In recent years, theoretical and phenomenological studies with effective field theories have become a trending and prolific line of research in the field of high-energy physics. In order to discuss present and future prospects concerning automated tools in this field, the SMEFT-Tools 2022 workshop was held at the University of Zurich from 14th-16th September 2022. The current document collects and summarizes the content of this workshop.

In recent years, theoretical and phenomenological studies with effective field theories have become a trending and prolific line of research in the field of high-energy physics. In order to discuss present and future prospects concerning automated tools in this field, the SMEFT-Tools 2022 workshop was held at the University of Zurich from 14th-16th September 2022. The current document collects and summarizes the content of this workshop.

This review provides a detailed introduction to chiral gauge theories, renormalization theory, and the application of dimensional regularization with the non-anticommuting BMHV scheme for γ5. One goal was to show how chiral gauge theories can be renormalized despite the spurious breaking of gauge invariance and how to obtain the required symmetry-restoring counterterms. A second goal was to familiarize the reader with the theoretical basis of the renormalization of chiral gauge theories, the theorems that guarantee the existence of renormalized chiral gauge theories at all orders as consistent quantum theories. Relevant topics include BPHZ renormalization, Slavnov–Taylor identities, the BRST formalism, and algebraic renormalization, as well as the theorems guaranteeing that dimensional regularization is a consistent regularization/renormalization scheme. All of these, including their proofs and interconnections, are explained and discussed in detail. Further, these theoretical concepts are illustrated in practical applications with the example of an Abelian and a non-Abelian chiral gauge theory. Not only the renormalization procedure for such chiral gauge theories is explained step by step, but also the results of all counterterms, including the symmetry-restoring ones, necessary for the consistent renormalization, are explicitly provided.

γ_5 is notoriously difficult to define in D dimensions. The traditional BMHV scheme employs a non-anticommuting γ_5. Its key advantage is mathematical consistency and the existence of all-order proofs. Its disadvantage is the spurious breaking of gauge invariance in chiral gauge theories like the electroweak standard model. Our research programme aims to determine the special finite counterterms which are necessary to restore gauge invariance, to allow more straightforward applications of the BMHV scheme and to cross-check alternative schemes. In these proceedings we present the key concepts and methods, and we outline the calculational procedure and present results for an abelian gauge theory at the 2-loop level. An important observation is the simplicity of the results – three types of symmetry-restoring counterterms are sufficient at the 2-loop level.

Abstract We apply the BMHV scheme for non-anticommuting γ 5 to an abelian chiral gauge theory at the two-loop level. As our main result, we determine the full structure of symmetry-restoring counterterms up to the two-loop level. These counterterms turn out to have the same structure as at the one-loop level and a simple interpretation in terms of restoration of well-known Ward identities. In addition, we show that the ultraviolet divergences cannot be canceled completely by counterterms generated by field and parameter renormalization, and we determine needed UV divergent evanescent counterterms. The paper establishes the two-loop methodology based on the quantum action principle and direct computations of Slavnov-Taylor identity breakings. The same method will be applicable to nonabelian gauge theories.

We present in these proceedings, our analysis (arXiv:2004.14398) at one-loop level within the Breitenlohner--Maison--'t~Hooft--Veltman (BMHV) scheme of Dimensional Regularization, of the counterterm structure arising due to the presence of the $\gamma_5$ matrix and the breaking of the BRST invariance, in a massless chiral Yang-Mills theory supplemented with real scalars. The full one-loop counterterm structure necessary for the renormalization is obtained. This comprises the singular counterterms, including evanescent ones, and by using techniques from algebraic renormalization the symmetry-restoring finite counterterms are evaluated as well. The latter are required to restore the BRST invariance, central to the consistency of the theory and for higher-order calculations. The renormalization group equations are derived within this framework, and are compared with the more ``familiar'' calculation in the context of symmetry-invariant renormalization.

The Bonneau identities are a very convenient tool for e.g. restoring BRST symmetry and deriving renormalization group equations in content of chiral gauge theories. The background for the Bonneau identities is Breitenlohner-Maison-'t Hooft-Veltman dimensional regularization scheme which is reviewed here with special emphasis to bridge the notational differences between the Breitenlohner-Maison and the Bonneau papers and identifying the notions in these references. The Bonneau identities are rederived but for a general theory and reexpressed in terms of the effective action, establishing the bridge to the expressions in the Martin--Sanchez-Ruiz reference. Several new interpretations of lemmas, theorems and notions are given.

