We compare theoretical and experimental predictions of two main classes of models addressing fermion mass hierarchies and flavour changing neutral currents (FCNC) effects in supersymmetry: Froggatt-Nielsen (FN) U(1) gauged flavour models and Nelson-Strassler/extra dimensional models with hierarchical wave functions for the families. We show that whereas the two lead to identical predictions in the fermion mass matrices, the second class generates a stronger suppression of FCNC effects. We prove that, whereas at first sight the FN setup is more constrained due to anomaly cancelation conditions, imposing unification of gauge couplings in the second setup generates conditions which precisely match the mixed anomaly constraints in the FN setup. Finally, we provide an economical extra dimensional realisation of the hierarchical wave functions scenario in which the leptonic FCNC can be efficiently suppressed due to the strong coupling (CFT) origin of the electron mass.
We investigate the impact on low energy flavour mixing phenomena of the renormalisation group running of parameters in supersymmetric theories. We have explicitly chosen flavour dependent supergravity couplings. The renormalisation group equations are displayed in general matrix form. We work in a scale dependent basis such that the hierarchy in the quark masses can be more easily utilised. Simple analytic solutions are provided in matrix form (for general boundary conditions) when only the third generation Yukawa couplings are retained in the renormalisation group equations. We solve the evol…
We clarify some aspects of the LSZ formalism and wave function renormalisation for unstable particles in the presence of electroweak interactions when mixing and CP violation are considered. We also analyse the renormalisation of the CKM mixing matrix which is closely related to wave function renormalisation. We critically review earlier attempts to define a set of "on-shell" wave function renormalisation constants. With the aid of an extensive use of the Nielsen identities complemented by explicit calculations we corroborate that the counter term for the CKM mixing matrix must be explicitly g…
We compute the finite renormalisation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix induced by gluino-squark diagrams in the MSSM with non-minimal sources of flavour violation. Subsequently we derive bounds on the flavour-off-diagonal elements of the squark mass matrices by requiring that the radiative corrections to the CKM elements do not exceed the experimental values. Our constraints on the associated dimensionless quantities delta^{d LR}_{ij}, j>i, are stronger than the bounds from flavour-changing neutral current (FCNC) processes if gluino and squarks are heavier than 500 GeV. Our bound …
In the Minimal Supersymmetric Standard Model (MSSM), there are numerous sources of flavour-violation in addition to the usual Kobayashi-Maskawa mixing matrix of the Standard Model. We reexamine the renormalisation group equations (RGEs) with a view to investigating flavour effects in a supersymmetric theory with an arbitrary flavour structure at some high scale. To incorporate (two-loop sized) threshold effects in the one-loop RGEs, we calculate the beta-functions using a sequence of (non-supersymmetric) effective theories with heavy particles decoupled at the scale of their mass, keeping trac…
An unified flavour model based on U(2) as flavour group is described. Besides to explain the main characteristics of the fermion spectrum, the model is predictive and agrees quantitatively with experimental data in flavour physics.
We discuss an approach for accessing bound state properties, like mass and decay width, of a theory within the functional renormalisation group approach. An important cornerstone is the dynamical hadronization technique for resonant interaction channels. The general framework is exemplified and put to work within the two-flavour quark-meson model. This model provides a low-energy description of the dynamics of two-flavour QCD with quark and hadronic degrees of freedom. We compare explicitly the respective results for correlation functions and observables with first principle QCD results in a q…
1. Data and implications. 2. Neutrino threshold effects. 3. Renormalisation of the neutrino mass operator and stability properties of neutrino textures. 4. Neutrino thresholds effects and Yukawa unification. 5. Renormalisation-induced lepton-flavour-violating processes from non-zero neutrino masses. 6. Summary.
