Deep Inelastic Scattering Cross Sections Research Articles

Disorder: Deep inelastic scattering at high orders

We present a Fortran 77/95 code capable of computing QCD corrections in deep inelastic scattering (DIS). The code uses the Projection-to-Born method to augment an existing \mathcal{O}(\alpha_{\mathrm{s}}^2)𝒪(αs2) dijet DIS code, thereby obtaining predictions for photon-mediated neutral-current single-jet DIS production in the laboratory frame. The code is lightweight and fast, and yet includes the most common functionalities found in typical perturbative QCD programs, like automatic renormalisation and factorisation scale uncertainties, options to run and combine multiple seeds, and interfaces to fastjet and LHAPDF. Due to the underlying disent and HOPPET codes, the program also provides stable results in the infrared, relevant for extracting logarithmic coefficients for analytic resummations, and access to the massless DIS structure functions and (reduced) cross sections up to \mathcal{O}(\alpha_{\mathrm{s}}^3)𝒪(αs3).

Codebase release r1.0 for disorder

We present a Fortran 77/95 code capable of computing QCD corrections in deep inelastic scattering (DIS). The code uses the Projection-to-Born method to augment an existing \mathcal{O}(\alpha_{\mathrm{s}}^2)𝒪(αs2) dijet DIS code, thereby obtaining predictions for photon-mediated neutral-current single-jet DIS production in the laboratory frame. The code is lightweight and fast, and yet includes the most common functionalities found in typical perturbative QCD programs, like automatic renormalisation and factorisation scale uncertainties, options to run and combine multiple seeds, and interfaces to fastjet and LHAPDF. Due to the underlying disent and HOPPET codes, the program also provides stable results in the infrared, relevant for extracting logarithmic coefficients for analytic resummations, and access to the massless DIS structure functions and (reduced) cross sections up to \mathcal{O}(\alpha_{\mathrm{s}}^3)𝒪(αs3).

Basics of factorization in a scalar Yukawa field theory

The factorization theorems of QCD apply equally well to most simple quantum field theories that require renormalization but where direct calculations are much more straightforward. Working with these simpler theories is convenient for stress testing the limits of the factorization program and for examining general properties of the parton density functions or other correlation functions that might be necessary for a factorized description of a process. With this view in mind, we review the steps of factorization in a real scalar Yukawa field theory for both deep inelastic scattering and semi-inclusive deep inelastic scattering cross sections. In the case of semi-inclusive deep inelastic scattering, we illustrate how to separate the small transverse momentum region, where transverse momentum dependent parton density functions are needed, from a purely collinear large transverse momentum region, and we examine the influence of subleading power corrections. We also review the steps for formulating transverse momentum dependent factorization in transverse coordinate space, and we study the effect of transforming to the well-known ${b}_{*}$ scheme. Within the Yukawa theory, we investigate the consequences of switching to a generalized parton model approach and compare it with a fully factorized approach. Our results highlight the need to address similar or analogous issues in QCD.

Massive Quarks at One Loop in the Dipole Picture of Deep Inelastic Scattering.

We calculate the light cone wave functions for a virtual photon to split into quark-antiquark states, including for the first time quark masses at one loop accuracy. These wave functions can be used to calculate cross sections for several precision probes of perturbative gluon saturation at the Electron-Ion Collider. Using these wave functions we derive, for the first time, the dipole picture deep inelastic scattering cross sections at one loop for longitudinal and transverse virtual photons including quark masses. The quark masses are renormalized in the pole mass scheme, satisfying constraints from the requirement of Lorentz invariance of the quark Dirac and Pauli form factors.

