Light cone QCD sum rules study of the rare radiative $Ξ^{*}_{bb}\toΞ_bγ$ decay

TL;DR

The paper tackles the rare radiative decay of a doubly heavy baryon via the flavor-changing neutral current $b \to s \gamma$. It applies light-cone QCD sum rules using heavy-baryon distribution amplitudes to derive sum rules for the tensor form factors $T_1^{V,A}(0)$ and $T_2^{V,A}(0)$ at $q^2 = 0$. The endpoint relations $T_1^{V}(0)=T_1^{A}(0)$ and $T_{2}^{V(A)}(0)= T_{2}^{A(V)}(0) \mp \frac{m_{Ξ^{*}_{bb}}}{m_{Ξ_b}} T_{1}^{A(V)}(0)$ emerge, constraining the form factors. Numerical analysis yields central values and uncertainties for the four form factors and computes the decay width $\Gamma(Ξ^{*}_{bb} \to Ξ_b γ) = (1.23 \pm 0.23) \times 10^{-19}$ GeV, suggesting potential observability at future high-luminosity experiments. The framework is extendable to related transitions such as $Ξ_{cc}^{*} \to Ξ_c γ$, highlighting the broader applicability of LCSR with heavy-baryon DAs.

Abstract

The rare radiative decay $Ξ^{*}_{bb}\toΞ_bγ$ is investigated within the light cone QCD sum rules approach. This decay proceeds through the flavor changing neutral current $b\to s$ transition in the Standard Model. The hadronic matrix element of the considered decay is parameterized in terms of four tensor form factors $T_1^{V}(q^2)$, $T_2^{V}(q^2)$, $T_1^{A}(q^2)$ and $T_2^{A}(q^2)$. The sum rules for these form factors describing the $Ξ^{*}_{bb}\toΞ_bγ$ decay are derived at $q^2=0$ point using the $Ξ_b$ distribution amplitudes. The results of the form factors are employed to calculate the corresponding decay width. Our finding indicates that this weak radiative decay could be within reach of future high statistics studies of doubly heavy baryons at LHCb and upcoming facilities.

Figures (2)

• Figure 1: The variation of the form factors of $\Xi^{*}_{bb} \rightarrow \Xi_{b}\gamma$ transition as a function of $M^2$ at different values of $s_0$.
• Figure 2: The histograms of the form factors obtained using randomly selected values of the auxiliary parameters $M^2$ and $s_0$.