Approximate NNLO Research Articles

Two-loop soft anomalous dimensions for single top quark associated production with aW−orH−

I present results for the two-loop soft anomalous dimensions for associated production of a single top quark with a W boson or a charged Higgs boson. The calculation uses expressions for the massive cusp anomalous dimension, which are presented in different forms, and it allows soft-gluon resummation at next-to-next-to-leading-logarithm (NNLL) accuracy. From the NNLL resummed cross section I derive approximate NNLO cross sections for bg -> tW- and bg -> tH- at LHC energies of 7, 10, and 14 TeV.

Giant QCD K-factors beyond NLO

Hadronic observables in Z+jet events can be subject to large NLO corrections at TeV scales, with K-factors that even reach values of order 50 in some cases. We develop a method, LoopSim, by which approximate NNLO predictions can be obtained for such observables, supplementing NLO Z+jet and NLO Z+2-jet results with a unitarity-based approximation for missing higher loop terms. We first test the method against known NNLO results for Drell-Yan lepton pt spectra. We then show our approximate NNLO results for the Z+jet observables. Finally we examine whether the LoopSim method can provide useful information even in cases without giant K-factors, with results for observables in dijet events that can be compared to early LHC data.

MODIFIED PERTURBATION THEORY FOR PAIR PRODUCTION AND DECAY OF FUNDAMENTAL UNSTABLE PARTICLES

We construct an asymptotic expansion in powers of the coupling constant directly of the cross-section for pair production and decay of fundamental unstable particles. The resonant and kinematic singularities arising in the expansion we treat in the sense of distributions. This mode allows us to transform formally divergent integrals into absolutely convergent ones with keeping the asymptotic property of the expansion. The appropriate procedure is elaborated up to an arbitrary order of the expansion. The peculiarity of application of the procedure in the threshold region is analyzed. The scheme of the calculations within the NNLO approximation is explicitly discussed.

Parton distribution functions up to NNLO

We calculate the unpolarized parton distribution functions up to NNLO approximation from the QCD analysis of the world DIS data. To study the proton structure functions \(F_2(x,Q^2)\), we need to use the orthogonal polynomials expansion method. This method is very useful to parameterize parton distribution function at the input of \(Q_0^2\). Our calculations for parton distribution functions based on the Jacobi polynomials method are in good agreement with the other theoretical models.

Asymmetric collision of two shock waves in AdS5

We consider high energy collisions of two shock waves in AdS5 as a model of ultrarelativistic nucleus-nucleus collisions in the boundary theory. We first calculate the graviton field produced in the collisions in the NLO and NNLO approximations, corresponding to three- and four-graviton exchanges with the shock waves. We then consider the asymmetric limit where the energy density in one shock wave is much higher than in the other one. In the boundary theory this setup corresponds to proton-nucleus collisions, with the nucleus being the denser of the two shock waves and the proton being the less dense one. Employing the eikonal approximation we find the exact high energy analytic solution for the metric in AdS5 for the asymmetric collision of two delta-function shock waves. The solution resums all-order graviton exchanges with the ``nucleus'' shock wave and a single-graviton exchange with the ``proton'' shock wave. Using the holographic renormalization prescription we read off the energy-momentum tensor of the matter produced in proton-nucleus collisions. We show in explicit detail that in the boundary theory the proton is completely stopped by strong-coupling interactions with the nucleus, in agreement with our earlier results [1]. We also apply the eikonal technique to the asymmetric collision of two unphysical delta-prime shock waves, which we introduced in [1] as a means of modeling nuclear collisions with weak coupling initial dynamics. We obtain a surprising result that, for delta-prime shock waves, the multiple bulk graviton exchange series giving the leading energy-dependent contribution to the energy-momentum tensor terminates at the order of two graviton exchanges with the nucleus.

Higher order predicted terms for an QCD observable, using PMS procedure

In this letter, we first review the principle of minimum sensitivity (PMS) in NLO, NNLO and higher order approximations to find an optimized expression for the desired observable at specific order. It is possible to expand the optimized quantities in terms of the quantities which exist in the standard approach of QCD for the observable. In this case we are able to obtain the predicted higher order terms. The calculations indicate that the predicted term, in the NNLO and higher approximations is not unique.

