A naive application of the heavy quark expansion (HQE) yields theory estimates for the decay rate of neutral $D$ mesons that are four orders of magnitude below the experimental determination. It is well known that this huge suppression results from severe GIM cancellations. We find that this mismatch can be solved by individually choosing the renormalisation scale of the different internal quark contributions. For $b$ and $c$ hadron lifetimes, as well as for the decay rate difference of neutral $B$ mesons the effect of our scale setting procedure lies within the previously quoted theory uncertainties, while we get enlarged theory uncertainties for the semi-leptonic CP asymmetries in the $B$ system.
We present new results for the renormalisation and subtraction constants for the four fermion Delta F=2 operators, computed non-perturbatively in the RI-MOM scheme (in the Landau gauge). From our preliminary analysis of the lattice data at beta=6.45, for the B-bar B mixing bag-parameter we obtain B_B^{RGI} = 1.46(7)(1).
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…
We review the Universal Extra-Dimensional Model compactified on a S1/Z2 orbifold, and the renormalisation group evolution of quark and lepton masses, mixing angles and phases both in the UED extension of the Standard Model and of the Minimal Supersymmetric Standard Model. We consider two typical scenarios: all matter fields propagating in the bulk, and matter fields constrained to the brane. The resulting renormalisation group evolution equations in these scenarios are compared with the existing results in the literature, together with their implications.
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 discuss the renormalisation properties of the complete set of $ΔB = 2$ four-quark operators with the heavy quark treated in the static approximation. We elucidate the role of heavy quark symmetry and other symmetry transformations in constraining their mixing under renormalisation. By employing the Schroedinger functional, a set of non-perturbative renormalisation conditions can be defined in terms of suitable correlation functions. As a first step in a fully non-perturbative determination of the scale-dependent renormalisation factors, we evaluate these conditions in lattice perturbation t…
Neutrino mixing sum rules are common to a large class of models based on the (discrete) symmetry approach to lepton flavour. In this approach the neutrino mixing matrix $U$ is assumed to have an underlying approximate symmetry form $\tilde{U}_ν$, which is dictated by, or associated with, the employed (discrete) symmetry. In such a setup the cosine of the Dirac CP-violating phase $δ$ can be related to the three neutrino mixing angles in terms of a sum rule which depends on the symmetry form of $\tilde{U}_ν$. We consider five extensively discussed possible symmetry forms of $\tilde{U}_ν$: i) bim…
The Littlest Seesaw (LS) model involves two right-handed neutrinos and a very constrained Dirac neutrino mass matrix, involving one texture zero and two independent Dirac masses, leading to a highly predictive scheme in which all neutrino masses and the entire PMNS matrix is successfully predicted in terms of just two real parameters. We calculate the renormalisation group (RG) corrections to the LS predictions, with and without supersymmetry, including also the threshold effects induced by the decoupling of heavy Majorana neutrinos both analytically and numerically. We find that the predictio…
An on-shell renormalisation programme for the chargino/neutralino and the sfermion sectors within the Minimal Supersymmetric Standard Model as implemented in a fully automated code, SloopS, for the calculation of one-loop processes at the colliders and in astrophysics, is presented. This is a sequel to our study in arXiv:0807.4668 [hep-ph] where an on-shell renormalisation of the Higgs (and the gauge/fermion) sector is performed. The issue of mixing is treated in a unified and coherent manner in all these sectors, in particular we give some new insight into the renormalisation of the mixing an…
We perform a renormalisation group (RG) analysis of neutrino masses and mixing angles in the see-saw mechanism in the minimal supersymmetric standard model with three right-handed neutrinos, including the effects of the heavy neutrino thresholds. We focus on the case that one of the right-handed neutrinos provides the dominant contribution to the 23 block of the light Majorana matrix, causing its determinant to approximately vanish and giving an automatic neutrino mass hierarchy, so called single right-handed neutrino dominance which may arise from a U(1) family symmetry. In these models radia…
We study renormalisation group (RG) corrections relevant for leptogenesis in the case of family symmetry models such as the Altarelli-Feruglio A4 model of tri-bimaximal lepton mixing or its extension to tri-maximal mixing. Such corrections are particularly relevant since in large classes of family symmetry models, to leading order, the CP violating parameters of leptogenesis would be identically zero at the family symmetry breaking scale, due to the form dominance property. We find that RG corrections violate form dominance and enable such models to yield viable leptogenesis at the scale of ri…
We discuss the renormalisation properties of the full set of $ΔF=2$ operators involved in BSM processes, including the definition of RGI versions of operators that exhibit mixing under RG transformations. As a first step for a fully non-perturbative determination of the scale-dependent renormalization factors and their runnings, we introduce a family of appropriate Schrödinger Functional schemes, and study them in perturbation theory. This allows, in particular, to determine the NLO anomalous dimensions of all $ΔF=1,2$ operators in these schemes. Finally, we discuss the systematic uncertaintie…
We compute the hadronic matrix elements of the four-quark operators relevant for $K^0-{\bar K^0}$ mixing beyond the Standard Model. Our results are from lattice QCD simulations with $n_f=2+1$ flavours of domain-wall fermion, which exhibit continuum-like chiral-flavour symmetry. The simulations are performed at two different values of the lattice spacing ($a\sim0.08$ and $a\sim 0.11 \, \fm $) and with lightest unitary pion mass $\sim 300\, \MeV$. For the first time, the full set of relevant four-quark operators is renormalised non-perturbatively through RI-SMOM schemes; a detailed description o…
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 calculate the renormalisation of different light ray operators with one light degree of freedom and a static heavy quark. Both $2\to2$- and $2\to3$-kernels are considered. A comparison with the light-light case suggests that the mixing with three-particle operators is solely governed by the light degrees of freedom. Additionally we show that conformal symmetry is already broken at the level of the one loop counterterms due to the additional UV-renormalisation of a cusp in the two contributing Wilson-lines. This general feature can be used to fix the $2\to2$-renormalisation kernels up to a c…
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 …
We perform a renormalisation group analysis of the SO(10) model proposed by Chang, Masiero and Murayama, which links the large atmospheric neutrino mixing angle to loop-induced transitions between right-handed b and s quarks. We compute the impact on B_s-B_s-bar mixing and find that the mass difference in the B_s system can exceed its Standard Model value by a factor of 16.
