Exclusive Radiative Higgs Decays as Probes of Light-Quark Yukawa Couplings

We present a detailed analysis of the rare exclusive Higgs-boson decays into a single vector meson and a photon and investigate the possibility of using these processes to probe the light-quark Yukawa couplings. We work with an effective Lagrangian with modified Higgs couplings to account for possible new-physics effects in a model-independent way. The h->V\gamma{} decay rate is governed by the destructive interference of two amplitudes, one of which involves the Higgs coupling to the quark anti-quark pair inside the vector meson. We derive this amplitude at next-to-leading order in \alpha_s using QCD factorization, including the resummation of large logarithmic corrections and accounting for the effects of flavor mixing. The high factorization scale \mu~m_h ensures that our results are rather insensitive to the hadronic parameters characterizing the light-cone distribution amplitude of the vector meson. The second amplitude arises from the loop-induced effective h\gamma\gamma* and h\gamma Z* couplings, where the off-shell gauge boson converts into the vector meson. We devise a strategy to eliminate theoretical uncertainties related to this amplitude to almost arbitrary precision. This opens up the possibility to probe for O(1) modifications of the c- and b-quark Yukawa couplings and O(30) modifications of the s-quark Yukawa coupling in the high-luminosity LHC run. In particular, we show that measurements of the ratios Br(h->\Upsilon(nS)\gamma)/Br(h->\gamma\gamma) and Br(h->bb)/Br(h->\gamma\gamma) can provide complementary information on the real and imaginary parts of the b-quark Yukawa coupling. More accurate measurements would be possible at a future 100 TeV proton-proton collider.Comment: 25 pages plus appendices, 9 figures, 5 tables; v2: NLO evolution of Gegenbauer moments implemented in Appendix B, some references added; v3: typo in the value of C_{\gamma Z}(0) after eq. (35) fixe

Non-Equilibrium relation between mobility and diffusivity of interacting Brownian particles under shear

We investigate the relation between mobility and diffusivity for Brownian particles under steady shear near the glass transition, using mode coupling approximations. For the two directions perpendicular to the shear direction, the particle motion is diffusive at long times and the mobility reaches a finite constant. Nevertheless, the Einstein relation holds only for the short-time in-cage motion and is violated for long times. In order to get the relation between diffusivity and mobility, we perform the limit of small wavevector for the relations derived previously [Phys. Rev. Lett. 102 (2009), 135701], without further approximation. We find good agreement to simulation results. Furthermore, we split the extra term in the mobility in an exact way into three terms. Two of them are expressed in terms of mean squared displacements. The third is given in terms of the (less handy) force-force correlation function.Comment: 14 pages, 4 figures, accepted for Prog. Theor. Phys. Suppl., issue for the workshop "Frontiers in Nonequilibrium Physics", Kyoto, 200

On the spin parameter of dark-matter haloes

The study by White (1984) on the growth of angular momentum in dark haloes is extended towards a more detailed investigation of the spin parameter $\lambda\equiv L\sqrt{E}/{G M^{2.5}}$. Starting from the Zel'dovich approximation to structure formation, a dark halo is approximated by a homogeneous ellipsoid with the inertial tensor of the (highly irregular) Lagrangian region $\Upsilon$ from which the dark halo forms. Within this approximation, an expression for the spin parameter can be derived, which depends on the geometry of $\Upsilon$, the cosmological density parameter $\Omega_0$, the overdensity of the dark halo, and the tidal torque exerted on it. For Gaussian random fields, this expression can be evaluated statistically. As a result, we derive a probability distribution of the spin parameter which gives $\lambda\simeq0.07^{+0.04}_{-0.05}$, consistent with numerical investigations. This probability distribution steeply rises with increasing spin parameter, reaching its maximum at $\lambda\simeq0.025$. The 10 (50,90) percentile values are $\lambda=0.02$ (0.05,0.11, respectively). There is a weak anticorrelation of the spin parameter with the peak height $\nu$ of the density fluctuation field $\lambda\propto \nu^{-0.29}$. The dependence on $\Omega_0$ and the variance $\sigma$ of the density-contrast field is very weak; there is only a marginal tendency for the spin parameter to be slightly larger for late-forming objects in an open universe. Due to the weak dependence on $\sigma$, our results should be quite generally applicable and independent onComment: 16 pages, preprint MPA 79

A Comparison of X-ray and Strong Lensing Properties of Simulated X-ray Clusters

We use gas-dynamical simulations of galaxy clusters to compare their X-ray and strong lensing properties. Special emphasis is laid on mass estimates. The cluster masses range between 6 x 10^14 solar masses and 4 x 10^15 solar masses, and they are examined at redshifts between 1 and 0. We compute the X-ray emission of the intracluster gas by thermal bremsstrahlung, add background contamination, and mimic imaging and spectral observations with current X-ray telescopes. Although the beta model routinely provides excellent fits to the X-ray emission profiles, the derived masses are typically biased low because of the restricted range of radii within which the fit can be done. For beta values of ~ 2/3, which is the average in our numerically simulated sample, the mass is typically underestimated by ~ 40 per cent. The masses of clusters which exhibit pronounced substructure are often substantially underestimated. We suggest that the ratio between peak temperature and emission-weighted average cluster temperature may provide a good indicator for ongoing merging and, therefore, for unreliable mass estimates. X-ray mass estimates are substantially improved if we fit a King density profile rather than the beta model to the X-ray emission, thereby dropping the degree of freedom associated with beta. Clusters selected for their strong lensing properties are typically dynamically more active than typical clusters. Bulk flows in the intracluster gas contain a larger than average fraction of the internal energy of the gas in such objects, hence the measured gas temperatures are biased low. The bulk of the optical depth for arc formation is contributed by clusters with intermediate rather than high X-ray luminosity. Arcs occur predominantly in clusters which exhibit substructure and are not in an equilibrium state. Finally we explain why theComment: 22 pages including figures, submitted to MNRA

Limit theory for the Gilbert graph

For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random geometric graph, is investigated as the intensity of the Poisson point process is increased and the distance parameter goes to zero. The asymptotic expectation and covariance structure of a class of length-power functionals are computed. Distributional limit theorems are derived that have a Gaussian, a stable or a compound Poisson limiting distribution. Finally, concentration inequalities are provided using a concentration inequality for the convex distance

Velocity Distribution of a Homogeneously Cooling Granular Gas

In contrast to molecular gases, granular gases are characterized by inelastic collisions and require therefore permanent driving to maintain a constant kinetic energy. The kinetic theory of granular gases describes how the average velocity of the particles decreases after the driving is shut off. Moreover it predicts that the rescaled particle velocity distribution will approach a stationary state with overpopulated high-velocity tails as compared to the Maxwell-Boltzmann distribution. While this fundamental theoretical result was reproduced by numerical simulations, an experimental confirmation is still missing. Using a microgravity experiment which allows the spatially homogeneous excitation of spheres via magnetic fields, we confirm the theoretically predicted exponential decay of the tails of the velocity distribution.Comment: 11 pages, 14 figure