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Physical review / D 107(6), 066018 (2023). doi:10.1103/PhysRevD.107.066018, We study a rich set of four-dimensional superconformal field theories (SCFTs) with both central charges identical: $a = c$. These are constructed via the diagonal $\mathcal{N}=2$ or $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres-Douglas theories of type $\mathcal{D}_p(G)$, with or without adjoint chiral multiplets, in arXiv:2106.12579 and arXiv:2111.12092. We compute superconformal indices of some theories where the rank of $G$ is low, performing a refined test for unitarity, and further determine the relevant and marginal operator content in detail. We find that most of these theories flow to interacting SCFTs with $a=c$ in the infrared., Published by Inst., Woodbury, NY

Physical review / D 105(12), 126006 (2022). doi:10.1103/PhysRevD.105.126006, We study a rich set of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) with both central charges identical: $a = c$. We construct them via the diagonal $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres--Douglas theories of type $\mathcal{D}_p(G)$, with or without additional adjoint chiral multiplets. In this way, we construct infinitely-many theories that flow to interacting SCFTs with $a = c$ in the infrared. Finally, we briefly highlight the features of the SCFTs without $a = c$ that arise from generalizing this construction., Published by Inst., Melville, NY

Physical review / D 105(4), 046006 (2022). doi:10.1103/PhysRevD.105.046006, We use the numerical conformal bootstrap to study six-dimensional N=(1,0) superconformal field theories with flavor symmetry so4k. We present evidence that minimal (Dk,Dk) conformal matter saturates the unitarity bounds for arbitrary k. Furthermore, using the extremal-functional method, we check that the chiral-ring relations are correctly reproduced, extract the anomalous dimensions of low-lying long superconformal multiplets, and find hints for novel operator product expansion selection rules involving type-B multiplets., Published by Inst., Melville, NY

We describe the mapping at high density of topological structure of baryonic matter to a nuclear effective field theory that implements hidden symmetries emergent from strong nuclear correlations. The theory so constructed is found to be consistent with no conflicts with the presently available observations in both normal nuclear matter and compact-star matter. The hidden symmetries involved are "local flavor symmetry" of the vector mesons identified to be (Seiberg-)dual to the gluons of QCD and hidden "quantum scale symmetry" with an IR fixed point with a "genuine dilaton (GD)" characterized by non-vanishing pion and dilaton decay constants. Both the skyrmion topology for $N_f \geq 2$ baryons and the fractional quantum Hall (FQH) droplet topology for $N_f=1$ baryons are unified in the "homogeneous/hidden" Wess-Zumino term in the hidden local symmetry (HLS) Lagrangian. The possible indispensable role of the FQH droplets in going beyond the density regime of compact stars approaching scale-chiral restoration is explored by moving toward the limit where both the dilaton and the pion go massless., Comment: A few typo corrections in published version. arXiv admin note: substantial text overlap with arXiv:2103.01860

We initiate a study of the holographic duals of a class of four-dimensional $\mathcal{N}=2$ superconformal field theories that are engineered by wrapping M5-branes on a sphere with an irregular puncture. These notably include the strongly-coupled field theories of Argyres-Douglas type. Our solutions are obtained in 7d gauged supergravity, where they take the form of a warped product of $AdS_5$ and a "half-spindle." The irregular puncture is modeled by a localized M5-brane source in the internal space of the gravity duals. Our solutions feature a realization of supersymmetry that is distinct from the usual topological twist, as well as an interesting St\"uckelberg mechanism involving the gauge field associated to a generator of the isometry algebra of the internal space. We check the proposed duality by computing the holographic central charge, the flavor symmetry central charge, and the dimensions of various supersymmetric probe M2-branes, and matching these with the dual Argyres-Douglas field theories. Furthermore, we compute the large-$N$ 't Hooft anomalies of the field theories using anomaly inflow methods in M-theory, and find perfect agreement with the proposed duality., Comment: 38 pages plus appendices; typos fixed

We study a rich set of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) with both central charges identical: $a = c$. We construct them via the diagonal $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres--Douglas theories of type $\mathcal{D}_p(G)$, with or without additional adjoint chiral multiplets. In this way, we construct infinitely-many theories that flow to interacting SCFTs with $a = c$ in the infrared. Finally, we briefly highlight the features of the SCFTs without $a = c$ that arise from generalizing this construction.

