https://www.zora.uzh.ch/id/eprint/191493/1/1-s2.0-S0370157320302556-main.pdf

The anomalous magnetic moment of the muon in the Standard Model

FIRE6: Feynman Integral REduction with Modular Arithmetic

The quark model was formulated in 1964 to classify mesons as bound states made of a quark-antiquark pair, and baryons as bound states made of three quarks. For a long time all known mesons and baryons could be classified within this scheme. Quantum Chromodynamics (QCD), however, in principle also allows the existence of more complex structures, generically called exotic hadrons or simply exotics. These include four-quark hadrons (tetraquarks and hadronic molecules), five-quark hadrons (pentaquarks) and states with active gluonic degrees of freedom (hybrids), and even states of pure glue (glueballs). Exotic hadrons have been systematically searched for in numerous experiments for many years. Remarkably, in the past fifteen years, many new hadrons that do not exhibit the expected properties of ordinary (not exotic) hadrons have been discovered in the quarkonium spectrum. These hadrons are collectively known as $XYZ$ states. Some of them, like the charged states, are undoubtedly exotic. Parallel to the experimental progress, the last decades have also witnessed an enormous theoretical effort to reach a theoretical understanding of the $XYZ$ states. Theoretical approaches include not only phenomenological extensions of the quark model to exotics, but also modern non-relativistic effective field theories and lattice QCD calculations. The present work aims at reviewing the rapid progress in the field of exotic $XYZ$ hadrons over the past few years both in experiments and theory. It concludes with a summary on future prospects and challenges.

The $XYZ$ states: experimental and theoretical status and perspectives

Version 3 of RunDec and CRunDec

We compute the relation between heavy quark masses defined in the modified minimal subtraction and the on-shell schemes. Detailed results are presented for all coefficients of the $\mathrm{SU}({N}_{c})$ color factors. The reduction of the four-loop on-shell integrals is performed for a general QCD gauge parameter. Altogether there are about 380 master integrals. Some of them are computed analytically, others with high numerical precision using Mellin-Barnes representations, and the rest numerically with the help of FIESTA. We discuss in detail the precise numerical evaluation of the four-loop master integrals. Updated relations between various short-distance masses and the $\overline{\mathrm{MS}}$ quark mass to next-to-next-to-next-to-leading order accuracy are provided for the charm, bottom and top quarks. We discuss the dependence on the renormalization and factorization scale.

/pdf/overline-rm-ms-on-shell-quark-mass-relation-up-to-four-loops-2xzdtchlmh.pdf

$\overline{\rm MS}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group

We compute the NLO virtual corrections to the partonic cross section of gg → HH, in the high energy limit. Finite Higgs boson mass effects are taken into account via an expansion which is shown to converge quickly. We obtain analytic results for the next-to-leading order form factors which can be used to compute the cross section. The method used for the calculation of the (non-planar) master integrals is described in detail and explicit results are presented.

/pdf/double-higgs-boson-production-at-nlo-in-the-high-energy-5bx5emriic.pdf

Double Higgs boson production at NLO in the high-energy limit: complete analytic results

We consider the virtual corrections to the process gg → HH at NLO in the high energy limit and compute the corresponding planar master integrals in an expansion for small top quark mass. We provide details on the evaluation of the boundary conditions and present analytic results expressed in terms of harmonic polylogarithms.

/pdf/double-higgs-boson-production-in-the-high-energy-limit-3cj33z4smm.pdf

Double-Higgs boson production in the high-energy limit: planar master integrals

We consider the next-to-leading order QCD corrections to Higgs boson pair production, using our recent calculation of the form factors in the high-energy limit. We compute the virtual corrections to the partonic cross section, applying Pad\'e approximations to extend the range of validity of the high-energy expansion. This enables us to compare to the exact numerical calculation in a significant part of the phase space and allows us to extend the virtual matrix element grid, based on the exact numerical calculation, to larger values of the (partonic) transverse momentum of the Higgs boson, which is important for boosted Higgs studies. Improved predictions for hadron colliders with centre-of-mass energies of $14\ \mathrm{TeV}$ and $100\ \mathrm{TeV}$ are presented. The updated grid is made publicly available.

/pdf/double-higgs-boson-production-at-nlo-combining-the-exact-1u6806np4a.pdf

Double Higgs boson production at NLO: combining the exact numerical result and high-energy expansion.

We consider the next-to-leading order QCD corrections to Higgs boson pair production, using our recent calculation of the form factors in the high-energy limit. We compute the virtual corrections to the partonic cross section, applying Pade approximations to extend the range of validity of the high-energy expansion. This enables us to compare to the exact numerical calculation in a significant part of the phase space and allows us to extend the virtual matrix element grid, based on the exact numerical calculation, to larger values of the (partonic) transverse momentum of the Higgs boson, which is important for boosted Higgs studies. Improved predictions for hadron colliders with centre-of-mass energies of 14 TeV and 100 TeV are presented. The updated grid is made publicly available.

/pdf/double-higgs-boson-production-at-nlo-combining-the-exact-1o2rt0j6be.pdf

David Wellmann

Papers

$\overline{\rm MS}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group

Double Higgs boson production at NLO in the high-energy limit: complete analytic results

Double-Higgs boson production in the high-energy limit: planar master integrals

Double Higgs boson production at NLO: combining the exact numerical result and high-energy expansion.

Double Higgs boson production at NLO: combining the exact numerical result and high-energy expansion