We present a general all-order formulation of Sudakov resummation in QCD in terms of dispersion integrals. We show that the Sudakov exponent can be written as a dispersion integral over spectral density functions, weighted by characteristic functions that encode information on power corrections. The characteristic functions are defined and computed analytically in the large-beta_0 limit. The spectral density functions encapsulate the non-Abelian nature of the interaction. They are defined by the time-like discontinuity of specific effective charges (couplings) that are directly related to the familiar Sudakov anomalous dimensions and can be computed order-by-order in perturbation theory. The dispersive approach provides a realization of Dressed Gluon Exponentiation, where Sudakov resummation is enhanced by an internal resummation of running-coupling corrections. We establish all-order relations between the scheme-invariant Borel formulation and the dispersive one, and address the difference in the treatment of power corrections. We find that in the context of Sudakov resummation the infrared-finite-coupling hypothesis is of special interest because the relevant coupling can be uniquely identified to any order, and may have an infrared fixed point already at the perturbative level. We prove that this infrared limit is universal: it is determined by the cusp anomalous dimension. To illustrate the formalism we discuss a few examples including B-meson decay spectra, deep inelastic structure functions and Drell-Yan or Higgs production.
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.
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 consider the higher-order resummation of Sudakov double logarithms in the presence of multiple coupled gauge interactions. The associated evolution equations depend on the coupled $β$ functions of two (or more) coupling constants $α_a$ and $α_b$, as well as anomalous dimensions that have joint perturbative series in $α_a$ and $α_b$. We discuss possible strategies for solving the system of evolution equations that arises. As an example, we obtain the complete three-loop (NNLL) QCD$\otimes$QED Sudakov evolution factor. Our results also readily apply to the joint higher-order resummation of el…
Soft-Collinear Factorization and Sudakov Resummation of Heavy Meson Decay Amplitudes with Effective Field Theories
在这篇论文中，我们介绍了软共线有效理论，它可以被用来证明（或反证）因式分解定理的强耦合常数的所有订单，一些B衰变到轻和高能粒子。具体地说，在重整化群改进的微扰理论中，计算了包含B->X_u l nu和排斥B->gamma l nu的可因式分解振幅到一阶非平凡.研究了B-> Pl nu和B-> Vl nu（P=轻赝标介子，V=轻矢量介子）衰变振幅的形状因子，证明了形状因子受不可因子化的Feynman机制支配.
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）
Starting from the first renormalized factorization theorem for a process described at subleading power in soft-collinear effective theory, we discuss the resummation of Sudakov logarithms for such processes in renormalization-group improved perturbation theory. Endpoint divergences in convolution integrals, which arise generically beyond leading power, are regularized and removed by systematically rearranging the factorization formula. We study in detail the example of the $b$-quark induced $h\toγγ$ decay of the Higgs boson, for which we resum large logarithms of the ratio $M_h/m_b$ at next-to…
The $B$-meson light-cone distribution amplitude is an important non-perturbative quantity arising in the factorization of the amplitudes for many exclusive decays of $B$ mesons, such as $B^-\toγ\,\ell^-\barν$. We reconsider the renormalization-group (RG) equation satisfied by this function and present its solution at next-to-leading order (NLO) in RG-improved perturbation theory in Laplace space and, for the first time, in momentum space and the so-called diagonal (or dual) space. Since the information needed to describe the $B$ decay processes at leading order in $Λ_{\rm QCD}/m_b$ is most dir…
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。
When the allowed range of an observable grows order-by-order in perturbation theory, its perturbative expansion can have discontinuities (as in the $C$ parameter) or discontinuities in its derivatives (as in thrust or heavy jet mass) called Sudakov shoulders. We explore the origin of these logarithms using both perturbation theory and effective field theory. We show that for thrust and heavy jet mass, the logarithms arise from kinematic configurations with narrow jets and deduce the next-to-leading logarithmic series. The left-shoulder logarithms in heavy jet mass ($ρ$) of the form $r\ α_s^n \…
We present a procedure to calculate the Sudakov radiator for a generic recursive infrared and collinear (rIRC) safe observable in two-scale problems. We give closed formulae for the radiator at next-to-next-to-leading-logarithmic (NNLL) accuracy, which completes the general NNLL resummation for this class of observables in the {\tt ARES} method for processes with two emitters at the Born level. As a byproduct, we define a physical coupling in the soft limit, and we provide an explicit expression for its relation to the $\overline{\rm MS}$ coupling up to ${\cal O}(α_s^3)$. This physical couplin…
We consider Drell-Yan production $pp \to Z/γ^* \to \ell^+\ell^-$ with the simultaneous measurement of the $Z$-boson transverse momentum $q_T$ and $0$-jettiness $\mathcal{T}_0$. Since both observables resolve the initial-state QCD radiation, the double-differential cross section in $q_T$ and $\mathcal{T}_0$ contains Sudakov double logarithms of both $q_T/Q$ and $\mathcal{T}_0/Q$, where $Q \sim m_Z$ is the dilepton invariant mass. We simultaneously resum the logarithms in $q_T$ and $\mathcal{T}_0$ to next-to-next-to-leading logarithmic order (NNLL) matched to next-to-leading fixed order (NLO). O…
Quark-antiquark pair (or dijet) production at the electron-ion collider (EIC) has been argued to be one of most important processes that allowing to access the Weizsäcker-Williams (WW) gluon distributions at small $x$ limit. Within the framework of Color Glass Condensate (CGC) effective field theory (EFT), we calculated the dijet cross sections and the azimuthal correlations by including the Sudakov resummations, numerical results shown that the back-to-back correlations are significantly suppressed when the Sudakov resummations are taken into account. In addition, by using the solutions of ru…
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）
