The six-photon amplitude
C. Bernicot
由于没有树的顺序，六光子过程是一个很好的实验室，研究多腿单圈图。特别是，有足够的壳层外腿观察一个特殊的朗道奇点：双部分子散射。
Thanks to the absence of tree order, the six-photon processes is a good laboratory to study multi-leg one-loop diagrams. Particularly, there are enough on-shell external legs to observe a special Landau singularity: the double parton scattering.
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One-Loop Six Gluon Amplitude
这篇文章把六个胶子单圈振幅的不同分量集中在一个地方
Unitarity Cuts: NLO Six-Gluon Amplitudes in QCD
本文报道了一种计算规范理论中单圈振幅的有限么正性割的方法，并讨论了它在QCD中六胶子振幅割可构造部分的应用。
Six-Photon Amplitudes in Scalar QED
给出了标量QED中六光子螺旋度振幅的解析结果。为了计算循环，最近开发的方法的基础上使用多个切口。QED和$QED^{\caln=1}$的振幅也得到了使用超对称分解连接的三个理论。
We present the full color two-loop six-point all-plus Yang-Mills amplitude in compact analytic form. The computation uses four dimensional unitarity and augmented recursion.
The one-loop amplitude for six-gluon scattering
我们给出了单圈六胶子散射振幅的结果。由于我们的方法是半数值的，它产生的结果为任意的动量和螺旋度的外部胶子。我们评估的颜色有序的子振幅胶子，费米子和标量运行在内部循环。这足以在QCD中给出六胶子单圈散射的完整描述。将这些结果与超对称杨-米尔斯的${\cal{N}}=4$和${\cal{N}}=1$多重态或内部循环中的复杂标量结合成振幅，可以与文献中的分析结果进行比较。对大多数复标量环螺旋度组合的数值结果是新的。
Numerical Evaluation of Six-Photon Amplitudes
我们应用最近提出的振幅缩减的被积函数水平的方法，计算散射过程的2光子-> 4光子，包括一个大质量的费米子环的情况。我们还提出了几个改进的方法，包括一个通用的策略来重建任何一个循环的振幅和消失的革兰氏行列式的处理的合理的一部分。
Contribution of dimension-six bosonic operators to Higgs decay into two photons at one-loop level
在有效拉格朗日方法内，以模型无关的方式研究了希格斯玻色子衰变为两个光子的过程。包含SU（2）× U（1）不变维六玻色子算子的单圈图的贡献被明确地评估。该计算旨在填补该主题当前文献中存在的空白。
Compact Formulas for Tree Amplitudes of Six Partons
利用推广的BCF/BCFW规则，得到了六个费米子和四个费米子加两个胶子的树能级非MHV振幅的紧致结果。结合以前的结果，现在可以以紧凑的形式获得六个部分子的完整树振幅集。
We present a simple parameterization of the two-photon exchange amplitude in elastic electron-proton scattering, suitable for fast numerical evaluation.
Six-Photon Amplitudes
我们提出了所有六光子螺旋振幅的分析结果。为了计算这一循环引起的过程中，两个最近开发的方法，形状因子分解的基础上，多个切口，已被使用。我们得到紧凑的结果，证明了这两种方法的适用性，以一个循环的幅度有关的精密对撞机现象。
Helicity Amplitudes for Charmonium Production in Hadron-Hadron and Photon-Hadron Collisions
本文给出了极化和非极化强子-强子和光子-强子碰撞中产生色单重态和八重态粲偶素的胶子-胶子和光子-胶子螺旋度振幅。
We discuss one-loop five-parton amplitudes with two-quark two-photon or three-photon external legs. The amplitudes are required to evaluate the NLO corrections for the $γγjet$ production process at hadron colliders. The results have been already discussed by several groups in terms of QCD amplitudes. Here, we present more straightforward version of one-loop calculations without using the QCD amplitudes.