Massive quarks in NLO dipole factorization for DIS: Transverse photon

We calculate the light cone wave functions for the QCD Fock components in a transverse virtual photon necessary for applications at next-to-leading order in the QCD coupling, including quark masses. We present a detailed calculation of both the one loop wave function for the quark-antiquark Fock component and the tree level wave function for the quark-antiquark-gluon Fock component. The quark masses are renormalized in the pole mass scheme, satisfying constraints from the requirement of Lorentz invariance. In particular the quark Pauli form factor at NLO is recovered from the on-shell limit of the quark-antiquark Fock component. We use our result to calculate the next-to-leading order correction to the high energy deep inelastic scattering (DIS) transverse structure function on a dense target in the dipole factorization framework. Together with our earlier result for longitudinal photons, this completes the calculation of the total deep inelastic scattering cross section in the dipole picture with massive quarks at next-to-leading order, enabling a comparison with experimental data.

Gluon-mediated inclusive Deep Inelastic Scattering from Regge to Bjorken kinematics

We revisit high energy factorization for gluon mediated inclusive Deep Inelastic Scattering (DIS) for which we propose a new semi-classical approach that accounts systematically for the longitudinal extent of the target in contrast with the shockwave limit. In this framework, based on a partial twist expansion, we derive a factorization formula that involves a new gauge invariant unintegrated gluon distribution which depends explicitly on the Feynman x variable. It is shown that both the Regge and Bjorken limits are recovered in this approach. We reproduce in particular the full one loop inclusive DIS cross-section in the leading twist approximation and the all-twist dipole factorization formula in the strict x = 0 limit. Although quantum evolution is not discussed explicitly in this work, we argue that the proper treatment of the x dependence of the gluon distribution encompasses the kinematic constraint that must be imposed on the phase-space of gluon fluctuations in the target to ensure stability of small-x evolution.

A novel formulation of the unintegrated gluon distribution for DIS

We provide a semi-classical description of the inclusive gluon mediated Deep Inelastic Scattering cross section in a way that accounts for the leading powers in both the Regge and Bjorken limits. Our approach thus allows a systematic matching of small and moderate xBj regimes of gluon proton structure functions. We find a new unintegrated gluon distribution with an explicit dependence on the longitudinal momentum fraction x which entirely spans both the dipole operator and the gluonic Parton Distribution Function. Computing this gauge invariant gluon operator on the lattice could allow to probe the energy dependence of the saturation scale from first principles.

Nuclear medium effects in the deep inelastic ντ/ν¯τ−Ar40 scattering at DUNE energies

The nuclear medium effects are studied in the $\nu_\tau/\bar\nu_\tau$ interactions from nuclei in the deep inelastic scattering (DIS) region and applied to the $^{40}Ar$ nucleus to obtain the scattering cross sections in the energy region of the proposed DUNE experiment. The free nucleon structure functions ($F_{iN}(x,Q^2);~(i=1-5)$) have been calculated at the next-to-leading order (NLO) using Martin-Motylinski-Harland Lang-Thorne 2014 as well as The Coordinated Theoretical-Experimental Project on QCD parameterizations for parton distribution functions (PDFs) and including the effect of perturbative and nonperturbative QCD corrections \cite{Ansari:2020xne}. These free nucleon structure functions are then convoluted with the nucleon spectral function in the nucleus to obtain the nuclear structure functions ($F_{iA}(x,Q^2);~(i=1-5)$). The nucleon spectral function takes into account the Fermi motion and the binding energy of the nucleons as well as the nucleon correlations within the nucleus. These nuclear structure functions are then used to calculate the deep inelastic scattering cross sections. Moreover, the contribution of $\pi$ and $\rho$ mesons as well as the corrections due to the shadowing and antishadowing effects in the relevant kinematic region of the Bjorken variable $x$ are also included. The numerical results for the cross sections have been presented and compared with the results obtained in the phenomenological approach using nuclear structure functions from nCTEQnu.

