Twist-four Contributions Research Articles

Pion-photon transition form factor using light-cone sum rules: theoretical results, expectations, and a global-data fit

A global fit to the data from different collaborations (CELLO, CLEO, BaBar) on the pion-photon transition form factor is carried out using light-cone sum rules. The analysis includes the next-to-leading QCD radiative corrections and the twist-four contributions, while the main next-to-next-to-leading term and the twist-six contribution are taken into account in the form of theoretical uncertainties. We use the information extracted from the data to investigate the pivotal characteristics of the pion distribution amplitude. This is done by dividing the data into two sets: one containing all data up to 9 GeV$^2$, whereas the other incorporates also the high-$Q^2$ tail of the BaBar data. We find that it is not possible to accommodate into the fit these BaBar data points with the same accuracy and conclude that it is difficult to explain these data in the standard scheme of OCD.

Pion–Photon Transition Form Factor

An analysis of all available data (CELLO, CLEO, \babar) in the range $[1\div 40]$ GeV$^2$ for the pion-photon transition form factor in terms of light-cone sum rules with next-to-leading-order accuracy is discussed, including twist-four contributions and next-to-next-to-leading order and twist-six corrections---the latter two via uncertainties. The antithetic trend between the \babar data for the $\gamma^*\gamma\pi^0$ and those for the $\gamma^*\gamma\eta(\eta')$ transition is pointed out, emphasizing the underlying antagonistic mechanisms: endpoint enhancement for the first and endpoint-suppression for the second---each associated with pseudoscalar meson distribution amplitudes with distinct endpoint characteristics.

Pion-photon transition: The new QCD frontier

We perform a detailed analysis of all existing data (CELLO, CLEO, BaBar) on the pion-photon transition form factor by means of light-cone sum rules in which we include the NLO QCD radiative corrections and the twist-four contributions. The NNLO radiative correction together with the twist-six contribution are also taken into account in terms of theoretical uncertainties. Keeping only the first two Gegenbauer coefficients $a_2$ and $a_4$, we show that the $1\sigma$ error ellipse of all data up to 9 GeV$^2$ greatly overlaps with the set of pion distribution amplitudes obtained from nonlocal QCD sum rules---within the range of uncertainties due to twist-four. This remains valid also for the projection of the $1\sigma$ error ellipsoid on the $(a_2,a_4)$ plane when including $a_6$. We argue that it is not possible to accommodate the high-$Q^2$ tail of the BaBar data with the same accuracy, despite opposite claims by other authors, and conclude that the BaBar data still pose a challenge to QCD.

Multiple parton scattering in nuclei: Quark–quark scattering

Modifications to quark and antiquark fragmentation functions due to quark–quark (antiquark) double scattering in nuclear medium are studied systematically up to order O ( α s 2 ) in deeply inelastic scattering (DIS) off nuclear targets. At the order O ( α s 2 ) , twist-four contributions from quark–quark (antiquark) rescattering also exhibit the Landau–Pomeranchuk–Migdal (LPM) interference feature similar to gluon bremsstrahlung induced by multiple parton scattering. Compared to quark–gluon scattering, the modification, which is dominated by t-channel quark–quark (antiquark) scattering, is only smaller by a factor of C F / C A = 4 / 9 times the ratio of quark and gluon distributions in the medium. Such a modification is not negligible for realistic kinematics and finite medium size. The modifications to quark (antiquark) fragmentation functions from quark–antiquark annihilation processes are shown to be determined by the antiquark (quark) distribution density in the medium. The asymmetry in quark and antiquark distributions in nuclei will lead to different modifications of quark and antiquark fragmentation functions inside a nucleus, which qualitatively explains the experimentally observed flavor dependence of the leading hadron suppression in semi-inclusive DIS off nuclear targets. The quark–antiquark annihilation processes also mix quark and gluon fragmentation functions in the large fractional momentum region, leading to a flavor dependence of jet quenching in heavy-ion collisions.

Tagging the pion quark structure in QCD

We combine the constraints on the pion quark structure available from perturbative QCD, nonperturbative QCD (nonlocal QCD sum rules and light-cone sum rules) with the analysis of current data on ${F}_{\ensuremath{\pi}\ensuremath{\gamma}{\ensuremath{\gamma}}^{*}}({Q}^{2})$, including recent high-precision lattice calculations of the second moment of the pion's distribution amplitude. We supplement these constraints with those extracted from the renormalon approach by means of the twist-four contributions to the pion distribution amplitude in order to further increase stability with respect to related theoretical uncertainties. We show which regions in the space of the first two nontrivial Gegenbauer coefficients ${a}_{2}$ and ${a}_{4}$ of all these constraints overlap, tagging this way the pion structure to the highest degree possible at present.

A lattice evaluation of four-quark operators in the nucleon

Nucleon matrix elements of various four-quark operators are evaluated in quenched lattice QCD using Wilson fermions. Some of these operators give rise to twist-four contributions to nucleon structure functions. Furthermore, they bear valuable information about the diquark structure of the nucleon. Mixing with lower-dimensional operators is avoided by considering appropriate representations of the flavour group. We find that for a certain flavour combination of baryon structure functions, twist-four contributions are very small.

Estimate of twist-four contributions at smallxBand lowQ2

We present a first study of gluonic twist-four corrections to the deep inelastic structure function ${F}_{2}$ at small x and small ${Q}^{2}.$ The calculations are based upon the double logarithmic approximation of the coupled twist-four evolution equations of the gluonic twist-four operators that are expected to be dominant at small x. We first review the analytical results which are presently available and define the framework of our calculation. In the second part we discuss the connection with DIS diffractive dissociation which can be used to estimate the size of some of the twist-four corrections. In the final part we show, for three different choices of the input distributions, the relative magnitude of the leading-twist and the twist-four contributions.

First study of twist-four contributions at small xB and low Q2

First study of twist-four contributions at small xB and low Q2

Twist-four corrections to deep-inelastic lepton scattering from a polarized spin-one target.

Twist-four contributions to the lowest moment of the quadrupole structure function {ital b}{sub 1}({ital x}), which is measurable in the deep-inelastic scattering of unpolarized electrons from a polarized spin-one target, are calculated in a quark-exchange model of the deuteron. The effect is small since it is proportional to the extent to which the nucleons overlap and represents a 5% correction to the twist-two result at the values of {ital Q}{sup 2} of interest.