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We have computed the even-N moments N =< 20 of the gluon-gluon splitting function P_{gg} at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. Our results, derived analytically for a general compact simple gauge group, agree with all results obtained for this function so far, in particular with the lowest five moments obtained via structure functions in deep-inelastic scattering. Using our new moments and all available endpoint constraints, we construct improved approximations for the four-loop P_{gg}(x) that should be sufficient for a wide range of collider-physics applications. The N^3LO contributions to the scale derivative of the gluon distribution, resulting from these and the corresponding quark-to-gluon splitting functions, amount to 1% or less at x >~ 10^{-4} at a standard reference scale with alpha_s = 0.2., Comment: 15 pages, LaTeX, 3 figures, 2 ancillary files (FORM file with results and FORTRAN subroutine). arXiv admin note: text overlap with arXiv:2404.09701

Parton evolution equations in QCD are controlled by the anomalous dimensions of gauge-invariant twist-two spin-$N$ quark and gluon operators. Under renormalization, these mix with gauge-variant operators of the same quantum numbers, referred to as alien operators. Our work addresses the systematic study of these alien operators at arbitrary spin $N$, using generalized BRST symmetry relations to derive their couplings and Feynman rules at all values of $N$. We observe how the all-$N$ structure of the generalized (anti-)BRST constraints relates the couplings of alien operators with $n+1$ gluons to those with $n$ gluons. Realizing a bootstrap, we present all one-loop results necessary for performing the operator renormalization up to four loops in QCD., Comment: 27 pages, LaTex, 4 figures, all-N results in ancillary Mathematica file

We present the even-N moments N =< 20 of the fourth-order (N^3LO) contribution P_{gq}^(3)(x) to the quark-to-gluon splitting function in perturbative QCD. These moments, obtained by analytically computing off-shell operator matrix elements for a general gauge group, agree with all known results, in particular with the moments N =< 10 derived before from structure functions in deep-inelastic scattering. Using the new moments and the available endpoint constraints, we construct approximations for P_{gq}^(3)(x) which improve upon those obtained from the lowest five even moments. The remaining uncertainties of this function are now practically irrelevant at momentum fractions x > 0.1. The resulting errors of the convolution of P_{gq} at N^3LO with a typical quark distribution are small at x >~ 10^{-3} and exceed 1% only at x ~< 10^{-4} for a strong coupling alpha_s = 0.2. The present results for P_{gq}^(3)(x) should thus be sufficient for most collider-physics applications., Comment: 15 pages, LaTex, 2 figures, 2 ancillary files (FORM file with results and FORTRAN subroutine)

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., Comment: 10 pages, LaTex, 1 eps-based figure. Analytical results in ancillary FORM files

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 $\alpha_s = 0.2$., Comment: journal version (v2 typos corrected); 17 pages latex, 3 figures, 2 ancillary files (v2 FORM file with results and FORTRAN subroutine)

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., Comment: 17 pages latex, 2 figures, 2 ancillary files (FORM file with results and FORTRAN subroutine)

We present the first calculations of next-to-next-to-next-to-next-to-leading order (N^4LO) contributions to anomalous dimensions of spin-N twist-2 operators in perturbative QCD. Specifically, we have obtained the respective non-singlet quark-quark anomalous dimensions at N=2 and N=3 to the fifth order in the strong coupling alpha_s. These results set the scale for the N^4LO contributions to the evolution of the non-singlet quark distributions of hadrons outside the small-x region, and facilitate a first approximate determination of the five-loop cusp anomalous dimension. While the N^4LO coefficients are larger than expected from the lower-order results, their inclusion stabilizes the perturbative expansions for three or more light flavours at a sub-percent accuracy for alpha_s < 0.3., Comment: 11 pages, LaTeX, 2 figures. FORM file of the main results available with the source. v2: Nikhef and DESY numbers added, one very minor text modification. Version to appear in Phys. Lett. B

We report on recent progress on the splitting functions for the evolution of parton distributions and related quantities, the (lightlike) cusp anomalous dimensions, in perturbative QCD. New results are presented for the four-loop (next-to-next-to-next-to-leading order, N^3LO) contributions to the flavour-singlet splitting functions and the gluon cusp anomalous dimension. We present first results, the moments N=2 and N=3, for the five-loop (N^4LO) non-singlet splitting functions., Comment: 10 pages, LaTeX (PoS style), 3 eps-figures. Contribution to the proceedings of `Loops & Legs 2018', St. Goar (Germany), April/May 2018

We sketch how the R*-operation can be used to compute the pole terms of Feynman diagrams. We identify computational difficulties when performing five-loop calculations, and provide four solutions that drastically reduce the number of terms that are generated. Using these methods, we have computed the beta function for Yang-Mills theory with fermions, the R-ratio in electron-positron annihilation, and Higgs decays to quarks and gluons at five-loop accuracy. The results for the beta function and Higgs decay width to gluons in the heavy-top limit are briefly discussed. There is no need for six-loop extensions of these calculations in the near future., Comment: 12 pages, LaTeX (PoS style), 2 eps-figures. Contribution to the proceedings of `RADCOR 2017', St. Gilgen (Austria), September 2017 and (shortened) to the proceedings of `ACAT 2017', Seattle (USA), August 2017

