arXiv subjects

Markus Diehl

Publications and source records attributed to Markus Diehl.

At least 19 recordsLinked to original sources

arXiv2026

A quantitative study of two-loop splitting in double parton distributions

Double parton distributions at small distances between the two partons are dominated by a mechanism in which the two observed partons originate from the splitting of a single parton. This contribution can be computed in terms of single-parton distributions and perturbative splitting kernels. We demonstrate that two-loop corrections to these kernels can have a substantial quantitative impact and considerably improve the stability of predictions for double parton scattering. We also consider the impact of heavy quark masses in the two-loop splitting kernels in an approximate manner.

hep-ph↗

arXiv2025

Extracting Mellin moments of double parton distributions from lattice data

Reconstructing Mellin moments of double parton distributions from calculations on a Euclidean lattice requires taking an integral over a variable that may be regarded as a Ioffe time. The Fourier conjugate of this variable plays the role of a kinematic skewness in the double parton distributions. We discuss the skewness dependence of the relevant hadronic correlation functions. Using several models, we study the impact of this dependence on extracting moments of double parton distributions from existing lattice data.

hep-lat↗

arXiv2024

Efficient computation of Fourier-Bessel transforms for transverse-momentum dependent parton distributions and other functions

We present a method for the numerical computation of Fourier-Bessel transforms on a finite or infinite interval. The function to be transformed needs to be evaluated on a grid of points that is independent of the argument of the Bessel function. We demonstrate the accuracy of the algorithm for a wide range of functions, including those that appear in the context of transverse-momentum dependent parton distributions in Quantum Chromodynamics.

hep-ph↗

arXiv2024

Double parton distributions with flavor interference from lattice QCD

We study double parton distributions with flavor interference in the nucleon and compare them with previous results for the flavor diagonal case. We investigate both unpolarized and polarized partons. We compare our lattice results with those obtained from the simple description of the proton in terms of an SU(6) symmetric three-quark wave function and find that this description fails for both flavor and polarization dependence. We also derive and test a factorization ansatz for the unpolarized flavor interference distribution in terms of single-parton distributions and find that this ansatz fails to a large extent.

hep-lat↗

arXiv2024

Evolution of colour correlated double parton distributions: a quantitative study

Double parton distributions satisfy the same evolution equations as ordinary single-parton densities, provided that the colours of the two partons are uncorrelated. The situation is different for colour correlated parton pairs, where evolution to higher scales results in a suppression by Sudakov double logarithms. We perform a detailed study of evolution for colour correlated double parton distributions, both analytically and numerically, at lowest order and beyond. When the two observed partons originate from the perturbative splitting of a single one, the Sudakov suppression of colour correlations at the cross section level is not as strong as one might expect.

hep-ph↗

arXiv2023

Quark mass effects in double parton distributions

Double parton distributions can be computed from the perturbative splitting of one parton into two if the distance between the two observed partons is small. We develop schemes to take into account quark mass effects in this computation, and we study these schemes numerically at leading order in the strong coupling. Furthermore, we investigate in detail the structure of the next-to-leading order corrections to the splitting kernels that include quark mass effects.

hep-ph↗

arXiv2023

Evolution and interpolation of double parton distributions using Chebyshev grids

Double parton distributions are the nonperturbative ingredients needed for computing double parton scattering processes in hadron-hadron collisions. They describe a variety of correlations between two partons in a hadron and depend on a large number of variables, including two independent renormalization scales. This makes it challenging to compute their scale evolution with satisfactory numerical accuracy while keeping computational costs at a manageable level. We show that this problem can be solved using interpolation on Chebyshev grids, extending the methods we previously developed for ordinary single-parton distributions. Using an implementation of these methods in the C++ library ChiliPDF, we study for the first time the evolution of double parton distributions beyond leading order in perturbation theory.

hep-ph↗

arXiv2023

Two-loop evolution kernels for colour dependent double parton distributions

A key ingredient in the description of double parton distributions is their scale dependence. If the colour of each individual parton is summed over, the distributions evolve with the same DGLAP kernels as ordinary parton distributions. This is no longer true if the two partons are colour correlated. We compute the relevant kernels for this case at next-to-leading order in the strong coupling, for unpolarised or longitudinally polarised partons and for transversely polarised quarks.

hep-ph↗

arXiv2022

ChiliPDF: Chebyshev Interpolation for Parton Distributions

Parton distribution functions (PDFs) are an essential ingredient for theoretical predictions at colliders. Since their exact form is unknown, their handling and delivery for practical applications relies on approximate numerical methods. We discuss the implementation of PDFs based on a global interpolation in terms of Chebyshev polynomials. We demonstrate that this allows for significantly higher numerical accuracy at lower computational cost compared with local interpolation methods such as splines. Whilst the numerical inaccuracy of currently used local methods can become a nontrivial limitation in high-precision applications, in our approach it is negligible for practical purposes. This holds in particular for differentiation and for Mellin convolution with kernels that have end point singularities. We illustrate our approach for these and other important numerical operations, including DGLAP evolution, and find that they are performed accurately and fast. Our results are implemented in the C++ library ChiliPDF.

