We analyse how $U(3)^5$ and $U(2)^5$ flavour symmetries act on the Standard Model Effective Field Theory, providing an organising principle to classify the large number of dimension-six operators involving fermion fields. A detailed counting of such operators, at different order in the breaking terms of both these symmetries, is presented. A brief discussion about possible deviations from these two reference cases, and a simple example of the usefulness of this classification scheme for high-$p_T$ analyses at the LHC, are also presented.
We perform an updated fit to LHC Higgs data and LEP electroweak precision tests in the framework of the Standard Model Effective Field Theory (SMEFT). We assume a generic structure of the SMEFT operators without imposing any flavour symmetries. The implementation is released as part of the public global SMEFT likelihood. This allows one to fit parameters of a broad class of new physics models to combined Higgs, electroweak, quark flavour, and lepton flavour observables.
We calculate the complete tree and one-loop matching of the dimension 6 Standard Model Effective Field Theory (SMEFT) with unbroken $U(3)^5$ flavour symmetry to the operators of the Weak Effective Theory (WET) which are responsible for flavour changing neutral current effects among down-type quarks. We also explicitly calculate the effects of SMEFT corrections to input observables on the WET Wilson coefficients, a necessary step on the way to a well-defined, complete prediction. These results will enable high-precision flavour data to be incorporated into global fits of the SMEFT at high energ…
We investigate the information that can be gained by including flavour data in fits of the Standard Model Effective Field Theory (SMEFT) with the assumption of Minimal Flavour Violation (MFV), allowing - as initial conditions at the high scale - leading terms in spurionic Yukawas only. Starting therefore from a theory with no tree level flavour changing neutral currents at the scale of new physics, we calculate effects in flavour changing processes at one loop, and the resulting constraints on linear combinations of SMEFT coefficients, consistently parameterising the electroweak parameters and…
We study Yukawa Renormalization Group (RG) running effects in the context of the Standard Model Effective Theory (SMEFT).The Yukawa running being flavour dependent leads to RG-induced off-diagonal entries, so that initially diagonal Yukawa matrices at the high scale have to be rediagonalized at the electroweak (EW) scale. Performing such flavour rotations can lead to flavour violating operators which differ from the ones obtained through SMEFT RG evolution. We show, that these flavour rotations can have a large impact on low-energy phenomenology. In order to demonstrate this effect, we compare…
A powerful aspect of effective field theories is connecting scales through renormalisation group (RG) flow. The anomalous dimension matrix of the Standard Model Effective Field Theory (SMEFT) encodes clues to where to find relics of heavy new physics in data, but its unwieldy 2499-by-2499 size (at operator dimension 6) makes it difficult to draw general conclusions. In this paper, we study the flavour structure of the SMEFT one loop anomalous dimension matrix of dimension 6 current-current operators, a 1460-by-1460 submatrix. We take an on-shell approach, laying bare simple patterns by factori…
University of Mississippi（密西西比大学）；Université Laval（拉瓦尔大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Université de Montréal（蒙特利尔大学）；University of Hawaii at Manoa（夏威夷大学马诺阿分校）
For a large set of flavor symmetries, the lowest-dimensional baryon- or lepton-number violating operators in the Standard Model effective field theory (SMEFT) with flavor symmetry are of mass dimension 9. As a consequence, baryon- and lepton-number violating processes are further suppressed with the introduction of flavor symmetries, e.g., the allowed scale associated with proton decay is typically lowered to $10^5$ GeV, which is significantly lower than the GUT scale. To illustrate these features, we discuss Minimal Flavor Violation for the Standard Model augmented by sterile neutrinos.
