A Theoretical Reappraisal of Branching Ratios and CP Asymmetries in the Decays B→(Xd,Xs)ℓ+ℓ−B \to (X_d,X_s) \ell^+ \ell^- and Determination of the CKM Parameters

We present a theoretical reappraisal of the branching ratios and CP asymmetries for the decays $B \to X_q \ell^+ \ell^-$, with $q=d,s$, taking into account current theoretical uncertainties in the description of the inclusive decay amplitudes from the long-distance contributions, an improved treatment of the renormalization scale dependence, and other parametric dependencies. Concentrating on the partial branching ratios $\Delta {\cal B}(B \to X_q \ell^+ \ell^-)$, integrated over the invariant dilepton mass region $1 {GeV}^2 \leq s \leq 6 {GeV}^2$, we calculate theoretical precision on the charge-conjugate averaged partial branching ratios $= (\Delta {\cal B}(B \to X_q \ell^+ \ell^-) + \Delta {\cal B}(\bar{B} \to \bar{X}_q \ell^+ \ell^-))/2$, CP asymmetries in partial decay rates $(a_{CP})_q=(\Delta {\cal B}(B \to X_q \ell^+ \ell^-) - \Delta {\cal B}(\bar{B} \to \bar{X}_q \ell^+ \ell^-))/(2 )$, and the ratio of the branching ratios $\Delta {\cal R} = /$. For the central values of the CKM parameters, we find $=(2.22^{+0.29}_{-0.30}) \times 10^{-6}$, $=(9.61^{+1.32}_{-1.47}) \times 10^{-8}$, $(a_{CP})_s =-(0.19^{+0.17}_{-0.19})$, $(a_{CP})_d =(4.40^{+3.87}_{-4.46})$, and $\Delta {\cal R} =(4.32 \pm 0.03)$. The dependence of $$ and $\Delta {\cal R}$ on the CKM parameters is worked out and the resulting constraints on the unitarity triangle from an eventual measurement of $\Delta {\cal R}$ are illustrated.Comment: 18 pages, 7 figures (require epsf.sty

Solution of the one-dimensional Dirac equation with a linear scalar potential

We solve the Dirac equation in one space dimension for the case of a linear, Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J. Phys. 69 (7), 817-818 (2001)] by eliminating unnecessary constraints. The spectrum is shown to match smoothly to the nonrelativistic spectrum in a weak-coupling limit.Comment: 7 pages, 1 figure, RevTE

Making sense of higher education: students as consumers and the value of the university experience

In the global university sector competitive funding models are progressively becoming the norm, and institutions/courses are frequently now subject to the same kind of consumerist pressures typical of a highly marketised environment. In the United Kingdom, for example, students are increasingly demonstrating customer-like behaviour and are now demanding even more ‘value’ from institutions. Value, though, is a slippery concept and has proven problematic both in terms of its conceptualisation and measurement. This article explores the relationship between student value and higher education and, via study in one United Kingdom business school, suggests how this might be better understood and operationalised. Adopting a combined qualitative/quantitative approach, this article also looks to identify which of the key value drivers has most practical meaning and, coincidentally, identifies a value-related difference between home and international students