Quark masses and mixing in string-inspired models

In this work, we examine the possibility that Quark‐Lepton Complementarity originates in the similar hierarchy of quarks and charged lepton masses and the seesaw mechanism type I that gives mass to the Majorana neutrinos. We assume that the similar mass hierarchies of charged lepton and quark masses allows us to represent all the mass matrices of Dirac fermions in terms of a two zeroes Fritzsch texture.

The fundamental theory of nature may allow a large landscape of vacua. Even if the theory contains a unified gauge symmetry, the 22 flavor parameters of the standard model, including neutrino masses, may be largely determined by the statistics of this landscape, and not by any symmetry. Then the measured values of the flavor parameters do not lead to any fundamental symmetries, but are statistical accidents; their precise values do not provide any insights into the fundamental theory, rather the overall pattern of flavor reflects the underlying landscape. We investigate whether random selection from the statistics of a simple landscape can explain the broad patterns of quark, charged lepton, and neutrino masses and mixings. We propose Gaussian landscapes as simplified models of landscapes where Yukawa couplings result from overlap integrals of zero-mode wave functions in higher-dimensional supersymmetric gauge theories. In terms of just five free parameters, such landscapes can account for all gross features of flavor, including the hierarchy of quark and charged-lepton masses; small quark mixing angles in the basis with quarks arranged according to mass, with 13 mixing less than 12 and 23 mixing; very light Majorana neutrino masses, with the solar to atmospheric neutrino mass ratio consistent with data; distributions for leptonic mixings $\mathrm{sin}2{\ensuremath{\theta}}_{12}$ and $\mathrm{sin}2{\ensuremath{\theta}}_{23}$ that are peaked at large values, while the distribution for $\mathrm{sin}2{\ensuremath{\theta}}_{13}$ is peaked at low values; and order unity $CP$-violating phases in both the quark and lepton sectors. While the statistical distributions for flavor parameters are broad, the distributions are robust to changes in the geometry of the extra dimensions. Constraining the distributions by loose cuts about observed values leads to narrower distributions for neutrino measurements of ${\ensuremath{\theta}}_{13}$, $CP$ violation, and neutrinoless double beta decay.

Lectures on flavor physics presented at the 2012 CERN HEP Summer School. Content: 1) flavor physics within the Standard Model, 2) phenomenology of B andD decays, 3) flavor physics beyond the Standard Model. In the limit of unbroken electroweak symmetry none of the basic constituent of matter could have a non-vanishing mass. The problem of quark and lepton masses is therefore intimately related to the other big open question in particle physics: which is the mechanism behind the breaking of the electroweak symmetry, or which is the mechanism responsible for the non-vanishing masses of the weak force carriers (theW andZ bosons). Within the SM these two problems are both addressed by the Higgs mechanism: the masses of quarks and leptons, as well as the masses ofW andZ bosons, are the result of the interaction of these basic fields (both matter constituents and force carriers) with a new type of field, the Higgs scalar field, whose ground state breaks spontaneously the electroweak symmetry. The recent observation by the ATLAS and CMS experiments of a new state compatible with the properties of the Higgs boson (or the spin-0 excitation of the Higgs field) has significantly reinforced the evidences in favor of the Higgs mechanisms and the validity of the SM. However, we have also clear indications that this theory is not complete: the phenomenon of neutrino oscillations and the evidence for dark matter cannot be explained within the SM. The SM is also affected by a serious theoretical problem because of the instability of the Higgs sector under quantum corrections. We have not yet enough information to unambiguously determine how this theory should be extended; however, most realistic proposals point toward the existence of new degrees of freedom in the TeV range, possibly accessible at the high-pT experiments at the LHC. The description of quark and lepton masses in terms of the Higgs mechanism is particularly un- satisfactory since the corresponding interactions is not controlled by any symmetry principle, contrary to all other known interactions, resulting in a large number of free parameters. Beside determining quark masses, the interaction of the quarks with the Higgs is responsible for the peculiar pattern of mixing of

