Eric Laenen, Lorenzo Magnea, Gerben Stavenga, Chris D. White
The eikonal approximation is at the heart of many theoretical and phenomenological studies involving multiple soft gauge boson emissions in high energy physics. We describe our efforts towards the extension of the eikonal approximation for scattering amplitudes to the first subleading power in the soft momentum.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Dressed Gluon Exponentiation is a well known method to study power corrections. We present here its eikonalized version -- Eikonal Dressed Gluon Exponentiation (EDGE) \cite{Agarwal:2020uxi} to determine the dominant power corrections to shape variables such as Thrust, $ C $- parameter, and Angularity. Our method remarkably simplifies the calculations.
Event shapes are classical tools for the determination of the strong coupling and for the study of hadronization effects in electron-positron annihilation. In the context of analytical studies, hadronization corrections take the form of power-suppressed contributions to the cross-section, which can be extracted from the perturbative ambiguity of Borel-resummed distributions. We propose a simplified version of the well-established method of Dressed Gluon Exponentiation (DGE), which we call Eikonal DGE (EDGE), which determines all dominant power corrections to event shapes by means of strikingly…
We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting with a soft gauge field is represented as a Wilson line for a semi-infinite line segment, together with calculable fluctuations. Combining such line segments, we show that exponentiation in an abelian field theory follows immediately from standard path-integral combinatorics. In the non-abelian case, w…
The aim of this note is to explore the interplay between the eikonal resummation in impact-parameter space and the exponentiation of infrared divergences in momentum space for gravity amplitudes describing collisions of massive objects. The eikonal governs the classical dynamics relevant to the two-body problem, and its infrared properties are directly linked to the zero-frequency limit of the gravitational wave emission spectrum and to radiation-reaction effects. Combining eikonal and infrared exponentiations it is possible to derive these properties at a given loop order starting from lower-…
We provide a recursive diagrammatic prescription for the exponentiation of gauge theory amplitudes involving products of Wilson lines and loops. This construction generalizes the concept of webs, originally developed for eikonal form factors and cross sections with two eikonal lines, to general soft functions in QCD and related gauge theories. Our coordinate space arguments apply to arbitrary paths for the lines.
We use $\mathcal N=8$ supergravity as a toy model for understanding the dynamics of black hole binary systems via the scattering amplitudes approach. We compute the conservative part of the classical scattering angle of two extremal (half-BPS) black holes with minimal charge misalignment at $\mathcal O(G^3)$ using the eikonal approximation and effective field theory, finding agreement between both methods. We construct the massive loop integrands by Kaluza-Klein reduction of the known $D$-dimensional massless integrands. To carry out integration we formulate a novel method for calculating the …
In calculations of (semi-) inclusive events within perturbative Quantum Chromodynamics, large logarithmic corrections arise from certain kinematic regions of interest which need to be resummed. When resumming soft gluon effects one encounters quantities built out of eikonal or Wilson lines (path ordered exponentials). In this thesis we develop a simplified method to calculate higher orders of the singular coefficients of parton distribution functions which is based on the exponentiation of cross sections built out of eikonal lines. As an illustration of the method we determine the previously u…
