arXiv subjects

G. K. Leontaris

Publications and source records attributed to G. K. Leontaris.

At least 19 recordsLinked to original sources

arXiv2021

$SU(5)\times{U(1)'}$ models with a vector-like fermion family

Motivated by experimental measurements indicating deviations from the Standard Model predictions we discuss F-theory inspired models, which, in addition to the three chiral generations contain a vector-like complete fermion family. The analysis takes place in the context of $SU(5)\times U(1)'$ GUT embedded in an $E_8$ covering group which is associated with the (highest) geometric singularity of the elliptic fibration. In this context, the $U(1)'$ is a linear combination of four abelian factors subjected to appropriate anomaly cancellation conditions. Furthermore, we require universal $U(1)'$ charges for the three chiral families and different ones for the corresponding fields of the vector-like representations. Under the aforementioned assumptions, we find 192 such models which can be classified into five distinct categories with respect to their specific GUT properties. We exhibit representative examples for each such class and construct the superpotential couplings and the fermion mass matrices. We explore the implications of the vector-like states in low energy phenomenology including the predictions regarding the B-meson anomalies. The rôle of R-parity violating terms appearing in some particular models of the above construction is also discussed.

hep-ph↗

arXiv2021

On the LHC signatures of $SU(5)\times U(1)'$ F-theory motivated models

We study low energy implications of F-theory GUT models based on $SU(5)$ extended by a $U(1)'$ symmetry which couples non-universally to the three families of quarks and leptons. This gauge group arises naturally from the maximal exceptional gauge symmetry of an elliptically fibred internal space, at a single point of enhancement, $E_8\supset SU(5)\times SU(5)'\supset SU(5)\times U(1)^4$. Rank-one fermion mass textures and a tree-level top quark coupling are guaranteed by imposing a $Z_2$ monodromy group which identifies two abelian factors of the above breaking sequence. The $U(1)'$ factor of the gauge symmetry is an anomaly free linear combination of the three remaining abelian symmetries left over by $Z_2$. Several classes of models are obtained, distinguished with respect to the $U(1)'$ charges of the representations, and possible extra zero modes coming in vector-like representations. The predictions of these models are investigated and are compared with the LHC results and other related experiments. Particular cases interpreting the B-meson anomalies observed in LHCb and BaBar experiments are also discussed.

hep-ph↗

arXiv2016

PSL(2,7) Representations and their relevance to Neutrino Physics

The investigation of the role of finite groups in flavor physics and particularly, in the interpretation of the neutrino data has been the subject of intensive research. Motivated by this fact, in this work we derive the three-dimensional unitary representations of the projective linear group PSL_2(7). Based on the observation that the generators of the group exhibit a latin square pattern, we use available computational packages on discrete algebra to determine the generic properties of the group elements. We present analytical expressions and discuss several examples which reproduce the neutrino mixing angles in accordance with the experimental data.

hep-ph↗

arXiv2015

Discrete Flavour Symmetries from the Heisenberg Group

Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular in the $PSL_2(p)$ groups which contain the phenomenologically interesting cases.

hep-th↗

arXiv2014

F-GUTs with Mordell-Weil U(1)'s

In this note we study the constraints on F-theory GUTs with extra $U(1)$'s in the context of elliptic fibrations with rational sections. We consider the simplest case of one abelian factor (Mordell-Weil rank one) and investigate the conditions that are induced on the coefficients of its Tate form. Converting the equation representing the generic hypersurface $P_{112}$ to this Tate's form we find that the presence of a U(1), already in this local description, is consistent with the exceptional ${\cal E}_6$ and ${\cal E}_7$ non-abelian singularities. We briefly comment on a viable ${\cal E}_6\times U(1)$ effective F-theory model.

hep-th↗

arXiv2014

A discrete anatomy of the neutrino mass matrix

We investigate the possibility of expressing the charged leptons and neutrino mass matrices as linear combinations of generators of a single finite group. Constraints imposed on the resulting mixing matrix by current data restrict the group types, but allow a non zero value for the theta_13 mixing angle

hep-ph↗

arXiv2013

Neutrino mass textures from F-theory

Experimental data on the neutrino mixing and masses strongly suggest an underlying approximate symmetry of the relevant Yukawa superpotential terms. Intensive phenomenological explorations during the last decade indicate that permutation symmetries such as S_4, A_4 and their subgroups, under certain assumptions and vacuum alignments, predict neutrino mass textures compatible with such data. Motivated by these findings, in the present work we analyse the neutrino properties in F-theory GUT models derived in the framework of the maximal underlying E_8 symmetry in the elliptic fibration. More specifically, we consider local F-SU(5) GUT models and study in detail spectral cover geometries with monodromies associated to the finite symmetries S_4, A_4 and their transitive subgroups, including the dihedral group D_4 and Z_2 X Z_2. We discuss various issues that emerge in the implementation of S_4, A_4 neutrino models in the F-theory context and suggest how these can be resolved. Realistic models are presented for the case of monodromies based on their transitive subgroups. We exemplify this procedure with a detailed analysis performed for the case of Z_2 X Z_2 model.

