Semi-inclusive Cross Sections Research Articles

XYZ spectroscopy at electron-hadron facilities. III. Semi-inclusive processes with vector exchange

Inclusive production processes will be important for the first observations of XYZ states at new generation electron-hadron colliders, as they generally benefit from larger cross sections than their exclusive counterparts. We make predictions of semi-inclusive photoproduction of the χc1(1P) and X(3872), whose peripheral production is assumed to be dominated by vector exchanges. We validate the applicability of vector meson dominance in the axial-vector charmonium sector and calculate production rates at center-of-mass energies relevant for future experimental facilities. We find the semi-inclusive cross sections near the threshold to be enhanced by a factor of ∼2–3 compared to the exclusive reaction and well-suited for a first observation in photoproduction. Published by the American Physical Society 2024

Understanding parton evolution in matter from renormalization group analysis

We perform a renormalization group (RG) analysis of collinear hadron production in deep inelastic scattering on nuclei. We consider the limit where the parent parton energy E is large, while the medium opacity L/λg remains small. We identify the fixed order and leading ln⁡(E/ξ2L) enhanced medium contributions to the semi-inclusive cross sections and derive RG equations that resum multiple emissions near the endpoints of the splitting functions at first order in opacity. These evolution equations treat the same type of radiation enhancement in matter as the modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi approach, but differ in the way one regulates the collinear divergences. They provide a unique analytic insight into the problem of resummation and a faster and more efficient path to phenomenology. The new RG evolution framework is applied to study fragmentation in eA reactions.

Semi-inclusive single-jet production in DIS at next-to-leading order in the Color Glass Condensate

Within the Color Glass Condensate (CGC) effective field theory, we derive the next-to-leading order (NLO) cross-section for the single-jet semi-inclusive cross-section in deep inelastic scattering (DIS) at small x, for both longitudinally and transversely polarized virtual photons. We provide analytic expressions, valid at finite Nc and suitable for numerical evaluation, for both the cross-section differential in rapidity and transverse momentum and the cross-section differential in rapidity only. Our NLO formulae demonstrate that the very forward rapidity regime is plagued by large double logarithmic corrections coming from phase space constraints on soft gluons close to the kinematic threshold for jet production. A joint resummation of small-x and threshold logarithms at single logarithmic accuracy is proposed to remedy the instability of the cross-section in this regime. By integrating over the single-jet phase space, we recover known results for the NLO DIS structure functions at small x, previously obtained using the optical theorem.

Exploring Semi-Inclusive Two-Nucleon Emission in Neutrino Scattering: A Factorized Approximation Approach

The semi-inclusive cross-section of two-nucleon emission induced by neutrinos and antineutrinos is computed by employing the relativistic mean field model of nuclear matter and the dynamics of meson-exchange currents. Within this model, we explore a factorization approximation based on the product of an integrated two-hole spectral function and a two-nucleon cross-section averaged over hole pairs. We demonstrate that the integrated spectral function of the uncorrelated Fermi gas can be analytically computed, and we derive a simple, fully relativistic formula for this function, showcasing its dependency solely on both missing momentum and missing energy. A prescription for the average momenta of the two holes in the factorized two-nucleon cross-section is provided, assuming that these momenta are perpendicular to the missing momentum in the center-of-mass system. The validity of the factorized approach is assessed by comparing it with the unfactorized calculation. Our investigation includes the study of the semi-inclusive cross-section integrated over the energy of one of the emitted nucleons and the cross-section integrated over the emission angles of the two nucleons and the outgoing muon kinematics. A comparison is made with the pure phase-space model and other models from the literature. The results of this analysis offer valuable insights into the influence of the semi-inclusive hadronic tensor on the cross-section, providing a deeper understanding of the underlying nuclear processes.

Semi-inclusive two-nucleon emission in (anti) neutrino charged current scattering within the relativistic mean field framework

This paper delves into the distribution of semi-inclusive events involving the emission of two nucleons in (anti) neutrino charged-current scattering. The analysis is conducted within the framework of relativistic mean-field theory applied to nuclear matter. To quantify the likelihood of such semi-inclusive events occurring, we employ a relativistic model of meson-exchange currents that aligns with the 2p2h inclusive cross section. The outcomes are presented in terms of onefold and twofold integrated semi-inclusive cross sections. To highlight disparities among the various emission channels, including proton-proton, neutron-proton, and neutron-neutron, we compare them against a purely phase-space isotropic distribution within the center of mass of the two nucleons. These comparisons reveal significant differences in the event distributions, shedding light on the distinctive characteristics of each channel. Published by the American Physical Society 2024

Infrared finite semi-inclusive cross section in two dimensional type 0B string theory

D-instanton induced S-matrix in type 0B string theory in two dimensions suffers from infrared divergences. This can be traced to the fact that these processes produce low energy rolling tachyon states that cannot be regarded as linear combination of finite number of closed string states. We compute semi-inclusive cross sections in this theory where we allow in the final state a fixed set of closed strings carrying given energies and any number of other closed string states carrying the rest of the energy. The result is infrared finite and agrees with the results in the dual matrix model, described by non-relativistic fermions moving in an inverted harmonic oscillator potential. In the matrix model the role of ‘any number of other closed string states’ is played by a fermion hole pair on opposite sides of the potential barrier.

