scholarly journals Soft matters, or the recursions with massive spinors

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Adam Falkowski ◽  
Camila S. Machado
Keyword(s):  
Scattering Amplitudes ◽  
Compton Scattering ◽  
Scattering Amplitude ◽  
Massless Particle ◽  
Technical Innovation ◽  
Recursion Relations ◽  
Soft Limit ◽  
Soft Matters ◽  
Two Parameter ◽  
Soft Factors

Abstract We discuss recursion relations for scattering amplitudes with massive particles of any spin. They are derived via a two-parameter shift of momenta, combining a BCFW-type spinor shift with the soft limit of a massless particle involved in the process. The technical innovation is that spinors corresponding to massive momenta are also shifted. Our recursions lead to a reformulation of the soft theorems. The well-known Weinberg’s soft factors are recovered and, in addition, the subleading factors appear reshaped such that they are directly applicable to massive amplitudes in the modern on-shell language. Moreover, we obtain new results in the context of non-minimal interactions of massive matter with photons and gravitons. These soft theorems are employed for practical calculations of Compton and higher-point scattering. As a by-product, we introduce a convenient representation of the Compton scattering amplitude for any mass and spin.

scholarly journals Open associahedra and scattering forms

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Aidan Herderschee ◽  
Fei Teng
Keyword(s):  
Scattering Amplitudes ◽  
Canonical Form ◽  
Recursion Relations ◽  
Fiber Product ◽  
New Phenomena

Abstract We continue the study of open associahedra associated with bi-color scattering amplitudes initiated in ref. [1]. We focus on the facet geometries of the open associahedra, uncovering many new phenomena such as fiber-product geometries. We then provide novel recursion procedures for calculating the canonical form of open associahedra, generalizing recursion relations for bounded polytopes to unbounded polytopes.

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 Factorization of gravitational Compton scattering amplitude in the linearized version of general relativity

1993 ◽  
Vol 48 (6) ◽  
pp. 2953-2956 ◽  
Author(s):  
S. Y. Choi ◽  
J. S. Shim ◽  
H. S. Song
Keyword(s):  
General Relativity ◽  
Compton Scattering ◽  
Scattering Amplitude

scholarly journals Scalar dipole dynamical polarizabilities from real Compton scattering data

2019 ◽  
Vol 199 ◽  
pp. 05008
Author(s):  
S. Sconfietti ◽  
B. Pasquini ◽  
P. Pedroni
Keyword(s):  
Compton Scattering ◽  
Pion Production ◽  
Scattering Amplitude ◽  
Parametric Bootstrap ◽  
Multipole Expansion ◽  
Scattering Data ◽  
Data Sets ◽  
Production Threshold ◽  
The Poor ◽  
Low Sensitivity

We present an extraction of the scalar dipole dynamical polarizabilities from proton real Compton scattering (RCS) data below pion-production threshold. The theoretical approach relies on dispersion relations, and on the low-energy expansion and multipole expansion of the scattering amplitude. The statistical analysis is based on the parametric bootstrap technique, that revealed to be crucial to deal with problems inherent to both the low sensitivity of the RCS cross section to the energy dependence of the dynamical polarizabilities and the poor accuracy of the available data sets.

scholarly journals ANALYTIC SCATTERING AMPLITUDES FOR QCD

2008 ◽  
Vol 23 (12) ◽  
pp. 847-856 ◽  
Author(s):  
DIANA VAMAN ◽  
YORK-PENG YAO
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Invariance ◽  
Recursion Relations

By analytically continuing QCD scattering amplitudes through specific complexified momenta, one can study and learn about the nature and the consequences of factorization and unitarity. In some cases, when coupled with the largest time equation and gauge invariance requirement, this approach leads to recursion relations, which greatly simplify the construction of multi-gluon scattering amplitudes. The setting for this discussion is in the space-cone gauge.

scholarly journals Recursion formulas for HOMFLY and Kauffman invariants

2014 ◽  
Vol 23 (05) ◽  
pp. 1450024
Author(s):  
Qingtao Chen ◽  
Nicolai Reshetikhin
Keyword(s):  
Universal Enveloping Algebras ◽  
Recursion Relations ◽  
Enveloping Algebras ◽  
Recursion Formulas ◽  
Quantized Universal Enveloping Algebras ◽  
Two Parameter

In this paper, we describe the recursion relations between two parameter HOMFLY and Kauffman polynomials of framed links. These relations correspond to embeddings of quantized universal enveloping algebras. The relation corresponding to embeddings gn ⊃ gk × sln-k where gn is either so2n+1, so2n or sp2n is new.

scholarly journals QUANTUM RINGS AND RECURSION RELATIONS IN 2D QUANTUM GRAVITY

1992 ◽  
Vol 07 (16) ◽  
pp. 1419-1425 ◽  
Author(s):  
SHAMIT KACHRU
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Quantum Gravity ◽  
Matrix Model ◽  
Ring Structure ◽  
Two Dimensional ◽  
Recursion Relations ◽  
Quantum Rings ◽  
Bulk Scattering

I study tachyon condensate perturbations to the action of the two-dimensional string theory corresponding to the c=1 matrix model. These are shown to deform the action of the ground ring on the tachyon modules, confirming a conjecture of Witten. The ground ring structure is used to derive recursion relations which relate (N+1) and N tachyon bulk scattering amplitudes. These recursion relations allow one to compute all bulk amplitudes.

Nucleon polarizabilities andπ0→2γ,η0→2γdecay rates from Compton-scattering amplitudes

1976 ◽  
Vol 14 (5) ◽  
pp. 1335-1351 ◽  
Author(s):  
I. Guiaşu ◽  
E. E. Radescu
Keyword(s):  
Scattering Amplitudes ◽  
Compton Scattering
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