An accidental U(1) Peccei-Quinn (PQ) symmetry automatically arises in a class of SO(10) unified theories upon gauging the SU(3)$_{f}$ flavour group. The PQ symmetry is protected by the $\mathbb{Z}_4 \times \mathbb{Z}_3$ center of $\text{SO(10)} \times \text{SU(3)}_f$ up to effective operators of canonical dimension six. However, high-scale contributions to the axion potential posing a PQ quality problem arise only at $d=9$. In the pre-inflationary PQ breaking scenario the axion mass window is predicted to be $m_a \in [7 \times 10^{-8}, 10^{-3}]$ eV, where the lower end is bounded by the seesaw scale and the upper end by iso-curvature fluctuations. A high-quality axion, that is immune to the PQ quality problem, is obtained for $m_a \gtrsim 0.02$ eV. We finally offer a general perspective on the PQ quality problem in grand unified theories.
We show how an accidental $U(1)$ Peccei-Quinn (PQ) symmetry can arise from a discrete $A_4$ family symmetry combined with a discrete flavour symmetry $ \mathbb{Z}_3 \times \mathbb{Z}_5^2 $, in a realistic Pati-Salam unified theory of flavour. Imposing only these discrete flavour symmetries, the axion solution to the strong $ CP $ problem is protected from PQ-breaking operators to the required degree. A QCD axion arises from a linear combination of $ A_4 $ triplet flavons, which are also responsible for fermion flavour structures due to their vacuum alignments. We find that the requirement of a…
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 phenomenology of a model where an SU(2)^3 flavour symmetry acting on the first two generation quarks is gauged and Yukawa couplings for the light generations are generated by a see-saw mechanism involving heavy fermions needed to cancel flavour-gauge anomalies. We find that, in constrast to the SU(3)^3 case studied in the literature, most of the constraints related to the third generation, like electroweak precision bounds or B physics observables, can be evaded, while characteristic collider signatures are predicted.
Combining Pati-Salam (PS) and flavour symmetries in a renormalisable setup, we devise a scenario which produces realistic masses for the charged leptons. Flavour-symmetry breaking scalar fields in the adjoint representations of the PS gauge group are responsible for generating different flavour structures for up- and down-type quarks as well as for leptons. The model is characterised by new heavy fermions which mix with the Standard Model quarks and leptons. In particular, the partners for the third fermion generation induce sizeable sources of flavour violation. Focusing on the charged-lepton…
Spontaneously broken, flavour-dependent, gauged $U(1)$ extensions of the Standard Model (SM) have many phenomenological uses. We chart the space of solutions to the gauge anomaly cancellation equations in such extensions, for both the SM chiral fermion content and the SM plus (up to) three right-handed neutrinos (SM$ν_R$). Methods from Diophantine analysis allow us to efficiently index the solutions arithmetically, and produce the complete solution space in particular cases. In order to solve the general case, we build a computer program which cycles through possible $U(1)$ charge assignments,…
We study classes of models which are based on some discrete family symmetry which is completely broken such that the observed neutrino flavour symmetry emerges indirectly as an accidental symmetry. For such "indirect" models we discuss the D-term flavon vacuum alignments which are required for such an accidental flavour symmetry consistent with tri-bimaximal lepton mixing to emerge. We identify large classes of suitable discrete family symmetries, namely the $Δ(3n^2)$ and $Δ(6n^2)$ groups, together with other examples such as $Z_7\rtimes Z_3$. In such indirect models the implementation of the …
We explore the possibility that lepton family numbers and baryon number are such good symmetries of Nature because they are the global remnant of a spontaneously broken gauge symmetry. An almost arbitrary linear combination of these symmetries (together with a component of global hypercharge) can be consistently gauged, if the Standard Model (SM) fermion content is augmented by three chiral SM singlet states. Within this framework of $U(1)$ extensions of the SM one generically expects flavour non-universality to emerge in the charged leptons, in such a way that naturally prevents lepton flavou…
The gauging of the lepton flavour group is considered in the Standard Model context and in its extension with three right-handed neutrinos. The anomaly cancellation conditions lead to a Seesaw mechanism as underlying dynamics for all leptons; requiring in addition a phenomenologically viable setup leads to Majorana masses for the neutral sector: the type I Seesaw Lagrangian in the Standard Model case and the inverse Seesaw in the extended model. Within the minimal extension of the scalar sector, the Yukawa couplings are promoted to scalar fields in the bifundamental of the flavour group. The r…
We propose that dark matter is stable as a consequence of an accidental Z2 that results from a flavour-symmetry group which is the double-cover group of the symmetry group of one of the regular geometric solids. Although model-dependent, the phenomenology resembles that of a generic Higgs portal dark matter scheme.
