We obtain new and complete asymptotic expansions of the confluent hypergeometric functions M(a, b; z) and U(a, b; z) for large b and z. The expansions are different in the three different regions: z + a + 1 - b > 0, z + a + 1 - b < 0 and z + a + 1 - b = 0. The expansions are not of Poincare type and we give explicit expressions for the terms of the expansions. In some cases, the expansions are valid for complex values of the variables too. We give numerical examples which show the accuracy of the expansions. (C) 2009 Elsevier B.V. All rights reserved.
The implications of the family non-universal Z ' model in the B. K(1)(1270, 1400)l(+)l(-) (l = e, mu, tau) decays are explored, where the mass eigenstates K(1)(1270, 1400) are the mixtures of 1P1 and 3P1 states with the mixing angle.. In this work, considering the Z' boson and setting the mixing angle 0 = (-34 +/- 13)degrees, we analyze the branching ratio, the dilepton invariant mass spectrum, the normalized forward- backward asymmetry and lepton polarization asymmetries of each decay mode. We find that all observables of B. K1(1270)mu(+)mu(-) are sensitive to the Z' contribution. Moreover, the observables of B -> K(1)(1400)mu(+)mu(-) have a relatively strong theta-dependence; thus, the Z' contribution will be buried by the uncertainty of the mixing angle.. Furthermore, the zero crossing position in the FBA spectrum of B -> K(1)(1270)mu(+)mu(-) at low dilepton mass will move to the positive direction with Z' contribution. For the tau modes, the effects of Z' are not remarkable due to the small phase space. These results could be tested in the running LHC-b experiment and Super-B factory.
In a combined investigation of B -> K(()*())l(+)l(-) decays, constraints on the related couplings in family non-universal Z' models are derived. We find that within the allowed parameter space, the recently observed forward-backward asymmetry in the B -> K(()*())l(+)l(-) decay can be explained by flipping the signs of the Wilson coefficients Q(9)(eff) and C(10). With the obtained constraints, we also calculate the branching ratio of the B(s) ->mu(+)mu(-) P-decay. The upper bound of our prediction is nearly an order of magnitude smaller than the upper bound given by the CDF Collaboration recently.
Motivated by the measured large branching ratio of (B) over bar (0) --> pi(0)pi(0) (the so-called pi pi puzzle), we investigate the effects of a family nonuniversal Z' model on the tree-dominated B --> pi pi decays. We find that the Z' coupling parameter zeta(LR)(d) similar to 0.05 with a nontrivial new weak phase phi(L)(d) similar to -50 degrees, which is relevant to the Z' contributions to the QCD penguin sector Delta C(5), is needed to reconcile the observed discrepancy. Combined with the recent fitting results from B --> pi K, pi K* and rho K decays, the Z' parameter spaces are severely reduced but still not excluded entirely, implying that both the "pi pi" and "pi K" puzzles could be accommodated simultaneously within such a family nonuniversal Z' model.
It is well known that the Diophantine equations x(4) + y(4) =3D z(4) + w(4) and x(4) + y(4) + z(4) =3D w(4) each have infinitely many rational solutions. It is also known for the equation x(6) + y(6) - z(6) =3D w(2). We extend the investigation to equations x(a) +/- y(b) =3D +/- z(c) +/- w(d), a, b, c, d is an element of Z, with 1/a + 1/b + 1/c + 1/d =3D 1. We show, with one possible exception, that if there is a solution of the equation in the reals, then the equation has infinitely many solutions in the integers. Of particular interest is the equation x(6) + y(6) + z(6) =3D w(2) because of its classical nature; but there seem to be no references in the literature.
We present a new approximate verification technique for falsifying the invariants of B models. The technique employs symmetry of B models induced by the use of deferred sets. The basic idea is to efficiently compute markers for states, so that symmetric states are guaranteed to have the same marker (but not the other way around). The falsification algorithm then assumes that two states with the same marker can be considered symmetric. We describe how symmetry markers can be efficiently computed and empirically evaluate an implementation, showing both very good performance results and a high degree of precision (i.e., very few non-symmetric states receive the same marker). We also identify a class of B models for which the technique is precise and therefore provides an efficient and complete verification method. Finally, we show that the technique can be applied to Z models as well.
We present a new approximate verification technique for falsifying the invariants of B models. The technique employs symmetry of B models induced by the use of deferred sets. The basic idea is to efficiently compute markers for states, so that symmetric states are guaranteed to have the same marker (but not the other way around). The falsification algorithm then assumes that two states with the same marker can be considered symmetric. We describe how symmetry markers can be efficiently computed and empirically evaluate an implementation, showing both very good performance results and a high degree of precision (i.e., very few non-symmetric states receive the same marker). We also identify a class of B models for which the technique is precise and therefore provides an efficient and complete verification method. Finally, we show that the technique can be applied to Z models as well.
We present a new approximate verification technique for falsifying the invariants of B models. The technique employs symmetry of B models induced by the use of deferred sets. The basic idea is to efficiently compute markers for states, so that symmetric states are guaranteed to have the same marker (but not the other way around). The falsification algorithm then assumes that two states with the same marker can be considered symmetric. We describe how symmetry markers can be efficiently computed and empirically evaluate an implementation, showing both very good performance results and a high degree of precision (i.e., very few non-symmetric states receive the same marker). We also identify a class of B models for which the technique is precise and therefore provides an efficient and complete verification method. Finally, we show that the technique can be applied to Z models as well.
We study the effect of Z'-mediated flavor-changing neutral current on the B -> pi pi decays. The branching ratios of these decays can be enhanced remarkably in the nonuniversal Z' model. Our estimated branching ratios B (B-0 -> pi(0)pi(0)) are enhanced significantly from their standard model (SM) value. For g'/g = 1, the branching ratios B (B-0 -> pi(0)pi(0)) are very close to the recently observed experimental values and for higher values of g'/g branching ratios are more. Our calculated branching ratios B (B-0 -> pi(+)pi(-)) and B (B+ -> pi(+)pi(0)) are also enhanced from the SM value as well as the recently observed experimental values. These enhancements of branching ratios from their SM value give the possibility of new physics.
The characteristics of latitudinal angles of solar wind flow (θv) observed near earth have been studied during the period 1973–2003. The average magnitude of θv shows distinct enhancements during the declining and maximum phases of the sunspot cycles. A close association of Bz component of IMF in the GSE system and the orientation of meridional flows in the solar wind is found which depends on the IMF sector polarity. This effect has been studied in typical geomagnetic storm periods. The occurrence of non-radial flows is also found to exhibit heliolatitudinal dependence during the years 1975 and 1985 as a characteristic feature of non-radial solar wind expansion from polar coronal holes.
The characteristics of latitudinal angles of solar wind flow (theta(v)) observed near earth have been studied during the period 1973-2003. The average magnitude of theta(v) shows distinct enhancements during the declining and maximum phases of the sunspot cycles. A close association of B, component of IMF in the GSE system and the orientation of meridional flows in the solar wind is found which depends on the IMF sector polarity. This effect has been studied in typical geomagnetic storm periods. The occurrence of non-radial flows is also found to exhibit heliolatitudinal dependence during the years 1975 and 1985 as a characteristic feature of non-radial solar wind expansion from polar coronal holes. (C) 2009 Elsevier Ltd. All rights reserved.