arXiv subjects

S. Moch

Publications and source records attributed to S. Moch.

At least 37 records · Page 2Linked to original sources

arXiv2024

Four-loop splitting functions in QCD -- The gluon-to-quark case

We have computed the even-$N$ moments $N \leq 20$ of the gluon-to-quark splitting function $P_{\rm qg}$ at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. Our results, derived analytically for a general gauge group, agree with all results obtained for this function so far, in particular with the lowest five moments obtained via physical cross sections. Using our new moments and all available endpoint constraints, we construct approximations for the four-loop $P_{\rm qg}(x)$ that should be sufficient for a wide range of collider-physics applications. The N$^3$LO corrections resulting from these and the corresponding quark-quark splitting functions lead to a marked improvement of the perturbative accuracy for the scale derivative of the singlet quark distribution, with effects of 1% or less at $x \gtrsim 10^{\,-4}$ at a standard reference scale with $α_s = 0.2$.

hep-ph↗

arXiv2023

Additional moments and x-space approximations of four-loop splitting functions in QCD

We have extended our previous computations of the even-N moments of the flavour-singlet four-loop splitting functions to N = 12 for the pure-singlet quark case and N = 10 for all other cases. These results, obtained using physical quantities in inclusive deep-inelastic scattering, have been and will be used to validate conceptionally much more challenging determinations of these splitting functions from off-shell operator matrix elements (OMEs). For the quark-gluon and gluon-gluon splitting functions, which have yet to be computed to higher N using OMEs, we construct approximations based on our moments and endpoint constraints, where we present new large-x results for the gluon-gluon case. These approximations facilitate an approximate N^3LO evolution of parton distributions which are sufficiently accurate outside the region of small momentum fractions x.

hep-ph↗

arXiv2023

The double fermionic contribution to the four-loop quark-to-gluon splitting function

We have computed the first 30 even-N moments for the double fermionic (nf^2) part of the quark-to-gluon splitting function P_{gq} at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. From these results we have determined the all-N form, and hence the exact x-space expression, using systems of Diophantine equations for its coefficients. The dominant and subdominant leading small-x nf^2 contributions to P_{gq}^(3)(x) are of the form 1/x ln x and ln^4 x, respectively; the leading large-x term is ln^4 (1-x). The coefficient of the first of these is new, the other two agree with results obtained before and thus provide checks of our results.

hep-ph↗

arXiv2023

$\mathbf{Z^\prime}$-boson dilepton searches and the high-$\mathbf{x}$ quark density

We study the influence of theoretical systematic uncertainties due to the quark density on LHC experimental searches for $Z^\prime$-bosons. Using an approach originally proposed in the context of the ABMP16 PDF set for the high-$x$ behaviour of the quark density, we presents results on observables commonly used to study $Z^\prime$ signals in dilepton channels.

hep-ph↗

arXiv2023

Snowmass 2021 whitepaper: Proton structure at the precision frontier

An overwhelming number of theoretical predictions for hadron colliders require parton distribution functions (PDFs), which are an important ingredient of theory infrastructure for the next generation of high-energy experiments. This whitepaper summarizes the status and future prospects for determination of high-precision PDFs applicable in a wide range of energies and experiments, in particular in precision tests of the Standard Model and in new physics searches at the high-luminosity Large Hadron Collider and Electron-Ion Collider. We discuss the envisioned advancements in experimental measurements, QCD theory, global analysis methodology, and computing that are necessary to bring unpolarized PDFs in the nucleon to the N2LO and N3LO accuracy in the QCD coupling strength. Special attention is given to the new tasks that emerge in the era of the precision PDF analysis, such as those focusing on the robust control of systematic factors both in experimental measurements and theoretical computations. Various synergies between experimental and theoretical studies of the hadron structure are explored, including opportunities for studying PDFs for nuclear and meson targets, PDFs with electroweak contributions or dependence on the transverse momentum, for incisive comparisons between phenomenological models for the PDFs and computations on discrete lattice, and for cross-fertilization with machine learning/AI approaches. [Submitted to the US Community Study on the Future of Particle Physics (Snowmass 2021).]

hep-ph↗

arXiv2023

Four-loop splitting functions in QCD -- The quark-quark case

We have computed the even-$N$ moments $N\leq 20$ of the pure-singlet quark splitting function $P_{\,\rm ps}$ at the fourth order of perturbative QCD via the anomalous dimensions of off-shell flavour-singlet operator matrix elements. Our results, derived analytically for a general gauge group, agree with all results obtained for this function so far, in particular with the lowest six even moments obtained via physical cross sections. Using these results and all available endpoint constraints, we construct approximations for $P_{\rm ps}$ at four loops that should be sufficient for most collider-physics applications. Together with the known results for the non-singlet splitting function $P_{\rm ns}^{\,+}$ at this order, this effectively completes the quark-quark contribution for the evolution of parton distribution at N$^{\:\!3}$LO accuracy. Our new results thus provide a major step towards fully consistent N$^{\:\!3}$LO calculations at the LHC and the reduction of the residual uncertainty in the parton evolution to the percent level.

