Next-to-leading Logarithmic Research Articles

Recent results on Sudakov logarithms in electroweak processes

Recent results for the asymptotic behavior of fermion scattering amplitudes in the Sudakov limit are discussed including next-to-leading logarithmic (NLL) and NNLL corrections. These are used for the analysis of the dominant electroweak corrections to the fermion-antifermion pair production in e + e − annihilation at high energy. The importance of angular dependent as well as subleading terms in emphasized.

Properties of Three-Body Decay Functions Derived with Time-Like Jet Calculus beyond Leading Order

Three-body decay functions in time-like parton branching are calculated using the jet calculus to the next-to-leading logarithmic (NLL) order in perturbative quantum chromodynamics (QCD). The phase space contributions from each of the ladder diagrams and interference diagrams are presented. We correct part of the results for the three-body decay functions calculated previously by two groups. Employing our new results, the properties of the three-body decay functions in the regions of soft partons are examined numerically. Furthermore, we examine the contribution of the three-body decay functions modified by the restriction resulting from the kinematical boundary of the phase space for two-body decay in the parton shower model. This restriction leads to some problems for the parton shower model. For this reason, we propose a new restriction introduced by the kinematical boundary of the phase space for two-body decay.

Resummation of large QCD logarithms inH→γγ

We study the strong corrections to the Higgs coupling to two photons. This coupling is the dominant mechanism for Higgs production in photon-photon collisions. In addition, the two photon decay mode of the Higgs is an important and relatively background free channel of relevance at the LHC and the Tevatron. We develop a method for the resummation of large QCD corrections in the form of Sudakov-like logarithms of the type \alpha_s^n\ln^{2n}(m/m_H) and \alpha_s^n\ln^{2n-1}(m/m_H) (where m is the light quark mass) which can contribute to this process in certain models (for example, the MSSM for large tan \beta) up to next-to-leading-logarithmic (NLL) accuracy. The NLL correction is moderate, the substantial part of which comes from terms not related to running coupling effects.

Calculation of next-to-leading QCD corrections tob→sg

A detailed standard model (SM) calculation of the O(alpha_s) virtual corrections to the decay width for b -> s g is presented (g denotes a gluon). Also the complete expressions for the corresponding bremsstrahlung corrections are given. Taking into account the existing next-to-leading logarithmic (NLL) result for the Wilson coefficient C_8^eff, a complete NLL result for the branching ratio BR(b->sg) is derived. Numerically, we obtain BR(b->sg)=(5.0 +/- 1.0) * 10^(-3), which is more than a factor of two larger than the leading logarithmic result. The impact of these corrections on the inclusive charmless hadronic branching ratio of B-mesons, which can be used to extract |V_(ub)/V_(cb)|, is shown to be of similar importance as NLL corrections to b-quark decay modes with three quarks in the final state. Finally, the impact of the NLL corrections to b->sg on the charmless hadronic branching ratio is investigated in scenarios, where the Wilson coefficient C_8 is enhanced by new physics.

Effects of higher-order threshold corrections in high-ETjet production

Results for higher-order threshold enhancements in high-${E}_{T}$ jet production in hadron-hadron collisions are presented. Expressions are given for the next-to-next-to-leading order (NNLO) threshold corrections to the single-jet inclusive cross section at next-to-leading logarithmic (NLL) accuracy. The corrections are found to be small for the specific choice of ${E}_{T}/2$ for the factorization and renormalization scales, and the corrected cross section shows a substantial reduction of the scale dependence. A comparison to experimental results from the Fermilab Tevatron is presented.

The rare decay b→ sg beyond leading logarithms

We calculate the O( α s ) virtual corrections to the decay width for b→ sg in the standard model ( g denotes a gluon). Also the corresponding O( α s ) bremsstrahlung corrections to b→ sg are systematically calculated in this Letter. The combined result is free of infrared and collinear singularities, in accordance with the KLN theorem. Taking into account the existing next-to-leading logarithmic (NLL) result for the Wilson coefficient C 8 eff, a complete NLL result for the branching ratio B NLL (b→sg) is derived. Numerically, we obtain B NLL =(5.0±1.0)×10 −3 , which is more than a factor of two larger than the leading logarithmic result B LL =(2.2±0.8)×10 −3 .

Rapidity-separation dependence and the large next-to-leading corrections to the BFKL equation

Recent concerns about the very large next-to-leading logarithmic (NLL) corrections to the BFKL equation are addressed by the introduction of a physical rapidity-separation parameter $\Delta$. At the leading logarithm (LL) this parameter enforces the constraint that successive emitted gluons have a minimum separation in rapidity, $y_{i+1}-y_i>\Delta$. The most significant effect is to reduce the BFKL Pomeron intercept from the standard result as $\Delta$ is increased from 0 (standard BFKL). At NLL this $\Delta$-dependence is compensated by a modification of the BFKL kernel, such that the total dependence on $\Delta$ is formally next-to-next-to-leading logarithmic. In this formulation, as long as $\Delta\gtrsim2.2$ (for $\alpha_{s}=0.15$): (i) the NLL BFKL pomeron intercept is stable with respect to variations of $\Delta$, and (ii) the NLL correction is small compared to the LL result. Implications for the applicability of the BFKL resummation to phenomenology are considered.

B→ η′ Xs in the standard model

We study B→ η′ X s within the framework of the Standard Model. Several mechanisms such as b→ η′ sg through the QCD anomaly, and b→ η′ s and B→η′s q ̄ arising from four-quark operators are treated simultaneously. Using QCD equations of motion, we relate the effective Hamiltonian for the first mechanism to that for the latter two. By incorporating next-to-leading-logarithmic(NLL) contributions, the first mechanism is shown to give a significant branching ratio for B→ η′ X s , while the other two mechanisms account for about 15% of the experimental value. The Standard Model prediction for B→ η′ X s is consistent with the CLEO data.

Sudakov resummation for prompt-photon production in hadron collisions

We present the explicit expressions for the resummation of large-x Sudakov effects in the transverse-energy distribution of prompt-photons produced in hadronic collisions, to next-to-leading logarithmic (NLL) accuracy. Fragmentation processes do not contribute to the Sudakov resummation at NLL level. In Mellin space, the resummed radiative factor factorizes in the product of independent radiators for the two initial and the one final coloured partons appearing in the Born process, times a simple factor describing the soft-gluon interferences between initial and final states. The formulae are given in terms of Mellin moments, and can be used for phenomenological applications using standard techniques for the inverse-Mellin transforms. The calculations presented in this work, when added to the existing works on DY and DIS production, complete the theoretical ground-work necessary to carry out global fits of parton densities with a uniform NLL accuracy in the large-x region.

Monte Carlo approach to QCD jets in the next-to-leading-logarithmic approximation.

We present a Monte Carlo model for the parton generation in the next-to-leading-logarithmic (NLL) approximation. This model provides us with the natural introduction of cross sections for nontrivial hard scatterings and it enables us to determine the scheme for the fundamental parameter \ensuremath{\Lambda} in QCD. The implementation of the NLL effects into the Monte Carlo approach is studied extensively. The stochastic treatment requires the positivity of functions for hard scatterings, two-body decays, and three-body decays. This leads to the condition of angular ordering which restricts the phase space. We apply this model to ${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$ annihilation and incorporate clean three-jet events into the QCD cascade.