Nuclear Potential of Final State Nucleons and Nucleons Plus Pions in Lepton Nucleus Scattering
Arie Bodek, Tejin Cai
备注：
6 pages 3 figures, presented by Arie Bodek at the 40th International Conference on High Energy physics - ICHEP2020, July 28 - August 6, 2020, Prague, Czech Republic (published in ICHEP2020 proceedings)
Within the impulse approximation, the modeling of the energy of final state leptons in electron and neutrino quasielastic and pion production processes on nuclear targets in the region of the $Δ$ resonance depends on several parameters. These parameters include the removal energy of the initial state nucleon from the nucleus $ε^{P,N}$, the potentials of electrons, nucleons and pions in the Coulomb field of the nucleus $|V_{eff}|$, and the kinetic energy dependent nuclear potential for final state nucleons ($U^{QE}_{opt}$) and "nucleon plus pion" final states in the region of the $Δ$ resonance which we refer to as $U^Δ_{opt}$. We extract these parameters from electron scattering data.
Previous studies have shown that real part of the optical potential for a nucleon bound in $_{6}^{12}C$ at zero kinetic energy $U^{P,N}_{opt}(T=0)\approx$ 44 MeV is larger than that for the $Δ$(1232) resonance $U^Δ_{opt}(T=0)\approx$ 30 MeV. We find the reverse at higher kinetic energies. For example at T=100 MeV we find a nucleon potential $U^{P,N}_{opt}(T=100 MeV)$=20$\pm$5 MeV and $U^Δ_{opt}(T=100 MeV)$= 30$\pm$5 MeV. The two results are consistent for two reasons. First, theoretically the kinetic energy dependence of the $Δ$ potential is flatter than that of the nucleon. Secondly, in our analysis the extracted $U^Δ_{opt}$ values are the nuclear potential for {\it"nucleon plus pion"} final states in the region of the $Δ$ resonances and therefore includes contributions from both resonance and non resonance pion production processes. For Monte Carlo generators that only include the effects of Fermi motion and nuclear potentials, the relevant parameter is the effective nuclear potential for the "nucleon plus pion" final state.
Rapidity-dependent transverse momentum spectra of negatively charged pions measured at different rapidities in proton-proton collisions at the Super Proton Synchrotron (SPS) at various energies within its Beam Energy Scan (BES) program are investigated by using one- and two-component standard distributions where the chemical potential and spin property of particles are implemented. The rapidity spectra are described by a double-Gaussian distribution. At the stage of kinetic freeze-out, the event patterns are structured by the scatter plots in the three-dimensional subspaces of velocity, moment…
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We study coherent pion production in neutrino-nucleus scattering in the energy region relevant to neutrino oscillation experiments of current interest. Our approach is based on a combined use of the Sato-Lee model of electroweak pion production on a nucleon and the Delta-hole model of pion-nucleus reactions. Thus we develop a model which describes pion-nucleus scattering and electroweak coherent pion production in a unified manner. Numerical calculations are carried out for the case of the 12C target. All the free parameters in our model are fixed by fitting to both total and elastic different…
The NuSTEC workshop held at the University of Pittsburgh in October 2019 brought theorists and experimentalists together to discuss the state of modeling and measurements related to pion production in neutrino-nucleus scattering in the kinematic region where pions are produced through both resonant and non-resonant mechanisms. Modeling of this region is of critical importance to the current and future accelerator- and atmospheric-based neutrino oscillation experiments. For the benefit of the community, links to the presentations are accompanied by annotations from the speakers highlighting sig…
We have investigated the neutrino induced coherent pion production reaction at low and intermediate energies including pion, nucleon and Delta(1232) resonance. Medium effects in the production mechanism and the distortion of the pion wave function are included in the calculation. We find a strong reduction of the cross section due to these effects and also substantial modifications in the energy distributions of the final pion. The dependence on the atomic number is discussed.