Journal of high energy physics 01(1), 175 (2021). doi:10.1007/JHEP01(2021)175, We apply the numerical conformal bootstrap to correlators of Coulomb and Higgs branch operators in 4d$ \mathcal{N} $ = 2 superconformal theories. We start by revisiting previous results on single correlators of Coulomb branch operators. In particular, we present improved bounds on OPE coefficients for some selected Argyres-Douglas models, and compare them to recent work where the same cofficients were obtained in the limit of large r charge. There is solid agreement between all the approaches. The improved bounds can be used to extract an approximate spectrum of the Argyres-Douglas models, which can then be used as a guide in order to corner these theories to numerical islands in the space of conformal dimensions. When there is a flavor symmetry present, we complement the analysis by including mixed correlators of Coulomb branch operators and the moment map, a Higgs branch operator which sits in the same multiplet as the flavor current. After calculating the relevant superconformal blocks we apply the numerical machinery to the mixed system. We put general constraints on CFT data appearing in the new channels, with particular emphasis on the simplest Argyres-Douglas model with non-trivial flavor symmetry., Published by SISSA, [Trieste]

We use the numerical conformal bootstrap to study six-dimensional $\mathcal{N}=(1,0)$ superconformal field theories with flavor symmetry $\mathfrak{so}_{4k}$. We present evidence that minimal $(D_k, D_k)$ conformal matter saturates the unitarity bounds for arbitrary $k$. Furthermore, using the extremal-functional method, we check that the chiral-ring relations are correctly reproduced, extract the anomalous dimensions of low-lying long superconformal multiplets, and find hints for novel OPE selection rules involving type-$\mathcal{B}$ multiplets.

We perform a lattice QCD calculation of the hadronic light-by-light contribution to $(g-2)_\mu$ at the SU(3) flavor-symmetric point $m_\pi=m_K\simeq 420\,$MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computing the connected contribution, and introduce a sparse-grid technique for computing the disconnected contribution. Thanks to our previous calculation of the pion transition form factor, we are able to correct for the residual finite-size effects and extend the tail of the integrand. We test our understanding of finite-size effects by using gauge ensembles differing only by their volume. After a continuum extrapolation based on four lattice spacings, we obtain $a_\mu^{\rm hlbl} = (65.4\pm 4.9 \pm 6.6)\times 10^{-11}$, where the first error results from the uncertainties on the individual gauge ensembles and the second is the systematic error of the continuum extrapolation. Finally, we estimate how this value will change as the light-quark masses are lowered to their physical values., Comment: 19 figures, 39 pages; improved references, in particular concerning the eta exchange; no figures or results changed

We apply the numerical conformal bootstrap to correlators of Coulomb and Higgs branch operators in $4d$ $\mathcal{N}=2$ superconformal theories. We start by revisiting previous results on single correlators of Coulomb branch operators. In particular, we present improved bounds on OPE coefficients for some selected Argyres-Douglas models, and compare them to recent work where the same cofficients were obtained in the limit of large $r$ charge. There is solid agreement between all the approaches. The improved bounds can be used to extract an approximate spectrum of the Argyres-Douglas models, which can then be used as a guide in order to corner these theories to numerical islands in the space of conformal dimensions. When there is a flavor symmetry present, we complement the analysis by including mixed correlators of Coulomb branch operators and the moment map, a Higgs branch operator which sits in the same multiplet as the flavor current. After calculating the relevant superconformal blocks we apply the numerical machinery to the mixed system. We put general constraints on CFT data appearing in the new channels, with particular emphasis on the simplest Argyres-Douglas model with non-trivial flavor symmetry.

