We present the first results from BlackHat, an automated C++ program for calculating one-loop amplitudes. The program implements the unitarity method and on-shell recursion to construct amplitudes. As input to the calculation, it uses compact analytic formulae for tree amplitudes for four-dimensional helicity states. The program performs all related computations numerically. We make use of recently developed on-shell methods for evaluating coefficients of loop integrals, introducing a discrete Fourier projection as a means of improving efficiency and numerical stability. We illustrate the numerical stability of our approach by computing and analyzing six-, seven- and eight-gluon amplitudes in QCD and comparing against previously-obtained analytic results.
We calculate one loop scattering amplitudes for arbitrary number of positive helicity on-shell gluons and one off-shell gluon treated within the quasi-multi Regge kinematics. The result is fully gauge invariant and possesses the correct on-shell limit. Our method is based on embedding the off-shell process, together with contributions needed to retain gauge invariance, in a bigger fully on-shell process with auxiliary quark or gluon line.
A method to define and calculate one-loop amplitudes with an off-shell space-like, or $k_T$-dependent, gluon is presented. It introduces a practical regularization to deal with the divergencies that appear due to linear denominators, and can be applied to arbitarary partonic scattering processes.
We report on the advances in the calculation of the two-loop scattering amplitudes for five-particle processes with one off-shell leg. Focusing on the production of a Higgs boson in association with a bottom quark pair, we outline how the newly developed technology allows us to overcome the computational bottlenecks. In particular, we discuss the use of finite field arithmetic and elucidate a convenient way to evaluate numerically the special functions appearing in the amplitudes.
Massless-Massive Amplitude Correspondence I: Helicity-chirality Matching and On-shell Higgsing
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）；Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院）；International Center for Theoretical Physics Asia-Pacific（亚太理论物理中心）；Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Scattering amplitudes in quantum field theory are independent of the field parameterization, which has a natural geometric interpretation as a form of `coordinate invariance.' Amplitudes can be expressed in terms of Riemannian curvature tensors, which makes the covariance of amplitudes under non-derivative field redefinitions manifest. We present a generalized geometric framework that extends this manifest covariance to $all$ allowed field redefinitions. Amplitudes satisfy a recursion relation that closely resembles the application of covariant derivatives to increase the rank of a tensor. Thi…
We study the three-particle and four-particle scattering amplitudes for an arbitrary, finite number of massive scalars, spinors and vectors by employing the on-shell massive spinor formalism. We consider the most general three-particle amplitudes with energy growing behavior at most of $\mathcal{O} (E)$. This is the special case of the requirement of tree unitarity, which states that the $N$-particle scattering amplitudes at tree-level should grow at most as $\mathcal{O} (E^{4-N})$ in the high energy hard scattering limit, i.e. at fixed non-zero angles. Then the factorizable parts of the four-…
IFAE and BIST, Universitat Autònoma de Barcelona（巴塞罗那自治大学）；School of Physics, Peking University（北京大学物理学院）；International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), University of Chinese Academy of Sciences (UCAS)（中国科学院大学亚太理论物理中心）；School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University（北京大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Beijing Laser Acceleration Innovation Center（北京激光加速创新中心）；CAS Key Laboratory of Theoretical Physics, 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）
On-shell amplitude methods allow to derive one-loop renormalization effects from just tree-level amplitudes, with no need of loop calculations. We derive a simple formula to obtain the anomalous dimensions of higher-dimensional operators from a product of tree-level amplitudes. We show how this works for dimension-6 operators of the Standard Model, providing explicit examples of the simplicity, elegance and efficiency of the method. Many anomalous dimensions can be calculated from the same Standard Model tree-level amplitude, displaying the attractive recycling aspect of the on-shell method. W…
We introduce matchmakereft, a fully automated tool to compute the tree-level and one-loop matching of arbitrary models onto arbitrary effective theories. Matchmakereft performs an off-shell matching, using diagrammatic methods and the background field method when gauge theories are involved. The large redundancy inherent to the off-shell matching together with explicit gauge invariance offers a significant number of non-trivial checks of the results provided. These results are given in the physical basis but several intermediate results, including the matching in the Green basis before and aft…