Forward scattering amplitude of the virtual longitudinal photon in QED
计算了在小光子虚度极限下，量子电动力学中零能量虚纵光子对电子的前向散射振幅。考虑了第一辐射修正。得到了光子虚性展开式中的两项。
Towards six W-boson amplitude at two loops
研究通过六维超对称方法构建质量W玻色子六腿振幅的两环展开，发现其在无质量极限下对应六胶子最大螺旋度破坏振幅，并重复了四维和五维振幅的模式。
We compute the six-particle maximally-helicity-violating (MHV) and next-to-MHV (NMHV) amplitudes in planar maximally supersymmetric Yang-Mills theory through seven loops and six loops, respectively, as an application of the extended Steinmann relations and using the cosmic Galois coaction principle. Starting from a minimal space of functions constructed using these principles, we identify the amplitude by matching its symmetries and predicted behavior in various kinematic limits. Through five loops, the MHV and NMHV amplitudes are uniquely determined using only the multi-Regge and leading coll…
The phase between the three gluon and one photon amplitudes in quarkonium decays
本文分析了psi（2S）和psi（3770）衰变中三胶子振幅与单光子振幅之间的相位关系。
One-loop corrections to five-parton amplitudes with external photons
最近完成了所有五部分子单圈QCD振幅的计算。本文描述了如何用一个光子代替一个胶子得到相应的振幅，并给出了过程$0 \to 2q 2Q 1\y$的显式结果。
Multi-Photon Amplitudes for Next-to-Leading Order QCD
我们给出了次首阶QCD计算三个末态粒子产生率所需的包含一个、两个和三个光子的树能级振幅。我们还提出了所需的单回路振幅在以前发表的结果。
Twist-4 photon helicity-flip amplitude in DVCS on a nucleon in the Wandzura-Wilczek approximation
在Wandzura-Wilczek近似下计算了核子与深虚康普顿散射中光子自旋翻转振幅的扭转4部分。我们发现了一个可因子分解的贡献，这是由于光子散射的夸克与非零角动量沿碰撞轴。由于真正的扭曲-2振幅出现在NLO，对于中等虚拟的硬光子，$Q^2 \le 10$ GeV $^2$，运动学扭曲-4校正可以给光子螺旋翻转振幅的数值重要的贡献。
We calculate the hadron tensor related to the photon-induced Drell-Yan process, with incoming nucleon being transversally polarised. We predict the new single spin asymmetry which probes gluon poles and which is expressed in terms of photon (both chiral-odd and chiral-even) distribution amplitudes and chiral-odd nucleon function stemming from the nucleon transverse polarization.
Photon Distribution Amplitudes in QCD
我们开发了一个一致的技术计算硬排他过程中的实际光子发射，这是基于背景场的形式主义，并允许一个方便的分离的硬电磁和软强子组件的光子。后者与电磁背景场中光锥算子的矩阵元有关，可以用光子分布振幅来参数化。我们构建了一套完整的光子分布振幅，并包括扭转4，为手性守恒和违反手性运营商。分布振幅涉及几个非微扰参数，最重要的是，夸克凝聚的磁化率。我们回顾和更新以前的估计的磁化率，也给出了新的估计参数描述更高的扭曲振幅QCD求和规则。
Photon Distribution Amplitude in approach with nonlocal condensates
在非定域凝聚近似的框架下，在微扰展开的LO精度下，我们研究了实光子的磁化率和主导扭转光锥分布振幅。
Two-Loop Amplitudes for Gluon Fusion into Two Photons
给出了QCD中两胶子散射成两光子的双圈矩阵元。当希格斯粒子衰变为两个光子时，这些矩阵元素将进入到对LHC产生希格斯粒子的QCD背景的改进估计中。当M_H < 140 GeV时，光子模尤为重要。我们还给出了交叉过程的振幅，胶水伽玛到胶水伽玛。
The relativistic six-quark equations are found in the framework of the dispersion relation technique. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The relativistic six-quark amplitudes of hexaquarks including the quarks of three flavors ($u$, $d$, $s$) are calculated. The poles of these amplitudes determine the masses of six-quark systems.