In QCD the anomalous dimensions of gauge invariant operators of twist 2 play a key role, because they control the scale dependence of the parton distribution functions. Notably, the flavour singlet operators, such as those associated to the gluon distribution, mix under renormalisation with a set of unphysical operators, also known as aliens. Missing this effect leads to wrong results already for the two-loop anomalous dimensions. The correct renormalisation of gluonic operators is an important step towards the computation of the scale evolution of flavour singlet parton distributions, which i…
A recent study of dynamical chiral symmetry breaking in N-flavour QED$_3$ at finite temperature is extended to include the effect of fermion wavefunction renormalisation in the Schwinger-Dyson equations. The simple ``zero-frequency'' truncation previously used is found to lead to unphysical results, especially as $T \to 0$. A modified set of equations is proposed, whose solutions behave in a way which is qualitatively similar to the $T=0$ solutions of Pennington et al. [5-8] who have made extensive studies of the effect of wavefunction renormalisation in this context, and who concluded that th…
We examine possibilities for the radiative generation of the Yukawa couplings and flavour structure in supersymmetric models in the supersymmetric phase. Not withstanding the non-renormalisation of the Wilsonian superpotential, this can occur through the 2-loop vertex renormalisation of the physical 1PI couplings. We describe this effect and construct models in which this occurs. For models attempting to reproduce the full flavour structure of the Standard Model, we analyse the tension between such models and constraints from low-energy flavour observables. We note that the tension is weakest …
We discuss the role played by the horizontal flavour symmetry in supersymmetric theories. In particular, we consider the horizontal symmetry $SU(3)_H$ between the three fermion families and show how this concept can help in explaining the fermion mass spectrum and mixing pattern in the context of SUSY GUTs.
We present a novel procedure for identifying discrete, leptonic flavour symmetries, given a class of unitary mixing matrices. By creating explicit 3D representations for generators of residual symmetries in both the charged lepton and neutrino sector, we reconstruct large(r) non-abelian flavour groups using the GAP language for computational finite algebra. We use experimental data to construct only those generators that yield acceptable (or preferable) mixing patterns. Such an approach is advantageous because it 1) can reproduce known groups from other 'top-down' scans while elucidating their…
The concept of non-abelian horizontal symmetry $SU(3)_H$ can greatly help in understanding the fermion and sfermion flavour structures in supersymmetric grand unification. For the sake of demonstration the $SU(5)\times SU(3)_H$ model, suggested earlier in ref. \cite{PLB85}, is revisited. We show that under very simple and natural assumption it links the sfermion mass pattern to those of fermions in a remarkable way. All dangerous supersymmetric flavour-changing contributions are naturally suppressed in a general case, independently of the concrete texture for fermion mass matrices. Nevertheles…
We present full renormalisation group equations for the MSSM with R-parity violation, including all soft supersymmetry breaking terms. The inclusion of dimensionless R-parity violating couplings can generate many possible low energy effects through the generation of off-diagonal soft masses violating lepton and quark flavour, and through the generation of lepton-Higgs mixing. We discuss the relation between the weak and unification scale R-parity violation and study the effects on neutrino mass generation and $μ\to eγ$.
We propose a theory of flavour based on abelian horizontal gauge symmetries and modular invariances. We construct explicit supergravity models where the scale of the horizontal $U(1)$ symmetry breaking is fixed by the Green-Schwarz mechanism for anomaly cancellation. The supersymmetric spectrum is obtained in terms of the $U(1)$ charges which are determined by the Yukawa matrices.
We compute the renormalisation factors (Z-matrices) of the $ΔF=2$ four-quark operators needed for Beyond the Standard Model (BSM) kaon mixing. We work with nf=2+1 flavours of Domain-Wall fermions whose chiral-flavour properties are essential to maintain a continuum-like mixing pattern. We introduce new RI-SMOM renormalisation schemes, which we argue are better behaved compared to the commonly-used corresponding RI-MOM one. We find that, once converted to MS, the Z-factors computed through these RI-SMOM schemes are in good agreement but differ significantly from the ones computed through the RI…
A method is described to probe high-scale physics in lower-energy experiments by employing sum rules in terms of renormalisation group invariants. The method is worked out in detail for the study of supersymmetry-breaking mechanisms in the context of the Minimal Supersymmetric Standard Model. To this end sum rules are constructed that test either specific models of supersymmetry breaking or general properties of the physics that underlies supersymmetry breaking, such as unifications and flavour-universality.
