Flavor Gauge Models Below the Fermi Scale

The mass and weak interaction eigenstates for the quarks of the third generation are very well aligned, an empirical fact for which the Standard Model offers no explanation. We explore the possibility that this alignment is due to an additional gauge symmetry in the third generation. Specifically, we construct and analyze an explicit, renormalizable model with a gauge boson, $X$, corresponding to the $B-L$ symmetry of the third family. Having a relatively light (in the MeV to multi-GeV range), flavor-nonuniversal gauge boson results in a variety of constraints from different sources. By systematically analyzing 20 different constraints, we identify the most sensitive probes: kaon, $B^+$, $D^+$ and Upsilon decays, $D-\bar{D}^0$ mixing, atomic parity violation, and neutrino scattering and oscillations. For the new gauge coupling $g_X$ in the range $(10^{-2} - 10^{-4})$ the model is shown to be consistent with the data. Possible ways of testing the model in $b$ physics, top and $Z$ decays, direct collider production and neutrino oscillation experiments, where one can observe nonstandard matter effects, are outlined. The choice of leptons to carry the new force is ambiguous, resulting in additional phenomenological implications, such as non-universality in semileptonic bottom decays. The proposed framework provides interesting connections between neutrino oscillations, flavor and collider physics.Comment: 44 pages, 7 figures, 3 tables; B physics constraints and references added, conclusions unchange

On the renormalization of the electroweak chiral Lagrangian with a Higgs

We consider the scalar sector of the effective non-linear electroweak Lagrangian with a light "Higgs" particle, up to four derivatives in the chiral expansion. The complete off-shell renormalization procedure is implemented, including one loop corrections stemming from the leading two-derivative terms, for finite Higgs mass. This determines the complete set of independent chiral invariant scalar counterterms required for consistency; these include bosonic operators often disregarded. Furthermore, new counterterms involving the Higgs particle which are apparently chiral non-invariant are identified in the perturbative analysis. A novel general parametrization of the pseudoescalar field redefinitions is proposed, which reduces to the various usual ones for specific values of its parameter; the non-local field redefinitions reabsorbing all chiral non-invariant counterterms are then explicitly determined. The physical results translate into renormalization group equations which may be useful when comparing future Higgs data at different energies

Fractional Hamiltonian analysis of higher order derivatives systems

The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives.Comment: 13 page

Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.Comment: 10 page

Quantum phase transition triggering magnetic BICs in graphene

Graphene hosting a pair of collinear adatoms in the phantom atom configuration has pseudogap with cubic scaling on energy, $\Delta\propto|\varepsilon|^{3}$ which leads to the appearance of spin-degenerate bound states in the continuum (BICs) [Phys. Rev. B 92, 045409 (2015)]. In the case when adatoms are locally coupled to a single carbon atom the pseudogap scales linearly with energy, which prevents the formation of BICs. In this Letter, we explore the effects of non-local coupling characterized by the Fano factor of interference $q_{0},$ tunable by changing the slope of the Dirac cones in the graphene band-structure. We demonstrate that three distinct regimes can be identified: i) for $q_{0}<q_{c1}$ (critical point) a mixed pseudogap $\Delta\propto|\varepsilon|,|\varepsilon|^{2}$ appears yielding a phase with spin-degenerate BICs; ii) near $q_{0}=q_{c1}$ when $\Delta\propto|\varepsilon|^{2}$ the system undergoes a quantum phase transition in which the new phase is characterized by magnetic BICs and iii) at a second critical value $q_{0}>q_{c2}$ the cubic scaling of the pseudogap with energy $\Delta\propto|\varepsilon|^{3}$ characteristic to the phantom atom configuration is restored and the phase with non-magnetic BICs is recovered. The phase with magnetic BICs can be described in terms of an effective intrinsic exchange field of ferromagnetic nature between the adatoms mediated by graphene monolayer. We thus propose a new type of quantum phase transition resulting from the competition between the states characterized by spin-degenerate and magnetic BICs

Catching the Bound States in the Continuum of a Phantom Atom in Graphene

We explore theoretically the formation of bound states in the continuum (BICs) in graphene hosting two collinear adatoms situated at different sides of the sheet and at the center of the hexagonal cell, where a phantom atom of a fictitious lattice emulates the six carbons of the cell. We verify that in this configuration the local density of states (LDOS) near the Dirac points exhibits two characteristic features: i) the cubic dependence on energy instead of the linear one for graphene as found in New J. Phys. 16, 013045 (2014) and ii) formation of BICs as aftermath of a Fano destructive interference assisted by the Coulomb correlations in the adatoms. For the geometry where adatoms are collinear to carbon atoms, we report absence of BICs