Boson Transverse Momentum Distribution Research Articles

Probing the Higgs boson trilinear self-coupling through Higgs boson+jet production

We present the calculation of the next-to-leading-order corrections for Higgs $\mathrm{boson}+\text{jet}$ production at the Large Hadron Collider, that arise from the Higgs trilinear self-coupling (${\ensuremath{\lambda}}_{HHH}$). We use the method of large top-quark mass expansion to tackle the challenging two-loop virtual amplitude and apply the Pad\'e approximation to extend the region of convergence of this expansion. We find that the ${\ensuremath{\lambda}}_{HHH}$-related corrections amount to 0.66% for the total cross section. For the invariant mass distribution and Higgs boson transverse momentum distribution, the corrections are mostly in the range 0.5%--0.7%. Our results can be used to set extra constraints on ${\ensuremath{\lambda}}_{HHH}$ from the experimental data.

PanScales showers for hadron collisions: all-order validation

We carry out extensive tests of the next-to-leading logarithmic (NLL) accuracy of the PanScales parton showers, as introduced recently for colour-singlet production in hadron collisions. The tests include comparisons to (semi-)analytic NLL calculations of a wide range of hadron-collider observables: the colour-singlet boson transverse momentum distribution; global and non-global hadronic energy flow variables related to jet vetoes and analogues of jettiness distributions; (sub)jet multiplicities; and observables sensitive to the DGLAP evolution of the incoming momentum fractions. In the tests, we also include an implementation of a standard transverse-momentum ordered dipole shower, to establish the size of missing NLL effects in such showers, which, depending on the observable, can reach 100%. This paper, together with [1], constitutes the first step towards process-independent NLL-accurate parton showers for hadronic collisions.

Towards ultimate parton distributions at the high-luminosity LHC

Since its start of data taking, the LHC has provided an impressive wealth of information on the quark and gluon structure of the proton. Indeed, modern global analyses of parton distribution functions (PDFs) include a wide range of LHC measurements of processes such as the production of jets, electroweak gauge bosons, and top quark pairs. In this work, we assess the ultimate constraining power of LHC data on the PDFs that can be expected from the complete dataset, in particular after the High-Luminosity (HL) phase, starting in around 2025. The huge statistics of the HL-LHC, delivering {mathcal {L}}=3hbox { ab}^{-1} to ATLAS and CMS and {mathcal {L}}=0.3hbox { ab}^{-1} to LHCb, will lead to an extension of the kinematic coverage of PDF-sensitive measurements as well as to an improvement in their statistical and systematic uncertainties. Here we generate HL-LHC pseudo-data for different projections of the experimental uncertainties, and then quantify the resulting constraints on the PDF4LHC15 set by means of the Hessian profiling method. We find that HL-LHC measurements can reduce PDF uncertainties by up to a factor of 2 to 4 in comparison to state-of-the-art fits, leading to few-percent uncertainties for important observables such as the Higgs boson transverse momentum distribution via gluon-fusion. Our results illustrate the significant improvement in the precision of PDF fits achievable from hadron collider data alone, and motivate the continuation of the ongoing successful program of PDF-sensitive measurements by the LHC collaborations.

Combined measurement of differential and total cross sections in the H → γγ and the H → ZZ⁎ → 4ℓ decay channels at [formula omitted] TeV with the ATLAS detector

A combined measurement of differential and inclusive total cross sections of Higgs boson production is performed using 36.1 fb−1 of 13 TeV proton–proton collision data produced by the LHC and recorded by the ATLAS detector in 2015 and 2016. Cross sections are obtained from measured H→γγ and H→ZZ⁎→4ℓ event yields, which are combined taking into account detector efficiencies, resolution, acceptances and branching fractions. The total Higgs boson production cross section is measured to be 57.0−5.9+6.0 (stat.) −3.3+4.0 (syst.) pb, in agreement with the Standard Model prediction. Differential cross-section measurements are presented for the Higgs boson transverse momentum distribution, Higgs boson rapidity, number of jets produced together with the Higgs boson, and the transverse momentum of the leading jet. The results from the two decay channels are found to be compatible, and their combination agrees with the Standard Model predictions.