Non-singlet QCD analysis in the NNLO approximation

A non-singlet QCD analysis of the structure function up to NNLO is performed based on the orthogonal polynomials approach. The results of valence quark distributions up to NNLO are in good agreement with the available theoretical models.

Charm-quark fragmentation with an effective coupling constant

We use a recently proposed non-perturbative model, based on an effective strong coupling constant and free from tunable parameters, to study c-flavoured hadron production in e+e- annihilation. Charm-quark production is described in the framework of perturbative fragmentation functions, with NLO coefficient functions, NLL non-singlet DGLAP evolution and NNLL large-x resummation. We model hadronization effects by means of the effective coupling constant in the NNLO approximation and compare our results with experimental data taken at the Z0 pole and at the Upsilon(4S) resonance. We find that, within the experimental and theoretical uncertainties, our model is able to give a reasonable description of D*+-meson spectra from ALEPH for x<1-Lambda/m_c. More serious discrepancies are instead present when comparing with D and D^* data from BELLE and CLEO in x-space. Within the errors, our model is nonetheless capable of reproducing the first ten Mellin moments of all considered data sets. However, the fairly large theoretical uncertainties call for a full NNLO/NNLL analysis.

Modelling non-perturbative corrections to bottom-quark fragmentation

We describe B-hadron production in e + e − annihilation at the Z 0 pole by means of a model including non-perturbative corrections to b-quark fragmentation as originating, via multiple soft emissions, from an effective QCD coupling constant, which does not exhibit the Landau pole any longer and includes absorptive effects due to parton branching. We work in the framework of perturbative fragmentation functions at NLO, with NLL DGLAP evolution and NNLL large- x resummation in both coefficient function and initial condition of the perturbative fragmentation function. We include hadronization corrections via the effective coupling constant in the NNLO approximation and do not add any further non-perturbative fragmentation function. As part of our model, we perform the Mellin transforms of our resummed expressions exactly. We present results on the energy distribution of b-flavored hadrons, which we compare with LEP and SLD data, in both x- and N-spaces. We find that, within the theoretical uncertainties on our calculation, our model is able to reasonably reproduce the data at x ≲ 0.92 and the first five moments of the B cross section.

Non-singlet structure function in the NNLO approximation

We use recently the next-to-next-to-leading order (NNLO) contributions to anomalous dimension which is governing the evolution of non-singlet quark distributions. The x F 3 data of the CCFR collaboration is used to parameterize the non-singlet parton distributions in higher order. In the fitting procedure, Bernstein polynomial method is employed. The results of valence quark distributions in the LO, NLO and NNLO are compered with different theoretical models.

Parton distribution functions from the precise NNLO QCD fit

We report the parton distribution functions (PDFs) determined from the NNLO QCD analysis of the world inclusive DIS data with account of the precise NNLO QCD corrections to the evolution equations kernel. The value of strong coupling constant \alpha_s^{NNLO}(M_Z)=0.1141(14), in fair agreement with one obtained using the earlier approximate NNLO kernel by van Neerven-Vogt. The intermediate bosons rates calculated in the NNLO using obtained PDFs are in agreement to the latest Run II results.

Approximate next-to-next-to-leading-order threshold resummation in heavy flavor decays

We present an approximate NNLO evaluation of the QCD form factor resumming large logarithmic perturbative contributions in semi-inclusive heavy flavour decays.

NNLO global parton analysis

We perform a NNLO (and a LO) global parton analysis in which we include the new precise data for deep inelastic scattering from HERA and for inclusive jet production at the Tevatron, together with the improved knowledge of the three-loop splitting functions. The results are compared with our recent NLO analyses. The LO fit produces significantly worse results in general, but gives a surprisingly good fit to the Tevatron high-E_T jet data. For the approximate NNLO analysis we notice a slight improvement in the quality of the global fit, and find that the partons are changed by up to 10% at Q^2=10 GeV^2$, in particular in the x<0.01 regime.