Upcoming searches for lepton flavour change (LFV) aim to probe New Physics(NP) scales up to $ \sim 10^4$ TeV, implying that they will be sensitive to NP at lower scales that is suppressed by loops or small couplings. We suppose that the NP responsable for LFV is beyond the reach of the LHC and can be parametrised in Effective Field Theory, introduce a small power-counting parameter à la Cabibbo-Wolfenstein, and assess whether the existing dimension six operator basis and one-loop RGEs provide a good approximation for LFV. We find that mu to e flavour-changing observables can be sensitive to a …
Constraining new physics effective interactions via a global fit of electroweak, Drell-Yan, Higgs, top, and flavour observables
Universidad de Granada（格拉纳达大学）；Florida State University（佛罗里达州立大学）；Universitat d’Alacant（阿利坎特大学）；University of Manchester（曼彻斯特大学）；INFN, Sezione di Roma（罗马国家核物理研究所）
We report codes for the Standard Model Effective Field Theory (SMEFT) in FeynRules -- the SMEFTsim package. The codes enable theoretical predictions for dimension six operator corrections to the Standard Model using numerical tools, where predictions can be made based on either the electroweak input parameter set $\{\hatα_{ew}, \hat{m}_Z, \hat{G}_F \}$ or $\{\hat{m}_{W}, \hat{m}_Z, \hat{G}_F\}$. All of the baryon and lepton number conserving operators present in the SMEFT dimension six Lagrangian, defined in the Warsaw basis, are included. A flavour symmetric ${\rm U}(3)^5$ version with possib…
We study implications of the four-fermion semileptonic operators at the low-energy and at electroweak (EW) scale in the framework of Standard Model Effective Field Theory (SMEFT). We show how the renormalization group (RG) running effects can play an important role in probing the \emph{generic flavour structure} of such operators. It is shown that at the 1-loop level, through RG running, depending upon the flavour structure, these operators can give rise to sizable effects at low energy in the electroweak precision (EWP) observables, the leptonic, quark, as well as the $Z$ boson flavour violat…
The extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix from flavour observables can be affected by physics beyond the Standard Model (SM). We provide a general roadmap to take this into account, which we apply to the case of the Standard Model Effective Field Theory (SMEFT). We choose a set of four input observables that determine the four Wolfenstein parameters, and discuss how the effects of dimension-six operators can be included in their definition. We provide numerical values and confidence intervals for the CKM parameters, and compare them with the results of CKM fits obtained in t…
Effective field theories, like the Standard Model Effective Field Theory (SMEFT), are defined by a chosen field content and a set of symmetries, up to a cut off scale $Λ$. Usually, in order to perform calculations, gauge independent field re-definitions consistent with the symmetries of the theory are then used to redefine the fields. This procedure results in a fixed (non-redundant) operator basis, that is not itself field re-definition invariant. Recently, an alternative approach of identifying and calculating with field space geometry has been developed. Field redefinition invariants, chara…
We calculate the $S$-matrix element for the Higgs boson decay to a $Z$-boson and a photon, $h\to Zγ$, at one-loop in the Standard-Model Effective Field Theory (SMEFT) framework and in linear $R_ξ$-gauges. Our SMEFT expansion includes all relevant operators up to dimension-6 considered in Warsaw basis without resorting to any flavour or CP-conservation assumptions. Within this approximation there are 23 dimension-6 operators affecting the amplitude, not including flavour and hermitian conjugation. The result for the on-shell $h\to Zγ$ amplitude is gauge invariant, renormalisation-scale invarian…
In this review article, we highlight the impact of models incorporating flavour symmetries on charged lepton flavour violating (LFV) processes. Flavour symmetries provide a natural approach to explain the peculiar mass hierarchies and mixing patterns of the Standard Model fermions. New sources of LFV are generally present in new physics beyond the Standard Model, and flavour symmetries can make distinctive predictions for LFV observables. Their discovery can provide crucial information to distinguish flavour symmetries and new physics scenarios in general. Because of their high sensitivity, we…
Based on flavour symmetries only, there are two ways to give rise to an effective description of flavour physics in the quark sector close to the CKM picture: one is based on $U(3)_q\times U(3)_u\times U(3)_d$ (or equivalent) and the other on $U(2)_q\times U(2)_u\times U(2)_d$ (or equivalent). In this context we analyze the current status of flavour physics measurements and we compare their impact, in the specific case of supersymmetry, with the direct searches of new particles at the LHC, present or foreseen.
We match the seesaw model for generating neutrino masses onto the Standard Model Effective Field Theory (SMEFT). We perform this matching at tree level up to dimension seven in the operator expansion. We explain how some of the perturbations of the neutrino mass matrix due to operators of mass dimension greater than five are tied to integrating out the heavy Majorana mass eigenstates in sequence. We demonstrate that the low energy limit of seesaw models are well described by the SMEFT, particularly when constructed using a flavour space expansion. Flavour space expansions of seesaw models are …
Flavour symmetries are fundamental tools in the search for an explanation to the flavour puzzle: fermion mass hierarchies, the neutrino mass ordering, the differences between the mixing matrices in the quark and lepton sector, can all find an explanation in models where the fermion generations undergo specific geometric relations. An overview on the implementation of continuous symmetries in the flavour sector is presented here, focussing on the lepton sector.
We re-examine the constraints on continuous family symmetries coming from flavour changing neutral current limits on the D-term contributions to squark and slepton masses. We show that, for a restricted choice of the familon sector, continuous family symmetries are consistent with even the most conservative limits both for the case of gauge mediated supersymmetry breaking and the case of gravity mediated supersymmetry breaking.
