Higgs production in bottom quark annihilation: Transverse momentum distribution at NNLO+NNLL

We present the inclusive transverse momentum distribution for Higgs bosons produced in bottom quark annihilation at the LHC. The results are obtained in the five-flavor scheme. The soft and collinear terms at small $p_T$ are resummed through NNLL accuracy and matched to the NNLO transverse momentum distribution at large $p_T$. We find that the theoretical uncertainty, derived from a variation of the unphysical scales entering the calculation, is significantly reduced with respect to lower orders.Comment: 35 pages, 22 figure

Soft gluon resummation for gluon-induced Higgs Strahlung

We study the effect of soft gluon emission on the total cross section predictions for the $gg\to HZ$ associated Higgs production process at the LHC. To this end, we perform resummation of threshold corrections at the NLL accuracy in the absolute threshold production limit and in the threshold limit for production of a $ZH$ system with a given invariant mass. Analytical results and numerical predictions for various possible LHC collision energies are presented. The perturbative stability of the results is verified by including universal NNLL effects. We find that resummation significantly reduces the scale uncertainty of the $gg\to HZ$ contribution, which is the dominant source of perturbative uncertainty to $ZH$ production. We use our results to evaluate updated numbers for the total inclusive cross section of associated $pp \to ZH$ production at the LHC. The reduced scale uncertainty of the $gg\to HZ$ component translates into a decrease of the overall scale error by about a factor of two.Comment: 22 pages, 4 figures, 2 table

Soft gluon resummation of Drell-Yan rapidity distributions: theory and phenomenology

We examine critically the theoretical underpinnings and phenomenological implications of soft gluon (threshold) resummation of rapidity distributions at a hadron collider, taking Drell-Yan production at the Tevatron and the LHC as a reference test case. First, we show that in perturbative QCD soft gluon resummation is necessary whenever the partonic (rather the hadronic) center-of-mass energy is close enough to threshold, and we provide tools to assess when resummation is relevant for a given process. Then, we compare different prescriptions for handling the divergent nature of the series of resummed perturbative corrections, specifically the minimal and Borel prescriptions. We assess the intrinsic ambiguities of resummed results, both due to the asymptotic nature of their perturbative expansion, and to the treatment of subleading terms. Turning to phenomenology, we introduce a fast and accurate method for the implementation of resummation with the minimal and Borel prescriptions using an expansion on a basis of Chebyshev polynomials. We then present results for W and Z production as well as both high- and low-mass dilepton pairs at the LHC, and show that soft gluon resummation effects are generally comparable in size to NNLO corrections, but sometimes affected by substantial ambiguities.Comment: 75 pages, 34 figures, pdflate

Associated ttˉHt \bar{t} H production at the LHC: theoretical predictions at NLO+NNLL accuracy

We perform threshold resummation of soft gluon corrections to the total cross section and the invariant mass distribution for the process $pp \to t\bar{t}H$. The resummation is carried out at next-to-next-to-leading-logarithmic (NNLL) accuracy using the direct QCD Mellin space technique in the three-particle invariant mass kinematics. After presenting analytical expressions we discuss the impact of resummation on the numerical predictions for the associated Higgs boson production with top quarks at the LHC. We find that NLO+NNLL resummation leads to predictions for which the central values are remarkably stable with respect to scale variation and for which theoretical uncertainties are reduced in comparison to NLO predictions.Comment: 21 pages, 9 figures; NNLL results accounting now for color decomposition of the one-loop hard function, discussion of the literature added, typos correcte

Soft-gluon resummation for pseudoscalar Higgs boson production at hadron colliders

We compute the threshold-resummed cross section for pseudo-scalar MSSM Higgs boson production by gluon fusion at hadron colliders. The calculation is performed at next-to-next-to leading logarithmic accuracy. We present results for both the LHC and Tevatron Run II. We analyze the factorization and renormalization scale dependence of the results, finding that after performing the resummation the corresponding cross section can be computed with an accuracy better than 10%.Comment: 10 pages, 7 figures, accepted by Physics Letters

Four-Loop Cusp Anomalous Dimension From Obstructions

We introduce a method for extracting the cusp anomalous dimension at L loops from four-gluon amplitudes in N=4 Yang-Mills without evaluating any integrals that depend on the kinematical invariants. We show that the anomalous dimension only receives contributions from the obstructions introduced in hep-th/0601031. We illustrate this method by extracting the two- and three-loop anomalous dimensions analytically and the four-loop one numerically. The four-loop result was recently guessed to be f^4 = - (4\zeta^3_2+24\zeta_2\zeta_4+50\zeta_6- 4(1+r)\zeta_3^2) with r=-2 using integrability and string theory arguments in hep-th/0610251. Simultaneously, f^4 was computed numerically in hep-th/0610248 from the four-loop amplitude obtaining, with best precision at the symmetric point s=t, r=-2.028(36). Our computation is manifestly s/t independent and improves the precision to r=-2.00002(3), providing strong evidence in favor of the conjecture. The improvement is possible due to a large reduction in the number of contributing terms, as well as a reduction in the number of integration variables in each term.Comment: 23 pages, revtex; v2,v3: minor typos fixed and references adde

Small-xx phenomenology at the LHC and beyond: HELL 3.0 and the case of the Higgs cross section

Small-$x$ resummation has been proven recently to be a crucial ingredient for describing small-$x$ HERA data, and the inclusion of small-$x$ resummation in parton distribution function (PDF) determination has a sizeable effect on the PDFs even at the electroweak scale. In this work we explore the implications of small-$x$ resummation at the Large Hadron Collider (LHC) and at a Future Circular Collider (FCC). We construct the theoretical machinery for resumming physical inclusive observables at hadron colliders, and describe its implementation in the public code HELL 3.0. We focus on Higgs production in gluon fusion as a prototypical example, both because it is sensitive to small-$x$ gluons and because of its importance for the LHC physics programme. We find that adding small-$x$ resummation to the N$^3$LO Higgs production cross section can lead to an increase of up to 10% at FCC, while the effect is smaller (+1%) at LHC but still important to achieve a high level of precision.Comment: 42 pages, 8 figures. Added new Fig 6 and some discussions. Final version published in EPJ

Soft-gluon resummation for squark and gluino hadroproduction

We consider the resummation of soft gluon emission for squark and gluino hadroproduction at next-to-leading-logarithmic (NLL) accuracy in the framework of the minimal supersymmetric standard model. We present analytical results for squark-squark and squark-gluino production and provide numerical predictions for all squark and gluino pair-production processes at the Tevatron and at the LHC. The size of the soft-gluon corrections and the reduction in the scale uncertainty are most significant for processes involving gluino production. At the LHC, where the sensitivity to squark and gluino masses ranges up to 3 TeV, the corrections due to NLL resummation over and above the NLO predictions can be as high as 35% in the case of gluino-pair production, whereas at the Tevatron, the NLL corrections are close to 40% for squark-gluino final states with sparticle masses around 500 GeV.Comment: 31 pages, 7 figure