Soft gluon exponentiation in non-abelian gauge theories can be described in terms of webs. So far this description has been restricted to amplitudes with two hard partons, where webs were defined as the colour-connected subset of diagrams. Here we generalise the concept of webs to the multi-leg case, where the hard interaction involves non-trivial colour flow. Using the replica trick from statistical physics we solve the combinatorial problem of non-abelian exponentiation to all orders. In particular, we derive an algorithm for computing the colour factor associated with any given diagram in t…
We consider the problem of soft gluon resummation for gauge theory amplitudes and cross sections, at next-to-eikonal order, using a Feynman diagram approach. At the amplitude level, we prove exponentiation for the set of factorizable contributions, and construct effective Feynman rules which can be used to compute next-to-eikonal emissions directly in the logarithm of the amplitude, finding agreement with earlier results obtained using path-integral methods. For cross sections, we also consider sub-eikonal corrections to the phase space for multiple soft-gluon emissions, which contribute to ne…
We extend the study of corrections to the eikonal approximation that was initiated in Ref. \cite{Altinoluk:2014oxa} to higher orders. These corrections associated with the finite width of the target are investigated and the gluon propagator in background field is calculated at next-to-next-to-eikonal accuracy. The result is then applied to the single inclusive gluon production cross section at central rapidities and the light-front helicity asymmetry, in pA collisions, in order to analyse these observables beyond the eikonal limit. The next-to-next-to-eikonal corrections to the unpolarized cro…
We study corrections suppressed by one power of the soft gluon energy to the resummation of threshold logarithms for the Drell-Yan cross section and for Deep Inelastic structure functions. While no general factorization theorem is known for these next-to-eikonal (NE) corrections, it is conjectured that at least a subset will exponentiate, along with the logarithms arising at leading power. Here we develop some general tools to study NE logarithms, and we construct an ansatz for threshold resummation that includes various sources of NE corrections, implementing in this context the improved coll…
Dijet production in DIS off a large nucleus at next-to-eikonal accuracy in a Gaussian model within the CGC framework
在CGC框架内，利用高斯模型研究深非弹性散射中二喷注产生的下一阶修正，发现其仅由特定算符和三点相关函数决定。
We revisit the calculation of quark and scalar propagators in a gluon background field at Next-to-Eikonal accuracy, which will provide the first power correction to scattering processes in the high-energy limit, including gluon saturation effects. The two main results of our study are as follows. First, we derive a very general Next-to-Eikonal expansion of the quark propagator in terms of the scalar propagator, which allows us to isolate spinor-specific Next-to-Eikonal corrections from the universal ones. Second, we present a new method allowing, for the first time, a systematic calculation of…
DIS dijet production at next-to-eikonal accuracy in the CGC
该研究在色玻璃凝聚（CGC）框架下推导了全次近轴阶包含性DIS双喷注产生截面，纳入靶有限宽度、夸克与背景场横向分量相互作用及靶动力学三类修正，完善了相关过程的高阶修正计算。
DIS dijet production at next-to-eikonal accuracy in the CGC
该研究在CGC偶极子形式下计算低x DIS双喷注产生，系统纳入靶有限宽度、横向背景场相互作用及z⁻依赖动力学等次沿修正。
We present a new method to systematically include corrections to the eikonal approximation in the background field formalism. Specifically, we calculate the subleading, power-suppressed corrections due to the finite width of the target or the finite energy of the projectile. Such power-suppressed corrections involve Wilson lines decorated by gradients of the background field - thus related to the density - of the target. The method is of generic applicability. As a first example, we study single inclusive gluon production in pA collisions, and various related spin asymmetries, beyond the eikon…
We derive Next-to-Eikonal (NEik) corrections to the background quark propagator, which stem from (i) considering a finite longitudinal width target instead of an infinitely thin shockwave and (ii) including the interaction of the quark with the transverse components of the background field. These two different corrections to the eikonal approximation combine together and provides a gauge covariant expression for the quark propagator at NEik accuracy. We then apply our results to quark (or antiquark) scattering on a nucleus at NEik accuracy, considering both unpolarized cross section and helici…