hep-ph↗

arXiv2022

Snowmass 2021 White Paper: Electron Ion Collider for High Energy Physics

Electron Ion Collider (EIC) is a particle accelerator facility planned for construction at Brookhaven National Laboratory on Long Island, New York by the United States Department of Energy. EIC will provide capabilities of colliding beams of polarized electrons with polarized beams of proton and light ions. EIC will be one of the largest and most sophisticated new accelerator facilities worldwide, and the only new large-scale accelerator facility planned for construction in the United States in the next few decades. The versatility, resolving power and intensity of EIC will present many new opportunities to address some of the crucial and fundamental open scientific questions in particle physics. This document provides an overview of the science case of EIC from the perspective of the high energy physics community.

hep-ph↗

arXiv2022

DIS coefficient functions at four loops in QCD and beyond

We report results for the lowest even-$N$ moments of the flavor-nonsinglet structure functions $F_2$ and $F_L$ in QCD at the fourth order in the perturbative expansion in the strong coupling constant $α_s$. Our results are presented in numerical form and we compare them with the leading and subleading terms of the threshold expansion for large values of $N$, which corresponds to the limit $x \to 1$.

hep-ph↗

arXiv2022

Off-forward anomalous dimensions in the leading-$n_f$ limit

We review the computation of off-forward anomalous dimensions in the limit of a large number of quark flavors $n_f$. The method is based on a consistency relation the anomalous dimensions have to obey, which is a direct consequence of the renormalization structure of the operators in the chiral limit. In addition, we present a way to generate the anomalous dimensions to all orders in the strong coupling $α_s$. This is based on exact conformal symmetry at the Wilson-Fisher critical point and provides an extension of previous calculations of this type for the forward anomalous dimensions.

hep-ph↗

arXiv2022

Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering

We present a comprehensive study of high-energy double logarithms in inclusive DIS. They appear parametrically as alpha_s^n ln^{2n-k} x at the n-th order in perturbation theory in the splitting functions for the parton evolution and the coefficient functions for the hard scattering process, and represent the leading corrections at small $x$ in the flavour non-singlet case. We perform their resummation, in terms of modified Bessel functions, to all orders in full QCD up to NNLL accuracy, and partly to N^3LL and beyond in the large-n_c limit, and provide fixed-order expansions up to five loops. In the flavour-singlet sector, where these double logarithms are sub-dominant at small x compared to single-logarithmic alpha_s^n x^{-1} ln^{n-k} x BFKL contributions, we construct fixed-order expansions up to five loops at NNLL accuracy in full QCD. The results elucidate the analytic small-x structure underlying inclusive DIS results in fixed-order perturbation theory and provide important information for present and future numerical and analytic calculations of these quantities.

hep-ph↗

arXiv2021

Low moments of the four-loop splitting functions in QCD

We have computed the four lowest even-N moments of all four splitting functions for the evolution of flavour-singlet parton densities of hadrons at the fourth order in the strong coupling constant alpha_s. The perturbative expansion of these moments, and hence of the splitting functions for momentum fractions x >~ 0.1, is found to be well behaved with relative alpha_s-coefficients of order one and sub-percent effects on the scale derivatives of the quark and gluon distributions at alpha_s ~< 0.2. More intricate computations, including other approaches such as the operator-product expansion, are required to cover the full x-range relevant to LHC analyses. Our results are presented analytically for a general gauge group for detailed checks and validations of such future calculations.

hep-ph↗

arXiv2021

The axial-vector contributions in two-photon reactions: pion transition form factor and deeply-virtual Compton scattering at NNLO in QCD

Using the approach based on conformal symmetry we calculate the two-loop coefficient function for the axial-vector contributions to two-photon processes in the $\overline{\rm MS}$ scheme. This is the last missing element for the complete next-to-next-to-leading order (NNLO) calculation of the the pion transition form factor $γ^\astγ\to π$ in perturbative QCD. The corresponding high-statistics measurement is planned by the Belle II collaboration and will allow one to put strong constraints on the pion light-cone distribution amplitude. The calculated NNLO corrections prove to be rather large and have to be taken into account. The same coefficient function determines the contribution of the axial-vector generalized parton distributions to deeply-virtual Compton scattering which is investigated at the JLAB 12 GeV accelerator, by COMPASS at CERN, and in the future will be studied at the Electron Ion Collider EIC.