Reinterpretation of proton strangeness between ATLAS and CMS measurements

We reexamine the shapes of the strange quark parton distribution functions (PDFs) of the proton by means of quantum chromodynamics (QCD) analysis of {\hera} deep inelastic scattering cross section measurement at DESY, and inclusive gauge boson production and $W$ boson production associated with a charm quark from LHC at CERN. We find that there is an overall agreement on the strange quark distributions obtained from CMS $W$ + charm and ATLAS $W/Z$ data at the parton momentum fraction range $x \lesssim 10^{-2}$. Meanwhile, there is also a strong tension between these data towards large $x$. We find that this tension fades away if the ATLAS measurement of $W/Z$ production is analyzed together with the ATLAS $W$ + charm data. The $W/Z$ and $W$ + charm data both from ATLAS and CMS experiments agree that the proton strangeness is enhanced towards small momentum fraction $x$ and is smoothly suppressed at large $x$. Furthermore, a strong $x$ dependence of the strange-to-non-strange parton ratio $R_s(x,Q^2)$ is observed.

TMD fragmentation functions at N3LO

We compute the unpolarized quark and gluon transverse-momentum dependent fragmentation functions (TMDFFs) at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. The calculation is based on a relation between the TMDFF and the limit of the semi-inclusive deep inelastic scattering cross section where all final-state radiation becomes collinear to the detected hadron. The required cross section is obtained by analytically continuing our recent computation of the Drell-Yan and Higgs boson production cross section at N3LO expanded around the limit of all final-state radiation becoming collinear to one of the initial states. Our results agree with a recent independent calculation by Luo et al.

Determination of collinear and TMD photon densities using the Parton Branching method

We present the first determination of transverse momentum dependent (TMD) photon densities with the Parton Branching method. The photon distribution is generated perturbatively without intrinsic photon component. The input parameters for quarks and gluons are determined from fits to precision measurements of deep inelastic scattering cross sections at HERA. The TMD densities are used to predict the mass and transverse momentum spectra of very high mass lepton pairs from both Drell-Yan production and Photon-Initiated lepton processes at the LHC.

Status and Physics of the SHiP experiment at CERN

SHiP is a new general purpose fixed target facility, whose Technical Proposal has been recently reviewed by the CERN SPS Committee and by the CERN Research Board. The two boards recommended that the experiment proceeds further to a Comprehensive Design phase in the context of the new CERN Working group ”Physics Beyond Colliders”, aiming at presenting a CERN strategy for the European Strategy meeting of 2019. In its initial phase, the 400 GeV proton beam extracted from the SPS will be dumped on a heavy target with the aim of integrating 2 × 1020 pot in 5 years. A dedicated detector, based on a long vacuum tank followed by a spectrometer and particle identification detectors, will allow probing a variety of models with light long-lived exotic particles and masses below O(10) GeV/c2. The main focus will be the physics of the so-called Hidden Portals, i.e. search for Dark Photons, Light scalars and pseudo-scalars, and Heavy Neutrinos. The sensitivity to Heavy Neutrinos will allow for the first time to probe, in the mass range between the kaon and the charm meson mass, a coupling range for which Baryogenesis and active neutrino masses could also be explained. Another dedicated detector will allow the study of neutrino cross-sections and angular distributions. ντ deep inelastic scattering cross sections will be measured with a statistics 1000 times larger than currently available, with the extraction of the F4 and F5 structure functions, never measured so far and allow for new tests of lepton non-universality with sensitivity to BSM physics.

Collinear and TMD parton densities from fits to precision DIS measurements in the parton branching method

Collinear and transverse momentum dependent (TMD) parton densities are obtained from fits to precision measurements of deep inelastic scattering (DIS) cross sections at HERA. The parton densities are evolved by DGLAP evolution with next-to-leading-order (NLO) splitting functions using the parton branching method, allowing one to determine simultaneously collinear and TMD densities for all flavors over a wide range in $x$, $\mu^2$ and $k_t$, relevant for predictions at the LHC. The DIS cross section is computed from the parton densities using perturbative NLO coefficient functions. Parton densities satisfying angular ordering conditions are presented. Two sets of parton densities are obtained, differing in the renormalization scale choice for the argument in the strong coupling alpha_s. This is taken to be either the evolution scale $\mu$ or the transverse momentum $q_t$. While both choices yield similarly good $\chi^2$ values for the fit to DIS measurements, especially the gluon density turns out to differ between the two sets. The TMD densities are used to predict the transverse momentum spectrum of Z-bosons at the LHC.

