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Photon Energy Spectrum in $B \to X_s γ$ and Comparison with Data

A. Ali, C. Greub

TL;DR

This work analyzes the inclusive photon energy spectrum in $B \to X_s \gamma$ to test SM predictions against CLEO data. It combines a full leading-log QCD framework with a B-meson bound-state model (ACCMM) to extract nonperturbative inputs $p_F$ and $m_q$, and evaluates the branching ratio and CKM ratio $|V_{ts}|/|V_{cb}|$. The authors obtain a SM BR of about $2.55\times10^{-4}$ with sizable theoretical uncertainties and find $|V_{ts}|/|V_{cb}|=1.1 \pm 0.43$, in agreement with CKM unitarity. The photon spectrum fits favor $p_F \approx 450$ MeV and $m_q \approx 0$, consistent with semileptonic decay analyses and supporting a coherent picture between radiative and semileptonic $B$ decays.

Abstract

A comparison of the inclusive photon energy spectrum in the radiative decay $\BGAMAXS$, measured recently by the CLEO collaboration, with the standard model is presented, using a $B$-meson wave function model and improving earlier perturbative QCD-based computations of the same. The dependence of the photon energy spectrum on the non-perturbative model parameters, $p_F$, the $b$-quark Fermi momentum in the $B$ hadron, and $m_q$, the spectator quark mass, is explicitly shown, allowing a comparison of these parameters with the ones obtained from the analysis of the lepton energy spectrum in semileptonic $B$ decays. Taking into account present uncertainties, we estimate $\BBGAMAXS = (2.55 \pm 1.28) \times 10^{-4}$ in the standard model, assuming $\absvts/\absvcb= 1.0$. Comparing this with the CLEO measurement $\BBGAMAXS = (2.32 \pm 0.67) \times 10^{-4}$ implies $\absvts/\absvcb= 1.1 \pm 0.43$, in agreement with the CKM unitarity.

Photon Energy Spectrum in $B \to X_s γ$ and Comparison with Data

TL;DR

This work analyzes the inclusive photon energy spectrum in to test SM predictions against CLEO data. It combines a full leading-log QCD framework with a B-meson bound-state model (ACCMM) to extract nonperturbative inputs and , and evaluates the branching ratio and CKM ratio . The authors obtain a SM BR of about with sizable theoretical uncertainties and find , in agreement with CKM unitarity. The photon spectrum fits favor MeV and , consistent with semileptonic decay analyses and supporting a coherent picture between radiative and semileptonic decays.

Abstract

A comparison of the inclusive photon energy spectrum in the radiative decay , measured recently by the CLEO collaboration, with the standard model is presented, using a -meson wave function model and improving earlier perturbative QCD-based computations of the same. The dependence of the photon energy spectrum on the non-perturbative model parameters, , the -quark Fermi momentum in the hadron, and , the spectator quark mass, is explicitly shown, allowing a comparison of these parameters with the ones obtained from the analysis of the lepton energy spectrum in semileptonic decays. Taking into account present uncertainties, we estimate in the standard model, assuming . Comparing this with the CLEO measurement implies , in agreement with the CKM unitarity.

Paper Structure

This paper contains 6 sections, 37 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Effective Hamiltonian for the decay $B \rightarrow X _{s} + \gamma$
  3. An anatomy of the processes $b \rightarrow s \gamma$ and $b \rightarrow s \gamma g$
  4. The photon energy spectrum at the partonic level
  5. $B$-meson Wave function Effects in $B \rightarrow X _{s} + \gamma$
  6. Estimates of $\hbox{BR} (B \rightarrow X _{s} + \gamma)$ in the SM and the Parameters $(p_F,m_q)$

Figures (5)

  • Figure 1: $\hbox{BR}(B \rightarrow X_s \gamma)$ as a function of $m_t$. The three solid lines correspond to the variation of the parameters $(\mu,\Lambda_5)$ as descibed in the text. The experimental $(\pm 1\sigma)$-bounds from CLEO CLEOrare2 are shown by the dashed lines.
  • Figure 2: $\hbox{BR}(B \rightarrow X_s \gamma)$ as a function of $(|V_{ts}|/|V_{cb}|)^2$. The solid lines correspond to the variation of the parametrs $(\mu,\Lambda_5,m_t)$ in the limits specified in table 2. The experimental $(\pm 1\sigma)$-bounds from CLEO CLEOrare2 are shown by the dashed lines.
  • Figure 3: Contourplot in the $(m_q,p_F)$ parameter space obtained from $\chi^2= \chi^2_{min} +1$.The minimum $\chi^2$ is for the values (0 MeV, 450 MeV).
  • Figure 4: Comparison of the normalized photon energy distribution using the corrected CLEO data CLEOrare2 and our theoretical distributions, both normalized to unit area in the photon energy interval between 1.95 GeV and 2.95 GeV. The solid curve corresponds to the values with the minimum $\chi^2$, $(m_q,p_F)$=(0,450 MeV), and the dashed curve to the values $(m_q,p_F)$=(300 MeV, 310 MeV).
  • Figure 5: The same as in Fig 4, but with absolute (i.e not normalized) differential branching ratio.