arXiv subjects
Publications and source records attributed to B. Nizic.
We briefly review the calculational procedure for the PQCD prediction for hard exclusive quantities and reconsider the problem of the factorization scale dependence.
We present a systematic method for reducing an arbitrary one-loop N-point massless Feynman integral with generic 4-dimensional momenta to a set comprised of eight fundamental scalar integrals: six box integrals in D=6, a triangle integral in D=4, and a general two-point integral in D space time dimensions. All the divergences present in the original integral are contained in the general two-point integral and associated coefficients. The problem of vanishing of the kinematic determinants has been solved in an elegant and transparent manner. Being derived with no restrictions regarding the external momenta, the method is completely general and applicable for arbitrary kinematics. In particular, it applies to the integrals in which the set of external momenta contains subsets comprised of two or more collinear momenta, which are unavoidable when calculating one-loop contributions to the hard-scattering amplitude for exclusive hadronic processes at large momentum transfer in PQCD. The iterative structure makes it easy to implement the formalism in an algebraic computer program.
We present a generally applicable reduction formalism which makes it possible to express an arbitrary tensor and scalar one-loop Feynman integral, with N external lines and massless propagators, in terms of a basic set of eight fundamental scalar Feynman integrals with 2, 3, and 4 external lines, for arbitrary external kinematics. The formalism is particularly suitable for the NLO calculations of exclusive processes at large momentum transfer in pQCD, where all previously developed reduction methods fail due to the presence of collinear external on-shell lines.
The IR finite one-loop box scalar integral with massless internal lines has been recalculated. The result is very compact, simple and valid for arbitrary values of the relevant kinematic variables. It is given in terms of only two dilogarithms and a few logarithms, all of very simple arguments.
Using the Feynman parameter method, we have calculated in an elegant manner a set of one$-$loop box scalar integrals with massless internal lines, but containing 0, 1, 2, or 3 external massive lines. To treat IR divergences (both soft and collinear), the dimensional regularization method has been employed. The results for these integrals, which appear in the process of evaluating one$-$loop $(N\ge 5)-$point integrals and in subdiagrams in QCD loop calculations, have been obtained for arbitrary values of the relevant kinematic variables and presented in a simple and compact form.
We comment on the results of a complete leading-twist next-to-leading order QCD analysis of the spacelike pion electromagnetic form factor at large-momentum transfer Q. For the asymptotic distribution amplitude, we have examined the sensitivity of the predictions to the choice of the renormalization scale. The results show that, regarding the size of the radiative corrections, reliable perturbative predictions for the pion electromagnetic form factor can already be made at a momentum transfer Q of the order of 5 to 10 GeV.
We comment on the results of a complete leading-twist next-to-leading order QCD analysis of the spacelike pion electromagnetic form factor at large-momentum transfer Q. For the asymptotic distribution amplitude, we have examined the sensitivity of the predictions to the choice of the renormalization scale. The results show that reliable perturbative predictions for the pion electromagnetic form factor can already be made at a momentum transfer Q below 10 GeV.
We present the results of a complete leading-twist next-to-leading order (NLO) QCD analysis of the spacelike pion electromagnetic form factor at large momentum transfer Q. We have studied their dependence on the form of the pion distribution amplitude. For a given distribution amplitude, we have examined the sensitivity of the predictions to the choice of the renormalization and factorization scales. Theoretical uncertainty of the LO results related to the renormalization scale ambiguity has been significantly reduced by including the NLO corrections. Adopting the criteria according to which a NLO prediction is considered reliable if, both, the ratio of the NLO to LO contributions and the strong coupling constant are reasonably small, we find that reliable perturbative predictions for the pion electromagnetic form factor with all distribution amplitudes considered can already be made at a momentum transfer Q<10 GeV, with corrections to the LO results being typically of the order of ~ 20%. To check our predictions and to discriminate between the distribution amplitudes, it is necessary to obtain experimental data extending to higher values of Q.
We present QCD results for the exclusive processes $γ{\rm N}\rightarrowγ{\rm N}$ ($\rm N=p,\;n$) at large momentum transfer and compare them to data for the proton. TALK given at DPF meeting, November 10-14, Fermilab.