Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $P$-wave charmonium annihilation into two photons $\chi_{c0,
  c2}\rightarrow \gamma\gamma$ with high-order QCD corrections   In this paper, we present a new analysis on the $P$-wave charmonium
annihilation into two photons up to next-to-next-to-leading order (NNLO) QCD
corrections by using the principle of maximum conformality (PMC). The
conventional perturbative QCD prediction shows strong scale dependence and
deviates largely from the BESIII measurements. After applying the PMC, we
obtain a more precise scale-invariant pQCD prediction, which also agrees with
the BESIII measurements within errors, i.e.
$R={\Gamma_{\gamma\gamma}(\chi_{c2})}
/{\Gamma_{\gamma\gamma}(\chi_{c0})}=0.246\pm0.013$, where the error is for
$\Delta\alpha_s(M_\tau)=\pm0.016$. By further considering the color-octet
contributions, even the central value can be in agreement with the data. This
shows the importance of a correct scale-setting approach. We also give a
prediction for the ratio involving $\chi_{b0, b2} \to\gamma\gamma$, which could
be tested in future Belle II experiment.

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The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc