Transverse-momentum resummation of colorless final states at the NNLL+NNLO
Marius Wiesemann
备注：
12 pages, 5 figures, to appear in the proceedings of the 12th International Symposium on Radiative Corrections (Radcor 2015) and LoopFest XIV (Radiative Corrections for the LHC and Future Colliders)
We present a general framework that allows to compute the resummed transverse-momentum distribution of a system of colorless particles. The implementation is fully differential in the degrees of freedom of the final-state system. As a first application, we consider the transverse-momentum spectrum of ZZ and WW boson pairs produced in hadron collisions, where we resum the logarithmically enhanced contributions due to multiple soft-gluon emission at small transverse momenta to all orders in perturbation theory. We exploit the most advanced perturbative information for the ZZ and WW production processes that is available at present by combining next-to-next-to-leading order QCD corrections with next-to-next-to-leading logarithmic resummation.
I present recent NNLO-NNLL results for top quark hadroproduction at the Tevatron. The total cross section as well as transverse momentum and rapidity distributions are shown.
The resummed transverse-momentum distribution for Higgs bosons produced via bottom-quark annihilation at the LHC is presented. Our results are obtained in the five-flavor scheme to NNLO+NNLL accuracy. We present a theoretical prediction which consistently matches the cross section at small and large transverse momenta. Theoretical uncertainties are derived from a variation of the unphysical scales entering the calculation. Their size is significantly reduced with respect to lower orders.
We present a comparison of the computation of energy-energy correlation in $e^{+}e^{-}$ collisions in the back-to-back region at next-to-next-to-leading logarithmic accuracy matched with the next-to-next-to-leading order perturbative prediction to LEP, PEP, PETRA, SLC and TRISTAN data. With these predictions we perform an extraction of the strong coupling constant taking into account non-perturbative effects modelled with Monte Carlo event generators. The final result at NNLO+NNLL precision is $α_{S}(M_{Z})=0.11750\pm 0.00018 {\text( exp.)}\pm 0.00102{\text(hadr.)}\pm0.00257{\text(ren.)}\pm 0.…
The rapidity-dependent jet veto observables $\mathcal{T}_{Bj}$ and $\mathcal{T}_{Cj}$ provide a tight jet veto at central rapidity, gradually transitioning to a loose veto at forward rapidities. They divide the phase space into exclusive jet bins in a different way to the traditional jet veto observable $p_{Tj}$, and are advantageous to use under harsh pile-up conditions. We obtain predictions for the $0$-jet gluon-fusion (ggF) Higgs cross section using both of these veto observables at NNLL$'+$NNLO, and compare these predictions to the prior state-of-the-art of NLL$'+$NLO. A significant reduc…
We present the resummed predictions for inclusive cross section for the production of Higgs boson at next-to-next-to leading logarithmic ($\rm \overline {NNLL}$) accuracy taking into account both soft-virtual ($\rm SV$) and next-to SV ($\rm NSV$) threshold logarithms. We derive the $N$-dependent coefficients and the $N$-independent constants in Mellin-$N$ space for our study. Using the minimal prescription we perform the inverse Mellin transformation and match it with the corresponding fixed order results. We report in detail the numerical impact of $N$-independent part of resummed result and …
In this article we have studied the transverse momentum distribution of the pseudo-scalar Higgs boson at the Large Hadron Collider (LHC). The small $\pt$ region which provides the bulk of the cross section is not accessible to fixed order perturbation theory due to the presence of large logarithms in the series. Using the universal infrared behaviour of the QCD we resum these large logarithms up to next-to-next-to-leading logarithmic (NNLL) accuracy. We observe a significant reduction in theoretical uncertainties due to the unphysical scales at NNLL level compared to the previous order. We pre…
We present the computation of energy-energy correlation in $e^+e^-$ collisions in the back-to-back region at next-to-next-to-leading logarithmic accuracy matched with the next-to-next-to-leading order perturbative prediction. We study the effect of the fixed higher order corrections in a comparison of our results to LEP and SLC data. The next-to-next-to-leading order correction has a sizable impact on the extracted value of $α_{\mathrm S}(M_Z)$, hence its inclusion is mandatory for a precise measurement of the strong coupling using energy-energy correlation.
