We calculate analytically tree level amplitudes for Higgs production via Weak Bosons Fusion (WBF) and QCD corrections to the Standard Model prediction (SM) by using the helicity spinor formalism. We provide the explicit expression for the amplitude with two gluons emission in the final state together with massless final two quarks. The massive generalization of the Britto-Cachazo-Feng-Witten (BCFW) recursion scheme is applied successfully obtaining compact results which agree with, and overcome in simplicity, the conventional Feynman diagrams approach.
We present a systematic procedure to compute complete, analytic form factors of gauge-invariant operators at loop level in pure Yang-Mills. We consider applications to operators of the form $\mathrm{Tr}\, F^n$ where $F$ is the gluon field strength. Our approach is based on an extension to form factors of the dimensional reconstruction technique, in conjunction with the six-dimensional spinor-helicity formalism and generalised unitarity. For form factors this technique requires the introduction of additional scalar operators, for which we provide a systematic prescription. We also discuss a gen…
We use the spinor helicity formalism to calculate the cross section for production of three partons of a given polarization in Deep Inelastic Scattering (DIS) off proton and nucleus targets at small Bjorken x. The target proton or nucleus is treated as a classical color field (shock wave) from which the produced partons scatter multiple times. We reported our result for the final expression for the production cross section and studied the azimuthal angular correlations of the produced partons in [1]. Here we provide the full details of the calculation of the production cross section using the …
Spinor formalism for massive fields with half-integral spin
在这篇文章中，我们将计算螺旋度振幅的Weyl-van der Waerden旋量技术推广到一般的半整数自旋的大质量场。我们发现，小群生成元可以表示为旋量形式的一阶微分算子。我们利用生成元的旋量形式得到了任意自旋和任意螺旋度的质量场的显式形式。我们还利用这些旋量形式生成元处理了三粒子S-矩阵，并发现我们能够将Benincasa和Cachazo得到的三粒子顶点的显式形式推广到有质量的情形。我们给出了最低螺旋度为-3/2的外部粒子的振幅的显式表达式。群论，在提高运营商的小团体的形式，然后决定其他振幅与更高的螺旋度在相同的自旋多重态。原则上，该形式主义允许确定任意螺旋度的带电粒子的电磁形状因子，而无需对潜在的拉格朗日量进行额外的假设。我们发现，从规范和洛伦兹不变性遵循的限制是几乎一样的限制，在无质量的情况下。
Massive On-shell Splitting Functions in Spinor-Helicity Formalism
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学学院）；International Centre for Theoretical Physics Asia-Pacific（亚太地区理论物理中心）
The spinor-helicity formalism has proven to be very efficient in the calculation of scattering amplitudes in quantum field theory, while the loop tree duality (LTD) representation of multi-loop integrals exhibits appealing and interesting advantages with respect to other approaches. In view of the most recent developments in LTD, we exploit the synergies with the spinor-helicity formalism to analyse illustrative one- and two-loop scattering processes. We focus our discussion on the local UV renormalisation of IR and UV finite amplitudes and present a fully automated numerical implementation th…
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 $3-$ …
We present a calculation of the helicity amplitudes for the process $gg\toγγ$ in three-loop massless QCD. We employ a recently proposed method to calculate scattering amplitudes in the 't Hooft-Veltman scheme that reduces the amount of spurious non-physical information needed at intermediate stages of the computation. Our analytic results for the three-loop helicity amplitudes are remarkably compact, and can be efficiently evaluated numerically. This calculation provides the last missing building block for the computation of NNLO QCD corrections to diphoton production in gluon fusion.
Inspired by the flow description of su(N) colour calculations, we recently showed how to simplify the spinor-helicity formalism (at the algebra level two copies of complexified su(2)) by treating each Weyl spinor as part of a flow line with definite chirality and momentum. This formalism, dubbed the chirality-flow formalism, eliminates all non-trivial algebra from tree-level spinor-helicity calculations, thus allowing the shortest possible route from Feynman diagrams to complex numbers (spinor inner products). In this presentation, we briefly introduce the main features of this method and show…
We present the master integrals relevant for computing the complete set of leading-colour analytic helicity amplitudes for top-quark pair production via gluon fusion at two-loops in QCD. We include corrections due to massive fermion loops which give rise to integrals involving elliptic curves. We also elaborate on the structure of singularities that play an important role in the numerical evaluation of the iterated integrals and their analytic continuation.