Journal of high energy physics 2020(1), 191 (2020). doi:10.1007/JHEP01(2020)191, 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 accidental Peccei-Quinn symmetry in some of those models. Such an axion is typically more coupled to matter than in models with spectator fermions., Published by SISSA, [Trieste]

Journal of high energy physics 2020(1), 194 (2020). doi:10.1007/JHEP01(2020)194, We employ a bottom-up and model-independent technique to search for non-Abelian discrete flavour symmetries capable of predicting viable CKM and PMNS matrices alongside of special patterns of leptoquark couplings. In particular, we analyze patterns de- rived when an ultra-violet flavour theory is assumed to break to global Abelian symmetries in Standard Model fermion masses and new Yukawa-like terms sourced by the leptoquark representation. The phenomenology of different classes of these ‘simplified models’ can be explored without reference to explicit model-building assumptions, e.g. the nature of flavour symmetry breaking or any additional field content associated to it, and are also capable of explaining hints of lepton non-universality in $ {\mathcal{R}}_{K^{\left(\ast \right)}} $. Assuming experimentally interesting CKM and PMNS matrix elements, our algorithm finds an abundance of predictive non-Abelian flavour groups and therefore provides promising directions for future model building in the flavoured leptoquark space, regardless of whether the anomalous $ {\mathcal{R}}_{K^{\left(\ast \right)}} $ measurements withstand further experimental scrutiny., Published by SISSA, [Trieste]

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., Comment: 11 pages; v2: references added, LEP results updated

We employ a bottom-up and model-independent technique to search for non-Abelian discrete flavour symmetries capable of predicting viable CKM and PMNS matrices alongside of special patterns of leptoquark couplings. In particular, we analyze patterns derived when an ultra-violet flavour theory is assumed to break to global Abelian symmetries in Standard Model fermion masses and new Yukawa-like terms sourced by the leptoquark representation. The phenomenology of different classes of these `simplified models' can be explored without reference to explicit model-building assumptions, e.g. the nature of flavour symmetry breaking or any additional field content associated to it, and are also capable of explaining hints of lepton non-universality in $\mathcal{R}_{K^{(\star)}}$. Assuming experimentally interesting CKM and PMNS matrix elements, our algorithm finds an abundance of predictive non-Abelian flavour groups and therefore provides promising directions for future model building in the flavoured leptoquark space, regardless of whether the anomalous $\mathcal{R}_{K^{(\star)}}$ measurements withstand further experimental scrutiny., version published in JHEP

The increasing interest in the phenomenology of the Standard Model Effective Field Theory (SMEFT), has led to the development of a wide spectrum of public codes which implement automatically different aspects of the SMEFT for phenomenological applications. In order to discuss the present and future of such efforts, the "SMEFT-Tools 2019" Workshop was held at the IPPP Durham on the 12th-14th June 2019. Here we collect and summarize the contents of this workshop., Comment: 63 pages. Based on the contributions to SMEFT-Tools 2019 (https://indico.cern.ch/event/787665/)

We deform two-dimensional quantum field theories by antisymmetric combinations of their conserved currents that generalize Smirnov and Zamolodchikov's $T\bar{T}$ deformation. We obtain that energy levels on a circle obey a transport equation analogous to the Burgers equation found in the $T\bar{T}$ case. This equation relates charges at any value of the deformation parameter to charges in the presence of a (generalized) Wilson line. We determine the initial data and solve the transport equations for antisymmetric combinations of flavor symmetry currents and the stress tensor starting from conformal field theories. Among the theories we solve is a conformal field theory deformed by $J\bar{T}$ and $T\bar{T}$ simultaneously. We check our answer against results from AdS/CFT., Comment: 42 pages

We employ a bottom-up and model-independent technique to search for non-Abelian discrete flavour symmetries capable of predicting viable CKM and PMNS matrices alongside of special patterns of leptoquark couplings. In particular, we analyze patterns derived when an ultra-violet flavour theory is assumed to break to global Abelian symmetries in Standard Model fermion masses and new Yukawa-like terms sourced by the leptoquark representation. The phenomenology of different classes of these `simplified models' can be explored without reference to explicit model-building assumptions, e.g. the nature of flavour symmetry breaking or any additional field content associated to it, and are also capable of explaining hints of lepton non-universality in $\mathcal{R}_{K^{(\star)}}$. Assuming experimentally interesting CKM and PMNS matrix elements, our algorithm finds an abundance of predictive non-Abelian flavour groups and therefore provides promising directions for future model building in the flavoured leptoquark space, regardless of whether the anomalous $\mathcal{R}_{K^{(\star)}}$ measurements withstand further experimental scrutiny.

