One loop scalar functions in the heavy quark effective theory

We find general solutions for the dimensionally regularised scalar one loop three-point and four-point functions with one heavy quark propagator. The scalar one-point function vanishes, while the expression for the two-point function has been found before. For the latter we give a detailed derivation. We also discuss some special cases and compile useful formulae.Comment: 18 pages, typos corrected, final results written out in more explicit form, further checks of results adde

Characteristic value determination from small samples

The paper deals with the characteristic value determination from relatively small samples. When the distribution and its parameters of a random variable are known, the characteristic value is deterministic quantity. However, in practical problems the parameters of distribution are unknown and can only be estimated from random samples. Therefore the characteristic value is by itself a random variable. The estimates of characteristic values are strongly dependant on the distribution of random variable. In the paper we show the analytical solution for characteristic value determination from random samples of normal and lognormal random variables. The confirmation of analytical results is accomplished by the use of computer simulations. For Gumbel, and Weibull distribution the characteristic value estimates are obtained numerically by combination of simulations and bisection method. In the paper the numerical results are presented for 5% characteristic values with 75% confidence interval, which is in accord with the majority of European building standards. The proposed approach is demonstrated on the data of experimentally obtained bending strengths of finger jointed wooden beams. (C) 2006 Elsevier Ltd. All rights reserved

Products of Farey graphs are totally geodesic in the pants graph

We show that for a surface S, the subgraph of the pants graph determined by fixing a collection of curves that cut S into pairs of pants, once-punctured tori, and four-times-punctured spheres is totally geodesic. The main theorem resolves a special case of a conjecture made by Aramayona, Parlier, and Shackleton and has the implication that an embedded product of Farey graphs in any pants graph is totally geodesic. In addition, we show that a pants graph contains a convex n-flat if and only if it contains an n-quasi-flat.Comment: v2: 25 pages, 16 figures. Completely rewritten, several figures added for clarit

Isospin-breaking effects on alpha extracted in B --> pi pi, rho rho, rho pi

Isospin-breaking in B --> pi pi caused by pi^0-eta-eta' mixing is studied in a model-independent way using flavor SU(3). Measured branching ratios for B^+ --> pi^+ pi^0, B^+ --> pi^+ eta^(') and B^0 --> pi^0 eta^(') imply an uncertainty in alpha smaller than 1.4 degree. We find a negligible effect of pi^0-eta-eta' mixing on alpha in B --> rho pi. Characterizing the effect of rho^0-omega mixing in B --> rho rho and in B --> rho pi by the two-pion invariant mass dependence, we point out a way of constraining this effect experimentally or eliminating it altogether. We show that a model-independent shift in alpha caused by electroweak penguin amplitudes in B --> pi pi and B --> rho rho, \Delta alpha_{EWP}=1.5+- 0.3 degree, may be slightly different in B --> rho pi. Other sources of isospin-breaking in these processes are briefly discussed.Comment: 21 pages, very slight changes, same version as in Physical Review

Right-handed Neutrinos and R(D(∗))R(D^{(*)})

We explore scenarios where the $R(D^{(*)})$ anomalies arise from semitauonic decays to a right-handed sterile neutrino. We perform an EFT study of all five simplified models capable of generating at tree-level the lowest dimension electroweak operators that give rise to this decay. We analyze their compatibility with current $R(D^{(*)})$ data and other relevant hadronic branching ratios, and show that one simplified model is excluded by this analysis. The remainder are compatible with collider constraints on the mediator semileptonic branching ratios, provided the mediator mass is of order TeV. We also discuss the phenomenology of the sterile neutrino itself, which includes possibilities for displaced decays at colliders and direct searches, measurable dark radiation, and gamma ray signals.Comment: 30 pages, 13 figures. Updated collider constraints and discussions. Matches published version in JHE

Angles from B Decays with Charm: Summary of Working Group 5 of the CKM Workshop 2006

We summarize the results presented in Working Group 5 (WG5) of the CKM 2006 Workshop in Nagoya. The charge of WG5 was to discuss the measurements of unitarity triangle angles $\beta/\phi_1$ and $\gamma/\phi_3$ from $B$-meson decays containing charm quark(s) in the final states.Comment: 9 pages, 8 postscript figures, to appear in the proceedings of 4th International Workshop on the CKM Unitarity Triangle (CKM 2006), Nagoya, Japan, 12-16 Dec 200

Computer Program for the Evaluation of Overlap Integrals

The program written in FORTRAN IV for evaluating the overlap integrals of o, n:, (), or cp type between two s, p, d, or f Slater AO\u27s with quantum number 1 to 6 is described and the computational method is discussed

Semi-inclusive hadronic B decays as null tests of the Standard Model

We propose a new set of observables that can be used as experimental null tests of the Standard Model in charged and neutral B decays. The CP asymmetries in hadronic decays of charged B mesons into inclusive final states containing at least one of the following mesons: K_{S,L}, eta', c\bar c bound states or neutral K^* or D mesons, for all of which a U-spin rotation is equivalent to a CP conjugation, are CKM suppressed and furthermore vanish in the exact U-spin limit. We show how this reduces the theoretical error by using Soft Collinear Effective Theory to calculate the CP asymmetries for K_{S,L} X_{s+d}, K^* X_{s+d} and eta' X_{s+d} final states in the endpoint region. For these CP asymmetries only the flavor and not the charge of the decaying B meson needs to be tagged up to corrections of NLO in 1/m_b, making the measurements more accessible experimentally.Comment: 8 pages, significantly expanded after the observation that both neutral and charged B decays can be used, calculation for decays involving eta' adde

Continuous catalytic decomposition of methane

Continuous catalytic decomposition of methane and application to space life support syste