Next-to-leading order QCD corrections to ${\chi }_{cJ}{W}^{+}b$ associated production from top-quark decay

We calculate the next-to-leading order QCD corrections to the excited charmonium ${\chi }_{cJ}$ associated with $W^{+}b$ production from top-quark decay. Our results show that detecting the ${\chi }_{c0}$ production from top-quark decay is very difficult, but the ${\chi }_{c1}$ and ${\chi }_{c2}$ productions have the potential to be detected at the LHC. If the prompt ${\chi }_{cJ}$ production from top-quark decay is really detected at the LHC, it will be useful not only for investigating $J/\psi$ production from top-quark decay but also for understanding the heavy quarkonium production mechanism.

Figure 1

Some representative LO and QCD NLO Feynman diagrams for the $t\to {\chi }_{cJ}+W^{+}+b$ decay processes. Where (a) and (b) are tree level diagrams, (c)–(j) are part loop diagrams, (k)–(l) are part counterterms diagrams and (m)–(p) are part real gluon emission diagrams for $t\to {\chi }_{cJ}+W^{+}+b$ decay process.

Figure 2

The IR and Coulomb singularity structures in the NLO QCD calculations for the $t\to {\chi }_{cJ}+W^{+}+b$ decay processes.

Figure 3

The ratio of ${\mathrm{\Gamma }}_{{}^3{P}_J^{(1)}}$ to ${\mathrm{\Gamma }}_{{}^3{S}_1^{(8)}}$ at NLO as a function of the matrix element ratio $r$ for the processes $t\to {\chi }_{cJ}+W^{+}+b$.

Figure 4

The ${\mu }_{\mathrm{\Lambda }}$ dependence of the ${\chi }_{c0}$ NLO total decay width, the ${}^3{S}_1^{(8)}$- and ${}^3{P}_0^{(1)}$-channel decay widths.

Figure 5

Branching ratio of the decay processes $t\to {\chi }_{cJ}+W^{+}+b$ at NLO as a function of the matrix element ratio $r$.

Figure 6

The ratio $R_{{\chi }_c}=\frac{{\mathrm{\Gamma }}_{{\chi }_{c2}}}{{\mathrm{\Gamma }}_{{\chi }_{c1}}}$ at the NLO as a function of the matrix element ratio $r$.