scholarly journals Feynman rules for the rational part of the electroweak 1-loop amplitudes in the Rξ gauge and in the unitary gauge

2011 ◽  
Vol 2011 (1) ◽  
Author(s):  
M. V. Garzelli ◽  
I. Malamos ◽  
R. Pittau
Keyword(s):  
Unitary Gauge ◽  
Rational Part ◽  
Feynman Rules ◽  
Loop Amplitudes

scholarly journals Feynman rules for the rational part of the QCD 1-loop amplitudes

2009 ◽  
Vol 2009 (04) ◽  
pp. 072-072 ◽  
Author(s):  
P Draggiotis ◽  
M.V Garzelli ◽  
C.G Papadopoulos ◽  
R Pittau
Keyword(s):  
Rational Part ◽  
Feynman Rules ◽  
Loop Amplitudes

scholarly journals Feynman rules for the rational part of the electroweak 1-loop amplitudes

2010 ◽  
Vol 2010 (1) ◽  
Author(s):  
M. V. Garzelli ◽  
I. Malamos ◽  
R. Pittau
Keyword(s):  
Rational Part ◽  
Feynman Rules ◽  
Loop Amplitudes

scholarly journals Erratum: Feynman rules for the rational part of the Electroweak 1-loop amplitudes

2010 ◽  
Vol 2010 (10) ◽  
Author(s):  
M. V. Garzelli ◽  
I. Malamos ◽  
R. Pittau
Keyword(s):  
Rational Part ◽  
Feynman Rules ◽  
Loop Amplitudes

Failure of the Feynman R1 gauge for the standard model: An explicit example

2016 ◽  
Vol 31 (04n05) ◽  
pp. 1650028 ◽  
Author(s):  
Tai Tsun Wu ◽  
Sau Lan Wu
Keyword(s):  
Standard Model ◽  
Correct Answer ◽  
Gauge Invariance ◽  
Higgs Particle ◽  
Great Care ◽  
Simple Argument ◽  
Incorrect Answer ◽  
Unitary Gauge ◽  
The Standard Model ◽  
Feynman Rules

The decay of the Higgs particle into two photons through a [Formula: see text] loop was calculated in a straightforward way four years ago on the basis of the standard model. This calculation was carried out in the unitary gauge. Nevertheless, all attempts to reproduce this correct answer using the Feynman rules in the [Formula: see text] gauge, or the more general [Formula: see text] gauge, have failed. In this paper, a detailed analysis is carried out to compare the unitary gauge with the [Formula: see text] gauge; through this comparison, the underlying reason is determined why the answer cannot be obtained using the Feynman rules in the [Formula: see text] gauge. This is the first example where the use of the Feynman rules in the [Formula: see text] gauge leads to an incorrect answer, and this incorrect answer cannot be ruled out by any simple argument such as gauge invariance. It means that great care must be exercised in using Feynman rules.

scholarly journals Towards Feynman rules for conformal blocks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sarah Hoback ◽  
Sarthak Parikh
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Hypergeometric Functions ◽  
Power Series Expansion ◽  
Effective Field ◽  
Conformal Block ◽  
Tree Level ◽  
Conformal Blocks ◽  
Simple Set ◽  
Feynman Rules

Abstract We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

scholarly journals Loops in AdS: from the spectral representation to position space. Part II

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Dean Carmi
Keyword(s):  
Spectral Representation ◽  
Tree Level ◽  
Point Function ◽  
Position Space ◽  
Gross Neveu Model ◽  
Loop Amplitudes

Abstract We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-N conformal Gross Neveu model on AdS3. The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [1] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in AdS. Finally, we compute various bulk 2-point correlators, extending the results of [1].

scholarly journals One-loop string corrections to AdS amplitudes from CFT

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
J.M. Drummond ◽  
H. Paul
Keyword(s):  
Stress Tensor ◽  
Analytic Structure ◽  
Position Space ◽  
Yang Mills ◽  
String Corrections ◽  
The One ◽  
Loop Amplitudes

Abstract We consider α′ corrections to the one-loop four-point correlator of the stress- tensor multiplets in $$ \mathcal{N} $$ N = 4 super Yang-Mills at order 1/N4. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS5 × S5. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in α′ not considered before.

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