Complete Study of Hadroproduction of a Υ\Upsilon Meson Associated with a Prompt J/ψJ/\psi

We present the first complete study of $\Upsilon$ and prompt $J/\psi$ production from single-parton scattering, including the complete $\mathcal{O}(\alpha_S^6)$ color-singlet contribution, the $\mathcal{O}(\alpha_S^2\alpha^2)$ electroweak contribution, the complete nonrelativistic S-wave and P-wave color-octet contribution as well as the feeddown contribution. Our study was motivated by the recent evidence reported by D0 Collaboration of prompt $J/\psi$ and $\Upsilon$ simultaneous production at the Tevatron. With our complete evaluation, we are able to refine the determination of the double parton scattering contribution made by D0 Collaboration. We find that the effective cross section characterizing the importance of double-parton scatterings is $\sigma_{\rm eff}\le 8.2$ mb at $68\%$ confidence level from the D0 measurement.Comment: 11 pages, 4 figures, 4 tables; v2: journal version, update the references and fix a few typo

Feynman Rules for the Rational Part of One-loop QCD Corrections in the MSSM

The complete set of Feynman rules for the rational part R of QCD corrections in the MSSM are calculated at the one-loop level, which can be very useful in the next-to-leading order calculations in supersymmetric models. Our results are expressed in the 't Hooft-Veltman regularization scheme and in the Four Dimensional Helicity scheme with non-anticommutating and anticommutating $\gamma_5$ strategies.Comment: version for publication, 50 pages, 6 figure

Test elements, retracts and automorphic orbits

Let $A_2$ be a free associative or polynomial algebra of rank two over a field $K$ of characteristic zero. Based on the degree estimate of Makar-Limanov and J.-T.Yu, we prove: 1) An element $p \in A_2$ is a test element if $p$ does not belong to any proper retract of $A_2$; 2) Every endomorphism preserving the automorphic orbit of a nonconstant element of $A_2$ is an automorphism.Comment: 11 page