We consider top-quark pair production at the LHC within the MSbar scheme for the renormalisation of the top-quark mass, and we present predictions for total and differential cross sections at next-to-next-to-leading order (NNLO) in QCD. Our state-of-the-art calculation extends the available differential results by one order in the perturbative expansion, and it is relevant for a precise determination of the top-quark mass, including possible effects of the running mass in the MSbar scheme. We consider variations of the scale at which the MSbar mass of the top quark is evaluated, extending the usual 7-point to a 15-point scale variation. This additional variation is crucial for a reliable estimate of the theoretical uncertainties, especially at low perturbative orders and close to the production threshold of the top-quark pair. We also compute, for the first time, the invariant-mass distribution of the top-quark pair by using a running mass, evaluated at a dynamic scale. Our predictions for the invariant-mass distribution in the MSbar scheme are compared with a recent measurement performed by the CMS Collaboration. We observe that the inclusion of the NNLO corrections improves the agreement with the data, and we discuss effects due to the QCD running of the MSbar mass of the top quark.
This contribution attempts to determine the $b$-quark pole mass $M_b$ and \MSbar running mass $\overline{m}_b$ with two different approaches at the next-to-next-to-leading order (NNLO) corrections. At the first approach, we derive a relation between the $b$-quark pole mass $M_b$ and its \MSbar running mass $\overline{m}_b$ at the NNLO corrections based on the perturbative Quantum Chromo Dynamics (pQCD) predictions. At the second approach, we extract numerical values of the $b$-quark pole and \MSbar running masses based on the NNLO phenomenology of H1 and ZEUS Collaborations combined beauty ver…
Top quark pair production is one of the cornerstones of the physics program at hadron colliders. In this contribution, we further explore the phenomenological implications of the recent NNLO calculation of the total inclusive cross-section. We provide a comparison of the scale dependence of the top pair hadroproduction cross section at different perturbative orders and study its perturbative convergence (with and without soft-gluon resummation). We also sketch how the NNLO top quark cross-section could be used to improve searches of physics beyond the Standard Model.
We compute the relation between the quark mass defined in the minimal modified $\MSbar$ scheme and the mass defined in the ``Regularization Invariant" scheme (RI), up to the NNLO order. The RI scheme is conveniently adopted in lattice QCD calculations of the quark mass, since the relevant renormalization constants in this scheme can be evaluated in a non-perturbative way. The NNLO contribution to the conversion factor between the quark mass in the two schemes is found to be large, typically of the same order of the NLO correction at a scale $μ\sim 2$ GeV. We also give the NNLO relation between…
We study the resummation of singular distributions for electroweak-boson production at large transverse momentum in hadronic collisions. We describe the factorization properties of the cross section near partonic threshold and construct the resummed cross section at next-to-leading logarithmic accuracy in moment space in terms of soft gluon anomalous dimensions. We present full analytical results for the expansion of the resummed cross section up to next-to-next-to-leading order. Our results can be applied to W, Z, and virtual gamma production at hadron colliders.
We report on a new calculation of the next-to-next-to-leading order (NNLO) QCD radiative corrections to the inclusive production of top-quark pairs at hadron colliders. The calculation is performed by using the $q_T$ subtraction formalism to handle and cancel infrared singular contributions at intermediate stages of the computation. We present numerical results for the total cross section in $pp$ collisions at $\sqrt{s}=8$ TeV and $13$ TeV, and we compare them with those obtained by using the publicly available numerical program Top++. Our computation represents the first complete application …
The study of top-quark production and decay is central in the LHC physics programme, allowing precise tests of the Standard Model and offering a window on possible new physics. Accurate theoretical predictions for this process are therefore crucial. We report on a new calculation of the next-to-next-to-leading order QCD radiative corrections to the production of top-quark pairs at hadron colliders. The calculation is performed by using the $q_T$-subtraction method to handle and cancel infrared singular contributions at intermediate stages of the computation, and it represents its first complet…
We calculate threshold soft-gluon corrections to total cross sections and transverse momentum distributions for bottom and charm quark production in fixed-target experiments, considering both pp and pi- p interactions. We investigate the quality of the near threshold soft-gluon approximation at next-to-leading order (NLO) and calculate next-to-next-to-leading order (NNLO) corrections through next-to-next-to-next-to-leading-logarithmic (NNNLL) accuracy, including some virtual terms. We find that the NNLO threshold corrections reduce the factorization and renormalization scale dependence of the …
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.