KTH Royal Institute of Technology（皇家理工学院）；Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；Universidad Complutense de Madrid（马德里康普顿斯大学）；Universidad de Castilla-La Mancha（卡斯蒂利亚-拉曼恰大学）
We propose a one-loop induced radiative neutrino mass model with anomaly free flavour dependent gauge symmetry: $μ$ minus $τ$ symmetry $U(1)_{μ-τ}$. A neutrino mass matrix satisfying current experimental data can be obtained by introducing a weak isospin singlet scalar boson that breaks $U(1)_{μ-τ}$ symmetry, an inert doublet scalar field, and three right-handed neutrinos in addition to the fields in the standard model. We find that a characteristic structure appears in the neutrino mass matrix: two-zero texture form which predicts three non-zero neutrino masses and three non-zero CP-phases fr…
We show how gauged flavour breaking and N = 1 supersymmetry breaking can be dynamically aligned to produce natural models. Supersymmetry is broken in a metastable vacuum, while a weakly gauged flavour symmetry is identified with an SU(3)_F subgroup of the global symmetry of the SQCD model. We find that alignment can easily occur either through strongly coupled flavour models, with SQCD bound states playing the role of flavons, or entirely weakly coupled and renormalizable models with elementary SU(3)_F adjoint flavons. In both cases it is essential that the SU(3)_F breaking, and hence all the …
We study UV-complete Froggatt-Nielsen-like models for the generation of mass and mixing hierarchies, assuming that the integrated heavy fields are chiral with respect to an abelian Froggatt-Nielsen symmetry. It modifies the mixed anomalies with respect to the Standard Model gauge group, which opens up the possibility to gauge the Froggatt-Nielsen symmetry without the need to introduce additional spectator fermions, while keeping mass matrices usually associated to anomalous flavour symmetries. We give specific examples where this happens, and we study the flavourful axion which arises from an …
We propose a model which generates neutrino masses by the inverse seesaw mechanism, provides a viable dark matter candidate and explains the muon ($g-2$) anomaly. The Standard Model (SM) gauge group is extended with a gauged U(1)$_{\rm B-L}$ as well as a gauged U(1)$_{\rm L_μ - L_τ}$. While U(1)$_{\rm L_μ - L_τ}$ is anomaly free, the anomaly introduced by U(1)$_{\rm B-L}$ is cancelled between the six SM singlet fermions introduced for the inverse seesaw mechanism and four additional chiral fermions introduced in this model. After spontaneous symmetry breaking the four chiral fermionic degrees …
A mechanism to generate realistic fermion mass hierarchies based on supersymmetric gauged $U(1)_F$ symmetry in flat five-dimensional (5D) spacetime is proposed. The fifth dimension is compactified on $S^1/Z_2$ orbifold. The standard model fermions charged under the extra abelian symmetry along with their superpartners live in the 5D bulk. Bulk masses of fermions are generated by the vacuum expectation value of $N=2$ superpartner of $U(1)_F$ gauge field, and they are proportional to $U(1)_F$ charges of respective fermions. This decides localization of fermions in the extra dimension, which in t…
The axion solution to the strong CP problem requires an anomalous global U(1) symmetry. We show that the existence of such a symmetry is a natural consequence of an extra dimension in which a gauged U(1) is spontaneously broken on one of two branes, leaving an accidental global symmetry on the other brane. Depending on where the standard model matter lives, the resulting axion can be either the DFSZ or hadronic type. Gaugino-mediated supersymmetry breaking fits comfortably in our framework. In addition, we present a model in which the supersymmetry-breaking and Peccei-Quinn breaking scales are…
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.
We present an extensive analysis of Delta F=2 observables and of B -> X_s gamma in the framework of a specific Maximally Gauged Flavour (MGF) model of Grinstein et al. including all relevant contributions, in particular tree-level heavy gauge boson exchanges that are considered in the present paper for the first time. The model allows in principle for significant deviations from the Standard Model predictions for epsilon_K, Delta M_{B_{d,s}}, mixing induced CP-asymmetries S_{psi K_S} and S_{psi phi} and B -> X_s gamma decay. The tension between epsilon_K and S_{psi K_S} present in the SM can b…
A local flavour symmetry acting on the quarks of the Standard Model can automatically give rise to an accidental global $U(1)$ which remains preserved from sources of explicit breaking up to a large operator dimension, while it gets spontaneously broken together with the flavour symmetry. Such non-fundamental symmetries are often endowed with a mixed QCD anomaly, so that the strong CP problem is automatically solved via the axion mechanism. We illustrate the general features required to realise this scenario, and we discuss a simple construction based on the flavour group $SU(3)\times SU(2) \t…
The flavour lepton symmetry is gauged for both the Standard Model flavor group and its extension with three degenerate right-handed neutrinos. As a consequence of anomaly cancellation, exotic leptons are introduced which induce a see-saw mechanism that generates the masses of the SM leptons. The model is compared with Minimal Flavour Violation, the difference between the low-energy effective operators resulting is identified, as well as the distinctive experimental signals, particularly promising in the $μ-τ$ sector.
We use supersymmetry to address the little hierarchy problem in Randall-Sundrum models by naturally generating a hierarchy between the IR scale and the electroweak scale. Supersymmetry is broken on the UV brane which triggers the stabilization of the warped extra dimension at an IR scale of order 10 TeV. The Higgs and top quark live near the IR brane whereas light fermion generations are localized towards the UV brane. Supersymmetry breaking causes the first two sparticle generations to decouple, thereby avoiding the supersymmetric flavour and CP problems, while an accidental R-symmetry protec…
While the $S_3$ scalar leptoquark presents a possible tree-level explanation of the $b \to s \ell \ell$ flavour anomalies, it suffers from two conceptual problems which are often disregarded by model-builders. Firstly, the quantum numbers of the $S_3$ allow for a renormalisable diquark operator that would trigger rapid proton decay unless its coupling were tuned away. Secondly, one expects the leptoquark to have generic couplings to leptons, which require tuning to avoid stringent experimental bounds on lepton flavour violation. By gauging a $U(1)$ current that acts as $L_μ- L_τ$ on the Standa…
We investigate a simple model where Lepton number is promoted to a local $U(1)_L$ gauge symmetry which is then spontaneously broken, leading to a viable thermal DM candidate and vector-like leptons as a byproduct. The dark matter arises as part of the exotic lepton sector required by the need to satisfy anomaly cancellation and is a Dirac electroweak (mostly) singlet neutrino. It is stabilized by an accidental global symmetry of the renormalizable Lagrangian which is preserved even after the gauged lepton number is spontaneously broken and can annihilate efficiently to give the correct thermal…
We show how two different family symmetries can be used to address the flavour problem in SO(10)-like models. The first is based on a gauged $U(1)_F$, whose problems dissappear in the context of a type I string model embedding. The second is based on $SU(3)_F$, the maximal family group consistent with SO(10); in this case the family symmetry is more constaining, so we merely look at it in the context of a supersymmetric field theory
We present a comprehensive discussion of the phenomenology of flavourful axions, including both standard Peccei-Quinn (PQ) axions, associated with the solution to the strong $CP$ problem, and non-standard axion-like particles (ALPs). We give the flavourful axion-fermion and axion-photon couplings and calculate the branching ratios of heavy meson ($K$, $D$, $B$) decays involving a flavourful axion. We also calculate the mixing between axions and heavy mesons $ K^0 $, $ D^0 $, $ B^0 $ and $ B_s^0 $, which affects the meson oscillation probability and mass difference. Mixing also contributes to m…
We present a class of models in which dark matter (DM) is a fermionic singlet under the Standard Model (SM) gauge group but is charged under a symmetry of flavour that acts as well on the SM fermions. Interactions between DM and SM particles are mediated by the scalar fields that spontaneously break the flavour symmetry, the so-called flavons. In the case of gauged flavour symmetries, the interactions are also mediated by the flavour gauge bosons. We first discuss the construction and the generic features of this class of models. Then a concrete example with an abelian flavour symmetry is cons…
We propose a gauged two-Higgs-doublet model (2HDM) featuring an anomalous Peccei-Quinn symmetry, $U(1)_{PQ}$. Dangerous tree-level flavour-changing neutral currents, common in 2HDMs, are forbidden by the extra gauge symmetry, $U(1)_X$. In our construction, the solutions to the important issues of neutrino masses, dark matter and the strong CP problem are interrelated. Neutrino masses are generated via a Dirac seesaw mechanism and are suppressed by the ratio of the $U(1)_X$ and the $U(1)_{PQ}$ breaking scales. Naturally small neutrino masses suggest that the breaking of $U(1)_X$ occurs at a rel…
In the context of supersymmetric theories, a weakly broken gauged SO(3) flavour symmetry is used to produce two highly degenerate right handed (RH) neutrinos. It is then shown that this SO(3) flavour symmetry is compatible with all fermion masses and mixings if it is supplemented with a further SU(3) flavour symmetry. A specific Susy breaking model is used to generate the light neutrino masses as well as a natural model of TeV scale resonant leptogenesis.
