Search

We present a flavour non-universal extension of the Standard Model combined with the idea of Higgs compositeness. At the TeV scale, the gauge groups SU(2)R and U(1)B−L are assumed to act in a non-universal manner on light- and third-generation fermions, while the Higgs emerges as a pseudo Nambu-Goldstone boson of the spontaneous global symmetry breaking Sp(4) → SU(2)L × SU 2 R 3 , attributed to new strong dynamics. The flavour deconstruction means the couplings of the light families to the composite sector (and therefore the pNGB Higgs) are suppressed by powers of a heavy mass scale (from which the Higgs is nevertheless shielded by compositeness), explaining the flavour puzzle. We present a detailed analysis of the radiatively generated Higgs potential, showing how this intrinsically-flavoured framework has the ingredients to justify the unavoidable tuning in the Higgs potential necessary to separate electroweak and composite scales. This happens for large enough values of the SU 2 R 3 gauge coupling and light enough flavoured gauge bosons resulting from the deconstruction, whose phenomenology is also investigated. The model is compatible with current experimental bounds and predicts new states at the TeV scale, which are within the reach of near future experimental searches. [ABSTRACT FROM AUTHOR]

While the light scalar mesons (S0) are considered to be either ordinary q q ¯ or exotic tetraquark states, we investigate the semileptonic decays D → S0e+νe, by taking into account the resonant effects of S0 → M1M2, where S0 = a0(980), f0(980), and f0(500)/σ0, and M1(2) represents a pseudoscalar meson. For the first time, the D → S0 form factors in the two quark structures are both presented. Subsequently, we calculate B ( D s + → σ0e+νe, σ0 → π+π−) = (20.3 ± 1.8 ± 0.5) × 10−4 in the q q ¯ structure, showing significant 9σ deviations from the experimental upper limit of 3.3 × 10−4. In contrast, B ( D s + → σ0e+νe, σ0 → π+π−) = ( 0.58 − 0.57 + 1.43 ± 0.01) × 10−4 in the q 2 q ¯ 2 structure is within the allowed experimental range. Clearly, the light scalar meson is tested as a non- q q ¯ state. We hence demonstrate a highly sensitive new approach for exploring the true nature of scalar mesons, which can be extended to non-leptonic D decays as well as B meson decays. [ABSTRACT FROM AUTHOR]

We perform a comprehensive bottom-up study of all the simplest lepton models based on non-holomorphic A5 modular flavor symmetry, in which neutrinos are assumed to be Majorana particles and their masses are generated by the Weinberg operator or the type I seesaw mechanism. In the case that the generalized CP (gCP) symmetry is not considered, we find that 21 Weinberg operator models and 174 seesaw models can accommodate the experimental data in lepton sector, and all of them depend on six dimensionless free parameters and two overall scales. If gCP symmetry compatible with A5 modular symmetry is imposed, one more free parameter would be reduced. Then only 4 of the 21 Weinberg operator models and 100 of the 174 seesaw models agree with the experimental data on lepton masses and mixing parameters. Furthermore, we perform a detailed numerical analysis for two example models for illustration. [ABSTRACT FROM AUTHOR]

We study the flavor structures of zero-modes, which are originated from the modular symmetry on T 1 2 × T 2 2 and its orbifold with magnetic fluxes. We introduce the constraint on the moduli parameters by τ2 = Nτ1, where τi denotes the complex structure moduli on T i 2 . Such a constraint can be derived from the moduli stabilization. The modular symmetry of T 1 2 × T 2 2 is SL 2 ℤ τ 1 × SL 2 ℤ τ 2 ⊂ Sp 4 ℤ and it is broken to Γ0(N) × Γ0(N) by the moduli constraint. The wave functions represent their covering groups. We obtain various flavor groups in these models. [ABSTRACT FROM AUTHOR]

Phenomenological aspects of non-invertible symmetries, in particular the flavor structure of quarks and leptons, are studied. We start with a ℤM discrete symmetry and gauge ℤ2 so as to obtain a non-invertible symmetry. We study which Yukawa textures can be derived from the non-invertible symmetries. Various textures can be realized and some of them cannot be realized by a conventional symmetry. For example, the nearest neighbor interaction texture as well as other interesting textures of quarks and leptons are obtained. [ABSTRACT FROM AUTHOR]

Models based on a U 1 L μ − L τ gauge symmetry can explain the discrepancy between the measured value and theoretical prediction of the muon anomalous magnetic moment. Based on the latest experimental results, we revisit the analysis of neutrino mass matrix structures in minimal U 1 L μ − L τ models where the U 1 L μ − L τ symmetry breaking is caused by a single scalar field. Due to the charge assignment of the scalar field, each model predicts a unique structure of the neutrino mass matrix, which demands non-trivial relations among neutrino mass and mixing parameters. We find that the model called type 2+1, which features an SU(2)L doublet scalar Φ+1 with the U 1 L μ − L τ charge +1 and the hypercharge +1/2 and predicts the B3 texture structure, is marginally acceptable under the current neutrino oscillation data and cosmological observation. When the U 1 L μ − L τ gauge symmetry is broken by the vacuum expectation value of the standard model non-singlet representation such as Φ+1, there are additional contributions to flavor-changing meson decay processes and atomic parity violation via mixing between the Z boson and the U 1 L μ − L τ gauge boson Z′. We newly evaluate the model-dependent constraints on the model and find that the type 2+1 model is robustly ruled out. The model is extended to have an additional vacuum expectation value of a standard model singlet scalar in order to avoid the stringent constraints via the Z – Z′ mixing. Finally, we clarify the allowed range of the ratio of these vacuum expectation values. [ABSTRACT FROM AUTHOR]

