The cold and dense QCD equation of state (EoS) at high baryon chemical potential $μ_B$ involves at order $α^2_S$ an all-loop summation of the soft mode $m_E\sim α_S^{1/2} μ_B$ contributions. Recently, the complete soft contributions at order $α^3_S$ were calculated, using the hard thermal loop (HTL) formalism. By identifying {\em massive} renormalization group (RG) properties within HTL, we resum to all orders $α_S^p, p\ge 3$ the leading and next-to-leading logarithmic soft contributions. We obtain compact analytical expressions, that show visible deviations from the state-of-the art results, and noticeably reduced residual scale dependence. Our results should help to reduce uncertainties in extending the EoS in the intermediate $μ_B$ regime, relevant in particular for the phenomenology of neutron stars.
We review the proposal to resum the physics of hard thermal loops in the thermodynamics of the quark-gluon plasma through nonperturbative expressions for entropy and density obtained from a Phi-derivable two-loop approximation. A comparison with the recently solved large-N_f limit of hot QCD is performed, and some updates, in particular on quark number susceptibilities, are made.
We discuss the Hard Dense Loop resummation at finite quark mass and evaluate the equation of state (EoS) of cold and dense QCD matter in $β$ equilibrium. The resummation in the quark sector has an effect of lowering the baryon number density and the EoS turns out to have much smaller uncertainty than the perturbative QCD estimate. Our numerical results favor smooth matching between the EoS from the resummed QCD calculation at high density and the extrapolated EoS from the nuclear matter density region. We also point out that the speed of sound in our EoS slightly exceeds the conformal limit.
Using the framework of soft-collinear effective theory (SCET), we factorize and calculate $e^+e^-$ angularity distributions, including perturbative resummation and the incorporation of a universal model for the nonperturbative soft function. Angularities $τ_a$ are a class of event shapes varying in their sensitivity to the substructure of jets in the final state, controlled by a continuous parameter $a<2$. We calculate the jet and soft functions in factorized angularity distributions for all $a<1$ to first order in the strong coupling $α_s$ and resum large logarithms to next-to-leading logarit…
We present a new framework for computing resummed and matched distributions in processes with many hard QCD jets. The intricate color structure of soft gluon emission at large angles renders resummed calculations highly non-trivial in this case. We automate all ingredients necessary for the color evolution of the soft function at next-to-leading-logarithmic accuracy, namely the selection of the color bases and the projections of color operators and Born amplitudes onto those bases. Explicit results for all QCD processes with up to $2\to 5$ partons are given. We also devise a new tree-level mat…
We present a simple proof of the all-order exponentiation of soft logarithmic corrections to hard processes in perturbative QCD. Our argument is based on proving that all large logs in the soft limit can be expressed in terms of a single dimensionful variable, and then using the renormalization group to resum them. Beyond the next-to-leading log level, our result is somewhat less predictive than previous all-order resummation formulae, but it does not rely on non-standard factorization, and it is thus possibly more general. We use our result to settle issues of convergence of the resummed seri…
We perform a detailed analysis of the predictions of resummed perturbation theory for the pressure and the second-, fourth-, and sixth-order diagonal quark number susceptibilities in a hot and dense quark-gluon plasma. First, we present an exact one-loop calculation of the equation of state within hard-thermal-loop perturbation theory (HTLpt) and compare it to a previous one-loop HTLpt calculation that employed an expansion in the ratios of thermal masses and the temperature. We find that this expansion converges reasonably fast. We then perform a resummation of the existing four-loop weak cou…
We analyze the electromagnetic pion and kaon form factor by including radiative and higher-twist effects within the framework of resummed pQCD in the space-like region. We focus on the transition from the perturbative to non-perturbative behavior in the phenomenological intermediate energy regime. Using a modified k_T factorization scheme with transverse degrees of freedom, we evaluate the non-perturbative soft contributions as distinct from the hard contributions, ensuring no double counting via the Ward identity at Q^2=0. The soft contributions are obtained via local quark-hadron duality whi…
We derive the general resummed effective Lagrangian for Higgs-mediated flavour-changing neutral-current (FCNC) interactions in the Minimal Supersymmetric Standard Model (MSSM), without resorting to particular assumptions that rely on the squark-mass or the quark-Yukawa structure of the theory. In our derivation we also include the possibility of explicit CP violation through the Cabibbo--Kobayashi--Maskawa mixing matrix and soft supersymmetry-breaking mass terms. The advantages of our resummed FCNC effective Lagrangian are explicitly demonstrated within the context of phenomenologically motiva…
We present the resummed predictions for inclusive cross-section for Drell-Yan (DY) production as well as onshell $Z,W^\pm$ productions at next-to-next-to-next-to leading logarithmic (N$^{3}$LL) accuracy. Using the standard techniques, we derive the $N$-dependent coefficients in the Mellin-$N$ space as well as the $N$-independent constants and match the resummed result through the minimal prescription matching procedure with that of existing next-to next-to leading order (NNLO). In addition to the standard $\ln N$ exponentiation, we study the numerical impacts of exponentiating $N$-independent …
We study how next-to-leading logarithms modify predictions from leading logarithmic soft-gluon resummation in the heavy quark production cross section near threshold. Numerical results are presented for top quark production at the Fermilab Tevatron and bottom quark production at fixed-target energies.