Tree-level accidental symmetries are known to play a fundamental role in the phenomenology of the Standard Model (SM) for electroweak interactions. So far, no significant deviations from the theory have been observed in precision, flavour and collider physics. Consequently, these global symmetries are expected to remain quite efficient in any attempt beyond the SM. Yet, they do not forbid rather unorthodox phenomena within the reach of current LHC experiments. This is illustrated with a vectophobic Two-Higgs-Doublet-Model (2HDM) where effects of a light, flavour-violating and custodian (pseudo…
The axion solution to the strong CP problem calls for an explanation as to why the Lagrangian should be invariant under the global Peccei-Quinn symmetry, U(1)_PQ, to such a high degree of accuracy. In this paper, we point out that the U(1)_PQ can indeed survive as an accidental symmetry in the low-energy effective theory, if the standard model gauge group is supplemented by a gauged and discrete R symmetry, Z_N^R, forbidding all dangerous operators that explicitly break the Peccei-Quinn symmetry. In contrast to similar approaches, the requirement that the Z_N^R symmetry be anomaly-free forces …
One of the greatest challenges for models of $b \to s$ anomalies is the necessity to produce a large contribution to a quark times a lepton current, $J_q \times J_\ell$, and to avoid accordingly large contributions to flavour-changing $J_q \times J_q$ and $J_\ell \times J_\ell$ amplitudes, which are severely constrained by data. We consider a gauged horizontal symmetry involving the two heaviest generations of all left-handed fermions. In the limit of degenerate masses for the horizontal bosons, and in the absence of mixing between the two heavier generations and the lighter one, such symmetry…
We extend the standard model with two extra Higgs doublets. Making use of a symmetry principle, we present flavour symmetries based on cycle groups $Z_N$ that oblige each Higgs doublet to contribute to the mass of only one generation, thus accommodating the quark mass hierarchy. We systematically search for all charge configurations that naturally lead to the alignment in flavour space of the quark sectors, resulting in a CKM matrix near to the identity, determined by the quark mass hierarchy, and with the correct overall phenomenological features. The minimal realisation is by the group $Z_7$…
We construct a simple model of fermion masses based on a spontaneously broken S3 X Z3 flavour group. At the leading order, in the neutrino sector S3 is broken down to a ν_μ-ν_τparity subgroup that enforces a maximal atmospheric mixing angle and a vanishing θ_{13}. In the charged lepton sector the ν_μ-ν_τparity is maximally broken and the resulting mass matrix is nearly diagonal. The charged lepton mass hierarchy is automatically reproduced by the S3 symmetry breaking parameter alone. A careful analysis shows that, after the inclusion of all relevant subleading effects, the model predicts θ_{23…
The gauged $B - L$ symmetry is one of the simplest and well studied extension of standard model. In the conventional case, addition of three singlet right handed neutrinos each transforming as $-1$ under the $B - L$ symmetry renders it anomaly free. It is usually assumed that the $B - L$ symmetry is spontaneously broken by a singlet scalar having two units of $B - L$ charge, resulting in a natural implementation of Majorana seesaw mechanism for neutrinos. However, as we discuss in this proceeding, there is another simple anomaly free solution which leads to Dirac or inverse seesaw masses for n…
Motivated by the intriguing discrepancies in $b\to s \ell\ell$ transitions, the fermion mass problem, and a desire to preserve the accidental symmetries of the Standard Model (SM), we extend the SM by an anomalous $U(1)_X$ gauge symmetry where $X=Y_3+a(L_μ-L_τ)/6$. The heavy $Z^\prime$ boson associated with spontaneously breaking $U(1)_X$ at the TeV scale mediates the $b\to s\ell\ell$ anomalies via $\mathcal{O}^μ_9 \sim\frac{1}{Λ^2}(\bar{s}γ_ρP_L b)(\barμ γ^ρμ)$. We show that this model, which features mixed gauge anomalies involving $U(1)_X$ and hypercharge, can be made anomaly-free for any $…