Bottom-quark effects in Higgs production at intermediate transverse momentum

We provide a precise description of the Higgs boson transverse momentum distribution including top and bottom quark contributions, that is valid for transverse momenta in the range mb ≲ p⊥ ≲ mt, where mb and mt are the bottom and top quark masses. This description is based on a combination of fixed next-to-leading order (NLO) results with next-to-next-to-leading logarithmic (NNLL) transverse momentum resummation. We show that ambiguities in the resummation procedure for the b-quark loops are of the same order as the related fixed-order uncertainties. We conclude that the current uncertainty in the top-bottom interference contribution to the Higgs transverse momentum spectrum is mathcal{O}left(20%right) .

Next-to-Leading-Order QCD Corrections to Higgs Boson Plus Jet Production with Full Top-Quark Mass Dependence.

We present the next-to-leading-order QCD corrections to the production of a Higgs boson in association with one jet at the LHC including the full top-quark mass dependence. The mass of the bottom quark is neglected. The two-loop integrals appearing in the virtual contribution are calculated numerically using the method of sector decomposition. We study the Higgs boson transverse momentum distribution, focusing on the high p_{t,H} region, where the top-quark loop is resolved. We find that the next-to-leading-order QCD corrections are large but that the ratio of the next-to-leading-order to leading-order result is similar to that obtained by computing in the limit of large top-quark mass.

Two-loop amplitudes for qg→Hq and qq¯→Hg mediated by a nearly massless quark

We compute the two-loop QCD corrections to $q g \to H q$ and $q \bar{q} \to H g$ amplitudes mediated by loops of nearly massless quarks. These amplitudes provide the last missing ingredient required to compute the NLO QCD corrections to the top-bottom interference contribution to the Higgs boson transverse momentum distribution at hadron colliders.

Two-loop gg → Hg amplitude mediated by a nearly massless quark

We analytically compute the two-loop scattering amplitude $gg \to Hg$ assuming that the mass of the quark, that mediates the ggH interaction, is vanishingly small. Our computation provides an important ingredient required to improve the theoretical description of the top-bottom interference effect in Higgs boson production in gluon fusion, and to elucidate its impact on the Higgs boson transverse momentum distribution.

The NNLO QCD corrections to Z boson production at large transverse momentum

The transverse momentum distribution of massive neutral vector bosons can be measured to high accuracy at hadron colliders. The transverse momentum is caused by a partonic recoil, and is determined by QCD dynamics. We compute the single and double-differential transverse momentum distributions for fully inclusive $Z/\gamma^*$ production including leptonic decay to next-to-next-to-leading order (NNLO) in perturbative QCD. We also compute the same distributions normalised to the cross sections for inclusive $Z/\gamma^*$ production, i.e. integrated over the transverse momentum of the lepton pair. We compare our predictions for the fiducial cross sections to the 8 TeV data set from the ATLAS and CMS collaborations, which both observed a tension between data and NLO theory predictions, using the experimental cuts and binning. We find that the inclusion of the NNLO QCD effects does not fully resolve the tension with the data for the unnormalised $p^Z_T$ distribution. However, we observe that normalising the NNLO $Z$-boson transverse momentum distribution by the NNLO Drell-Yan cross section substantially improves the agreement between experimental data and theory, and opens the way for precision QCD studies of this observable.

QCD evolution of (un)polarized gluon TMDPDFs and the Higgs qT -distribution

We provide the proper definition of all the leading-twist (un)polarized gluon transverse momentum dependent parton distribution functions (TMDPDFs), by considering the Higgs boson transverse momentum distribution in hadron-hadron collisions and deriving the factorization theorem in terms of them. We show that the evolution of all the (un)polarized gluon TMDPDFs is driven by a universal evolution kernel, which can be resummed up to next-to-next-to-leading-logarithmic accuracy. Considering the proper definition of gluon TMDPDFs, we perform an explicit next-to-leading-order calculation of the unpolarized ($f_1^g$), linearly polarized ($h_1^{\perp g}$) and helicity ($g_{1L}^g$) gluon TMDPDFs, and show that, as expected, they are free from rapidity divergences. As a byproduct, we obtain the Wilson coefficients of the refactorization of these TMDPDFs at large transverse momentum. In particular, the coefficient of $g_{1L}^g$, which has never been calculated before, constitutes a new and necessary ingredient for a reliable phenomenological extraction of this quantity, for instance at RHIC or the future AFTER@LHC or Electron-Ion Collider. The coefficients of $f_1^g$ and $h_1^{\perp g}$ have never been calculated in the present formalism, although they could be obtained by carefully collecting and recasting previous results in the new TMD formalism. We apply these results to analyze the contribution of linearly polarized gluons at different scales, relevant, for instance, for the inclusive production of the Higgs boson and the $C$-even pseudoscalar bottomonium state $\eta_{b}$. Applying our resummation scheme we finally provide predictions for the Higgs boson $q_T$-distribution at the LHC.

