The B -> X_s gamma Photon Spectrum

Abstract

The photon energy spectrum in inclusive weak radiative B -> X_s gamma decay is computed to order alpha_s^2 beta_0. This result is used to extract a value for the HQET parameter $\barΛ$ from the average <1-2E_γ/m_B>, and a value of the parameter $λ_1$ from <(1-2E_γ/m_B)^2>. An accurate measurement of <1-2E_γ/m_B> can determine the size of the nonperturbative contributions to the Upsilon(1S) mass which cannot be absorbed into the b quark pole mass.

Figures (5)

• Figure 1: $B$ decay background to the photon spectrum due to the operators $(\bar{c}_L \gamma^\mu b_L) (\bar{d}_L \gamma_\mu u_L)$ (solid curve) and $(\bar{u}_L \gamma^\mu b_L) (\bar{d}_L \gamma_\mu u_L)$ (dashed curve).
• Figure 2: The sum of the 77, 22, 78, and 27 contributions to $(1/\Gamma_0)d\Gamma/dx_b$ at order $\alpha_s$ (thick dashed curve) and $\alpha_s^2\beta_0$ (thick solid curve). The thin curves show the 77 contribution only. The scale is the same as in Fig. 1.
• Figure 3: The sum of the 77, 22, 78, and 27 contributions to $\langle 1-x_b \rangle |_{x_b>1-\delta}$ at order $\alpha_s$ (thick dashed curve) and $\alpha_s^2\beta_0$ (thick solid curve). The thin curves show the 77 contribution only.
• Figure 4: Prediction for $\overline{(1 - x_B)} |_{x_B > 1-\delta}$ in the upsilon expansion at order $\epsilon$ (thick dashed curve) and $(\epsilon^2)_{\rm BLM}$ (thick solid curve). The thin curves show the 77 contribution only.
• Figure 5: The sum of the 77, 22, 78, and 27 contributions to $\langle (1-x_b)^2 \rangle |_{x_b>1-\delta}$ at order $\alpha_s$ (thick dashed curve) and $\alpha_s^2\beta_0$ (thick solid curve). The thin curves show the 77 contribution only.