hep-ph↗

arXiv2021

Renormalization of non-singlet quark operator matrix elements for off-forward hard scattering

We calculate non-singlet quark operator matrix elements of deep-inelastic scattering in the chiral limit including operators with total derivatives. This extends previous calculations with zero-momentum transfer through the operator vertex which provides the well-known anomalous dimensions for the evolution of parton distributions, as well as calculations in off-forward kinematics utilizing conformal symmetry. Non-vanishing momentum-flow through the operator vertex leads to mixing with total derivative operators under renormalization. In the limit of a large number of quark flavors $n_f$ and for low moments in full QCD, we determine the anomalous dimension matrix to fifth order in the perturbative expansion in the strong coupling $α_s$ in the $\overline{\mbox{MS}}$-scheme. We exploit consistency relations for the anomalous dimension matrix which follow from the renormalization structure of the operators, combined with a direct calculation of the relevant diagrams up to fourth order.

hep-ph↗

arXiv2021

Two-loop coefficient function for DVCS: Vector contributions

Using the approach based on conformal symmetry we calculate the two-loop coefficient function for the vector flavor-nonsinglet contribution to deeply-virtual Compton scattering (DVCS). The analytic expression for the coefficient function in momentum fraction space is presented in the $\overline{\text{MS}}$ scheme. The corresponding next-to-next-to-leading order correction to the Compton form factor $\mathcal{H}$ for a simple model of the generalized parton distribution appears to be rather large: a factor two smaller than the next-to-leading order correction, approximately $\sim 10$\% of the tree level result in the bulk of the kinematic range, for $Q^2=4$ GeV$^2$.

hep-ph↗

arXiv2021

Precision studies for Drell-Yan processes at NNLO

We present a detailed comparison of the fixed-order predictions computed by four publicly available computer codes for Drell-Yan processes at the LHC and Tevatron colliders. We point out that while there is agreement among the predictions at the next-to-leading order accuracy, the predictions at the next-to-next-to-leading order (NNLO) differ, whose extent depends on the observable. The sizes of the differences in general are at least similar, sometimes larger than the sizes of the NNLO corrections themselves. We demonstrate that the neglected power corrections by the codes that use global slicing methods for the regularization of double real emissions can be the source of the differences. Depending on the fiducial cuts, those power corrections become linear, hence enhanced as compared to quadratic ones that are considered standard.

hep-ph↗

arXiv2021

Calculating Four-Loop Corrections in QCD

We review the current status of perturbative corrections in QCD at four loops for scattering processes with space- and time-like kinematics at colliders, with specific focus on deep-inelastic scattering and electron-positron annihilation. The calculations build on the parametric reduction of loop and phase space integrals up to four-loop order using computer algebra programs such as FORM, designed for large scale computations.

hep-ph↗

arXiv2021

Heavy-flavor hadro-production with heavy-quark masses renormalized in the ${\overline{\rm MS}}$, MSR and on-shell schemes

We present predictions for heavy-quark production at the Large Hadron Collider making use of the ${\overline{\rm MS}}$ and MSR renormalization schemes for the heavy-quark mass as alternatives to the widely used on-shell renormalization scheme. We compute single and double differential distributions including QCD corrections at next-to-leading order and investigate the renormalization and factorization scale dependence as well as the perturbative convergence in these mass renormalization schemes. The implementation is based on publicly available programs, ${\texttt{MCFM}}$ and ${\texttt{xFitter}}$, extending their capabilities. Our results are applied to extract the top-quark mass using measurements of the total and differential $t\bar{t}$ production cross-sections and to investigate constraints on parton distribution functions, especially on the gluon distribution at low $x$ values, from available LHC data on heavy-flavor hadro-production.

hep-ph↗

arXiv2021

Three-loop off-forward evolution kernel for axial-vector operators in Larin's scheme

Evolution equations for leading twist operators in high orders of perturbation theory can be restored from the spectrum of anomalous dimensions and the calculation of the special conformal anomaly at one order less using conformal symmetry of QCD at the Wilson-Fisher critical point at non-integer $d=4-2ε$ space-time dimensions. In this work we generalize this technique to axial-vector operators. We calculate the corresponding three-loop evolution kernels in Larin's scheme and derive explicit expressions for the finite renormalization kernel that describes the difference to the vector case to restore the conventional ${\overline{\mathrm{MS}}}$-scheme. The results are directly applicable to deeply-virtual Compton scattering and the transition form factor $γ^*γ\toπ$.

hep-ph↗