In the collinear factorization of the form factor for the transition $γ^* π^0 \to π$ the hard part contains double log terms. These terms will spoil the perturbative expansion of the hard part. A simple exponentiation for resummation leads to divergent results. We study the resummation of these double log's. We make an analysis to show the origin of the double log's. With the understanding of the origin one can introduce soft factors and Nonstandard Light-Cone Wave Functions(NLCWF) to derive a factorized form for the form factor, where the hard part does not contain the double log's. There is a perturbative relation between NLCWF and the standard Light-Cone Wave Function(LCWF). Beside the renormalization scale $μ$ the introduced NLCWF's and soft factors have extra scales to characterize the double log's. Using the evolutions of the extra scales and the relation we can do the resummation of the double log's perturbatively in sense that LCWF's are the only nonpertubative objects in the resumed formula. Our results with some models of LCWF show that there is a significant difference between numerical predictions with or without the resummation.
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…
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…
The QCD Trace Anomaly in Pion Gravitational Form Factors with Sudakov Resummation
Dipartimento di Matematica e Fisica, Università del Salento（萨伦托大学数学与物理系）；INFN Sezione di Lecce（意大利国家核物理研究所莱切分部）；National Centre for HPC, Big Data and Quantum Computing（高性能计算、大数据与量子计算国家中心）；CNR Nanotec（意大利国家研究委员会纳米技术研究所）
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 sum the leading logarithms $α_s^n \ln^{2 n-1}(1-z)$, n=1,2,... near the kinematic threshold $z=m_H^2/\hat{s}\to 1$ at next-to-leading power in the expansion in (1-z) for Higgs production in gluon fusion. We highlight the new contributions compared to Drell-Yan production in quark-antiquark annihilation and show that the final result can be obtained to all orders by the substitution of the colour factor $C_F\to C_A$, confirming previous fixed-order results and conjectures. We also provide a numerical analysis of the next-to-leading power leading logarithms, which indicates that they are nume…
For many observables, the most difficult part of a single logarithmic resummation is the analytical treatment of the observable's dependence on multiple emissions. We present a general numerical method, which allows the resummation specifically of these single logarithms. Some first applications and new results for the thrust major, the oblateness and the two-jet rate in the Durham algorithm are also presented.
We present a comprehensive study of high-energy double logarithms in inclusive DIS. They appear parametrically as alpha_s^n ln^{2n-k} x at the n-th order in perturbation theory in the splitting functions for the parton evolution and the coefficient functions for the hard scattering process, and represent the leading corrections at small $x$ in the flavour non-singlet case. We perform their resummation, in terms of modified Bessel functions, to all orders in full QCD up to NNLL accuracy, and partly to N^3LL and beyond in the large-n_c limit, and provide fixed-order expansions up to five loops. …