hep-th↗

arXiv2013

Closed form solution for the surface area, the capacitance and the demagnetizing factors of the ellipsoid

We derive the closed form solutions for the surface area, the capacitance and the demagnetizing factors of the ellipsoid immersed in the Euclidean space R^3. The exact solutions for the above geometrical and physical properties of the ellipsoid are expressed elegantly in terms of the generalized hypergeometric functions of Appell of two variables. Various limiting cases of the theorems of the exact solution for the surface area, the demagnetizing factors and the capacitance of the ellipsoid are derived, which agree with known solutions for the prolate and oblate spheroids and the sphere. Possible applications of the results achieved, in various fields of science, such as in physics, biology and space science are briefly discussed.

math-ph↗

arXiv2012

Building SO(10) models from F-theory

We revisit local F-theory SO(10) and SU(5) GUTs and analyze their properties within the framework of the maximal underlying E_8 symmetry in the elliptic fibration. We consider the symmetry enhancements along the intersections of seven-branes with the GUT surface and study in detail the embedding of the abelian factors undergoing monodromies in the covering gauge groups. We combine flux data from the successive breaking of SO(10) to SU(5) gauge symmetry and subsequently to the Standard Model one, and further constrain the parameters determining the models' particle spectra. In order to eliminate dangerous baryon number violating operators we propose ways to construct matter parity like symmetries from intrinsic geometric origin. We study implementations of the resulting constrained scenario in specific examples obtained for a variety of monodromies.

hep-th↗

arXiv2012

On Topological Modifications of Newton's Law

Recent cosmological data for very large distances challenge the validity of the standard cosmological model. Motivated by the observed spatial flatness the accelerating expansion and the various anisotropies with preferred axes in the universe we examine the consequences of the simple hypothesis that the three-dimensional space has a global R^2 X S^1 topology. We take the radius of the compactification to be the observed cosmological scale beyond which the accelerated expansion starts. We derive the induced corrections to the Newton's gravitational potential and we find that for distances smaller than the S^1-radius the leading 1/r-term is corrected by convergent power series of multipole form in the polar angle making explicit the induced anisotropy by the compactified third dimension. On the other hand, for distances larger than the compactification scale the asymptotic behavior of the potential exhibits a logarithmic dependence with exponentially small corrections. The change of Newton's force from 1/r^2 to 1/r behavior implies a weakening of the deceleration for the expanding universe. Such topologies can also be created locally by standard Newtonian axially symmetric mass distributions with periodicity along the symmetry axis. In such cases we can use our results to obtain measurable modifications of Newtonian orbits for small distances and flat rotation spectra, for large distances at the galactic level.

astro-ph.CO↗

arXiv2011

On the GUT scale of F-Theory SU(5)

In F-theory GUTs, threshold corrections from Kaluza-Klein massive modes arising from gauge and matter multiplets play an important role in the determination of the weak mixing angle and the strong gauge coupling of the effective low energy model. In this letter we further explore the induced modifications on the gauge couplings running and the GUT scale. In particular, we focus on the KK-contributions from matter curves and analyse the conditions on the chiral and Higgs matter spectrum which imply a GUT scale consistent with the minimal unification scenario. As an application, we present an explicit computation of these thresholds for matter fields residing on specific non-trivial Riemann surfaces.

hep-th↗

arXiv2011

Knitting neutrino mass textures with or without Tri-Bi maximal mixing

The solar and baseline neutrino oscillation data suggest bimaximal neutrino mixing among the first two generations, and trimaximal mixing between all three neutrino flavors. It has been conjectured that this indicates the existence of an underlying symmetry for the leptonic fermion mass textures. The experimentally measured quantities however, are associated to the latter indirectly and in a rather complicated way through the mixing matrices of the charged leptons and neutrinos. Motivated by these facts, we derive exact analytical expressions which directly link the charged lepton and neutrino mass and mixing parameters to measured quantities and obtain constraints on the parameter space. We discuss deviations from Tri-Bi mixing matrices and present minimal extensions of the Harrison Perkins and Scott matrices capable of interpreting all neutrino data.

hep-ph↗

arXiv2011

Yukawa couplings in F-theory SU(5)