A calculation of the next-to-leading order cross section for the inclusive hadroproduction of charm quarks including heavy quark mass effects in the hard scattering cross sections is presented. It is described how the massive hard scattering cross sections are constructed from the corresponding cross sections in a fixed order calculation where collinear pieces associated with the heavy quark are not yet subtracted. By adjusting suitable subtraction terms a massive theory with MSbar subtraction is established which approaches the massless theory with increasing transverse momentum. These result…
We present a detailed discussion of the collinear subtraction terms needed to establish a massive variable-flavour-number scheme for the one-particle inclusive production of heavy quarks in hadronic collisions. The subtraction terms are computed by convoluting appropriate partonic cross sections with perturbative parton distribution and fragmentation functions relying on the method of mass factorization. We find (with one minor exception) complete agreement with the subtraction terms obtained in a previous publication by comparing the zero-mass limit of a fixed-order calculation with the genui…
We describe calculations of $c \bar c$ production to next-to-next-to-leading order (NNLO) and next-to-next-to-leading logarithm (NNLL) near threshold in $pp$ and $π^- p$ interactions. We study the relevance of these calculations for existing $c \bar c$ total cross section data by examining their sensitivity to partonic threshold kinematics, their convergence properties and scale dependence.
We take a look at how the differential distributions for top-quark production are affected by changing to the running mass scheme. Specifically we consider the transverse momentum, rapidity and pair-invariant mass distributions at NLO for the top-quark mass in the MSbar scheme. It is found that, similar to the total cross section, the perturbative expansion converges faster and the scale dependence improves using the mass in the MSbar scheme as opposed to the on-shell scheme. We also update the analysis for the total cross section using the now available full NNLO contribution.
The energy dependence of the total hadroproduction cross section of pseudo-scalar quarkonia is computed via matching Next-to-Leading Order (NLO) Collinear-Factorisation (CF) results with resummed higher-order corrections, proportional to $α_s^{n}\ln^{n-1}(1/z)$, to the CF hard-scattering coefficient, where $z=M^2/\hat{s}$ with $M$ and $\hat{s}$ being the quarkonium mass and the partonic center-of-mass energy squared. The resummation is performed using High-Energy Factorisation (HEF) in the Doubly-Logarithmic (DL) approximation, which is a subset of the leading logarithmic $\ln (1/z)$ approxima…
We present the first exact analytic result for all partonic channels contributing to the total cross section for the production of a pair of heavy flavors in hadronic collisions in NLO QCD. Our calculation is an essential step in the derivation of the top quark pair production cross section at NNLO in QCD, which is a cornerstone of the precision LHC program. Our results uncover the analytical structures behind observables with heavy flavors at higher orders. They also reveal surprising and non-trivial implications for kinematics close to partonic threshold.
