scholarly journals Note on the Labelled tree graphs

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Bo Feng ◽  
Yaobo Zhang
Keyword(s):  
Feynman Diagrams ◽  
Tree Level ◽  
Scalar Theory ◽  
Tree Graphs ◽  
Pole Structure ◽  
Interesting Generalization

Abstract In the CHY-frame for the tree-level amplitudes, the bi-adjoint scalar theory has played a fundamental role because it gives the on-shell Feynman diagrams for all other theories. Recently, an interesting generalization of the bi-adjoint scalar theory has been given in [1] by the “Labelled tree graphs”, which carries a lot of similarity comparing to the bi-adjoint scalar theory. In this note, we have investigated the Labelled tree graphs from two different angels. In the first part of the note, we have shown that we can organize all cubic Feynman diagrams produces by the Labelled tree graphs to the “effective Feynman diagrams”. In the new picture, the pole structure of the whole theory is more manifest. In the second part, we have generalized the action of “picking pole” in the bi-adjoint scalar theory to general CHY-integrands which produce only simple poles.

scholarly journals Generalized planar Feynman diagrams: collections

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Francisco Borges ◽  
Freddy Cachazo
Keyword(s):  
Compatibility Condition ◽  
Natural Generalization ◽  
Feynman Diagrams ◽  
Tree Level ◽  
Scalar Theory ◽  
Metric Tree

Abstract Tree-level Feynman diagrams in a cubic scalar theory can be given a metric such that each edge has a length. The space of metric trees is made out of orthants joined where a tree degenerates. Here we restrict to planar trees since each degeneration of a tree leads to a single planar neighbor. Amplitudes are computed as an integral over the space of metrics where edge lengths are Schwinger parameters. In this work we propose that a natural generalization of Feynman diagrams is provided by what are known as metric tree arrangements. These are collections of metric trees subject to a compatibility condition on the metrics. We introduce the notion of planar col lections of Feynman diagrams and argue that using planarity one can generate all planar collections starting from any one. Moreover, we identify a canonical initial collection for all n. Generalized k = 3 biadjoint amplitudes, introduced by Early, Guevara, Mizera, and one of the authors, are easily computed as an integral over the space of metrics of planar collections of Feynman diagrams.

scholarly journals A general expression for symmetry factors of Feynman diagrams

2002 ◽  
Vol 80 (8) ◽  
pp. 847-854 ◽  
Author(s):  
C D Palmer ◽  
M E Carrington
Keyword(s):  
General Expression ◽  
Feynman Diagram ◽  
Simple Formula ◽  
Feynman Diagrams ◽  
Scalar Theory ◽  
Symmetry Factor

The calculation of the symmetry factor corresponding to a given Feynman diagram is well known to be a tedious problem. We have derived a simple formula for these symmetry factors. Our formula works for any diagram in scalar theory (ϕ3 and ϕ4 interactions), spinor QED, scalar QED, or QCD. PACS Nos.: 11.10-z, 11.15-q, 11.15Bt

scholarly journals On differential operators and unifying relations for 1-loop Feynman integrands

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Kang Zhou
Keyword(s):  
Sigma Model ◽  
Differential Operators ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Maxwell Theory ◽  
Scalar Theory ◽  
Yang Mills ◽  
Loop Level ◽  
Wide Range ◽  
Non Linear

Abstract We generalize the unifying relations for tree amplitudes to the 1-loop Feynman integrands. By employing the 1-loop CHY formula, we construct differential operators which transmute the 1-loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, including Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at 1-loop level is established. Under the well known unitarity cut, the 1-loop level operators will factorize into two tree level operators. Such factorization is also discussed.

scholarly journals PAIRS-PRODUCTION OF HIGGS IN ASSOCIATION WITH BOTTOM QUARKS PAIRS AT e+e- COLLIDERS

2005 ◽  
Vol 20 (34) ◽  
pp. 2629-2638 ◽  
Author(s):  
A. GUTIÉRREZ-RODRÍGUEZ ◽  
M. A. HERNÁNDEZ-RUÍZ ◽  
O. A. SAMPAYO
Keyword(s):  
Pair Production ◽  
Cross Section ◽  
Center Of Mass ◽  
Feynman Diagrams ◽  
Tree Level ◽  
Bottom Quarks ◽  
Mass Energy ◽  
Center Of Mass Energy ◽  
The Standard Model ◽  
Complete Set

In a previous paper, we studied the Higgs pair production in the standard model with the reaction [Formula: see text]. Based on this, we study the Higgs pair production via [Formula: see text]. We evaluate the total cross-section of [Formula: see text] and calculate the total number of events considering the complete set of Feynman diagrams at tree-level, and compare this process with the process [Formula: see text]. The numerical computation is done for the energy which is expected to be available at a possible Next Linear e+e- Collider with a center-of-mass energy 800, 1000, 1600 GeV and luminosity 1000 fb-1.

