Monotone and boolean unitary Brownian motions

The additive monotone (resp. boolean) unitary Brownian motion is a non-commutative stochastic process with monotone (resp. boolean) independent and stationary increments which are distributed according to the arcsine law (resp. Bernoulli law) . We introduce the monotone and booleen unitary Brownian motions and we derive a closed formula for their associated moments. This provides a description of their spectral measures. We prove that, in the monotone case, the multiplicative analog of the arcsine distribution is absolutely continuous with respect to the Haar measure on the unit circle, whereas in the boolean case the multiplicative analog of the Bernoulli distribution is discrete. Finally, we use quantum stochastic calculus to provide a realization of these processes as the stochastic exponential of the correspending additive Brownian motions.Comment: 19 page

An Introduction to Dark Matter Direct Detection Searches & Techniques

Weakly Interacting Massive Particles (WIMPs), are a leading candidate for the dark matter that is observed to constitute ~25% of the total mass-energy density of the Universe. The direct detection of relic WIMPs (those produced during the early moments of the Universe's expansion) is at the forefront of active research areas in particle astrophysics with a numerous international experimental collaborations pursuing this goal. This paper presents an overview of the theoretical and practical considerations common to the design and operation of direct detection experiments, as well as their unique features and capabilities

SUSY in Silico: numerical D-brane bound state spectroscopy

We numerically construct the BPS and non-BPS wavefunctions of an $\mathcal{N}=4$ quiver quantum mechanics with two Abelian nodes and a single arrow. This model captures the dynamics of a pair of wrapped D-branes interacting via a single light string mode. A dimensionless parameter $\nu$, which is inversely proportional to the Fayet-Iliopoulos parameter, controls whether the bulk of the wavefunctions are supported on the Higgs branch or the Coulomb branch. We demonstrate how the BPS and excited states morph as $\nu$ is tuned. We also numerically compute the energy gap between the ground state and the first excited states as a function of $\nu$. An expression for the gap, computed on the Coulomb branch, matches nicely with our numerics at large $\nu$ but deviates at small $\nu$ where the Higgs branch becomes the relevant description of the physics. In the appendix, we provide the Schr\"{o}dinger equations fully reduced via symmetries which, in principle, allow for the numerical determination of the entire spectrum at any point in moduli space. For the ground states, this numerical determination of the spectrum can be thought of as the first \emph{in silico} check of various Witten index calculations.Comment: 23 pages, 4 figures, v2. slight modifications, v3. references added, typos correcte

Effective Lagrangian for the χj+χk−Hl0\chi^{+}_j \chi^{-}_kH^{0}_l interaction in the minimal supersymmetric standard model and neutral Higgs decays

We extend previous analyses of the supersymmetric loop correction to the neutral Higgs couplings to include the coupling $\chi^{+}_j \chi^{-}_kH^{0}_l$. The analysis completes the previous analyses where similar corrections were computed for the $\bar{\tau} \tau H^{0}_l$, $\bar{b} b H^{0}_l$, $\bar{c} c H^{0}_l$ and for $\bar{t} t H^{0}_l$ couplings within the minimal supersymmetric standard model. The effective one loop Lagrangian is then applied to the computation of the neutral Higgs decays. The sizes of the supersymmetric loop corrections of the neutral Higgs decay widths into $\chi^{+}_i \chi^{-}_j$ ($i=1,2$; $j=1,2$) are investigated and the supersymmetric loop correction is found to be in the range of $7\sim15$ in significant regions of the parameter space. By including the loop corrections of the other decay channels $\bar{b} b$, $\bar{t} t$, $\bar{\tau} \tau$, $\bar{c} c$, and $\chi^0_i \chi^0_j$ ($i=1-4$; $j=1-4$), the corrections to branching ratios for $H^{0}_l\to \chi^{+}_i \chi^{-}_j$ can reach as high as 40%. The effects of CP phases on the branching ratio are also investigated.Comment: 36 pages, 14 figues, revised version was published in Phys. Rev.

Sensitivity of atmospheric neutrinos in Super-Kamiokande to Lorentz violation

This talk, given at CPT'13, showed Super-Kamiokande atmospheric-neutrino Monte Carlo sensitivity to Lorentz-violation effects using the perturbative model derived from the Standard-Model Extension.Comment: 4 pages, 1 figure, presented at the Sixth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 17-21, 201