Neutrino energy reconstruction from semi-inclusive samples

We study neutrino-nucleus charged-current reactions on finite nuclei for the situation in which an outgoing muon and a proton are detected in coincidence, i.e., we focus on semi-inclusive cross sections. We limit our attention to one-body current interactions (quasielastic scattering) and assess the impact of different nuclear effects in the determination of the neutrino energy. We identify the regions in phase space where the neutrino energy can be reconstructed relatively well, and study whether the cross section in those regions is significant. Our results indicate that it is possible to filter more than 50% of all events according to the muon and proton kinematics, so that for the DUNE and T2K fluxes the neutrino energy can be determined with an uncertainty of less than 1% and 3%, respectively. Furthermore, we find that the reconstructed neutrino energy does not depend strongly on how one treats the final-state interactions and is not much affected by the description of the initial state. On the other hand, the estimations of the uncertainty on the neutrino energy show important sensitivity to the modeling of the initial state.

High energy leptonic collisions and electroweak parton distribution functions

In high-energy leptonic collisions well above the electroweak scale, the collinear splitting mechanism of the electroweak gauge bosons becomes the dominant phenomena via the initial state radiation and the final state showering. We point out that at future high-energy lepton colliders, such as a multi-TeV muon collider, the electroweak parton distribution functions (EW PDFs) should be adopted as the proper description for partonic collisions of the initial states. The leptons and electroweak gauge bosons are the EW partons, that evolve according to the unbroken Standard Model (SM) gauge group and that effectively resum potentially large collinear logarithms. We present a formalism for the EW PDFs at the Next-to-Leading-Log (NLL) accuracy. We calculate semi-inclusive cross sections for some important SM processes at a future multi-TeV muon collider. We conclude that it is appropriate to adopt the EW PDF formalism for future high-energy lepton colliders.

Nuclear theory and event generators for charge-changing neutrino reactions

Semi-inclusive $\mathrm{CC}\ensuremath{\nu}$ cross sections based on factorized cross sections are studied for a selection of spectral function models with the objective of facilitating the choice of models for use as input into event generators. The basic formalism for such cross sections is presented along with an introduction to constructing spectral functions for simple models based on the independent-particle shell model, the relativistic Fermi gas model (RFG), and a local density approximation (LDA) based on the RFG. Spectral functions for these models are shown for $^{16}\mathrm{O}$ along with a more sophisticated model which includes nucleon-nucleon interactions [Alvarez-Ruso et al., Prog. Part. Nucl. Phys. 100, 1 (2018)]. Inclusive and semi-inclusive cross sections are calculated for these models. Although the inclusive cross sections are all of similar size and shape, the semi-inclusive cross sections are substantially different depending upon whether the spectral functions contain some features associated with the nuclear shell model or are based on the RFG and LDA models. Calculations of average values and standard deviations of the initial neutrino energy using the semi-inclusive cross section for the various models are presented and indicate that there may be simple kinematical descriptions of the average neutrino energy which is common to all of these models.

Fragmentation in jets: Cone and threshold effects

We study the fragmentation of (light) quarks and gluons to hadrons inside a jet of cone size R. This allows for a more exclusive analysis of fragmentation than is currently the case. The shape of semi-inclusive cross sections in the hadron energy fraction z is described by fragmenting jet functions (FJFs), which we calculate in terms of R and the jet energy E. We introduce a new joint resummation to sum the double logarithms of R and 1-z in the FJFs, which may similarly be applied to initial-state radiation at hadron colliders. Our results at next-to-leading logarithmic order indicate that the resummation of the threshold logarithms of 1-z is already important for z > 0.5 and improves the convergence of perturbation theory. Our framework may be used to analyze LHC and RHIC data and to test and tune Monte Carlo event generators.