We perform a comprehensive analysis of the minimal eclectic flavor group Q8 ⋊ S3 which is isomorphic to GL(2, 3), and all its irreducible representations are induced from the irreducible representations of Q8 and S3. The consistency conditions between EFG and generalized CP (gCP) symmetry are revisited, and we find the gCP symmetry compatible with the minimal EFG Q8 ⋊ S3. The most general forms of Kähler potential and superpotential based on Q8 ⋊ S3 are discussed, and the corresponding fermion mass matrices are presented. A concrete lepton model invariant under Q8 ⋊ S3 and gCP is constructed, in which the experimental data of all six lepton masses and six mixing parameters can be successfully described through seven real input parameters. The model predicts a vanishing effective mass mββ in neutrinoless double beta decay. [ABSTRACT FROM AUTHOR]

Discrete flavor symmetries have been an appealing approach for explaining the observed flavor structure, which is not justified in the Standard Model (SM). Typically, these models require a so-called flavon field in order to give rise to the flavor structure upon the breaking of the flavor symmetry by the vacuum expectation value (VEV) of the flavon. Generally, in order to obtain the desired vacuum alignment, a flavon potential that includes additional so-called driving fields is required. On the other hand, allowing the flavor symmetry to be modular leads to a structure where the couplings are all holomorphic functions that depend only on a complex modulus, thus greatly reducing the number of parameters in the model. We show that these elements can be combined to simultaneously explain the flavor structure and dark matter (DM) relic abundance. We present a modular model with flavon vacuum alignment that allows for realistic flavor predictions while providing a successful fermionic DM candidate. [ABSTRACT FROM AUTHOR]

A rich mathematical structure underlying flavor sum rules has been discovered recently. In this work, we extend these findings to systems with a direct sum of representations. We prove several results for the general case. We derive an algorithm that enables the determination of all U-spin amplitude sum rules at arbitrary order of the symmetry breaking for any system containing a direct sum of the representations 0 ⨁ 1. Potential applications are numerous and include, for example, higher order sum rules for CP-violating charm decays with an arbitrary number of final states. [ABSTRACT FROM AUTHOR]

Sixty years after the experimental discovery of CP violation in the quark sector, the existence of a similar CP violation in the lepton sector is still to be established. Actually, the structure of such a violation depends crucially on the origin of the neutrino masses. In an attempt at categorizing the leptonic sources of CP violation, we studied the νSM, the Standard Model extended with three generations of sterile neutrinos, that can interpolate continuously between the Dirac and Majorana scenarios of neutrino masses. In particular, we perform a classification of the Jarlskog-like flavor invariants entering CP-violating observables and we study their suppression with the heavy Majorana mass in the seesaw limit of the model. To simplify the construction of the invariants, we introduce a graph-based method. With the guidance of the Hilbert series and plethystic logarithm of the theory, we construct the generating and primary sets of invariants for the νSM for the first time. Unlike in the Standard Model and some other theories, we find that the numbers of generating invariants and the syzygies among them cannot immediately be read off from the plethystic logarithm, but require a more careful examination. Our analysis reveals that the generating set contains 459 invariants, out of which 208 are CP-even and 251 are CP-odd. In the seesaw limit of the νSM, we show that all parameters of the UV theory can be captured in the effective theory with a certain suppression with the heavy Majorana mass, while these parameters can only appear in a flavor-invariant way with a higher mass suppression. Furthermore, we discuss how the necessary and sufficient conditions for CP violation can be captured by utilizing these invariants. Along the way, we present useful algorithms to enumerate and build the flavor invariants. [ABSTRACT FROM AUTHOR]

Abstract In the formalism of the non-supersymmetric modular invariance approach to the flavour problem the elements of the Yukawa coupling and fermion mass matrices are expressed in terms of polyharmonic Maaß modular forms of level N in addition to the standard modula forms of the same level and a small number of constant parameters. Non-trivial polyharmonic Maaß forms exist for zero, negative and positive integer modular weights. Employing the finite modula group S 4 as a flavour symmetry group and assuming that the three left-handed lepton doublets furnish a triplet irreducible representation of S 4, we construct all possible 7- and 8-parameter lepton flavour models in which the neutrino masses are generated either by the Weinberg effective operator or by the type-I seesaw mechanism. We identify the phenomenologically viable models and obtain predictions for each of these models for the neutrino mass ordering, the absolute neutrino mass scale, the Dirac and Majorana CP-violation phases and, correspondingly, for the sum of neutrino masses and the neutrinoless double beta decay effective Majorana mass. We comment on how these models can be tested and conclude that they are all falsifiable. Detailed analyses are presented in the case of three representative benchmark lepton flavour scenarios.

Abstract : The so-called Golden Mass Relation provides a testable correlation between charged-lepton and down-type quark masses, that arises in certain flavor models that do not rely on Grand Unification. Such models typically involve broken family symmetries. In this work, we demonstrate that realistic fermion mass relations can emerge naturally in modular invariant models, without relying on ad hoc flavon alignments. We provide a model-independent derivation of a class of mass relations that are experimentally testable. These relations are determined by both the Clebsch-Gordan coefficients of the specific finite modular group and the expansion coefficients of its modular forms, thus offering potential probes of modular invariant models. As a detailed example, we present a set of viable mass relations based on the Γ4 ≅ S4 symmetry, which have calculable deviations from the usual Golden Mass Relation.

