Pion transition form factor at the two-loop level vis-\`a-vis experimental data

We use light-cone QCD sum rules to calculate the pion-photon transition form factor, taking into account radiative corrections up to the next-to-next-to-leading order of perturbation theory. We compare the obtained predictions with all available experimental data from the CELLO, CLEO, and the BaBar Collaborations. We point out that the BaBar data are incompatible with the convolution scheme of QCD, on which our predictions are based, and can possibly be explained only with a violation of the factorization theorem. We pull together recent theoretical results and comment on their significance.Comment: 10 pages, 4 figures, 3 tables. Presented by the first author at Workshop "Recent Advances in Perturbative QCD and Hadronic Physics", 20--25 July 2009, ECT*, Trento (Italy), in Honor of Prof. Anatoly Efremov's 75th Birthday. v2 wrong reference tag removed. v3 Fig. 4 and Ref. [27] correcte

π0→γ∗γ\pi^0\to\gamma^*\gamma transition form factor within Light Front Quark Model

We study the transition form factor of $\pi^0\to\gamma^* \gamma$ as a function of the momentum transfer $Q^2$ within the light-front quark model (LFQM). We compare our result with the experimental data by BaBar as well as other calculations based on the LFQM in the literature. We show that our predicted form factor fits well with the experimental data, particularly those at the large $Q^2$ region.Comment: 11 pages, 4 figures, accepted for publication in PR

Study of pesudoscalar transition form factors within light front quark model

We study the transition form factors of the pesudoscalar mesons ($\pi,\eta$ and $\eta^{\prime}$) as functions of the momentum transfer $Q^2$ within the light-front quark model. We compare our results with the recent experimental data by CELLO, CLEO, BaBar and Belle. By considering the possible uncertainties from the quark masses, we illustrate that our predicted form factors can fit with all the data, including those at the large $Q^2$ regions.Comment: 10 pages, 4 figures, accepted for publication in Phys. Rev.

Hadronic Form Factors: Combining QCD Calculations with Analyticity

I discuss recent applications of QCD light-cone sum rules to various form factors of pseudoscalar mesons. In this approach both soft and hard contributions to the form factors are taken into account. Combining QCD calculation with the analyticity of the form factors, one enlarges the region of accessible momentum transfers.Comment: 12 pages, 3 figures, Talk at the Workshop "Shifmania, Crossing the boundaries: Gauge dynamics at strong coupling", May 14-17,2009, Minneapolis, USA; table entry and reference update

Photon-meson transition form factors of light pseudoscalar mesons

The photon-meson transition form factors of light pseudoscalar mesons $\pi ^{0}$, $\eta$, and $\eta ^{\prime}$ are systematically calculated in a light-cone framework, which is applicable as a light-cone quark model at low $Q^{2}$ and is also physically in accordance with the light-cone pQCD approach at large $Q^{2}$. The calculated results agree with the available experimental data at high energy scale. We also predict the low $Q^{2}$ behaviors of the photon-meson transition form factors of $\pi ^{0}$, $\eta$ and $\eta ^{\prime }$, which are measurable in $e+A({Nucleus})\to e+A+M$ process via Primakoff effect at JLab and DESY.Comment: 22 Latex pages, 7 figures, Version to appear in PR

A Comprehensive Analysis on the Pion-Photon Transition Form Factor Beyond the Leading Fock State

We perform a comprehensive analysis of the pion-photon transition form factor $F_{\pi \gamma}(Q^2)$ involving the transverse momentum corrections with the present CLEO experimental data, in which the contributions beyond the leading Fock state have been taken into consideration. As is well-known, the leading Fock-state contribution dominates of $F_{\pi \gamma}(Q^2)$ at large momentum transfer ($Q^2$) region. One should include the contributions beyond the leading Fock state in small $Q^2$ region. In this paper, we construct a phenomenological expression to estimate the contributions beyond the leading Fock state based on its asymptotic behavior at $Q^2\to0$. Our present theoretical results agree well with the experimental data in the whole $Q^2$ region. Then, we extract some useful information of the pionic leading twist-2 distribution amplitude (DA) by comparing our results of $F_{\pi \gamma}(Q^2)$ with the CLEO data. By taking best fit, we have the DA moments, $a_2(\mu_0^2)=0.002^{+0.063}_{-0.054}$, $a_4(\mu_0^2)=-0.022_{-0.012}^{+0.026}$ and all of higher moments, which are closed to the asymptotic-like behavior of the pion wavefunction.Comment: 25 pages, 7 figures. Typo error correcte

Information on the Pion Distribution Amplitude from the Pion-Photon Transition Form Factor with the Belle and BaBar Data