hep-ph↗

arXiv2021

Double parton distributions out of bounds in colour space

We investigate the positivity of double parton distributions with a non-trivial dependence on the parton colour. It turns out that positivity is not preserved by leading-order evolution from lower to higher scales, in contrast to the case in which parton colour is summed over. We also study the positivity properties of the distributions at small distance between the two partons, where they can be computed in terms of perturbative splitting kernels and ordinary parton densities.

hep-ph↗

arXiv2021

Double parton distributions in the nucleon from lattice QCD

We evaluate nucleon four-point functions in the framework of lattice QCD in order to extract the first Mellin moment of double parton distributions (DPDs) in the unpolarized proton. In this first study, we employ an nf = 2 + 1 ensemble with pseudoscalar masses of mpi = 355 MeV and mK = 441 MeV. The results are converted to the scale mu = 2 GeV. Our calculation includes all Wick contractions, and for almost all of them a good statistical signal is obtained. We analyze the dependence of the DPD Mellin moments on the quark flavor and the quark polarization. Furthermore, the validity of frequently used factorization assumptions is investigated.

hep-lat↗

arXiv2021

Two-loop splitting in double parton distributions: the colour non-singlet case

At small inter-parton distances, double parton distributions receive their dominant contribution from the splitting of a single parton. We compute this mechanism at next-to-leading order in perturbation theory for all colour configurations of the observed parton pair. Rapidity divergences are handled either by using spacelike Wilson lines or by applying the delta regulator. We investigate the behaviour of the two-loop contributions in different kinematic limits, and we illustrate their impact in different channels.

hep-ph↗

arXiv2021

Transverse momentum in double parton scattering: factorisation, evolution and matching

We give a description of double parton scattering with measured transverse momenta in the final state, extending the formalism for factorisation and resummation developed by Collins, Soper and Sterman for the production of colourless particles. After a detailed analysis of their colour structure, we derive and solve evolution equations in rapidity and renormalisation scale for the relevant soft factors and double parton distributions. We show how in the perturbative regime, transverse momentum dependent double parton distributions can be expressed in terms of simpler nonperturbative quantities and compute several of the corresponding perturbative kernels at one-loop accuracy. We then show how the coherent sum of single and double parton scattering can be simplified for perturbatively large transverse momenta, and we discuss to which order resummation can be performed with presently available results. As an auxiliary result, we derive a simple form for the square root factor in the Collins construction of transverse momentum dependent parton distributions.

hep-ph↗

arXiv2021

Double parton distributions in the pion from lattice QCD

We perform a lattice study of double parton distributions in the pion, using the relationship between their Mellin moments and pion matrix elements of two local currents. A good statistical signal is obtained for almost all relevant Wick contractions. We investigate correlations in the spatial distribution of two partons in the pion, as well as correlations involving the parton polarisation. The patterns we observe depend significantly on the quark mass. We investigate the assumption that double parton distributions approximately factorise into a convolution of single parton distributions.

hep-lat↗

arXiv2020

Sum rule improved double parton distributions in position space

Models for double parton distributions that are realistic and consistent with theoretical constraints are crucial for a reliable description of double parton scattering. We show how an ansatz that has the correct behaviour in the limit of small transverse distance between the partons can be improved step by step, such as to fulfil the sum rules for double parton distributions with an accuracy around 10%.

hep-ph↗

arXiv2020

Gluons and sea quarks in the proton at low scales

We study the evolution of parton distributions down to low scales by considering several of their Mellin moments. For the initial conditions, we use a broad array of current parton density fits. Confirming earlier findings in the literature, we conclude that current determinations of parton distributions are incompatible with the idea that gluon or antiquark densities are generated by purely perturbative radiation as it is encoded in the DGLAP evolution equations.

hep-ph↗

arXiv2019

Two-loop splitting in double parton distributions

Double parton distributions (DPDs) receive a short-distance contribution from a single parton splitting to yield the two observed partons. We investigate this mechanism at next-to-leading order (NLO) in perturbation theory. Technically, we compute the two-loop matching of both the position and momentum space DPDs onto ordinary PDFs. This also yields the 1 -> 2 splitting functions appearing in the evolution of momentum-space DPDs at NLO. We give results for the unpolarised, colour-singlet DPDs in all partonic channels. These quantities are required for calculations of double parton scattering at full NLO. We discuss various kinematic limits of our results, and we verify that the 1 -> 2 splitting functions are consistent with the number and momentum sum rules for DPDs.

hep-ph↗

arXiv2019

Factorisation of soft gluons in multiparton scattering

We show that soft gluons exchanged between the two colliding protons in multiparton scattering processes can be decoupled, such that their effects are described by the vacuum expectation values of Wilson lines. Our argument relies on nonabelian Ward identities and generalises the proof of factorisation for single Drell-Yan production given by Collins, Soper and Sterman.

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