The spinor-helicity formalism has become an invaluable tool for understanding the S-matrix of massless particles in four dimensions. In this paper we construct a spinor-helicity formalism in six dimensions, and apply it to derive compact expressions for the three, four and five point tree amplitudes of Yang-Mills theory. Using the KLT relations, it is a straightforward process to obtain amplitudes in linearized gravity from these Yang-Mills amplitudes; we demonstrate this by writing down the gravitational three and four point amplitudes. Because there is no conserved helicity in six dimensions…
Long vs. short distance dispersive two-photon K_L \to μ^+ μ^- amplitude
本文报道了双圈电弱双光子介导的短程色散K_L \to μ^+μ^衰变振幅的计算。QCD修正改变了这种贡献的符号，并将其减少了一个数量级。由此产生的振幅使我们能够提供一个约束，否则不确定的长距离色散振幅。
Within the framework of the massive O($N$) nonlinear sigma model extended to the next-to-leading order in the chiral counting (for $N=3$ corresponding to the two(-quark)-flavor Chiral Perturbation Theory), we calculate the relativistic six-pion scattering amplitude at low energy up to and including terms $\mathcal{O}(p^4)$. Results for the pion mass, decay constant and the four-pion amplitude in the case of $N$ (meson) flavors at $\mathcal{O}(p^4)$ are also presented.
On the Forward Scattering Amplitude of the Virtual Longitudinal Photon at Zero Energy
在小光子虚度$Q^2$的极限下，给出了零能量虚纵光子在任意强子靶上前向散射振幅的判定定理。该定理是严格的，仅基于洛伦兹和规范不变性。除了质谱中的间隙外，没有使用关于强相互作用的假设。计算了在$Q^2$上展开式中的两项。给出了弹性项$Q^2$能代表纵向虚光子-质子散射总振幅的估计。
Distribution amplitudes of light mesons and photon in the instanton model
在瞬子液体模型下，分析了π介子、$ρ$介子、实光子和虚光子的超前和高扭分布振幅。
Photon-Proton and Photon-Photon Scattering from Nucleon-Nucleon Forward Amplitudes
我们表明，$γp$和$γγ$相互作用的数据可以得到的$pp$和$\bar p p$前向散射振幅使用矢量介子优势和加性夸克模型。核子-核子数据使用一个模型进行参数化，其中高能截面随着碰撞粒子中软部分子数量的增加而随能量增加。我们提出了详细的描述数据的总截面和弹性截面，前向散射振幅的实部与虚部的比率，并对$pp$，$\bar p p$，$γp$，$γγ$，$γp \to γV$和$γγ\to V_i V_j$反应的微分截面的斜率，其中$V= ρ, ω, ϕ$。我们对未来的HERA和LHC实验以及LEP的$γγ$测量进行了广泛的预测。
Photon distribution amplitudes up to twist four are calculated within the nonlocal chiral quark model with a simple pole ansatz for momentum dependence of the constituent quark mass. Calculations are performed using modified electromagnetic vector current in order to satisfy Ward identities. Quark condensate and magnetic susceptibility of the QCD vacuum entering definitions of the distribution amplitudes are computed and compared with existing phenomenological estimates. Both real and off-shell photons are considered and relevant form factors are calculated. Our results are analytical up to th…
Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N) gauge theory satisfy constraints that arise from group theory alone. These constraints break into subsets associated with irreducible representations of the symmetric group S_n, which allows them to be presented in a compact and natural way. Using an iterative approach, we derive the constraints for six-point amplitudes at all loop orders, extending earlier results for n=4 and n=5. We then decompose the four-, five-, and six-point group-theory constraints into their irreducible S_n subspaces. We c…
Using the available cross section and polarization data for elastic electron-proton scattering, we provide an extraction of the two-photon exchange amplitudes at a common value of four-momentum transfer, around Q^2 = 2.5 GeV^2. This analysis also predicts the e^+ p / e^- p elastic scattering cross section ratio, which will be measured by forthcoming experiments.
