scholarly journals One-loop scattering equations and amplitudes from forward limit

2015 ◽  
Vol 92 (10) ◽  
Author(s):  
Song He ◽  
Ellis Ye Yuan
Keyword(s):  
Forward Limit

scholarly journals Causality, unitarity and symmetry in effective field theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Timothy Trott
Keyword(s):  
Effective Field ◽  
Tree Level ◽  
Global Symmetry ◽  
Fundamental Limits ◽  
Effective Interactions ◽  
Effective Contact ◽  
Higher Dimensional ◽  
Forward Limit ◽  
Mass Dimension ◽  
Flavour Violation

Abstract Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the S-matrix, these imply that the size of higher dimensional corrections to transition amplitudes between different states is bounded by the strength of their contributions to elastic forward scattering processes. This places fundamental limits on the extent to which hypothetical symmetries can be broken by effective interactions. All analysis is for dimension 8 operators in the forward limit. Included is a thorough derivation of all positivity bounds for a chiral fermion in SU(2) and SU(3) global symmetry representations resembling those of the Standard Model, general bounds on flavour violation, new bounds for interactions between particles of different spin, inclusion of loops of dimension 6 operators and illustration of the resulting strengthening of positivity bounds over tree-level expectations, a catalogue of supersymmetric effective interactions up to mass dimension 8 and 4 legs and the demonstration that supersymmetry unifies the positivity theorems as well as the new bounds.

scholarly journals High Energy Rho Meson Leptoproduction §

2014 ◽  
Vol 1 (1) ◽  
pp. 33-35
Author(s):  
Adrien Besse ◽  
Lech Szymanowski ◽  
Samuel Wallon
Keyword(s):  
Cross Sections ◽  
Scattering Amplitude ◽  
Good Description ◽  
High Energy ◽  
Energy Limit ◽  
Rho Meson ◽  
Forward Limit ◽  
Helicity Amplitudes ◽  
Impact Parameter Space ◽  
The Impact

We investigate the longitudinal and transverse polarized cross-sections of the leptoproduction of the ρ meson in the high energy limit. Our model is based on the computation of the impact factor γ*(λγ)→ ρ (λρ) using the twist expansion in the forward limit which is expressed in the impact parameter space. This treatment involves in the final stage the twist 2 and twist 3 distribution amplitudes (DAs) of the ρ meson and the dipole scattering amplitude. Taking models that exist for the DAs and for the dipole cross-section. We get a phenomenological model for the helicity amplitudes. We compare our predictions with HERA data and get a fairly good description for large enough virtualities of the photon. PACS number(s): 13.60.Le, 12.39.St, 12.38.Bx.

scholarly journals Two-loop scattering amplitudes: double-forward limit and colour-kinematics duality

2019 ◽  
Vol 2019 (12) ◽  
Author(s):  
Yvonne Geyer ◽  
Ricardo Monteiro ◽  
Ricardo Stark-Muchão
Keyword(s):  
Scattering Amplitudes ◽  
Forward Limit

scholarly journals A functional approach to the next-to-eikonal approximation of high energy gravitational scattering

2021 ◽  
pp. 2150138
Author(s):  
A. R. Fazio ◽  
E. A. Reyes R.
Keyword(s):  
Center Of Mass ◽  
Scalar Particle ◽  
Eikonal Approximation ◽  
High Energy ◽  
Functional Approach ◽  
Relativistic Limit ◽  
Center Of Mass Energy ◽  
Functional Methods ◽  
Forward Limit ◽  
Schwarzschild Radius

The Fradkin–Schwinger functional methods to represent a Green function in an external gravitational field are used to study the eikonal and the next-to-eikonal limit, including the nonlinear gravitational interactions, of the scattering amplitudes of an ultra-relativistic scalar particle on a static super-massive scalar target in the nearly forward limit. The functional approach confirms the exponentiation of the leading eikonal which also applies to the first non-leading power in the energy of the light particle, moreover includes the interaction at impact parameter much larger than the Schwarzschild radius associated with the center of mass energy in the ultra-relativistic limit.

scholarly journals The Missing Link: A Closed Form Solution to the Kermack and McKendrick Model Equations

2021 ◽  
Author(s):  
Theodore G Duclos ◽  
Thomas A Reichert
Keyword(s):  
Closed Form ◽  
Complete Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Policy Makers ◽  
Mobility Data ◽  
Forward Limit ◽  
Containment Measures ◽  
Model Equations ◽  
Analytical Tools

Susceptible infectious recovered (SIR) models are widely used for estimating the dynamics of epidemics. Such models project that containment measures flatten the curve, i.e., reduce but delay the peak in daily infections, cause a longer epidemic, and increase the death toll. These projections have entered common understanding; individuals and governments often advocate lifting containment measures such as social distancing to shift the peak forward, limit societal and economic disruption, and reduce mortality. It was, then, an extraordinary surprise to discover that COVID-19 pandemic data exhibit phenomenology opposite to the projections of SIR models. With the knowledge that the commonly used SIR equations only approximate the original equations developed to describe epidemics, we identified a closed form solution to the original epidemic equations. Unlike the commonly used approximations, the closed form solution replicates the observed phenomenology and quantitates pandemic dynamics with simple analytical tools for policy makers. The complete solution is validated using independently measured mobility data and accurately predicts COVID19 case numbers in multiple countries.

