Effects of Screening on Quark-Antiquark Cross Sections in Quark-Gluon Plasma

Lowest-order cross sections for $q\bar q$ production and annihilation can be approximately corrected for higher-order QCD effects by using a corrective $K$-factor. For energies where quark masses cannot be ignored, the $K$-factor is dominated by the wave function distortion arising from the initial- or final-state interaction between the quark and the antiquark. We evaluate this $K$-factor for $q \bar q$ production and annihilation in a quark-gluon plasma by taking into account the effects of Debye screening through a color-Yukawa potential. We present the corrective $K$-factor as a function of dimensionless parameters which may find applications in other systems involving attractive or repulsive Yukawa interactions. Prominent peaks of the $K$-factor occur for an attractive $q$-$\bar q$ color-Yukawa interaction with Debye screening lengths of 0.835 and 3.23 times the Bohr radius, corresponding to two lowest $s$-wave $q\bar q$ bound states moving into the continuum to become $q\bar q$ resonances as the Debye screening length decreases. These resonances, especially the $c\bar c$ and the $b \bar b$ resonances, may be utilized to search for the quark-gluon plasma by studying the systematics of the temperature dependence of heavy-quark pair production just above the threshold.