Subleading Logarithms Research Articles

Renormalization-mass scale dependence in QCD contributions to semileptonic b → u decay

QCD contributions to the b → ul − v l decay rate, which are known to two-loop order in the MS scheme, exhibit sufficient dependence on the renormalization mass μ to compromise phenomenological predictions for inclusive semileptonic B → X u processes. Such scale dependence is ameliorated by the renormalization-group (RG) extraction and summation of all leading and RG-accessible subleading logarithms occurring subsequent to two-loop order in the perturbative series. This optimal RG-improvement of the known portion of the perturbative series virtually eliminates μ-dependence as a source of theoretical uncertainty in the predicted semileptonic B → X u inclusive rate.

Resummation of Yukawa enhanced and subleading Sudakov logarithms in longitudinal gauge boson and Higgs boson production

Future colliders will probe the electroweak theory at energies much larger than the gauge boson masses. Large double (DL) and single (SL) logarithmic virtual electroweak Sudakov corrections lead to significant effects for observable cross sections. Recently, leading and subleading universal corrections for external fermions and transverse gauge boson lines were resummed by employing the infrared evolution equation method. The results were confirmed at the DL level by explicit two loop calculations with the physical Standard Model (SM) fields. Also for longitudinal degrees of freedom the approach was utilized for DL-corrections via the Goldstone boson equivalence theorem. In all cases, the electroweak Sudakov logarithms exponentiate. In this paper we extend the same approach to both Yukawa enhanced as well as subleading Sudakov corrections to longitudinal gauge boson and Higgs production. We use virtual contributions to splitting functions of the appropriate Goldstone bosons in the high energy regime and find that all universal subleading terms exponentiate. The approach is verified by employing a non-Abelian version of Gribov's factorization theorem and by explicit comparison with existing one loop calculations. As a side result, we obtain also all top-Yukawa enhanced subleading logarithms for chiral fermion production at high energies to all orders. In all cases, the size of the subleading contributions at the two loop level is non-negligible in the context of precision measurements at future linear colliders.

High-order corrections and subleading logarithms for top quark production

We derive high-order threshold corrections for top quark production in hadronic collisions from resummation calculations. We present analytical expressions for the cross section through next-to-next-to-next-to-next-to-leading order (N^4LO) and next-to-next-to-leading logarithmic accuracy. Special attention is paid to the role of subleading logarithms and how they relate to the convergence of the perturbation series and differences between various resummation prescriptions. It is shown that care must be taken to avoid unphysical terms in the expansions. Numerical results are presented for top quark production at the Tevatron. We find sizeable increases to the total cross section and differential distributions and a dramatic reduction of the factorization scale dependence relative to next-to-leading order.

On the resummation of subleading logarithms in the transverse momentum distribution of vector bosons produced at hadron colliders

The perturbation series for electroweak vector boson production at small transverse momentum is dominated by large double logarithms at each order in perturbation theory. An accurate theoretical prediction therefore requires a resummation of these logarithms. This can be performed either directly in transverse momentum space or in impact parameter (Fourier transform) space. While both approaches resum the same leading double logarithms, the subleading logarithms are, in general, treated differently. We comment on two recent approaches to this problem, emphasising the particular subleading logarithms resummed in each case and the numerical differences in the cross sections which result.

Multiplicity of (mini-)jets at small x

We derive closed expressions for the mean and variance of the (mini-)jet multiplicity distribution in hard scattering processes at low x. Here (mini-)jets are defined as those due to initial-state radiation of gluons with transverse momenta greater than some resolution scale m_R, where Lambda^2 << m_R^2 << Q^2, Lambda being the intrinsic QCD scale and Q the momentum transfer scale of the hard scattering. Our results are valid to leading order in log(1/x) but include all sub-leading logarithms of Q^2/m_R^2. As an illustration, we predict the mini-jet multiplicity in Higgs boson production at the Large Hadron Collider.

Jet rates at small x to single-logarithmic accuracy

We present predictions of jet rates in deep inelastic scattering at small x to leading-logarithmic order in x, including all sub-leading logarithms of Q^2/m_R^2 where m_R is the transverse momentum scale at which jets are resolved. We give explicit results for up to three jets, and a perturbative expansion for multi-jet rates and jet multiplicities.

Subleading logarithms in QCD hard scattering

We discuss the resummation of corrections from the elastic limit (partonic threshold) in hadronic QCD hard-scattering cross sections, such as heavy quark production. We recall why these corrections can be large even at high orders in perturbation theory, and describe their resummation to arbitrary logarithmic accuracy, generalizing resummation in the Drell-Yan and other electroweak processes. Resummation is based on the factorization of soft gluons, whose dynamics is then generated by gauge field path-ordered exponentials, linked by color-dependent vertices. The renormalization of these composite vertices determines subleading logarithms. We illustrate our results for the case of heavy quark production by light quark annihilation.

Analytic approach to small x structure functions

We present a method for the analytic solution of small x structure functions. The essential small x logarithms are summed to all orders in the anomalous dimensions and coefficient functions. Although we work at leading logarithmic accuracy, the method is general enough to allow the systematic inclusion of sub-leading logarithms. Results and predictions are presented for the gluon density, and the structure functions F 2(x, Q 2 ) and F L (x, Q 2). We find that corrections to the simple double logarithmic calculation are important in the HERA range and obtain good fits to all available data.

LEADING INFRARED LOGARITHMS AND VACUUM STRUCTURE OF QCD3

QCD 3 is a superrenormalizable massless theory; therefore off-mass-shell infrared divergences appear in the loop expansion. We show how certain infrared divergences can be subtracted by changing the boundary conditions in the functional integral, letting the vector potentials approach non-zero constant values at infinity. Infrared divergences, in the Green's functions, come together with powers of logarithms of the external momenta, and among the infrared divergences we deal with, there are those that give rise to the leading and first subleading logarithms. We show how for two-point functions it is possible to sum the leading and first subleading logarithms to all orders. This procedure defines a nonperturbative approximation for QCD 3. We find that in the ultraviolet region these summations are well defined, while in the infrared region, some additional prescription is needed to make sense out of them. From the construction developed to cancel infrared divergences, we derive the presence of arbitrarily large field strengths in the vacuum. We respect Lorentz invariance, because in this construction, one averages all directions and strengths of these fields. Possible applications to the infrared problem of QCD 4 are indicated.