Note on new interesting baryon channels to measure the photon polarization in b -> s gamma

At LHC a large number of b-flavored baryons will be produced. In this note we propose new baryon modes to determine the photon helicity of the penguin transition $b \to s \gamma$. The decay $\Lambda_b \to \Lambda \gamma$ has the drawback that the $\Lambda$, being neutral and long-lived, will escape detection most of the time. To overcome this difficulty, transitions of the type $\Lambda_b \to \Lambda^{*} \gamma$ have been proposed, where $\Lambda^{*}$ denotes an excited state decaying strongly within the detector into the clean mode $p K^-$. The doublet $\Xi_b$, that decays weakly, has a number of good features. The charged baryon $\Xi_b^-$ will decay into the mode $\Xi^- \gamma$, where the ground state hyperon $\Xi^-$, although it will decay most of the time outside the detector, can be detected because it is charged. We consider also the decay of $\Xi_b$ into $\Xi^{*} \gamma$, where a higher mass state $\Xi^{*}$ can decay strongly within the detector. We point out that the initial transverse polarization of $\Xi_b$ has to be known in all cases. To determine this parameter through the transition $\Xi_b \to J/\Psi\ \Xi$, we distinguish between different cases, and underline that in some situations one needs {\it theoretical input} on the asymmetry parameter $\alpha_{\Xi_b}$ of the primary decay. {\it A fortiori} the same considerations apply to the case of the $\Lambda_b$

Bound on the curvature of the Isgur-Wise function of the baryon semileptonic decay Lambda_b -> Lambda_c + l + nu

In the heavy quark limit of QCD, using the Operator Product Expansion, the formalism of Falk for hadrons or arbitrary spin, and the non-forward amplitude, as proposed by Uraltsev, we formulate sum rules involving the Isgur-Wise function $\xi_{\Lambda} (w)$ of the baryon transition $\Lambda_b \to \Lambda_c \ell \overline{\nu}_{\ell}$, where the light cloud has $j^P=0^+$ for both initial and final baryons. We recover the lower bound for the slope $\rho_\Lambda^2 = - \xi '_\Lambda (1) \geq 0$ obtained by Isgur et al., and we generalize it by demonstrating that the IW function $\xi_{\Lambda} (w)$ is an alternate series in powers of $(w-1)$, i.e. $(-1)^n \xi_{\Lambda}^{(n)} (1) \geq 0$. Moreover, exploiting systematically the sum rules, we get an improved lower bound for the curvature in terms of the slope, $\sigma_\Lambda^2 = \xi "_\Lambda (1) \geq {3 \over 5} [\rho_\Lambda^2 + (\rho_\Lambda^2)^2]$. This bound constrains the shape of the Isgur-Wise function and it will be compelling in the analysis of future precise data on the differential rate of the baryon semileptonic decay $\Lambda_b \to \Lambda_c \ell \overline{\nu}_{\ell}$, that has a large measured branching ratio, of about 5%.Comment: 16 page

Sum rules for leading and subleading form factors in Heavy Quark Effective Theory using the non-forward amplitude

Within the OPE, we the new sum rules in Heavy Quark Effective Theory in the heavy quark limit and at order 1/m_Q, using the non-forward amplitude. In particular, we obtain new sum rules involving the elastic subleading form factors chi_i(w) (i = 1,2, 3) at order 1/m_Q that originate from the L_kin and L_mag perturbations of the Lagrangian. To the sum rules contribute only the same intermediate states (j^P, J^P) = ((1/2)^-, 1^-), ((3/2)^-, 1^-) that enter in the 1/m_Q^2 corrections of the axial form factor h_(A_1)(w) at zero recoil. This allows to obtain a lower bound on -delta_(1/m^2)^(A_1) in terms of the chi_i(w) and the shape of the elastic IW function xi(w). An important theoretical implication is that chi'_1(1), chi_2(1) and chi'_3(1) (chi_1(1) = chi_3(1) = 0 from Luke theorem) must vanish when the slope and the curvature attain their lowest values rho^2->3/4, sigma^2->15/16. These constraints should be taken into account in the exclusive determination of |V_(cb)|.Comment: Invited talk to the International Workshop on Quantum Chromodynamics : Theory and Experiment, Conversano (Bari, Italy), 16-20 June 200