We examine the contributions of soft gluons to the Higgs production cross section at the LHC in the Standard Model and its minimal supersymmetric extension. The soft gluon radiation effects of this reaction share many features with the Drell-Yan process, but arise at lowest order from a purely gluonic initial state. We provide an extension of the conventional soft gluon resummation formalism to include a new class of contributions which we argue to be universal, and resum these and the usual Sudakov effects to all orders. The effect of these new terms is striking: only if they are included, do…
We present the NNLL$'$ resummed $2$-jettiness distribution for decays of the Standard Model Higgs boson to a $b\bar{b}$-quark pair and to gluons. The calculation exploits a factorisation formula derived using Soft-Collinear Effective Theory, in which large logarithms of the $2$-jettiness are resummed by renormalisation group evolution of the hard, soft and jet contributions to the differential decay rate. We match the resummed predictions to the fixed-order NNLO result using the GENEVA framework, extending the validity of the results to all values of the resolution variable and providing a ful…
We present three loop soft-plus-virtual (SV) corrections to the spin-2 production at the Large Hadron Collider (LHC). For this calculation, we make use of the recently computed quark and gluon three loop form factors for the spin-2 production, the universal soft-collinear coefficients as well as the mass factorization kernels. The SV coefficients are presented up to next-to-next-to-next-to leading order (N$^3$LO). We also use these coefficients at three loops to compute the resummed prediction for inclusive cross-section to next-to-next-to-next-to leading logarithmic accuracy (N$^3$LL) matched…
Using soft-collinear effective theory (SCET), which provides a unified framework for factorization, resummation of logarithms, and incorporation of universal nonperturbative functions in hard-scattering QCD cross-sections, we present a new prediction of angularity distributions in e+e- annihilation. Angularities tau_a are an infinite class of event shapes which vary in their sensitivity to the substructure of jets in the final state, controlled by a continuous parameter a<2. We calculate angularity distributions for all a<1 to first order in the strong coupling alpha_s and resum large logarith…
We uncover a contribution to the NLO/NLL threshold resummed total cross section for top quark pair production at hadron colliders, which has not been taken into account in earlier literature. We derive this contribution - the difference between the singlet and octet hard (matching) coefficients - in exact analytic form. The numerical impact of our findings on the Sudakov resummed cross section turns out to be large, and comparable in size to the current estimates for the theoretical uncertainty of the total cross section. A rough estimate points toward a few percent decrease of the latter at t…
Azimuthal asymmetries $v_n$ in the soft transverse momentum spectra of hadronic collisions can result as a consequence of quantum interference and color flow which translates spatial anisotropies into momentum anisotropies via multipole radiation patterns. Here, we analyze to what extent these effects result in signal strengths $v_n\lbrace 2s\rbrace$ that can persist in higher order $(2s)$ cumulants. In a simple model of soft multi-particle production with quantum interference effects in which $m$ particles are emitted from $N$ sources and in which interference contributions appear naturally o…
We present a new prescription for the resummation of the divergent series of perturbative corrections, due to soft gluon emission, to hard processes near threshold in perturbative QCD (threshold resummation). This prescription is based on Borel resummation, and contrary to the commonly used minimal prescription, it does not introduce a dependence of resummed physical observables on the kinematically unaccessible x->0 region of parton distributions. We compare results for resummed deep-inelastic scattering obtained using the Borel prescription and the minimal prescription and exploit the compar…
We present state of the art resummation predictions for differential cross sections in top-quark pair production at the LHC. They are derived from a formalism which allows the simultaneous resummation of both soft and small-mass logarithms, which endanger the convergence of fixed-order perturbative series in the boosted regime, where the partonic center-of-mass energy is much larger than the mass to the top quark. We combine such a double resummation at NNLL$'$ accuracy with standard soft-gluon resummation at NNLL accuracy and with NLO calculations, so that our results are applicable throughou…
Some of the most arduous and error-prone aspects of precision resummed calculations are related to the partonic hard process, having nothing to do with the resummation. In particular, interfacing to parton-distribution functions, combining various channels, and performing the phase space integration can be limiting factors in completing calculations. Conveniently, however, most of these tasks are already automated in many Monte Carlo programs, such as MadGraph, Alpgen or Sherpa. In this paper, we show how such programs can be used to produce distributions of partonic kinematics with associated…
We study next-to-leading-power (NLP) threshold corrections in colour-singlet production processes, with particular emphasis on Drell-Yan (DY) and single-Higgs production. We assess the quality of the partonic and hadronic threshold expansions for each process up to NNLO. We determine numerically the NLP leading-logarithmic (LL) resummed contribution in addition to the leading-power next-to-next-to-leading logarithmic (LP NNLL) resummed DY and Higgs cross sections, matched to NNLO. We find that the inclusion of NLP logarithms is numerically more relevant than increasing the precision to N$^3$LL…
We investigate the effect of large-x resummation on parton distributions by performing a fit of Deep Inelastic Scattering data from the NuTeV, BCDMS and NMC collaborations, using NLO and NLL soft-resummed coefficient functions. Our results show that soft resummation has a visible impact on quark densities at large x. Resummed parton fits would therefore be needed whenever high precision is required for cross sections evaluated near partonic threshold.
We perform factorization of the most general distribution in semileptonic B -> X_u decays and we resum the threshold logarithms to next-to-leading order. From this (triple-differential) distribution, any other distribution is obtained by integration. As an application of our method, we derive simple analytical expressions for a few distributions, resummed to leading approximation. It is shown that the shape function can be directly determined by measuring the distribution in m_X^2/E_X^2, not in m_X^2/m_B^2. We compute the resummed hadron energy spectrum, which has a ``Sudakov shoulder'', and w…
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…
I discuss general unified formulas for resumming collinear and soft contributions to QCD hard scattering cross sections at large x. Expansions of the resummed cross sections to next-to-next-to-next-to-leading order are also shown along with applications of the formalism.
We study the impact of leading soft-collinear effects on threshold and joint-resummed calculations for the production of prompt photons via parton fragmentation, complementing a previous study for direct production. We assess these effects for both fixed-target and collider kinematics. We find them to be small, but noticeable and comparable to the direct case.
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 …
We present an accurate theoretical prediction for the production of Higgs boson through bottom quark annihilation at the LHC up to next-to-next-to-next-to leading order (N$^3$LO) plus next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. We determine the third order perturbative Quantum Chromodynamics (QCD) correction to the process dependent constant in the resummed expression using the three loop bottom quark form factor and third order quark soft distribution function. Thanks to the recent computation of N$^3$LO corrections to this production cross-section from all the partonic ch…
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…
We construct a set of parton distribution functions (PDFs) in which fixed-order NLO and NNLO calculations are supplemented with soft-gluon (threshold) resummation up to NLL and NNLL accuracy respectively, suitable for use in conjunction with any QCD calculation in which threshold resummation is included at the level of partonic cross sections. These resummed PDF sets, based on the NNPDF3.0 analysis, are extracted from deep-inelastic scattering, Drell-Yan, and top quark pair production data, for which resummed calculations can be consistently used. We find that, close to threshold, the inclusio…
The gold-plated discovery mode of a Standard Model like Higgs boson at the CERN Large Hadron Collider (LHC) is the H -> Z^0 Z^0 decay mode. To find and then measure the properties of the Higgs, it is crucial to have the most precise theoretical prediction both for the signal and the QCD background in this mode. In this work we calculate the effects of the initial-state multiple soft-gluon emission on the kinematic distributions of photon and Z^0 pairs produced in hadron collisions. The Collins-Soper-Sterman formalism is extended to resum the large logarithmic terms due to soft-gluons. The resu…
We present a framework for resumming the contributions from soft-virtual and next-to-soft virtual (NSV) logarithms. Numerical impact for these resummed predictions are discussed for the inclusive cross section for Drell-Yan di-lepton process up to next-to-next-to leading logarithmic accuracy, restricting to only diagonal partonic channels.
A procedure is developed for using Soft Collinear Effective Theory (SCET) to generate fully exclusive events, which can then be compared to data from collider experiments. We show that SCET smoothly interpolates between QCD for hard emissions, and the parton shower for soft emissions, while resumming all large logarithms. In SCET, logarithms are resummed using the renormalization group, instead of classical Sudakov factors, so subleading logarithms can be resummed as well. In addition, all loop effects of QCD can be reproduced in SCET, which allows the effective theory to incorporate next-to-l…
Jet vetoes play an important role at the LHC in the search for the Higgs and ultimately in precise measurements of its properties. Many Higgs analyses divide the cross section into exclusive jet bins to maximize the sensitivity in different production and decay channels. For a given jet category, the veto on additional jets introduces sensitivity to soft and collinear emissions, which causes logarithms in the perturbative expansion that need to be resummed to obtain precise predictions. We study the higher-order resummation properties of several conceptually distinct kinematic variables that c…
We develop threshold resummation for single-particle inclusive cross sections in hadron-hadron collisions to the level of next-to-next-to-leading logarithm, up to full matching with two-loop hard functions. We define and calculate all one-loop soft functions for all partonic channels. This enables us to separate the hard and soft functions at one loop. Along with these results, the one-loop finite parts of jet functions are used to check that the full soft, collinear and virtual corrections are reproduced to one loop for all partonic reactions. We exhibit these NLO results explicitly. NLO expa…
We compute analytically the diagonal quark number susceptibilities for a quark-gluon plasma at finite temperature and zero chemical potential, and compare with recent lattice results. The calculation uses the approximately self-consistent resummation of hard thermal and dense loops that we have developed previously. For temperatures between 1.5 to 5 $T_c$, our results follow the same trend as the lattice data, but exceed them in magnitude by about 5-10%. We also compute the lowest order contribution, of order $α_s^3\log(1/α_s)$, to the off-diagonal susceptibility. This contribution, which is n…
The next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation describing the high-energy evolution of the scattering between a dilute projectile and a dense target suffers from instabilities unless it is supplemented by a proper resummation of the radiative corrections enhanced by (anti-)collinear logarithms. Earlier studies have shown that if one expresses the evolution in terms of the rapidity of the dilute projectile, the dominant anti-collinear contributions can be resummed to all orders. However, in applications to physics, the results must be re-expressed in terms of the rapidity of t…
We have studied color-octet contributions for $J/ψ$ inclusive production at B factories, i.e., $e^+e^-\to J/ψ(^3P_J^{[8]},^1S_0^{[8]}) + X_{\mathrm{non}-c\bar c}$, using the soft gluon factorization (SGF) approach, in which the $J/ψ$ energy spectrum is expressed in a form of perturbatively calculable short-distance hard parts convoluted with one-dimensional soft gluon distributions (SGDs). The series of velocity corrections originated from kinematic effect can be naturally resummed in this approach. Short-distance hard parts have been calculated analytically to next-to-leading order in $α_s$. …
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.
I present results for the two-loop soft anomalous dimensions for associated production of a single top quark with a W boson or a charged Higgs boson. The calculation uses expressions for the massive cusp anomalous dimension, which are presented in different forms, and it allows soft-gluon resummation at next-to-next-to-leading-logarithm (NNLL) accuracy. From the NNLL resummed cross section I derive approximate NNLO cross sections for bg -> tW- and bg -> tH- at LHC energies of 7, 10, and 14 TeV.
We report on recent results on the differential cross section for slepton pair-production at hadron colliders. We use an approach to threshold resummation, based on soft-collinear effective theory, to quantify the dynamical enhancement of the partonic threshold region. We evaluate the resummed invariant mass distribution and total cross section at next-to-next-to-next-to-leading logarithmic order, and match the result onto next-to-leading order calculation.