We study the application of the Breitenlohner-Maison-’t Hooft-Veltman (BMHV) scheme of Dimensional Regularization to the renormalization of chiral gauge theories, focusing on the specific counterterm structure required by the non-anticommuting Dirac γ5 matrix and the breaking of the BRST invariance. Calculations are performed at the one-loop level in a massless chiral Yang-Mills theory with chiral fermions and real scalar fields. We discuss the setup and properties of the regularized theory in detail. Our central results are the full counterterm structures needed for the correct renormalization: the singular UV-divergent counterterms, including evanescent counterterms that have to be kept for consistency of higher-loop calculations. We find that the required singular, evanescent counterterms associated with vector and scalar fields are uniquely determined but are not gauge invariant. Furthermore, using the framework of algebraic renormalization, we determine the symmetry-restoring finite counterterms, that are required to restore the BRST invariance, central to the consistency of the theory. These are the necessary building blocks in one-loop and higher-order calculations. Finally, renormalization group equations are derived within this framework, and the derivation is compared with the more customary calculation in the context of symmetry-invariant regularizations. We explain why, at one-loop level, the extra BMHV-specific counterterms do not change the results for the RGE. The results we find complete those that have been obtained previously in the literature in the absence of scalar fields.

We study the anomalous magnetic and electric dipole moments of charged leptons in supersymmetric low-scale seesaw models with right-handed neutrino superfields. We consider a minimally extended framework of minimal supergravity, by assuming that CP violation originates from complex soft SUSY-breaking bilinear and trilinear couplings associated with the right-handed sneutrino sector. We present numerical estimates of the muon anomalous magnetic moment and the electron electric dipole moment, as functions of key model parameters, such as the Majorana mass scale m(N) and tan beta. In particular, we find that the contributions of the singlet heavy neutrinos and sneutrinos to the electron electric dipole moment are naturally small in this model, of order 10(-27) - 10(-28) ecm, and can be probed in present and future experiments.

One-loop functions with loop masses larger than external masses and momenta can always be expanded in terms of external masses and momenta. The precision requested for observables determines the number of the expansion terms retained in the evaluation. The evaluation of these expansion terms turns out to be much simpler than the exact evaluation of the corresponding one-loop function. Here we present the program which evaluates those expansion terms. This Mathematica package provides two subroutines. First one performs analytical evaluation of basic one loop integrals. The second one is used to construct composite functions out of those integrals. Composite functions thus obtained are ready for numerical evaluation with literary no time consumption.

The authors of a recent communication [arXiv:1312.5318] claim to have traced an error in the existing literature regarding the evaluation of the one-loop right-handed sneutrino contributions to lepton-flavour-violating observables in supersymmetric low-scale seesaw models. In this short note, we emphasize that contrary to those authors' claim, our paper [arXiv:1212.5939] contains no such a flaw, and both our analytical and numerical results exhibit the expected decoupling property of the heavy sneutrinos in the Z-penguin graphs.

The triple neutral gauge boson and direct U(1)_Y-neutrino interactions, being absent in ordinary field theory, can arise quite naturally in noncommutative gauge field theories. Using non-perturbative methods and a Seiberg-Witten map based covariant approach to noncommutative gauge theory, we have found theta-exact expressions for both interactions, thereby eliminating previous restrictions to low-energy phenomena. In particular we obtain for the first time the covariant, theta-exact, triple neutral gauge boson interactions within the noncommutative Standard Model gauge sector including an additional gauge-field deformation freedom. Finally we discuss implications for Z->2gamma and Z->neutrino-pair decays, and show that our results behave quite reasonably throughout all interaction energy scales.

We study charged lepton flavor violation in low-scale seesaw models of minimal supergravity, which realize large neutrino Yukawa couplings thanks to approximate lepton-number symmetries. There are two dominant sources of lepton flavor violation in such models. The first source originates from the usual soft supersymmetry-breaking sector, whilst the second one is entirely supersymmetric and comes from the supersymmetric neutrino Yukawa sector. Within the framework of minimal supergravity, we consider both sources of lepton flavor violation, soft and supersymmetric, and calculate a number of possible lepton-flavor-violating transitions, such as the photonic decays of muons and taus, mu -> e gamma, tau -> e gamma and tau -> mu gamma, their neutrinoless three-body decays, mu -> eee, tau -> eee, tau -> mu mu mu, tau -> ee mu and tau -> e mu mu, and the coherent mu -> e conversion in nuclei. After taking into account the exclusion bounds placed by present experiments of lepton flavor violation, we derive combined theoretical limits on the universal heavy Majorana mass scale m(N) and the light-to-heavy neutrino mixings. Supersymmetric low-scale seesaw models offer distinct correlated predictions for lepton-flavor-violating signatures, which might be discovered in current and projected experiments, such as MEG, COMET/PRISM, Mu2e, super-BELLE and LHCb. DOI: 10.1103/PhysRevD.87.053014