Numerical solution of [formula omitted] evolution equations for fragmentation functions

Semi-inclusive hadron-production processes are becoming important in high-energy hadron reactions. They are used for investigating properties of quark–hadron matters in heavy-ion collisions, for finding the origin of nucleon spin in polarized lepton–nucleon and nucleon–nucleon reactions, and possibly for finding exotic hadrons. In describing the hadron-production cross sections in high-energy reactions, fragmentation functions are essential quantities. A fragmentation function indicates the probability of producing a hadron from a parton in the leading order of the running coupling constant αs. Its Q2 dependence is described by the standard DGLAP (Dokshitzer–Gribov–Lipatov–Altarelli–Parisi) evolution equations, which are often used in theoretical and experimental analyses of the fragmentation functions and in calculating semi-inclusive cross sections. The DGLAP equations are complicated integro-differential equations, which cannot be solved in an analytical method. In this work, a simple method is employed for solving the evolution equations by using Gauss–Legendre quadrature for evaluating integrals, and a useful code is provided for calculating the Q2 evolution of the fragmentation functions in the leading order (LO) and next-to-leading order (NLO) of αs. The renormalization scheme is MS¯ in the NLO evolution. Our evolution code is explained for using it in oneʼs studies on the fragmentation functions. Program summaryProgram title: ffevol1.0Catalogue identifier: AELJ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELJ_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 1535No. of bytes in distributed program, including test data, etc.: 10 191Distribution format: tar.gzProgramming language: Fortran77Computer: Tested on an HP DL360G5-DC-X5160Operating system: Linux 2.6.9-42.ELsmpRAM: 130 M bytesClassification: 11.5Nature of problem: This program solves time-like DGLAP Q2 evolution equations with or without next-to-leading order αs effects for fragmentation functions. The evolved functions can be calculated for Dgh, Duh, Du¯h, Ddh, Dd¯h, Dsh, Ds¯h, Dch, Dc¯h, Dbh and Db¯h of a hadron h.Solution method: The DGLAP integro-differential equations are solved by the Euler method for the differentiation of lnQ2 and the Gauss–Legendre method for the x integral as explained in Section 4 of the manuscript.Restrictions: This program is used for calculating Q2 evolution of fragmentation functions in the leading order or in the next-to-leading order of αs. Q2 evolution equations are the time-like DGLAP equations. The double precision arithmetic is used. The renormalization scheme is the modified minimal subtraction scheme (MS¯). A user provides initial fragmentation functions as the subroutines FF_INI and HQFF in the end of the distributed code FF_DGLAP.f. In FF_DGLAP.f, the subroutines are given by taking the HKNS07 (2) functions as an example of the initial functions. Then, the user inputs kinematical parameters in the file setup.ini as explained in Section 5.2 of the manuscript.Running time: A few seconds on HP DL360G5-DC-X5160.

Light quark fragmentations into pions

We discuss a process of hadronization of light quarks into charged pions in e+e− annihilations and in deep inelastic scatering of charged leptons and neutrino off nucleons. The corresponding semi-inclusive cross-sections of pions production we write in terms of quark fragmentation functions and fracture functions. We suggest a new method of measurements of fragmentation and fracture functions based on analysis of semiinclusive data.

Core excitation contributions to the breakup of the one-neutron halo nucleusBe11on a proton

The effect of the core excitation in the breakup of a one-neutron halo nucleus is studied within two different reaction formalisms, namely, the core excited model and the single-scattering approximation of the three-body Faddeev--Alt-Grassberger-Sandhas equations with target-core potential allowing for the core excitation. As an example, we consider the breakup of $^{11}\mathrm{Be}$ on a proton target at 63.7 MeV/nucleon incident energy and calculate the semi-inclusive cross section in the excitation energy interval ${E}_{x}=3.0$--5.5 MeV (${E}_{\mathrm{rel}}=2.5$--5 MeV) containing the $3/{2}^{+}$ resonance with dominant contribution of the $^{10}\mathrm{Be}$(${2}^{+}$) core excited state. The effect of the core excitation to the breakup cross section integrated around this resonance is found to be very significant. Moreover, when resonant and nonresonant contributions are added, the resulting semi-inclusive cross section is in reasonable agreement with the existing data, demonstrating the relevance of the core excitation mechanism for this observable. The present calculations also show the importance of incorporating the energy dependence of the core-target transition operators in the reaction formalism.

Measurement of leading neutron production in deep-inelastic scattering at HERA

The production of leading neutrons, where the neutron carries a large fraction x_L of the incoming proton's longitudinal momentum, is studied in deep-inelastic positron-proton scattering at HERA. The data were taken with the H1 detector in the years 2006 and 2007 and correspond to an integrated luminosity of 122 pb^{-1}. The semi-inclusive cross section is measured in the phase space defined by the photon virtuality 6 < Q^2 < 100 GeV^2, Bjorken scaling variable 1.5x10^{-4} < x < 3x10^{-2}, longitudinal momentum fraction 0.32 < x_L < 0.95 and neutron transverse momentum p_T < 0.2 GeV. The leading neutron structure function, F_2^{LN(3)}(Q^2,x,x_L), and the fraction of deep-inelastic scattering events containing a leading neutron are studied as a function of Q^2, x and x_L. Assuming that the pion exchange mechanism dominates leading neutron production, the data provide constraints on the shape of the pion structure function.

