ALP — SMEFT interference

Published for SISSA by Springer Received: May 6, 2021 Accepted: June 6, 2021 Published: June 23, 2021 ALP — SMEFT interference a PRISMA+ Cluster of Excellence & Mainz Institute for Theoretical Physics, Johannes Gutenberg University, 55099 Mainz, Germany b Physik-Institut, Universität Zürich, CH-8057, Switzerland c Department of Physics & LEPP, Cornell University, Ithaca, NY 14853, U.S.A. d SISSA International School for Advanced Studies & INFN, Sezione di Trieste, Via Bonomea 265, 34136, Trieste, Italy E-mail: , , Abstract: The Standard Model Effective Field Theory (SMEFT) offers a powerful theoretical framework for parameterizing the low-energy effects of heavy new particles with masses far above the scale of electroweak symmetry breaking. Additional light degrees of freedom extend the effective theory. We show that light new particles that are weakly coupled to the SM via non-renormalizable interactions induce non-zero Wilson coefficients in the SMEFT Lagrangian via renormalization-group evolution. For the well-motivated example of axions and axion-like particles (ALPs) interacting with the SM via classically shift-invariant dimension-5 interactions, we calculate how these interactions contribute to the one-loop renormalization of the dimension-6 SMEFT operators, and how this running sources additional contributions to the Wilson coefficients on top of those expected from heavy new states. As an application, we study the ALP contributions to the magnetic dipole moment of the top quark and comment on implications of electroweak precision constraints on ALP couplings. Keywords: Effective Field Theories, Beyond Standard Model, Renormalization Group ArXiv ePrint: 2105.01078 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP06(2021)135 JHEP06(2021)135 Anne Mareike Galda,a Matthias Neuberta,b,c and Sophie Rennerd Contents 1 2 ALP couplings to the SM 4 3 Green’s functions requiring SMEFT counterterms 3.1 Purely bosonic operators 3.2 Operators containing a single fermion current 3.3 Four-fermion operators 3.4 Elimination of redundant operators 7 7 10 12 13 4 Derivation of the source terms 4.1 Renormalizable operators 4.2 Source terms of purely bosonic operators 4.3 Source terms of single fermion-current operators 4.4 Source terms of four-fermion operators 4.5 Structure of the source terms 14 14 15 17 18 19 5 Sample applications 5.1 Chromo-magnetic moment of the top quark 5.2 Example of a Z-pole constraint 21 21 23 6 Conclusions 24 A ALP source terms in an alternative operator basis 25 B RG evolution of ALP couplings 27 1 Introduction The absence of a discovery of new particles at the LHC suggests that additional degrees of freedom not contained in the Standard Model (SM) of particle physics have masses far above the scale of electroweak symmetry breaking. Existing hints of departures from the SM, indicated for instance by recent data on semileptonic decays of B mesons [1] and the anomalous magnetic moment of the muon [2], are in line with this expectation. Assuming that the theory above the electroweak scale respects the full SM gauge symmetry and that the Higgs is an SU(2)L doublet, the Standard Model Effective Field Theory (SMEFT) [3] provides a systematic approach for describing the virtual effects of heavy new particles on low-energy precision measurements (for a review, see [4]). –1– JHEP06(2021)135 1 Introduction Leff = LSM + 1 m2 (∂µ a)(∂ µ a) − a a2 + LSM+ALP + LSMEFT , 2 2 (1.1) where the last two terms consist of higher-dimensional operators starting at dimension-5 order. By definition the term LSMEFT consists of operators not containing the ALP field. We will refer to these operators as “SMEFT operators”, although of course the theory we are working in is not the pure SMEFT, but rather the effective theory whose degrees of freedom are the SM fields plus the ALP. Like any other new particle not contained in the SM, an ALP can be searched for either directly or indirectly. Direct searches using particle-physics detectors aim at detecting ALPs produced in a collider experiment by reconstructing them in various possible decay modes [15–26]. Our focus in this work is on indirect searches, which look for hints of the effects of virtual ALP exchange on precision measurements. As long as the scale f suppressing the ALP couplings to the SM is not excessively large,1 this opens up new, complementary ways to search for the effects of an ALP and place bounds on its couplings to the SM. An advantage is that, contrary to direct searches, indirect probes are independent of the way in which the ALP decays, and if it is long- or short-lived. Prominent examples of such precision observables are the anomalous magnetic moment of the muon and the electron [20, 21, 31–33], electroweak precision observables [21], and various rates for flavor-changing decays of kaons, B-mesons and charged leptons [34–42]. It has been observed in several of these studies that the one-loop contributions to such quantities arising from virtual ALP exchange can be ultraviolet (UV) divergent, but a consistent treatment of these divergences has so far not been presented in the literature. 1 Otherwise one needs to resort to cosmological and astrophysical bounds, see e.g. [27–30]. –2– JHEP06(2021)135 On the other hand, there remains the possibility of the existence of light new particles interacting very weakly with the SM, for instance because these interactions are mediated by higher-dimensional operators. A prominent example are axions and axion-like particles, to which we will collectively refer as ALPs in this work. The existence of such particles is theoretically well motivated because of their potential relevance for solving the strong CP problem [5–7]. More generally, ALPs are gauge-singlet pseudoscalar particles, which arise in many theories beyond the SM as pseudo Nambu-Goldstone bosons of a global symmetry spontaneously broken in the ultra-violet (UV) theory, and are thus naturally lighter than other new states whose masses may be out of reach of current direct searches. While the QCD axion is the original example of such a particle, ALPs with a variety of masses and couplings can arise also more generally, for example in theories which address the flavor [8, 9] and hierarchy [10–14] problems. Here we remain agnostic about the underlying theory and study a general effective field theory, to which explicit models can be matched. Since the ALP couplings to SM fields are constrained by a shift symmetry, these interactions first appear at the level of dimension-5 operators in the effective theory. The existence of a light ALP extends the SMEFT, because operators can now be built out of SM fields and the ALP field. The most general effective Lagrangian above the electroweak scale can then be written in the form The renormalization-group (RG) evolution of the dimension-5 ALP couplings in the effective Lagrangian LSM+ALP has recent (...truncated)