Combination and QCD Analysis of Charm and Beauty Production Cross-section Measurements in Deep Inelastic $ep$ Scattering at HERA

Measurements of open charm and beauty production cross sections in ep deep inelastic scattering (DIS) at HERA from the H1 and ZEUS collaborations are combined. Reduced cross sections are obtained in a restricted kinematic range. Perturbative QCD calculations are compared to the combined data. Next-to-leading order QCD analysis is performed using these data together with combined inclusive HERA DIS cross sections.

Combination and QCD analysis of charm and beauty production cross-section measurements in deep inelastic ep scattering at HERA

Measurements of open charm and beauty production cross sections in deep inelastic ep scattering at HERA from the H1 and ZEUS Collaborations are combined. Reduced cross sections are obtained in the kinematic range of negative four-momentum transfer squared of the photon 2.5~hbox {GeV}^2le Q^2 le 2000, hbox {GeV}^2 and Bjorken scaling variable 3 cdot 10^{-5} le x_mathrm{Bj} le 5 cdot 10^{-2}. The combination method accounts for the correlations of the statistical and systematic uncertainties among the different datasets. Perturbative QCD calculations are compared to the combined data. A next-to-leading order QCD analysis is performed using these data together with the combined inclusive deep inelastic scattering cross sections from HERA. The running charm- and beauty-quark masses are determined as m_c(m_c) = 1.290^{+0.046}_{-0.041} mathrm{(exp/fit)}{}^{+0.062}_{-0.014} mathrm{(model)}{}^{+0.003}_{-0.031} mathrm{(parameterisation)} GeV and m_b(m_b) = 4.049^{+0.104}_{-0.109} mathrm{(exp/fit)}{}^{+0.090}_{-0.032} mathrm{(model)}{}^{+0.001}_{-0.031} mathrm{(parameterisation)}~mathrm{GeV}.

One-loop corrections to light cone wave functions: The dipole picture DIS cross section

We develop methods to perform loop calculations in light cone perturbation theory using a helicity basis, refining the method introduced in our earlier work. In particular this includes implementing a consistent way to contract the four-dimensional tensor structures from the helicity vectors with d-dimensional tensors arising from loop integrals, in a way that can be fully automatized. We demonstrate this explicitly by calculating the one-loop correction to the virtual photon to quark–antiquark dipole light cone wave function. This allows us to calculate the deep inelastic scattering cross section in the dipole formalism to next-to-leading order accuracy. Our results, obtained using the four dimensional helicity scheme, agree with the recent calculation by Beuf using conventional dimensional regularization, confirming the regularization scheme independence of this cross section.

Electron-deuteron deep-inelastic scattering with spectator nucleon tagging and final-state interactions at intermediate x