We propose a modification of standard QCD description of the colour triplet of quarks describing quark fields endowed with colour degree of freedom by introducing a 12-component colour generalization of Dirac spinor, with built-in Z_3 grading playing an important algebraic role in quark confinement. In "colour Dirac equations" the SU(3) colour symmetry is entangled with the Z_3-graded generalization of Lorentz symmetry, containing three 6-parameter sectors related by Z_3 maps. The generalized Lorentz covariance requires simultaneous presence of 24 colour Dirac multiplets, which lead to the description of all internal symmetries of quarks: besides SU(3) \times SU(2) \times U(1), the flavour symmetries and three quark families., LaTeX, 14 pages, no figures; v2 improved LaTeX format and small corrections in Sect 3, v3 changes in Introduction: mainly formula (2) deleted and formula (3) shifted to Sect.2;v4 small change in formula (27) and exposed role of Lorentz-covariant doublets of colour multiplets v5 extended version by three pages, new content of Sect 4

International audience; The weak phase γ is extracted from three-body charmless decays of B mesons following a method proposed by Bhattacharya, et al. The result is obtained by combining the BABAR amplitude analyses for the processes B0→K+π0π-, B0→KS0π+π-, B0→KS0KS0KS0, B0→K+KS0K-, and B+→K+π+π-, under the assumption of SU(3) flavor symmetry. Six possible solutions are found, γ1=(12.9−4.3+8.4±1.3)°,γ2=(36.6−6.1+6.6±2.6)°,γ3=(68.9−8.6+8.6±2.4)°,γ4=(223.2−7.5+10.9±1.0)°,γ5=(266.4−10.8+9.2±1.9)°,γ6=(307.5−8.1+6.9±1.1)°,where the first uncertainty is statistical and the second systematic. The γ3 solution is compatible with the world-average value γ=(73.5-5.1+4.2)°, while the other solutions are not. It is also found that, when averaged over the entire Dalitz plane, the effect of SU(3) breaking on the analysis is only at the percent level.

We study maximally supersymmetric AdS$_D$ solutions of gauged supergravities in dimensions $D \geq 4$. We show that such solutions can only exist if the gauge group after spontaneous symmetry breaking is a product of two reductive groups $H_R \times H_\mathrm{mat}$, where $H_R$ is uniquely determined by the dimension D and the number of supersymmetries N while $H_\mathrm{mat}$ is unconstrained. This resembles the structure of the global symmetry groups of the holographically dual SCFTs, where $H_R$ is interpreted as the R-symmetry and $H_\mathrm{mat}$ as the flavor symmetry. Moreover, we discuss possible supersymmetry preserving continuous deformations, which correspond to the conformal manifolds of the dual SCFTs. Under the assumption that the scalar manifold of the supergravity is a symmetric space we derive general group theoretical conditions on these moduli. Using these results we determine the AdS solutions of all gauged supergravities with more than 16 real supercharges. We find that almost all of them do not have supersymmetry preserving deformations with the only exception being the maximal supergravity in five dimensions with a moduli space given by $SU(1,1)/U(1)$. Furthermore, we determine the AdS solutions of four-dimensional N=3 supergravities and show that they similarly do not admit supersymmetric moduli., Comment: 69 pages; v2: minor changes, references added, to appear in JHEP