Next-to-Leading Order corrections to the Next-to-Eikonal DIS structure functions
本文研究了次Eikonal DIS结构函数在次领先阶的修正，发现纵向结构函数修正有限，而横纵结构函数存在发散问题，并进行了发散分析。
Next-to-leading power gluon TMDs from back-to-back DIS dijets at next-to-eikonal accuracy at low x
在CGC有效场论中，于次厄ikonal精度计算低x下背对背DIS双喷注的次领头幂次胶子TMD，强调三点关联函数及其对应，并给出双喷注截面。
Back-to-back dijet production in DIS at next-to-eikonal accuracy and twist-3 gluon TMDs
本文在次程函精度下研究小x深度非弹性散射中背靠背双喷注产生，将其表示为扭度-2和扭度-3胶子TMD的因子化形式，并发现新的扭度-3胶子TMD及三胶子场强张量关联子。
Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$
研究在低$x_{Bj}$下，通过次eikonal修正探讨DIS和SIDIS的dipole因子化，区分横向和纵向极化光子对修正的影响。
Forward parton-nucleus scattering at next-to-eikonal accuracy in the CGC
本文推导了CGC框架下胶子与夸克传播子的完整次程函修正，并计算了夸克-核与胶子-核散射中前向快度夸克和胶子产生的单举截面。
Non-factorizable virtual corrections to Higgs boson production in weak boson fusion beyond the eikonal approximation
本文计算弱玻色子聚变希格斯产生中超越 eikonal 近似的领头幂次虚修正，发现其受横动量、质量和快度影响，并使基准截面贡献降低约 O(30)%。
The triple differential spectrum in \bar{B} -> X_u l \barν is computed by Dressed Gluon Exponentiation (DGE). In this framework the on-shell calculation, converted into hadronic variables, can be directly used as an approximation to the meson decay spectrum, without involving a leading-power non-perturbative function. Sudakov resummation for the fully differential \bar{B} -> X_u l \barν width is formulated in moment space, where moments are defined using the ratio between the lightcone momentum components of the partonic jet p^+/p^- and the hard scale is p^-. In these variables the corresponde…
Quark TMDs from back-to-back dijet production at forward rapidities in pA collisions beyond eikonal accuracy in the CGC
本研究在次eikonal精度下研究pA碰撞前向快度双喷注产生，考虑靶夸克背景场修正，计算各通道散射振幅，得到背对背截面因子化表达式，其中包含夸克TMD与硬因子。
Colour structure of next-to-eikonal correlator webs at three loops
本文研究三圈阶次程函关联子网的颜色结构，建立次程函与程函Cweb的关系，并利用直接构造方法获得首次出现的非平凡混合矩阵。
Exponentiation of soft quark effects from the replica trick
该研究利用复制技巧证明多重极软（反）夸克与胶子辐射可在振幅或截面层面指数化，推广了Wilson线算符，结果具普适性，并以深度非弹性散射的次领头道修正为例验证了结论。
Probing quark transverse momentum distributions in the Color Glass Condensate: quark-gluon dijets in Deep Inelastic Scattering at next-to-eikonal accuracy
本研究采用色玻璃凝聚方法，在次程函近似下研究高能深度非弹性散射中的夸克-胶子双喷注产生，推导截面因子化表达式，提出背景抑制方案，为电子离子对撞机探测夸克横动量依赖分布提供新方法。
The modified evolution equation for parton distributions of Dokshitzer, Marchesini and Salam is extended to non-singlet Deep Inelastic Scattering coefficient functions and the physical evolution kernels which govern their scaling violation. Considering the x->1 limit, it is found that the leading next-to-eikonal logarithmic contributions to the momentum space physical kernels at any loop order can be expressed in term of the one loop cusp anomalous dimension, a result which can presumably be extended to all orders in (1-x). Similar results hold for fragmentation functions in semi-inclusive e^{…
The thrust distribution in e+e- annihilation is calculated exploiting its exponentiation property in the two-jet region t = 1-T << 1. We present a general method (DGE) to calculate a large class of logarithmically enhanced terms, using the dispersive approach in renormalon calculus. Dressed Gluon Exponentiation is based on the fact that the exponentiation kernel is associated primarily with a single gluon emission, and therefore the exponent is naturally represented as an integral over the running coupling. Fixing the definition of Lambda is enough to guarantee consistency with the exact expon…
We describe a new framework for soft gluon resummation, based on path integral methods. The approach recovers previous results obtained in the eikonal approximation, in which all emitted gluons become soft. Furthermore, a clear physical interpretation allows straightforward extension of the framework to beyond the eikonal approximation, and we use this to classify the structure of next-to-eikonal corrections to matrix elements.
