Renormalisation group effects on SMEFT interpretations of LHC data

Published for SISSA by Springer Received: January 11, 2023 Revised: August 19, 2023 Accepted: September 19, 2023 Published: September 27, 2023 Rafael Aoude,a Fabio Maltoni,a,b Olivier Mattelaer,a Claudio Severic and Eleni Vryonidouc a Centre for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium b Dipartimento di Fisica e Astronomia, Università di Bologna and INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy c Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, U.K. E-mail: , , , , Abstract: We explore the impact of Renormalisation Group (RG) effects in the Standard Model Effective Field Theory (SMEFT) interpretations of LHC measurements. We implement the RG running and mixing for the Wilson coefficients as obtained from the one-loop anomalous dimension matrix in the SMEFT into a Monte Carlo generator. This allows to consistently predict and combine in global fits collider observables characterised by different scales. As a showcase, we examine the impact of RG running in the strong coupling on the SMEFT predictions for tt̄ production cross sections and differential distributions as well as on the bounds on the Wilson coefficients that can be obtained from current LHC data. Keywords: Renormalization Group, SMEFT, Automation ArXiv ePrint: 2212.05067 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP09(2023)191 JHEP09(2023)191 Renormalisation group effects on SMEFT interpretations of LHC data Contents 1 2 Computation and Monte Carlo implementation setup 3 3 RGE of top quark operators 3.1 Bosonic and two-quark operators 3.2 Four-fermion operators 4 4 6 4 Results for top pair production at the LHC 4.1 Scale choices 4.2 Cross-section results 4.3 Differential distributions 4.4 Comparison of NLO with the RGE-evolved LO 9 10 10 12 13 5 Impact of RGE effects on constraints on the EFT 14 6 Conclusion 17 A Conventions for operators with repeated currents 20 B Additional results for differential distributions 20 C Generation details 20 1 Introduction In the light of no evidence for the existence of new degrees of freedom at the weak scale or below, the Standard Model Effective Field Theory (SMEFT) [1–3] provides a conceptually simple, compelling, and powerful framework to probe beyond the Standard Model physics. The SMEFT allows us to consistently and systematically parameterise possible deviations from the SM predictions in the interactions among the known particles, using minimal theoretical assumptions. The interest in the SMEFT approach has triggered considerable efforts over the last years not only in the quest for the best SM predictions, which are necessary to detect deviations, but also to improve the accuracy of the SMEFT predictions by consistently including higher order corrections in QCD and EW couplings. With improved predictions at hand and more and more precise measurements coming from the LHC, performing global interpretations of LHC measurements has become imperative and first results in the top quark sector [4–7], the Higgs and electroweak gauge sector [8–10] as well as combinations of the two [11, 12] have appeared. –1– JHEP09(2023)191 1 Introduction –2– JHEP09(2023)191 These first studies have demonstrated that global interpretations in the SMEFT are feasible and that order of tens of operator coefficients can be determined simultaneously, by also exploiting the crucial fact that the SMEFT correlates observables from different sectors. Whilst the combination of different processes is needed to maximise the potential of SMEFT interpretations, it comes with various complications and challenges. One such complication is the fact that observables are typically associated to specific energy scales, even in the same experiment. The same SMEFT operators are therefore probed at different scales. In order to consistently combine the results, however, Renormalisation Group (RG) effects should be taken into account, as RG Equations (RGE) are necessary to account for different natural scales of different processes. In principle, an approximate RGE flow can be computed off-line and once and for all. The complete RGE of the SMEFT at dimension-6 are known at one-loop [13–15], and several codes exist which allow one to input a set of Wilson coefficients at a given scale and extract them at a different one [16–20]. Results on the SMEFT RGE for selected dimension-8 operators are also available at one loop [21–24]. Up to now, the RGE evolution in SMEFT interpretations of LHC measurements has either been neglected altogether, or it has been taken from a high-scale µ0 to a fixed low-scale µ. Analyses where the scale µ is chosen bin-by-bin for differential distributions have started to appear in the literature [25]. However, the analysis of observables such as differential distributions, that span orders of magnitude in energy, calls for an event-by-event choice of renormalisation scale, that can only be handled in a Monte Carlo tool at runtime. A dynamical scale choice requires recomputing the Wilson coefficients at every phase-space point, and the only practical way of incorporating such RGE effects into theoretical predictions is to include them into suitable MC generators. Up to now, no dedicated implementation has been made available. In this work we present the first implementation of RGE effects in a Monte Carlo generator, Madgraph5_aMC@NLO [26]. We discuss the implementation and then present phenomenological examples where the impact of RGE is investigated within the context of SMEFT interpretations, and compare it with the next-to-leading order predictions. RG improved predictions for SMEFT can potentially form an intermediate step towards a full next-to-leading (NLO) order computation by resumming large logarithms. Our current implementation focuses on leading-order RGE improved results, which capture the leading effects arising from the presence of separated energy scales. We nevertheless envision that our setup, combined with the NLO computations of [27] and the two-loop anomalous dimension matrix (once available) will form the basis of state-of-the-art SMEFT predictions in the coming years. The paper is organised as follows. We describe the setup used and implementation details in section 2. In section 3 we discuss RGE effects for top quark operators presenting the relevant anomalous dimension matrix and several examples of operator running and mixing. In section 4, as an example we focus on top pair production and show the results for the LHC taking into account running and mixing for different choices of dynamical and fixed scales. These results are then used in section 5 to perform a toy fit to illustrate the impact of RGE effects when constraining the Wilson coefficients. Finally we conclude in section 6. 2 Computation and Monte Carlo implementation setup In the conte (...truncated)