The fermion mass textures are discussed in the context of F-theory SU(5) GUT. The tree-level up, down and charged lepton Yukawa couplings are computed in terms of the integrals of overlapping wavefunctions at the intersection points of three matter curves. All remaining entries in the fermion mass matrices can also be reliably estimated from higher order non-renormalizable Yukawa couplings mediated by heavy string modes and/or Kaluza-Klein states.

hep-ph↗

arXiv2011

Unification, KK-thresholds and the top Yukawa coupling in F-theory GUTs

In a class of F-theory SU(5) GUTs the low energy chiral mass spectrum is obtained from rank one fermion mass textures with a hierarchical structure organised by U(1) symmetries embedded in the exceptional E_8 group. In these theories chiral fields reside on matter `curves' and the tree level masses are computed from integrals of overlapping wavefuctions of the particles at the triple intersection points. This calculation requires knowledge of the exact form of the wavefuctions. In this work we propose a way to obtain a reliable estimate of the various quantities which determine the strength of the Yukawa couplings. We use previous analysis of KK threshold effects to determine the (ratios of) heavy mass scales of the theory which are involved in the normalization of the wave functions. We consider similar effects from the chiral spectrum of these models and discuss possible constraints on the emerging matter content. In this approach, we find that the Yukawa couplings can be determined solely from the U(1) charges of the states in the `intersection' and the torsion which is a topological invariant quantity. We apply the results to a viable SU(5) model with minimal spectrum which satisfies all the constraints imposed by our analysis. We use renormalization group analysis to estimate the top and bottom masses and find that they are in agreement with the experimental values.

hep-ph↗

arXiv2010

Yukawa couplings and fermion mass structure in F-theory GUTs

The calculation of Yukawa couplings in F-theory GUTs is developed. The method is applied to the top and bottom Yukawa couplings in an SU(5) model of fermion masses based on family symmetries coming from the SU(5)_\perp factor in the underlying E(8) theory. The remaining Yukawa couplings involving the light quark generations are determined by the Froggatt Nielsen non-renormalisable terms generated by heavy messenger states. We extend the calculation of Yukawa couplings to include massive states and estimate the full up and down quark mass matrices in the SU(5) model. We discuss the new features of the resulting structure compared to what is usually assumed for Abelian family symmetry models and show how the model can give a realistic quark mass matrix structure. We extend the analysis to the neutrino sector masses and mixing where we find that tri-bi-maximal mixing is readily accommodated. Finally we discuss mechanisms for splitting the degeneracy between the charged leptons and the down quarks and the doublet triplet splitting in the Higgs sector.

hep-th↗

arXiv2010

Gravitational Atom in Compactified Extra Dimensions

We consider quantum mechanical effects of the modified Newtonian potential in the presence of extra compactified dimensions. We develop a method to solve the resulting Schroedinger equation and determine the energy shifts caused by the Yukawa-type corrections of the potential. We comment on the possibility of detecting the modified gravitational bound state Energy spectrum by present day and future experiments.

hep-ph↗

arXiv2010

Gauge coupling flux thresholds, exotic matter and the unification scale in F-SU(5) GUT

We explore the gauge coupling relations and the unification scale in F-theory SU(5) GUT broken down to the Standard Model by an internal U(1)Y gauge flux. We consider variants with exotic matter representations which may appear in these constructions and investigate their role in the effective field theory model. We make a detailed investigation on the conditions imposed on the extraneous matter to raise the unification scale and make the color triplets heavy in order to avoid fast proton decay. We also discuss in brief the implications on the gaugino masses.

hep-ph↗

arXiv2010

Family symmetries in F-theory GUTs

We discuss F-theory SU(5) GUTs in which some or all of the quark and lepton families are assigned to different curves and family symmetry enforces a leading order rank one structure of the Yukawa matrices. We consider two possibilities for the suppression of baryon and lepton number violation. The first is based on Flipped SU(5) with gauge group SU(5)\times U(1)_χ\times SU(4)_{\perp} in which U(1)_χ plays the role of a generalised matter parity. We present an example which, after imposing a Z_2 monodromy, has a U(1)_{\perp}^2 family symmetry. Even in the absence of flux, spontaneous breaking of the family symmetry leads to viable quark, charged lepton and neutrino masses and mixing. The second possibility has an R-parity associated with the symmetry of the underlying compactification manifold and the flux. We construct an example of a model with viable masses and mixing angles based on the gauge group SU(5)\times SU(5)_{\perp} with a U(1)_{\perp}^3 family symmetry after imposing a Z_2 monodromy.

hep-ph↗