Abstract Minimal Flavor Violation (MFV) offers an appealing framework for exploring physics beyond the Standard Model. Interestingly, within the MFV framework, a new colorless field that transforms non-trivially under a global SU(3)3 quark flavor group can naturally be stable. Such a new field is thus a promising dark matter candidate, provided it is electrically neutral. We extend the MFV framework for dark matter and demonstrate that dark matter can naturally be multi-component across a broad parameter space. For illustration, we consider a gauge singlet, flavor triplet scalar field and identify parameter spaces for multi-component dark matter, where only the lightest flavor component is absolutely stable and heavy flavor components are decaying with lifetimes sufficiently longer than the age of the universe. Phenomenological, cosmological and astrophysical aspects of multi-component flavored dark matter are briefly discussed.

Abstract We study the flavor invariants of the SM augmented by one singlet vector-like quark. Aided by the Hilbert series, we construct all the basic invariants with which any flavor invariant can be written as a polynomial. In special, this theory contains one CP odd invariant of degree six which has degree much lower than the usual Jarlskog invariant of the SM. We find the nonlinear polynomial relations (syzygies) of lowest degrees involving these basic invariants, including the expression of the square of the CP odd invariant of lowest degree in terms of CP even invariants. The SU(3) identity underlying this syzygy is uncovered in terms of invariant tensors, which can be applied to rewrite any square of a CP odd invariant of the same form, involving three hermitean matrices of size three. We demonstrate by an example that there is CP violation that is not detected by the CP odd invariants proposed in the literature so far but it can be detected with the full list of CP odd invariants found here.

Abstract We discuss non-invertible symmetries in toroidal compactifications of higher dimensional Yang-Mills theory with magnetic fluxes, which can be regarded as an effective action of type IIB string theory with magnetized D-branes. Specifically, we derive fusion rules of discrete isometry operators, which are invariant under the ℤ N orbifold twist. It turns out that degenerate chiral zero-modes non-trivially transform under the non-invertible symmetries in the context of quantum mechanics. Hence, non-invertible symmetries correspond to flavor symmetries of chiral zero modes and determine their flavor structure. We explicitly show the representations and selection rules of chiral zero modes on their wave functions. These zero modes may correspond to generations of quarks and leptons in four-dimensional low-energy effective field theory.

Abstract We study physical implications of general CP symmetry including CP-like symmetry. Various scattering amplitudes of CP asymmetry are calculated in CP-like symmetric models. We explicitly show that the CP-like transformation leads to a specific relation between different CP asymmetries. The resultant relation is similar to the one obtained in GUT baryogenesis and sphaleron processes, where we also obtain a required condition for generating particle number asymmetry in CP-like symmetric models. In addition, we propose a generalization of a CP-like transformation for continuous symmetry groups. Since the CP transformation is an outer automorphism, which depends on the internal symmetry group, it turns out that the physical CP and CP-like symmetries can be mutually converted through the spontaneous symmetry breaking (SSB) of the internal symmetry. We investigate properties of physical CP asymmetry in both CP and CP-like symmetric phases, and find that the spontaneous CP violation and restoration can be observed even in models with continuous groups. We demonstrate that CP-like symmetric models with continuous Lie groups can be naturally realized in physical CP symmetric models through the SSB.

Abstract We study the realization of spontaneous CP violation through moduli stabilization. In modular flavor models, the source of CP violation is the vacuum expectation values of the complex structure moduli of toroidal compact space. We demonstrate that the combined effects of Type IIB flux compactifications with modular invariant couplings between the moduli and matter fields can induce spontaneous CP violation without or with supersymmetry breaking. Furthermore, some general properties of CP and modular invariant scalar potentials are presented. It is found that certain modifications or partial breakings of modular symmetry are useful in generating spontaneous CP violation.

We study the flavor invariants of the SM augmented by one singlet vector-like quark. Aided by the Hilbert series, we construct all the basic invariants with which any flavor invariant can be written as a polynomial. In special, this theory contains one CP odd invariant of degree six which has degree much lower than the usual Jarlskog invariant of the SM. We find the nonlinear polynomial relations (syzygies) of lowest degrees involving these basic invariants, including the expression of the square of the CP odd invariant of lowest degree in terms of CP even invariants. The SU(3) identity underlying this syzygy is uncovered in terms of invariant tensors, which can be applied to rewrite any square of a CP odd invariant of the same form, involving three hermitean matrices of size three. We demonstrate by an example that there is CP violation that is not detected by the CP odd invariants proposed in the literature so far but it can be detected with the full list of CP odd invariants found here. [ABSTRACT FROM AUTHOR]

Minimal Flavor Violation (MFV) offers an appealing framework for exploring physics beyond the Standard Model. Interestingly, within the MFV framework, a new colorless field that transforms non-trivially under a global SU(3)3 quark flavor group can naturally be stable. Such a new field is thus a promising dark matter candidate, provided it is electrically neutral. We extend the MFV framework for dark matter and demonstrate that dark matter can naturally be multi-component across a broad parameter space. For illustration, we consider a gauge singlet, flavor triplet scalar field and identify parameter spaces for multi-component dark matter, where only the lightest flavor component is absolutely stable and heavy flavor components are decaying with lifetimes sufficiently longer than the age of the universe. Phenomenological, cosmological and astrophysical aspects of multi-component flavored dark matter are briefly discussed. [ABSTRACT FROM AUTHOR]

