Tree-level contribution to B[over ¯]→X_{d}γ using fragmentation functions

We evaluate the most important tree-level contributions connected with the b→uu ¯ ¯ dγ transition to the inclusive radiative decay B ¯ ¯ ¯ →X d γ using fragmentation functions. In this framework the singularities arising from collinear photon emission from the light quarks (u , u ¯ ¯ , and d ) can be absorbed into the (bare) quark-to-photon fragmentation function. We use as input the fragmentation function extracted by the ALEPH group from the two-jet cross section measured at the large electron positron (LEP) collider, where one of the jets is required to contain a photon. To get the quark-to-photon fragmentation function at the fragmentation scale μ F ∼m b , we use the evolution equation, which we solve numerically. We then calculate the (integrated) photon energy spectrum for b→uu ¯ ¯ dγ related to the operators P u 1,2 . For comparison, we also give the corresponding results when using nonzero (constituent) masses for the light quarks.

Measurement of inclusive jet charged-particle fragmentation functions in Pb+Pb collisions at √sNN = 2.76 TeV with the ATLAS detector

Measurements of charged-particle fragmentation functions of jets produced in ultra-relativistic nuclear collisions can provide insight into the modification of parton showers in the hot, dense medium created in the collisions. ATLAS has measured jets in √sNN=2.76 TeV Pb+Pb collisions at the LHC using a data set recorded in 2011 with an integrated luminosity of 0.14 nb−1. Jets were reconstructed using the anti-kt algorithm with distance parameter values R = 0.2, 0.3, and 0.4. Distributions of charged-particle transverse momentum and longitudinal momentum fraction are reported for seven bins in collision centrality for R=0.4 jets with pjetT>100 GeV. Commensurate minimum pT values are used for the other radii. Ratios of fragment distributions in each centrality bin to those measured in the most peripheral bin are presented. These ratios show a reduction of fragment yield in central collisions relative to peripheral collisions at intermediate z values, 0.04≲z≲0.2 and an enhancement in fragment yield for z≲0.04. A smaller, less significant enhancement is observed at large z and large pT in central collisions.

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.

NLL QCD contribution of the electromagnetic dipole operator to B -> Xs gamma gamma with a massive strange quark

We calculate the O(αs) corrections to the double differential decay width dΓ77/(ds1ds2) for the process B¯→Xsγγ, originating from diagrams involving the electromagnetic dipole operator O7. The kinematical variables s1 and s2 are defined as si=(pb−qi)2/m2b, where pb, q1, q2 are the momenta of the b quark and two photons. We introduce a nonzero mass ms for the strange quark to regulate configurations where the gluon or one of the photons become collinear with the strange quark and retain terms which are logarithmic in ms, while discarding terms which go to zero in the limit ms→0. When combining virtual and bremsstrahlung corrections, the infrared and collinear singularities induced by soft and/or collinear gluons drop out. By our cuts the photons do not become soft, but one of them can become collinear with the strange quark. This implies that in the final result a single logarithm of ms survives. In principle, the configurations with collinear photon emission could be treated using fragmentation functions. In a related work we find that similar results can be obtained when simply interpreting ms appearing in the final result as a constituent mass. We do so in the present paper and vary ms between 400 and 600 MeV in the numerics. This work extends a previous paper by us, where only the leading power terms with respect to the (normalized) hadronic mass s3=(pb−q1−q2)2/m2b were taken into account in the underlying triple differential decay width dΓ77/(ds1ds2ds3).