We present the calculation of the virtual-and bremsstrahlung corrections of O(α s ) to the matrix elements d ℓ + ℓ − |O i |b . This is the missing piece in the full next-to-next-to-leading logarithmic (NNLL) results for various observables associated with the process B → X d ℓ + ℓ − , like the branching ratio, the CP-rate asymmetry and the forward-backward asymmetry. This paper is an extension of analogous calculations done by some of us for the process B → X s ℓ + ℓ − . As the contributions of the diagrams induced by the four-quark operators O u 1 and O u 2 with a u-quark running in the quark loop are strongly CKM suppressed, they were omitted in the analysis of B → X s ℓ + ℓ − . This is no longer possible for B → X d ℓ + ℓ − , as the corresponding contributions are not suppressed. The main new work therefore consists of calculating the O(α s ) corrections to d ℓ + ℓ − |O u 1,2 |b . In this paper we restrict ourselves to the range 0.05 ≤ s/m 2 b ≤ 0.25 (s is the invariant mass of the lepton pair), which lies above the ρ-and ω-resonances and below the J/ψ-resonance. We present the analytic results for the mentioned observables related to the process B → X d ℓ + ℓ − as expansions in the small parametersŝ = s/m 2 b , z = m 2 c /m 2 b and s/(4 m 2 c). In the phenomenological analysis at the end of the paper we discuss the impact of the NNLL corrections on the observables mentioned above. * Electronic address: hrachia@jerewan1.yerphi.am † Electronic address: bierik@itp.unibe.ch ‡ Electronic address: greub@itp.unibe.ch § Electronic address: walker@itp.unibe.ch,mwalker@bioc.unizh.ch However, restricting √ s to a region below thecc resonances, the long distance effects in B → X s ℓ + ℓ − are under control. The same is true for B → X d ℓ + ℓ − when choosing a region of √ s which is below the J/ψ-and above the ρ, ω-resonance regions. It turns out that in those ranges of √ s the corrections to the pure perturbative picture can be analyzed within the heavy quark effective theory (HQET). In particular, all available studies indicate that for the region 0.05 <ŝ = s/m 2 b < 0.25 the non-perturbative effects are below 10% [ [12][13][14][15][16][17]. Consequently, observables like differential decay rates, forward-backward asymmetries and CP-rate asymmetries for B → X s,d ℓ + ℓ − can be precisely predicted in this region of √ s using renormalization group improved perturbation theory. It was pointed out in the literature
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In a recent paper [1], we presented the calculation of the O(α s ) virtual corrections to b → s + − and of those bremsstrahlung terms which are needed to cancel the infrared divergences. In the present paper we work out the remaining O(α s ) bremsstrahlung corrections to b → s + − , which do not suffer from infrared and collinear singularities. These new contributions turn out to be small numerically. In addition, we also investigate the impact of the definition of m c on the numerical results. * Work partially supported by Schweizerischer Nationalfonds and SCOPES program
We present two-dimensional (2D) two-particle angular correlations measured with the STAR detector on relative pseudorapidity η and azimuth φ for charged particles from Au-Au collisions at √ s NN = 62 and 200 GeV with transverse momentum p t 0.15 GeV/c, |η| 1, and 2π in azimuth. Observed correlations include a same-side (relative azimuth <π/2) 2D peak, a closely related away-side azimuth dipole, and an azimuth quadrupole conventionally associated with elliptic flow. The same-side 2D peak and away-side dipole are explained by semihard parton scattering and fragmentation (minijets) in proton-proton and peripheral nucleus-nucleus collisions. Those structures follow N -N binary-collision scaling in Au-Au collisions until midcentrality, where a transition to a qualitatively different centrality trend occurs within one 10% centrality bin. Above the transition point the number of same-side and away-side correlated pairs increases rapidly relative to binary-collision scaling, the η width of the same-side 2D peak also increases rapidly (η elongation), and the φ width actually decreases significantly. Those centrality trends are in marked contrast with conventional expectations for jet quenching in a dense medium. The observed centrality trends are compared to perturbative QCD predictions computed in HIJING, which serve as a theoretical baseline, and to the expected trends for semihard parton scattering and fragmentation in a thermalized opaque medium predicted by theoretical calculations and 064902-2 ANOMALOUS CENTRALITY EVOLUTION OF TWO-. . .PHYSICAL REVIEW C 86, 064902 (2012) phenomenological models. We are unable to reconcile a semihard parton scattering and fragmentation origin for the observed correlation structure and centrality trends with heavy-ion collision scenarios that invoke rapid parton thermalization. If the collision system turns out to be effectively opaque to few-GeV partons the present observations would be inconsistent with the minijet picture discussed here.
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