In this article, we study the coherent pion production in neutrino-nucleus interaction in the resonance region using the formalism based on partially conserved axial current (PCAC) theorem which relates the neutrino-nucleus cross section to the pion-nucleus elastic cross section. The pion nucleus elastic cross section is calculated using the Glauber model in terms of pion-nucleon cross sections obtained by parameterizing the experimental data. We calculate the differential and integrated cross sections for charged current coherent pion production in neutrino carbon scattering. The results of i…
We study one pion production in both charged and neutral current neutrino nucleus scattering for neutrino energies below 2 GeV. We use a theoretical model for one pion production at the nucleon level that we correct for medium effects. The results are incorporated into a cascade program that apart from production also includes the pion final state interaction inside the nucleus. Besides, in some specific channels coherent pion production is also possible and we evaluate its contribution as well. Our results for total and differential cross sections are compared with recent data from the MiniBo…
We study coherent pion production in neutrino-nucleus scattering in the energy region relevant to the recent neutrino oscillation experiments. Our approach is based on the combined use of the Sato-Lee model and the Delta-hole model. Our initial numerical results are compared with the recent data from K2K and SciBooNE.
In this article, we present the charged and neutral current coherent pion production in the neutrino-nucleus interaction in the resonance region using the formalism based on the partially conserved axial current (PCAC) theorem which relates the neutrino-nucleus cross section to the pion-nucleus elastic cross section. The pion nucleus elastic cross section is calculated using the Glauber model approach. We calculate the integrated cross sections for neutrino-carbon, neutrino-iron and neutrino-oxygen scattering. The results of integrated cross-section calculations are compared with the measured …
We use our model for neutrino pion production on the nucleon to study pion production on a nucleus. The model is conveniently modified to include in-medium corrections and its validity is extended up to 2 GeV neutrino energies by the inclusion of new resonant contributions in the production process. Our results are compared with recent MiniBooNE data measured in mineral oil. Our total cross sections are below data for neutrino energies above 1 GeV. As with other theoretical calculations, the agreement with data improves if we neglect pion final state interaction. This is also the case for diff…
We propose to use the ratio of the pion-proton correlation functions evaluated under different conditions to study the relative space-time asymmetries in pion and proton emission (pion and nucleon source relative shifts) in high energy heavy ion collision. We address the question of the non-central collisions, where the sources can be shifted spatially both in the longitudinal and in the transverse directions in the reaction plane. We use the RQMD event generator to illustrate the effect and the technique.
High-p_T pion and kaon production is studied in relativistic proton-proton, proton-nucleus, and nucleus-nucleus collisions in a wide energy range. Cross sections are calculated based on perturbative QCD, augmented by a phenomenological transverse momentum distribution of partons (``intrinsic k_T''). An energy dependent width of the transverse momentum distribution is extracted from pion and charged hadron production data in proton-proton/proton-antiproton collisions. Effects of multiscattering and shadowing in the strongly interacting medium are taken into account. Enhancement of the transvers…
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The cross section for exclusive $π^+π^-$ and $π^0π^0$ meson pairs production in peripheral ultrarelativistic heavy-ion collisions is calculated at the energy available at the CERN Large Hadron Collider, i.e., $\sqrt{s_{NN}}=3.5$ TeV. The cross section for elementary $γγ\toππ$ process is calculated with the help of the pQCD Brodsky-Lepage approach with the distribution amplitude used recently to describe the pion transition form factor measured by the BaBar Collaboration.
We analyze the experimental data on the inclusive double differential cross section by neutrinos charged current, measured by T2K, with the same model which was successful for the MiniBooNE quasielastic cross sections. As in our previous analysis the multinucleon component is needed in order to reproduce the data. For the total cross section our evaluation is smaller than the SciBooNE data above 1 GeV. This indicates the opening of a new channel not included in our evaluation, presumably the two pion emission channel. We also check that our description holds for the exclusive single pion produ…
We have shown that a local-density-dependent term, $F[ρ(r)] ρ(r)$, of the pion-nucleus potential with a nuclear density, $ρ(r)$, can be transposed to a conventional density-linear term, $F(ρ_e) ρ(r)$, with an effective nuclear density, $ρ_e$, which is close to $\sim 0.6 ρ(0)$ for most $π^-$ bound states. The presently found relations, {\it generalized Seki-Masutani relations}, for the density-quadratic term, the medium-modified isovector term and the double-scattering isoscalar term of the s-wave pion-nucleus interaction assure that the constant parameters in the conventional pion-nucleus pote…
The experimental discovery that the nucleus is approximately transparent to low energy pions is reviewed. The consequences of this for nuclear deep inelastic scattering and Drell-Yan interactions are discussed. I argue that low energy nucleus data imply that there is little nuclear enhancement of the pion cloud of a nucleon, and try to interpret this in terms of nucleon-nucleon correlations.