We study one-loop photon (Π) and neutrino (Σ) self-energies in a U(1) covariant gauge-theory on d-dimensional noncommutative spaces determined by a antisymmetric-constant tensor θ μν . For the general fermion-photon (S f ) and photon self-interaction (S g ) the closed form results reveal self-energies besetting with all kind of pathological terms: the UV divergence, the quadratic UV/IR mixing terms as well as a logarithmic IR divergent term of the type ln(μ 2(θp)2). In addition, the photon-loop produces new tensor structures satisfying transversality condition by themselves. We show that the photon self-energy in four-dimensional Euclidean space-time can be reduced to two finite terms by imposing a specific full rank of θ μν and setting parameters (κ f , κ g ) = (0, 3). In this case the neutrino two-point function vanishes. Thus for a specific point (0, 3) in the parameter-space (κ f , κ g ), a covariant θ-exact approach is able to produce a divergence-free result for one-loop quantum corrections, having also well-defined both the commutative limit as well as the pointlike limit of an extended object. While in two-dimensional space the photon self-energy is finite for arbitrary (κ f , κ g ) combinations, the neutrino self-energy still contains an superficial IR divergence.

We consider Yukawa couplings in a θ-exact approach to noncommutative gauge field theory and show that both Dirac and singlet Majorana neutrino mass terms can be consistently accommodated. This shows that in fact the whole neutrino-mass extended standard model on noncommutative spacetime can be formulated in the new nonperturbative (in θ) approach which eliminates the previous restriction of Seiberg–Witten map based theories to low-energy phenomena. Spacetime noncommutativity induced couplings between neutrinos and photons as well as Z-bosons appear quite naturally in the model. We derive relevant Feynman rules for the type I seesaw mechanism.

One-loop θ-exact quantum corrections to the neutrino propagator are computed in noncommutative U⋆(1) gauge-theory based on Seiberg-Witten maps. Our closed form results show that the one-loop correction contains a hard 1/ǫ UV divergence, as well as a logarithmic IR-divergent term of the type ln \( \sqrt {{{{\left( {\theta p} \right)}^{{2}}}}} \), thus considerably softening the usual UV/IR mixing phenomenon. We show that both of these problematic terms vanish for a certain choice of the noncommutative parameter θ which preserves unitarity. We find non-perturbative modifications of the neutrino dispersion relations which are assymp-totically independent of the scale of noncommutativity in both the low and high energy limits and may allow superluminal propagation. Finally, we demonstrate how the prodigious freedom in Seiberg-Witten maps may be used to affect neutrino propagation in a profound way.

We investigate the influence of the boundary conditions of minimal supergravity (mSUGRA) on the supersymmetric mechanism for lepton flavour violation (LFV) proposed recently [1], within the framework of the MSSM extended by TeV-scale singlet heavy neutrinos. We find that the consideration of the mSUGRA boundary condition may increase the branching ratios of the muon and tauon decaying into three charged leptons by up to a factor of 5, whereas the corresponding branching ratio for their photonic decays remains almost unchanged.

In formulating gauge field theories on noncommutative (NC) spaces it is suggested that particles carrying gauge invariant quantities should not be viewed as pointlike, but rather as extended objects whose sizes grow linearly with their momenta. This and other generic properties deriving from the nonlocal character of interactions (showing thus unambiguously their quantum-gravity origin) lead to a specific form of UV/IR mixing as well as to a pathological behavior at the quantum level when the noncommutativity parameter θ is set to be arbitrarily small. In spite of previous suggestions that in a NC gauge theory based on the θ-expanded Seiberg-Witten (SW) maps UV/IR mixing effects may be under control, a fairly recent study of photon self-energy within a SW θ-exact approach has shown that UV/IR mixing is still present. We study the self-energy contribution for neutral massless fermions in the θ-exact approach of NC QED, and show by explicit calculation that all but one divergence can be eliminated for a generic choice of the noncommutativity parameter θ. The remaining divergence is linked to the pointlike limit of an extended object.

The influence of boson peak (BP) excitations on low-temperature spin–lattice relaxation rate of a paramagnetic center embedded in a glassy matrix is investigated in the context of multi-frequency electron paramagnetic resonance (EPR) detection. In the theoretical analysis, the transition rate of spin one-half in the presence of a phonon field is calculated within the approximation of Fermi’s golden rule. Several phonon densities of states are compared, among which one originating from a model of quasi-localized vibrations has been introduced into electron spin relaxation formalism for the first time. The respective frequency dependencies of spin–lattice relaxation rates are predicted which should lead to observable effects of BP modes if a multi-frequency study at very low temperatures is performed.