scholarly journals The analytic continuation of the high-energy parton–parton scattering amplitude with an IR cutoff

2002 ◽  
Vol 625 (1-2) ◽  
pp. 312-326 ◽  
Author(s):  
Enrico Meggiolaro
Keyword(s):  
Analytic Continuation ◽  
Scattering Amplitude ◽  
High Energy ◽  
Parton Scattering

scholarly journals Two-parton scattering amplitudes in the Regge limit to high loop orders

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Simon Caron-Huot ◽  
Einan Gardi ◽  
Joscha Reichel ◽  
Leonardo Vernazza
Keyword(s):  
Scattering Amplitudes ◽  
Scattering Amplitude ◽  
Dimensional Regularization ◽  
High Energy ◽  
Logarithmic Order ◽  
Finite Radius ◽  
High Loop ◽  
Parton Scattering ◽  
Infrared Divergences ◽  
Regge Limit

Abstract We study two-to-two parton scattering amplitudes in the high-energy limit of perturbative QCD by iteratively solving the BFKL equation. This allows us to predict the imaginary part of the amplitude to leading-logarithmic order for arbitrary t-channel colour exchange. The corrections we compute correspond to ladder diagrams with any number of rungs formed between two Reggeized gluons. Our approach exploits a separation of the two-Reggeon wavefunction, performed directly in momentum space, between a soft region and a generic (hard) region. The former component of the wavefunction leads to infrared divergences in the amplitude and is therefore computed in dimensional regularization; the latter is computed directly in two transverse dimensions and is expressed in terms of single-valued harmonic polylogarithms of uniform weight. By combining the two we determine exactly both infrared-divergent and finite contributions to the two-to-two scattering amplitude order-by-order in perturbation theory. We study the result numerically to 13 loops and find that finite corrections to the amplitude have a finite radius of convergence which depends on the colour representation of the t-channel exchange.

scholarly journals Universal opening of four-loop scattering amplitudes to trees

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Selomit Ramírez-Uribe ◽  
Roger J. Hernández-Pinto ◽  
Germán Rodrigo ◽  
German F. R. Sborlini ◽  
William J. Torres Bobadilla
Keyword(s):  
Scattering Amplitudes ◽  
General Expression ◽  
High Energy Physics ◽  
Scattering Amplitude ◽  
Causal Structure ◽  
High Energy ◽  
Quantum Field Theories ◽  
Efficient Computation ◽  
Perturbative Approach ◽  
Theoretical Predictions

Abstract The perturbative approach to quantum field theories has made it possible to obtain incredibly accurate theoretical predictions in high-energy physics. Although various techniques have been developed to boost the efficiency of these calculations, some ingredients remain specially challenging. This is the case of multiloop scattering amplitudes that constitute a hard bottleneck to solve. In this paper, we delve into the application of a disruptive technique based on the loop-tree duality theorem, which is aimed at an efficient computation of such objects by opening the loops to nondisjoint trees. We study the multiloop topologies that first appear at four loops and assemble them in a clever and general expression, the N4MLT universal topology. This general expression enables to open any scattering amplitude of up to four loops, and also describes a subset of higher order configurations to all orders. These results confirm the conjecture of a factorized opening in terms of simpler known subtopologies, which also determines how the causal structure of the entire loop amplitude is characterized by the causal structure of its subtopologies. In addition, we confirm that the loop-tree duality representation of the N4MLT universal topology is manifestly free of noncausal thresholds, thus pointing towards a remarkably more stable numerical implementation of multiloop scattering amplitudes.

scholarly journals High energy scattering of Dirac particles on smooth potentials

2016 ◽  
Vol 31 (23) ◽  
pp. 1650126 ◽  
Author(s):  
Nguyen Suan Han ◽  
Le Anh Dung ◽  
Nguyen Nhu Xuan ◽  
Vu Toan Thang
Keyword(s):  
Dirac Equation ◽  
Cross Sections ◽  
Differential Cross ◽  
Scattering Amplitude ◽  
High Energy ◽  
Type Representation ◽  
Dirac Particles ◽  
Energy Scattering ◽  
Two Component ◽  
High Energy Scattering

The derivation of the Glauber type representation for the high energy scattering amplitude of particles of spin 1/2 is given within the framework of the Dirac equation in the Foldy–Wouthuysen (FW) representation and two-component formalism. The differential cross-sections on the Yukawa and Gaussian potentials are also considered and discussed.

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