Some of the recent progress in the physics of pion production induced by neutrinos on nucleons and nuclei is reviewed from a theoretical perspective. The importance of Watson's theorem to reconcile ANL and BNL data with the off-diagonal Goldberger-Treiman relation for the $Δ(1232)$ is discussed. The disagreement between MiniBooNE data and theoretical calculations is presented in the light of the new MINERvA data. The coherent pion production data on $^{12}$C obtained by MINERvA are also compared to different microscopic and PCAC models.
We compare our pion production results with recent MiniBooNE data measured in mineral oil. Our total cross sections lie below experimental data for neutrino energies above 1 GeV. Differential cross sections show our model produces too few high energy pions in the forward direction as compared to data. The agreement with experiment improves by artificially removing pion final state interaction.
The remarkable observations in the pion induced and charge exchange reactions on a nucleus are the significant shift and broadening of the $Δ(1232)$-peak relative to free pion nucleon scattering. For the forward going massless leptons, the weak process $(ν_l,l)$ on a nucleon, according to Adler's partially conserved axial current theorem, is connected to the pion nucleon scattering. This mechanism is also applicable to the nucleus. Therefore, the modification of the $Δ$-peak in a nucleus can be seen in the $(ν_l,l)$ reaction since it is connected to the pion nucleus scattering. To investigate …
We present a study of coherent pion production in neutrino-nucleus interactions using the formalism based on partially conserved axial current theorem which connects the neutrino-nucleus cross section to the pion-nucleus elastic scattering cross section. Pion-nucleus elastic scattering cross section is calculated using Glauber model which takes three inputs, nuclear densities, pion-nucleon cross section and $α_{πN}$ which is the ratio of real to imaginary part of $πN$ forward scattering amplitude, for which the parametrizations are obtained from measured data. We calculate the differential and…
The space-time structure of the multipion system created in central relativistic heavy-ion collisions is investigated. Using the microscopic transport model UrQMD we determine the freeze-out hypersurface from equation on pion density n(t,r)=n_c. It turns out that for proper value of the critical energy density ε_c equation ε(t,r)=ε_c gives the same freeze-out hypersurface. It is shown that for big enough collision energies E_kin > 40A GeV/c (sqrt(s) > 8A GeV/c) the multipion system at a time moment τ ceases to be one connected unit but splits up into two separate spatial parts (drops), which m…
[Background] Long-Baseline experiments such as T2K, NOvA or the planned Deep Underground Neutrino Experiment (DUNE) require theoretical descriptions of the complete event in a neutrino-nucleus reaction. Since nuclear targets are used this requires a good understanding of neutrino-nucleus interactions. [Purpose] One of the dominant reaction channels in neutrino-nucleus interactions is pion production. This paper aims for a coherent view on all charged current charged pion production data that are avaible from the experiments MiniBooNE, the near detector experiment at T2K and MINERvA. [Methods] …
In this paper, it is shown that the experimental values of the nonextensive scattering entropies $S_L (p)$ and $S_θ(q)$ for the pion-nucleus ($π^0 He, π^0 C, π^0 O, π^0 Ca$) scatterings, in the energy region corresponding to $Δ(1236)$ resonance in the elementary pion-nucleon interaction, are well described by the entropic optimal resonance predictions $S_L^o1 (p)$ and $S_θ^o1 (q)$ and when the nonextensivities indices are correlated by a Riesz-Thorin-like relation: 1/2p+1/2q=1.
