The production of vector bosons in association with jets contains at least two unrelated scales. The first is the mass of the vector boson m_V and the second is the hard interaction scale giving rise to large transverse momenta of the produced jets. The production cross sections depend logarithmically on the ratio of these scales, which can lead to a poor convergence in fixed order perturbation theory. We illustrate how to resum all leading logarithmic terms using effective theory methods, and show that they can be resummed by a simple choice of the factorization scale. Implementing this scale choice we show that the large discrepancies between next-to-leading calculations and leading order calculations using more traditional choices of scales disappear.
We study the effect of soft gluon resummation on the gaps-between-jets cross-section at the LHC. We review the theoretical framework that enables one to sum logarithms of the hard scale over the veto scale to all orders in perturbation theory. We then present a study of the phenomenological impact of Coulomb gluon contributions and super-leading logarithms on the gaps between jets cross-section at the LHC.
I derive an all-order resummation formula for the logarithmically enhanced contributions proportional to $\frac{α_s^n}{x \pm ξ} \log (\frac{ξ\pm x}{2ξ})^k$ in the quark coefficient function of deeply-virtual-Compton scattering and the pion-photon transition form factor in momentum space. The resummation is performed at the next-to-next-to-leading logarithmic accuracy. The key observation is that the quark coefficient function itself factorizes in the $x \rightarrow \pm ξ$ limit, which allows for a resummation using renormalization group equations. A preliminary numerical analysis suggests that…
The large double logarithm in loop-induced processes is one kind of logarithm at subleading power, which has a different origin from Sudakov double logarithms. We develop a method with soft-collinear effective theory to resum these large double logarithms to all orders in the strong coupling constant.
We extend the threshold resummation of the large logarithms $\ln x$ which appear in factorization formulas for exclusive $B$ meson decays, $x$ being a spectator momentum fraction, to the next-to-leading-logarithm (NLL) accuracy. It is shown that the NLL resummation effect provides suppression in the end-point region with $x\sim 0$ stronger than the leading-logarithm (LL) one, and thus improves perturbative analyses of the above processes. We revisit the $B\to Kπ$ decays under the NLL resummation, and find that it induces 20-25\% variation of the direct CP asymmetries compared to those from the…
We construct an evolution equation for the invariant-mass distribution of light-quark and gluon jets in the framework of QCD resummation. The solution of the evolution equation exhibits a behavior consistent with Tevatron CDF data: the jet distribution vanishes in the small invariant-mass limit, and its peak moves toward the high invariant-mass region with the jet energy. We also construct an evolution equation for the energy profile of the light-quark and gluon jets in the similar framework. The solution shows that the energy accumulates faster within a light-quark jet cone than within a gluo…
We summarize recent developments in the study of high-energy resummation effects in Mueller-Navelet jets production at the LHC and discuss possible relations with multiparton interactions.
A factorization formalism for jet processes involving massive colored particles such as the top quark is developed, extending earlier results for the massless case. The factorization of soft emissions from the underlying hard process is implemented in an effective field theory framework, which forms the basis for the resummation of large logarithms. The renormalization group evolution giving rise to non-global logarithms is implemented into a parton shower code in the large-$N_c$ limit. After a comparison of the massive and massless radiations patterns, the cross section for $t\bar{t}$ product…
Large logarithms that arise in cross sections due to the collinear and soft singularities of QCD are traditionally treated using parton showers or analytic resummation. Parton showers provide a fully-differential description of an event but are challenging to extend beyond leading logarithmic accuracy. On the other hand, resummation calculations can achieve higher logarithmic accuracy but often for only a single observable. Recently, there have been many resummation calculations that jointly resum multiple logarithms. Here we investigate the benefits and limitations of joint resummation in a c…
We present version 2.1 of the High Energy Jets (HEJ) event generator for hadron colliders. HEJ is a Monte Carlo generator for processes at high energies with multiple well-separated jets in the final state. To achieve accurate predictions, conventional fixed-order perturbative QCD is supplemented with an all-order resummation of large high-energy logarithms. The new version 2.1 now supports processes with final-state leptons originating from a charged or neutral vector boson together with multiple jets, in addition to processes available in earlier versions. Furthermore, the all-order resummat…