Small $x$ Physics Beyond Eikonal Approximation: an Effective Hamiltonian Approach
本文提出一种超越程函近似的有效哈密顿量方法，在冲击波形式体系中纳入自旋自由度，揭示次程函阶背景胶子场诱导胶子辐射及其与色电偏振Wilson线关联子的关系。
We consider the recently developed diagrammatic approach to soft-gluon exponentiation in multiparton scattering amplitudes, where the exponent is written as a sum of webs - closed sets of diagrams whose colour and kinematic parts are entangled via mixing matrices. A complementary approach to exponentiation is based on the multiplicative renormalizability of intersecting Wilson lines, and their subsequent finite anomalous dimension. Relating this framework to that of webs, we derive renormalization constraints expressing all multiple poles of any given web in terms of lower-order webs. We exami…
Non-eikonal corrections to dijet production in DIS
本文研究了在深度非弹性散射中双喷注产生中的非Eikonal修正，重点分析了核纵向尺寸有限性带来的影响，并通过谐振子近似计算了修正后的路径积分表达式。
Next-to-eikonal corrections to dijet production in Deep Inelastic Scattering in the dilute limit of the Color Glass Condensate
该研究在色玻璃凝聚框架下分析核靶深度非弹性散射双喷注的近程程函修正，构建大核线性模型推导解析表达式，结合EIC能区数值验证并对比程函近似下的不同模型结果。
Reggeization of quarks from next-to-eikonal high-energy QCD
本文通过Wilson线方法构建了QCD中夸克Regge化的完整表述，推导了其快度演化，并推广到有质量夸克，表明该算子直到次领头对数精度仍是本征态。
The interaction of the partonic fluctuation of the virtual photon in deep inelastic scattering with soft color fields describing the hadron is treated in an eikonal approximation. It is known that, in this approach, the small-x limit of the leading-order gluon distribution xg(x,Q^2) is a constant characterizing the averaged local field strength in the target. Matching the next-to-leading order calculation in this semiclassical framework with the one-loop parton model result, we obtain the next-to-leading order contribution to xg(x,Q^2). It shows a ln(1/x) enhancement at small x and is sensitiv…
We present a computation of the global soft function for single-inclusive hadronic jet production at next-to-next-to-leading order (NNLO) in the strong coupling constant involving four light-like Wilson lines. Our soft function belongs to SCET$_{\text I}$ observables obeying the non-Abelian exponentiation theorem. We provide the calculation of the soft function involving four collinear light-cone directions for all $2\rightarrow2$ processes extending the previous result. We perform the threshold resummation for these processes at the next-to-next-to-leading logarithmic accuracy and present the…
We compute next to eikonal (NE) and next to next to eikonal (NNE) corrections to the Lipatov vertex due to a finite target thickness. These arise from electric field insertions into the eikonal Wilson lines. We then derive a $k_T$-factorization formula for single inclusive gluon production at NNE accuracy and find that nuclear effects are absent. We also analyze NNE corrections to two-gluon production where some of the contributions are found to exhibit corrections proportional to $A^{2/3}$.
We compute the differential B -> X_s gamma decay width in the Standard Model as a function of the photon energy using Dressed Gluon Exponentiation (DGE). The resummed spectrum is matched with the fixed-order expansion, making use of the next-to-next-to-leading order (NNLO) results for the matrix element of the magnetic dipole interaction O_7 and NLO ones for other operators in the effective Weak Hamiltonian. We develop a new technique to implement constraints on the analytic structure of the Sudakov factor in moment space. This improves the behavior of the resummed spectrum away from the Sudak…
Back-to-back dijet production in DIS with finite-energy corrections and twist-3 gluon TMDs
该研究在小 x 的深度非弹性散射中计算反向反 jets 产率，通过 TMD 部子分布表达，并探讨了次 eikonal 修正与扭-3 胶子 TMDs 的关系。
The complete soft-enhanced and virtual-gluon contributions are derived for the quark coefficient functions in semi-inclusive e^+e^- annihilation to the third order in massless perturbative QCD. These terms enable us to extend the soft-gluon resummation for the fragmentation functions by two orders to the next-to-next-to-next-to-leading logarithmic (N^3LL) accuracy. The resummation exponent is found to be the same as for the structure functions in inclusive deep-inelastic scattering. This finding, together with known results on the higher-order quark form factor, facilitates the determination o…
We perform a case study of the behavior of gluon radiation beyond the soft approximation, using as an example the Drell-Yan production cross section at NNLO. We draw a careful distinction between the eikonal expansion, which is in powers of the soft gluon energies, and the expansion in powers of the threshold variable $1 - z$, which involves important hard-collinear effects. Focusing on the contribution to the NNLO Drell-Yan K-factor arising from real-virtual interference, we use the method of regions to classify all relevant contributions up to next-to-leading power in the threshold expansion…
