Bhabha scattering at NNLO with next-to-soft stabilisation

Banerjee, Pulak; Engel, Tim; Schalch, Nicolas; Signer, Adrian; Ulrich, Yannick

doi:10.1016/j.physletb.2021.136547

Cited by 30 publications

(46 citation statements)

References 39 publications

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“…So far the NNLO cross section is only known in the massless limit, supplemented by the non power-suppressed finite mass effects (see, e.g., ref. [1] for recent results). Complete NNLO results including the full dependence on the electron mass, however, are not yet available.…”

Section: Introductionmentioning

confidence: 94%

“…As a byproduct of our analysis, we will also provide a very compact analytic result for the remaining master integral in the first family in figure 1(a) in terms of the same class of functions. 1 The rest of the paper is organised as follows. In section 2 we explain the notation, present the system of canonical differential equations for the problem at hand, and introduce the alphabet needed to describe the planar family in figure 1(b).…”

Section: Introductionmentioning

confidence: 99%

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Analytic results for two-loop planar master integrals for Bhabha scattering

Duhr¹,

Smirnov

Tancredi

2021

J. High Energ. Phys.

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We analytically evaluate the master integrals for the second type of planar contributions to the massive two-loop Bhabha scattering in QED using differential equations with canonical bases. We obtain results in terms of multiple polylogarithms for all the master integrals but one, for which we derive a compact result in terms of elliptic multiple polylogarithms. As a byproduct, we also provide a compact analytic result in terms of elliptic multiple polylogarithms for an integral belonging to the first family of planar Bhabha integrals, whose computation in terms of polylogarithms was addressed previously in the literature.

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Analytic results for two-loop planar master integrals for Bhabha scattering

Duhr¹,

Smirnov

Tancredi

2021

J. High Energ. Phys.

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“…(1) ISR , while the ones for the other light particle (outgoing electron) contributes to √ Z (1) . The renormalised results for J (1) ISR and √ Z (1) are given in Appendix B. The factor √ Z (1) corresponds to the one-loop massification constant of [28].…”

Section: Collinear Factorisation At One Loopmentioning

confidence: 99%

“…The approximation of the corresponding expression using the soft expansion up to subleading power yields an elegant solution to this problem. This next-to-soft stabilisation has facilitated the first calculation of fullydifferential NNLO QED corrections to Bhabha [1] and Møller [2] scattering. Even though the soft expansion can straightforwardly be computed with the method of regions [3] the corresponding calculation is cumbersome.…”

Section: Introductionmentioning

confidence: 97%

Universal structure of radiative QED amplitudes at one loop

Engel,

Signer,

Ulrich

2021

Preprint

Self Cite

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We present two novel results about the universal structure of radiative QED amplitudes in the soft and in the collinear limit. On the one hand, we extend the well-known Low-Burnett-Kroll theorem to the one-loop level and give the explicit relation between the radiative and non-radiative amplitude at subleading power in the soft limit. On the other hand, we consider a factorisation formula at leading power in the limit where the emitted photon becomes collinear to a light fermion and provide the corresponding one-loop splitting function. In addition to being interesting in their own right these findings are particularly relevant in the context of fully-differential higher-order QED calculations. One of the main challenges in this regard is the numerical stability of radiative contributions in the soft and collinear regions. The results presented here allow for a stabilisation of real-virtual amplitudes in these delicate phase-space regions by switching to the corresponding approximation without the need of explicit computations.

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“…At next-to-next-to-leading order (NNLO) the required two-loop amplitudes still need to be derived on a process-by-process basis. To date, full NNLO predictions for 2 → 2 processes are widely available (see [11][12][13][14][15][16][17][18][19] for recent progress), while for 2 → 3 processes only a few two-loop amplitudes [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and pioneering NNLO results [36][37][38][39] exist. The complexity and the status of NLO calculations for loop-induced processes is similar, with an increasing number of 2 → 2 predictions [40][41][42][43][44] and first results for 2 → 3 processes [45].…”

Section: Introductionmentioning

confidence: 99%

Two-loop tensor integral coefficients in OpenLoops

Pozzorini,

Schär,

Zoller

2022

Preprint

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We present a new and fully general algorithm for the automated construction of the integrands of two-loop scattering amplitudes. This is achieved through a generalisation of the open-loops method to two loops. The core of the algorithm consists of a numerical recursion, where the various building blocks of two-loop diagrams are connected to each other through process-independent operations that depend only on the Feynman rules of the model at hand. This recursion is implemented in terms of tensor coefficients that encode the polynomial dependence of loop numerators on the two independent loop momenta. The resulting coefficients are ready to be combined with corresponding tensor integrals to form scattering probability densities at two loops. To optimise CPU efficiency we have compared several algorithmic options identifying one that outperforms naive solutions by two orders of magnitude. This new algorithm is implemented in the OpenLoops framework in a fully automated way for two-loop QED and QCD corrections to any Standard Model process. The technical performance is discussed in detail for several 2 → 2 and 2 → 3 processes with up to order 10 5 two-loop diagrams. We find that the CPU cost scales linearly with the number of two-loop diagrams and is comparable to the cost of corresponding real-virtual ingredients in a NNLO calculation. This new algorithm constitutes a key building block for the construction of an automated generator of scattering amplitudes at two loops.

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Bhabha scattering at NNLO with next-to-soft stabilisation

Cited by 30 publications

References 39 publications

Analytic results for two-loop planar master integrals for Bhabha scattering

Analytic results for two-loop planar master integrals for Bhabha scattering

Universal structure of radiative QED amplitudes at one loop

Two-loop tensor integral coefficients in OpenLoops

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