We develop a model of ours fitting the quark and lepton masses and mixing angles by removing from the model a Higgs field previously introduced to organise a large atmospheric mixing angle for neutrino oscillations. Due to the off-diagonal elements dominating in the see-saw neutrino mass matrix the large atmospheric mixing angle comes essentially by itself. It turns out that we have now only five adjustable Higgs field vacuum expectation values needed to fit all the masses and mixings order of magnitudewise taking into account the renormalisation group runnings in all sectors. The CHOOZ angle …
The evolution equations of the Yukawa couplings and quark mixings are performed for the one-loop renormalisation group equations in six-dimensional models compactified in different possible ways to yield standard four space-time dimensions. Different possibilities for the matter fields are discussed, that is where they are in the bulk or localised to the brane. These two possibilities give rise to quite similar behaviours when studying the evolution of the Yukawa couplings and mass ratios. We find that for both scenarios, valid up to the unification scale, significant corrections are observed.
We consider a minimal non-supersymmetric $SO(10)$ Grand Unified Theory (GUT) model that can reproduce the observed fermionic masses and mixing parameters of the Standard Model. We calculate the scales of spontaneous symmetry breaking from the GUT to the Standard Model gauge group using two-loop renormalisation group equations. This procedure determines the proton decay rate and the scale of $U(1)_{B-L}$ breaking, which generates cosmic strings and the right-handed neutrino mass scales. Consequently, the regions of parameter space where thermal leptogenesis is viable are identified and correlat…
We conduct a systematic study of the impact of new physics in quark-level $b \to c \bar{c} s$ transitions on $B$-physics, in particular rare $B$-decays and $B$-meson lifetime observables. We find viable scenarios where a sizable effect in rare semileptonic $B$-decays can be generated, compatible with experimental indications and with a possible dependence on the dilepton invariant mass, while being consistent with constraints from radiative $B$-decay and the measured $B_s$ width difference. We show how, if the effect is generated at the weak scale or beyond, strong renormalisation-group effect…
A three Higgs-doublet model admitting an $S_3$-symmetry can predict the observed pattern of the quark masses and their mixings. However the same symmetry also introduces potential flavour-changing neutral currents at the tree level. We assume in this work that the scalar potential contains appropriate \emph{soft} $S_3$-breaking terms in order to keep the choices of the scalar masses flexible. We identify the parameters in the Yukawa Lagrangian in the quark sector responsible for such FCNCs and constrain them using data from some of the flavour physics observables like meson-decays and meson-mi…
We determine the flavour dependence of the renormalisation-group-invariant running interaction through judicious use of both unquenched Dyson-Schwinger equation and lattice results for QCD's gauge-sector two-point functions. An important step is the introduction of a physical scale setting procedure that enables a realistic expression of the effect of different numbers of active quark flavours on the interaction. Using this running interaction in concert with a well constrained class of dressed--gluon-quark vertices, we estimate the critical number of active lighter-quarks above which dynamica…
We compute the decay width of $h^0 \to c \bar{c}$ in the MSSM with quark flavor violation (QFV) at full one-loop level adopting the $\overline{\rm DR}$ renormalisation scheme. We study the effects of $\tilde{c}-\tilde{t}$ mixing, taking into account the constraints from the B meson data. We show that the full one-loop corrected decay width $Γ(h^0 \to c \bar{c})$ is very sensitive to the MSSM QFV parameters. In a scenario with large $\tilde{c}_{L,R}-\tilde{t}_{L,R}$ mixing $Γ(h^0 \to c \bar{c})$ can differ up to $\sim \pm 35\%$ from its SM value. After estimating the uncertainties of the width,…
We discuss the determination of deep-inelastic hadron structure in lattice QCD. By using a fictitious heavy quark, direct calculations of the Compton scattering tensor can be performed in Euclidean space that allow the extraction of the moments of structure functions. This overcomes issues of operator mixing and renormalisation that have so far prohibited lattice computations of higher moments. This approach is especially suitable for the study of the twist-two contributions to isovector quark distributions, which is practical with current computing resources. While we focus on the isovector u…
We discuss Higgs boson decays in the CP-violating MSSM, and examine their phenomenological impact using cross section limits from the LEP Higgs searches. This includes a discussion of the full 1-loop results for the partial decay widths of neutral Higgs bosons into lighter neutral Higgs bosons (h_a -> h_b h_c) and of neutral Higgs bosons into fermions (h_a -> f fbar). In calculating the genuine vertex corrections, we take into account the full spectrum of supersymmetric particles and all complex phases of the supersymmetric parameters. These genuine vertex corrections are supplemented with Hig…
We compute the width of the decay $h^0$ (125 GeV) $\to b \bar{b}$ at next-to-leading order in the general MSSM with quark-flavour violation (QFV). We study the effect of mixing between the second and the third generation of squarks, taking into account the constraints on QFV from B-meson data. We discuss the renormalisation of the process as well as the resummation of the bottom Yukawa coupling at large $\tan β$. We show numerical results on the decay width $Γ(h^0 \to b \bar{b})$ as a function of the involved QFV parameters and compare them with the corresponding width in the Standard Model.
