English
Related papers

Related papers: Analytic results for planar three-loop integrals f…

200 papers

We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…

High Energy Physics - Phenomenology · Physics 2026-03-06 Pau Petit Rosàs

All three-loop on-shell QCD Feynman integrals with two masses can be reduced to 27 master integrals. Here we calculate these master integrals, expanded in epsilon, both exactly in the mass ratio and as series in limiting cases.

High Energy Physics - Phenomenology · Physics 2009-12-27 S. Bekavac , A. G. Grozin , D. Seidel , V. A. Smirnov

In modern quantum field theory, one of the most important tasks is the calculation of loop integrals. Loop integrals appear when evaluating the Feynman diagrams with one or more loops by integrating over the internal momenta. Even though…

High Energy Physics - Theory · Physics 2020-06-24 Maxim Bezuglov

The quarkonic contributions to the three-loop heavy-quark form factors for vector, axial-vector, scalar and pseudoscalar currents are described by closed form difference equations for the expansion coefficients in the limit of small…

High Energy Physics - Phenomenology · Physics 2023-07-07 Johannes Blümlein , Abilio De Freitas , Peter Marquard , Narayan Rana , Carsten Schneider

We calculate all three-loop, five-point, massless planar Feynman integral families in the dimensional regularization scheme. This is a new milestone in Feynman integral computations. The analysis covers four distinct families of Feynman…

High Energy Physics - Phenomenology · Physics 2025-12-22 Dmitry Chicherin , Yu Wu , Zihao Wu , Yongqun Xu , Shun-Qing Zhang , Yang Zhang

The computation of Feynman integrals is often the bottleneck of multi-loop calculations. We propose and implement a new method to efficiently evaluate such integrals in the physical region through the numerical integration of a suitable set…

High Energy Physics - Phenomenology · Physics 2019-05-01 Manoj K. Mandal , Xiaoran Zhao

We present an analytical method to calculate the three-loop massive Feynman integral in arbitrary dimensions. The method is based on the Mellin-Barnes representation of the Feynman integral. The Meijer theorem and its corollary are used to…

High Energy Physics - Phenomenology · Physics 2024-08-06 Jian Wang , Dongyu Yang

We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs$\to 3$ partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to…

High Energy Physics - Phenomenology · Physics 2017-02-01 Roberto Bonciani , Vittorio Del Duca , Hjalte Frellesvig , Johannes M. Henn , Francesco Moriello , Vladimir A. Smirnov

We present the color planar and complete light quark QCD contributions to the three loop heavy quark form factors in the case of vector, axial-vector, scalar and pseudo-scalar currents. We evaluate the master integrals applying a new method…

High Energy Physics - Phenomenology · Physics 2018-07-18 Jakob Ablinger , Johannes Bluemlein , Peter Marquard , Narayan Rana , Carsten Schneider

We present the analytic expressions for the color-planar contributions to the heavy-light form factors at three loops in perturbative QCD. These form factors play an important role in the precision predictions of various observables in top…

High Energy Physics - Phenomenology · Physics 2023-08-24 Sudeepan Datta , Narayan Rana , V. Ravindran , Ratan Sarkar

We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential…

High Energy Physics - Theory · Physics 2015-06-16 Johannes M. Henn , Vladimir A. Smirnov

We summarize the results for the master integrals of the three-loop quark and gluon form factor in massless QCD. Working in dimensional regularization we extract poles up to 1/epsilon^6. The computational techniques involve, among others,…

High Energy Physics - Phenomenology · Physics 2010-01-20 T. Huber

We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\tau =2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing…

High Energy Physics - Phenomenology · Physics 2015-06-19 Jakob Ablinger , Johannes Blümlein , Clemens Raab , Carsten Schneider , Fabian Wißbrock

A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…

High Energy Physics - Phenomenology · Physics 2016-04-14 Johannes Bluemlein , Khiem Hong Phan , Tord Riemann

The three-loop form factors in massless QCD can be expressed as a linear combination of master integrals. Besides a number of master integrals which factorise into products of one-loop and two-loop integrals, one finds 16 genuine three-loop…

High Energy Physics - Phenomenology · Physics 2010-04-05 T. Gehrmann , G. Heinrich , T. Huber , C. Studerus

We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes…

High Energy Physics - Phenomenology · Physics 2014-06-13 Thomas Gehrmann , Andreas von Manteuffel , Lorenzo Tancredi , Erich Weihs

We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…

High Energy Physics - Phenomenology · Physics 2020-12-30 S. Abreu , H. Ita , F. Moriello , B. Page , W. Tschernow , M. Zeng

We studied the two-loop non-factorizable Feynman diagrams for the $t$-channel single-top production process in quantum chromodynamics. We present a systematic computation of master integrals of the two-loop Feynman diagrams with one…

High Energy Physics - Phenomenology · Physics 2023-07-12 Zihao Wu , Ming-Ming Long

In this manuscript, we elaborate on a procedure to derive $\epsilon$-factorised differential equations for multi-scale, multi-loop classes of Feynman integrals that evaluate to special functions beyond multiple polylogarithms. We…

High Energy Physics - Theory · Physics 2023-08-09 Lennard Görges , Christoph Nega , Lorenzo Tancredi , Fabian J. Wagner

I describe a method to calculate a class of three-loop selfenergy diagrams for arbitrary internal masses and external momentum. This method combines analytical results and numerical integration, and is suitable for implementation in a…

High Energy Physics - Phenomenology · Physics 2009-10-28 Adrian Ghinculov