Speaker
Mr
HyungJoo Kim
(Yonsei University)
Description
Understanding the temperature dependence of the gluon condensate in the purge gauge theory offers a useful picture on the nature of the QCD phase transition. In a recent work[1], we identified the independent dim 6 twist 4 gluon operators$(O_1=D_\beta G^a_{\mu\nu}D_\alpha G^a_{\mu\nu},O_2=D_\mu G^a_{\alpha\mu}D_\nu G^a_{\beta\nu},O_3=D_\beta G^a_{\alpha\mu}D_\nu G^a_{\mu\nu})$ and calculated their renormalization upto one loop order in the pure gauge theory. We found the scale invariant operators are given as follows:
\begin{equation}
\phi_1=\alpha_s^{-9/11}\left\langle O_1\right\rangle ,\\
\phi_{2,3}=\alpha_s^{-(15 \mp \sqrt{17})/44}\left\langle \frac{-653 \pm 21\sqrt{17}}{424}O_1+\frac{1 \mp \sqrt{17}}{8}O_2+O_3\right\rangle.
\end{equation}
Together with the dim 6 scalar operators whose renormalization has been worked out before[2],
our result completes the calculation of renormalization of all the dim 6 gluon operators, hence is a first step toward identifying their mixing and thus a systematic analysis in the operator product expansion (OPE) of heavy quark correlation functions up to dimension 6. After using the equation of motion in the purge gauge theory, only $O_1$ remains nonzero.
As an application, we rewrite the dim 6 scalar and twist 4 operators as $f^{abc}B^a\cdot(B^b \times B^c)$ and $f^{abc}B^a\cdot(E^b \times E^c)$ and estimate their temperature dependence using inputs of dim 4 electric and magnetic condensate extracted from lattice gauge theory. We then improve the previous QCD sum rules for $J/\Psi$ mass near the $T_c$ based on dim 4 operators, by including the contribution of the dim 6 operators to the OPE. We find an enhanced stability in the sum rule and confirm that the $J/\psi$ will undergo an abrupt change in the property across $T_c$.
[1]H.J.Kim and S.H.Lee, arXiv:1503.02280[hep-ph]
[2]S.Narison and R.Tarrach, Phys.Lett.B 125 217 (1983)
| On behalf of collaboration: | NONE |
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Primary author
Mr
HyungJoo Kim
(Yonsei University)
Co-author
Su Houng Lee
(Yonsei University)