We present a determination of parton distribution functions (ABM11) and the strong coupling constant alpha_s at next-to-leading order and next-to-next-to-leading order (NNLO) in QCD based on world data for deep-inelastic scattering and fixed-target data for the Drell-Yan process. The analysis is performed in the fixed-flavor number scheme for n_f=3,4,5 and uses the MSbar-scheme for alpha_s and the heavy-quark masses. At NNLO we obtain the value alpha_s(M_Z) = 0.1134 +- 0.0011. The fit results are used to compute benchmark cross sections at hadron colliders to NNLO accuracy and to compare to da…
We compare the theoretical status and the numerical predictions of two approaches for heavy quark production in the high energy hadron collisions, namely the conventional LO parton model with collinear approximation and $k_T$-factorization approach. The main assumptions used in the calculations are discussed. To extract the differences coming from the matrix elements we use very simple gluon structure function and fixed coupling. It is shown that the $k_T$-factorization approach calculated formally in LO and with Sudakov form factor accounts for many contributions related usually to NLO (and e…
The ambiguity in the choice of a renormalization scheme and scale for the top-quark mass leads to an additional source of theoretical uncertainty in the calculation of the Higgs boson production cross section via gluon fusion. These uncertainties were found to be dominant in the case of off-shell Higgs production at next-to-leading order in QCD for large values of the Higgs virtuality $m_H^*$. In this work, we study the uncertainties related to the top-quark mass definition up to next-to-next-to-leading order (NNLO) in QCD. We include the full top-quark mass dependence up to three loops in the…
We update the study of the QCD corrections to direct J/psi and Upsilon hadroproduction in association with a photon in the QCD-based approach of the Colour-Singlet (CS) Model. After comparison with the recent full next-to-leading-order (NLO) computation for this process, we provide an independent confirmation to the inclusive case that NLO QCD corrections to quarkonium-production processes whose LO exhibits a non-leading P_T behaviour can be reliably computed at mid and large P_T by considering only the real emission contributions accompanied with a kinematical cut. In turn, we evaluate the le…
We present the O(alphas^4) virtual QCD corrections to gluon-gluon scattering due to the self-interference of the one-loop amplitude. We give analytic expressions renormalised in the MSbar scheme and work in conventional dimensional regularisation. We write the structure of the infrared divergences from direct Feynman diagram evaluation in terms of the Catani formalism for infrared divergences. Formulae for the finite remainder are given in terms of logarithms that are real in the physical region. These results, together with those previously obtained for quark-quark and quark-gluon scattering …
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 analyze the properties of the ACOT scheme for heavy quark production and make use of the \MSbar massless results at NNLO and N3LO for the structure functions F2 and FL in neutral current deep-inelastic scattering to estimate the higher order corrections. For this purpose we decouple the heavy quark mass entering the phase space from the one entering the dynamics of the short distance cross section. We show numerically that the phase space mass is generally more important. Therefore, the dominant heavy quark mass effects at higher orders can be taken into account using the massless Wilson co…
Next-to-next-to-leading order (NNLO) QCD corrections to Higgs boson hadroproduction have recently been calculated in the heavy top-quark limit m_t -> \infty. The m_t -> \infty limit introduces double-logarithmic corrections in ln x, with x = m_H^2 / s. We identify these corrections order by order in alpha_s. As an application, we derive an analytic expression for the dominant x << 1 part of the NNLO coefficient.
We compute the structure functions F2 and FL in the ACOT scheme for heavy quark production. We use the complete ACOT results to NLO, and make use of the MSbar massless results at NNLO and N3LO to estimate the higher order mass-dependent corrections. We show numerically that the dominant heavy quark mass effects can be taken into account using massless Wilson coefficients together with an appropriate rescaling prescription. Combining the exact NLO ACOT scheme with these expressions should provide a good approximation to the full calculation in the ACOT scheme at NNLO and N3LO.
We have calculated the splitting functions governing the evolution of the unpolarized parton distributions of the photon at the next-to-next-to-leading order (NNLO) of massless perturbative QCD. The results, presented here mainly in terms of compact and accurate parametrizations, are consistent with our previous approximations based on the lowest six even-integer Mellin moments. Consequently the NNLO corrections are small in both the MSbar and the DIS_gamma factorization schemes at momentum fractions x >~ 0.1.