Parton distributions for the LHC run II

We present NNPDF3.0, the first set of parton distribution functions (PDFs) determined with a methodology validated by a closure test. NNPDF3.0 uses a global dataset including HERA-II deep-inelastic inclusive cross-sections, the combined HERA charm data, jet production from ATLAS and CMS, vector boson rapidity and transverse momentum distributions from ATLAS, CMS and LHCb, W +c data from CMS and top quark pair production total cross sections from ATLAS and CMS. Results are based on LO, NLO and NNLO QCD theory and also include electroweak corrections. To validate our methodology, we show that PDFs determined from pseudo-data generated from a known underlying law correctly reproduce the statistical distributions expected on the basis of the assumed experimental uncertainties. This closure test ensures that our methodological uncertainties are negligible in comparison to the generic theoretical and experimental uncertainties of PDF determination. This enables us to determine with confidence PDFs at different perturbative orders and using a variety of experimental datasets ranging from HERA-only up to a global set including the latest LHC results, all using precisely the same validated methodology. We explore some of the phenomenological implications of our results for the upcoming 13 TeV Run of the LHC, in particular for Higgs production cross-sections.

Measurement of the Z/γ * boson transverse momentum distribution in pp collisions at s = 7 $$ \sqrt{s}=7 $$ TeV with the ATLAS detector

This paper describes a measurement of the $Z/\gamma^*$ boson transverse momentum spectrum using ATLAS proton-proton collision data at a centre-of-mass energy of $\sqrt{s}$ = 7 TeV at the LHC. The measurement is performed in the $Z/\gamma^* \rightarrow e^+e^-$ and $Z/\gamma^* \rightarrow \mu^+\mu^-$ channels, using data corresponding to an integrated luminosity of 4.7 fb$^{-1}$. Normalized differential cross sections as a function of the $Z/\gamma^*$ boson transverse momentum are measured for transverse momenta up to 800 GeV. The measurement is performed inclusively for $Z/\gamma^*$ rapidities up to 2.4, as well as in three rapidity bins. The channel results are combined, compared to perturbative and resummed QCD calculations and used to constrain the parton shower parameters of Monte Carlo generators.

NNLO soft-gluon corrections for theZboson andWboson transverse momentum distributions

We present results for the $Z$ boson and $W$ boson transverse momentum (${p}_{T}$) distributions for large ${p}_{T}$ at LHC and Tevatron energies. We calculate complete next-to-leading-order QCD corrections as well as soft-gluon corrections at next-to-next-to-leading order (NNLO) to the differential cross section. The NNLO soft-gluon contributions are derived from next-to-next-to-leading-logarithm resummation at two loops. We find enhancements of the ${p}_{T}$ distributions and reductions of the scale dependence when the NNLO corrections are included.

NLO corrections to WWZ production at the LHC

The production of W + W − Z at the LHC is an important process to test the quartic gauge couplings of the Standard Model as well as an important background for new physics searches. A good theoretical understanding at next-to-leading order (NLO) is therefore valuable. In this paper, we present the calculation of the NLO electroweak (EW) correction to this channel with on-shell gauge bosons in the final state. It is then combined with the NLO QCD correction to get the most up-to-date prediction. We study the impact of these corrections on the total cross section and some distributions. The NLO EW correction is small for the total cross section but becomes important in the high energy regime for the gauge boson transverse momentum distributions.

Higher-order QCD corrections for theW-boson transverse momentum distribution

We present results for $W$-boson production at large transverse momentum at LHC and Tevatron energies. We calculate complete next-to-leading-order QCD corrections and higher-order soft-gluon corrections to the differential cross section. The soft-gluon contributions are resummed at next-to-next-to-leading-logarithm accuracy via the two-loop soft anomalous dimensions. Both next-to-leading-order and approximate next-to-next-to-leading-order ${p}_{T}$ distributions are presented. Our numerical results are in good agreement with recent data from the LHC.