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Jet quenching of quarks and gluons in central A+A collisions suppresses the high-p_T meson production and exposes novel baryon dynamics that we attribute to (gluonic) baryon junctions. This mechanism predicts baryon enhancement in a finite moderate-p_T window that decreases with increasing impact parameter. We also extend recent calculations of the transverse momentum behavior of p/pi^+ and p-bar/pi^- to other baryon species and show that a similar pattern is expected for the K^-/Lambda and K^+/bar{Lambda} ratios. Within the framework of the model constant p-bar/p and bar{Lambda}/Lambda ratios…
A self-consistent symmetry arises when the nucleon angular momentum j and the isospin t are coupled to a grand spin G. Closed G shells become sources of a classical pion field with a hedgehog shape. Although the amplitude of the pion field, as measured by the chiral angle, is small, it is found to perturb significantly the energies of the nucleon orbits.
The NEUT intranuclear cascade model is described and fit to a large body of \pipm--nucleus scattering data. Methods are developed to deal with deficiencies in the available historical data, and robust uncertainty estimates are produced. The results are compared to a variety of simulation packages, and the data itself. This work provides a method for tuning Final State Interaction models, which are of particular interest to neutrino experiments that operate in the few-GeV energy region, and provides results which can be used directly by the T2K and Super-Kamiokande collaborations, for whom NEUT…
A hypothesis is proposed herein, suggesting that a pion-nuclear resonance may be observed in the $α+d\to{}^6\mathrm{Li}(3.563)+π^0$ reaction. The resonance has a $πNNα$ structure, containing $αNN$ and $πNN$ subsystems. The former corresponds to the $A=6$ isotriplet ($^6\mathrm{He}_\text{g.s.}$, $^6\mathrm{Li}(3.563)$, $^6\mathrm{Be}_\text{g.s.}$), whereas the latter is a hypothetical $NN$-decoupled dibaryon. We propose an experiment to search for this resonance using the $^7\mathrm{Li}(p,d)$ reaction.
We analyse pion-nucleus reactions in a microscopic transport model of the BUU type, which propagates nucleons, pions, deltas and N(1440)-resonances explicitly in space and time. In particular we examine pion absorption and inelastic scattering cross sections for pion kinetic energies T(pi) =85-315MeV and various target masses. In general, the mass-dependence of the experimental data is well described for energies up to the delta-resonance (\approx 160 MeV) while the absorption cross sections are somewhat overestimated for the higher energies. In addition we study the possible dynamical effects…
The nuclear sigma term is calculated including the nuclear matrix element of the derivative of the NN interaction with respect to the quark mass, $m_q\frac{\partial V_{NN}}{\partial m_q}$. The NN potential is evaluated in the skyrmion-skyrmion picture within the quantized product ansatz. The contribution of the NN potential to the nuclear sigma term provides repulsion to the pion-nucleus interaction. The strength of the s-wave pion-nucleus optical potential is estimated including such contribution. The results are consistent with the analysis of the experimental data.
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Experimental data on the pion-nucleus total cross sections are analyzed in terms of the optimal resonances predictions (OR). The OR-predictions are found in a good agreement with the actual experimental data in the region corresponding to the Delta(1236) resonance in elementary pi-N scattering. The essential signatures of the optimal resonances are experimentally verified with high accuracy.
The reaction mechanisms for neutrino interactions with an $^{40}Ar$ nucleus with the LBNF flux are calculated with the Giessen-Boltzmann-Uehling-Uhlenbeck (GiBUU) transport-theoretical implementation of these interactions. Quasielastic scattering, many-body effects, pion production and absorption and Deep Inelastic Scattering are discussed; they all play a role at the LBNF energies and are experimentally entangled with each other. Quasielastic scattering makes up for only about 1/3 of the total cross section whereas pion production channels make up about 2/3 of the total. This underlines the n…
Pion-nucleus bremsstrahlung offers a possibility of measuring the structure functions of pion-Compton scattering from a study of the small-momentum-transfer region where the bremsstrahlung reaction is dominated by the single-photon-exchange mechanism. The corresponding cross-section distribution is characterized by a sharp peak at small momentum transfers. But there is also a hadronic contribution which is smooth and constitutes an undesired background. In this communication the modification of the single-photon exchange amplitude by multiple-Coulomb scattering is investigated as well as the C…
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Hadronic interactions are crucial for the dynamical description of heavy-ion reactions at low collision energies and in the late dilute stages at high collision energies. In particular, the properties and decay channels of resonances are an essential ingredient of hadronic transport approaches. The HADES collaboration measured particle production in collisions of pions with carbon and tungsten nuclei at $E_\text{kin} = 1.7\,\text{GeV}$. Such reactions are of high interest, because they allow to probe the properties of baryonic resonances produced in a much cleaner environment than the usual nu…
I explain the Sato-Lee (SL) model and its extension to the neutrino-induced pion production off the nucleon. Then I discuss applications of the SL model to incoherent and coherent pion productions in the neutrino-nucleus scattering. I mention a further extension of this approach with a dynamical coupled-channels model developed in Excited Baryon Analysis Center of JLab.