Enlarging local symmetries: A nonlocal Galilean model

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040009
Author(s):  
Luca Buoninfante ◽  
Gaetano Lambiase ◽  
Masahide Yamaguchi
Keyword(s):  
Infinite Order ◽  
Field Theories ◽  
Tree Level ◽  
Complex Conjugate ◽  
Nonlocal Operators ◽  
Graviton Propagator ◽  
Pole Structure ◽  
Local Symmetries ◽  
Spacetime Metric ◽  
Infinite Derivative

We consider the possibility to enlarge the class of symmetries realized in standard local field theories by introducing infinite order derivative operators in the actions, which become nonlocal. In particular, we focus on the Galilean shift symmetry and its generalization in nonlocal (infinite derivative) field theories. First, we construct a nonlocal Galilean model which may be UV finite, showing how the ultraviolet behavior of loop integrals can be ameliorated. We also discuss the pole structure of the propagator which has infinitely many complex conjugate poles, but satisfies tree level unitarity. Moreover, we will introduce the same kind of nonlocal operators in the context of linearized gravity. In such a scenario, the graviton propagator turns out to be ghost-free and the spacetime metric generated by a point-like source is non-singular.

scholarly journals MULTIPARTICLE THRESHOLD AMPLITUDES EXPONENTIATE IN ARBITRARY SCALAR THEORIES

1996 ◽  
Vol 11 (31) ◽  
pp. 2539-2546 ◽  
Author(s):  
M.V. LIBANOV
Keyword(s):  
Particle Production ◽  
Tree Level ◽  
Exponential Behavior ◽  
Scalar Theory ◽  
Scalar Theories

Threshold amplitudes are considered for n-particle production in arbitrary scalar theory. It is found that, like in Φ4, leading-n corrections to the tree level amplitudes, being summed over all loops, exponentiate. This result provides more evidence in favor of the conjecture on the exponential behavior of the multiparticle amplitudes.

scholarly journals A Mathematica package for calculation of one-loop penguins in FCNC processes

2015 ◽  
Vol 26 (04) ◽  
pp. 1550042 ◽  
Author(s):  
Alexander Vadimovich Bednyakov ◽  
Şükrü Hanif Tanyıldızı
Keyword(s):  
Neutral Current ◽  
New Physics ◽  
Feynman Diagrams ◽  
Tree Level ◽  
Flavor Changing ◽  
Flavor Changing Neutral Current ◽  
Physics Model ◽  
The One ◽  
Effective Operators

In this work, we present a Mathematica package Peng4BSM@LO which calculates the contributions to the Wilson Coefficients of certain effective operators originating from the one-loop penguin Feynman diagrams. Both vector and scalar external legs are considered. The key feature of our package is the ability to find the corresponding expressions in almost any New Physics model which extends the SM and has no flavor changing neutral current (FCNC) transitions at the tree level.

YANG-MILLS AMPLITUDES FROM STRING THEORY IN TWISTOR SPACE

2005 ◽  
Vol 20 (15) ◽  
pp. 3416-3419 ◽  
Author(s):  
MARCUS SPRADLIN
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Twistor Space ◽  
Mathematical Structure ◽  
Feynman Diagrams ◽  
Tree Level ◽  
Algebraic Equations ◽  
Yang Mills

Tree-level gluon scattering amplitudes in Yang-Mills theory frequently display simple mathematical structure which is completely obscure in the calculation of Feynman diagrams. We describe a novel way of calculating these amplitudes, motivated by a conjectured relation to twistor space, in which the problem of summing Feynman diagrams is replaced by the problem of solving a certain set of algebraic equations.

scholarly journals The chirality-flow formalism

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Andrew Lifson ◽  
Christian Reuschle ◽  
Malin Sjodahl
Keyword(s):  
Graphical Method ◽  
Feynman Diagrams ◽  
Tree Level ◽  
Flow Lines ◽  
Helicity Formalism ◽  
Inner Products

AbstractWe take a fresh look at Feynman diagrams in the spinor-helicity formalism. Focusing on tree-level massless QED and QCD, we develop a new and conceptually simple graphical method for their calculation. In this pictorial method, which we dub the chirality-flow formalism, Feynman diagrams are directly represented in terms of chirality-flow lines corresponding to spinor inner products, without the need to resort to intermediate algebraic manipulations.

TREE LEVEL LIE ALGEBRA STRUCTURES OF PERTURBATIVE INVARIANTS

2003 ◽  
Vol 12 (03) ◽  
pp. 333-345 ◽  
Author(s):  
NATHAN HABEGGER ◽  
WOLFGANG PITSCH
Keyword(s):  
Lie Algebra ◽  
Free Group ◽  
Automorphism Groups ◽  
Feynman Diagrams ◽  
Tree Level

We study two different Lie algebra structures on the space of Feynman diagrams at tree level. We show that each such structure arises naturally from a tower of automorphism groups of nilpotent quotients of a free group.

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