Neutrino mass sum rules are an important class of predictions in flavour models relating the Majorana phases to the neutrino masses. This leads, for instance, to enormous restrictions on the effective mass as probed in experiments on neutrinoless double beta decay. While up to now these sum rules have in practically all cases been taken to hold exactly, we will go here beyond that. After a discussion of the types of corrections that could possibly appear and elucidating on the theory behind neutrino mass sum rules, we estimate and explicitly compute the impact of radiative corrections, as thes…
We study the splitting in the screening mass of pions and the $η$-meson across the chiral crossover. This splitting is determined by the 't Hooft determinant. We use results for the renormalisation group scale dependence of the 't Hooft determinant obtained within the functional renomalisation group in quenched QCD with two flavours. The scale dependence of the 't Hooft determinant is mapped to its temperature dependence with the help of a Polyakov-quark-meson model. As a result we obtain the temperature dependence of the splitting in the screening mass of pions and the $η$-meson.
Both discrete flavour symmetries and Grand Unified symmetries explain apparent structures in the mass sector of the Standard Model. A model that combines both symmetries is therefore very appealing. We construct a model with the $S_4$ flavour symmetry and the Pati-Salam unification. We show that this model can indeed explain many observable relations between the masses of the quarks and leptons and that it is predictive in the neutrino sector. However, the combination of the two symmetries leads to new complications in the Higgs sector and in the running of the renormalisation group equations.
We study the impact of an additional $U(1)'$ gauge symmetry with flavour-dependent charges for quarks and leptons on the LHC flavour anomalies observed in $B \to K^* μ^+μ^-$, $R(K) = B \to K μ^+μ^-/B \to K e^+e^-$, and $h \to μτ$. In its minimal version with two scalar doublets, the resulting model naturally explains the deviations from the Standard Model observed in $B \to K^* μ^+μ^-$ and $R(K)$. The CMS access in $h \to μτ$ can be explained by introducing a third scalar doublet, which gives rise to a prediction for $τ\to 3μ$. We investigate constraints from flavour observables and direct LHC…
We study the consequences of the existence and breaking of a Peccei--Quinn symmetry within the context of a dynamical model of electroweak symmetry breaking based on broken gauged flavour symmetries. We perform an estimate of the axion mass by including flavour instanton effects and show that, for low cut--offs, the axion is sufficiently massive to prevent it from being phenomenologically unacceptable. We conclude with an examination of the strong CP problem and show that our axion cannot solve the problem, though we indicate ways in which the model can be extended so that the strong CP proble…
The inclusion of physical effects from sea quarks has been one of the main advances in lattice QCD simulations over the last few years. We report on recent studies with four flavours of dynamical quarks and address some of the potential issues arising in this new setup. First results for physical observables in the light, strange and charm sectors are presented together with the status of dedicated simulations to perform the non-perturbative renormalisation in mass-independent schemes.
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.
Recent work on flavour changing neutral current effects in supersymmetric models is reviewed. The emphasis is put on new issues related to solutions to the flavour problem through new symmetries: GUTs, horizontal symmetries, modular invariances.