Flavor effects can have a significant impact on the final estimate of the lepton (and therefore baryon) asymmetry in scenarios of leptogenesis. It is therefore necessary to account fully for this flavor dynamics in the relevant transport equations that describe the production (and washout) of the asymmetry. Doing so can both open up and restrict viable regions of parameter space relative to the predictions of more approximate calculations. In this review, we identify the regimes in which flavor effects can be relevant and illustrate their impact in a number of phenomenological models. These include type I and type II seesaw embeddings, and low-scale resonant scenarios. In addition, we provide an overview of the semi-classical and field-theoretic methods that have been developed to capture flavor effects in a consistent way., 69 pages, 8 figures. Chapter 1 of the review volume "Leptogenesis: Current Challenges for Model Building, Phenomenology and Non-Equilibrium Field Theory". Matches published version

Physics letters / B 786, 373 - 377 (2018). doi:10.1016/j.physletb.2018.10.015, We show that the dynamics responsible for the variation of the Yukawa couplings of the Standard Model fermions generically leads to a very strong first-order electroweak phase transition, assuming that the Yukawa couplings are large and of order 1 before the electroweak phase transition and reach their present value afterwards. There are good motivations to consider that the flavour structure could emerge during electroweak symmetry breaking, for example if the Froggatt–Nielsen field dynamics were linked to the Higgs field. In this paper, we do not need to assume any particular theory of flavour and show in a model-independent way how the nature of the electroweak phase transition is completely changed when the Standard Model Yukawas vary at the same time as the Higgs is acquiring its vacuum expectation value. The thermal contribution of the fermions creates a barrier between the symmetric and broken phase minima of the effective potential, leading to a first-order phase transition. This offers new routes for generating the baryon asymmetry at the electroweak scale, strongly tied to flavour models., Published by North-Holland Publ., Amsterdam

International audience; Measurements of CP violation in B 0 → J/ψ K 0 S , B 0 s → J/ψ φ and B 0 s → D − s D + s decays play key roles in testing the quark-flavour sector of the Standard Model. The theoretical interpretation of these observables is, however, limited by uncertainties from doubly Cabibbo-suppressed penguin topologies. With continuously increasing experimental precision, it is mandatory to get a handle on these contributions, which cannot be calculated reliably in QCD. In this summary, we discuss a data driven method based on the SU(3) flavour symmetry of QCD to relate the penguin contributions in B 0 → J/ψ K 0 S , B 0 s → J/ψ φ and B 0 s → D − s D + s to unsuppressed counterparts in decay modes with similar dynamics. The fit results obtained with the currently available data are presented for all three modes. In addition, we discuss prospects for the LHCb upgrade and Belle II era, and illustrate the possibilities for the determination of hadronic parameters.

Physical review / D covering particles, fields, gravitation, and cosmology 94(7), 073004(2016). doi:10.1103/PhysRevD.94.073004, We discuss the parameter space reach of future experiments searching for heavy neutral leptons (HNLs). We consider the GeV seesaw model with three HNL generations and focus on two classes of models: generic assumptions (such as random mass matrices or the Casas-Ibarra parametrization) and flavor symmetry-generated models. We demonstrate that the generic approaches lead to comparable parameter space predictions, which tend to be at least partially within the reach of future experiments. On the other hand, specific flavor symmetry models yield more refined predictions, and some of these can be more clearly excluded. We also highlight the importance of measuring the flavor-dependent couplings of the HNLs as a model discriminator, and we clarify the impact of assumptions frequently used in the literature to show the parameter space reach for the active-sterile mixings., Published by Inst., Woodbury, NY

Physical review / D 94(7), 073004(2016). doi:10.1103/PhysRevD.94.073004, We discuss the parameter space reach of future experiments searching for heavy neutral leptons (HNLs) at the GeV scale in terms of neutrino mass models with three HNL generations. We focus on two classes of models: Generic assumptions (such as random mass matrices or the Casas-Ibarra parameterization) and flavor symmetry-generated models. We demonstrate that the generic approaches lead to comparable parameter space predictions, which tend to be at least partially within the reach of future experiments. On the other hand, specific flavor symmetry models yield more refined predictions, some of these can be more clearly excluded. We also highlight the importance to measure the flavor-dependent couplings of the HNLs as a model discriminator, and we clarify the impact of assumptions frequently used in the literature to show the parameter space reach for the active-sterile mixings., Published by Inst., Woodbury, NY

