusses implications for neutrino oscillation experiments

Abstract

In this work we have presented current understanding of neutrino-nucleon/nucleus cross sections in the few GeV energy region relevant for a precise determination of neutrino oscillation parameters and CP violation in the leptonic sector. In this energy region various processes like quasielastic and inelastic production of single and multipion production, coherent pion production, kaon, eta, hyperon production, associated particle production as well as deep inelastic scattering processes contribute to the neutrino event rates.

Figures

Equations

$$\mathrm{QE}:{\nu }_{\mathrm{l}}+\mathrm{n}$$

$$\pi :{\nu }_{\mathrm{l}}+\mathrm{N}$$

$$\mathrm{K}:{\nu }_{\mathrm{l}}+\mathrm{N}$$

$$\eta :{\nu }_{\mathrm{l}}+\mathrm{N}$$

$$\mathrm{AP}:{\nu }_{\mathrm{l}}+\mathrm{N}$$

$$\mathrm{DIS}:{\nu }_{\mathrm{l}}+\mathrm{N}$$

Full text

I Introduction

The neutrino-nucleus($\nu$-A) cross sections are important input to the systematics of analysing $\nu$ oscillation experiments. The measured events are a convolution of energy-dependent neutrino flux and $\nu$-A cross section. For precise measurements, there are two challenging tasks, (i) good knowledge of neutrino fluxes and (ii) well understood nuclear medium effects(NME) in the entire region of neutrino energy spectrum. In this presentation, we have considered the following neutrino interactions:

[TABLE]

on nucleon and nuclear targets. Similar reactions take place with $\bar{\nu}_{l}$. It is estimated that due to NME the cross sections have an overall uncertainty of 20-25$\%$Katori:2016yel ; Morfin:2012kn . We present here a short review of current understanding of $\nu-A$ cross section.

II Quasielastic(QE) reactions

Most of the present Monte Carlo generators use relativistic Fermi gas model(FGM) given by Smith and MonizSmith:1972xh to analyse the experimental results on $\nu-A$ cross section. However, other variants of FGM like the model used by Aligarh Singh:1993rg ; Athar:1999fu and Valencia Nieves:2004wx groups, where local FGM with long range correlations of the particle-hole excitations in the nuclear medium were included or the calculations where nucleon spectral functions are used to include the initial state interactionsBenhar:2014qaa . First high statistics experimental results from MiniBooNE AguilarArevalo:2007ab , and later K2KGran:2006jn and MINOSDorman:2009zz could not be explained by using Smith and MonizSmith:1972xh model of QE reactions using the standard values of weak vectors and axial vector form factors. These experiments required a value of $M_{A}$ which was much larger than the world average value of 1.026GeV. It was shown by Martini et al.Martini:2013sha and later Nieves et al.Nieves:2013fr , the importance of two particle-two hole(2p-2h) contribution(which is basically multi-nucleon correlation effect). The inclusion of 2p-2h to the CCQE results obtained using FGM with RPA effect gives satisfactory explanation of the data with $M_{A}=1.03$ GeV which are consistent with the values reported from NOMADLyubushkin:2008pe and MINERvAWilkinson:2016wmz that corresponds to high $\nu$ energies. It is likely that these 2p-2h contributions are important in the region of low energies and are small at higher energies. The results are shown in Fig.1(left). Recently Stowell et al.Stowell:2016exm compared the MINERvA CCQE data with two different MC generators NEUT and NuWro, the results of which have been shown in Fig.1(mid and right). It may be seen that the data and the results from the MC generators are not in agreement particularly in the low $Q^{2}$ region. Therefore, better theoretical models to understand NME in $\nu$-A scattering process for analysing CCQE events are needed.

III Single $\pi$ production

The experimental data on weak pion production in $\nu$-A scattering in the experiments performed at MiniBooNE, SciBooNE and more recently from MINER$\nu$A collaboration have highlighted the inadequacy of our present understanding of nuclear medium and final state interaction effects. In addition there is lack of consensus in the theoretical modeling of basic reaction mechanism of $\nu(\bar{\nu})$ induced pion production from free nucleon, specially concerning the role of background terms and higher resonances. By including the contribution of background terms and higher resonances along with the dominant $\Delta$ resonance, Aligarh group Alam:2015gaa has studied weak charged and neutral current induced single pion production from nucleons and fitted the reanalysed ANL and BNL data Wilkinson:2014yfa , and the results are shown in Fig.2(left). It was concluded that the best description of the reanalyzed experimental data of ANL and BNL experiments is obtained when we take $C_{5}^{A}(0)$=1.0 and $M_{A}$=1.026GeV for N$-\Delta$ axial vector transition current form factor $C_{5}^{A}(Q^{2})$. In an another work by Valencia group Alvarez-Ruso:2015eva , implementing unitarity using Watson’s theorem and applying it to fit old and reanalysed ANL and BNL data, the best fit was found with $C_{5}^{A}(0)=1.12\pm 0.11$ and $C_{5}^{A}(0)=1.14\pm 0.07$ respectively, and $M_{A}$=$0.954\pm 0.063$GeV.

