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 result.
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 pr…
We point out that an unorthodox way to describe the production of rapidity gaps in deep inelastic scattering, recently proposed by Buchmüller and Hebecker, suggests a description of the production of heavy quark bound states which is in agreement with data. The approach questions the conventional treatment of the color quantum number in perturbative QCD.
We present a systematic framework to study the threshold contributions of the differential rapidity distribution for the production of any number of colorless particles in the hadronic colliders. This has been achieved based on the universality structure of the soft enhancements associated with the real emissions, along with the factorization property of the differential cross section and the renormalization group invariance. In this formalism, we present a universal soft-collinear operator to compute the soft virtual differential cross section for a generic $2\rightarrow n$ scattering process…
Threshold Resummation of Drell-Yan type colorless processes at LHC
RWTH Aachen University（亚琛工业大学）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Physical Research Laboratory（物理研究实验室）；Indian Institute of Technology Guwahati（古瓦哈提印度理工学院）；Durham University（杜伦大学）
We present the general form of a universal soft-collinear distribution operator to compute the soft-virtual cross-section to next-to-next-to-next-to-next-to-leading order (N$^4$LO) in QCD for a process with any number of final state colorless particles in hadron colliders. By acting this universal operator on the pure virtual corrections, which need to be computed explicitly for a process, the soft-virtual cross-section can be obtained. The operator is constructed by exploiting the factorization and renormalization group evolution of amplitudes in QCD, and the universality of soft gluon contri…
We study the effects of threshold resummation on the rapidity dependence of single-particle-inclusive cross sections, using the prompt photon cross section as an example. We make use of the full resummation formula at next-to-leading logarithmic accuracy and develop a new technique for treating rapidity in resummation. We compare our phenomenological results with those of previous studies and discuss differences and similarities of the two existing resummation formalisms.
We investigate the QCD resummation for the Higgs boson plus a high $P_T$ jet production with large rapidity separations in proton-proton collisions at the LHC. The relevant Balitsky-Fadin-Kuraev-Lipatov (BFKL) and Sudakov logs are identified and resummed. In particular, we apply recent developments of the transverse momentum dependent factorization formalism in the impact factors, which provides a systematic framework to incorporate both the BFKL and Sudakov resummations.
Threshold resummation of rapidity distributions at fixed partonic rapidity
Technische Universität München（慕尼黑工业大学）；Johannes Gutenberg-Universität Mainz（美因茨约翰内斯·古腾堡大学）；Università di Milano and INFN, Sezione di Milano（米兰大学与意大利国家核物理研究所米兰分部）；Università di Genova and INFN, Sezione di Genova（热那亚大学与意大利国家核物理研究所热那亚分部）
We present a derivation of the threshold resummation formula for the Drell-Yan rapidity distribution. Our argument is valid for all values of rapidity and to all orders in perturbative QCD and can be applied to all Drell-Yan processes in a universal way, i.e. both for the production of a virtual photon γ^{*} and the production of a vector boson W^{\pm}, Z^{0}. We show that for the fixed-target experiment E866/NuSea used in current parton fits, the NLL resummation corrections are comparable to NLO fixed-order corrections and are crucial to obtain agreement with the data.
Transverse-momentum dependent (TMD) hadronic wave functions develop light-cone divergences under QCD corrections, which are commonly regularized by the rapidity $ζ$ of gauge vector defining the non-light-like Wilson lines. The yielding rapidity logarithms from infrared enhancement need to be resummed for both hadronic wave functions and short-distance functions, to achieve scheme-independent calculations of physical quantities. We briefly review the recent progress on the rapidity resummation for $B$-meson wave functions which are the key ingredients of TMD factorization formulae for radiative…
We discuss the generalisation of high-energy resummation to rapidity distributions to leading logarithmic accuracy. We test our procedure applying it to Higgs production in gluon-gluon fusion both with finite top mass and in the infinite mass limit. We check that they reproduce the known results at fixed order and we estimate finite top mass corrections to the NLO distribution.
We analyze transverse momentum ($Q_T$) resummation of a colorless final state, e.g. Higgs production in gluon fusion or the production of a lepton pair via the Drell-Yan mechanism, in the limit where the invariant mass of the final state is much less then the center-of-mass energy, i.e. $Q^2\ll s$. We show how the traditional resummation of logarithms of $Q_T/Q$ can be supplemented with the resummation of the leading logarithmic contributions at small $x=Q^2/s$ and we compute the necessary ingredients to perform such joint resummation.
