One-loop Feynman integral reduction by differential operators

Hu, Chang; Li, Tingfei; Li, Xiaodi

doi:10.1103/physrevd.104.116014

“…As pointed out in several papers [18,50,[54][55][56][57], arbitrary tensor structure can be compactly organized using an auxiliary vector R. Thus for TR of one-loop n-point integrals, we enlarge the set of propagators given in (2.1) by adding one new propagator, i.e.,…”

Section: The Methodsmentioning

confidence: 99%

Module Intersection and Uniform Formula for Iterative Reduction of One-loop Integrals

Chen¹,

Bao²

2022

Preprint

0

View full text Add to dashboard Cite

In this paper, we develop an iterative sector-level reduction strategy for Feynman integrals, which bases on module intersection in the Baikov representation and auxiliary vector for tensor structure. Using this strategy we have studied the reduction of general one-loop integrals, i.e., integrals having arbitrary tensor structures and arbitrary power for propagators. Inspired by these studies, a uniform and compact formula that iteratively reduces all one-loop integrals has been written down, where messy polynomials in integration-by-parts (IBP) relations have organized themselves to Gram determinants.

show abstract

“…It is easy to see that with higher and higher tensor rank, there will be more and more different tensor structures to be written down in (2.2) and more and more algebraic relations to be established to fix them. A nice observation made in [1,2] is that the complicated tensor structure can be simply recovered from…”

Section: Jhep08(2022)110mentioning

confidence: 99%

“…Recently, we proposed a new framework for general one-loop tensor reduction by employing an auxiliary vector R and two kinds of differential operators [1,2]. Similar to other reduction methods, our method also suffers from divergences for vanishing Gram determinant, which appears as the inverse of Gram matrix in the recursion constructions of reduction coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…To see this picture clearly, calculating analytic coefficients will be important, which is exactly the merit of our new method. In this paper, we will systematically study the degenerate case with vanishing Gram determinant using the results in [1,2]. It turns out that the decomposition coefficients can easily be solved as a series in the Gram determinant.…”

Section: Introductionmentioning

confidence: 99%

“…

An improved PV-reduction (Passarino-Veltman) method for one-loop integrals with auxiliary vector R has been proposed in [1,2]. It has also been shown that the new method is a self-completed method in [3].

…”

mentioning

confidence: 99%

See 2 more Smart Citations

Reduction with degenerate Gram matrix for one-loop integrals

Feng

¹

,

Hu

²

,

Li

³

et al. 2022

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

An improved PV-reduction (Passarino-Veltman) method for one-loop integrals with auxiliary vector R has been proposed in [1, 2]. It has also been shown that the new method is a self-completed method in [3]. Analytic reduction coefficients can be easily produced by recursion relations in this method, where the Gram determinant appears in denominators. The singularity caused by Gram determinant is a well-known fact and it is important to address these divergences in a given frame. In this paper, we propose a systematical algorithm to deal with this problem in our method. The key idea is that now the master integral of the highest topology will be decomposed into combinations of master integrals of lower topologies. By demanding the cancellation of divergence for obtained general reduction coefficients, we solve decomposition coefficients as a Taylor series of the Gram determinant. Moreover, the same idea can be applied to other kinds of divergences.

show abstract

Module intersection and uniform formula for iterative reduction of one-loop integrals

Chen

¹

,

Feng

²

2023

J. High Energ. Phys.

View full text Add to dashboard Cite

In this paper, we develop an iterative sector-level reduction strategy for Feynman integrals, which bases on module intersection in the Baikov representation and auxiliary vector for tensor structure. Using this strategy we have studied the reduction of general one-loop integrals, i.e., integrals having arbitrary tensor structures and arbitrary power for propagators. Inspired by these studies, a uniform and compact formula that iteratively reduces all one-loop integrals has been written down, where messy polynomials in integration-by-parts (IBP) relations have organized themselves to Gram determinants.

show abstract

One-loop Feynman integral reduction by differential operators

Cited by 11 publications

References 43 publications

Module Intersection and Uniform Formula for Iterative Reduction of One-loop Integrals

Module Intersection and Uniform Formula for Iterative Reduction of One-loop Integrals

Reduction with degenerate Gram matrix for one-loop integrals

Module intersection and uniform formula for iterative reduction of one-loop integrals

Contact Info

Product

Resources

About