In this talk, I will describe two features of a recently proposed class of extended technicolor (ETC) models lV5 . The first is the possible existence of a seesaw mechanism for neutrino masses, and the second is CP violation as manifested in the quark electric (and chromo-electric) dipole moments. The class of ETC models is based on the gauge group SU(5)ETC which commutes with the standard-model (SM) gauge group. It breaks sequentially to a residual exact su(2)TC technicolor gauge symmetry, naturally producing a hierarchy of charged lepton and quark masses. Thus, S U ( ~ ) E T C -+ SU(4)ETC at a scale hl, with the first-generation standardmodel fermions separating from the other four components of the original 5 or 5 representations; then su(4)ETC -+ S U ( ~ ) E T C -+ s u ( 2 ) ~ c at still lower scales with the secondand third-generation fermions separating in the same way, leaving the technifermions. exhibit charged-current flavor mixing, intra-family mass splittings without excessive contributions to the difference p 1 where p = m$/(m% cos2 Ow), a dynamical origin of CP-violating phases in the quark and lepton sectors, and a potential see-saw mechanism for light neutrinos without the presence of a grand unified scale '. The choice of SU(2) The models of Ref.

We study Froggatt-Nielsen (FN) like flavor models with modular symmetry. The FN mechanism is a convincing solution to the flavor puzzle in the quark sector. The FN mechanism requires an extra U(1) gauge symmetry which is broken at high energies. Alternatively, in the framework of modular symmetry the modular weights can play the role of the FN charges of the extra U(1) symmetry. Based on the FN-like mechanism with modular symmetry we present new flavor models for the quark sector. Assuming that the three generations have a common representation under the modular symmetry, our models simply reproduce the FN-like Yukawa matrices. We also show that the realistic mass hierarchy and mixing angles, which are related to each other through the modular parameters and a scalar vev, can be realized in models with several finite modular groups (and their double covering groups) without unnatural hierarchical parameters.

Without Higgs field interaction, accurate pole mass values are obtained for the charged leptons and quarks from a Z3-symmetric linear superposition self-interference of the Dirac fields in the effective free-field Lagrangian. The charged lepton and quark pole masses evidence the discrete Z3 symmetry, the theoretical-experimental deviations δm/m are $$ \mathcal{O} $$(10−5) for all three charged leptons, and the quark pole masses are in very satisfactory overall agreement with the experimental data.

We analyze the renormalization group equations for the Standard Model at the one and two loops levels. At one loop level we find an exact constant of evolution built from the product of the quark masses and the gauge couplings g1 and g3 of the U(1) and SU(3) groups. For leptons at one loop level we find that the ratio of the charged lepton mass and the power of g1 varies ≃4×10−5 in the whole energy range. At the two loop level we have found two relations between the quark masses and the gauge couplings that vary ≃4% and ≃1%, respectively. For leptons at the two loop level we have derived a relation between the charged lepton mass and the gauge couplings g1 and g2 that varies ≃0.1%. This analysis significantly simplifies the picture of the renormalization group evolution of the Standard Model and establishes new important relations between its parameters. There is also included a discussion of the gauge invariance of our relations and its possible relation to the reduction of couplings method.

Recent measurements of the neutrino and quark mixing angles satisfy the empirical relations called quark-lepton complementarity. This empirical data suggests the existence of a correlation between the mixing matrices of leptons and quarks. In this work, we examine the possibility that this correlation between the mixing angles of quarks and leptons originates in the similar hierarchy of quarks and charged lepton masses and the seesaw mechanism type I that gives mass to the Majorana neutrinos. We asssume that the similar mass hierarchies of charged lepton masses and quark masses allows one to represent all the mass matrices of Dirac fermions in terms of a four zeros Fritzsch texture.

Extremal transitions in heterotic string theory

Exactly Solvable String Compactifications on Manifolds of Su(N) Holonomy

This paper studies F-theory SU(5) GUT models where the three generations of the standard model come from three different curves. All the matter is taken to come from curves intersecting at a point of enhanced E8 gauge symmetry. Giving a vev to some of the GUT singlets naturally implements a Froggatt-Nielsen approach to flavour structure. A scan is performed over all possible models and the results are filtered using phenomenological constraints. We find a unique model that fits observations of quark and lepton masses and mixing well. This model suffers from two drawbacks: R-parity must be imposed by hand and there is a doublet-triplet splitting problem.