Golem95: a numerical program to calculate one-loop tensor integrals with up to six external legs
我们提出了一个程序的形状因子的数值计算进入一个循环的幅度与多达六个外部腿。该程序是在Fortran 95中编写的，并执行减少到一定的一组基础积分数值，使用的形式主义，可以避免逆革兰氏行列式。它可以用来计算一个快速和数值稳定的方式与无质量的内部粒子的单圈振幅。
We combine the six-dimensional helicity formalism of Cheung and O'Connell with D-dimensional generalized unitarity to obtain a new formalism for computing one-loop amplitudes in dimensionally regularized QCD. With this procedure, we simultaneously obtain the pieces that are constructible from four-dimensional unitarity cuts and the rational pieces that are missed by them, while retaining a helicity formalism. We illustrate the procedure using four- and five-point one-loop amplitudes in QCD, including examples with external fermions. We also demonstrate the technique's effectiveness in next-to-…
A method to derive the convenient representations for many two-photon amplitudes is suggested. It is based on the use of the gauge in which the photon propagator has only space components. The amplitudes obtained have no any strong numerical cancellations and, therefore, are very convenient for numerical evaluations. Our approach is illustrated by the consideration of the processes $e^+e^-\to e^+e^-e^+e^-$, $e^+e^-\rightarrow e^+e^-μ^+μ^-$, and $e^+e^-\to μ^+μ^-π^+π^-$. The method is extended on the case of polarized particles. The amplitudes obtained in this approach have been employed for ex…
A compact representation of the 2 photon 3 gluon amplitude
给出了环路幅度gamma gamma ggg -> 0的紧凑表示。利用螺旋度方法和关于不可约函数基的排序得到了结果。我们将展示如何将旋量表示转换为振幅的场强表示。振幅定义了LHC在通道H -> gamma gamma +喷流中搜索希格斯玻色子的背景贡献，这是早先从5-胶子振幅的单圈表示中间接提取的。
We estimate the two-photon exchange contribution to elastic electron-proton scattering at large momentum transfer $Q^2$. It is shown that the leading two-photon exchange amplitude behaves as $1/Q^4$ relative to the one-photon amplitude, and can be expressed in a model independent way in terms of the leading twist nucleon distribution amplitudes. Using several models for the nucleon distribution amplitudes, we provide estimates for existing data and for ongoing experiments.
On the dispersive two-photon K_L -> μ^+ μ^- amplitude
我们提出了一个完整的帐户的双圈电弱，双光子介导的短距离色散$K_L \toμ^+μ^-$衰减幅度。QCD修正改变了这个振幅的符号，并将其降低了一个数量级。因此，经QCD校正的双圈振幅仅代表一圈弱短距离贡献的一小部分（中心值为5%），并且具有相同的符号。结合最近的测量，标准模型预测的短距离振幅，在本文中完成，提供了一个约束，否则不确定的长距离色散振幅。
Off-Shell Scattering Amplitudes for WW Scattering and the Role of the Photon Pole
推导了弱矢量玻色子高能$2 \to 2$离壳散射振幅的解析表达式。它们是从$e^+ e^- \to \barν_e + (WW) + ν_e \to \barν_e + (lν)(lν) + ν_e$型过程中的六个费米子末态得到的。作为应用，我们重新考虑希格斯质量的幺正性界限。特别注意的是在早期的调查中没有考虑的光子交换的作用，我们发现，光子削弱了希格斯质量的约束。
Analytic evaluation of the amplitudes for orthopositronium decay to three photons to one-loop order
正电子偶素衰变为三个光子的矩阵元可以用三个独立的振幅表示。我们描述了这些振幅的分析评价，无论是最低阶，并列入所有的单回路校正。我们利用这些振幅来找到正电子偶素衰变率的单圈修正值γ_1 =-10.286606（10）（alpha/pi）Gamma_{LO}，以及衰变率的α ^2阶“平方”修正值γ_2（square）= 28.860（2）（alpha/pi）^2 Gamma_{LO}，其中Gamma_{LO}是最低阶衰变率。给出了描述末态光子相空间分布单圈修正的显式函数。
Light-by-light scattering amplitudes from generalized unitarity in massive QED
我们用多重切割方法计算了大质量理论中单圈水平的所有四光子螺旋度振幅。振幅是在标量QED、QED和$\textrm{QED}^{\caln =1}$理论中导出的。我们将看到理性项的起源。我们将计算扩展到最简单的六光子螺旋度振幅，其中所有光子具有相同的螺旋度。
Helicity amplitudes for the small--angle process e^-e^{\pm}\to e^-γγ+ e^{\pm} with both photons along one direction and its cross channel
本文研究了两个光子沿电子方向运动的喷流运动学中$e^-e^\pm$散射的小角双韧致辐射。该区域对截面有主要贡献。我们提出了所有64个振幅的解析表达式与任意螺旋度状态的初始和最终轻子和产生的光子方便的分析和数值研究。给出了仅略去m ^2/E_j^2、θ_j^2和θ_j m/E_j量级的振幅的精度。给出了交叉通道γe^ \pm \to γe^+e^- + e^ \pm的螺旋度振幅。硬或软最终粒子的螺旋度振幅的几个限制被认为是。
We present three-loop helicity amplitudes for the production of a single photon in association with one jet in Quantum Chromodynamics, a final state which provides a standard candle of the Standard Model at the Large Hadron Collider. We employ a recently-proposed variation of the so-called tensor projection method in the 't Hooft-Veltman scheme (tHV) which avoids the computation of contributions due to unphysical (-2$ε$)-dimensional polarisations of the external states. We obtain compact analytic results expressed in terms of harmonic polylogarithms.