Non-Standard ZZ Production with Leptonic Decays at the Large Hadron Collider

The prospects of anomalous ZZγ and ZZZ triple gauge boson couplings are investigated at the Large Hadron Collider (LHC) through an excess of events in ZZ diboson production. Two such channels are selected and the tree level results including leptonic final states are discussed: ZZ → ℓ1−ℓ1+ℓ2−ℓ2+ and ZZ → ℓ−ℓ+νν̄(ℓ, ℓ1,2 = e, μ). The results in the full finite width method are compared with the narrow width approximation (NWA) method in detail. Besides the Z boson transverse momentum distributions, the azimuthal angle between the Z boson decay to fermions, ΔΦ, and their separations in the pseudo-rapidity-azimuthal angle plane, ΔR, as well as the sensitivity on anomalous couplings are displayed at the 14 TeV LHC.

Two-loop QCD corrections to the helicity amplitudes for H → 3 partons

Many search strategies for the Standard Model Higgs boson apply specific selection criteria on hadronic jets observed in association with the Higgs boson decay products, either in the form of a jet veto, or by defining event samples according to jet multiplicity. To improve the theoretical description of Higgs-boson-plus-jet production (and the closely related Higgs boson transverse momentum distribution), we derive the two-loop QCD corrections to the helicity amplitudes for the processes $H \to ggg$ and $H\to q \bar q g$ in an effective theory with infinite top quark mass. The helicity amplitudes are extracted from the coefficients appearing in the general tensorial structure for each process. The coefficients are derived from the Feynman graph amplitudes by means of projectors within the conventional dimensional regularization scheme. The infrared pole structure of our result agrees with the expectation from infrared factorization and the finite parts of the amplitudes are expressed in terms of one- and two-dimensional harmonic polylogarithms.

Measurement of the transverse momentum distribution ofWbosons inppcollisions ats=7 TeVwith the ATLAS detector

This paper describes a measurement of the W boson transverse momentum distribution using ATLAS pp collision data from the 2010 run of the LHC at sqrt(s) = 7 TeV, corresponding to an integrated luminosity of about 31 pb^-1. Events from both W -> e nu and W -> mu nu are used, and the transverse momentum of the W candidates is measured through the energy deposition in the calorimeter from the recoil of the W. The resulting distributions are unfolded to obtain the normalized differential cross sections as a function of the W boson transverse momentum. We present results for pTW < 300 GeV in the electron and muon channels as well as for their combination, and compare the combined results to the predictions of perturbative QCD and a selection of event generators.

Z boson transverse momentum spectrum from the lepton angular distributions

In view of recent discussions concerning the possibly limiting energy resolution systematics on the measurement of the Z boson transverse momentum distribution at hadron colliders, we propose a novel measurement method based on the angular distributions of the decay leptons. We also introduce a phenomenological parametrization of the transverse momentum distribution that adapts well to all currently available predictions, a useful tool to quantify their differences.

Factorization and resummation of Higgs boson differential distributions in soft-collinear effective theory

We derive a factorization theorem for the Higgs boson transverse momentum (${p}_{T}$) and rapidity ($Y$) distributions at hadron colliders, using the soft-collinear effective theory (SCET), for ${m}_{h}\ensuremath{\gg}{p}_{T}\ensuremath{\gg}{\ensuremath{\Lambda}}_{\mathrm{QCD}}$, where ${m}_{h}$ denotes the Higgs mass. In addition to the factorization of the various scales involved, the perturbative physics at the ${p}_{T}$ scale is further factorized into two collinear impact-parameter beam functions (IBFs) and an inverse soft function (ISF). These newly defined functions are of a universal nature for the study of differential distributions at hadron colliders. The additional factorization of the ${p}_{T}$-scale physics simplifies the implementation of higher order radiative corrections in ${\ensuremath{\alpha}}_{s}({p}_{T})$. We derive formulas for factorization in both momentum and impact parameter space and discuss the relationship between them. Large logarithms of the relevant scales in the problem are summed using the renormalization group equations of the effective theories. Power corrections to the factorization theorem in ${p}_{T}/{m}_{h}$ and ${\ensuremath{\Lambda}}_{\mathrm{QCD}}/{p}_{T}$ can be systematically derived. We perform multiple consistency checks on our factorization theorem including a comparison with known fixed-order QCD results. We compare the SCET factorization theorem with the Collins-Soper-Sterman approach to low-${p}_{T}$ resummation.