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Elastic scattering of pions from finite nuclei is investigated utilizing a contemporary, momentum--space first--order optical potential combined with microscopic estimates of second--order corrections. The calculation of the first--order potential includes:\ \ (1)~full Fermi--averaging integration including both the delta propagation and the intrinsic nonlocalities in the $π$-$N$ amplitude, (2)~fully covariant kinematics, (3)~use of invariant amplitudes which do not contain kinematic singularities, and (4)~a finite--range off--shell pion--nucleon model which contains the nucleon pole term. The…
The production of backward pions in lepton-nucleus collisions is analyzed. We show that a large yield of high momentum backward pions can be explained by the Regge asymptotic of the distribution of nucleons carrying a large momentum fraction in the nuclear target. The calculated spectra of pions emitted in the neutrino + Ne --> muon + pion + X reaction are in satisfactory agreement with the available experimental data.
We solve a radial Schrödinger equation for the case of a multichannel square well plus an exponential potential in one of the channels. The solution is obtained by summing exactly the infinite terms of the perturbative series for the evolution operator of the system. Analytical expressions for the scattering matrix and the scattering length are given, a Deser-like formula which connects approximate ground energies and scattering length is obtained for a particular case. Possible physical applications of these results are discussed briefly.
We have extended our model for charged current neutrino-nucleus interactions to neutral current reactions. For the elementary neutrino-nucleon interaction, we take into account quasielastic scattering, Delta excitation and the excitation of the resonances in the second resonance region. Our model for the neutrino-nucleus collisions includes in-medium effects such as Fermi motion, Pauli blocking, nuclear binding, and final-state interactions. They are implemented by means of the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) coupled-channel transport model. This allows us to study exclusive channe…
Rescattering following a neutrino-nucleus reaction changes the number, energy, and direction of detectable hadrons. In turn, this affects the selection and kinematic distributions of subsamples of neutrino events used for interaction or oscillation analysis. This technical note focuses on three forms of two-body rescattering. Elastic hadron+nucleus scattering primarily changes the direction of the hadron with very little energy transfer. Secondly, a hadron+nucleon quasi-elastic process leads to the knockout of a single struck nucleon, possibly with charge exchange between the two hadrons. Also…
A careful reanalysis is done of the contribution to $K^{+}$ nucleus scattering from the interaction of the kaon with the virtual pion cloud. The usual approximations made in the evaluation of the related kaon selfenergy are shown to fail badly. We also find new interaction mechanisms which provide appreciable corrections to the kaon selfenergy. Some of these contribute to the imaginary part below pion creation threshold. The inclusion of these new mechanisms in the inelastic part of the optical potential produces a significant improvement in the differential and total $K^{+}$ nuclear cross sec…
The total cross section for Coulomb photoproduction of neutral pion pairs in the reaction gamma A --> pi0 pi0 A is estimated within the effective chiral lagrangian approach. The amplitude of gamma gamma* --> pi0 pi0 with one off-shell photon is calculated at O(p^6) in the momentum expansion; in addition, nuclear absorption is taken into account. Besides its experimental feasibility, the results of the calculation demonstrate that the reaction gamma A --> pi0 pi0 A is a powerful source of information on the process gamma gamma --> pi0 pi0 close to threshold.