We discuss non-invertible symmetries in toroidal compactifications of higher dimensional Yang-Mills theory with magnetic fluxes, which can be regarded as an effective action of type IIB string theory with magnetized D-branes. Specifically, we derive fusion rules of discrete isometry operators, which are invariant under the ℤN orbifold twist. It turns out that degenerate chiral zero-modes non-trivially transform under the non-invertible symmetries in the context of quantum mechanics. Hence, non-invertible symmetries correspond to flavor symmetries of chiral zero modes and determine their flavor structure. We explicitly show the representations and selection rules of chiral zero modes on their wave functions. These zero modes may correspond to generations of quarks and leptons in four-dimensional low-energy effective field theory. [ABSTRACT FROM AUTHOR]

We study physical implications of general CP symmetry including CP-like symmetry. Various scattering amplitudes of CP asymmetry are calculated in CP-like symmetric models. We explicitly show that the CP-like transformation leads to a specific relation between different CP asymmetries. The resultant relation is similar to the one obtained in GUT baryogenesis and sphaleron processes, where we also obtain a required condition for generating particle number asymmetry in CP-like symmetric models. In addition, we propose a generalization of a CP-like transformation for continuous symmetry groups. Since the CP transformation is an outer automorphism, which depends on the internal symmetry group, it turns out that the physical CP and CP-like symmetries can be mutually converted through the spontaneous symmetry breaking (SSB) of the internal symmetry. We investigate properties of physical CP asymmetry in both CP and CP-like symmetric phases, and find that the spontaneous CP violation and restoration can be observed even in models with continuous groups. We demonstrate that CP-like symmetric models with continuous Lie groups can be naturally realized in physical CP symmetric models through the SSB. [ABSTRACT FROM AUTHOR]

We study the realization of spontaneous CP violation through moduli stabilization. In modular flavor models, the source of CP violation is the vacuum expectation values of the complex structure moduli of toroidal compact space. We demonstrate that the combined effects of Type IIB flux compactifications with modular invariant couplings between the moduli and matter fields can induce spontaneous CP violation without or with supersymmetry breaking. Furthermore, some general properties of CP and modular invariant scalar potentials are presented. It is found that certain modifications or partial breakings of modular symmetry are useful in generating spontaneous CP violation. [ABSTRACT FROM AUTHOR]

Abstract Predicting the rate for μ → e conversion in nuclei for a given set of effective operators mediating the violation of lepton flavor symmetry crucially depends on hadronic and nuclear matrix elements. In particular, the uncertainties inherent in this non-perturbative input limit the discriminating power that can be achieved among operators by studying different target isotopes. In order to quantify the associated uncertainties, as a first step, we go back to nuclear charge densities and propagate the uncertainties from electron scattering data for a range of isotopes relevant for μ → e conversion in nuclei, including 40,48Ca, 48,50Ti, and 27Al. We provide as central results Fourier-Bessel expansions of the corresponding charge distributions with complete covariance matrices, accounting for Coulomb-distortion effects in a self-consistent manner throughout the calculation. As an application, we evaluate the overlap integrals for μ → e conversion mediated by dipole operators. In combination with modern ab-initio methods, our results will allow for the evaluation of general μ → e conversion rates with quantified uncertainties.

Abstract We study two-site deconstructions of the SU(2) L gauge group factor of the SM. Models based on this approach can explain the hierarchies of the quark masses and CKM mixing between third and light families if these fields are localised on different sites by the presence of hierarchical new physics scales. The model leads to an accidental global U(2) q × U(3) u × U(3) d flavour symmetry which prevents dangerously large effects in flavour observables, making a TeV extension of the SM possible. Given the structure of the PMNS matrix in the neutrino sector, we explore different possibilities for the arrangement of the leptons on the two sites, and consider different models with U(2) ℓ or U(3) ℓ flavour symmetries. The phenomenology of the models is mostly governed by a massive vector triplet of SU(2) L . We study the interesting interplay between LHC searches and precision observables. In particular, one of the models can give a sizeable lepton flavour universal effect in the Wilson coefficient C 9 while naturally suppressing contributions to C 10, as suggested by current b → sℓ + ℓ − data, predicting simultaneously a mild positive shift in the W boson mass.

Abstract The flavor structure of quarks and leptons and quark-lepton unification are studied in the framework of Pati-Salam models with A 4 modular symmetry. The three generations of the left-handed and right-handed fermions are assigned to be triplet or singlets of A 4. The light neutrino masses are generated through the type-I seesaw mechanism. We perform a systematic classification of Pati-Salam models according to the transformations of matter fields under the A 4 modular symmetry, and the general form of the fermion mass matrix is given. We present four phenomenologically viable benchmark models which provide excellent descriptions of masses and flavor mixing of quarks and leptons, including neutrinos. In such models we find that the normal ordered neutrino mass spectrum is preferred over the inverted case, with neutrinoless double beta decay predicted to be too small to be observed by the next generation of experiments.

Abstract In our recent attempt to explain flavor hierarchies [1], a gauged SU(2) flavor symmetry acting on left-handed fermions provides a ground to introduce three independent rank-one contributions to the Yukawa matrices: a renormalizable one for the third family, a mass-suppressed one for the second family, and an additional loop-suppressed factor for the first family. Here, we demonstrate how minimal quark-lepton unification à la Pati-Salam, relating down-quarks to charged leptons, can significantly improve this mechanism. We construct and thoroughly analyze a renormalizable model, performing a comprehensive one-loop matching calculation that reveals how all flavor hierarchies emerge from a single ratio of two scales. The first signatures may appear in the upcoming charged lepton flavor violation experiments.

