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Jan Piclum

Publications and source records attributed to Jan Piclum.

15 recordsLinked to original sources
arXiv2022

Feynman integral reduction using Gr\"obner bases

We investigate the reduction of Feynman integrals to master integrals using Gr\"obner bases in a rational double-shift algebra Y in which the integration-by-parts (IBP) relations form a left ideal. The problem of reducing a given family of integrals to master integrals can then be solved once and for all by computing the Gr\"obner basis of the left ideal formed by the IBP relations. We demonstrate this explicitly for several examples. We introduce so-called first-order normal-form IBP relations which we obtain by reducing the shift operators in Y modulo the Gr\"obner basis of the left ideal of IBP relations. For more complicated cases, where the Gr\"obner basis is computationally expensive, we develop an ansatz based on linear algebra over a function field to obtain the normal-form IBP relations.

hep-ph↗
arXiv2022

IBP reduction via Gr\"obner bases in a rational double-shift algebra

We report on an approach to integration-by-parts reduction based on Gr\"obner bases. We establish the underlying noncommutative rational double-shift algebra wherein the integration-by-parts relations form a left ideal. We describe in detail the one-loop massless box as an example where we achieved the full reduction to master integrals by means of the Gr\"obner basis approach, and report on the performance of the implementation. We also identify potential bottlenecks in more complicated examples and elaborate on interesting further directions.

hep-ph↗
arXiv2021

Charm-quark mass effects in NRQCD matching coefficients and the leptonic decay of the $Υ(1S)$ meson

We compute two-loop corrections to the vector current matching coefficient involving two heavy quark masses. The result is applied to the computation of the $Υ(1S)$ decay width into an electron or muon pair. We complement the next-to-next-to-next-to-leading order corrections of Ref. arXiv:1401.3005 by charm quark mass effects up to second order in perturbation theory. Furthermore, we apply the formalism to $Γ(J/Ψ\to \ell^+\ell^-)$ and compare to the experimental data.

hep-ph↗
arXiv2020

Logarithmically enhanced Euler-Heisenberg Lagrangian contribution to the electron gyromagnetic factor

Contrary to what was previously believed, two-loop radiative corrections to the $g$-factor of an electron bound in a hydrogen-like ion at $\mathcal{O}\left(α^2 (Zα)^5\right)$ exhibit logarithmic enhancement. This previously unknown contribution is due to a long-distance light-by-light scattering amplitude. Taking an effective field theory approach, and using the Euler-Heisenberg Lagrangian, we find $Δg = -\left( \fracαπ \right)^2\left(Zα\right)^5 \frac{56 π}{135}\ln Zα$.

hep-ph↗
arXiv2018

Soft-gluon and Coulomb corrections to hadronic top-quark pair production beyond NNLO

We construct a resummation at partial next-to-next-to-next-to-leading logarithmic accuracy for hadronic top-quark pair production near partonic threshold, including simultaneously soft-gluon and Coulomb corrections, and use this result to obtain approximate next-to-next-to-next-to-leading order predictions for the total top-quark pair-production cross section at the LHC. We generalize a required one-loop potential in non-relativistic QCD to the colour-octet case and estimate the remaining unknown two-loop potentials and three-loop anomalous dimensions. We obtain a moderate correction of $1.5\%$ relative to the next-to-next-to-leading order prediction and observe a reduction of the perturbative uncertainty below $\pm 5\%$.

hep-ph↗
arXiv2017

Two-loop binding corrections to the electron gyromagnetic factor

We compute corrections to the gyromagnetic factor of an electron bound in a hydrogen-like ion at order alpha^2(Z alpha)^5. This result removes a major uncertainty in predictions for silicon and carbon ions, used to determine the atomic mass of the electron.

physics.atom-ph↗
arXiv2016

NNLL soft and Coulomb resummation for squark and gluino production at the LHC

We present predictions for the total cross sections for pair production of squarks and gluinos at the LHC including a combined NNLL resummation of soft and Coulomb gluon effects. We derive all terms in the NNLO cross section that are enhanced near the production threshold, which include contributions from spin-dependent potentials and so-called annihilation corrections. The NNLL corrections at $\sqrt{s}=13$ TeV range from up to $20\%$ for squark-squark production to $90\%$ for gluino pair production relative to the NLO results and reduce the theoretical uncertainties of the perturbative calculation to the $10\%$ level. Grid files with our numerical results are publicly available.

hep-ph↗
arXiv2016

Next-to-next-to-leading logarithmic resummation for transverse thrust

We obtain a prediction for the hadron-collider event-shape variable transverse thrust in which the terms enhanced in the dijet limit are resummed to next-to-next-to-leading logarithmic accuracy. Our method exploits universality properties made manifest in the factorized expression for the cross section and only requires one-loop calculations. The necessary two-loop ingredients are extracted using known results and existing numerical codes. Our technique is general and applicable to other observables as well.

hep-ph↗
arXiv2016

NNNLO determination of the bottom-quark mass from non-relativistic sum rules

The mass of the bottom quark can be determined with high precision from moments of the pair-production cross section sigma(e+ e- -> b bbar) near threshold. We present the first complete NNNLO determination from non-relativistic sum rules, obtaining a bottom-quark mass of mb^PS(2 GeV) = (4.532 +0.013 -0.039) GeV in the potential-subtracted scheme. For the mass in the MSbar scheme we find mb^MS(mb^MS) = (4.203 +0.016 -0.034) GeV using the recently computed four-loop correction to the scheme conversion.

hep-ph↗
arXiv2015

Non-QCD contributions to top-pair production near threshold

The threshold scan of top pair production at a future lepton collider allows to determine several Standard Model parameters with very high precision. The recent completion of the third-order QCD corrections to the inclusive top-pair production cross section demonstrated that strong dynamics are under control. We investigate effects from P-wave production and Higgs contributions at third order and from QED and the nonresonant production of the physical $W^+W^-b\bar{b}$ final state at first order. We discuss the sensitivity of the cross section to the top mass, width and Yukawa coupling as well as to the strong coupling.

hep-ph↗
arXiv2015

Higgs effects in top anti-top production near threshold in e+ e- annihilation

The completion of the third-order QCD corrections to the inclusive top-pair production cross section near threshold demonstrates that the strong dynamics is under control at the few percent level. In this paper we consider the effects of the Higgs boson on the cross section and, for the first time, combine the third-order QCD result with the third-order P-wave, the leading QED and the leading non-resonant contributions. We study the size of the different effects and investigate the sensitivity of the cross section to variations of the top-quark Yukawa coupling due to possible new physics effects.

hep-ph↗
arXiv2014

Leptonic decay of the Upsilon(1S) meson at third order in QCD

We present the complete next-to-next-to-next-to-leading order short-distance and bound-state QCD correction to the leptonic decay rate Gamma(Upsilon(1S)->l+l-) of the lowest-lying spin-1 bottomonium state. The perturbative QCD prediction is compared to the measurement Gamma(Upsilon(1S)->e+e-)=1.340(18) keV.

hep-ph↗