We consider electron-deuteron deep-inelastic scattering (DIS) with detection of a proton in the nuclear fragmentation region ("spectator tagging") as a method for extracting the free neutron structure functions and studying their nuclear modifications. Such measurements could be performed at a future Electron-Ion Collider (EIC) with suitable forward detectors. The measured proton recoil momentum (~< 100 MeV in the deuteron rest frame) specifies the deuteron configuration during the high-energy process and permits a controlled theoretical treatment of nuclear effects. Nuclear and nucleonic structure are separated using methods of light-front quantum mechanics. The impulse approximation (IA) to the tagged DIS cross section contains the free neutron pole, which can be reached by on-shell extrapolation in the recoil momentum. Final-state interactions (FSI) distort the recoil momentum distribution away from the pole. In the intermediate-x region 0.1 < x < 0.5 FSI arise predominantly from interactions of the spectator proton with slow hadrons produced in the DIS process on the neutron (rest frame momenta ~< 1 GeV, target fragmentation region). We construct a schematic model describing this effect, using final-state hadron distributions measured in nucleon DIS experiments and low-energy hadron scattering amplitudes. We investigate the magnitude of FSI, their dependence on the recoil momentum (angular dependence, forward/backward regions), their analytic properties, and their effect on the on-shell extrapolation. We comment on the prospects for neutron structure extraction in tagged DIS with EIC. We discuss possible extensions of the FSI model to other kinematic regions (large/small x). In tagged DIS at x << 0.1 FSI resulting from diffractive scattering on the nucleons become important and require separate treatment.

Impact of beauty and charm H1-ZEUS combined measurements on PDFs and determination of the strong coupling

In this QCD analysis, we investigate the impact of recent measurements of heavy-flavor charm and beauty cross sections data sets on the simultaneous determination of Parton Distribution Functions (PDFs) and the strong coupling, $\alpha_s(M^2_Z)$. We perform three different fits based on Variable-Flavour Number Scheme (VFNS) at the Leading Order (LO) and Next-to-Leading Order (NLO) and choose the full HERA run I and II combined data as a new measurement of inclusive Deep Inelastic Scattering (DIS) cross sections for our base data set. We show that including charm and beauty cross sections data reduces the uncertainty of gluon distribution and improves the fit quality up to 4.1\% from leading order to next-to-leading order and up to 1.7\% for only NLO without and with beauty and charm data contributions.

SHiP: a new facility with a dedicated detector for studying tau-neutrino properties and nucleon structure functions

SHiP is a new general purpose fixed target facility, whose Technical Proposal has been recently reviewed by the CERN SPS Committee, who recommended that the experiment proceeds further to a Comprehensive Design phase. In its initial phase, the 400 GeV proton beam extracted from the SPS will be dumped on a heavy target with the aim of integrating 2 × 1020 pot in 5 years. A dedicated detector downstream of the target will allow to probe a variety of models with light long-lived exotic particles and masses below a few GeV/c2. Another dedicated detector will allow the study of neutrino cross-sections and angular distributions, which was the focus of the poster. ντ deep inelastic scattering cross sections will be measured with a statistics 1000 times larger than currently available, with the extraction of the F4 and F5 structure functions, never measured so far and allow for new tests of lepton non-universality with sensitivity to BSM physics. Moreover, ντ’s will be distinguished from ’s, thus providing the first observation of the . With νµ scattering it will be possible to reduce by about 50% the current uncertainty on the strange content of the nucleon in the range of the x variable between 0.05 and 0.3, complementary to LHC measurements. The detector will be based on several techniques developed for the OPERA experiment at LNGS.

First measurement of unpolarized semi-inclusive deep-inelastic scattering cross sections from a He3 target

The unpolarized semi-inclusive deep-inelastic scattering (SIDIS) differential cross sections in $^3$He($e,e^{\prime}\pi^{\pm}$)$X$ have been measured for the first time in Jefferson Lab experiment E06-010 performed with a $5.9\,$GeV $e^-$ beam on a $^3$He target. The experiment focuses on the valence quark region, covering a kinematic range $0.12 < x_{bj} < 0.45$, $1 < Q^2 < 4 \, \textrm{(GeV/c)}^2$, $0.45 < z_{h} < 0.65$, and $0.05 < P_t < 0.55 \, \textrm{GeV/c}$. The extracted SIDIS differential cross sections of $\pi^{\pm}$ production are compared with existing phenomenological models while the $^3$He nucleus approximated as two protons and one neutron in a plane wave picture, in multi-dimensional bins. Within the experimental uncertainties, the azimuthal modulations of the cross sections are found to be consistent with zero.