We present first results on the resummation of Next-to-Soft Virtual (NSV) logarithms for the threshold production of pseudoscalar Higgs boson through gluon fusion at the LHC. These results are presented after resumming the NSV logarithms of the kind ${\log}^{i}(1-z)$ to $\overline{\text{NNLL}}$ accuracy and matching them systematically to the fixed order NNLO cross-sections. These results are obtained using collinear factorization, renormalization group invariance and recent developments in the NSV resummation techniques. The phenomenological implications of these NSV resummed results for 13 T…
This paper presents a phenomenological study for the differential cross section of the forward Z boson production in leptonic decay channels as a function of the angular variable $ϕ^{*}_η$ in proton-proton collisions. The $ϕ^{*}_η$ distribution is predicted for the forward pseudorapidity region $2.0 < η_{l} < 4.5$ of the decay leptons at center-of-mass energies 8, 13, and 14 TeV. Accurate prediction of the $ϕ^{*}_η$ distribution is achieved by means of the state-of-the-art calculations including fixed-order perturbative QCD and large logarithmic corrections. The predicted distributions are obt…
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.
I discuss threshold resummation at NNLL accuracy in the standard moment-space approach in perturbative QCD for top-pair and single-top production. For top quark pair production I present new approximate NNLO results for the total cross section and for the top quark transverse momentum and rapidity distributions at 8 TeV LHC energy. I discuss the accuracy of the soft-gluon approximation and show that the NLO and NNLO approximate results from resummation are practically indistinguishable from exact NLO and partial NNLO results. For single top production I present new approximate NNLO results for…
We present results for the Higgsstrahlung process within the GENEVA Monte Carlo framework. We combine the fully differential NNLO calculation with the higher-order resummation in the 0-jettiness resolution variable (beam-thrust). The resulting parton-level events are further showered and hadronised by Pythia8. The beam-thrust resummation is carried out to NNLL$'$ accuracy, which consistently incorporates all singular virtual and real NNLO corrections. It thus provides a natural perturbative connection between the NNLO calculation and the parton shower regime, including a systematic assessment …
The QCD coupling $α_s$ is extracted from the energy evolution of the first two moments (multiplicity and mean) of the parton-to-hadron fragmentation functions at low fractional hadron momentum $z$. Comparisons of the experimental $e^+e^-$ and deep-inelastic $e^\pm$p jet data to our NNLO$^*$+NNLL predictions, allow us to obtain $α_s(m_{_{\rm Z}})$ = 0.1205$\pm$0.0010$^{+0.0022}_{-0.0000}$, in excellent agreement with the current world average determined using other methods at the same level of accuracy.
We describe predictions for top-quark pair differential distributions at hadron colliders, which combine state-of-the-art NNLO QCD calculations and NLO electroweak corrections together with double resummation at NNLL$'$ accuracy of threshold logarithms and small-mass logarithms. This is the first time that such a combination has appeared in the literature. Numerical results are presented for the invariant-mass distribution, the transverse-momentum distribution as well as rapidity distributions.
