arXiv subjects
Publications and source records attributed to Pervez Hoodbhoy.
A systematic gauge-invariant method is used to calculate the rate for an upsilon meson to decay inclusively into a prompt photon. An expansion is made in the quark relative velocity v, which is a small natural parameter for heavy quark systems. Inclusion of these O(v^2) corrections tends to increase the photon rate in the middle z range and to lower it for larger z, a feature supported by the data.
We present a method which, starting directly from QCD, permits a systematic gauge-invariant expansion to be made for all hard processes involving quarkonia in powers of the quark relative velocity, a small natural parameter for heavy quark systems. Our treatment automatically introduces soft gluons in the expansion. Corrections arising from the incorporation of gauge symmetry turn out to be important for decay and fragmentation processes involving $Q \bar{Q}$ systems. The contribution of soft gluons is shown to be of higher order in $v$ and so is neglected for calculations done upto and including O($v^2$).
An effective, low-energy, field theory of s-wave quarkonia, constituent heavy quarks, and gluons is constructed which is manifestly gauge invariant. The interaction Lagrangian has the form of a twist expansion, as typically encountered in hard processes, and involves derivatives of arbitrary order. The parameters in the interaction are related with the non-relativistic wave function, and standard results for $Q\bar{Q}$ inclusive decays and radiative transitions are shown to be easily recovered. The light-cone gluon momentum distribution at very small $x$ is calculated and shown to be uniquely determined by the non-relativistic wave function. The distribution has a part which goes as $x^{-1}logx$, ie. is more singular than the usually assumed $1/x$ behaviour. The fragmentation function for a virtual gluon to inclusively decay into an $η_c$ or $η_b$ is also calculated. We find that the emission of low momentum gluons makes this process quite sensitive to assumptions about the binding of heavy quarks in quarkonia.
A simple quark-diquark model for nucleon and $Λ$ structure is used to calculate leading twist light-cone fragmentation functions for a quark to inclusively decay into P or $Λ$. The parameters of the model are determined by fitting to the known deep-inelastic structure functions of the nucleon. When evolved from the initial to the final $Q^2$ scale, the calculated fragmentation functions are in remarkable agreement (for $z>0.4 $) with those extracted from partially inclusive $ep$ and $e^+ e^-$ experiments at high energies. Predictions are made, using no additional parameters, for longitudinally and transversely polarized quarks to fragment into p or $Λ$.