#
APS April Meeting 2011

## Volume 56, Number 4

##
Saturday–Tuesday, April 30–May 3 2011;
Anaheim, California

### Session Y4: QCD in Nuclear Physics

1:30 PM–3:18 PM,
Tuesday, May 3, 2011

Room: Garden 4

Sponsoring
Units:
GHP DNP

Chair: Doug Higinbotham, Thomas Jefferson National Accelerator Facility

Abstract ID: BAPS.2011.APR.Y4.2

### Abstract: Y4.00002 : Abelian anomaly and neutral pion production*

2:06 PM–2:42 PM

Preview Abstract
Abstract

####
Author:

Craig Roberts

(Physics Division, Argonne National Laboratory)

The process $\gamma^\ast \gamma \to \pi^0$ is fascinating because
in order to explain the associated transition form factor within
the Standard Model on the full domain of momentum transfer, one
must combine, using a single internally-consistent framework, an
explanation of the essentially nonperturbative Abelian anomaly
with the features of perturbative QCD. The case for attempting
this has received a significant boost with the publication of
data from the BaBar Collaboration [Phys.\ Rev.\ D {\bf 80},
052002 (2009)] because, while they agree with earlier experiments
on their common domain of squared-momentum-transfer [CELLO - Z.\
Phys.\ C {\bf 49}, 401 (1991); CLEO - Phys.\ Rev.\ D {\bf 57},
33 (1998)], the BaBar data are unexpectedly far \emph{above} the
prediction of perturbative QCD at larger values of $Q^2$.
I will elucidate the sensitivity of the $\gamma^\ast \gamma \to
\pi^0$ transition form factor, $G_{\gamma^\ast \gamma \pi}(Q^2)$,
to the pointwise behaviour of the interaction between quarks; and
use existing Dyson-Schwinger equation calculations of this and
the kindred $\gamma^\ast \gamma^\ast \to \pi^0$ form factor to
characterize the $Q^2$-dependence of $G_{\gamma^\ast \gamma \pi}
(Q^2)$. It will become apparent that in fully-self-consistent
treatments of pion: static properties; and elastic and transition
form factors, the asymptotic limit of the product $Q^2
G_{\gamma^\ast\gamma \pi^0}(Q^2)$, which is determined \emph{a
priori} by the interaction employed, is not exceeded at any
finite value of spacelike momentum transfer: the product is a
monotonically-increasing concave function.
Studies exist which interpret the BaBar data as an indication
that the pion's distribution amplitude, $\phi_\pi(x)$, deviates
dramatically from its QCD asymptotic form, indeed, that
$\phi_\pi(x)=\,$constant, or is at least flat and nonvanishing at
$x=0,1$. I will explain that such a distribution amplitude
characterises an essentially-pointlike pion; and show that, when
used in a fully-consistent treatment, it produces results for
pion elastic and transition form factors that are in striking
disagreement with experiment. A bound-state pion with a
pointlike component will produce the hardest possible form
factors; i.e., form factors which become constant at large-$Q^2$.
On the other hand, QCD-based studies produce soft pions, a
valence-quark distribution amplitude for the pion that vanishes
as $\sim (1-x)^2$ for $x\sim 1$, and results that agree well with
the bulk of existing data.
It can thus be argued that the large-$Q^2$ BaBar data is
inconsistent with QCD and also inconsistent with a vector
current-current contact interaction; and hence that the large-
$Q^2$ data reported by BaBar is not a true representation of the
$\gamma^\ast\gamma \to \pi^0$ transition form factor.

*This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, contract no. DE-AC02-06CH11357.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.APR.Y4.2