We present complete analytical ${\mathcal O}(ε^2)$ results on the one-loop amplitudes relevant for the NNLO quark-parton model description of the hadroproduction of heavy quarks as given by the so-called loop-by-loop contributions. All results of the perturbative calculation are given in the dimensional regularization scheme. These one-loop amplitudes can also be used as input in the determination of the corresponding NNLO cross sections for heavy flavor photoproduction, and in photon-photon reactions.
We present the first direct determination of the running top-quark mass based on the total cross section of top-quark pair-production as measured at the Tevatron. Our theory prediction for the cross section includes various next-to-next-to-leading order QCD contributions, in particular all logarithmically enhanced terms near threshold, the Coulomb corrections at two loops and all explicitly scale dependent terms at NNLO accuracy. The result allows for an exact and independent variation of the renormalization and factorization scales. For Tevatron and LHC we study its dependence on all scales, …
In this paper, we calculate the $t\bar{t}$ pQCD production cross-section at NNLO and determine the top-quark pole mass from recent measurements at the LHC at $\sqrt{S}=13$ TeV center-of-mass energy to high precision by applying the Principle of Maximum Conformality (PMC). The PMC provides a systematic method which rigorously eliminates QCD renormalization scale ambiguities by summing the nonconformal $β$ contributions into the QCD coupling constant. The PMC predictions satisfy the requirements of renormalization group invariance, including renormalization scheme independence, and the PMC scale…
We calculate the complete NNLO QCD corrections to the charm contribution of the rare decay K+ -> pi+ nu nu-bar. We encounter several new features, which were absent in lower orders. We discuss them in detail and present the results for the 2-loop matching conditions of the Wilson coefficients, the 3-loop anomalous dimensions, and the 2-loop matrix elements of the relevant operators that enter the NNLO renormalization group analysis of the Z-penguin and the electroweak box contribution. The inclusion of the NNLO QCD corrections leads to a significant reduction of the theoretical uncertainty fro…
We compute the two-loop heavy quark jet-function in the heavy quark limit. This is one of the key ingredients in next-to-next-to-leading order (NNLO) and next-to-next-to-leading-log order (NNLL) computations of the invariant mass distribution of top-jets at a future e+e- collider. The shape of the top invariant mass distribution is affected by large logs which we compute at NNLL order. Exploiting the non-abelian exponentiation theorem, a definition of the top jet-mass is given which is transitive and whose renormalization group evolution is determined by the cusp-anomalous dimension to all ord…
We discuss a general framework for the inclusion of heavy quark mass contributions to deep-inelastic structure functions and their perturbative matching to structure functions computed in variable-mass schemes. Our approach is based on the so-called FONLL method, previously introduced and applied to heavy quark hadroproduction and photoproduction. We define our framework, provide expressions up to second order in the strong coupling, and use them to construct matched expressions for structure functions up to NNLO. After checking explicitly the consistency of our results, we perform a study of …
I discuss three different selected topics in top quark physics. The first topic concerns the next-to-next-to-leading order calculation of the hadroproduction of top quark pairs and the role of multiple polylogarithms in this calculation. I report on an ongoing next-to-next-to-leading order calculation of heavy quark pair production in hadron collisions where the loop--by--loop part of the calculation is about to be completed. Calculating the loop-by-loop part allows one to take a glimpse at the mathematical structure of the full NNLO calculation. The loop-by-loop contributions bring in a new c…
The renormalization scale uncertainty can be eliminated by the Principle of Maximum Conformality (PMC) in a systematic scheme-independent way. Applying the PMC for the $t\bar{t}$-pair hadroproduction at the NNLO level, we have found that the total cross-sections $σ_{t\bar{t}}$ at both the Tevatron and LHC remain almost unchanged when taking very disparate initial scales $μ^{\rm init}_R$ equal to $m_t$, $10\,m_t$, $20\,m_t$ and $\sqrt{s}$, which is consistent with renormalization group invariance. As an important new application, we apply PMC scale-setting to study the top-quark forward-backwar…