Perturbative corrections beyond leading-log accuracy to BFKL and BK equations, describing the rapidity evolution of QCD scattering amplitudes at high energy, exhibit strong convergence problems due to radiative corrections enhanced by large single and double transverse logs. We identify explicitly the physical origin of double transverse logs and resum them directly in coordinate space as appropriate for BK equation, in terms of an improved local-in-rapidity evolution kernel. Numerical results show the crucial role of double-logarithmic resummation for BK evolution, which is stabilized and slo…
In this paper we discuss the survival probability for exclusive central diffractive production of a colorless small size system at the LHC. This process has a clear signature of two large rapidity gaps. Using the eikonal approach for the description of soft interactions, we predict the value of the survival probability to be about 5~6% for single channel models, while for a two channel model the survival probability is about 3%. The dependence of the survival probability factor (damping factor) on the transverse momenta of the recoiled protons is discussed, and we suggest it be measured at the…
We provide a method for the all order computation of small x contributions at the leading logarithmic level to cross-sections which are differential in rapidity. The method is based on a generalization to rapidity distributions of the high energy (or k_T) factorization theorem hitherto proven for inclusive cross-sections. We apply the method to Higgs production in gluon-gluon fusion, both with finite top mass and in the infinite mass limit: in both cases, we determine all-order resummed expressions, as well as explicit expressions for the leading small x terms up to NNLO. We use our result to …
We demonstrate that theoretical predictions using current resummation techniques for the lepton pair production (LPP) rapidity and $x_F$ distributions can be inconsistent with data in high rapidity and $x_F$ kinematic regions by observing their effect in global fits of parton distribution functions (PDFs). We present an enhanced resummation technique for the LPP rapidity and $x_F$ distributions that agrees with LPP data. The enhanced resummation method is used in conjunction with threshold resummation in deep inelastic scattering (DIS) to perform two global fits of PDFs using the minimal and B…
Jet vetoes are widely used in experimental analyses at the LHC to distinguish different hard-interaction processes. Experimental jet selections require a cut on the (pseudo)rapidity of reconstructed jets, $|η_{\rm jet}| \leq η_{\rm cut}$. We extend the standard jet-$p_T$ (jet-veto) resummation, which implicitly works in the limit $η_{\rm cut}\to\infty$, by incorporating a finite jet rapidity cut. We also consider the case of a step in the required $p_T^{\rm cut}$ at an intermediate value of $|η| \simeq 2.5$, which is of experimental relevance to avoid the increased pile-up contamination beyond…
Gluon-induced processes such as Higgs production typically exhibit large perturbative corrections. These partially arise from large virtual corrections to the gluon form factor, which at timelike momentum transfer contains Sudakov logarithms evaluated at negative arguments $\ln^2(-1) = -π^2$. It has been observed that resumming these terms in the timelike form factor leads to a much improved perturbative convergence for the total cross section. We discuss how to consistently incorporate the resummed form factor into the perturbative predictions for generic cross sections differential in the Bo…
Soft function relevant for transverse-momentum resummation for Drell-Yan or Higgs production at hadron colliders are computed through to three loops in the expansion of strong coupling, with the help of bootstrap technique and supersymmetric decomposition. The corresponding rapidity anomalous dimension is extracted. An intriguing relation between anomalous dimensions for transverse-momentum resummation and threshold resummation is found.
In this paper we study a general framework to perform leading log high energy resummation with complete dependence from the rapidity and the transverse momentum of the studied system. As an application, high energy resummed expression for the Higgs boson production in the effective field theory framework will be derived. Explicit result for this process will be cross-checked against fixed order evaluations up to NNLO. Consistency with known high energy resummation for single differential rapidity or transverse momentum distribution, as well as for inclusive cross section, will also be shown.