The flavour puzzle is an open problem both in the Standard Model and in its possible supersymmetric or grand unified extensions. In this thesis, we discuss possible explanations of the origin of fermion mass hierarchies and mixings by the use of non-Abelian discrete flavour symmetries. We present a T'- and an S4-based realisations in which the spontaneous breaking of the symmetry produces realistic fermion mass hierarchies, the quark mixing matrix comparable to the Wolfenstein parametrisation and the lepton mixing matrix close to the so-called tribimaximal pattern. We also present an alternati…
In extensions of the Standard Model with two Higgs doublets, flavour changing Yukawa couplings of the neutral scalars may be present at tree level. In this work we consider the most general scenario in which those flavour changing couplings are absent. We re-analyse the conditions that the Yukawa coupling matrices must obey for such \emph{general flavour conservation} (gFC), and study the one loop renormalisation group evolution of such conditions in both the quark and lepton sectors. We show that gFC in the leptonic sector is one loop stable under the Renormalization Group Evolution (RGE) and…
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…
If the mechanism of Supersymmetry breaking is not flavour blind, some flavour symmetry is likely to be needed to prevent excessive flavour changing neutral current effects. We discuss two flavour models (based respectively on a U(2) and on a SU(3) horizontal symmetry) providing a good fit to fermion masses and mixings and particularly constraining the supersymmetry soft breaking terms. We show that, while reproducing successfully the Standard Model fit of the unitarity triangle, it is possible to obtain sizable deviations from the Standard Model predictions for three very clean B-physics obser…
We reconsider models of fermion masses and mixings based on a gauge anomalous horizontal U(1) symmetry. In the simplest model with a single flavon field and horizontal charges of the same sign for all Standard Model fields, only very few charge assignements are allowed when all experimental data, including neutrino oscillation data, is taken into account. We show that a precise description of the observed fermion masses and mixing angles can easily be obtained by generating sets of the order one parameters left unconstrained by the U(1) symmetry. The corresponding Yukawa matrices show several …
Flavour-changing neutral-current interactions of the top quark can be searched for in top-quark pair production with one top quark decaying to an up-type quark and a neutral boson, and they can be searched for in the single production of a top quark in association with such a boson. Both processes interfere if an additional up-type quark is produced in the case of single production. The impact of these interference effects on searches for flavour-changing neutral currents at the LHC is studied for the case where the neutral boson is a photon or a $Z$ boson. Interference effects are found to be…
We consider an $SU(2)_L \times SU(2)_R \times U(1)_{B-L} \times SU(3)_H^{VL}$ gauge model with natural flavour conservation in the Higgs sector, in which CP-violation occurs due to the horizontal interactions only. We calculate the CP-violating observables $ε$ and $ε'$ of the neutral kaon sector and $d_n$, the electric dipole moment of the neutron. The regions of the parameter space which yield a value of $ε$ that is in agreement with the experiment, lead to predictions for $ε'$ and $d_n$ which are at least five orders of magnitude smaller than the current experimental upper bounds.
We present data for the axial coupling constant g_A of the nucleon obtained in lattice QCD with two degenerate flavours of dynamical non-perturbatively improved Wilson quarks. The renormalisation is also performed non-perturbatively. For the analysis we give a chiral extrapolation formula for g_A based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavours. Applying this formalism in a finite volume we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattic…
After a quarter of century of intense search for new physics beyond the Standard Model (SM), two ideas stand out to naturally cope with (i) small neutrino masses and (ii) a light higgs boson : Seesaw and SUSY. The combination of these two ideas, i.e. SUSY seesaw exhibits a potentially striking signature: a strong (or even very strong) enhancement of lepton flavour violation (LFV), which on the contrary remains unobservable in the SM seesaw. Indeed, even when supersymmetry breaking is completely flavour blind, Renormalisation Group running effects are expected to generate large lepton flavour v…
We investigate the renormalisation group effects induced on neutrino mass and mixing parameters in a triplet-extended minimal supersymmetric standard model where a vector-like pair of hypercharge $\pm 1$ triplet superfields is added. We first rederive the one-loop renormalisation group equation for the effective neutrino mass operator and, for the case in which this operator originates solely from the decoupling of the triplets, the corresponding equations for neutrino masses, mixing parameters and CP-violating phases. We compare our results with the ones obtained previously, and quantify the …
Different approaches to the fermion mass problem are reviewed. We illustrate these approaches by summarizing recent developments in models of quark and lepton mass matrices. Dynamical calculations of the top quark mass are discussed, based on (a) infrared quasi-fixed points of the renormalisation group equations, and (b) the multiple point criticality principle in the pure Standard Model. We also consider Yukawa unification and mass matrix texture. Models with approximately conserved gauged chiral flavour charges beyond the Standard Model are shown to naturally give a fermion mass hierarchy.