Thresholds for Inducing Protective Stepping Responses to External Perturbations of Human Standing

2003 ◽  
Vol 90 (2) ◽  
pp. 666-674 ◽  
Author(s):  
M.-L. Mille ◽  
M. W. Rogers ◽  
K. Martinez ◽  
L. D. Hedman ◽  
M. E. Johnson ◽  
...  
Keyword(s):  
Body Movement ◽  
Entire Study ◽  
External Perturbations ◽  
Age Related ◽  
Forward Limit ◽  
Perturbation Velocity ◽  
Threshold Position ◽  
Study Population ◽  
Older Subjects ◽  
Base Of Support

Standing subjects were unexpectedly pulled forward to identify a threshold boundary that evokes stepping in terms of the size of the pull relative to the base of support (BoS). Performances in a range of sensorimotor tests were correlated with the threshold boundary parameters. Younger and older subjects were studied to identify age-related changes in stepping and the threshold boundaries. The threshold boundary had a forward limit (TL) that, when crossed, always made subjects step no matter how slowly they were pulled. As velocity increased, the threshold position that produced a step shifted nearer to the ankles. Eventually a pull velocity was reached above which velocity had no further effect and a position threshold (TH) was identified behind which subjects never stepped. Thus the position threshold boundary for stepping is a posterior-going sigmoidal function of perturbation velocity. Older subjects stepped more than the young (69% vs. 40% of trials). For the older subjects, TL (91% vs. 107% BoS) and TH (59% vs. 72% BoS) were closer to the ankles, and the transition between TL and TH occurred at lower velocities (96% vs. 121% BoS.s–1). Across the entire study population many sensorimotor factors were associated with TL and TH. However, these associations were not present when age was removed as a factor. Thus, although the older subjects use protective stepping more often, this cannot be attributed directly to the sensorimotor factors tested here. It can be explained by stepping as a triggered response to the perturbation event rather than later sensory input about body movement.

scholarly journals Masses and electric charges: gauge anomalies and anomalous thresholds

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
César Gómez ◽  
Raoul Letschka
Keyword(s):  
Perturbation Theory ◽  
Lower Bound ◽  
Quantum Interference ◽  
Charged Fermion ◽  
Free Theory ◽  
Forward Limit ◽  
Long Range Interactions ◽  
Anomalous Threshold ◽  
Gauge Anomalies ◽  
Gauge Anomaly

AbstractWe work out in the forward limit and up to order $$e^6$$ e 6 in perturbation theory the collinear divergences. In this kinematical regime we discover new collinear divergences that we argue can be only cancelled using quantum interference with processes contributing to the gauge anomaly. This rules out the possibility of a quantum consistent and anomaly free theory with massless charges and long range interactions. We use the anomalous threshold singularities to derive a gravitational lower bound on the mass of the lightest charged fermion.

scholarly journals Propagators, BCFW recursion and new scattering equations at one loop

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Joseph A. Farrow ◽  
Yvonne Geyer ◽  
Arthur E. Lipstein ◽  
Ricardo Monteiro ◽  
Ricardo Stark-Muchão
Keyword(s):  
Gauge Theory ◽  
Tree Level ◽  
Loop Momentum ◽  
Planar Case ◽  
Linear Type ◽  
Recursion Relations ◽  
Loop Level ◽  
Alternative Approach ◽  
Forward Limit ◽  
Limit Procedure

Abstract We investigate how loop-level propagators arise from tree level via a forward-limit procedure in two modern approaches to scattering amplitudes, namely the BCFW recursion relations and the scattering equations formalism. In the first part of the paper, we revisit the BCFW construction of one-loop integrands in momentum space, using a convenient parametrisation of the D-dimensional loop momentum. We work out explicit examples with and without supersymmetry, and discuss the non-planar case in both gauge theory and gravity. In the second part of the paper, we study an alternative approach to one-loop integrands, where these are written as worldsheet formulas based on new one-loop scattering equations. These equations, which are inspired by BCFW, lead to standard Feynman-type propagators, instead of the ‘linear’-type loop-level propagators that first arose from the formalism of ambitwistor strings. We exploit the analogies between the two approaches, and present a proof of an all-multiplicity worldsheet formula using the BCFW recursion.

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