119753398
Ultralight Dirac neutrinos from possible supergrand scenario
Persistent experimental suggestions about the electron neutrino being an ultralight Dirac particle in the mass range 20 to 55 eV have underlined the need to theoretically generate such a mass naturally, i.e., without any arbitrarily small Yukawa coupling or Higgs-field vacuum expectation value. A mechanism for this is proposed in this paper in terms of a 4\ifmmode\times\else\texttimes\fi{}4 neutral-fermion Majorana mass matrix for a single-generation world. The physical eigenstates turn out to be one ultralight and one very heavy Dirac neutrino within each fermion family. A general discussion (including the many-generation case) is given of the necessary and sufficient conditions for the emergence of such ultralight Dirac neutrinos. We also consider the skeleton of an illustrative, though incomplete, SO(10) supersymmetric (SUSY) grand unified theory (GUT) scenario\char22{}with a geometric type of hierarchy and some global symmetries\char22{}in which the aforesaid mass matrix is likely to arise. The ultralight neutrino Dirac mass is related at the tree level to that of its charge-$\frac{2}{3}$ family member by ${m}_{\ensuremath{\nu}}\ensuremath{\sim}m(\frac{2}{3})\frac{{M}_{\mathrm{SUSY}}}{{M}_{\mathrm{GUT}}}$ and radiative corrections are shown to be controllably small. Various implications of this result are brought out.
121584805
Current-commutators and high energy hadron production in e+e− annihilation
Abstract We consider the asymptotic behavior of the structure-functions for the process e + e − → H + everything (where H is a detectable hadron) in terms of commutators involving the electromagnetic current.
125018064
Supersymmetry working group report, 'From strings to LHC' workshop, Goa, (January, 2007)
31086876
Stringent low-energy mass constraints in no-scale supergravity.
Spectacular mass constraints are shown to exist at low energies in minimal no-scale supergravity theories. The top quark cannot be too light, the lowest-lying Higgs particle cannot be too heavy, and the pseudoscalar Higgs boson must weigh nearly a quarter as much as the gluino.
119370491
Oblique corrections and the quadratic approximation in electroweak precision testing
This paper is withdrawn. A revised and expanded version of this work is available as hep-ph/9603323.
122353884
Parton description of the forward peak in single particle electroproduction with highly virtual photons
The parton mode or the reaction eN→eAB (N = nucleon, A, B = hadrons) in the fixed ω Bj limit is used to discuss the width of the corresponding forward peak as a function of the photon mass.
121026122
A Variational approach to the Liouville model
We perform a variational analysis of the Liouville model. In particular we evaluate the effective potential and examine the possibility of restoring translation invariance.
8409689
Pseudo Hermitian Interactions in the Dirac Equation
We consider a (2 + 1)-dimensional massless Dirac equation in the presence of complex vector potentials. It is shown that such vector potentials (leading to complex magnetic fields) can produce bound states, and the Dirac Hamiltonians are η-pseudo Hermitian. Some examples have been explicitly worked out.
8745854
Quasi-exact solvability of Dirac–Pauli equation and generalized Dirac oscillators
Abstract In this paper we demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact solvability of the system based on the sl (2) symmetry are discussed separately in the spherical, cylindrical, and Cartesian coordinates. Some exactly solvable field configurations are also exhibited.
115157994
Non-hermitian quantum mechanics in non-commutative space
AbstractA recent investigation of the possibility of having a 
$\mathcal{PT}$
-symmetric periodic potential in an optical lattice stimulated the urge to generalize non-hermitian quantum mechanics beyond the case of commutative space. We thus study non-hermitian quantum systems in non-commutative space as well as a 
$\mathcal{PT}$
-symmetric deformation of this space. Specifically, a 
$\mathcal{PT}$
-symmetric harmonic oscillator together with an iC(x1+x2) interaction are discussed in this space, and solutions are obtained. We show that in the 
$\mathcal{PT}$ 
deformed non-commutative space the Hamiltonian may or may not possess real eigenvalues, depending on the choice of the non-commutative parameters. However, it is shown that in standard non-commutative space, the iC(x1+x2) interaction generates only real eigenvalues despite the fact that the Hamiltonian is not 
$\mathcal{PT}$
-symmetric. A complex interacting anisotropic oscillator system also is discussed.
119146278
Pseudo-Hermitian generalized Dirac oscillators
Abstract We study generalized Dirac oscillators with complex interactions in ( 1 + 1 ) dimensions. It is shown that for the choice of interactions considered here, the Dirac Hamiltonians are η -pseudo-Hermitian with respect to certain metric operators η . Exact solutions for the generalized Dirac oscillator for some choices of the interactions have also been obtained. It is also shown that generalized Dirac oscillators can be identified with an anti-Jaynes–Cummings-type model and by spin flipping they can also be identified with a Jaynes–Cummings-type model.