We present a new model of composite Higgs based on a gauged SU(N) group with 4 Dirac fermions in the fundamental representation. At low energy, the model has a global symmetry SU(4)$\times$SU(4) broken to the diagonal SU(4), containing 2 Higgs doublets in the coset. We study in detail the generation of the top mass via 4-fermion interactions, and the issue of the vacuum alignment. In particular, we prove that, without loss of generality, the vacuum can always be aligned with one doublet. Under certain conditions on the top pre-Yukawas, the second doublet, together with the additional triplets,…
Discrete flavour symmetries have been proven successful in explaining the leptonic flavour structure. To account for the observed mixing pattern, the flavour symmetry has to be broken to different subgroups in the charged and neutral lepton sector. However, cross-couplings via non-trivial contractions in the scalar potential force the group to break to the same subgroup. We present a solution to this problem by extending the flavour group in such a way that it preserves the flavour structure, but leads to an 'accidental' symmetry in the flavon potential. We have searched for symmetry groups up…
Minimal complete tri-hypercharge theories of flavour
School of Physics & Astronomy, University of Glasgow（格拉斯哥大学物理与天文学学院）；School of Physics & Astronomy, University of Southampton（南安普顿大学物理与天文学学院）；Instituto de Física Corpuscular, CSIC-Universitat de València（瓦伦西亚大学-CSIC粒子物理研究所）；Departament de Física Teòrica, Universitat de València（瓦伦西亚大学理论物理系）
本文提出两种最小的三超荷理论，通过三个物理尺度解释费米子质量和混合，且所有基本系数为$\mathcal{O}(1)$，并探讨其在LHC Run 3中的实验可探测性。
The top condensate see-saw mechanism of Dobrescu and Hill allows electroweak symmetry to be broken while deferring the problem of flavour to an electroweak singlet, massive sector. We provide an extended version of the singlet sector that naturally accommodates realistic masses for all the standard model fermions, which play an equal role in breaking electroweak symmetry. The models result in a relatively light composite Higgs sector with masses typically in the range of (400-700)~GeV. In more complete models the dynamics will presumably be driven by a broken gauged family or flavour symmetry …
We show how the SUSY flavour and CP problems can be solved using gauged SU(3) family symmetry previously introduced to describe quark and lepton masses and mixings, in particular neutrino tri-bimaximal mixing via constrained sequential dominance. The Yukawa and soft trilinear and scalar mass squared matrices and kinetic terms are expanded in powers of the flavons used to spontaneously break the SU(3) family symmetry, and the canonically normalized versions of these matrices are constructed. The soft mass matrices are then expressed in the Super-CKM basis, and the leading order mass insertion p…
Constraining Ultra-Light Vector Bosons via Solar Neutrino Oscillations: The Gauged $L_μ- L_τ$ Model and Prospects for JUNO and XLZD
Centro de Astrofísica e Gravitação - CENTRA, Departamento de Física, Instituto Superior Técnico - IST, Universidade de Lisboa - UL（里斯本大学技术研究所物理系天体物理学与引力中心）
The "gauged'' Peccei-Quinn (PQ) mechanism of Fukuda, Ibe, Suzuki and Yanagida is implemented in the flavorful axion model of Carone and Merchand. This model of flavor is similar to other successful ones based on the double tetrahedral group, but the flavor symmetry includes a global U(1) factor that leads to the presence of a flavorful axion. Here we gauge that U(1) symmetry and introduce a heavy sector that includes (1) the fermions necessary to cancel anomalies and (2) a second scalar flavon field that spontaneously breaks the U(1) symmetry. The full theory has an accidental U(1)$\times$U(1)…
