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Lepton pair production at NNLO in QED with EW effects
by Sophie Kollatzsch, Yannick Ulrich
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Sophie Kollatzsch · Yannick Ulrich |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202303_00002v2 (pdf) |
| Code repository: | https://gitlab.com/mule-tools/mcmule/ |
| Data repository: | https://gitlab.com/mule-tools/user-library/-/tree/master/dilepton/belle |
| Date accepted: | 2023-07-20 |
| Date submitted: | 2023-05-17 10:55 |
| Submitted by: | Ulrich, Yannick |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Computational, Phenomenological |
Abstract
We present a fully differential calculation of lepton pair production, taking into account the dominant next-to-next-to-leading order QED corrections as well as next-to-leading order electroweak, and polarisation effects. We include all lepton masses, hard photon emission, as well as non-perturbative hadronic corrections. The corresponding matrix elements are implemented in the Monte Carlo framework McMule. In order to obtain a numerically stable implementation, we extend next-to-soft stabilisation, a universal technique based on a next-to-leading-power expansion, to calculations with polarised leptons. As an example, we show results tailored to the Belle II detector with the current setup as well as a potential future configuration that includes polarised beams.
Author comments upon resubmission
In response to Report 3, we have further clarified what is included in our result, both in terms of diagrams and counting. Further, we have rectified the discussion of the renormalisation by clarifying what is meant by variables in the code. Hence, we now believe that the explanation of our renormalisation procedure is clear at NLO and NNLO. Regarding the self-energy contributions, we argue that the symbol $\Sigma$ is defined unambiguously through (10). While we agree that $\Sigma_{\gamma\gamma}(0)$ and $\Sigma_{\gamma Z,f}(0)$ vanish, we would argue in favour of keeping (11) and thus (14) unchanged for the sake of completeness. In the interest of clarity and to address the referee's comment, we have added a footnote explaining the issue. We have also added a footnote discussing the top quark contribution to the fermionic self-energy. We have further stressed the connection of our expansion to low-energy effective theory (LEFT), which should also allay any concerns regarding Ward identities and the systematic nature of the expansion.
In response to Report 2, we have clarified the text before (42) and apologise for any confusion we have caused. We further believe that our explanation of LEFT will explain what is meant by dimension-six terms in the context of this work.
Finally, we have fixed a number of typos and, partially in response to Report 3, improved the notation in Section 2.1. We trust that the paper is now acceptable for publication.
List of changes
* We have clarified what is included at what order, both in terms of diagrams and counting.
* We have removed the split into $Q_e^i Q_\tau^j$ for the NLO-EW contribution in response to Referee 3.
* We have connected our expansion to effective field theories and thereby explained dimension-six and dimension-eight contributions.
* We have clarified the choice of the input scheme as well as how it is implemented in the code.
* We have added footnotes in Section 2.1 discussing top quarks and the verbosity in the discussion of the self-energies.
* We have fixed a number of typos and improved the notation.
* We have clarified and improved the discussion of EW cross sections in Section 4.1.
Published as SciPost Phys. 15, 104 (2023)