Difference between revisions of "Photoproduction & Lattice QCD"

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photocouplings can be extracted. To give an idea of the accuracy of
 
photocouplings can be extracted. To give an idea of the accuracy of
 
the method as it currently stands see the plots below which have
 
the method as it currently stands see the plots below which have
comparison with the measured radiative transition rates.
+
comparison with the measured radiative transition rates. The plots show the transition amplitude (in lattice units) versus the virtuality of the photon, <math>Q^2</math> - the real photon point is <math>Q^2=0</math>.  
  
 
<gallery>
 
<gallery>

Latest revision as of 18:48, 23 February 2009

The basic idea is to assume that the production of mesons has some dominant contribution from diagrams schematically like

Photoprod.jpg

The effect of 'exchanging' a t-channel meson can be parameterised (Regge for example) and tested using pion beam data, but the coupling \langle \gamma M_{i}|M_{f}\rangle (the 'photocoupling') is not known. It is this that we are seeking to compute using lattice QCD for a range of mesons M_{i} and M_{f}.

The same sort of couplings appear in radiative transitions

Radtrans.jpg

In charmonium there are high precision measurements of several radiative transitions between states that are stable to OZI-allowed hadronic decay. Because of this, and the fact that charm quarks are relatively "cheap" computationally, we have begun our lattice studies considering charmonium. The same basic technology, once developed, can be applied to light-quark systems.

The development are testing of the basic technology is described in RadTrans1, in this paper the only combinations of quark and gluon fields considered where {\bar  {\psi }}\Gamma \psi which limited the study to the lightest states with quantum numbers 0^{{-+}},\,0^{{++}},\,1^{{--}},\,1^{{++}},\,1^{{+-}}.

A set of operators suitable to consider excited states and exotics was trialed in Spectrum where they were used to determine a spectrum of charmonium states. This study was performed on quenched lattices which had the simplifying effect of removing the possible multiquark interpretations of exotic states leaving only the hybrid possibility.

In the most recent work RadTrans2, the operators established in Spectrum were used in the construction of three-point functions from which the photocouplings can be extracted. To give an idea of the accuracy of the method as it currently stands see the plots below which have comparison with the measured radiative transition rates. The plots show the transition amplitude (in lattice units) versus the virtuality of the photon, Q^{2} - the real photon point is Q^{2}=0.

The completely new physics here is the measurement of transitions featuring an exotic quantum numbered meson. Results involving the 1^{{-+}} state are shown below.

Turning the 1^{{-+}}\to 1^{{--}}\gamma amplitude into a partial decay width gives something of the order of 100 keV which is of the same order of magnitude as conventional electric dipole transition widths in charmonium. If the folk-wisdom that the same basic patterns observed in heavy-quark systems are duplicated in light quark systems is right, then this bodes well for photoproduction of 1^{{-+}} exotics to the extent that \rho exchange is present.

The paper RadTrans2 contains an extensive phenomenology section that should be accessible to a general meson spectroscopy audience.