scholarly journals Mathematical properties of nested residues and their application to multi-loop scattering amplitudes

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
J. Jesús Aguilera-Verdugo ◽  
Roger J. Hernández-Pinto ◽  
Germán Rodrigo ◽  
German F. R. Sborlini ◽  
William J. Torres Bobadilla
Keyword(s):  
Scattering Amplitudes ◽  
Particle Physics ◽  
Mathematical Proof ◽  
Mathematical Structure ◽  
High Energy ◽  
The Novel ◽  
Feynman Integrals ◽  
Mathematical Properties ◽  
Theoretical Predictions ◽  
Physical Information

Abstract The computation of multi-loop multi-leg scattering amplitudes plays a key role to improve the precision of theoretical predictions for particle physics at high-energy colliders. In this work, we focus on the mathematical properties of the novel integrand-level representation of Feynman integrals, which is based on the Loop-Tree Duality (LTD). We explore the behaviour of the multi-loop iterated residues and explicitly show, by developing a general compact and elegant proof, that contributions associated to displaced poles are cancelled out. The remaining residues, called nested residues as originally introduced in ref. [1], encode the relevant physical information and are naturally mapped onto physical configurations associated to nondisjoint on-shell states. By going further on the mathematical structure of the nested residues, we prove that unphysical singularities vanish, and show how the final expressions can be written by using only causal denominators. In this way, we provide a mathematical proof for the all-loop formulae presented in ref. [2].

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.

Microfabrication research at the National Submicron Facility

1983 ◽  
Vol 41 ◽  
pp. 86-89
Author(s):  
E.D. Wolf
Keyword(s):  
Integrated Circuits ◽  
Particle Physics ◽  
High Speed ◽  
New Technology ◽  
High Energy ◽  
High Energy Particle ◽  
New Science ◽  
Wide Range ◽  
Intermediate Domain ◽  
Circuit Function

Most microelectronics devices and circuits operate faster, consume less power, execute more functions and cost less per circuit function when the feature-sizes internal to the devices and circuits are made smaller. This is part of the stimulus for the Very High-Speed Integrated Circuits (VHSIC) program. There is also a need for smaller, more sensitive sensors in a wide range of disciplines that includes electrochemistry, neurophysiology and ultra-high pressure solid state research. There is often fundamental new science (and sometimes new technology) to be revealed (and used) when a basic parameter such as size is extended to new dimensions, as is evident at the two extremes of smallness and largeness, high energy particle physics and cosmology, respectively. However, there is also a very important intermediate domain of size that spans from the diameter of a small cluster of atoms up to near one micrometer which may also have just as profound effects on society as “big” physics.

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 REVIEW OF THE PHENOMENOLOGY OF NONCOMMUTATIVE GEOMETRY

2004 ◽  
Vol 19 (02) ◽  
pp. 179-204 ◽  
Author(s):  
I. HINCHLIFFE ◽  
N. KERSTING ◽  
Y. L. MA
Keyword(s):  
Electric Dipole ◽  
Particle Physics ◽  
Extra Dimensions ◽  
Linear Collider ◽  
Dipole Moments ◽  
High Energy ◽  
Low Energy ◽  
Electric Dipole Moments ◽  
The Status ◽  
High Energy Scattering

We present a pedagogical review of particle physics models that are based on the noncommutativity of space–time, [Formula: see text], with specific attention to the phenomenology these models predict in particle experiments either in existence or under development. We summarize results obtained for high energy scattering such as would occur, for example, in a future e+e-linear collider with [Formula: see text], as well as low energy experiments such as those pertaining to elementary electric dipole moments and other CP violating observables, and finally comment on the status of phenomenological work in cosmology and extra dimensions.

All-Union Conference on High Energy Particle Physics

Atomic Energy ◽  
1956 ◽  
Vol 1 (4) ◽  
pp. 621-632
Author(s):  
V. A. Biryukov ◽  
B. M. Golovin ◽  
L. I. Lapidus
Keyword(s):  
Particle Physics ◽  
High Energy ◽  
High Energy Particle ◽  
Energy Particle ◽  
Union Conference

An interpretation of the high-energy πN scattering amplitudes and data

1972 ◽  
Vol 39 (4) ◽  
pp. 531-538 ◽  
Author(s):  
B.J. Hartley ◽  
G.L. Kane
Keyword(s):  
Scattering Amplitudes ◽  
High Energy

scholarly journals Programmable combinational logic trigger system for high energy particle physics experiments

1977 ◽  
Vol 140 (3) ◽  
pp. 549-552 ◽  
Author(s):  
E.D. Platner ◽  
A. Etkin ◽  
K.J. Foley ◽  
J.H. Goldman ◽  
W.A. Love ◽  
...  
Keyword(s):  
Particle Physics ◽  
High Energy ◽  
High Energy Particle ◽  
Combinational Logic ◽  
Trigger System ◽  
Energy Particle ◽  
Physics Experiments

scholarly journals Dosimetric Characterization of Small Radiotherapy Electron Beams Collimated by Circular Applicators with the New Microsilicon Detector

2022 ◽  
Vol 12 (2) ◽  
pp. 600
Author(s):  
Serenella Russo ◽  
Silvia Bettarini ◽  
Barbara Grilli Leonulli ◽  
Marco Esposito ◽  
Paolo Alpi ◽  
...  
Keyword(s):  
Radiation Therapy ◽  
Electron Beams ◽  
High Energy ◽  
Field Size ◽  
The Novel ◽  
Linear Accelerators ◽  
Depth Dose ◽  
Dosimetric Data ◽  
Output Factors ◽  
Dose Measurements

High-energy small electron beams, generated by linear accelerators, are used for radiotherapy of localized superficial tumours. The aim of the present study is to assess the dosimetric performance under small radiation therapy electron beams of the novel PTW microSilicon detector compared to other available dosimeters. Relative dose measurements of circular fields with 20, 30, 40, and 50 mm aperture diameters were performed for electron beams generated by an Elekta Synergy linac, with energy between 4 and 12 MeV. Percentage depth dose, transverse profiles, and output factors, normalized to the 10 × 10 cm2 reference field, were measured. All dosimetric data were collected in a PTW MP3 motorized water phantom, at SSD of 100 cm, by using the novel PTW microSilicon detector. The PTW diode E and the PTW microDiamond were also used in all beam apertures for benchmarking. Data for the biggest field size were also measured by the PTW Advanced Markus ionization chamber. Measurements performed by the microSilicon are in good agreement with the reference values for all the tubular applicators and beam energies within the stated uncertainties. This confirms the reliability of the microSilicon detector for relative dosimetry of small radiation therapy electron beams collimated by circular applicators.

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