In this article we show how the resummation of infrared and collinear logarithms within Soft-Collinear Effective Theory (SCET) can be formulated in a way that makes it suitable for a Monte-Carlo implementation. This is done by applying the techniques developed for automated resummation using the branching formalism, which have resulted in the general resummation approach CAESAR/ARES. This work builds a connection between the two resummation approaches, and paves the way to automated resummation in SCET. As a case study we consider the resummation of the thrust distribution in electron-positron…
We discuss the resummation of the large logarithmic terms appearing in the heavy quark effects on parton distribution functions inside the virtual photon. We incorporate heavy quark mass effects by changing the initial condition of the leading-order DGLAP evolution equation. In a certain kinematical limit, we recover the logarithmic terms of the next-to-leading order heavy quark effects obtained in the previous work. This method enables us to resum the large logarithmic terms due to heavy quark mass effects on the parton distributions in the virtual photon. We numerically calculate parton dist…
Over the past few years considerable progress has been made on the resummation of double-logarithmically enhanced threshold (large-x) and high-energy (small-x) higher-order contributions to the splitting functions for parton and fragmentation distributions and to the coefficient functions for inclusive deep-inelastic scattering and semi-inclusive e^+e^- annihilation. We present an overview of the methods which allow, in many cases, to derive the coefficients of the highest three logarithms at all orders in the strong coupling from next-to-next-to-leading order results in massless perturbative …
We present all-order results for the highest three large-x logarithms of the splitting functions P_qg and P_gq and of the coefficient functions C_phi,q, C_2,g and C_L,g for structure functions in Higgs- and gauge-boson exchange DIS in massless perturbative QCD. The corresponding coefficients have been derived by studying the unfactorized partonic structure functions in dimensional regularization independently in terms of their iterative structure and in terms of the constraints imposed by the functional forms of the real- and virtual-emission contributions together with their Kinoshita--Lee-Na…
In this talk we report on the recent progresses on IR logarithms resummation for the Thrust distribution in e^{+}e^{-} collisions. Using renormalisation group (RG) evolution in Laplace space, the resummation of logarithmically enhanced corrections is performed to next-to-next-to-leading logarithmic (NNLL) accuracy. To combine the resummed expressions with the fixed-order results, we derive the log(R)-matching and R-matching of the NNLL approximation to the fixed-order NNLO distribution.
In the context of inter-jet energy flow, we present the first quantitative result of the resummation of non-global logarithms at finite N_c. This is achieved by refining Weigert's approach in which the problem is reduced to the simulation of associated Langevin dynamics in the space of Wilson lines. We find that, in e+e- annihilation, the exact result is rather close to the result previously obtained in the large-N_c mean field approximation. However, we observe enormous event-by-event fluctuations in the Langevin process which may have significant consequences in hadron collisions.
Explicit applications of factorization theorems for processes at hadron colliders near the hadronic endpoint have largely focused on simple final states with either no jets (e.g., Drell-Yan) or one inclusive jet (e.g., deep inelastic scattering and prompt photon production). Factorization for the former type of process gives rise to a soft function that depends on timelike momenta, whereas the soft function for the latter type depends on null momenta. We derive in soft-collinear effective theory a factorization theorem that allows for an arbitrary number of jets, where the jets are defined wit…
We consider the associated production of a vector or Higgs boson with a jet in hadronic collisions. When the transverse momentum $q_T$ of the boson-jet system is much smaller than its invariant mass $Q$, the QCD perturbative expansion is affected by large logarithmic terms that must be resummed to all orders. We discuss the all-order resummation structure of the logarithmically enhanced contributions up to next-to-leading logarithmic accuracy. Resummation is performed at the differential level with respect to the kinematical variables of the boson-jet system. Soft-parton radiation produces azi…
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…
More than 25 years ago, Mueller and Navelet proposed to study the production of two jets separated by a large interval of rapidity at hadron colliders to look for high-energy resummation effects. We here present the results of a next-to-leading logarithmic BFKL study of the azimuthal decorrelation of these jets. This includes next-to-leading corrections both to the Green's function and to the jet vertices. We compare our results with recent LHC data and results obtained in a fixed order treatment.
We obtain a prediction for the hadron-collider event-shape variable transverse thrust in which the terms enhanced in the dijet limit are resummed to next-to-next-to-leading logarithmic accuracy. Our method exploits universality properties made manifest in the factorized expression for the cross section and only requires one-loop calculations. The necessary two-loop ingredients are extracted using known results and existing numerical codes. Our technique is general and applicable to other observables as well.
We present a calculation of non-global logs at finite $\mathrm{N_c}$ for the hemisphere mass distribution in $e^+e^-\to 2$ jets at single log accuracy up to fifth order in the strong coupling constant. Our results suggest a possible all-orders resummation of these large logs into an exponential. Comparing our results to those at large $\mathrm{N_c}$, recently reported in literature, we find an agreement. We additionally compare our findings with the numerical all-orders resummation at large $\mathrm{N_c}$ and discuss the significance of neglected finite-$\mathrm{N_c}$ corrections on the said d…
We consider the transverse-momentum (qT) distribution of a diphoton pair produced in hadron collisions. At small values of qT , we resum the logarithmically-enhanced perturbative QCD contributions up to next-to-next-to-leading logarithmic accuracy. At intermediate and large values of qT, we consistently combine resummation with the known next-to-leading order perturbative result. All perturbative terms up to order α_S^2 are included in our computation which, after integration over qT, reproduces the known next-to-next-to-leading order result for the diphoton pair production total cross section…
A method is developed for calculating the jet mass distribution at hadron colliders using an expansion about the kinematic threshold. In particular, we consider the mass distribution of jets of size R produced in association with a hard photon at the Large Hadron Collider. Expanding around the kinematic threshold, where all the energy goes into the jet and the photon, provides a clean factorization formula and allows for the resummation of logarithms associated with soft and collinear divergences. All of the large logarithms of jet mass are resummed at next-to-leading logarithmic level (NLL), …
We compute the resummed on-shell $W^+ W^-$ production cross section under a jet-veto at the LHC to partial N$^3$LL order matched to the fixed order NNLO result. Differential NNLO cross sections are obtained from an implementation of $q_T$ subtraction in Sherpa. The two-loop virtual corrections to the $q \bar q \rightarrow W^+ W^-$ amplitude, used in both fixed order and resummation predictions, are extracted from the public code {\tt qqvvamp}. We perform resummation using soft collinear effective theory (SCET), with approximate beam functions where only the logarithmic terms are included at tw…
We study the transverse momentum resummation for dijet correlation in hadron collisions based on the Collins-Soper-Sterman formalism. The complete one-loop calculations are carried out in the collinear factorization framework for the differential cross sections at low imbalance transverse momentum between the two jets. Important cross checks are performed to demonstrate that the soft divergences cancelled out between different diagrams, and in particular, those associated with final state jets. The leading and sub-leading logarithms are identified. All order resummation is derived following th…
Incorporating all recent theoretical advances, we resum soft-gluon corrections to the total $t\bar t$ cross-section at hadron colliders at the next-to-next-to-leading logarithmic (NNLL) order. We perform the resummation in the well established framework of Mellin $N$-space resummation. We exhaustively study the sources of systematic uncertainty like renormalization and factorization scale variation, power suppressed effects and missing two- and higher-loop corrections. The inclusion of soft-gluon resummation at NNLL brings only a minor decrease in the perturbative uncertainty with respect to t…
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…
We present a flexible Monte Carlo implementation of the perturbative framework of High Energy Jets, describing multi-jet events at hadron colliders. The description includes a resummation which ensures leading logarithmic accuracy for large invariant mass between jets, and is matched to tree-level accuracy for multiplicities up to 4 jets. The resummation includes all-order hard corrections, which become important for increasing centre-of-mass energy of the hadronic collision. We discuss observables relevant for confronting the perturbative framework with 7 TeV data from the LHC, and the impact…
Resummation of double logarithms in electroweak high energy processes
在未来TeV范围内的线性$e^+e^-$对撞机实验中，源于大质量玻色子交换的Sudakov双粒子可以导致对可观察过程的截面的显著修正。这些效应对于Next Linear Collider的高精度目标非常重要。我们利用基于规范不变色散方法的红外演化方程，得到了散射振幅的双对数渐近性，并讨论了在规范对称性破缺的情况下，如何将其应用于电弱过程的标准模型。讨论了双对数效应对无辐射过程和伴随软规范玻色子辐射过程的影响。在所有的情况下，Sudakov双矩阵被发现指数。我们还讨论了Regge类过程中出现的非Sudakov型双对数效应。
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…
