Friday, July 13, 2012

1207.3073 (Yan-Qing Ma)

General Form of $s$, $t$, $u$ Symmetric Polynomial and Heavy Quarkonium
physics
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Yan-Qing Ma
Induced by three gluons symmetry, $s$, $t$, $u$ symmetric expressions are widely involved in collider physics, especially in heavy quarkonium physics. In this work we study general form of $s$, $t$, $u$ symmetric polynomials, and find that they can be expressed as polynomials where the symmetry is manifest. The general form is then used to simplify expressions which asymptotically reduces the length of original expression to one-sixth. Based on the general form, we reproduce the exact differential cross section of $J/\psi$ hadron production at leading order in $v^2$ up to four unknown constant numbers by simple analysis. Furthermore, we prove that differential cross section at higher order in $v^2$ is proportional to that at leading order. This proof explains the proportion relation at next-to-leading order in $v^2$ found in previous work and generalizes it to all order.
View original: http://arxiv.org/abs/1207.3073

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