The surgery obstruction groups of the infinite dihedral group

This paper computes the quadratic Witt groups (the Wall L-groups) of the polynomial ring Z[t] and the integral group ring of the infinite dihedral group, with various involutions. We show that some of these groups are infinite direct sums of cyclic groups of order 2 and 4. The techniques used are quadratic linking forms over Z[t] and Arf invariants.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper29.abs.htm

Solving the SUSY CP problem with flavor breaking F-terms

Supersymmetric flavor models for the radiative generation of fermion masses offer an alternative way to solve the SUSY-CP problem. We assume that the supersymmetric theory is flavor and CP conserving. CP violating phases are associated to the vacuum expectation values of flavor violating susy-breaking fields. As a consequence, phases appear at tree level only in the soft supersymmetry breaking matrices. Using a U(2) flavor model as an example we show that it is possible to generate radiatively the first and second generation of quark masses and mixings as well as the CKM CP phase. The one-loop supersymmetric contributions to EDMs are automatically zero since all the relevant parameters in the lagrangian are flavor conserving and as a consequence real. The size of the flavor and CP mixing in the susy breaking sector is mostly determined by the fermion mass ratios and CKM elements. We calculate the contributions to epsilon, epsilon^{prime} and to the CP asymmetries in the B decays to psi Ks, phi Ks, eta^{\prime} Ks and Xs gamma. We analyze a case study with maximal predictivity in the fermion sector. For this worst case scenario the measurements of Delta mK, Delta mB and epsilon constrain the model requiring extremely heavy squark spectra.Comment: 21 pages, RevTex

Probing New Physics via an Angular Analysis of B --> V1 V2 decays

We show that an angular analysis of B --> V1 V2 decays yields numerous tests for new physics in the decay amplitudes. Unlike direct CP asymmetries, many of these new-physics observables are nonzero even if the strong phase differences vanish. For certain observables, neither time-dependent measurements nor tagging is necessary. Should a signal for new physics be found, one can place a lower limit on the size of the new-physics parameters, as well as on their effect on the measurement of the phase of B0--Bbar0 mixing.Comment: 9 pages, plain latex, no figures. Title modified slightly. Paragraph added about viability of method. Conclusions unchanged. To be published in Europhysics Letter

Is there New Physics in B Decays ?

Rare decays of the $B$ meson are sensitive to new physics effects. Several experimental results on these decays have been difficult to understand within the standard model (SM) though more precise measurements and a better understanding of SM theory predictions are needed before any firm conclusions can be drawn. In this talk we try to understand the present data assuming the presence of new physics. We find that the data points to new physics of an extended Higgs sector and we present a two higgs doublet model with a 2-3 flavor symmetry in the down type quark sector that can explain the deviations from standard model reported in several rare B decays.Comment: 8 pages, Talk presented at Theory Canada II, Perimeter Institute, Waterloo, Canada. New references added and update

Topological rigidity and H_1-negative involutions on tori

We prove there is only one involution (up to conjugacy) on the n-torus which acts as $-\mathrm{Id}$ on the first homology group when $n$ is of the form $4k$, is of the form $4k+1$, or is less than $4$. In all other cases we prove there are infinitely many such involutions up to conjugacy, but each of them has exactly $2^n$ fixed points and is conjugate to a smooth involution. The key technical point is that we completely compute the equivariant structure set for the corresponding crystallographic group action on $\mathbb{R}^n$ in terms of the Cappell $\mathrm{UNil}$-groups arising from its infinite dihedral subgroups. We give a complete analysis of equivariant topological rigidity for this family of groups.Comment: 50 pages, to appear in Geometry & Topolog

Aspects Of Heavy Quark Theory

Recent achievements in the heavy quark theory are critically reviewed. The emphasis is put on those aspects which either did not attract enough attention or cause heated debates in the current literature. Among other topics we discuss (i) basic parameters of the heavy quark theory; (ii) a class of exact QCD inequalities; (iii) new heavy quark sum rules; (iv) virial theorem; (v) applications (|V_cb| from the total semileptonic width and from the B->D* transition at zero recoil). In some instances new derivations of the previously known results are given, or new aspects addressed. In particular, we dwell on the exact QCD inequalities. Furthermore, a toy model is considered that may shed light on the controversy regarding the value of the kinetic energy of heavy quarks obtained by different methods.Comment: 67 pages, 6 Figures; plain LaTeX. Changes: Some equations in Sect.4 related to spin-nonsinglet sum rules are corrected. The references are updated

Constraints on charged Higgs bosons from D(s)+- -> mu+- nu and D(s)+- -> tau+- nu

The decays D(s)+- -> mu+- nu and D(s)+- -> tau+- nu have traditionally been used to measure the D(s)+- meson decay constant f_D(s). Recent measurements at CLEO-c and the B factories suggest a branching ratio for both decays somewhat higher than the Standard Model prediction using f_D(s) from unquenched lattice calculations. The charged Higgs boson (H+-) in the Two Higgs Doublet Model (Type II) would also mediate these decays, but any sizeable contribution from H+- can only suppress the branching ratios and consequently is now slightly disfavoured. It is shown that constraints on the parameters tan(beta) and m_H+- from such decays can be competitive with and complementary to analogous constraints derived from the leptonic meson decays B+- -> tau+- nu_tau and K+- -> mu+- nu_mu, especially if lattice calculations eventually prefer f_D(s) < 250 MeV.Comment: 18 pages, 4 figure

Inclusive η′\eta' production in B decays and the Enhancement due to charged technipions

The new contributions to the charmless B decay $B \to X_{s}\eta^{\prime}$ from the unit-charged technipions $P^{\pm}$ and $P^{\pm}_{8}$ are estimated. The technipions can provide a large enhancement to the inclusive branching ratio: $Br(B \to X_{s}\eta^{\prime}) \sim 7\times 10^{-4}$ for $m_{p1}=100GeV$ and $m_{p8}=250 \sim 350 GeV$ when the effect of QCD gluon anomaly is also taken into account. The new physics effect is essential to interpret the CLEO data.Comment: Latex file, 7 pages with two EPS figure

Measuring V_ub and probing SUSY with double ratios of purely leptonic decays of B and D mesons

The experimental prospects for precise measurements of the leptonic decays B_u -> tau nu / mu nu, B_s -> mu+ mu-, D -> mu nu and D_s -> mu nu / tau nu are very promising. Double ratios involving four of these decays can be defined in which the dependence on the values of the decay constants is essentially eliminated, thus enabling complementary measurements of the CKM matrix element V_ub with a small theoretical error. We quantify the experimental error in a possible future measurement of |V_ub| using this approach, and show that it is competitive with the anticipated precision from the conventional approaches. Moreover, it is shown that such double ratios can be more effective than the individual leptonic decays as a probe of the parameter space of supersymmetric models. We emphasize that the double ratios have the advantage of using |V_ub| as an input parameter (for which there is experimental information), while the individual decays have an uncertainty from the decay constants (e.g. f_B_s), and hence a reliance on theoretical techniques such as lattice QCD.Comment: 21 pages, 4 figure