Axial Vector Amplitudes, Second Order Fermions, and Standard Model Photon -- Neutrino Processes
我们提出了一个扩展的字符串启发的技术适用于计算振幅和有效的拉格朗日矢量和轴向矢量规范场。该技术很容易适用于涉及恒定外场的问题。通过计算一般恒定电磁场中的单圈矢量-轴向矢量振幅，证明了该形式的优越性。这种计算的光子中微子过程的相关性进行了评论。我们还澄清的性质的形式主义方面的手征对称性，其连接到二阶费米子。
Based on the principle of the Lorentz covariance the transition matrix elements from an off-shell photon state to the vacuum are decomposed into the light-cone photon DAs, in which only two transversal DAs survive in the on-shell limit. The eight off-shell light-cone photon distribution amplitudes (DAs) corresponding to chiral-odd and chiral-even up to twist-four and the corresponding coupling constants are studied systematically in the instanton vacuum model of quantum chromodynamics (QCD). The various individual photon DA multiplied by its corresponding coupling constant is expressed in term…
Pion-photon Transition Distribution Amplitudes in the Spectral Quark Model
在谱夸克模型中分析了矢量和轴向π介子-光子跃迁分布振幅。我们继续通过使用一个明显的协变计算的基础上的阿尔法表示的传播的双分布的评价。结果多项式被纳入和计算变得相当简单。得到了在低能夸克模型尺度下的显式公式。相应的形状因子的反常衰变π 0-> γ γ * 和辐射π衰变也评估和面对的数据。
Using non-local chiral quark model with simple pole ansatz for mass dependence on momentum and non-local currents satisfying Ward-Takahashi identities, we calculate pion to photon transition distribution amplitudes and relevant form factors. For vector amplitude we recover correct normalization fixed by the axial anomaly. We find that due to the non-locality in the vector current, the value of axial form factor at zero momentum transfer is lowered with respect to the vector form factor. Such behaviour - consistent with experiment - is not seen in the local models. Where possible we compare our…
We derive the general structure of dimension-six derivative interactions in the N Higgs doublet models, where Higgs fields arise as pseudo Nambu-Goldstone modes of a strongly interacting sector. We show that there are several relations among the dimension-six operators, and therefore the number of independent operators decreases compared with models on which only SU(2)_L x U(1)_Y invariance is imposed. As an explicit example, we derive scattering amplitudes of longitudinal gauge bosons and Higgs bosons at high energy on models involving two Higgs doublets, and compare them with the amplitudes …
Distribution amplitude for the photon-pion transition
利用γ \to π^-跃迁分布振幅研究了在虚光子高度离壳的前向运动学区域，硬γ^{ \star }γ散射中ππ和πρ的唯一产生.计算是基于协变的贝特-萨尔彼得方法，适用于Nambu - Jona-Lasinio模型，用于确定的π束缚态。特别是它示出的π介子极的贡献产生了一个大的增强的微分截面的π介子对生产相对于以前的估计。
The two photon exchange amplitude in $ep$ and $eμ$ elastic scattering: a comparison
在本说明中，我们给出的论点赞成的声明，计算的电子μ子弹性散射的箱形图的贡献可以被认为是一个上限的电子质子散射。由于可以进行精确的QED计算，这一陈述对于约束涉及质子结构的模型计算是有用的。
Multi-photon decays of the Higgs boson at the LHC
本研究针对暗轴子门户模型中的希格斯玻色子六光子衰变信号，分类了不同多光子共振的主导质量区间，利用LHC现有数据约束了希格斯到暗光子对的分支比，并提出可通过重分析现有数据寻找新物理信号。
Algebraic evaluation of rational polynomials in one-loop amplitudes
单圈振幅在很大程度上取决于它们在四维中的么正性切割。我们表明，剩余的合理的条款，可以从紫外线行为的振幅，并确定普遍的形状因子，这些合理的部分，通过应用减少技术的费曼图形表示的振幅。该方法适用于无质量和有质量的内部粒子。我们通过计算gg-> H的单圈振幅、4光子和4胶子振幅、2光子加3胶子振幅和6光子振幅的有理数项来说明这种方法。