We construct a supersymmetric model with the flavor symmetry D 14 in which the CKM matrix element | V u d | can take the value | V u d | = cos ( π 14 ) ≈ 0.97493 implying that the Cabibbo angle θ C is sin ( θ C ) ≈ | V u s | ≈ sin ( π 14 ) ≈ 0.2225 . These values are very close to those observed in experiments. The value of | V u d | ( θ C ) is based on the fact that different Z 2 subgroups of D 14 are conserved in the up and down quark sector. In order to achieve this, D 14 is accompanied by a Z 3 symmetry. The spontaneous breaking of D 14 is induced by flavons, which are scalar gauge singlets. The quark mass hierarchy is partly due to the flavor group D 14 and partly due to a Froggatt–Nielsen symmetry U ( 1 ) FN under which only the right-handed quarks transform. The model is natural in the sense that the hierarchies among the quark masses and mixing angles are generated with the help of symmetries. The issue of the vacuum alignment of the flavons is solved up to a small number of degeneracies, leaving four different possible values for | V u d | . Out of these, only one of them leads to a phenomenological viable model. A study of the Z 2 subgroup breaking terms shows that the results achieved in the symmetry limit are only slightly perturbed. At the same time they allow | V u d | ( θ C ) to be well inside the small experimental error bars.

The idea of the universe having a mirror sector in which all particles and forces are identical to those in the familiar sector has been proposed recently in the context of neutrino physics as well as superstring theories some time ago. Assuming that all the quark and charged lepton masses in the mirror universe are scaled by a common factor, ζ, as is required in one interpretation of the neutrino data, we investigate domains of the parameter ζ where physical conditions are favorable for the formation of compact structures given the initial condition ΩB Ω ( denoting the mirror baryon). We consider both isocurvature and curvature perturbations; we address primordial mirror molecule formation, mirror Compton cooling, mirror Silk and collisionless damping, and various mirror cooling mechanisms that can lead to compact mirror structures for various regions of ζ space, so that the mirror model can be confronted with astrophysical observations. For isocurvature perturbations, we find a variety of possible structural final states. For curvature (or adiabatic) perturbations, we find a likelihood that part of ζ space would result in detectable effects that are not observed, while a part would not.

It is shown that embedding a four-dimensional flipped SU(5) model in a five-dimensional SO(10) model, preserves the best features of both flipped SU(5) and SO(10). The missing partner mechanism, which naturally achieves both doublet-triplet splitting and suppression of d=5 proton decay operators, is realized as in flipped SU(5), while the gauge couplings are unified as in SO(10). The masses of down quarks and charged leptons, which are independent in flipped SU(5), are related by the SO(10). Distinctive patterns of quark and lepton masses can result. The gaugino mass M_1 is independent of M_3 and M_2, which are predicted to be equal.

We show that the observed structure of quark and lepton masses and mixing angles can arise entirely geometrically from superstring constructions, at the renormalizable level. The model we consider is a $Z_3$ orbifold compactification of heterotic string with two Wilson lines, where three families of particles of $SU(3)_c\times SU(2)_L\times U(1)_Y$, including Higgses, are automatically present. In orbifold models, Yukawa couplings can be calculated explicitly, and it is known that they get exponential supression factors depending on the distance between the fixed points to which the fields are attached. We find that in the $Z_3$ case, the quark and charged-lepton mass hierarchies can easily be obtained for reasonable values of the three moduli determining the radii of the compactified space, $T_i\sim 1$. For the neutrinos, due to the smallness of their Dirac masses, the required scale for the see-saw mechanism to give the correct masses is found to be within reach of the electroweak scale. Finally, we find that one of the small number of possibilities for quark and lepton mass matrices yields consistent results for the mixing angles and the weak CP violation phase. Although our scheme relies on the mixing between fields due to Fayet-Iliopoulos breaking, it is considerably more predictive than alternative models of flavour.