Abstract The formalism of non-holomorphic modular flavor symmetry is developed, and the Yukawa couplings are level N polyharmonic Maaß forms satisfying the Laplacian condition. We find that the integer (even) weight polyharmonic Maaß forms of level N can be decomposed into multiplets of the finite modular group Γ N ′ $$ {\Gamma}_N^{\prime } $$ (Γ N ). The original modular invariance approach is extended by the presence of negative weight polyharmonic Maaß forms. The non-holomorphic modular flavor symmetry can be consistently combined with the generalized CP symmetry. We present three example models for lepton sector based on the Γ3 ≅ A 4 modular symmetry, the charged lepton masses and the neutrino oscillation data can be accommodated very well, and the predictions for the leptonic CP violation phases and the effective Majorana neutrino mass are studied.

Abstract We formulate general conditions under which the strong CP problem is solved by spontaneous CP violation. Quark-mass matrix elements are polynomials in the CP-breaking order parameters, engineered such that their determinant is a real constant. This scheme permits only a limited number of textures. These conditions can be realized in supersymmetric theories with CP as an anomaly-free local flavor symmetry, suggesting a unified solution to the strong CP problem and the flavor puzzle. Our solution can be implemented using either modular invariance or a local U(1) symmetry. We present modular-invariant realizations where matter fields are assigned small modular weights ±2 (±1), utilising higher levels N = 2 (N = 3). Heavy quarks are in general not required, but their presence allows for models where colored particles fill non-singlet representations of the flavor group.

Abstract Flavor deconstruction refers to ultraviolet completions of the Standard Model where the gauge group is split into multiple factors under which fermions transform non-universally. We propose a mechanism for charging same-family fermions into different factors of a deconstructed gauge theory in a way that gauge anomalies are avoided. The mechanism relies in the inclusion of a strongly-coupled sector, responsible of both anomaly cancellation and the breaking of the non-universal gauge symmetry. As an application, we propose different flavor deconstructions of the Standard Model that, instead of complete families, uniquely identify specific third-family fermions. All these deconstructions allow for a new physics scale that can be as low as few TeV and provide an excellent starting point for the explanation of the Standard Model flavor hierarchies.

Abstract We investigate quantum entanglement in high-energy 2 → 2 scalar scattering, where the scalars are characterized by an internal flavor quantum number acting like a qubit. Working at the 1-loop order in perturbation theory, we build the final-state density matrix as a function of the scattering amplitudes connecting the initial to the outgoing state. In this construction, the unitarity of the S-matrix is guaranteed at the required order by the optical theorem. We consider the post-scattering entanglement between the momentum and flavor degrees of freedom of the final-state particles, as well as the entanglement of the two-qubit flavor subsystem. In each case we identify the couplings of the scalar potential that can generate, destroy, or transfer entanglement between different bipartite subspaces of the Hilbert space.

Abstract We study the effects of anomalous thresholds on the non-local form factors describing the hadronization of the light-quark contribution to B → (P, V)γ * transitions. Starting from a comprehensive discussion of anomalous thresholds in the triangle loop function for different mass configurations, we detail how the dispersion relation for ππ intermediate states is affected by contour deformations mandated by the anomalous branch points. Phenomenological estimates of the size of the anomalous contributions to the form factors are provided with couplings determined from measured branching fractions and Dalitz plot distributions. Our key finding is that anomalous effects are suppressed on the ρ(770) resonance, while off-peak the effects can become as large as O $$ \mathcal{O} $$ (10%) of the full (light-quark-loop induced) non-local form factors. We comment on future generalizations towards higher intermediate states and the charm loop, outlining how the dispersive framework established in this work could help improve the non-local form factors needed as input for a robust interpretation of B → (P, V)ℓ + ℓ − decays.

Abstract We elaborate how to apply the Hilbert series method to enumerating group covariants, which transform under any given representation, including but going beyond group invariants. Mathematically, group covariants form a module over the ring of the invariants. The number of independent covariants is given by the rank of the module, which can be computed by taking a ratio of two Hilbert series. In many cases, the rank equals the dimension of the group covariant representation. When this happens, we say that there is a rank saturation. We apply this technology to revisit the hypothesis of Minimal Flavor Violation in constructing Effective Field Theories beyond the Standard Model. We find that rank saturation is guaranteed in this case, leading to the important consequence that the MFV symmetry principle does not impose any restriction on the EFT, i.e. MFV SMEFT = SMEFT, in the absence of additional assumptions.

Abstract Recently, the Belle II collaboration announced the first measurement of the branching ratio B B + → K + ν ν ¯ $$ \mathcal{B}\left({B}^{+}\to {K}^{+}\nu \overline{\nu}\right) $$ , which is found to be about 2.7σ higher than the Standard Model (SM) prediction. We decipher the data with two new physics scenarios: the underlying quark-level b → sν ν ¯ $$ b\to s\nu \overline{\nu} $$ transition is, besides the SM contribution, further affected by heavy new mediators that are much heavier than the electroweak scale, or amended by an additional decay channel with undetected light final states like dark matter or axion-like particles. These two scenarios can be most conveniently analyzed in the SM effective field theory (SMEFT) and the dark SMEFT (DSMEFT) framework, respectively. We consider the flavour structures of the resulting effective operators to be either generic or satisfy the minimal flavour violation (MFV) hypothesis, both for the quark and lepton sectors. In the first scenario, once the MFV assumption is made, only one SM-like low-energy effective operator induced by the SMEFT dimension-six operators can account for the Belle II excess, whose parameter space is, however, excluded by the Belle upper bound of the branching ratio B B 0 → K ∗ 0 ν ν ¯ $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}\nu \overline{\nu}\right) $$ . In the second scenario, it is found that the Belle II excess can be accommodated by 22 of the DSMEFT operators involving one or two scalar, fermionic, or vector dark matters as well as axion-like particles. These operators also receive dominant constraints from the B 0 → K *0 + inv and B s → inv decays. Once the MFV hypothesis is assumed, the number of viable operators is reduced to 14, and the B + → π + + inv and K + → π + + inv decays start to put further constraints on them. Within the parameter space allowed by all the current experimental data, the q 2 distributions of the B → K (*) + inv decays are then studied for each viable operator. We find that the resulting prediction of the operator Q qχ = q ¯ p γ μ q r χ ¯ γ μ χ $$ {\mathcal{Q}}_{q\chi}=\left({\overline{q}}_p{\gamma}_{\mu }{q}_r\right)\left(\overline{\chi}{\gamma}^{\mu}\chi \right) $$ with a fermionic dark matter mass m χ ≈ 700 MeV can closely match the Belle II event distribution in the bins 2 ≤ q 2 ≤ 7 GeV2. In addition, we, for the first time, calculate systematically the longitudinal polarization fraction F L of K * in the B → K * + inv decays within the DLEFT. By combining the decay spectra and F L , almost all the DSMEFT operators are found to be distinguishable from each other. Finally, the future prospects at Belle II, CEPC and FCC-ee are also discussed for some of these FCNC processes.

We formulate general conditions under which the strong CP problem is solved by spontaneous CP violation. Quark-mass matrix elements are polynomials in the CP-breaking order parameters, engineered such that their determinant is a real constant. This scheme permits only a limited number of textures. These conditions can be realized in supersymmetric theories with CP as an anomaly-free local flavor symmetry, suggesting a unified solution to the strong CP problem and the flavor puzzle. Our solution can be implemented using either modular invariance or a local U(1) symmetry. We present modular-invariant realizations where matter fields are assigned small modular weights ±2 (±1), utilising higher levels N = 2 (N = 3). Heavy quarks are in general not required, but their presence allows for models where colored particles fill non-singlet representations of the flavor group. [ABSTRACT FROM AUTHOR]

The formalism of non-holomorphic modular flavor symmetry is developed, and the Yukawa couplings are level N polyharmonic Maaß forms satisfying the Laplacian condition. We find that the integer (even) weight polyharmonic Maaß forms of level N can be decomposed into multiplets of the finite modular group Γ N ′ (ΓN). The original modular invariance approach is extended by the presence of negative weight polyharmonic Maaß forms. The non-holomorphic modular flavor symmetry can be consistently combined with the generalized CP symmetry. We present three example models for lepton sector based on the Γ3 ≅ A4 modular symmetry, the charged lepton masses and the neutrino oscillation data can be accommodated very well, and the predictions for the leptonic CP violation phases and the effective Majorana neutrino mass are studied. [ABSTRACT FROM AUTHOR]

The flavor structure of quarks and leptons and quark-lepton unification are studied in the framework of Pati-Salam models with A4 modular symmetry. The three generations of the left-handed and right-handed fermions are assigned to be triplet or singlets of A4. The light neutrino masses are generated through the type-I seesaw mechanism. We perform a systematic classification of Pati-Salam models according to the transformations of matter fields under the A4 modular symmetry, and the general form of the fermion mass matrix is given. We present four phenomenologically viable benchmark models which provide excellent descriptions of masses and flavor mixing of quarks and leptons, including neutrinos. In such models we find that the normal ordered neutrino mass spectrum is preferred over the inverted case, with neutrinoless double beta decay predicted to be too small to be observed by the next generation of experiments. [ABSTRACT FROM AUTHOR]

Predicting the rate for μ → e conversion in nuclei for a given set of effective operators mediating the violation of lepton flavor symmetry crucially depends on hadronic and nuclear matrix elements. In particular, the uncertainties inherent in this non-perturbative input limit the discriminating power that can be achieved among operators by studying different target isotopes. In order to quantify the associated uncertainties, as a first step, we go back to nuclear charge densities and propagate the uncertainties from electron scattering data for a range of isotopes relevant for μ → e conversion in nuclei, including 40,48Ca, 48,50Ti, and 27Al. We provide as central results Fourier-Bessel expansions of the corresponding charge distributions with complete covariance matrices, accounting for Coulomb-distortion effects in a self-consistent manner throughout the calculation. As an application, we evaluate the overlap integrals for μ → e conversion mediated by dipole operators. In combination with modern ab-initio methods, our results will allow for the evaluation of general μ → e conversion rates with quantified uncertainties. [ABSTRACT FROM AUTHOR]

We study two-site deconstructions of the SU(2)L gauge group factor of the SM. Models based on this approach can explain the hierarchies of the quark masses and CKM mixing between third and light families if these fields are localised on different sites by the presence of hierarchical new physics scales. The model leads to an accidental global U(2)q × U(3)u × U(3)d flavour symmetry which prevents dangerously large effects in flavour observables, making a TeV extension of the SM possible. Given the structure of the PMNS matrix in the neutrino sector, we explore different possibilities for the arrangement of the leptons on the two sites, and consider different models with U(2)ℓ or U(3)ℓ flavour symmetries. The phenomenology of the models is mostly governed by a massive vector triplet of SU(2)L. We study the interesting interplay between LHC searches and precision observables. In particular, one of the models can give a sizeable lepton flavour universal effect in the Wilson coefficient C9 while naturally suppressing contributions to C10, as suggested by current b → sℓ+ℓ− data, predicting simultaneously a mild positive shift in the W boson mass. [ABSTRACT FROM AUTHOR]

In our recent attempt to explain flavor hierarchies [1], a gauged SU(2) flavor symmetry acting on left-handed fermions provides a ground to introduce three independent rank-one contributions to the Yukawa matrices: a renormalizable one for the third family, a mass-suppressed one for the second family, and an additional loop-suppressed factor for the first family. Here, we demonstrate how minimal quark-lepton unification à la Pati-Salam, relating down-quarks to charged leptons, can significantly improve this mechanism. We construct and thoroughly analyze a renormalizable model, performing a comprehensive one-loop matching calculation that reveals how all flavor hierarchies emerge from a single ratio of two scales. The first signatures may appear in the upcoming charged lepton flavor violation experiments. [ABSTRACT FROM AUTHOR]

We investigate quantum entanglement in high-energy 2 → 2 scalar scattering, where the scalars are characterized by an internal flavor quantum number acting like a qubit. Working at the 1-loop order in perturbation theory, we build the final-state density matrix as a function of the scattering amplitudes connecting the initial to the outgoing state. In this construction, the unitarity of the S-matrix is guaranteed at the required order by the optical theorem. We consider the post-scattering entanglement between the momentum and flavor degrees of freedom of the final-state particles, as well as the entanglement of the two-qubit flavor subsystem. In each case we identify the couplings of the scalar potential that can generate, destroy, or transfer entanglement between different bipartite subspaces of the Hilbert space. [ABSTRACT FROM AUTHOR]

Flavor deconstruction refers to ultraviolet completions of the Standard Model where the gauge group is split into multiple factors under which fermions transform non-universally. We propose a mechanism for charging same-family fermions into different factors of a deconstructed gauge theory in a way that gauge anomalies are avoided. The mechanism relies in the inclusion of a strongly-coupled sector, responsible of both anomaly cancellation and the breaking of the non-universal gauge symmetry. As an application, we propose different flavor deconstructions of the Standard Model that, instead of complete families, uniquely identify specific third-family fermions. All these deconstructions allow for a new physics scale that can be as low as few TeV and provide an excellent starting point for the explanation of the Standard Model flavor hierarchies. [ABSTRACT FROM AUTHOR]

We study the effects of anomalous thresholds on the non-local form factors describing the hadronization of the light-quark contribution to B → (P, V)γ* transitions. Starting from a comprehensive discussion of anomalous thresholds in the triangle loop function for different mass configurations, we detail how the dispersion relation for ππ intermediate states is affected by contour deformations mandated by the anomalous branch points. Phenomenological estimates of the size of the anomalous contributions to the form factors are provided with couplings determined from measured branching fractions and Dalitz plot distributions. Our key finding is that anomalous effects are suppressed on the ρ(770) resonance, while off-peak the effects can become as large as O (10%) of the full (light-quark-loop induced) non-local form factors. We comment on future generalizations towards higher intermediate states and the charm loop, outlining how the dispersive framework established in this work could help improve the non-local form factors needed as input for a robust interpretation of B → (P, V)ℓ+ℓ− decays. [ABSTRACT FROM AUTHOR]

Recently, the Belle II collaboration announced the first measurement of the branching ratio B B + → K + ν ν ¯ , which is found to be about 2.7σ higher than the Standard Model (SM) prediction. We decipher the data with two new physics scenarios: the underlying quark-level b → sν ν ¯ transition is, besides the SM contribution, further affected by heavy new mediators that are much heavier than the electroweak scale, or amended by an additional decay channel with undetected light final states like dark matter or axion-like particles. These two scenarios can be most conveniently analyzed in the SM effective field theory (SMEFT) and the dark SMEFT (DSMEFT) framework, respectively. We consider the flavour structures of the resulting effective operators to be either generic or satisfy the minimal flavour violation (MFV) hypothesis, both for the quark and lepton sectors. In the first scenario, once the MFV assumption is made, only one SM-like low-energy effective operator induced by the SMEFT dimension-six operators can account for the Belle II excess, whose parameter space is, however, excluded by the Belle upper bound of the branching ratio B B 0 → K ∗ 0 ν ν ¯ . In the second scenario, it is found that the Belle II excess can be accommodated by 22 of the DSMEFT operators involving one or two scalar, fermionic, or vector dark matters as well as axion-like particles. These operators also receive dominant constraints from the B0 → K*0 + inv and Bs → inv decays. Once the MFV hypothesis is assumed, the number of viable operators is reduced to 14, and the B+ → π+ + inv and K+ → π+ + inv decays start to put further constraints on them. Within the parameter space allowed by all the current experimental data, the q2 distributions of the B → K(*) + inv decays are then studied for each viable operator. We find that the resulting prediction of the operator Q qχ = q ¯ p γ μ q r χ ¯ γ μ χ with a fermionic dark matter mass mχ ≈ 700 MeV can closely match the Belle II event distribution in the bins 2 ≤ q2 ≤ 7 GeV2. In addition, we, for the first time, calculate systematically the longitudinal polarization fraction FL of K* in the B → K* + inv decays within the DLEFT. By combining the decay spectra and FL, almost all the DSMEFT operators are found to be distinguishable from each other. Finally, the future prospects at Belle II, CEPC and FCC-ee are also discussed for some of these FCNC processes. [ABSTRACT FROM AUTHOR]

We elaborate how to apply the Hilbert series method to enumerating group covariants, which transform under any given representation, including but going beyond group invariants. Mathematically, group covariants form a module over the ring of the invariants. The number of independent covariants is given by the rank of the module, which can be computed by taking a ratio of two Hilbert series. In many cases, the rank equals the dimension of the group covariant representation. When this happens, we say that there is a rank saturation. We apply this technology to revisit the hypothesis of Minimal Flavor Violation in constructing Effective Field Theories beyond the Standard Model. We find that rank saturation is guaranteed in this case, leading to the important consequence that the MFV symmetry principle does not impose any restriction on the EFT, i.e. MFV SMEFT = SMEFT, in the absence of additional assumptions. [ABSTRACT FROM AUTHOR]

Abstract We introduce the idea of flavour transfer from a non-abelian horizontal SU(2) f flavour gauge group embedded in the Standard Model flavour structure. The new flavour vector bosons, in the mass range from the tens of GeV to multi-TeV, do not induce large flavour-changing neutral currents and meson oscillations, which usually provide the dominant constraints on this type of structure. Instead, the main constraints arise from “flavour-transfer” operators that we will study in detail. Several explicit models are presented and their prospects are thoroughly explored, including their phenomenology in the lepton and quark sectors at colliders and lower energy experiments. We perform a complete numerical fit in one such scenario, showing that LHC-based lepton-flavour violating searches are competitive with intensity frontier observables.

Abstract We present comprehensive global fits of the SMEFT under the minimal minimal flavour violation (MFV) hypothesis, i.e. assuming that only the flavour-symmetric and CP-invariant operators are relevant at the high scale. The considered operator set is determined by this flavour assumption rather than the used datasets. We establish global limits on these Wilson coefficients using leading order and next-to-leading order SMEFT predictions for electroweak precision observables, Higgs, top, flavour and dijet data as well as measurements from parity violation experiments and lepton scattering. Our investigations reveal an intriguing crosstalk among different observables, underscoring the importance of combining diverse observables from various energy scales in global SMEFT analyses.

Abstract We construct two concrete examples of flavour non-universal gauge theories which, after the inclusion of all d ≤ 4 gauge invariant operators, allow to describe the observed pattern of flavour in the charged fermion sector without any small Yukawa coupling (y ≳ 0.1). Guided by the criterium of minimality, we assume that flavour non universality is confined to the Abelian sector of the gauge group: the universal hypercharge emerges after a sequence of symmetry-breaking steps characterised by two high mass scales, Λ[23] < Λ[12], where the second and the first fermion generations get their mass respectively. At least in one of the two models the smaller of these scales can be in the 10 TeV range, consistently with current bounds from flavour observables. Both models are extended to include as well neutrino masses and mixings.

Abstract We analyze a general class of locally supersymmetric, CP and modular invariant models of lepton masses depending on two complex moduli taking values in the vicinity of a fixed point, where the theory enjoys a residual symmetry under a finite group. Like in models that depend on a single modulus, we find that all physical quantities exhibit a universal scaling with the distance from the fixed point. There is no dependence on the level of the construction, the weights of matter multiplets and their representations, with the only restriction that electroweak lepton doublets transform as irreducible triplets of the finite modular group. Also the form of the kinetic terms, which here are assumed to be neither minimal nor flavor blind, is irrelevant to the outcome. The result is remarkably simple and the whole class of examined theories gives rise to five independent patterns of neutrino mass matrices. Only in one of them, the predicted scaling agrees with the observed neutrino mass ratios and lepton mixing angles, exactly as in single modulus theories living close to τ = i.

Abstract Inspired by the structure of top-down derived models endowed with modular flavor symmetries, we investigate the yet phenomenologically unexplored binary dihedral group 2D 3. After building the vector-valued modular forms in the representations of 2D 3 with small modular weights, we systematically classify all (Dirac and Majorana) mass textures of fermions with fractional modular weights and all possible 2 + 1-family structures. This allows us to explore the parameter space of fermion models based on 2D 3, aiming at a description of both quarks and leptons with a minimal number of parameters and best compatibility with observed data. We consider the separate possibilities of neutrino masses generated by either a type-I seesaw mechanism or the Weinberg operator. We identify a model that, besides fitting all known flavor observables, delivers predictions for six not-yet measured parameters and favors normal-ordered neutrino masses generated by the Weinberg operator. It would be interesting to figure out whether it is possible to embed our model within a top-down scheme, such as $${\mathbb{T}}^{2}/{\mathbb{Z}}_{4}$$ heterotic orbifold compactifications.

Abstract We revisit the Next-to-Leading Order (two-loop) contributions to the Anomalous Dimensions of ∆F = 1 four-quark operators in QCD. We devise a test for anomalous dimensions, that we regard as of general interest, and by means of which we detect a problem in the results available in the literature. Deconstructing the steps leading to the available result, we identify the source of the problem, which is related to the operator known as Q 11. We show how to fix the problem and provide the corrected anomalous dimensions. With the insight of our findings, we propose an alternative approach to the one used in the literature which does not suffer from the identified disease, and which confirms our corrected results. We assess the numerical impact of our corrections, which happens to be in the ballpark of 5% in certain entries of the evolution matrix. Our results are important for the correct resummation of Next-to-Leading Logarithms in analyses of physics beyond the Standard Model in ∆F = 1 processes, such as the decays of Kaons and B-mesons.