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The discrepancy between the PQCD calculation and the CLEO data for$\chi_{c1}\to \gamma V$ ($V=\rho^0,\,\omega,\,\phi$) stimulates our interest inexploring extra mechanism of $\chi_{c1}$ decay. In this work, we apply animportant non-perturbative QCD effect, i.e., hadronic loop mechanism, to study$\chi_{c1}\to \gamma V$ radiative decay. Our numerical result shows that thetheoretical results including the hadronic loop contribution and the PQCDcalculation of $\chi_{c1}\to \gamma V$ are consistent with the correspondingCLEO data of $\chi_{c1}\to \gamma V$. We expect further experimentalmeasurement of $\chi_{c1}\to \gamma V$ at BES-III, which will be helpful totest the hadronic loop effect on $\chi_{c1}$ decay.

Long-distant contribution and $\chi_{c1}$ radiative decays to light vector meson