Normal origamis of Mumford curves

An origami (also known as square-tiled surface) is a Riemann surface covering a torus with at most one branch point. Lifting two generators of the fundamental group of the punctured torus decomposes the surface into finitely many unit squares. By varying the complex structure of the torus one obtains easily accessible examples of Teichm\"uller curves in the moduli space of Riemann surfaces. The p-adic analogues of Riemann surfaces are Mumford curves. A p-adic origami is defined as a covering of Mumford curves with at most one branch point, where the bottom curve has genus one. A classification of all normal non-trivial p-adic origamis is presented and used to calculate some invariants. These can be used to describe p-adic origamis in terms of glueing squares.Comment: 21 pages, to appear in manuscripta mathematica (Springer

A series of coverings of the regular n-gon

We define an infinite series of translation coverings of Veech's double-n-gon for odd n greater or equal to 5 which share the same Veech group. Additionally we give an infinite series of translation coverings with constant Veech group of a regular n-gon for even n greater or equal to 8. These families give rise to explicit examples of infinite translation surfaces with lattice Veech group.Comment: A missing case in step 1 in the proof of Thm. 1 b was added. (To appear in Geometriae Dedicata.

Non-factorizable contribution in nonleptonic weak interactions of K mesons

Two pion decays of K mesons, K_L-K_S mass difference, two photon and the Dalitz decays of K_L are studied systematically by assuming that their amplitude is given by a sum of factorizable and non-factorizable ones. The former is estimated by using a naive factorization while the latter is assumed to be dominated by dynamical contributions of various hadron states.Comment: 23 pages,1 figur

On the Correlations between Flavour Observables in Minimal U(2)^3 Models

The stringent correlations between flavour observables in models with CMFV are consistent with the present data except for the correlation Delta M_{s,d}-epsilon_K. Motivated by the recent work of Barbieri et al, we compare the CMFV correlations with the ones present in a special class of models with an approximate global U(2)^3 flavour symmetry, constrained by a minimal set of spurions governing the breakdown of this symmetry and the assumption that only SM operators are relevant in flavour physics. This analog of CMFV to be called MU(2)^3 allows to avoid the Delta M_{s,d}-epsilon_K tension in question because of reduced flavour symmetry and implied non-MFV contributions to Delta M_{s,d}. While the patterns of flavour violation in K meson system is the same as in CMFV models, the CP-violation in B_{s,d} meson systems can deviate from the one in the SM and CMFV models. We point out a stringent triple S_{psi K_S}-S_{psi phi}-|V_ub| correlation in this class of models that could in the future provide a transparent distinction between different MU(2)^3 models and in the context of these models determine |V_ub| by means of precise measurements of S_{psi K_S} and S_{psi phi} with only small hadronic uncertainties. For fixed S_{psi K_S} the correlation between B(B^+ -> tau^+nu_tau) and S_{psi phi} follows. We also find that MU(2)^3 models could in principle accommodate a negative value of S_{psi phi}, provided |V_ub| is found to be in the ballpark of exclusive determinations and the particular MU(2)^3 model provides a 25% enhancement of epsilon_K. A supersymmetric U(2)^3 model worked out in the Barbieri-School appears to satisfy these requirements. However if B(B^+ -> tau^+nu_tau)>1.0 10^{-4} will be confirmed by future experiments only positive S_{psi phi} is allowed in this framework. We summarize briefly the pattern of flavour violation in rare K and B_{s,d} decays in MU(2)^3 models.Comment: 28 pages, 6 figures; v2: Few references and discussion on CP violation in B_s-> mu^+ mu^- added; v3: Several clarifying comments added, conclusions unchanged, version accepted for publication in JHE

Two-photon exclusive decays Bs→η(η′)γγB_s \to \eta (\eta') \gamma\gamma and B→KγγB \to K \gamma\gamma

The exclusive decay modes $B \to K \gamma\gamma$ and $B_s \to \eta (\eta') \gamma\gamma$ are shown to have significant branching ratios of approximately $0.5\times 10^{-7}$. This first calculation of these modes employs a model based on a cascade transition $B\to V\gamma\to P\gamma\gamma$ for estimating the long-distance contribution and the process $b\to s\gamma\gamma$ for the short distance one.Comment: 11 Page

SUSY_FLAVOR v2.5: a computational tool for FCNC and CP-violating processes in the MSSM

We present SUSY_FLAVOR version 2.5 - a Fortran 77 program that calculates low-energy flavor observables in the general $R$-parity conserving MSSM. For a set of MSSM parameters as input, the code gives predictions for: 1. Electric dipole moments of the leptons and the neutron. 2. Anomalous magnetic moments (i.e. $g-2$) of the leptons. 3. Radiative lepton decays ($\mu\to e\gamma$ and $\tau\to \mu\gamma, e\gamma$). 4. Rare Kaon decays ($K^0_L\to \pi^0\bar\nu\nu$ and $K^+\to \pi^+ \bar\nu\nu$). 5. Leptonic $B$ decays ($B_{s,d}\to l^+ l^-$, $B\to \tau \nu$, $B\to D \tau \nu$ and $B\to D^\star \tau \nu$). 6. Radiative $B$ decays ($B\to\bar X_s \gamma$). 7. Rare decays of top quark to Higgs boson ($t\to ch,uh$). 8. $\Delta F=2$ processes ($\bar K^0-K^0$, $\bar D-D$, $\bar B_d-B_d$ and $\bar B_s-B_s$ mixing). SUSY_FLAVOR performs the resummation of all chirally enhanced corrections, i.e. takes into account the effects enhanced by $\tan\beta$ and/or large trilinear soft mixing terms to all orders in perturbation theory. All calculations are done using exact diagonalization of the sfermion mass matrices. Comparing to previous versions, in SUSY_FLAVOR v2.5 parameter initialization in SLHA2 format has been significantly generalized and simplified, so that program accepts without modifications most of the output files produced by other codes calculating MSSM spectra and processes. In addition, the routine calculating branching ratios for rare decays of top quark to Higgs boson has been included. The program can be obtained from www.fuw.edu.pl/susy_flavor.Comment: Updated from arXiv:1003.4260 [hep-ph] (SUSY_FLAVOR v1 manual), 61 pages; updated sections on modified user interface and on newly added processes. SUSY_FLAVOR code available at http://www.fuw.edu.pl/susy_flavo

Implications of the Unitarity Triangle `uc' for J, δ\delta and ∣VCKM∣|V_{CKM}| elements

The Jarlskog rephasing invariant parameter $|J|$ is evaluated using one of the six Unitarity Triangles involving well known CKM matrix elements \vud, \vus,~\rub, ~\vcd, ~\vcs~ and ~\vcb. With PDG2000 values of \vud~ etc. as input, we obtain $|J|=(2.71 \pm 1.12) \times 10^{-5}$, which in the PDG representation of CKM matrix leads to the range $21^o~to~159^o$ for the CP violating phase $\delta$. The CKM matrix elements evaluated using this range of $\delta$ are in agreement with the PDG CKM matrix. The implications of refinements in the input on $|J|$, $\delta$ and CKM matrix elements have also been studied.Comment: 14 pages, 3 figures (eps), updated in the light of latest PDG2000 dat