Dilated Floor Functions That Commute

We determine all pairs of real numbers $(\alpha, \beta)$ such that the dilated floor functions $\lfloor \alpha x\rfloor$ and $\lfloor \beta x\rfloor$ commute under composition, i.e., such that $\lfloor \alpha \lfloor \beta x\rfloor\rfloor = \lfloor \beta \lfloor \alpha x\rfloor\rfloor$ holds for all real $x$.Comment: 6 pages, to appear in Amer. Math. Monthl

Top quark forward-backward asymmetry from new t-channel physics

Motivated by recent measurements of the top quark forward-backward asymmetry at the Tevatron, we study how t-channel new physics can contribute to a large value. We concentrate on a theory with an abelian gauge boson possessing flavor changing couplings between up and top quarks, but satisfies flavor physics constraints. Collider constraints are strong, but can be consistent with the aid of small flavor diagonal couplings. We find that M_Z' ~ 160 GeV can yield a total lab-frame asymmetry of ~18% without being in conflict with other observables. There are implications for future collider searches, including exotic top quark decays, like-sign top quark production, and detailed measurements of the top production cross section. An alternate model with a gauged non-Abelian flavor symmetry would have similar phenomenology, but lacks the like-sign top signal.Comment: 5 pages, 4 figure

Models of Neutrino Mass with a Low Cutoff Scale

In theories with a low quantum gravity scale, global symmetries are expected to be violated, inducing excessive proton decay or large Majorana neutrino masses. The simplest cure is to impose discrete gauge symmetries, which in turn make neutrinos massless. We construct models that employ these gauge symmetries while naturally generating small neutrino masses. Majorana (Dirac) neutrino masses are generated through the breaking of a discrete (continuous) gauge symmetry at low energies, e.g., 2 keV to 1 GeV. The Majorana case predicts \Delta N_\nu \simeq 1 at BBN, neutrinoless double beta decay with scalar emission, and modifications to the CMB anisotropies from domain walls in the universe as well as providing a possible Dark Energy candidate. For the Dirac case, despite the presence of a new light gauge boson, all laboratory, astrophysical, and cosmological constraints can be avoided.Comment: 11 pages, 4 figure

Light U(1) Gauge Boson Coupled to Baryon Number

We discuss the phenomenology of a light U(1) gauge boson, $\gamma_B$, that couples only to baryon number. Gauging baryon number at high energies can prevent dangerous baryon-number violating operators that may be generated by Planck scale physics. However, we assume at low energies that the new U(1) gauge symmetry is spontaneously broken and that the $\gamma_B$ mass $m_B$ is smaller than $m_Z$. We show for $m_\Upsilon<m_B<m_Z$ that the $\gamma_B$ coupling $\alpha_B$ can be as large as $\sim 0.1$ without conflicting with the current experimental constraints. We argue that $\alpha_B\sim 0.1$ is large enough to produce visible collider signatures and that evidence for the $\gamma_B$ could be hidden in existing LEP data. We show that there are realistic models in which mixing between the $\gamma_B$ and the electroweak gauge bosons occurs only as a radiative effect and does not lead to conflict with precision electroweak measurements. Such mixing may nevertheless provide a leptonic signal for models of this type at an upgraded Tevatron.Comment: 8pp. LaTeX, 5 figures included as uuencoded, gzipped, encapsulated postscript files. Talk presented by C. Carone at the Workshop on Particle Theory and Phenomenology, May 17-19, 1995, Iowa State University, Ames Iowa. Full postscript available from http://theor1.lbl.gov/www/theorgroup/papers/37432.p

Transport properties of a quantum wire: the role of extended time-dependent impurities

We study the transport properties of a quantum wire, described by the Tomonaga-Luttinger model, in the presence of a backscattering potential provided by several extended time-dependent impurities (barriers). Employing the B\" uttiker-Landauer approach, we first consider the scattering of noninteracting electrons ($g=1$) by a rectangular-like barrier and find an exact solution for the backscattering current, as well as a perturbative solution for a weak static potential with an arbitrary shape. We then include electron-electron interactions and use the Keldysh formalism combined with the bosonization technique to study oscillating extended barriers. We show that the backscattering current off time-dependent impurities can be expressed in terms of the current for the corresponding static barrier. Then we determine the backscattering current for a static extended potential, which, in the limit of noninteracting electrons ($g=1$), coincides with the result obtained using the B\" uttiker-Landauer formalism. In particular, we find that the conductance can be increased beyond its quantized value in the whole range of repulsive interactions $0<g<1$ already in the case of a single oscillating extended impurity, in contrast %contrary to the case of a point-like impurity, where this phenomenon occurs only for $0<g<1/2$.Comment: 9 pages, 5 figure