The \bar{B} \to X_s γγdecay: NLL QCD contribution of the Electromagnetic Dipole operator O_7

We calculate the set of O(\alpha_s) corrections to the double differential decay width d\Gamma_{77}/(ds_1 \, ds_2) for the process \bar{B} \to X_s \gamma \gamma originating from diagrams involving the electromagnetic dipole operator O_7. The kinematical variables s_1 and s_2 are defined as s_i=(p_b - q_i)^2/m_b^2, where p_b, q_1, q_2 are the momenta of b-quark and two photons. While the (renormalized) virtual corrections are worked out exactly for a certain range of s_1 and s_2, we retain in the gluon bremsstrahlung process only the leading power w.r.t. the (normalized) hadronic mass s_3=(p_b-q_1-q_2)^2/m_b^2 in the underlying triple differential decay width d\Gamma_{77}/(ds_1 ds_2 ds_3). The double differential decay width, based on this approximation, is free of infrared- and collinear singularities when combining virtual- and bremsstrahlung corrections. The corresponding results are obtained analytically. When retaining all powers in s_3, the sum of virtual- and bremstrahlung corrections contains uncanceled 1/\epsilon singularities (which are due to collinear photon emission from the s-quark) and other concepts, which go beyond perturbation theory, like parton fragmentation functions of a quark or a gluon into a photon, are needed which is beyond the scope of our paper.

Decision-making in amnesia: do advantageous decisions require conscious knowledge of previous behavioural choices?

Previous work has reported that in the Iowa gambling task (IGT) advantageous decisions may be taken before the advantageous strategy is known [Bechara, A., Damasio, H., Tranel, D., ; Damasio, A. R. (1997). Deciding advantageously before knowing the advantageous strategy. Science, 275, 1293-1295]. In order to test whether explicit memory is essential for the acquisition of a behavioural preference for advantageous choices, we measured behavioural performance and skin conductance responses (SCRs) in five patients with dense amnesia following damage to the basal forebrain and orbitofrontal cortex, six amnesic patients with damage to the medial temporal lobe or the diencephalon, and eight control subjects performing the IGT. Across 100 trials healthy participants acquired a preference for advantageous choices and generated large SCRs to high levels of punishment. In addition, their anticipatory SCRs to disadvantageous choices were larger than to advantageous choices. However, this dissociation occurred much later than the behavioural preference for advantageous alternatives. In contrast, though exhibiting discriminatory autonomic SCRs to different levels of punishment, 9 of 11 amnesic patients performed at chance and did not show differential anticipatory SCRs to advantageous and disadvantageous choices. Further, the magnitude of anticipatory SCRs did not correlate with behavioural performance. These results suggest that the acquisition of a behavioural preference--be it for advantageous or disadvantageous choices--depends on the memory of previous reinforcements encountered in the task, a capacity requiring intact explicit memory.