We study the pion Distribution Amplitude (πDA) in the context of a nonlocal chiral quark model. The corresponding Lagrangian reproduces the phenomenological values of the pion mass and decay constant, as well as the momentum dependence of the quark propagator obtained in lattice calculations. It is found that the obtained πDA has two symmetric maxima, which arise from the new contributions generated by the nonlocal character of the interactions. This πDA is applied to leading order and next-to-leading order calculations of the pion-photon transition form factor. Implications of the results are…
Leptoquarks are one of the possible candidates for explaining various anomalies in flavour physics. Nonetheless, their existence is yet to be confirmed from experimental side. In this paper we have shown how zeros of single photon tree-level amplitude can be used to extract information about leptoquarks in case of $e$-$γ$ colliders. Small number of standard model backgrounds keep the signal clean in this kind of colliders. Unlike other colliders, the zeros of single photon amplitude here depend on $\sqrt{s}$ as well as the mass of leptoquark along with its electric charge. We perform a PYTHIA …
The photon is a very interesting object for QCD studies since it has both a pointlike coupling to quarks, which yields a perturbative part of photon's wave function, and a non-perturbative coupling related to the magnetic susceptibility of the QCD vacuum and which builds its chiral-odd twist-2 distribution amplitude. The first feature allows us to compute the photon anomalous generalized parton distributions (GPD) and the diphoton generalized distribution amplitudes. The second feature allows us to use a transverse spin asymmetry to probe the chiral odd distribution amplitude of the photon.
Direct numerical integration of one-loop Feynman diagrams for N-photon amplitudes
计算次领先级高能碰撞中红外安全可观测量的散射截面的一种方法是用Monte Carlo数值积分进行所有的积分，包括虚环积分。在以前的论文中，我们中的两个人已经展示了如何在首次引入费曼参数表示后进行这样的虚拟回路积分。在本文中，我们直接进行积分，不引入费曼参数，适当变形后的积分轮廓。我们的例子是N光子散射振幅与无质量的电子环。我们报告了N = 6和N = 8的结果。
We combine the unitarity method with the six-dimensional helicity formalism of Cheung and O'Connell to construct loop-level scattering amplitudes. As a first example, we construct dimensionally regularized QCD one-loop four-point amplitudes. As a nontrivial multiloop example, we confirm that the recently constructed four-loop four-point amplitude of N=4 super-Yang-Mills theory, including nonplanar contributions, is valid for dimensions less than or equal to six. We comment on the connection of our approach to the recently discussed Higgs infrared regulator and on dual conformal properties in s…
The rational parts of one-loop QCD amplitudes III: The six-gluon case
本文用新发展的直接由Feynman积分计算有理部分的方法计算了标量环中循环的6-胶子单圈振幅的有理部分。给出了两种MHV螺旋度组态：$(1^-2^+3^+4^-5^+6^+)$和$(1^-2^+3^-4^+5^+6^+)$，以及两种NMHV螺旋度组态：$(1^-2^-3^+4^-5^+6^+)$和$(1^-2^+3^-4^+5^-6^+)$的解析结果.结合先前计算的切割构造部分的结果，我们的结果是6-胶子单圈QCD振幅的完整部分螺旋度振幅的最后缺失的部分。
We show that a natural spinor-helicity formalism that can describe massive scattering amplitudes exists in $D=6$ dimensions. This is arranged by having helicity spinors carry an index in the Dirac spinor {\bf 4} of the massive little group, $SO(5) \sim Sp(4)$. In the high energy limit, two separate kinds of massless helicity spinors emerge as required for consistency with arXiv:0902.0981, with indices in the two $SU(2)$'s of the massless little group $SO(4)$. The tensors of ${\bf 4}$ lead to particles with arbitrary spin, and using these and demanding consistent factorization, we can fix $3-$ …
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