Precision Predictions for Higgs Differential Distributions at the LHC

Ebert, Markus; Tackmann, Frank

Book/Dissertation / PhD Thesis

PUBDB-2017-08764

Precision Predictions for Higgs Differential Distributions at the LHC

Ebert, M. (Corresponding author)DESY* ; Tackmann, F. (Thesis advisor)DESY*

2017
Verlag Deutsches Elektronen-Synchrotron Hamburg

Hamburg : Verlag Deutsches Elektronen-Synchrotron, DESY-THESIS 217 pp. (2017) [10.3204/PUBDB-2017-08764] = Dissertation, Universität Hamburg, 2017

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Report No.: DESY-THESIS-2017-033

Abstract: After the discovery of a Standard-Model-like Higgs boson at the LHCa central aspect of the LHC physics program is to studythe Higgs boson's couplings to Standard Model particles in detailin order to elucidate the nature of the Higgs mechanismand to search for hints of physics beyond the Standard Model.This requires precise theory predictions for both inclusiveand differential Higgs cross sections.In this thesis we focus on the application of resummation techniquesin the framework of Soft-Collinear Effective Theory (SCET)to obtain accurate predictions with reliable theory uncertaintiesfor various observables.We first consider transverse momentum distributions,where the resummation of large logarithms in momentum (or distribution) spacehas been a long-standing open question.We show that its two-dimensional nature leads to additional difficultiesnot observed in one-dimensional observables such as thrust,and solving the associated renormalization group equations (RGEs)in momentum space thus requires a very careful scale setting.This is achieved using distributional scale setting,a new technique to solve differential equations such as RGEs directly in distribution space,as it allows one to treat logarithmic plus distributions like ordinary logarithms.We show that the momentum space solution fundamentally differs from the standard resummationin Fourier space by different boundary terms to all orders in perturbation theoryand hence provides an interesting and complementary approach to obtain new insightinto the all-order perturbative and nonperturbative structure oftransverse momentum distributions.Our work lays the ground for a detailed numerical study of themomentum space resummation.We then show that in the case of a discovery of a new heavy color-singlet resonancesuch as a heavy Higgs boson, one can reliably and model-independently inferits production mechanism by dividing the data into two mutually exclusive jet bins.The method is based on a resummation framework that preciselypredicts the jet cut dependence and systematically incorporates theory uncertaintiesand their correlations among the jet bins. The technique is demonstratedfor an example scalar resonance of mass $m_X = 750~\mathrm{GeV}$.It can also be applied to and tested in diphoton productionwhich receives contributions from both quark annihilation and gluon fusion.Here, the presence of final state photons requires photon isolation cutswhich yield unresummed nonglobal logarithms.As a first step towards the full analysis, we show that these are numerically smalland can be incorporated in fixed-order perturbation theory.Vice versa, we find that the jet veto renders contributions from fragmentation photons power suppressed,and thus is a particularly clean channel to study direct diphoton production at the LHC.Lastly, we discuss the resummation of timelike logarithms $\ln^2(-1)=-\pi^2$in Higgs production, arising in the form factor at timelike momentum transfer.Their resummation is well understood in exclusive cross sections known to factorize.We show how to consistently incorporate the resummation into inclusive cross sections,discussing in detail the validity of the technique and associated uncertainties.The method is first applied to the total cross section in gluon fusion Higgs productionat N$^3$LO$+$N$^3$LL$^\prime$, where it significantly improves perturbative convergenceand reduces perturbative uncertainties by about a factor of two.We also obtain the currently most precise Higgs rapidity spectrum at NNLO$+$NNLL$^\prime$with a similar reduction of uncertainties.The effect is less pronounced in bottom-quark annihilation,but still shows that the resummation of timelike logarithmsis a beneficial and viable tool for Higgs production.

Note: Dissertation, Universität Hamburg, 2017

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