In the case of single $\pi$ production from nuclear targets, the dominant contribution from the $\Delta$ resonance is suppressed due to modifications of mass and width of the $\Delta$ propagator in the nuclear medium Athar:2007wd . Moreover, the produced pions undergo final state interaction(FSI) with the residual nucleus which further reduces the pion production. In Fig.2(mid), the results for CC1$\pi$ production in ${}^{12}C$ obtained by different theoretical groups are shown along with the MINER$\nu$A data Eberly:2014mra . Recently McGivern et al.McGivern:2016bwh have published MINER$\nu$A data of CC1$\pi$ production and compared the results with different theoretical approach incorporated in MC generators(Fig.2 right). It may be clearly observed that there is a discrepancy between the theoretical and experimental results which need further study.

There is another mode of pion production from nuclear target known as coherent pion production where a nucleus after the interaction remains in the ground state and all the energy is transferred to the outgoing pion. The work by the Aligarh groupSingh:2006br and the Valencia group AlvarezRuso:2007tt have shown that the contribution from coherent pion production is highly suppressed due to NME and is 2-3$\%$ of the total pion production. Besides 1$\pi$ production there can be 2$\pi$ or multipion production for which details can be found in Ref. Hernandez:2007ej .

IV Deep-inelastic scattering (DIS)

There is no sharp kinetic region to distinguish the onset of the DIS region from the resonance region but the region $W\geq 2.0$ GeV and $Q^{2}\geq 1.0$ GeV2 is considered to be DIS region. At high energy and $Q^{2}$, the inclusive DIS cross sections are usually expressed in terms of the structure functions which are derived in terms of quark PDFs using the methods of perturbative QCD. These structure functions are experimentally determined from DIS experiments on nucleon and nuclear targets. The observation of EMC effect has led to the presence of strong NME in DIS region. Phenomenologically NME on quark PDFs and nucleon SF have been determined by many groups Kovarik:2012zz . There is considerable theoretical work on studying NME in structure functions Malace:2014uea . Recently a comparative study of NME in $F_{2A}^{EM}(x,Q^{2})$ and $F_{2A}^{Weak}(x,Q^{2})$ has been done by Aligarh group Haider:2011qs ; Haider:2016zrk and Kulagin and Petti Kulagin:2007ju .

The Aligarh group has studied NME in structure functions for moderate as well as heavy nuclear targets. We construct a relativistic nucleon spectral function for a nucleon in an interacting Fermi sea within a field theoretical formalism which uses nucleon propagators in the nucleus. The spectral function takes into account binding energy, Fermi motion and nucleon correlations. Other effects like target mass correction, next to leading order correction, pion and rho mesons cloud contributions, shadowing and antishadowing corrections are also included in numerical calculations of structure functions. In Fig.3, we show the curves for $F_{2A}^{EM,Weak}(x,Q^{2})$ obtained using the spectral function only, also including the mesonic contribution, and finally using the full model which also includes shadowing. The use of spectral function leads to a reduction in $F_{2A}^{EM}(x,Q^{2})$ as well as in $F_{2A}^{Weak}(x,Q^{2})$ nuclear structure functions as compared to the free nucleon case. The inclusion of mesonic contributions from pion and rho mesons leads to an enhancement in these structure functions at low and mid values of $x$. The inclusion of shadowing effects further reduces these structure functions and are effective in low region of $x~{}(~{}<~{}0.1)$.

V $|\Delta S|=0$ and $|\Delta S|=1$ processes off nucleon

The other inelastic processes like $K$, $\eta$ and AP production have also been discussed briefly. The strange particles are produced by both $|\Delta S|=0$ and $|\Delta S|=1$ processes. At the neutrino energies of $\sim$1GeV it is the single hyperon(by $\bar{\nu}$) or single kaon($K/\bar{K}$) that are produced by $|\Delta S|=1$ reaction mechanism while $\eta$ meson and associated production of kaon are induced by the $|\Delta S|=0$ weak currents. The reaction cross sections are smaller than the pion production due to Cabibbo suppression in $|\Delta S|=1$ process. It has been shown by Aligarh group  RafiAlam:2010kf ; Alam:2015zla ; Singh:2015ama ; Akbar:2016awk that for the precise determination of neutrino oscillation parameters and to estimate the background for a study of nucleon decay searches, these reactions are important. In Fig.4, we have presented the results for CC induced $K$, ${\bar{K}}$ and $\eta$ production cross sections. The details are given in Ref. RafiAlam:2010kf -Akbar:2016awk .