The global R* operation is a powerful method for computing renormalisation group functions. This technique, based on the principle of infrared rearrangement, allows to express all the ultraviolet counterterms in terms of massless propagator integrals. In this talk we present the main features of global R* and its application to the renormalisation of QCD. By combining this approach with the use of the program Forcer for the evaluation of the relevant Feynman integrals, we renormalise for the first time QCD at five loops in covariant gauges., Comment: 10 pages, 6 figures, contribution to the proceedings of the 13th International Symposium on Radiative Corrections (RADCOR 2017)

We present the complete set of vertex, wave function and charge renormalisation constants in QCD in a general simple gauge group and with the complete dependence on the covariant gauge parameter $\xi$ in the minimal subtraction scheme of conventional dimensional regularisation. Our results confirm all already known results, which were obtained in the Feynman gauge, and allow the extraction of other useful gauges such as the Landau gauge. We use these results to extract the Landau gauge five-loop anomalous dimensions of the composite operator $A^2$ as well as the Landau gauge scheme independent gluon, ghost and fermion propagators at five loops., Comment: 17 pages; FORM and Mathematica result files available with the source; corrected minor typos, added references, journal ref, 1 remark, 1 note and 1 additional result file

We present the first determination of Higgs-boson decay to hadrons at the next-to-next-to-next-to-next-to-leading order of perturbative QCD in the limit of a heavy top quark and massless light flavours. This result has been obtained by computing the absorptive parts of the relevant five-loop self-energy for a general gauge group and combining the outcome with the corresponding coefficient function already known to this order in QCD. Our new result reduces the uncertainty due to the truncation of the perturbation series to a fraction of the uncertainty due to the present error of the strong coupling constant. We have also performed the corresponding but technically simpler computations for direct Higgs decay to bottom quarks and for the electromagnetic R-ratio in e^+ e^- -> hadrons, thus verifying important fifth-order results obtained so far only by one group., Comment: 26 pages, LaTeX, 2 axodraw2 and 4 eps figures. FORM files of the main results available with the source. v2: version accepted by JHEP: introduction and summary slightly extended, minor other text changes, a few additional references

The spin splitting of conduction band electrons in inversion-asymmetric InGaAs/InP quantum wells is studied by Shubnikov-de Haas measurements combining the analysis of beating patterns and coincidence measurements in doubly tilted magnetic fields. The method allows us to determine the absolute values of the Rashba and linear Dresselhaus spin-orbit interaction coefficients, their relative sign and the full Land\'e g-tensor. This is achieved by analyzing the anisotropy of the beat node positions with respect to both polar and azimuthal angles between the magnetic field direction and the quantum well normal. We show that the spin-orbit interaction is dominated by a large Rashba coefficient together with a linear Dresselhaus coefficient that is 10 $\%$ of the Rashba coefficient. Their relative sign is found to be positive. The g-tensor is found to have a marked out-of-plane anisotropy and a smaller but distinct in-plane anisotropy due to spin-orbit interaction.

We have computed the five-loop corrections to the scale dependence of the renormalized coupling constant for Quantum Chromodynamics (QCD), its generalization to non-Abelian gauge theories with a simple compact Lie group, and for Quantum Electrodynamics (QED). Our analytical result, obtained using the background field method, infrared rearrangement via a new diagram-by-diagram implementation of the R* operation and the Forcer program for massless four-loop propagators, confirms the QCD and QED results obtained by only one group before. The numerical size of the five-loop corrections is briefly discussed in the standard MSbar scheme for QCD with n_f flavours and for pure SU(N) Yang-Mills theory. Their effect in QCD is much smaller than the four-loop contributions, even at rather low scales., Comment: 19 pages, LaTex, 4 figures. FORM file of the main results available with the source. v2: version accepted by JHEP: minor text changes, a few additional references, typos corrected

This Report summarizes the results of the activities of the LHC Higgs Cross Section Working Group in the period 2014-2016. The main goal of the working group was to present the state-of-the-art of Higgs physics at the LHC, integrating all new results that have appeared in the last few years. The first part compiles the most up-to-date predictions of Higgs boson production cross sections and decay branching ratios, parton distribution functions, and off-shell Higgs boson production and interference effects. The second part discusses the recent progress in Higgs effective field theory predictions, followed by the third part on pseudo-observables, simplified template cross section and fiducial cross section measurements, which give the baseline framework for Higgs boson property measurements. The fourth part deals with the beyond the Standard Model predictions of various benchmark scenarios of Minimal Supersymmetric Standard Model, extended scalar sector, Next-to-Minimal Supersymmetric Standard Model and exotic Higgs boson decays. This report follows three previous working-group reports: Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables (CERN-2011-002), Handbook of LHC Higgs Cross Sections: 2. Differential Distributions (CERN-2012-002), and Handbook of LHC Higgs Cross Sections: 3. Higgs properties (CERN-2013-004). The current report serves as the baseline reference for Higgs physics in LHC Run 2 and beyond., Comment: 869 pages, 295 figures, 248 tables and 1645 citations. Working Group web page: https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHXSWG