O. P. Solovtsova, Yu. D. Chernichenko
The new relativistic Coulomb-like threshold resummation $S$-factor in quantum chromodynamics is obtained. The consideration is given within the framework of quasipotential approach in quantum field theory which is formulated in relativistic configuration representation for two particles of unequal masses.
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A short overview of recent developments on resummations in QCD is presented.
A relativistic Coulomb-like resummation factor in QCD is suggested, based on the solution of the quasipotential equation.
We present a master formula, with applicability conditions, which allows us to automate the resummation of infrared and collinear logarithms appearing in distributions of jet observables in QCD at next-to-leading logarithmic accuracy.
The bilocal expansion of Borel transform provides an efficient way of Borel resummation with low order perturbations in QCD. Its applications to the heavy quark pole mass, static potential, and lattice calculation are reviewed.
We describe the resummation of singular distributions at partonic threshold in heavy quark production, generalizing results for Drell-Yan and other electroweak hard-scattering processes.
It is shown that amplitude-based, exact resummation tames the un-cancelled IR divergences at O(alpha_s^2) in initial state radiation in QCD with massive quarks. Implications for precision predictions for LHC physics are discussed.
I briefly review some recent results on soft-gluon resummation and present applications to heavy-quark and jet production in hadron collisions.
We present the theory of QED x QCD resummation and its interplay with shower/matrix element matching in precision LHC physics scenarios. We illustrate the theory using single heavy gauge boson production at hadron colliders.
I give a pedagogical introduction to resummation and power corrections, using the thrust variable in electron-positron annihilation as an example, followed by an discussion of issues of predictability in perturbative QCD.
A method of evaluation of spacelike QCD observables ${\cal D}(Q^2)$ is presented, motivated by the renormalon structure of these quantities.
I present results for the resummation of soft and collinear gluon contributions to QCD hard-scattering cross sections at two loops. This requires the calculation of UV and IR divergences through two loops and the construction of soft anomalous dimensions that control resummation at NNLL. Explicit results are provided for processes that involve massless and/or massive quarks, including single top and top pair production.
We study applications of QCD soft-gluon resummations to electroweak annihilation cross sections. We focus on a formalism that allows to resum logarithmic corrections arising near partonic threshold and at small transverse momentum simultaneously.
We show that the resummation of large radiative corrections in QCD processes can be performed both in covariant gauge and in axial gauge. We extend the resummation technique to inclusive processes, concentrating on deeply inelastic scattering, Drell-Yan production, and inclusive heavy meson decays in end-point regions. Leading and next-to-leading logarithms produced by radiative corrections are organized into Sudakov factors, whose expressions are the same as those derived from the conventional Wilson-loop approach. The gauge invariance of the resummation in the end-point region is demonstrate…
I present results for the resummation of soft-gluon contributions to QCD hard-scattering cross sections at next-to-next-to-leading logarithm accuracy. A key ingredient is the calculation of two-loop soft anomalous dimensions for the partonic processes. Explicit expressions and applications are provided for processes that involve massless partons and/or massive quarks.
We summarize our recent results on small x resummation in full QCD with n_f quark flavours and discuss their phenomenological impact in the extraction of parton distributions from present day structure function data and their extrapolation to the kinematics relevant for future colliders such as the LHC.
We build a computer code that fully automates the resummation of jet-observable distributions at next-to-leading logarithmic accuracy. As an application we present results for a jet shape in hadronic dijet production.
The resummation of logarithmically-enhanced terms to all perturbative orders is a prerequisite for many studies of QCD final-states. Until now such resummations have always been performed by hand, for a single observable at a time. In this letter we present a general `master' resummation formula (and applicability conditions), suitable for a large class of observables. This makes it possible for next-to-leading logarithmic resummations to be carried out automatically given only a computer routine for the observable. To illustrate the method we present the first next-to-leading logarithmic resu…
We perform a systematic comparison of soft-gluon resummation in SCET and in a standard "direct" QCD (dQCD) approach, both from an analytical and a phenomenological point of view. In particular, we concentrate on Higgs boson production in gluon-gluon fusion at a hadron collider. Using specifically a saddle point argument, we arrive at a detailed understanding of the quantitative differences between these two approaches.
Motivated by current searches for electroweak superpartners at the Large Hadron Collider, we present precision predictions for pair production of such particles in the framework of the Minimal Supersymmetric Standard Model. We make use of various QCD resummation formalisms and match the results to pure perturbative QCD computations. We study the impact of scale variations and compare our results to predictions obtained by means of traditionally used Monte Carlo event generators.
We investigate the resummation of large logarithmic perturbative corrections to hadron production in electron-positron annihilation and semi-inclusive deep-inelastic scattering. We find modest, but significant, enhancements of hadron multiplicities in the kinematic regimes accessible in present high-precision experiments. Our results are therefore relevant for the determination of hadron fragmentation functions from data for these processes.
We present calculations of next-to-leading order and resummed QCD corrections for semi-inclusive deep-inelastic scattering and single-inclusive e+e- annihilation. The resummation is performed to next-to-leading logarithmic accuracy. Knowing these QCD corrections is important in order to extract parton distribution functions and fragmentation functions from present and future data for these reactions. We present comparisons of our results to recent data by the COMPASS, HERMES, Belle, and BaBar experiments.
We present an innovative method to resum infrared and collinear logarithms appearing in distributions of jet observables in QCD. The method, based on a general master formula with applicability conditions, allows resummations at next-to-leading logarithmic accuracy in an automated way. As a sample application we present resummed results in hadronic dijet events.
It is argued why thermodynamic approximations in terms of dressed propagators may, at larger coupling strength, be better behaved than perturbative results, and why in hot QCD the hard thermal loop approximation of the thermodynamic potential cannot be expected to work close to the phase transition.
We discuss the resummation of distributions that are singular at the elastic limit of partonic phase space (partonic threshold) in QCD hard-scattering cross sections, such as heavy quark production. We show how nonleading soft logarithms exponentiate in a manner that depends on the color structure within the underlying hard scattering. This result generalizes the resummation of threshold singularities for the Drell-Yan process, in which the hard scattering proceeds through color-singlet annihilation. We illustrate our results for the case of heavy quark production by light quark annihilation, …
We review the basic concepts of all-order calculations in Quantum Chromodynamics (QCD) and their application to collider phenomenology. We start by discussing the factorization properties of QCD amplitudes and cross-sections in the soft and collinear limits and their resulting all-order exponentiation. We then discuss several applications of this formalism to observables which are of great interest at particle colliders. In this context, we describe the all-order resummation of event-shape distributions, as well as observables that probe the internal structure of hadronic jets.
We study the transverse momentum dependent factorization for single spin asymmetries in Drell-Yan and semi-inclusive deep inelastic scattering processes at one-loop order. The next-to-leading order hard factors are calculated in the Ji-Ma-Yuan factorization scheme. We further derive the QCD resummation formalisms for these observables following the Collins-Soper-Sterman method. The results are expressed in terms of the collinear correlation functions from initial and/or final state hadrons coupled with the Sudakov form factor containing all order soft-gluon resummation effects. The scheme inde…
We present the current status of the comparisons with the respective data of the predictions of our approach of exact amplitude-based resummation in quantum field theory as applied to precision QCD calculations as needed for LHC physics, using the MC Herwiri1.031. The agreement between the theoretical predictions and the data exhibited continues to be encouraging.
We compute the Standard Model scalar coupling ($λ$) evolution in a particular QCD resummation scheme, where the QCD coupling becomes infrared finite due to the presence of a dynamically generated gluon mass, leading to the existence of a non-perturbative infrared fixed point. We discuss how this scheme can be fixed taking recourse to phenomenological considerations in the infrared region. The QCD $β$ function associated to this non-perturbative coupling when introduced into the SM renormalization group equations increases the $λ$ values at high energies.
The resummation of $O(α^{l+1} \ln^{2l} x)$ terms in the evolution kernels of non--singlet combinations of structure functions is investigated for both QED abd QCD. Numerical results are presented for unpolarized and polarized structure functions.
In this article, we assume that the two quarks have unequal masses and calculate the next-to-leading order contributions to the spectral densities of the mesonic two-point correlation functions of the vector, axialvector, scalar and pseudoscalar currents. We take dimensional regularization to regularize both the ultraviolet and infrared divergences, and use optical theorem to obtain the spectral densities directly, furthermore, we present some necessary technical details for readers convenience. The analytical expressions are applicable in many phenomenological analysis besides the QCD sum rul…
In this contribution, I present a new QCD fit to final combined HERA deep-inelastic scattering cross-section data incorporating $\ln(1/x)$-resummation terms. This fit has been performed within the xFitter framework. The main effect of including such resummed terms results not only in a better description of the low-$x$ and low-$Q^{2}$ data, but also in a steeply rising gluon PDF at low x for low scales. Furthermore, the kinematic region where this resummation is important is delineated. This contribution is based on the results presented in arXiv:1802.00064.
We discuss issues related to the resummation of non-global observables in QCD, those that are sensitive to radiation in only a part of phase space. Examples of such observables are certain single-hemisphere event shapes in e+e- and DIS. Compared to global observables (those sensitive to all emissions, e.g. the e+e- thrust) a new class of single-logarithmic terms arises. These have been neglected in recent calculations in the literature. For a whole set of single hemisphere e+e- and DIS event shapes, we analytically evaluate the first such term, at order alpha_s^2, and give numerical results fo…
We present the elements of three applications of resummation methods in non-Abelian gauge theories: (1), QED X QCD exponentiation and shower/ME matching for LHC physics; (2), IR improvement of DGLAP theory; (3), resummed quantum gravity and the final state of Hawking radiation. In all cases, the extension of the YFS approach, originally introduced for Abelian gauge theory, to non-Abelian gauge theories, QCD and quantum general relativity, leads to new results and solutions which we briefly summarize.
We calculate the transverse-momentum $Q_T$ spectrum of the dilepton in the transversely polarized Drell-Yan process on the basis of the factorization theorem in QCD. We take into account universal logarithmically enhanced corrections in edge region of phase space by resumming multiple soft-gluon emissions to all orders in the small $Q_T$ region.
We provide a novel development in jet physics by predicting the energy profiles of light-quark and gluon jets in the framework of perturbative QCD. Resumming large logarithmic contributions to all orders in the coupling constant, our predictions are shown to agree well with Tevatron CDF and Large-Hadron-Collider CMS data. We also extend our resummation formalism to the invariant mass distributions of light-quark and gluon jets produced in hadron collisions. The predicted peak positions and heights in jet mass distributions are consistent with CDF data within uncertainties induced by parton dis…
We present the general expressions for the resummation, up to next-to-leading logarithmic accuracy, of Sudakov-type logarithms in processes with an arbirtrary number of hard-scattering partons. These results document the formulae used by the authors in several previous phenomenological studies. The resummation formulae presented here, which are valid for phase-space factorizable observables, determine the resummation correction in a process-independent fashion. All process dependence is encoded in the colour and flavour structure of the leading order and virtual one-loop amplitudes, and in Sud…
We discuss the resummation of the potentially large O((β_0α_s)^n) QCD corrections to the total cross section of the process e^+e^- \to t \bar t near the threshold. In this approximation, the cross section factorization into the short- and long-distance parts is valid. The short-distance correction is reduced to the production vertex renormalization. It amounts to -9.5% and is well under control. The long distance corrections are accounted for as the effect of the coupling's running in the QCD potential. We argue that the accuracy of present predictions for the cross section in the scheme with …
We summarize and extend previous results on the comparison of threshold resummation, performed, using soft-collinear effective theory (SCET), in the Becher-Neubert approach, to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross sections. We show that the logarithmic accuracy of this SCET result can be extended by half a logarithmic order, thereby bringing it in full agreement with the standard QCD result if a suitable choice is made for the soft scale mu_s which characterizes the SCET result. We provide a master formula relating t…
We present a formalism that improves the applicability of perturbative QCD in the current region of semi-inclusive deep inelastic scattering. The formalism is based on all-order resummation of large logarithms arising in the perturbative treatment of hadron multiplicities and energy flows in this region. It is shown that the current region of semi-inclusive DIS is similar to the region of small transverse momenta in vector boson production at hadron colliders. We use this resummation formalism to describe transverse energy flows and charged particle multiplicity measured at the electron-proton…
We explore similarities and differences between widely-used threshold resummation formalisms, employing electroweak boson production as an instructive example. Resummations based on both full QCD and soft-collinear effective theory (SCET) share common underlying factorizations and resulting evolution equations. The formalisms differ primarily in their choices of boundary conditions for evolution, in moment space for many treatments based on full QCD, and in momentum space for treatments based on soft-collinear effective theory. At the level of factorized hadronic cross sections, these choices …
We study the distributions of leptons from the decay of electroweak vector bosons produced in hadron collisions. The effects of the initial state multiple soft-gluon emission, using the Collins--Soper resummation formalism, are included. The resummed results are compared with the next-to-leading-order results for the distributions of the transverse momentum, rapidity asymmetry, and azimuthal angle of the decay leptons.
Fits to the final combined HERA deep-inelastic scattering cross-section data within the conventional DGLAP framework of QCD have shown some tension at low $x$ and low $Q^2$. A resolution of this tension incorporating $\ln(1/x)$-resummation terms into the HERAPDF fits is investigated using the xFitter program. The kinematic region where this resummation is important is delineated. Such high-energy resummation not only gives a better description of the data, particularly of the longitudinal structure function $F_L$, it also results in a gluon PDF which is steeply rising at low $x$ for low scales…
We address the problem of resumming leading clustering logs in QCD jet observables defined using the k_t, CA and SISCone algorithms. We specifically choose the jet mass distribution as an example and calculate up to order(alpha_s^4) clustering-log terms in the series expansion at single-log accuracy. These terms are found to exhibit a pattern of exponentiation and we are thus able to perform an all-orders analytical resummation for the clustering logs. We also numerically calculate the non-global logs at large N_c. We show that our result for the resummation of clustering logs is a very good a…
The resummation of multiple soft gluon emission affects the production rate and kinematic distributions of $W^+h$ (where h is a Higgs boson) and $t \bar b$ pairs at the Tevatron with $\sqrt{s}=2$ TeV. Using the Collins-Soper-Sterman resummation formalism, the production rate is enhanced over the next-to-leading-order (NLO) prediction by 2-3% for the $W^+h$ process, for Higgs boson masses between 80-120 GeV, and over 3% for the $t\bar b$ process for $m_t=175$ GeV. After resummation, the $t\bar b$ rate changes by 12-13% when $m_t$ is varied by $\pm 5$ GeV. Various kinematic distributions are pre…
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.
We study the nonperturbative functions in the Collins--Soper--Sterman resummation formalism by examing Drell--Yan data in both fixed target and collider experiments and then predict the transverse momentum distributions of the $W^\pm$ and $Z^0$ bosons at the Tevatron. Our results differ from that in the literature and agree better with published CDF data. Using statistical arguments, we find a $1\,$fb${}^{-1}$ luminosity at the Fermilab Tevatron should be able to provide useful constraints on the nonperturbative functions.
The procedure to improve the convergence in transverse momentum space of the NLL BFKL kernel using a w-shift is revisited. An accurate approximation to this shift only depending on transverse momenta is presented. This approximation is based on a Bessel function of the first kind with argument depending on the strong coupling and a double logarithm of the ratio of transverse scales. A comparison between different renormalization schemes is also included.
We present new results for QCD corrections to the top-pair invariant mass and top-quark $p_T$ distributions in boosted top-quark pair production at hadron colliders. They are derived from a formalism which allows the joint resummation of soft and small-mass logarithms at NNLL$'$ order, thus taking into account all potentially large corrections in the boosted regime, where the partonic center-of-mass energy is parameterically much larger than the mass of the top quark. We match these results with those from standard soft-gluon resummation away from the small-mass limit to NNLL order and also wi…
In this dissertation a detailed analysis of heavy quark production is given with an emphasis on the resummation of soft gluon corrections. First we calculate the production cross sections for top quark production at the Fermilab Tevatron and for bottom quark production at fixed-target $pp$ experiments, and in particular HERA-B. We consider both the order $α_s^3$ cross sections and the resummation of soft gluon corrections in all orders of QCD perturbation theory. Then we calculate the inclusive transverse momentum and rapidity distributions for top quark production at the Fermilab Tevatron and…
A precise determination of the $W$ boson mass at the CERN LHC requires a theoretical calculation in which the effect of the initial-state multiple soft-gluon emission and the final-state photonic correction are simultaneously included. Here, we present such a calculation and discuss its prediction on a few most relevant distributions of the decay leptons.
The proton spin dependent structure function $g_1^p$ is analysed using the unified scheme incorporating both Altarelli-Parisi evolution and the double $ln^2(1/x)$ effects at low $x$. The latter are found to be very important in the region of $x$ which can possibly be probed at HERA. Predictions for the polarized gluon distribution $ΔG(x)$ at low $x$ are also given.