We extend our framework for the simultaneous resummation of soft and small-mass logarithms to rapidity distributions in top quark pair production. We give numerical results for the rapidity distribution of the top quark or the anti-top quark, as well as the rapidity distribution of the $t\bar{t}$ pair, finding that resummation effects stabilize the dependence of the differential cross sections on the choice of factorization scale. We compare our results with recent measurements at the Large Hadron Collider and find good agreement. Our results may be useful in the extraction of the gluon parton…
We consider Higgs boson production by gluon fusion in hadron collisions. We study the doubly-differential transverse-momentum (q_T) and rapidity (y) distribution of the Higgs boson in perturbative QCD. In the region of small q_T (q_T << M_H, M_H being the mass of the Higgs boson), we include the effect of logarithmically-enhanced contributions due to multiparton radiation to all perturbative orders. We use the impact parameter and double Mellin moments to implement and factorize the multiparton kinematics constraint of transverse- and longitudinal-momentum conservation. The logarithmic terms a…
We derive a general expression for the threshold resummation of transverse momentum distributions for processes with a colorless final state, by suitably generalizing the renormalization-group based approach to threshold resummation previously pursued by two of us. The ensuing expression holds to all logarithmic orders, and it can be used to extend available results in the literature, which only hold up to the next-to-leading log (NLL) level. We check agreement of our result with the existing NLL result, as well as against the known fixed next-to-leading order results for the Higgs transverse …
We construct an evolution equation for the $B$ meson wave functions in the $k_T$ factorization theorem, whose solutions sum the double logarithms associated with the light-cone singularities, namely, the rapidity logarithms. The derivation is subtler than that of the Sudakov resummation for an energetic light hadron, due to the involvement of the effective heavy-quark field. The renormalization-group evolution in the factorization scale needs to be included in order to derive an ultraviolet-finite and scale-invariant kernel for resumming the rapidity logarithms. It is observed that this kernel…
New results are presented for total ${\rm pp}/ {\rm \bar p p}$ cross-sections, in the framework of our QCD based model (GGPS). This is an improved eikonal mini-jet model, where soft gluon radiation tames the fast energy rise normally present in mini-jet models. We discuss the variability in our predictions and provide a handy parametrization of our results for the LHC. We find that our model predictions span the range $σ_{tot}^{LHC}=100 ^{+10}_{-13} mb$. While this matches nicely with the range of most other models, it does not agree with recent ones which include a "hard" Pomeron, even though…
We derive and solve renormalization group equations that allow for the resummation of subleading power rapidity logarithms. Our equations involve operator mixing into a new class of operators, which we term the "rapidity identity operators", that will generically appear at subleading power in problems involving both rapidity and virtuality scales. To illustrate our formalism, we analytically solve these equations to resum the power suppressed logarithms appearing in the back-to-back (double light cone) limit of the Energy-Energy Correlator (EEC) in $\mathcal{N}$=4 super-Yang-Mills. These logar…
In this contribution we examine the transverse momentum distributions in dijet production at large rapidity intervals at the Tevatron, using the BFKL resummation.
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 present a formalism that sums up both soft-virtual (SV) and next to SV (NSV) contributions to all orders in perturbative QCD for the rapidity distribution of any colorless particle produced in hadron colliders. We have exploited the factorization properties and the renormalisation group (RG) invariance of the differential cross-section to achieve this. Using the state-of-the-art multiloop and multileg results, we determine the complete NSV contributions to third order in strong coupling constant for the rapidity distributions for a pair of leptons in Drell-Yan and also for Higgs boson in gl…
In this paper, using the Higgs production in forward rapidity region in proton-nucleus collisions as an example, we demonstrate that we can construct a systematic formalism for the threshold resummation for forward rapidity particle productions in the saturation formalism. The forward threshold jet function, which satisfies the corresponding renormalization group equation, is introduced into the new factorization formula. This calculation can be easily generalized to other processes, such as single forward hadron productions at forward rapidity region, and have important phenomenological impli…
We examine critically the theoretical underpinnings and phenomenological implications of soft gluon (threshold) resummation of rapidity distributions at a hadron collider, taking Drell-Yan production at the Tevatron and the LHC as a reference test case. First, we show that in perturbative QCD soft gluon resummation is necessary whenever the partonic (rather the hadronic) center-of-mass energy is close enough to threshold, and we provide tools to assess when resummation is relevant for a given process. Then, we compare different prescriptions for handling the divergent nature of the series of r…
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…
The Leding-Logarithmic (LL) gluon Sudakov formfactor is derived from rapidity-ordered BFKL evolution with longitudinal-momentum conservation. This derivation further clarifies the relation between High-Energy and TMD-factorizations and can be extended beyond LL-approximation as well.
We present studies of QCD corrections to dilepton production in transversely polarized pp and \bar{p}p scattering. In particular we briefly discuss the effects of NNLL threshold resummation on the rapidity distribution of the lepton pair.
Using a recent calculation of the perturbative hard part for dilepton production that sums large threshold corrections to all orders in perturbative QCD, we compute the corresponding cross sections. The hard part has been evaluated using principal value resummation and contains all singular momentum-dependent corrections. We also include a resummation of large Sudakov terms, which are independent of parton momenta. We give predictions for the dilepton-mass distribution, the rapidity distribution and the rapidity-integrated $K$-factor at fixed-target energies and compare with various experiment…
I present NNLO approximate calculations, based on NNLL resummation, for top quark differential transverse momentum and rapidity distributions. In particular recent results are presented for top-pair production and single-top production processes and compared to the latest experimental data from the LHC.
