<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>D</mml:mi><mml:msup><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math> scattering and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>χ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>3872</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> in nuclear matter
M. Albaladejo, J. Nieves, Laura Tolós
Abstract
We study the behavior of the ${\ensuremath{\chi}}_{c1}(3872)$, also known as $X(3872)$, in dense nuclear matter. We begin from a picture in vacuum of the $X(3872)$ as a purely molecular $(D{\overline{D}}^{*}\text{-c.c.})$ state, generated as a bound state from a heavy-quark symmetry leading-order interaction between the charmed mesons, and analyze the $D{\overline{D}}^{*}$ scattering $T$ matrix (${T}_{D{\overline{D}}^{*}}$) inside of the medium. Next, we consider also mixed-molecular scenarios and, in all cases, we determine the corresponding $X(3872)$ spectral function and the $D{\overline{D}}^{*}$ amplitude, with the mesons embedded in the dense environment. We find important nuclear corrections for ${T}_{D{\overline{D}}^{*}}$ and the pole position of the resonance, and discuss the dependence of these results on the $D{\overline{D}}^{*}$ molecular component in the $X(3872)$ wave function. These predictions could be tested in the finite-density regime that can be accessed in the future CBM and PANDA experiments at the Facility for Antiproton and Ion Research (FAIR).