Physical review / D 90(7), 074022 (2014). doi:10.1103/PhysRevD.90.074022, In an effective theory approach, the full minimal set of leading contributions to anomalous charged-current top couplings comprises various new trilinear $tbW$ as well as quartic $tbf{f}^{\prime }$ interaction vertices, some of which are related to one another by equations of motion. While much effort in earlier work has gone into the extraction of the trilinear couplings from single top measurements, we argue in this article that these structures can be assessed independently by other observables, while single top production forms a unique window to the four-fermion sector. An effective theory approach is employed to infer and classify the minimal set of such couplings from dimension six operators in the minimal flavor violation scheme. In the phenomenological analysis, we present a Monte Carlo study at detector level to quantify the expected performance of the next LHC run to bound as well as distinguish the various contact couplings. Special attention is directed toward differential final state distributions including detector effects as a means to optimize the signal sensitivity as well as the discriminative power with respect to the possible coupling structures., Published by Soc., [S.l.]

149 pp. (1999)., The interactions of electroweak gauge bosons are severely constrained by the symmetries inferred from low energy observables. The exploration of the dynamics of electroweak symmetry breaking requires therefore both an experimental sensitivity and a theoretical precision that is better than the natural scale of deviations from minimal extrapolations of the low energy effective theory. Some techniques for obtaining improved theoretical predictions for precision tests at a future $e^+e^-$ linear collider are discussed.

(2016)., The chirally rotated Schr\'odinger functional ($\chi$SF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schr\'odinger functional (SF), with different lattice symmetries and a common continuum limit expected from universality. The explicit breaking of flavour and parity symmetries needs to be repaired by tuning the bare fermion mass and the coefficient of a dimension 3 boundary counterterm. Once this is achieved one expects the mechanism of automatic O($a$) improvement to be operational in the $\chi$SF, in contrast to the standard formulation of the SF. This is expected to significantly improve the attainable precision for step-scaling functions of some composite operators. Furthermore, the $\chi$SF offers new strategies to determine finite renormalization constants which are traditionally obtained from chiral Ward identities. In this paper we consider a complete set of fermion bilinear operators, define corresponding correlation functions and explain the relation to their standard SF counterparts. We discuss renormalization and O($a$) improvement and then use this set-up to formulate the theoretical expectations which follow from universality. Expanding the correlation functions to one-loop order of perturbation theory we then perform a number of non-trivial checks. In the process we obtain the action counterterm coefficients to one-loop order and reproduce some known perturbative results for renormalization constants of fermion bilinears. By confirming the theoretical expectations, this perturbative study lends further support to the soundness of the $\chi$SF framework and prepares the ground for non-perturbative applications.

We consider an inverse seesaw mechanism of neutrino mass generation in which the Standard Model is extended by $3+3$ (heavy) sterile states, and endowed with a flavour symmetry $G_f$, $G_f=\Delta (3 \, n^2)$ or $G_f=\Delta (6 \, n^2)$, and a CP symmetry. These symmetries are broken in a peculiar way, so that in the charged lepton sector a residual symmetry $G_\ell$ is preserved, while the neutral fermion sector remains invariant under the residual symmetry $G_\nu=Z_2 \times CP$. We study the concrete setup, where the Majorana mass term for three of the sterile states conserves $G_\nu$, while the remaining mass terms (i.e. couplings of left-handed leptons and heavy sterile states, as well as the Dirac-type couplings among the latter) do not break the flavour or CP symmetry. We perform a comprehensive analysis of lepton mixing for different classes of residual symmetries, giving examples for each of these, and study in detail the impact of the additional sterile states on the predictions for lepton mixing. We further confront our results with those obtained in the model-independent scenario, in which the light neutrino mass matrix leaves the residual symmetry $G_\nu$ intact. We consider the phenomenological impact of the inverse seesaw mechanism endowed with flavour and CP symmetries, in particular concerning effects of non-unitarity of the lepton mixing matrix (which strongly constrain the parameter space of the scenario), prospects for neutrinoless double beta decay and for charged lepton flavour violating processes., Comment: 42 pages, 12 figures