We study the factorization and resummation of the $t\bar{t}W^\pm$ production at hadron colliders. The cross section in the threshold limit can be factorized into a convolution of hard and soft functions and parton distribution functions with the soft-collinear effective theory. We calculate the next-to-leading order soft function for the associated production of the heavy quark pair and colorless particle, and we perform the resummation calculation with the next-to-next-to-leading logarithms accuracy. Our results show that the resummation effects reduce the dependence of the cross section on t…
We present recent phenomenological studies, tailored on kinematic configurations typical of current and forthcoming analyses at the LHC, for two novel probe channels of the BFKL resummation of energy logarithms. Particular attention is drawn to the behavior of distributions differential in azimuthal angle and rapidity, where significant high-energy effects are expected.
We present a combined resummation for the transverse momentum distribution of a colorless final state in perturbative QCD, expressed as a function of transverse momentum pt and the scaling variable x. Its expression satisfies three requirements: it reduces to standard transverse momentum resummation to any desired logarithmic order in the limit pt-> 0 for fixed x, up to power suppressed corrections in pt; it reduces to threshold resummation to any desired logarithmic order in the limit x-> 1 for fixed pt, up to power suppressed correction in 1-x; upon integration over transverse momentum it re…
High-energy logarithmic correction are enhanced when the ratio, $x = \frac{Q^2}{s}$ between the typical energy scale of a scattering process $Q$ and the total centre of mass energy available $s$ is small. We discuss recent developments on their resummation in differential cross sections in rapidity, transverse momentum and invariant mass and their application to heavy flavour production at the LHC.
It is suggested that the colorless systems of interacting soft-gluons in large-rapidity-gap events are open dynamical complex systems in which self-organized criticality and BTW-clusters play an important role. Theoretical arguments and experimental evidences supporting such a statistical approach to deep-inelastic scattering are presented.
In this PhD thesis, we analyze and generalize the renormalization group approach to the resummation of large logarithms in the perturbative expansion due to soft and collinear multiparton emissions. In particular, we present a generalization of this approach to prompt photon production. It is interesting to see that also with the more intricate two-scale kinematics that characterizes prompt photon production in the soft limit, it remains true that resummation simply follows from general kinematic properties of the phase space. Also, this approach does not require a separate treatment of indivi…
We present results with soft-gluon resummation for the associated production of a single top quark and a Higgs boson. We present analytical results for the higher-order soft-gluon corrections and numerical results for the total cross section and top-quark transverse momentum and rapidity distributions at LHC energies.
We present a phenomenological study of Drell-Yan pair production at hadron colliders based on the NNLO fixed order calculation and on NNLL resummation of threshold logarithms. We give an argument to prove that resummation effects are relevant also for values of x=M^2/s far from threshold. We compare different prescriptions for the calculation of resummed quantities, emphasizing the differences coming from subleading terms, which are important when x is small. We present phenomenological predictions for Drell-Yan rapidity distributions at the LHC, we study the ambiguity related to the resummati…
We present our predictions for the inclusive production of two heavy quark-antiquark pairs, separated by a large rapidity interval, in the collision of (quasi-)real photons at the energies of LEP2 and of some future electron-positron colliders. We include in our calculation the full resummation of leading logarithms in the center-of-mass energy and a partial resummation of the next-to-leading logarithms, within the Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach.
We study the semi-inclusive limit of the deep inelastic scattering and Drell-Yan (DY) processes in soft collinear effective theory. In this regime so-called threshold logarithms must be resummed to render perturbation theory well behaved. Part of this resummation occurs via the Dokshitzer, Gribov, Lipatov, Altarelli, Parisi (DGLAP) equation, which at threshold contains a large logarithm that calls into question the convergence of the anomalous dimension. We demonstrate here that the problematic logarithm is related to rapidity divergences, and by introducing a rapidity regulator can be tamed. …
We study the power corrections for electroweak boson production that are implied by threshold resummation, which we have extended to massive particles produced at measured transverse momentum, $p_T$, and rapidity. Power corrections in the resulting expressions arise from ambiguities in the low-scale behavior of the perturbative running coupling. Arguing for the relevance of the eikonal approximation, we show that such power corrections begin at order $1/p_T^2$ in full QCD, consistent with fixed-order, massive-gluon analysis. For large-$N$ Mellin moments, the leading behavior is $N^2/p_T^2$, wh…
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.
I present a calculation of next-to-next-to-next-to-leading-order (NNNLO) soft-gluon corrections for differential distributions in top-antitop pair production in hadronic collisions. Approximate NNNLO (aNNNLO) results are obtained from soft-gluon resummation. Theoretical predictions are shown for the top-quark aNNNLO transverse momentum ($p_T$) and rapidity distributions at LHC and Tevatron energies. The aNNNLO corrections enhance previous results for the distributions but have smaller theoretical uncertainties.
