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.

Fundamentality

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
High Energy Physics ◽  
Physical Property ◽  
Natural World ◽  
High Energy ◽  
Quantum Field Theories ◽  
Fundamental Physics ◽  
The World ◽  
Energy Physics

The metaphor that fundamental physics is concerned to say what the natural world is like at the deepest level may be cashed out in terms of entities, properties, or laws. The role of quantum field theories in the Standard Model of high-energy physics suggests that fundamental entities, properties, and laws are to be sought in these theories. But the contextual ontology proposed in Chapter 12 would support no unified compositional structure for the world; a quantum state assignment specifies no physical property distribution sufficient even to determine all physical facts; and quantum theory posits no fundamental laws of time evolution, whether deterministic or stochastic. Quantum theory has made a revolutionary contribution to fundamental physics because its principles have permitted tremendous unification of science through the successful application of models constructed in conformity to them: but these models do not say what the world is like at the deepest level.

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 May the four be with you: novel IR-subtraction methods to tackle NNLO calculations

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
W. J. Torres Bobadilla ◽  
G. F. R. Sborlini ◽  
P. Banerjee ◽  
S. Catani ◽  
A. L. Cherchiglia ◽  
...  
Keyword(s):  
High Energy Physics ◽  
High Energy ◽  
Higher Order ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Link Type ◽  
Mathematical Properties ◽  
Energy Physics ◽  
The Way

AbstractIn this manuscript, we report the outcome of the topical workshop: paving the way to alternative NNLO strategies (https://indico.ific.uv.es/e/WorkStop-ThinkStart_3.0), by presenting a discussion about different frameworks to perform precise higher-order computations for high-energy physics. These approaches implement novel strategies to deal with infrared and ultraviolet singularities in quantum field theories. A special emphasis is devoted to the local cancellation of these singularities, which can enhance the efficiency of computations and lead to discover novel mathematical properties in quantum field theories.

Discrete quantum gravity and causal sets

2001 ◽  
Vol 79 (1) ◽  
pp. 1-16 ◽  
Author(s):  
D D Reid
Keyword(s):  
Quantum Gravity ◽  
High Energy Physics ◽  
Causal Structure ◽  
High Energy ◽  
Research Community ◽  
Small Scale ◽  
Causal Sets ◽  
Important Approach ◽  
Nonrelativistic Quantum Mechanics ◽  
Energy Physics

This paper provides a thorough introduction to the physical and conceptual need for a theory of quantum gravity; some knowledge of general relativity and nonrelativistic quantum mechanics is assumed. A theory of quantum gravity would have wide-ranging implications for high-energy physics, astrophysics, and cosmology. The paper goes on to describe an important approach to quantum gravity that is not well known outside of the quantum gravity research community — causal sets. The causal-set approach falls within the framework of discrete quantum gravity, which considers the possibility that the small-scale structure of spacetime might be discrete rather than continuous. Herein, I elucidate the arguments for why a discrete causal structure might be appropriate for a theory of quantum gravity. The logical and formal development of a causal-set theory as well as a few illuminating examples are also provided. PACS Nos.: 04.60-m, 04.60Nc

Reduction, Unity and the Nature of Science: Kant's Legacy?

2008 ◽  
Vol 63 ◽  
pp. 37-62 ◽  
Author(s):  
Margaret Morrison
Keyword(s):  
High Energy Physics ◽  
Modern Science ◽  
Good Deal ◽  
High Energy ◽  
Mathematical Framework ◽  
Quantum Field Theories ◽  
Unified Field Theory ◽  
Unified Field ◽  
Theory Of Everything ◽  
Mathematical Techniques

One of the hallmarks of Kantian philosophy, especially in connection with its characterization of scientific knowledge, is the importance of unity, a theme that is also the driving force behind a good deal of contemporary high energy physics. There are a variety of ways that unity figures in modern science—there is unity of method where the same kinds of mathematical techniques are used in different sciences, like physics and biology; the search for unified theories like the unification of electromagnetism and optics by Maxwell; and, more recently, the project of grand unification or the quest for a theory of everything which involves a reduction of the four fundamental forces (gravity, electromagnetism, weak and strong) under the umbrella of a single theory. In this latter case it is thought that when energies are high enough, the forces (interactions), while very different in strength, range and the types of particles on which they act, become one and the same force. The fact that these interactions are known to have many underlying mathematical features in common suggests that they can all be described by a unified field theory. Such a theory describes elementary particles in terms of force fields which further unifies all the interactions by treating particles and interactions in a technically and conceptually similar way. It is this theoretical framework that allows for the prediction that measurements made at a certain energy level will supposedly indicate that there is only one type of force. In other words, not only is there an ontological reduction of the forces themselves but the mathematical framework used to describe the fields associated with these forces facilitates their description in a unified theory. Specific types of symmetries serve an important function in establishing these kinds of unity, not only in the construction of quantum field theories but also in the classification of particles; classifications that can lead to new predictions and new ways of understanding properties like quantum numbers. Hence, in order to address issues about unification and reduction in contemporary physics we must also address the way that symmetries facilitate these processes.

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].

FRACTIONAL FIELD THEORIES FROM MULTI-DIMENSIONAL FRACTIONAL VARIATIONAL PROBLEMS

2008 ◽  
Vol 05 (06) ◽  
pp. 863-892 ◽  
Author(s):  
RAMI AHMAD EL-NABULSI
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Fractional Differential Equations ◽  
High Energy Physics ◽  
Wave Theory ◽  
High Energy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Fractional Differential

Fractional calculus has recently attracted considerable attention. In particular, various fractional differential equations are used to model nonlinear wave theory that arises in many different areas of physics such as Josephson junction theory, field theory, theory of lattices, etc. Thus one may expect fractional calculus, in particular fractional differential equations, plays an important role in quantum field theories which are expected to satisfy fractional generalization of Klein–Gordon and Dirac equations. Until now, in high-energy physics and quantum field theories the derivative operator has only been used in integer steps. In this paper, we want to extend the idea of differentiation to arbitrary non-integers steps. We will address multi-dimensional fractional action-like problems of the calculus of variations where fractional field theories and fractional differential Dirac operators are constructed.

scholarly journals Tetra- and Penta-Quark Structures in the Constituent Quark Model

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1869 ◽  
Author(s):  
Gang Yang ◽  
Jialun Ping ◽  
Jorge Segovia
Keyword(s):  
Quark Model ◽  
High Energy Physics ◽  
Constituent Quark ◽  
Expansion Method ◽  
High Energy ◽  
Constituent Quark Model ◽  
Theoretical Predictions ◽  
Exotic Hadrons ◽  
Physics Experiments ◽  
Energy Physics

With the development of high energy physics experiments, a large amount of exotic states in the hadronic sector have been observed. In order to shed some light on the nature of the tetraquark and pentaquark candidates, a constituent quark model, along with the Gaussian expansion method, has been employed systematically in real- and complex-range investigations. We review herein the double- and fully-heavy tetraquarks, but also the hidden-charm, hidden-bottom and doubly charmed pentaquarks. Several exotic hadrons observed experimentally were well reproduced within our approach; moreover, their possible compositeness and other properties, such as their decay widths and general patterns in the spectrum, are analyzed. Besides, we report also some theoretical predictions of tetra- and penta-quark states which have not seen by experiment yet.

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