Seminar über aktuelle Frage der theoretischen Kernphysik

14.10.14 16:15

Light quark mass dependence and finite volume effects for the $\bm{X(3872)}$ in an effective field theory

Max Jansen, Darmstadt

The quark mass and volume dependence of hadrons are an important input for lattice calculations. We investigate the light quark mass dependence of the binding energy of the $X(3872)$ and the $\bar{D}^0D^{*0}$ scattering length in the $C=+1$ channel to next-to-leading order in an effective field theory for the $X$ (XEFT) where pion interactions are perturbative. At this order, the quark mass dependence is determined by a quark mass-dependent contact interaction in addition to the one-pion exchange. Using naturalness arguments to constrain unknown parameters, we find a moderate sensitivity of the binding energy for quark masses up to twice the physical value while the scattering length is more sensitive. Recent simulations for the $X$ are performed on lattices with spatial box lengths being small compared to the typical length scale of the $\bar{D}^0D^{*0}$ system. Finite volume corrections are hence essential in order to make reliable predictions for observables of the $X$. Preliminary results for shifts of the the binding energy of the $X$ in a finite volume are given in a detailed outlook.

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