Possibility of charmoniumlike state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3915</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>χ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mi>P</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> state
Ming-Xiao Duan, Si-Qiang Luo, Xiang Liu, Takayuki Matsuki
Abstract
In this work, we seriously discuss whether $X(3915)$ can be treated as a ${\ensuremath{\chi}}_{c0}(2P)$ state. Based on an unquenched quark model, we give the mass spectrum of the ${\ensuremath{\chi}}_{cJ}(2P)$ states, where there are no free input parameters in our calculation. Our result shows that the mass gap between ${\ensuremath{\chi}}_{c0}(2P)$ and ${\ensuremath{\chi}}_{c2}(2P)$ can reach 13 MeV, which can reproduce the mass difference between $Z(3930)$ and $X(3915)$. Additionally, the calculated masses of ${\ensuremath{\chi}}_{c0}(2P)$ and ${\ensuremath{\chi}}_{c2}(2P)$ are consistent with experimental values of $X(3915)$ and $Z(3930)$, respectively. Besides, giving the mass spectrum analysis to support $X(3915)$ as ${\ensuremath{\chi}}_{c0}(2P)$, we also calculate the width of ${\ensuremath{\chi}}_{c0}(2P)$ with the same framework, which is also consistent with the experimental data of $X(3915)$. Thus, the possibility of charmoniumlike state $X(3915)$ as ${\ensuremath{\chi}}_{c0}(2P)$ state is further enforced.