We study the approximate flavour symmetries imposed on the lepton sector assuming see-saw mechanism as the neutrino mass structure. We apply the symmetry to various neutrino phenomenologies and obtain constraints on neutrino masses and mixings.
We consider a class of discrete flavour symmetries for leptons based on the group S(3) and A(4) with an hybrid breaking pattern. The aim is to construct models in which the same flavon fields producing the mixing pattern are also responsible for the mass hierarchy.
The so-called supersymmetric flavour problem does not exist in isolation to the Standard Model flavour problem. We show that a realistic flavour symmetry can simultaneously solve both problems without ad hoc modifications of the SUSY model. Furthermore, departures from the SM expectations in these models can be used to discriminate among different possibilities. In particular we present the expected values for the electron EDM in a flavour model solving the supersymmetric flavour and CP problems.
We propose a theory of flavour based on abelian horizontal gauge symmetries and modular invariances. We construct explicit supergravity models where the scale of the horizontal $U(1)$ symmetry breaking is fixed by the Green-Schwarz mechanism for anomaly cancellation. The supersymmetric spectrum is obtained in terms of the $U(1)$ charges which are determined by the Yukawa matrices.
We provide a general classification of flavour symmetries according to their interplay with the proper Poincare' and gauge groups and to their linear or nonlinear action in field space. We focus on the lepton sector and we review the different types of symmetries describing neutrino masses and the lepton mixing matrix. For each type of symmetry we present several illustrative examples and we discuss specific strengths and limitations.
Both discrete flavour symmetries and Grand Unified symmetries explain apparent structures in the mass sector of the Standard Model. A model that combines both symmetries is therefore very appealing. We construct a model with the $S_4$ flavour symmetry and the Pati-Salam unification. We show that this model can indeed explain many observable relations between the masses of the quarks and leptons and that it is predictive in the neutrino sector. However, the combination of the two symmetries leads to new complications in the Higgs sector and in the running of the renormalisation group equations.
The classification of lepton mixing matrices from finite residual symmetries is reviewed, with emphasis on the role of vanishing sums of roots of unity for the solution of this problem.
Cartography of LNV dim-9 SMEFT: Implications for Radiative Neutrino Masses and $0νββ$
Institute of Particle and Nuclear Physics (IPNP), Faculty of Mathematics and Physics, Charles University（查尔斯大学数学物理学院粒子与核物理研究所）；Institute of Physics, Silesian University in Opava（俄帕瓦西里西亚大学物理研究所）；Instituto de Física Corpuscular (IFIC), Universidad de Valencia-CSIC（巴伦西亚大学-西班牙国家科学研究委员会粒子物理研究所）
We discuss the tension between discrete flavour symmetries and extended scalar sectors arising from lepton flavour violation experiments. The key point is that extended scalar sectors will generically lead to flavour changing neutral currents, which are strongly constrained by experiments. Due to the large parameter space in the scalar sector such models will, however, usually have no big problems with existing and future bounds (even though the models might be constrained). This changes considerably once a flavour symmetry is imposed in addition: Due to the symmetry, additional relations betw…
The interplay between flavour symmetries connecting Bs-->KK decays with the recently measured Bd--> K0 anti-K0 decay and QCD Factorisation opens new strategies to describe the decays Bs--> K0 anti-K0 and Bs--> K+ K- in the SM and in supersymmetry. A new relation, emerging from the sum-rule for the Bs--> K0 anti-K0 decay mode, is presented offering a new way to determine the weak mixing angle phi_s of the Bs system.
We investigate precision observables sensitive to custodial symmetric/violating UV physics beyond the Standard Model. We use the SMEFT framework which in general includes non-oblique corrections that requires a generalization of the Peskin-Takeuchi $T$ parameter to unambiguously detect custodial symmetry/violation. We take a first step towards constructing a SMEFT reparameterization-invariant replacement, that we call $\mathscr{T}$, valid at least for tree-level custodial violating contributions. We utilize a new custodial basis of $ν$SMEFT (SMEFT augmented by right-handed neutrinos) which exp…
We discuss charged lepton flavour violating processes such as mu -> e gamma in supersymmetric extensions of the Standard Model and in models with gauge-Higgs unification and a warped extra dimension. In both classes of models the processes turn out to be compatible with present experimental bounds, but can be detected by future experiments, thanks to the presence of a flavour symmetry G_f which constrains the form of the relevant couplings. The symmetry G_f is chosen to be finite, discrete and non-abelian and also helps to predict the peculiar lepton mixing pattern.
In view of the fact that the data on neutrino mixing are still compatible with a situation where Bimaximal mixing is valid in first approximation and it is then corrected by terms of order of the Cabibbo angle, we present examples where these properties are naturally realized. The models are supersymmetric in 4-dimensions and based on the discrete non-Abelian flavour symmetry S4.
Here we propose an $A_4$ flavour symmetry model which implies a lower bound on the neutrinoless double beta decay rate, corresponding to an effective mass parameter $M_{ee} \gsim 0.03$ eV, and a direct correlation between the expected magnitude of CP violation in neutrino oscillations and the value of $\sin^2θ_{13}$, as well as a nearly maximal CP phase $δ$.
We study the implications of the recent measurements of $R_K$ and $R_{K^*}$ by the LHCb collaboration. We do that by adopting a model-independent approach based on the Standard Model Effective Field Theory (SMEFT), in which the dominant new physics effects are encoded in the coefficients of dimension-six operators respecting the full Standard Model (SM) gauge symmetry. After providing simplified expressions for $R_K$ and $R_{K^\ast}$, we determine the implications of the recent LHCb results for these observables on the coefficients of the SMEFT operators at low and high energies. We also take …
We establish the full list of flavour symmetry groups which may be enforced, without producing any further accidental symmetry, on the Yukawa-coupling matrices of an SO(10) Grand Unified Theory with arbitrary numbers of scalar multiplets in the 10, $\overline{126}$, and 120 representations of SO(10). For each of the possible discrete non-Abelian symmetry groups, we present examples of minimal models which do not run into obvious contradiction with the phenomenological fermion masses and mixings.
The impact of rare lepton decays ($μ\to e γ$, $τ\to μγ$, >...) and rare $B$ and $K$ decays ($B\to \ell^+\ell^-$, $B\to \ellν$, $K\to πνν$, $K\to\ellν$, ...) in probing the existence of an underlying flavour symmetry is reviewd. Particualar emphasis is deveoted to the connections between quark and lepton flavour strucutres, in the context of generic effective field theory approach to physics beyond the SM.
We consider a new approach to fermion masses and mixings in which no special "horizontal" dynamics is invoked to account for the hierarchical pattern of charged fermion masses and for the peculiar features of neutrino masses. The hierarchy follows from the vertical, family-independent structure of the model, in particular from the breaking pattern of the Pati-Salam group. The lightness of the first two fermion families can be related to two family symmetries emerging in this context as accidental symmetries.
We study the set of models in which the Standard Model symmetry is extended with the flavour group A4 and there are three copies of the Standard Model Higgs that transform as a triplet under this group. In this setup, new channels for flavour violating processes can be studied once the A4 representations of the fermions in the theory are given. We show that it is of great importance to take these constraints into account as they can put severe constraints on the viability of flavour models.
We briefly review some recent developments in theoretical models of fermion masses, mixings and CP violation with discrete non-Abelian symmetries. Then, we explain the main ideas of a recently proposed Minimal S_3 Invariant Extension of the Standard Model and its application to a unified analysis of masses, mixings and CP violation in the leptonic and quark sectors as well as the explicit computation of the V_PMNS and V_CKM mixing matrices.
We investigate to what extent a generic, generation-dependent $U(1)$ symmetry acting on the quark Yukawa operators can reduce the number of free parameters by forcing some entries in the Yukawa matrices to vanish. The maximal reduction compatible with CP violation yields nine real parameters and one phase, which matches the number of physical observables, implying that such models have no free parameters. We derive a set of results: (i) the only possible structures have the form $M_4 \oplus M_5$, where the subscripts indicate the number of real parameters in the Yukawa matrices, (ii) there are…
We demonstrate how residual flavour symmetries, infrared signatures of symmetry breaking in complete models of flavour, can naturally forbid (or limit in a flavour specific way) flavour-changing neutral currents (FCNC) in multi-Higgs-doublet models (MHDM) without using mass hierarchies. We first review how this model-independent mechanism can control the fermionic mixing patterns of the Standard Model, and then implement the symmetries in the Yukawa sector of MHDM, which allows us to intimately connect the predictivity of a given flavour model with its ability to sequester FCNC. Finally, after…
Flavour symmetries have been used to constrain both quark and lepton mixing parameters. In particular, they can be used to completely fix the mixing angles. For the lepton sector, assuming that neutrinos are Majorana particles, we have derived the complete list of mixing patterns achievable in this way, as well as the symmetry groups associated to each case. Partial computer scans done in the past have hinted that such list is limited, and this does indeed turn out to be the case. In addition, most mixing patterns are already 3-sigma excluded by neutrino oscillation data.