We study Two-Higgs-Doublet Models (2HDM) where Abelian symmetries have been introduced, leading to a drastic reduction in the number of free parameters in the 2HDM. Our analysis is inspired in BGL models, where, as the result of a symmetry of the Lagrangian, there are tree-level scalar mediated Flavour-Changing-Neutral-Currents, with the flavour structure depending only on the CKM matrix. A systematic analysis is done on the various possible schemes, which are classified in different classes, depending on the way the extra symmetries constrain the matrices of couplings defining the flavour str…
Neutrino mass sum rules are an important class of predictions in flavour models relating the Majorana phases to the neutrino masses. This leads, for instance, to enormous restrictions on the effective mass as probed in experiments on neutrinoless double beta decay. While up to now these sum rules have in practically all cases been taken to hold exactly, we will go here beyond that. While the effect of the renormalisation group running can be visible, the qualitative features do not change. This changes somewhat for model dependent corrections which might alter even the qualitative predictions …
The $B_K$ parameter is computed in quenched lattice QCD with Wilson twisted mass fermions. Two variants of tmQCD are used; in both of them the relevant $ΔS = 2$ four-fermion operator is renormalised multiplicatively. The renormalisation adopted is non-perturbative, with a Schroedinger functional renormalisation condition. Renormalisation group running is also non-perturbative, up to very high energy scales. In one of the two tmQCD frameworks the computations have been performed at the physical $K$-meson mass, thus eliminating the need of mass extrapolations. Simulations have been performed at …
We discuss the QCD phase structure at finite temperature and chemical potential for $2$-flavour and $2+1$-flavour QCD. The results are achieved by computing QCD correlation functions within a generalised functional approach that combines Dyson-Schwinger equations (DSE) and the functional renormalisation group (fRG). In this setup fRG precision data from arXiv:1706.06326 for the vacuum quark-gluon vertex and gluon propagator of $2$-flavour QCD are used as input, and the respective DSEs are expanded about this input. While the vacuum results for other correlation functions serve as a self-consis…
Spontaneous breaking of inter-family (horizontal) gauge symmetries can be at the origin of the mass hierarchy between the fermion families. The corresponding gauge bosons have flavor-nondiagonal couplings which generically induce the flavour changing phenomena, and this puts strong lower limits on the flavor symmetry breaking scales. However, in the special choices of chiral horizontal symmetries the flavor changing effects can be naturally suppressed. For the sake of demonstration, we consider the case of leptonic gauge symmetry $SU(3)_e$ acting between right-handed leptons and show that the …
A flavour symmetry based on Z_4 is analysed in the context of SU(5) Grand Unification with the standard fermionic content plus three right-handed neutrinos. The role of Z_4 is to forbid some Yukawa couplings of up- and down-quarks to Higgs scalars such that the quark mass matrices M_u, M_d have Nearest-Neighbour-Interaction (NNI) structure, once they are generated through the electroweak symmetry breaking. It turns out in this framework that Z_4 is indeed the minimal discrete symmetry and its implementation requires the introduction of at least two Higgs quintets, which leads to a two Higgs do…
We discuss the phase structure of the two-flavour quark-meson model including quantum, thermal, density and critical fluctuations with the functional renormalisation group. This study combines two technical advances in the literature, that are also chiefly important for the quantitative access of the phase boundary of QCD at large density or baryon chemical potential. Specifically we allow for the formation and propagation of shocks as well as a fully self-consistent computation of the order parameter potential for chiral symmetry breaking.