We present a complete set of analytic helicity amplitudes for top quark pair production via gluon fusion at two-loops in QCD. For the first time, we include corrections due to massive fermion loops which give rise to integrals over elliptic curves. We present the results of the missing master integrals needed to compute the amplitude and obtain an analytic form for the finite remainders in terms of iterated integrals using rationalised kinematics and finite field sampling. We also study the numerical evaluation of the iterated integrals.
Methods of spinor calculus in particle physics are described in this series of four chapters written in french. A special emphasis is made on the well-known helicity-coupling scheme which is the guiding thread of all these methods. Numerous explicit formulas are given for projectors onto two-particles helicity states as well as for bilinears of Dirac spinors, for the s and t channels of a given two-body process involving spin 1/2 particles. In the last chapter, applications to various elementary processes are given.
Two-component spinors are the basic ingredients for describing fermions in quantum field theory in four space-time dimensions. We develop and review the techniques of the two-component spinor formalism and provide a complete set of Feynman rules for fermions using two-component spinor notation. These rules are suitable for practical calculations of cross-sections, decay rates, and radiative corrections in the Standard Model and its extensions, including supersymmetry, and many explicit examples are provided. The unified treatment presented in this review applies to massless Weyl fermions and m…
We establish a simple formula for the minimal dimension of operators leading to any helicity amplitude. It eases the systematic enumeration of independent operators from the construction of massless non-factorizable on-shell amplitudes. Little-group constraints can then be solved algorithmically for each helicity configuration to extract a complete set of spinor structures with lowest dimension. Occasionally, further reduction using momentum conservation, on-shell conditions and Schouten identities is required. A systematic procedure to account for the latter is presented. Dressing spinor stru…
The novel massive spinor-helicity formalism of Arkani-Hamed, Huang and Huang provides an elegant way to calculate scattering amplitudes in quantum chromodynamics for arbitrary quark spin projections. In this note we compute two families of tree-level QCD amplitudes with one massive quark pair and n-2 gluons. The two cases include all gluons with identical helicity and one opposite-helicity gluon being color-adjacent to one of the quarks. Our results naturally incorporate the previously known amplitudes for both quark spins quantized along one of the gluonic momenta. In the all-multiplicity for…
We compute the contribution of third generation quarks ($t,\ b$) to the two-loop amplitude for on-shell $W$ boson pair production in gluon fusion $gg \to WW$. We present plots for the amplitude across partonic phase space as well as reference values for two kinematic points. The master integrals are efficiently evaluated by numerically solving a system of ordinary differential equations.
We compute the top quark contribution to the two-loop amplitude for on-shell $Z$ boson pair production in gluon fusion, $gg \to ZZ$. Exact dependence on the top quark mass is retained. For each phase space point the integral reduction is performed numerically and the master integrals are evaluated using the auxiliary mass flow method, allowing fast computation of the amplitude with very high precision.
We study representations of the Poincaré group that have a privileged transformation law along a p-dimensional hyperplane, and uncover their associated spinor helicity variables in D spacetime dimensions. Our novel representations generalize the recently introduced celestial states and transform as conformal primaries of SO(p,1), the symmetry group of the p-hyperplane. We will refer to our generalized states as ``partially celestial." Following Wigner's method, we find the induced representations, including spin degrees of freedom. Defining generalized spinor helicity variables for every D and…
The factorization of multi-leg gauge theory amplitudes in the soft and collinear limits provides strong constraints on the structure of amplitudes, and enables efficient calculations of multi-jet observables at the LHC. There is significant interest in extending this understanding to include subleading powers in the soft and collinear limits. While this has been achieved for low point amplitudes, for higher point functions there is a proliferation of variables and more complicated phase space, making the analysis more challenging. By combining the subleading power expansion of spinor-helicity …
The spinor helicity formalism (SHF) has been efficiently applied to compute perturbative amplitudes in plenty of processes and reactions in gauge theories (including gravity), mostly in the massless case. Some work has been done in order to extend the SHF to the massive case. We have used these powerful tools to evaluate amplitudes in a local supersymmetric model where the gravitino is the lightest supersymmetric particle (LSP). Two decays have been evaluated in order to show the capability of the SHF in the massive extension, namely the two body neutralino decays $\tildeχ_0\to V\tildeΨ^μ$ wit…
Covariant canonical-spinor amplitudes for partial wave analysis
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学学院，UCAS）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；International Centre for Theoretical Physics Asia-Pacific（亚太地区理论物理中心）
