Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the “bible of computer algebra”, gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany oneor two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.

Modern computer algebra

Combined measurements of Higgs boson production cross sections and branching fractions arc presented. The combination is based on the analyses of the Higgs boson decay modes H -> gamma gamma, ZZ ...

https://cds.cern.ch/record/2688596/files/scoap3-fulltext.pdf

Combined measurements of Higgs boson production and decay using up to 80 fb− 1 of proton-proton collision data at √s=13 TeV collected with the ATLAS experiment

FIRE6: Feynman Integral REduction with Modular Arithmetic

The prescription for the γ5 matrix within dimensional regularization in multiloop calculations is elaborated. The three-loop anomalous dimension of the singlet axial current is calculated.

The renormalization of the axial anomaly in dimensional regularization

The discovery of the Higgs boson in 2012, by the ATLAS and CMS experiments, was a success achieved with only a percent of the entire dataset foreseen for the LHC. It opened a landscape of possibilities in the study of Higgs boson properties, Electroweak Symmetry breaking and the Standard Model in general, as well as new avenues in probing new physics beyond the Standard Model. Six years after the discovery, with a conspicuously larger dataset collected during LHC Run 2 at a 13 TeV centre-of-mass energy, the theory and experimental particle physics communities have started a meticulous exploration of the potential for precision measurements of its properties. This includes studies of Higgs boson production and decays processes, the search for rare decays and production modes, high energy observables, and searches for an extended electroweak symmetry breaking sector. This report summarises the potential reach and opportunities in Higgs physics during the High Luminosity phase of the LHC, with an expected dataset of pp collisions at 14 TeV, corresponding to an integrated luminosity of 3 ab$^{-1}$. These studies are performed in light of the most recent analyses from LHC collaborations and the latest theoretical developments. The potential of an LHC upgrade, colliding protons at a centre-of-mass energy of 27 TeV and producing a dataset corresponding to an integrated luminosity of 15 ab$^{-1}$, is also discussed.

Higgs Physics at the HL-LHC and HE-LHC

We suggest to isolate the loop-induced gluon-initiated component (
 $$gg\rightarrow ZH$$
 ) for associated $$ZH$$
 production by using the similarity of the Drell–Yan-like component for $$ZH$$
 production to the $$WH$$
 process. We argue that the cross-section ratio of the latter two processes can be predicted with high theoretical accuracy. Comparing it to the experimental $$ZH/WH$$
 cross-section ratio should allow to probe for new physics in the $$gg\rightarrow ZH$$
 component at the HL-LHC. We consider typical BSM scenarios in order to exemplify the effect they would have on the proposed observable.

/pdf/exploiting-the-wh-zh-symmetry-in-the-search-for-new-physics-hhmbe88y7j.pdf

Exploiting the WH/ZH symmetry in the search for new physics.

We present a calculation of the light neutral CP-even Higgs boson pole mass in the real MSSM which combines state-of-the-art EFT and fixed-order results, including the three-loop fixed-order QCD corrections as well as the resummation of logarithmic terms in the ratio of the weak to the SUSY scale up to fourth logarithmic order. This hybrid calculation should be valid for arbitrary SUSY scales above the weak scale. Comparison to the pure fixed-order and EFT results provides an estimate of their individual validity range.

/pdf/the-light-cp-even-mssm-higgs-mass-including-n-3-lo-n-3-ll-2bfslbxmwx.pdf

The light CP-even MSSM Higgs mass including N$^3$LO+N$^3$LL QCD corrections

Introducing version 2 of the code vh@nnlo, we study the effects of a number of new-physics scenarios on the Higgs-Strahlung process. In particular, the cross section is evaluated within a general 2HDM and the MSSM. While the Drell-Yan-like contributions are consistently taken into account by a simple rescaling of the SM result, the gluon-initiated contribution is supplemented by squark-loop mediated amplitudes, and by the $s$-channel exchange of additional scalars which may lead to conspicuous interference effects. The latter holds as well for bottom-quark initiated Higgs Strahlung, which is also included in the new version of vh@nnlo. Using an orthogonal rotation of the three Higgs CP eigenstates in the 2HDM and the MSSM, vh@nnlo incorporates a simple means of CP mixing in these models. Moreover, the effect of vector-like quarks in the SM on the gluon-initiated contribution can be studied. Beyond concrete models, vh@nnlo allows to include the effect of higher-dimensional operators on the production of CP-even Higgs bosons. Transverse momentum distributions of the final state Higgs boson and invariant mass distributions of the $V\phi$ final state for the gluon- and bottom-quark initiated contributions can be studied. Distributions for the Drell-Yan-like component of Higgs-Strahlung can be included through a link to MCFM. vh@nnlo can also be linked to FeynHiggs and 2HDMC for the calculation of Higgs masses and mixing angles. It can also read these parameters from an SLHA-file as produced by standard spectrum generators. Throughout the manuscript, we highlight new-physics effects in various numerical examples, both at the inclusive level and for distributions.

/pdf/vh-nnlo-v2-new-physics-in-higgs-strahlung-dne8pf8m5e.pdf

vh@nnlo-v2: New physics in Higgs Strahlung

We present a calculation of the light neutral CP-even Higgs boson pole mass in the real $$\text {MSSM}$$ which combines state-of-the-art EFT and fixed-order results, including the three-loop fixed-order QCD corrections as well as the resummation of logarithmic terms in the ratio of the weak to the SUSY scale up to fourth logarithmic order This hybrid calculation should be valid for arbitrary SUSY scales above the weak scale Comparison to the pure fixed-order and EFT results provides an estimate of their individual validity range

/pdf/the-light-cp-even-mssm-higgs-mass-including-n-mathbf-3-lo-n-7jkvedo3kc.pdf

The light CP-even MSSM Higgs mass including N$^\mathbf {3}$LO+N$^\mathbf {3}$LL QCD corrections

We present results for the two-loop helicity amplitudes entering the NLO QCD corrections to the production of a Higgs boson in association with a Z -boson in gluon fusion. The two-loop integrals, involving massive top quarks, are calculated numerically. Results for the interference of the finite part of the two-loop amplitudes with the Born amplitude are shown as a function of the two kinematic invariants on which the amplitudes depend.

/pdf/zh-production-in-gluon-fusion-two-loop-amplitudes-with-full-2oz8ujrsu8.pdf

Jonas Klappert

Papers

Exploiting the WH/ZH symmetry in the search for new physics.

The light CP-even MSSM Higgs mass including N$^3$LO+N$^3$LL QCD corrections

vh@nnlo-v2: New physics in Higgs Strahlung

The light CP-even MSSM Higgs mass including N\(^\mathbf {3}\)LO+N\(^\mathbf {3}\)LL QCD corrections

ZH production in gluon fusion: two-loop amplitudes with full top quark mass dependence