We study the role of the threshold variable in soft-gluon threshold resummation. We focus on the computation of the resummed total cross section, the final-state invariant-mass distribution, and transverse-momentum distribution of the Higgs boson when produced in association with a top-anti-top quark pair for the Large Hadron Collider operating at 13 TeV. We show that different choices for the threshold variable result in differences at next-to-leading power, i.e. contributions that are down by one power of the threshold variable. These contributions are noticeable numerically, although their …
We present the threshold resummation for the cross section for electroproduction of heavy quarks. We work to next-to-leading logarithmic accuracy, and in single-particle inclusive kinematics. We provide next-to-leading and next-to-next-to-leading order expansions of our resummed formula, and examine numerically the quality of these finite order approximations. For the case of charm we study their impact on the structure function $F_2$ and its differential distribution with respect to the charm transverse momentum.
The production of hard photons in hadronic collisions is studied using Soft-Collinear Effective Theory (SCET). This is the first application of SCET to a physical, observable cross section involving energetic partons in more than two directions. A factorization formula is derived which involves a non-trivial interplay of the angular dependence in the hard and soft functions, both quark and gluon jet functions, and multiple partonic channels. The relevant hard, jet and soft functions are computed to one loop and their anomalous dimensions are determined to three loops. The final resummed inclus…
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%.
We present the threshold resummation for the cross section of heavy quark production in polarized deep-inelastic scattering to next-to-leading logarithmic accuracy and in single-particle inclusive kinematics. We expand our resummed result in alpha_s to next-to-leading and next-to-next-to-leading order and study the impact of these higher order corrections on the charm structure function g_1 in the kinematical range accessible to the HERMES and COMPASS experiments.
I present approximate results that include third-order soft-gluon corrections for the associated production of a single top quark with a $W$ boson. The calculation uses expressions from soft-gluon resummation at next-to-next-to-leading-logarithm (NNLL) accuracy. From the NNLL resummed cross section I derive approximate next-to-next-to-next-to-leading order (aN$^3$LO) cross sections for the process $bg \rightarrow tW^-$ at LHC and Tevatron energies. The aN$^3$LO top-quark transverse-momentum and rapidity distributions in $tW$ production are also presented.
We present the resummed predictions for inclusive cross section for Drell-Yan (DY) production up to next-to-next-to leading logarithmic ($\rm \overline{ NNLL}$) accuracy taking into account both soft virtual (SV) and next-to SV (NSV) threshold logarithms. We restrict ourselves to resummed contributions only from quark anti-quark ($q \bar q$) initiated channels. The resummation is performed in Mellin-$N$ space. We derive the $N$-dependent coefficients and the $N$-independent constants to desired accuracy for our study. The resummed results are matched through the minimal prescription procedure …
The hard-scattering contributions to heavy-to-light form factors at large recoil are studied systematically in soft-collinear effective theory (SCET). Large logarithms arising from multiple energy scales are resummed by matching QCD onto SCET in two stages via an intermediate effective theory. Anomalous dimensions in the intermediate theory are computed, and their form is shown to be constrained by conformal symmetry. Renormalization-group evolution equations are solved to give a complete leading-order analysis of the hard-scattering contributions, in which all single and double logarithms are…
The resummation of threshold logarithms for direct photon production cross sections in hadronic collisions is presented. The resummation is based on the factorization properties of the cross section and is formulated at next-to-leading logarithmic or higher accuracy. Full analytical and numerical results for the next-to-next-to-leading order expansion of the resummed cross section are given. A substantial reduction of factorization scale dependence is observed. A comparison to experimental results from the E-706 and UA-6 experiments is presented.
We use a recent approach to soft-gluon resummation based on effective field theory to implement soft-gluon resummation at NNNLL order for slepton-pair production in SUSY extensions of the Standard Model. This approach resums large logarithmic corrections arising from the dynamical enhancement of the partonic threshold region caused by steeply falling parton luminosities. We evaluate the resummed invariant-mass distribution and total cross section for slepton-pair production at the Tevatron and LHC, matching our results onto NLO fixed-order calculations. As a byproduct, we also study virtual SU…
The N-jettiness event shape divides phase space into N+2 regions, each containing one jet or beam. These jet regions are insensitive to the distribution of soft radiation and, with a geometric measure for N-jettiness, have circular boundaries. We give a factorization theorem for the cross section which is fully differential in the mass of each jet, and compute the corresponding soft function at next-to-leading order (NLO). For N-jettiness, all ingredients are now available to extend NLO cross sections to resummed predictions at next-to-next-to-leading logarithmic order.
