Probability distribution for the relative velocity of colliding particles in a relativistic classical gas

We find the probability density function $\mathcal{P}(V_{\texttt{r}})$ of the relativistic relative velocity for two colliding particles in a non-degenerate relativistic gas. The distribution reduces to Maxwell distribution for the relative velocity in the non-relativistic limit. We find an exact formula for the mean value $\langle V_{\texttt{r}}\rangle$. The mean velocity tends to the Maxwell's value in the non-relativistic limit and to the velocity of light in the ultra-relativistic limit. At a given temperature $T$, when at least for one of the two particles the ratio of the rest energy over the thermal energy $m c^2/k_B T$ is smaller than 40 the Maxwell distribution is inadequate.Comment: 5 pages, 2 figures. V2: text revised. Part of this material is published in Phys. Rev. D 89, 103533 (2014) in a merged version with arXiv:1311.450

Exact theory of freeze out

We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature $x_\ast=m_\chi /T_\ast$. The point $x_\ast$, which coincides with the stationary point of the equation for the quantity $\Delta= Y-Y_0$, is where the maximum departure of the WIMPs abundance $Y$ from the thermal value $Y_0$ is reached. For each mass $m_\chi$ and total annihilation cross section $\langle \sigma_\text{ann}v_\text{r}\rangle$, the temperature $x_\ast$ and the actual WIMPs abundance $Y(x_\ast)$ are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval $x\ge x_\ast$. The matching of the two abundances at $x_\ast$ is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of $1\%-2\%$ in the case of $S$-wave and $P$-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non equilibrium thermodynamics.Comment: 10 pages, 2 figure: V3 similar to the published version in EPJ

Higgs sector of the MSSM: lepton flavor violation at colliders and neutralino dark matter

We examine the prospects for the detection of Higgs mediated lepton flavor violation at LHC and at a photon collider in the minimal supersymmetric standard model with large lepton flavor violating mass insertions in the $\mu-\tau$ sector constraining the parameter space with several experimental bounds. We find rates probably too small to be observed at future experiments if models have to accommodate for a neutralino relic density as measured by WMAP and explain the $(g-2)_{\mu}$ anomaly: better prospects are found if these two constraints are applied only as upper bounds. The spin-independent neutralino-nucleon cross section in the studied constrained parameter space is just below the present CDMS limit while gamma rates from neutralino annihilation in the halo are strongly suppressed.Comment: 6 pages, 2 figures, Prepared for the proceedings of the workshop: "LC09: $e^+ e^-$ Physics at the TeV Scale and the Dark Matter Connection", 21-24 September 2009, Perugia, Ital

Gamma gamma \to mu tau b bbar in Susy Higgs mediated lepton flavor violation

The process gamma gamma \to mu tau b bbar is studied in the minimal supersymmetric standard model within a large tan_beta scenario imposing on the parameter space present direct and indirect constraints from B physics and rare LFV tau-decays. At a photon collider based on an e+e- linear collider with a center of mass energy of 800 GeV with the parameters of the TESLA proposal (expected integrated gamma-gamma luminosity L=200-500 inverse fb) the LFV signal can be probed for masses of the heavy neutral Higgs bosons A,H from 300 GeV up to the kinematical limit ~ 600 GeV for tan_beta in the range 30,60.Comment: Prepared for "Incontri di Fisica delle Alte Energie", IFAE 2009, Bari, Italy, 15-17 Aprile 2009. To appear in the proceedings to be published by the Societa' Italiana di Fisica in the Nuovo Cimento C - Colloquia on Physic

Friendship and romantic relationships during early and middle childhood

Ideas about romantic relationships have been studied in adolescents. This article extends this study to younger children. We asked two hundred seventy 5- to 11-year-olds to draw “two children who have a romance” and “two children who are friends,” and we subsequently interviewed each participant about the characters’ relationships. The drawings were coded with three scales of Pictorial Assessment of Interpersonal Relationships (PAIR), an instrument by Bombi, Pinto, and Cannoni. Interviews were categorized by the characters’ age and identity and by the distinguishing features of romance and friendship: location, intimacy, activity, personal characteristics, and emotions. Scale scores were compared with variance analyses, whereas the categories frequencies were submitted to chi-square. Results showed that all participants were able to distinguish the two relationships, even if the descriptions increased in detail with age. Girls provided more information than boys about romance, but were less inclined to talk about their own romantic experience

Testing SUSY models of lepton flavor violation at a photon collider

The loop level lepton flavor violating signals $\gamma \gamma \to \ell \ell' (\ell=e,\mu,\tau, \ell \neq \ell^\prime)$ are studied in a scenario of low-energy, R-parity conserving, supersymmetric seesaw mechanism within the context of a high energy photon collider. Lepton flavor violation is due to off diagonal elements in the left s-lepton mass matrix induced by renormalization group equations. The average slepton masses ${\widetilde{m}}$ and the off diagonal matrix elements $\Delta m$ are treated as model independent free phenomenological parameters in order to discover regions in the parameter space where the signal cross section may be observable. At the energies of the $\gamma \gamma$ option of the future high-energy linear collider the signal has a potentially large standard model background, and therefore particular attention is paid to the study of kinematical cuts in order to reduce the latter at an acceptable level. We find, for the ($e\tau$) channel, non-negligible fractions of the parameter space ($\delta_{LL}=\Delta m^2/\widetilde{m}^2 \gtrsim 10^{-1}$) where the statistical significance ($SS$) is $SS \gtrsim 3$.Comment: 26 pages, 12 figures, Revtex

How does a bicycle work? A new instrument to assess mechanical reasoning in school aged children

This study demonstrated that a brief interview can reveal the mechanical reasoning that could not be assessed via the Bicycle Drawing Test. This study, conducted on 190 children (6 to 11 years old), shows that mechanical reasoning improves with age. It shows correlations with spatial reasoning and motor control, and with visual reasonin