Perturbative QCD- and Power-Corrected Hadron Spectra and Spectral Moments in the Decay B→Xsℓ+ℓ−B \to X_s \ell^+ \ell^-

We compute the leading order (in $\alpha_s$) perturbative QCD and power ($1/m_b^2)$ corrections to the hadronic invariant mass and hadron energy spectra in the decay $B \to X_s \ell^+ \ell^-$ in standard model. This is done both by using the heavy quark expansion technique (HQET) and a perturbative-QCD improved Fermi motion (FM) model which takes into account $B$-meson wave-function effects. The corrections in the hadron energy ($E_H$) spectrum are found to be small over a good part of this spectrum in both the methods. However, the expansion in $1/m_b$ in HQET fails near the lower kinematic end-point and at the $c\bar{c}$ threshold. The hadronic invariant mass ($S_H$) spectrum is calculable only over a limited range $S_H > \bar{\Lambda}m_B$ in the heavy quark expansion, where $\bar{\Lambda} \simeq m_B-m_b$. We also present results for the first two hadronic moments $$and$$, $n=1,2$, working out their sensitivity on the HQET and FM model parameters. For equivalent values of these parameters, the moments in these methods are remarkably close to each other. Using the FM model, we study the effect of the experimental cuts, used recently by the CLEO collaboration in searching for the decay $B \to X_s \ell^+ \ell^-$, on the hadron spectra and hadronic invariant mass moments. The constraints following from assumed values of $$ on the HQET parameters $\lambda_1$ and $\bar{\Lambda}$ are worked out. Data from the forthcoming B facilities could be used to measure the short-distance contribution in $B \to X_s \ell^+ \ell^-$ and determine the HQET parameters $\lambda_1$ and $\bar{\Lambda}$. This could be combined with complementary constrains in $B \to X \ell \nu_\ell$ to determine them precisely.Comment: 44 pages, 15 figure (require epsf.sty);, March 1998; Several typos and composition errors corrected; four references added; no change in formulae or result

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

Evolution of galaxy groups in the Illustris simulation

We present the first study of evolution of galaxy groups in the Illustris simulation. We focus on dynamically relaxed and unrelaxed galaxy groups representing dynamically evolved and evolving galaxy systems, respectively. The evolutionary state of a group is probed from its luminosity gap and separation between the brightest group galaxy and the center of mass of the group members. We find that the Illustris simulation, over-produces large luminosity gap galaxy systems, known as fossil systems, in comparison to observations and the probed semi-analytical predictions. However, this simulation is equally successful in recovering the correlation between luminosity gap and luminosity centroid offset, in comparison to the probed semi-analytic model. We find evolutionary tracks based on luminosity gap which indicate that a large luminosity gap group is rooted in a small luminosity gap group, regardless of the position of the brightest group galaxy within the halo. This simulation helps, for the first time, to explore the black hole mass and its accretion rate in galaxy groups. For a given stellar mass of the brightest group galaxies, the black hole mass is larger in dynamically relaxed groups with a lower rate of mass accretion. We find this consistent with the latest observational studies of the radio activities in the brightest group galaxies in fossil groups. We also find that the IGM in dynamically evolved groups is hotter for a given halo mass than that in evolving groups, again consistent with earlier observational studies.Comment: 10 pages, 10 figures. Accepted for publication in Ap

A Comparative Study of the Decays B→(K,K∗)ℓ+ℓ−B \to (K,K^*) \ell^+ \ell^- in Standard Model and Supersymmetric Theories

Using improved theoretical calculations of the decay form factors in the Light Cone-QCD sum rule approach, we investigate the decay rates, dilepton invariant mass spectra and the forward-backward (FB) asymmetry in the decays $B \to (K,K^*) \ell^+ \ell^-$ ($\ell^\pm =e^\pm,\mu^\pm,\tau^\pm$) in the standard model (SM) and a number of popular variants of the supersymmetric (SUSY) models. Theoretical precision on the differential decay rates and FB-asymmetry is estimated in these theories taking into account various parametric uncertainties. We show that existing data on $B \to X_s \gamma$ and the experimental upper limit on the branching ratio ${\cal B}(B \to K^* \mu^+ \mu^-)$ provide interesting bounds on the coefficients of the underlying effective theory. We argue that the FB-asymmetry in $B \to K^* \ell^+ \ell^-$ constitutes a precision test of the SM and its measurement in forthcoming experiments may reveal new physics. In particular, the presently allowed large-$\tan \beta$ solutions in SUGRA models, as well as more general flavor-violating SUSY models, yield FB-asymmetries which are characteristically different from the corresponding ones in the SM.Comment: 36 pages, 12 figures (require epsfig.sty), 8 Tables, LaTeX2e; subsection 6.4 corrected, minor changes in numerical results, Figures 3 and 9 to 12 modified; submitted to Physical Review

Fuzzy image segmentation of generic shaped clusters

The segmentation performance of any clustering algorithm is very sensitive to the features in an image, which ultimately restricts their generalisation capability. This limitation was the primary motivation in our investigation into using shape information to improve the generality of these algorithms. Fuzzy shape-based clustering techniques already consider ring and elliptical profiles in segmentation, though most real objects are neither ring nor elliptically shaped. This paper addresses this issue by introducing a new shape-based algorithm called fuzzy image segmentation of generic shaped clusters (FISG) that incorporates generic shape information into the framework of the fuzzy c-means (FCM) algorithm. Both qualitative and quantitative analyses confirm the superiority of FISG compared to other shape-based fuzzy clustering methods including, Gustafson-Kessel algorithm, ring-shaped, circular shell, c-ellipsoidal shells and elliptic ring-shaped clusters. The new algorithm has also been shown to be application independent so it can be applied in areas such as video object plane segmentation in MPEG-4 based coding

O(αs)O(\alpha_s) Corrections to B→Xse+e−B \to X_s e^+ e^- Decay in the 2HDM

$O(\alpha_s)$ QCD corrections to the inclusive $B \to X_s e^+ e^-$ decay are investigated within the two - Higgs doublet extension of the standard model (2HDM). The analysis is performed in the so - called off-resonance region; the dependence of the obtained results on the choice of the renormalization scale is examined in details. It is shown that $O(\alpha_s)$ corrections can suppress the $B \to X_s e^+ e^-$ decay width up to $1.5 \div 3$ times (depending on the choice of the dilepton invariant mass $s$ and the low - energy scale $\mu$). As a result, in the experimentally allowed range of the parameters space, the relations between the $B \to X_s e^+ e^-$ branching ratio and the new physics parameters are strongly affected. It is found also that though the renormalization scale dependence of the $B \to X_s e^+ e^-$ branching is significantly reduced, higher order effects in the perturbation theory can still be nonnegligible.Comment: 16 pages, latex, including 6 figures and 3 table