We investigate the continuum spectrum of the SU(2) gauge theory with $N_f=2$ flavours of fermions in the fundamental representation. This model provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics that range from composite (Goldstone) Higgs theories to several intriguing types of dark matter candidates, such as the SIMPs. We improve our previous lattice analysis [1] by adding more data at light quark masses, at two additional lattice spacings, by determining the lattice cutoff via a Wilson flow measure of the $w_0$ parameter, …
We continue our study of strongly-coupled, approximately scale-invariant gauge theories with a large number of flavours, which provide a suitable ultraviolet completion of the composite-Higgs scenario. We identify the requisite operators to realise partial compositeness of the Standard-Model fermions. In order to compute the spectrum of composite fermionic states, we extend the bottom-up holographic models, which we previously introduced to capture the main features of the non-perturbative dynamics in the Veneziano limit, by adding fermion fields in the bulk. We identify regions in parameter s…
An effective theory is proposed, combining the standard gauge group $SU(3)_{C}\otimes SU(2)_{L}\otimes U(1)_{Y}$ with a horizontal discrete symmetry. By assigning appropriate charges under this discrete symmetry to the various fermion fields and to (at least) two Higgs doublets, the broad spread of the fermion mass and mixing angle spectrum can be explained as a result of suppressed, non-renormalisable terms. A particular model is constructed which achieves the above while simultaneously suppressing neutral Higgs-induced flavour-changing processes.
The supersymmetric $SU(6)$ model accompanied by the flavour-blind discrete symmetry $Z_3$ can succesfully deal with such key problems of SUSY GUTs, as are the gauge hierarchy/doublet-triplet splitting, $μ$-problem and flavour problem. The Higgs doublets arise as Goldstone modes of the spontaneously broken {\em accidental} global $SU(6)\times U(6)$ symmetry of the Higgs superpotential. Their couplings to fermions have peculiarities leading to the consistent picture of the quark and lepton masses and mixing, without invoking any of horizontal symmetry/zero texture concepts. In particular, the on…
Minimal Flavour Violation (MFV) postulates that the only source of flavour changing neutral currents and CP violation, as in the Standard Model, is the CKM matrix. However it does not address the origin of fermion masses and mixing and models that do usually have a structure that goes well beyond the MFV framework. In this paper we compare the MFV predictions with those obtained in models based on spontaneously broken (horizontal) family symmetries, both Abelian and non-Abelian. The generic suppression of flavour changing processes in these models turns out to be weaker than in the MFV hypothe…
Gravity mediation supersymmetry breaking become comparable to gauge mediated supersymmetry breaking contributions when messenger masses are close to the GUT scale. By suitably tuning the gravity contributions one can then modify the soft supersymmetry breaking sector to generate a large stop mixing parameter and a light higgs mass of 125 GeV. In this kind of hybrid models, however the nice features of gauge mediation like flavour conservation etc, are lost. To preserve the nice features, gravitational contributions should become important for lighter messenger masses and should be important on…
We propose a new scenario that solves the slepton negative mass squared problem of the minimal supersymmetric standard model with anomaly mediated supersymmetry breaking. The solution is achieved by including three trilinear R-parity violating operators in the superpotential. The soft supersymmetry breaking terms satisfy renormalisation group invariant relations in terms of supersymmetric couplings and the overall supersymmetry breaking mass scale. Flavour changing neutral currents can be naturally highly suppressed. A specific model predicts tan beta=4.2+/-1.0. Excluding sleptons, the supersy…
The supersymmetric $SU(6)$ model equipped by the flavour-blind discrete gauge symmetry $Z_3$ is considered. It provides simultaneous solution to the doublet-triplet splitting problem, $μ$-problem and leads to natural understanding of fermion flavour. The Higgs doublets arise as Goldstone modes of the spontaneously broken {\em accidental} global symmetry $SU(6)\times U(6)$ of the Higgs superpotential. Their couplings to fermions have peculiarities leading to the consistent picture of the quark and lepton masses and mixing, without invoking the horizontal symmetry or zero texture concepts. In pa…
Using unimproved and non-perturbatively O(a) improved Wilson fermions, results are given for the three lowest moments of unpolarised nucleon structure functions. Renormalisation, chiral extrapolation and the continuum limit of the matrix elements are briefly discussed. The simulations are performed for both quenched and two flavours of unquenched fermions. No obvious sign of deviation from linearity in the chiral extrapolations are found. (This is most clearly seen in our quenched unimproved data, which extends to lighter quark mass.) Possible quenching effects also seem to be small. The lowes…