Interactions of neutrinos with nuclei in the energy ranges relevant for the MiniBooNE, T2K, NO$ν$A, MINER$ν$A and MINOS experiments are discussed. It is stressed that any theoretical treatment must involve all the relevant reaction mechanisms: quasielastic scattering, pion production and DIS. In addition, also many-body interactions play a role. In this talk we show how a misidentification of the reaction mechanism can affect the energy reconstruction. We also discuss how the newly measured pion production cross sections, as reported recently by the MiniBooNE collaboration, can be related to t…
We introduce a global analysis of collinearly factorized nuclear parton distribution functions (PDFs) including, for the first time, data constraints from LHC proton-lead collisions. In comparison to our previous analysis, EPS09, where data only from charged-lepton-nucleus deep inelastic scattering (DIS), Drell-Yan (DY) dilepton production in proton-nucleus collisions and inclusive pion production in deuteron-nucleus collisions were the input, we now increase the variety of data constraints to cover also neutrino-nucleus DIS and low-mass DY production in pion-nucleus collisions. The new LHC da…
Recently developed chiral effective field theory models provide excellent descriptions of the bulk characteristics of finite nuclei, but have not been tested with other observables. In this work, densities from both relativistic point-coupling models and mean-field meson models are used in the analysis of meson-nucleus scattering at medium energies. Elastic scattering observables for 790 MeV/$c$ $π^{\pm}$ on $^{208}$Pb are calculated in a relativistic impulse approximation, using the Kemmer-Duffin-Petiau formalism to calculate the $π^{\pm}$ nucleus optical potential.
The subtracted kernel approach is shown to be a powerful method to be implemented recursively in scattering equations with regular plus point-like interactions. The advantages of the method allows one to recursively renormalize the potentials, with higher derivatives of the Dirac-delta, improving previous results. The applicability of the method is verified in the calculation of the $^1S_0$ nucleon-nucleon phase-shifts, when considering a potential with one-pion-exchange plus a contact interaction and its derivatives. The $^1S_0$ renormalization parameters are fitted to the data. The method ca…
We have developed a dynamical model for a unified description of the pion-nucleus scattering and photo- and neutrino-induced coherent pion production on nuclei. Our approach is based on a combined use of the Sato-Lee model for the electroweak pion production on a single nucleon and the Delta-hole model of pion-nucleus scattering. Numerical calculations are carried out for the case of the C12 target. After testing our model with the use of the pion photo-production data, we confront our predictions of the neutrino-induced coherent pion production reactions with the recent data from K2K and Mini…
We calculate cross sections for coherent pion production in nuclei induced by neutrinos and antineutrinos of the electron and muon type. The analogies and differences between this process and the related ones of coherent pion production induced by photons, or the (p,n) and $(^3 He, t)$ reactions are discussed. The process is one of the several ones occurring for intermediate energy neutrinos, to be considered when detecting atmospheric neutrinos. For this purpose the results shown here can be easily extrapolated to other energies and other nuclei.
We investigate theoretical approaches to pion--nucleus elastic scattering at high energies (300 $\le T_π\le$ 1 GeV). A ``model--exact'' calculation of the lowest--order microscopic optical model, carried out in momentum space and including the full Fermi averaging integration, a realistic off--shell pion--nucleon scattering amplitude and fully covariant kinematics, is used to calibrate a much simpler theory. The simpler theory utilizes a local optical potential with an eikonal propagator and includes the Coulomb interaction and the first Wallace correction, both of which are found to be import…
Recent proposals for the use of light nuclei as dark matter direct detection targets necessitate a strong theoretical understanding of the nuclear physics involved. We perform relevant calculations for dark matter-light nucleus scattering in a combined pionless effective field theory and large-$N_c$ expansion, where $N_c$ is the number of quark colors. We include a general set of one-nucleon currents that have been used in other effective theories, as well as novel two-nucleon contact currents. First, we obtain constraints for the relative sizes of the dark matter couplings to the one- and two…
We present in this article an optical potential for the $π$-nucleus interaction that can be used in various studies involving $π$-nucleus channels. Based on earlier treatments of the low energy $π$-nucleus optical potential, we have derived a potential expression applicable from threshold up to the $Δ$-resonance region. We extracted the impulse approximation form for this potential from the $π-N$ scattering amplitude and then added to it kinematical and physical corrections. The kinematic corrections arise from transforming the impulse approximation expression from the $π-N$ center of mass fra…