The pion-photon transition form factor (TFF) provides strong constraints on the pion distribution amplitude (DA). We perform an analysis of all existing data (CELLO, CLEO, BaBar, Belle) on the pion-photon TFF by means of light-cone pQCD approach in which we include the next-to-leading order correction to the valence-quark contribution and estimate the non-valence-quark contribution by a phenomenological model based on the TFF's limiting behavior at both $Q^2\to 0$ and $Q^2\to\infty$. At present, the pion DA is not definitely determined, it is helpful to have a pion DA model that can mimic all the suggested behaviors, especially to agree with the constraints from the pion-photon TFF in whole measured region within a consistent way. For the purpose, we adopt the conventional model for pion wavefunction/DA that has been constructed in our previous paper \cite{hw1}, whose broadness is controlled by a parameter $B$. We fix the DA parameters by using the CELLO, CLEO, BABAR and Belle data within the smaller $Q^2$ region ($Q^2 \leq 15$ GeV$^2$), where all the data are consistent with each other. And then the pion-photon TFF is extrapolated into larger $Q^2$ region. We observe that the BABAR favors $B=0.60$ which has the behavior close to the Chernyak-Zhitnitsky DA, whereas the recent Belle favors $B=0.00$ which is close to the asymptotic DA. We need more accurate data at large $Q^2$ region to determine the precise value of $B$, and the definite behavior of pion DA can be concluded finally by the consistent data in the coming future.Comment: 6 pages, 5 figures. Slightly changed and references update

η−η′\eta-\eta^\prime mixing and the next-to-leading-order power correction

The next-to-leading-order $O(1/Q^4)$ power correction for $\eta\gamma$ and $\eta^\prime\gamma$ form factors are evaluated and employed to explore the $\eta-\eta^\prime$ mixing. The parameters of the two mixing angle scheme are extracted from the data for form factors, two photon decay widths and radiative $J/\psi$ decays. The $\chi^2$ analysis gives the result: $f_{\eta_1}=(1.16\pm0.06)f_\pi, f_{\eta_8}=(1.33\pm0.23)f_\pi, \theta_1=-9^\circ\pm 3^\circ, \theta_8=-21.3^\circ\pm 2.3^\circ$, where $f_{\eta_{1(8)}}$ and $\theta_{1(8)}$ are the decay constants and the mixing angles for the singlet (octet) state. In addition, we arrive at a stringent range for $f_{\eta^\prime}^c:-10$ MeV$\le f_{\eta^\prime}^c\le -4$ MeV.Comment: 23 pages, 9 figures, To be publshied in Phys. Rev.

A New 5 Flavour NLO Analysis and Parametrizations of Parton Distributions of the Real Photon

New, radiatively generated, NLO quark (u,d,s,c,b) and gluon densities in a real, unpolarized photon are presented. We perform three global fits, based on the NLO DGLAP evolution equations for Q^2>1 GeV^2, to all the available structure function F_2^gamma(x,Q^2) data. As in our previous LO analysis we utilize two theoretical approaches. Two models, denoted as FFNS_{CJK}1 & 2 NLO, adopt the so-called Fixed Flavour-Number Scheme for calculation of the heavy-quark contributions to F_2^gamma(x,Q^2), the CJK NLO model applies the ACOT(chi) scheme. We examine the results of our fits by a comparison with the LEP data for the Q^2 dependence of the F_2^gamma, averaged over various x-regions, and the F_2,c^gamma. Grid parametrizations of the parton densities for all fits are provided.Comment: 49 pages, 27 postscript figures; FORTRAN programs available at http://www.fuw.edu.pl/~pjank/param.htm

Distributed Testing of Excluded Subgraphs

We study property testing in the context of distributed computing, under the classical CONGEST model. It is known that testing whether a graph is triangle-free can be done in a constant number of rounds, where the constant depends on how far the input graph is from being triangle-free. We show that, for every connected 4-node graph H, testing whether a graph is H-free can be done in a constant number of rounds too. The constant also depends on how far the input graph is from being H-free, and the dependence is identical to the one in the case of testing triangles. Hence, in particular, testing whether a graph is K_4-free, and testing whether a graph is C_4-free can be done in a constant number of rounds (where K_k denotes the k-node clique, and C_k denotes the k-node cycle). On the other hand, we show that testing K_k-freeness and C_k-freeness for k>4 appear to be much harder. Specifically, we investigate two natural types of generic algorithms for testing H-freeness, called DFS tester and BFS tester. The latter captures the previously known algorithm to test the presence of triangles, while the former captures our generic algorithm to test the presence of a 4-node graph pattern H. We prove that both DFS and BFS testers fail to test K_k-freeness and C_k-freeness in a constant number of rounds for k>4