Resummation of large infrared logarithms in perturbation theory can, in certain circumstances, enhance the sensitivity to small gluon momenta and introduce spurious nonperturbative contributions. In particular, different procedures -- equivalent in perturbation theory -- to organize this resummation can differ by $1/Q$ power corrections. The question arises whether one can formulate resummation procedures that are explicitly consistent with the infrared behaviour of finite-order Feynman diagrams. We explain how this problem can be treated and resolved in Drell-Yan (lepton pair) production and …
We consider the production of a generic system of non-strongly interacting particles with a high total invariant mass M in hadron collisions. We examine the transverse-momentum (q_T) distribution of the system in the small-q_T region (q_T << M), and we present a study of the perturbative QCD contributions that are enhanced by powers of large logarithmic terms of the type ln (M^2/q_T^2). These terms can be resummed to all orders in QCD perturbation theory. The partonic production mechanism of the final-state system can be controlled by quark-antiquark (qqbar) annihilation and/or by gluon fusion…
When computed to next-to-leading order in perturbative QCD, the non-linear Balitsky-Kovchegov (BK) equation for the high-energy evolution of the dipole-hadron scattering appears to be unstable. We show that this instability can be avoided by using the rapidity of the dense hadronic target (instead of that of the dilute dipole projectile) as the evolution time. Using this variable, we construct a collinearly-improved version of the BK equation, where the dominant radiative corrections to the kernel -- those enhanced by double collinear logarithms -- are resummed to all orders.
We investigate the QCD effects in the production of neutral Higgs bosons via bottom quark fusion in both the standard model and the minimal supersymmetric standard model at the CERN Large Hadron Collider. We include the next-to-leading order (NLO) QCD corrections (including supersymmetric QCD) and the threshold resummation effects. We use the soft-collinear effective theory to resum the large logarithms near threshold from soft gluon emission. Our results show that the resummation effects can enhance the total cross sections by about 5% compared with the NLO results.
A precise determination of the W boson mass at the Fermilab Tevatron requires a theoretical calculation in which the effects of the initial-state multiple soft-gluon emission and the final-state photonic correction are simultaneously included . Here, we present such a calculation and discuss its prediction on the transverse mass distribution of the W boson and the transverse momentum distribution of its decay charged lepton, which are the most relevant observables for measuring the W boson mass at hadron colliders.
We thoroughly investigate both transverse momentum and threshold resummation effects on scalar-pseudoscalar pair production via quark-antiquark annihilation at the $13~ \text{TeV}$ Large Hadron Collider at QCD NLO+NLL accuracy. A factorization method is introduced to properly supplement the soft-gluon (threshold) resummation contribution from parton distribution functions to the resummed results obtained by the Collins-Soper-Sterman resummation approach. We find that the impact of the threshold-resummation improved PDFs is comparable to the resummation effect of the partonic matrix element and…
We have derived the coefficients of the highest three 1/x-enhanced small-x logarithms of all timelike splitting functions and the coefficient functions for the transverse fragmentation function in one-particle inclusive e^+e^- annihilation at (in principle) all orders in massless perturbative QCD. For the longitudinal fragmentation function we present the respective two highest contributions. These results have been obtained from KLN-related decompositions of the unfactorized fragmentation functions in dimensional regularization and their structure imposed by the mass-factorization theorem. Th…
We resum distributions that are singular at partonic threshold (the elastic limit) in heavy quark production, in terms of logarithmic behavior in moment space. The method may be applied to a variety of cross sections sensitive to the edge of phase space, including transverse momentum distributions. Beyond leading logarithm, dependence on the moment variable is controlled by a matrix renormalization group equation, reflecting the evolution of composite operators that represent the color structure of the underlying hard scattering. At next-to-leading logarithmic accuracy, these evolution equatio…
We study the kinematic distributions of top--antitop quark pairs produced at the Tevatron, including the effects of initial state and final state multiple soft gluon emission, using the Collins--Soper--Sterman resummation formalism. The resummed results are compared with those predicted by the showering event generator PYTHIA for various distributions involving the top--antitop quark pair and the individual top quark or antiquark. The comparison between the experimental and predicted distributions will be a strong test of our understanding and application of perturbative QCD. Our results indic…
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