Quasi-Classical Gluon Fields and Low's Soft Theorem at Small $x$
该研究推导了致密核区软胶子经典杨-米尔斯方程的次程函阶解，验证了小x下Low软定理可通过稀薄区单胶子态间准经典色电场非对角矩阵元得到，并提出扩展该定理以纳入致密区胶子饱和效应。
We present a systematic framework for the calculation of soft functions that are defined in terms of $N\geq2$ light-like Wilson lines. The formalism represents an extension of a method that we developed earlier for the calculation of dijet soft functions to the general $N$-jet case. We discuss the technical aspects of this generalisation, focussing on SCET-1 soft functions that obey the non-Abelian exponentiation theorem in this contribution. As a first application of our method, we consider the $N$-jettiness observable and present numerical results for the $1$-jettiness and $2$-jettiness hadr…
We present a parton shower which implements the DGLAP evolution of parton densities and fragmentation functions at next-to-leading order precision up to effects stemming from local four-momentum conservation. The Monte-Carlo simulation is based on including next-to-leading order collinear splitting functions in an existing parton shower and combining their soft enhanced contributions with the corresponding terms at leading order. Soft double counting is avoided by matching to the soft eikonal. Example results from two independent realizations of the algorithm, implemented in the two event gene…
I discuss top quark production in hadronic collisions. I present the soft-gluon resummation formalism and its derivation from factorization and renormalization-group evolution, and two-loop calculations of soft anomalous dimensions in the eikonal approximation. I discuss the contributions of next-to-next-to-leading order (NNLO) soft-gluon corrections to the total cross sections and top-quark transverse momentum and rapidity distributions for top-antitop pair production, and for single-top production in the $t$ and $s$ channels and in association with a $W$ boson or a charged Higgs boson.
NNLO soft functions for heavy-quark pair production at hadron colliders
该研究推广SoftSERVE框架，完成强子对撞机顶夸克对产生NNLO软函数的自动计算，给出0-jettiness软函数二维网格结果，详述重整化流程并分析三极色关联奇异性。
Jet functions for next-to-leading power factorization
该研究探讨部分子阈值附近散射过程的次领头功率因子化，在SCET和直接QCD方法中分析功率压低贡献，验证因子化公式，指出次领头功率对数重求和的两个挑战。
We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO). We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme. We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation. We also explicitly confirm the non-Abelian exponentiation of the TMD…
On the breakdown of eikonal approximation and survival of Reggeization in presence of dimension-5 Higgs-gluon coupling
该研究针对含5维希格斯-胶子耦合的高能过程，发现常用程函近似与区域展开会得到不完整振幅，而精确QCD振幅的Regge极限单圈阶符合Regge极点形式，支持了Regge化假说。
In this note we address the issue of theoretical estimates of the hadronic cross-sections for \gamgam processes. We compare the predictions of the minijet model with data as well as other models, highlighting the band of uncertainties in the theoretical predictions as well as those in the final values of the $σ(\gamgam \go {\rm hadrons})$ extracted from the data. We find that the rise of $σ_{γγ}^{\rm tot}$ with energy shown in the latest \gamgam data is in tune with the faster rise expected in the Eikonal Minijet Models (EMM). We present an estimate of the accuracy with which this cross-sectio…
We examine the Regge (high energy) limit of 4-point scattering in both QCD and gravity, using recently developed techniques to systematically compute all corrections up to next-to-leading power in the exchanged momentum i.e. beyond the eikonal approximation. We consider the situation of two scalar particles of arbitrary mass, thus generalising previous calculations in the literature. In QCD, our calculation describes power-suppressed corrections to the Reggeisation of the gluon. In gravity, we confirm a previous conjecture that next-to-soft corrections correspond to two independent deflection …
We derive the in-medium gluon radiation spectrum off a quark within the path integral formalism at finite energies, including all next-to-eikonal corrections in the propagators of quarks and gluons. Results are computed for finite formation times, including interference with vacuum amplitudes. By rewriting the medium averages in a convenient manner we present the spectrum in terms of dipole cross sections and a colour decoherence parameter with the same physical origin as that found in previous studies of the antenna radiation. This factorisation allows us to present a simple physical picture …
Soft Gluon Wave Function and Evolution Operator in the CGC at Next-to-Leading Order
该研究在色玻璃凝聚框架下构建快速运动强子的软胶子光锥波函数及演化算符至\(\mathcal{O}(g^{2})\)阶，通过玻恩 - 奥本海默分离等方法确定系数，应用中对角化软哈密顿量，发现福克扇区非对角混合元素抵消，背景场能量与\(\rho^{2}\)成正比。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。