| 1. |
- Alcock-Zeilinger, Judith, et al.
(författare)
-
Wigner 6 j symbols for SU(N) : Symbols with at least two quark-lines
- 2023
-
Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 64:2
-
Tidskriftsartikel (refereegranskat)abstract
- We study a class of SU(N) Wigner 6j symbols involving two fundamental representations and derive explicit formulas for all 6j symbols in this class. Our formulas express the 6j symbols in terms of the dimensions of the involved representations, and they are thereby functions of N. We view these explicit formulas as a first step toward efficiently decomposing SU(N) color structures in terms of group invariants.
|
|
| 2. |
- Alnefjord, Joakim, et al.
(författare)
-
A Brief Look at the Chirality-Flow Formalism for Standard Model Amplitudes
- 2021
-
Ingår i: The Ninth Annual Conference on Large Hadron Collider Physics : LHCP2021 - LHCP2021. - 1824-8039. ; 397
-
Konferensbidrag (refereegranskat)abstract
- Inspired by the flow description of su(N) colour calculations, we recently showed how to simplify the spinor-helicity formalism (at the algebra level two copies of complexified su(2)) by treating each Weyl spinor as part of a flow line with definite chirality and momentum. This formalism, dubbed the chirality-flow formalism, eliminates all non-trivial algebra from tree-level spinor-helicity calculations, thus allowing the shortest possible route from Feynman diagrams to complex numbers (spinor inner products). In this presentation, we briefly introduce the main features of this method and show some examples.
|
|
| 3. |
- Alnefjord, Joakim, et al.
(författare)
-
The chirality-flow formalism for the standard model
- 2021
-
Ingår i: European Physical Journal C. - : Springer Science and Business Media LLC. - 1434-6044 .- 1434-6052. ; 81:4
-
Tidskriftsartikel (refereegranskat)abstract
- In a recent paper we introduced the chirality-flow formalism, a method for simple and transparent calculations of Feynman diagrams based on the left- and right-chiral sl(2 , C) nature of spacetime. While our previous work focused on massless QED and QCD at tree-level, we here extend the chirality-flow formalism to the full (tree-level) Standard Model, including massive particles and electroweak interactions – for which the W-interaction simplifies elegantly due to its chiral nature. We illustrate how values of Feynman diagrams can be immediately written down with some representative examples.
|
|
| 4. |
- Boman, Emil, et al.
(författare)
-
Simplifying QCD event generation with chirality flow, reference vectors and spin directions
- 2024
-
Ingår i: Journal of High Energy Physics. - 1029-8479. ; 2024:2
-
Tidskriftsartikel (refereegranskat)abstract
- The chirality-flow formalism, combined with good choices of gauge reference vectors, simplifies tree-level calculations to the extent that it is often possible to write down amplitudes corresponding to Feynman diagrams immediately. It has also proven to give a very sizable speedup in a proof of concept implementation of massless tree-level QED in MadGraph5_aMC@NLO. In the present paper we extend this analysis to QCD, including massive quarks. We define helicity-dependent versions of the gluon vertices, derive constraints on the spinor structure of propagating gluons, and explore the Schouten identity to simplify the four-gluon vertex further. For massive quarks, the chirality-flow formalism sheds light on how to exploit the freedom to measure spin along any direction to shorten the calculations. Overall, this results in a clear speedup for treating the Lorentz structure at high multiplicities.
|
|
| 5. |
|
|
| 6. |
- Keppeler, Stefan, et al.
(författare)
-
Wigner 6j symbols with gluon lines : completing the set of 6j symbols required for color decomposition
- 2024
-
Ingår i: Journal of High Energy Physics. - 1029-8479. ; 2024:5
-
Tidskriftsartikel (refereegranskat)abstract
- We construct a set of Wigner 6j symbols with gluon lines (adjoint representations) in closed form, expressed in terms of similar 6j symbols with quark lines (fundamental representations). Together with these Wigner 6j symbols with quark lines, this gives a set of 6j symbols sufficient for treating QCD color structure for any number of external particles, in or beyond perturbation theory. This facilitates a complete treatment of QCD color structure in terms of orthogonal multiplet bases, without the need of ever explicitly constructing the corresponding bases. We thereby open up for a completely representation theory based treatment of SU(N) color structure, with the potential of significantly speeding up the color structure treatment.
|
|
| 7. |
- Lifson, Andrew, et al.
(författare)
-
One-loop calculations in the chirality-flow formalism
- 2023
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In a few recent papers we introduced the chirality-flow formalism, which was shown to make calculations of tree-level Feynman diagrams simple and transparent. Chirality flow, which is based on the spinor-helicity formalism, allows to often immediately analytically write down a tree-level Feynman diagram in terms of spinor inner products. In this paper, we argue that there is also a significant simplification of the Lorentz structure at the one-loop level, at least when using the four-dimensional formulation of the four-dimensional helicity scheme. Additionally, we find that the possible terms in a tensor decomposition of loop integrals are highly constrained, and therefore the tensor reduction procedure is simplified.
|
|
| 8. |
- Lifson, Andrew, et al.
(författare)
-
The chirality-flow formalism
- 2020
-
Ingår i: European Physical Journal C. - : Springer Science and Business Media LLC. - 1434-6044 .- 1434-6052. ; 80:11
-
Tidskriftsartikel (refereegranskat)abstract
- We 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.
|
|
| 9. |
- Plätzer, Simon, et al.
(författare)
-
Color matrix element corrections for parton showers
- 2018
-
Ingår i: Journal of High Energy Physics. - 1029-8479. ; 2018:11
-
Tidskriftsartikel (refereegranskat)abstract
- We investigate the effects of keeping the full color structure for parton emissions in parton showers for both LEP and LHC. This is done within the Herwig 7 dipole shower, and includes gluon emission, gluon splitting, initial state branching processes, as well as hadronization. The subleading Nc terms are included as color matrix element corrections to the splitting kernels by evolving an amplitude-level density operator and correcting the radiation pattern for each parton multiplicity, up to a fixed number of full color emissions, after which a standard leading color shower takes over. Our results are compared to data for a wide range of LEP and LHC observables and show that the subleading Nc corrections tend to be small for most observables probing hard, perturbative dynamics, for both LEP and LHC. However, for some of these observables they exceed 10%. On soft physics we find signs of significantly larger effects.
|
|
| 10. |
- Sjodahl, Malin, et al.
(författare)
-
QCD multiplet bases with arbitrary parton ordering
- 2018
-
Ingår i: Journal of High Energy Physics. - 1029-8479. ; 2018:11
-
Tidskriftsartikel (refereegranskat)abstract
- We develop an algorithm for recursively constructing orthogonal multiplet bases for the color space of QCD, for any order of partons and any Nc. This recipe is then applied for explicitly constructing some of these bases. Using the bases, a corresponding set of Wigner 6j coefficients are calculated. The Wigner coefficients offer a method of using multiplet bases without resorting to the explicit expressions of the basis vectors, which lead to a significant speed-up compared to other methods of treating full color structure.
|
|