Collider experiments have recently measured the production cross section of hard jets separated by a rapidity gap as a function of transverse momentum and gap size. We show that these measurements reveal the relative frequencies for the production of rapidity gaps in quark-quark, quark-gluon and gluon-gluon interactions. The results are at variance with the idea that the exchange of 2 gluons is a first order approximation for the mechanism producing colorless states, i.e. the hard QCD Pomeron. They do qualitatively support the "soft color" or "color evaporation" scheme developed in the context…
We study the resummation of large logarithmic perturbative corrections to the partonic cross sections relevant for the process pp -> W^+- X at the BNL Relativistic Heavy Ion Collider (RHIC). At RHIC, polarized protons are available, and spin asymmetries for this process will be used for precise measurements of the up and down quark and anti-quark distributions in the proton. The corrections arise near the threshold for the partonic reaction and are associated with soft-gluon emission. We perform the resummation to next-to-leading logarithmic accuracy, for the rapidity-differential cross sectio…
In high energy hadron-hadron collisions, dijet production with large rapidity separation proposed by Mueller and Navelet, is one of the most interesting processes which can help us to directly access the well-known Balitsky-Fadin-Kuraev-Lipatov evolution dynamics. The objective of this work is to study the Sudakov resummation of Mueller-Navelet jets. Through the one-loop calculation, Sudakov type logarithms are obtained for this process when the produced dijets are almost back-to-back. These results could play an important role in the phenomenological study of dijet correlations with large rap…
New evidence for the rapidity evolution in Mueller-Navelet dijet production: BFKL, Sudakov, and RG-invariance
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research（鲍里索夫理论物理实验室，核物理研究所）；Physics Department, Ben-Gurion University of the Negev（内盖夫本-古里安大学物理系）；Samara National Research University（萨马拉国立研究大学）
We investigate threshold resummation effects in the production of a color sextet (antitriplet) scalar at next-to-next-to-leading logarithmic (NNLL) order at the LHC in the frame of soft-collinear effective theory. We show the total cross section and the rapidity distribution with NLO+NNLL accuracy, and we compare them with the NLO results. Besides, we use recent dijet data at the LHC to give the constraints on the couplings between the colored scalars and quarks.
We investigate the inclusive hadroproduction of a Higgs boson in association with a jet, featuring large transverse momenta and separated by a large rapidity distance. We propose this reaction, that can be studied at the LHC as well as at new-generation colliding machines, as a novel probe channel for the manifestation of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) dynamics. We bring evidence that high-energy resummed distributions in rapidity and transverse momentum exhibit a solid stability under higher-order corrections, thus offering us a faultless chance to gauge the feasibility of precision…
Partonic cross sections for the production of massive objects in hadronic collisions receive large corrections when the invariant mass of the initial-state partons is just above the production threshold. Since typically the center-of-mass energy of the hadronic collision is much higher than the mass of the heavy objects, it is not obvious that these contributions translate into large corrections to the hadronic cross section. Using a recent approach to threshold resummation based on effective field theory, we quantify to which extent the fall-off of the parton densities at high x leads to a dy…
Finding an efficient and compelling regularization of soft and collinear degrees of freedom at the same invariant mass scale, but separated in rapidity is a persistent problem in high-energy factorization. In the course of a calculation, one encounters divergences unregulated by dimensional regularization, often called rapidity divergences. Once regulated, a general framework exists for their renormalization, the rapidity renormalization group (RRG), leading to fully resummed calculations of transverse momentum (to the jet axis) sensitive quantities. We examine how this regularization can be i…
Many observables in QCD rely upon the resummation of perturbation theory to retain predictive power. Resummation follows after one factorizes the cross section into the rele- vant modes. The class of observables which are sensitive to soft recoil effects are particularly challenging to factorize and resum since they involve rapidity logarithms. In this paper we will present a formalism which allows one to factorize and resum the perturbative series for such observables in a systematic fashion through the notion of a "rapidity renormalization group". That is, a Collin-Soper like equation is rea…
We calculate several differential cross sections for Z0 and high-pT jet production in the forward rapidity region at the LHC using the hybrid High Energy Factorization. We test various unintegrated gluon distributions involving subleading BFKL effects (such as kinematic constraint, running strong coupling and DGLAP correction) and compare the results with experimental data obtained by the LHCb experiment. We find that the hard scale dependence of unintegrated gluon distributions, which effectively resums the Sudakov-type logarithms on the top of the resummation of the small x logarithms, is es…
