Universality class for bootstrap percolation with m=3m=3 on the cubic lattice

We study the $m=3$ bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with probability $p$ or $1-p$, respectively. Occupied sites with less than $m$ occupied first-neighbours are then rendered unoccupied; this culling process is repeated until a stable configuration is reached. We evaluate the percolation critical probability, $p_c$, and both scaling powers, $y_p$ and $y_h$, and, contrarily to previous calculations, our results indicate that the model belongs to the same universality class as usual percolation (i.e., $m=0$). The critical spanning probability, $R(p_c)$, is also numerically studied, for systems with linear sizes ranging from L=32 up to L=480: the value we found, $R(p_c)=0.270 \pm 0.005$, is the same as for usual percolation with free boundary conditions.Comment: 11 pages; 4 figures; to appear in Int. J. Mod. Phys.

Flavour Physics and CP Violation in the Standard Model and Beyond

We present the invited lectures given at the Third IDPASC School which took place in Santiago de Compostela in January 2013. The students attending the school had very different backgrounds, some of them were doing their Ph.D. in experimental particle physics, others in theory. As a result, and in order to make the lectures useful for most of the students, we focused on basic topics of broad interest, avoiding the more technical aspects of Flavour Physics and CP Violation. We make a brief review of the Standard Model, paying special attention to the generation of fermion masses and mixing, as well as to CP violation. We describe some of the simplest extensions of the SM, emphasising novel flavour aspects which arise in their framework.Comment: Invited talk at the Third IDPASC School 2013, January 21st - February 2nd 2013, Santiago de Compostela, Galiza, Spain; 36 pages, 8 figures, 2 tables; version with few misprints correcte

Leptogenesis and Low energy CP violation, a link

How is CP violation of low energy related to CP violation required from baryon number asymmetry ? We give an example which shows a direct link between CP violation of neutrino oscillation and baryogenesis through leptogenesis.Comment: 3 pages and 2 figures, Talk presented at 4th Nufac02, July 1-6, 200

Non-universal behavior for aperiodic interactions within a mean-field approximation

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following two deterministic aperiodic sequences: Fibonacci or period-doubling ones. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponent $\beta$, $\gamma$ and $\delta$. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.Comment: 6 pages, 7 figures, to be published in Phys. Rev.

CP violation in neutrino oscillation and leptogenesis

We study the correlation between CP violation in neutrino oscillations and leptogenesis in the framework with two heavy Majorana neutrinos and three light neutrinos. Among three unremovable CP phases, a heavy Majorana phase contributes to leptogenesis. We show how the heavy Majorana phase contributes to Jarlskog determinant $J$ as well as neutrinoless double $\beta$ decay by identifying a low energy CP violating phase which signals the CP violating phase for leptogenesis. For some specific cases of the Dirac mass term of neutrinos, a direct relation between lepton number asymmetry and $J$ is obtained. For the most general case of the framework, we study the effect on $J$ coming from the phases which are not related to leptogenesis, and also show how the correlation can be lost in the presence of those phases.Comment: 4 pages and 3 figure

Tree FCNC and non-unitarity of CKM matrix

We discuss possible signatures of the tree level FCNC, which results from the non-unitarity of CKM matrix. We first define the unitaity step-by-step, and possible test of the non-unitaity through the 4-value-KM parametrization. We, then, show how the phase angle of the unitary triangle would change in case of the vector-like down quark model. As another example of tree FCNC, we investigate the leptophobic $Z'$ model and its application to the recent $B_s$ mixing measurements.Comment: Talk given at Neutrino Masses and Mixings 2006 (NMM2006), Shizuoka, Japan (December 2006

Small violations of unitarity, the phase in Bs mixing and visible t->cZ decays at the LHC

We show that it is possible to accommodate the observed size of the phase in $B^0_s$--$\bar B^0_s$, mixing in the framework of a model with violation of $3\times 3$ unitarity. This violation is associated to the presence of a new $Q=2/3$ isosinglet quark $T$, which mixes both with $t$ and $c$ and has a mass not exceeding 500 GeV. The crucial point is the fact that this framework allows for $\chi\equiv\arg(-V_{ts}V_{cb}V_{tb}^*V_{cs}^*)$ of order $\lambda$, to be contrasted with the situation in the Standard Model, where $\chi$ is constrained to be of order $\lambda^2$. We point out that this scenario implies rare top decays $t\to cZ$ at a rate observable at the LHC and $|V_{tb}|$ significantly different from unity. In this framework, one may also account for the observed size of $D^0$--$\bar D^0$ mixing without having to invoke long distance contributions. It is also shown that in the present scenario, the observed size of $D^0$--$\bar D^0$ mixing constrains $\chi^\prime\equiv\arg(-V_{cd}V_{us}V_{cs}^*V_{ud}^*)$ to be of order $\lambda^4$, which is significantly smaller than what is allowed in generic models with violations of $3\times 3$ unitarity.Comment: 20 pages. References added. Additional observables considered, updated numerical examples, conclusions unchange