We present a formalism to resum large threshold logarithms to all orders in perturbative QCD for the rapidity distribution of any colorless particle at the hadron colliders. Using the derived resummed coefficients in two dimensional Mellin space, we present the rapidity distributions for the Higgs as well as for the Drell-Yan production to NNLO+NNLL accuracy at the LHC. The resummed distributions give stable prediction against the variation of unphysical renormalisation and factorisation scales in both the cases. Perturbative convergence is also improved with the inclusion of the resummed resu…
If supersymmetry near the TeV scale is realized in Nature, the pair production of scalar top squarks is expected to be observable at the Large Hadron Collider. Recently, effective field-theory methods were employed to obtain approximate predictions for the cross section for this process, which include soft-gluon emission effects up to next-to-next-to-leading order (NNLO) in perturbation theory. In this work we employ the same techniques to resum soft-gluon emission effects to all orders in perturbation theory and with next-to-next-to-logarithmic (NNLL) accuracy. We analyze the effects of NNLL …
We consider the production of pairs of lepton through the Drell-Yan process at the LHC and present the most accurate prediction on their rapidity distribution. While the fixed order prediction is already known to next-to-next-to-leading order in perturbative QCD, the resummed contribution coming from threshold region of phase space up to next-to-next-to-leading logarithmic (NNLL) accuracy has been computed in this article. The formalism developed in [1-3] has been used to resum large threshold logarithms in the two dimensional Mellin space to all orders in perturbation theory. We have done a d…
We construct predictions for top quark pair differential distributions at hadron colliders that combine state-of-the-art NNLO QCD calculations with double resummation at NNLL' accuracy of threshold logarithms arising from soft gluon emissions and of small mass logarithms. This is the first time a resummed calculation at full NNLO+NNLL' accuracy in QCD for a process with non-trivial color structure has been completed at the differential level. Of main interest to us is the stability of the M_{tt} and top-quark p_T distributions in the boosted regime where fixed order calculations may become str…
We present results for Drell-Yan production from the GENEVA Monte-Carlo framework. We combine the fully-differential NNLO calculation with higher-order resummation in the 0-jettiness resolution variable. The resulting parton-level events are further combined with parton showering and hadronization provided by PYTHIA8. The 0-jettiness resummation is carried out to NNLL', which consistently incorporates all singular virtual and real NNLO corrections. It thus provides a natural perturbative connection between the NNLO calculation and the parton shower regime, including a systematic assessment of …
The next-to-leading order (NLO) QCD radiative corrections to W+W- production at hadron colliders are well understood. We combine NLO perturbative QCD calculations with soft-gluon resummation of threshold logarithms to find a next-to-next-to leading logarithmic (NNLL) prediction for the total cross section and the invariant mass distribution at the LHC. We also obtain approximate next-to-next-to-leading order (NNLO) results for the total W+W- cross section at the LHC which includes all contributions from the scale dependent leading singular terms. Our result for the approximate NNLO total cross…
The complete next-to-next-to leading order (NNLO) QCD correction has been studied to the di-lepton invariant mass distribution within the Randall-Sundrum (RS) framework. In addition, the soft-virtual (SV) cross-section at next-to-next-to-next-to leading order (N$^3$LO) as well as threshold resummation to next-to-next-to leading logarithms (NNLL) level have been presented. The analytical coefficient for SV production has been obtained up to three loops very recently along with the process-dependent coefficients needed to perform resummation up to NNLL. These coefficients are universal for any u…
We present new results for W-boson production at large transverse momentum at the LHC and the Tevatron. The contribution of soft-gluon corrections is derived from NNLL resummation and added to the exact NLO result. Numerical results and their uncertainties for the approximate NNLO W-boson transverse momentum distributions are derived and compared to recent data from the LHC.
We propose a new approach to the resummation of the transverse-momentum distribution of a high-mass colour-singlet system in hadronic collisions. The resummation is performed in momentum space and is free of kinematic singularities at small transverse momentum. We derive a formula accurate at the next-to-next-to-leading-logarithmic level, and present the first matched predictions to next-to-next-to-leading order for Higgs-boson production in gluon fusion at the LHC. This method can be adapted to all observables featuring kinematic cancellations in the infrared region.
We present a formalism that resums threshold-enhanced logarithms to all orders in perturbative QCD for the rapidity distribution of any colorless particle produced in hadron colliders. We achieve this by exploiting the factorization properties and K+G equations satisfied by the soft and virtual parts of the cross section. We compute for the first time compact and most general expressions in two-dimensional Mellin space for the resummed coefficients. Using various state-of-the-art multiloop and multileg results, we demonstrate the numerical impact of our resummed results up to next-to-next-to-l…
We consider the transverse-momentum ($p_T$) distribution of $ZZ$ and $W^+W^-$ boson pairs produced in hadron collisions. At small $p_T$, the logarithmically enhanced contributions due to multiple soft-gluon emission are resummed to all orders in QCD perturbation theory. At intermediate and large values of $p_T$, we consistently combine resummation with the known fixed-order results. We exploit the most advanced perturbative information that is available at present: next-to-next-to-leading logarithmic resummation combined with the next-to-next-to-leading fixed-order calculation. After integrati…
We present predictions for Higgs production via gluon fusion with a p_T veto on jets and with the resummation of jet-veto logarithms at NNLL'+$NNLO order. These results incorporate explicit O(alphas^2) calculations of soft and beam functions, which include the dominant dependence on the jet radius R. In particular the NNLL' order accounts for the correct boundary conditions for the N3LL resummation, for which the only unknown ingredients are higher-order anomalous dimensions. We use scale variations in a factorization theorem in both rapidity and virtuality space to estimate the perturbative u…
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 (NLO) 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 (NNLL) resummation at two loops. We find enhancements of the $p_T$ distributions and reductions of the scale dependence when the NNLO corrections are included.
I present approximate next-to-next-to-leading-order (aNNLO) transverse-momentum ($p_T$) distributions in single-top production processes. The aNNLO results are derived from next-to-next-to-leading-logarithm (NNLL) resummation of soft-gluon corrections in the differential cross section. Single-top as well as single-antitop $p_T$ distributions are shown in $t$-channel, $s$-channel, and $tW$ production for LHC energies.
A major ingredient in Higgs searches at the Tevatron and LHC is the elimination of backgrounds with jets. In current H -> WW -> lnulnu searches, jet algorithms are used to veto central jets to obtain a 0-jet sample, which is then analyzed to discover the Higgs signal. Imposing this tight jet veto induces large double logarithms which significantly modify the Higgs production cross section. These jet-veto logarithms are presently only accounted for at fixed order or with the leading-logarithmic summation from parton-shower Monte Carlos. Here we consider Higgs production with an inclusive event-…
I present approximate next-to-next-to-leading-order (aNNLO) total and differential cross sections for charged Higgs production in association with a top quark at LHC energies. The aNNLO results for the process $bg \rightarrow tH^-$ are derived from next-to-next-to-leading-logarithm (NNLL) resummation of soft-gluon corrections. Scale and parton-distribution uncertainties for the cross sections are shown. The top-quark transverse-momentum and rapidity distributions are also calculated.
Les Houches study on inclusive jet production at NNLO+NNLL
Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室）；Michigan State University（密歇根州立大学）；Argonne National Laboratory（阿贡国家实验室）；Yale University（耶鲁大学）；Institute of Nuclear Physics（核物理研究所）；Massachusetts Institute of Technology（麻省理工学院）
The $q_{\mathrm{T}}$ and $Δϕ_{t\bar{t}}$ spectra in top-antitop hadroproduction at NNLL+NNLO: the interplay of soft-collinear resummation and Coulomb singularities
We present an event generator for the process $pp\to \ellν_\ellγ$ at next-to-next-to-leading order (NNLO) in QCD and matched to the PYTHIA8 parton shower. The calculation makes use of the GENEVA framework, which combines a resummed calculation obtained via Soft-Collinear Effective Theory (SCET) with the fixed-order result. We validate the NNLO accuracy of our results by comparing predictions for inclusive quantities with an independent fixed-order calculation, and then present the resummed 0-jettiness spectrum at next-to-next-to-leading logarithmic (NNLL$'$) accuracy. Finally, we compare our p…
We present new results for the jet-veto efficiency and zero-jet cross section in Higgs production through gluon fusion. We incorporate the N$^3$LO corrections to the total cross section, the NNLO corrections to the 1-jet rate, NNLL resummation for the jet $p_t$ and LL resummation for the jet radius dependence. Our results include known finite-mass corrections and are obtained using the jet-veto efficiency method, updated relative to earlier work to take into account what has been learnt from the new precision calculations that we include. For 13 TeV collisions and using our default choice for …
We consider the quark beam function that describes collinear initial-state radiation that is constrained by a veto on reconstructed jets. As the veto is imposed on the transverse momenta of the jets, the beam function is subject to rapidity divergences, and we use the collinear-anomaly framework to extract the perturbative matching kernels to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our calculation is based on a novel framework that automates the computation of beam functions in Mellin space and it provides the ingredients to extend jet-veto resummations for quark…
We present compact analytic formulas that describe the decay of colorless particles to both $q \bar q$ and $gg$ final states through next-to-next-to-leading order in perturbative QCD in the context of the nested soft-collinear subtraction scheme. In addition to their relevance for the description of decays like $V \to q \bar q'$, $V= Z,W$, $H \to b \bar b$ and $H \to gg$, these results provide an important building block for calculating NNLO QCD corrections to arbitrary processes at colliders within the nested soft-collinear subtraction scheme.
