FeynCalc goes multiloop

Shtabovenko, Vladyslav

doi:10.1088/1742-6596/2438/1/012140

Cited by 9 publications

(4 citation statements)

References 134 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While we can compute any Feynman diagram in principle as a practical matter the combinatoric explosion in indexes requires the use of dedicated software. An appropriate starting point may be provided by the open source Mathematica packages FeynGrav, FeynCalc, FeynArts [62][63][64][65][66][67]95,96,[143][144][145][146].…”

Section: Discussionmentioning

confidence: 99%

A Renormalizable Model of Quantum Gravity

Ashmead

2023

Preprint

View full text Add to dashboard Cite

Two main problems stand in the way of unifying quantum mechanics and general relativity. First, the treatment of time and space in quantum electrodynamics (QED) is not fully covariant. Second, the ultraviolet divergences in QED are not renormalizable. In previous work, we ad- dressed the rst problem by promoting time from parameter to operator: with this the treatment of time and space in QED became fully covari- ant. The most obvious prediction was additional dispersion in time at the attosecond scale; such eects are falsiable with current technology. As an unexpected but welcome side-eect, this regularized the ultraviolet divergences in QED. We therefore ask \will promoting time to opera- tor regularize the ultraviolet divergences in quantum general relativity (QGR)?" Using the existing literature on QGR as a base, we show we can rewrite QGR with time as an operator. And that the ultraviolet diver- gences are contained in QGR just as they are in QED. We show that there are feasible tests which can distinguish between standard QGR and TGR. We conclude that TGR represents a renormalizable model of quantum gravity which is consistent with existing observational and experimental evidence and which is falsiable in principle.

show abstract

Section: Discussionmentioning

confidence: 99%

A Renormalizable Model of Quantum Gravity

Ashmead

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…In each family of three-loop Feynman integrals for the P -wave case, there are twelve inverse propagators where nine are free from the small momentum k and the remaining three are irreducible numerators involving k [56]. Based on the symmetry among different families, we use our Mathematica code + LiteRed [163] + FIRE6 [164] to minimize [165][166][167][168][169][170] the total number of families for all Feynman integrals. For each current J coupled to the P -wave c b meson, the total number of families for three-loop Feynman integrals is minimized from 841 to 102.…”

Section: Jhep06(2024)012mentioning

confidence: 99%

Decay constants of $$ c\overline{b} $$ mesons involving the ten heavy flavor-changing currents at N3LO QCD

Tao,

Xiao

2024

J. High Energ. Phys.

View full text Add to dashboard Cite

Within the nonrelativistic QCD (NRQCD) framework, we complete the three-loop calculations of the NRQCD renormalization constants and the matching coefficients, for the heavy flavor-changing temporal vector, spatial-spatial tensor, spatial-temporal axial-tensor currents, which are coupled to the P-wave $$ c\overline{b} $$ c b ¯ mesons. We further study the ten decay constants for the $$ c\overline{b} $$ c b ¯ mesons (Bc, $$ {B}_c^{\ast } $$ B c ∗ , $$ {B}_{c0}^{\ast } $$ B c 0 ∗ , Bc1) coupled with the ten heavy flavor-changing currents involving (pseudo-)scalar, (axial-)vector and (axial-)tensor up to the next-to-next-to-next-to-leading order (N3LO) of αs. We obtain the six ratios of decay constants by approximating them to the corresponding ratios of matching coefficients. We find the N3LO perturbative QCD results for the six ratios of decay constants have good convergence and weak scale-dependence. We finally predict the hierarchical relationship among the ten decay constants for the $$ c\overline{b} $$ c b ¯ mesons coupled with the ten currents.

show abstract

“…The Dirac and color algebra is performed with FORM [48]. Subsequently, the Feynman integrals are classified into different integral families with an in-house code invoking Reduze 2 [49] and the latest version of FeynCalc [50,51]. During the topology classification, partial fractions with respect to the Feynman propagators are also needed, and they are performed using Apart [52].…”

Section: Jhep04(2023)041mentioning

confidence: 99%

Renormalization of twist-two operators in covariant gauge to three loops in QCD

Gehrmann

Manteuffel

Yang

2023

J. High Energ. Phys.

View full text Add to dashboard Cite

The leading short-distance contributions to hadronic hard-scattering cross sections in the operator product expansion are described by twist-two quark and gluon operators. The anomalous dimensions of these operators determine the splitting functions that govern the scale evolution of parton distribution functions. In massless QCD, these anomalous dimensions can be determined through the calculation of off-shell operator matrix elements, typically performed in a covariant gauge, where the physical operators mix with gauge-variant operators of the same quantum numbers. We derive a new method to systematically extract the counterterm Feynman rules resulting from these gauge-variant operators. As a first application of the new method, we rederive the unpolarized three-loop singlet anomalous dimensions, independently confirming previous results obtained with other methods. Employing a general covariant gauge, we observe the explicit cancellation of the gauge parameter dependence in these results.

show abstract

FeynCalc goes multiloop

Cited by 9 publications

References 134 publications

A Renormalizable Model of Quantum Gravity

A Renormalizable Model of Quantum Gravity

Decay constants of $$ c\overline{b} $$ mesons involving the ten heavy flavor-changing currents at N3LO QCD

Renormalization of twist-two operators in covariant gauge to three loops in QCD

Contact Info

Product

Resources

About