Multiple parton scattering in nuclei: Modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution for fragmentation functions

Within the framework of generalized factorization of higher-twist contributions to semi-inclusive cross sections of deeply inelastic scattering (DIS) off a large nucleus, multiple parton scattering leads to an effective medium-modified fragmentation function and the corresponding medium-modified DGLAP evolution equations. We extend the study to include gluon multiple scattering and induced quark-antiquark production via gluon fusion. We numerically solve these medium-modified DGLAP (mDGLAP) evolution equations and study the scale (${Q}^{2}$), energy ($E$), length ($L$), and jet transport parameter ($\mathrm{q\ifmmode \hat{}\else \^{}\fi{}}$) dependence of the modified fragmentation functions for a jet propagating in a uniform medium with finite length (a ``brick'' problem). We also discuss the concept of parton energy loss within such mDGLAP evolution equations and its connection to the modified fragmentation functions. With a realistic Wood-Saxon nuclear geometry, we calculate the modified fragmentation functions and compare them to experimental data on DIS off large nuclei. The extracted jet transport parameter at the center of a large nucleus is found to be ${\mathrm{q\ifmmode \hat{}\else \^{}\fi{}}}_{0}=0.024\ifmmode\pm\else\textpm\fi{}0.008$ GeV${}^{2}$/fm.

Hadron mass corrections in semi-inclusive deep inelastic scattering

We derive mass corrections for semi-inclusive deep inelastic scattering of leptons from nucleons using a collinear factorization framework which incorporates the initial state mass of the target nucleon and the final state mass of the produced hadron. The formalism is constructed specifically to ensure that physical kinematic thresholds for the semi-inclusive process are explicitly respected. A systematic study of the kinematic dependencies of the mass corrections to semi-inclusive cross sections reveals that these are even larger than for inclusive structure functions, especially at very small and very large hadron momentum fractions. The hadron mass corrections compete with the experimental uncertainties at kinematics typical of current facilities, and will be important to efforts at extracting parton distributions or fragmentation functions from semi-inclusive processes at intermediate energies.

One-neutron knockout reaction of halo nuclei

Full Faddeev-type calculations are performed for one-neutron knockout from 11Be on a proton target at 38.4 and 200MeV/u incident energies. Semi-inclusive cross-sections are calculated and the results are compared with the Plane-Wave Impulse Approximation (PWIA).

Spectroscopy of unbound states under quasifree scattering conditions: One-neutron knockout reaction ofBe14

Full Faddeev-type calculations are performed for one-neutron knockout reaction of $^{14}\mathrm{Be}$ on proton target at 69 MeV/nucleon incident energy. Inclusive transverse momentum distributions for the outgoing $(^{12}\mathrm{Be}+n)$ system and semi-inclusive cross sections are presented. A significant proton-core single scattering contribution emerges where the valence neutron has nonzero angular momentum relative to the core. This indicates that distorted-wave impulse approximation is inadequate and the complete multiple scattering series must be taken into account for the considered reaction. The magnitude of the semi-inclusive cross section at quasifree scattering conditions is a clear signature of the angular momentum of the valence nucleon.

Multiple parton scattering in nuclei: Gauge invariance

Within the framework of a generalized collinear factorization for multiple parton scattering in nuclear medium, twist-4 contributions to DIS off a large nucleus can be factorized as a convolution of hard parts and two-parton correlation functions. The hard parts for the quark scattering in the light-cone gauge correspond to interaction with a transverse (physical) gluon in the target, while they are given by the second derivative of the cross section with a longitudinal gluon in the covariant gauge. We provide a general proof of the equivalence of the hard parts in the light-cone and covariant gauge. We further demonstrate the equivalence in calculations of twist-4 contributions to semi-inclusive cross section of DIS in both lowest order and next leading order. Calculations of the nuclear transverse momentum broadening of the struck quark in the light-cone and covariant gauge are also discussed.

Azimuthal and single-spin asymmetry in deep-inelastic lepton-nucleon scattering

The collinear expansion technique is generalized to thefactorization of unintegrated parton distributions and other higher twistparton correlations from the corresponding collinear hard parts thatinvolve multiple parton final state interaction. Such a generalizedfactorization provides a consistent approach to the calculation ofinclusive and semi-inclusive cross sections of deep-inelasticlepton-nucleon scattering. As an example, the azimuthal asymmetry iscalculated to the order of 1/Q in semi-inclusive deeply inelasticlepton-nucleon scattering with transversely polarized target. Anon-vanishing single-spin asymmetry in the triggered inclusive processis predicted to be 1/Q suppressed with a part of the coefficient relatedto a moment of the Sivers function.