Search

We discuss $1/Q$ corrections to hard processes in QCD where $Q$ is a large mass parameter like the total energy in $e^+e^-$ annihilation. The main problem we address ourselves to is whether these corrections to different processes (concentrating for definiteness on the Thrust and the Drell-Yan cross section) can be related to each other in a reliable way so that the phenomenology of the $1/Q$ corrections can be developed. We derive first the relation valid to lowest order using both the renormalon and finite-gauge-boson mass techniques to check its independence on the infrared cut- off procedure. We then argue that the $1/Q$ corrections are due to soft gluons which factorize into a universal factor such that the lowest order relations are preserved in higher orders.

We discuss the effects of q, ~' mixing and of the gluon anomaly in the decays q~3n °, q' o3n °, ~¢~y and ~rl' 7. These effects are particularly important for 11' ~ 3n ° in reducing the total rate by about two orders of magnitude from the naive estimate. The decay rates are calculated for various values of the 1], rl' mixing angle (0) and a reasonable fit with experiment is obtained for -20 °~0~ for the 11, analogously for the q'. The mixing between the rl and 11' is characterized by a mixing angle 0 and an analysis based on the Gell-Mann-Okubo quadratic mass formula for broken SU (3) gave an estimate of 0.~ - 10 °. A more recent analysis [ 1 ] allows a value closer to - 20 °. With a view to further testing the above picture, in this paper we will consider decays involving pseudoscalar mesons that are sensitive to the mixing angle, to the gluon anomaly and to the non-vanishing topological charges ( 01 GGI q >, < 01GGI q' ) of the physical q and q' respectively.

When one takes into account that different quarks have unequal masses, five-point functions associated with pentagon graphs with two external gluons (2g) are modified by terms involving quark mass ratios. In this context we prove an exact low energy theorem for the amplitudes (2g) →rjl with r,j,l in the octet of pseudoscalar Goldstone bosons. A possible manifestation of these effects could be an enhancement of processes (2g) →KK¯π over(2g) → ηππ ones as indeed are seen experimentally in ι decays. A contribution to η′ → ηππ is also found.

We point out that neither a softly broken Peccei-Quinn symmetry nor a softly broken supersymmetry per se suffices to insure the finiteness of θ QCD renormalization. This is due to a logarithmic divergence that in general occurs in the higher loop corrections to the gluino mass.

We discuss the constraints imposed by the unitary of the S -matrix on the theory of a closed basonic string propagating in a background consisting of a condensate of the string modes. The equations of motion for some of the low mass modes are thus obtained to all orders in α′ but to second order in a weak field expansion about a flat background.