Total and fiducial top pair ($t\bar{t}$) production cross sections in proton-lead (pPb) collisions at $\sqrt{s_{NN}}$ = 8.16 TeV are computed at next-to-next-to-leading-order (NNLO) accuracy including next-to-next-to-leading-log (NNLL) gluon resummation, using the CT14 and CT10 proton parton distribution functions (PDF), and the EPPS16 and EPS09 nuclear PDF parametrizations for the lead ion. The total cross sections amount to $σ(pPb\to t\bar{t}+X) = 59.0 \pm 5.3$(CT14+EPPS16)$\,^{+1.6}_{-2.1}$(scale) nb, and $57.5 \pm \,^{+4.3}_{-3.3}$(CT10+EPS09)$\,^{+1.5}_{-2.0}$(scale) nb, with small modifi…
We present the combination of fully differential cross sections for colour-singlet production processes at next-to-next-to-leading order (NNLO) QCD obtained with MATRIX and all-order resummation through RadISH. This interface allows us to achieve unprecedented accuracy for various transverse observables in $2 \rightarrow 2$ production processes. As an important application we consider $W^+ W^-$ production at the LHC, more precisely the full leptonic process $pp\to \ell^+\ell^{\prime\, -}ν_{\ell}{\barν}_{\ell^\prime}+X$ with $\ell'\neq\ell$, and we present resummed predictions for differential …
We determine approximate next-to-next-to-leading order (NNLO) corrections to unpolarized and polarized semi-inclusive DIS. They are derived using the threshold resummation formalism, which we fully develop to next-to-next-to-leading logarithmic (NNLL) accuracy, including the two-loop hard factor. The approximate NNLO terms are obtained by expansion of the resummed expression. They include all terms in Mellin space that are logarithmically enhanced at threshold, or that are constant. In terms of the customary SIDIS variables $x$ and $z$ they include all double distributions (that is, "plus" dis…
The thrust distribution in electron-positron annihilation is a classical precision QCD observable. Using renormalization group (RG) evolution in Laplace space, we perform the resummation of logarithmically enhanced corrections in the dijet limit, $T\to 1$ to next-to-next-to-leading logarithmic (NNLL) accuracy. We independently derive the two-loop soft function for the thrust distribution and extract an analytical expression for the NNLL resummation coefficient $g_3$. To combine the resummed expressions with the fixed-order results, we derive the $\log(R)$-matching and $R$-matching of the NNLL …
In this talk we report on the recent progresses on IR logarithms resummation for the Thrust distribution in e^{+}e^{-} collisions. Using renormalisation group (RG) evolution in Laplace space, the resummation of logarithmically enhanced corrections is performed to next-to-next-to-leading logarithmic (NNLL) accuracy. To combine the resummed expressions with the fixed-order results, we derive the log(R)-matching and R-matching of the NNLL approximation to the fixed-order NNLO distribution.
I present the next-to-next-to-leading-logarithm (NNLL) resummation of soft and collinear gluon corrections to single top quark production in the s channel. Attaining NNLL accuracy involves the calculation of the two-loop soft anomalous dimension for the partonic subprocesses. Finite-order expansions of the resummed cross section are calculated through next-to-next-to-leading order (NNLO). Numerical results are presented for s-channel single top quark production at the Tevatron and the LHC, including the dependence of the cross sections on the top quark mass and the uncertainties in the theoret…
