arXiv subjects

J. Vermaseren

Publications and source records attributed to J. Vermaseren.

10 recordsLinked to original sources

arXiv2025

Five-loop beta function for gauge theories: computations, results and consequences

At the end of 2016, we computed the five-loop (N$^4$LO) contributions to the beta function in perturbative Quantum Chromodynamics (QCD), its generalization to non-Abelian gauge theories with a simple compact Lie group, and for Quantum Electrodynamics (QED). Here we recall main tools used in and specifically developed for this computation and its main analytic and numerical results. The development work carried out for this project facilitated further even more involved analytic five-loop computations. We briefly summarize also their numerical QCD results for Higgs-boson decay to hadrons in the heavy-top limit and for two N$^4$LO splitting functions for the evolution of quark distributions of hadrons. The latter lead to a first realistic estimate of the five-loop contribution to another important quantity in perturbative QCD, the quark cusp anomalous dimension.

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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.

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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.

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arXiv2009

On Higgs-exchange DIS, physical evolution kernels and fourth-order splitting functions at large x

We present the coefficient functions for deep-inelastic scattering (DIS) via the exchange of a scalar phi directly coupling only to gluons, such as the Higgs boson in the limit of a very heavy top quark and n_f effectively massless light flavours, to the third order in perturbative QCD. The two-loop results are employed to construct the next-to-next-to-leading order physical evolution kernels for the system (F_2 F_phi) of flavour-singlet structure functions. The practical relevance of these kernels as an alternative to MSbar factorization is bedevilled by artificial double logarithms at small values of the scaling variable x, where the large top-mass limit ceases to be appropriate. However, they show an only single-logarithmic enhancement at large x. Conjecturing that this feature persists to the next order also in the present singlet case, the three-loop coefficient functions facilitate exact predictions (backed up by their particular colour structure) of the double-logarithmic contributions to the fourth-order singlet splitting functions, i.e., of the terms (1-x)^a ln^k(1-x) with k = 4, 5, 6 and k = 3, 4, 5, respectively, for the off-diagonal and diagonal quantities to all powers a in 1-x.

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arXiv2008

Third-order QCD corrections to the charged-current structure function F_3

We compute the coefficient function for the charge-averaged W^(+/-)-exchange structure function F_3 in deep-inelastic scattering (DIS) to the third order in massless perturbative QCD. Our new three-loop contribution to this quantity forms, at not too small values of the Bjorken variable x, the dominant part of the next-to-next-to-next-to-leading order corrections. It thus facilitates improved determinations of the strong coupling alpha_s and of 1/Q^2 power corrections from scaling violations measured in neutrino-nucleon DIS. The expansion of F_3 in powers of alpha_s is stable at all values of x relevant to measurements at high scales Q^2. At small x the third-order coefficient function is dominated by diagrams with the colour structure d_abc d^abc not present at lower orders. At large x the coefficient function for F_3 is identical to that of F_1 up to terms vanishing for x to 1.

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arXiv2006

Third-order QCD results on form factors and coefficient functions

We summarize recent higher-order QCD results based, directly or indirectly, on the Mellin-space computation of the next-to-next-to-leading-order splitting functions governing the evolution of hadronic parton distributions. Specifically, we briefly present third-order results for the coefficient functions in inclusive deep-inelastic scattering (including the structure function F_3 not published so far), the on-shell quark and gluon form factors, and the total cross section for Higgs production at hadron colliders.

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arXiv2005

Photon-Parton Splitting Functions at the Next-to-Next-to-Leading Order of QCD

We have calculated the splitting functions governing the evolution of the unpolarized parton distributions of the photon at the next-to-next-to-leading order (NNLO) of massless perturbative QCD. The results, presented here mainly in terms of compact and accurate parametrizations, are consistent with our previous approximations based on the lowest six even-integer Mellin moments. Consequently the NNLO corrections are small in both the MSbar and the DIS_gamma factorization schemes at momentum fractions x >~ 0.1.

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arXiv2005

Sudakov Resummations at Higher Orders

We summarize our recent results on the resummation of hard-scattering coefficient functions and on-shell form factors in massless perturbative QCD. The threshold resummation has been extended to the fourth logarithmic order for deep-inelastic scattering, Drell-Yan lepton pair production and Higgs production via gluon-gluon fusion. The leading six infrared pole terms have been derived to all orders in the strong coupling constant for the photon-quark-quark and the (heavy-top) Higgs-gluon-gluon form factors. These results have many implications, most notably they lead to a new best estimate for the Higgs production cross section at the LHC.

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arXiv2004

The Three-Loop Splitting Functions in QCD

We have computed the next-to-next-to-leading-order (NNLO) contributions to the evolution of unpolarized parton distributions in perturbative QCD. In this talk, we briefly recall why this huge computation was necessary and outline how it was performed. We then illustrate the structure of the results and discuss their end-point limits which include the three-loop cusp anomalous dimensions of the Wilson lines. Finally the numerical impact of the new contributions is illustrated.

hep-ph↗

arXiv1996

Pomerons and Jet Events at HERA

We study two and three jet events with a large rapidity gap at HERA. Unlike in the Ingelman-Schlein approach we do not adscribe a structure to the Pomeron. Instead, the coupling of the Pomeron to quarks or gluons is taken pointlike, which makes the model easy to test: the only degrees of freedom are the coupling constants of the Pomeron to the quarks or the gluons and a cutoff procedure to keep the Pomeron-gluon coupling well behaved.

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