Bled Workshops in Physics Vol. 14, No. 1 p. 50
Charmonium-like states and K* resonances from lattice QCD
Sasa Prelovseka'b
a Jozef Stefan Institute, Jamova 39,1000 Ljubljana, Slovenia
b Department of Physics, University of Ljubljana, Jadranska 19,1000 Ljubljana, Slovenia
Abstract. I presented the first evidence for X(3872) from lattice QCD, the first search for Z+ (3900) and the first extraction of K* (892) strong decay width.
The charmonium-like state X(3872) with JPC = 1++ has never been unambigously identified from the lattice, since it was not established in addition to the discrete scattering states like DD*. These should namely appear as energy levels with the same quantum number JPC = 1++ and are particularly important as X(3872) lies almost on top of DD* threshold. In the simulation [1] we established X(3872) with I = 0 in addition to all the nearby DD* and J/^ w scattering states for the first time. We found large and negative DD* scattering length, which agrees with the presence of a very shallow bound state X(3872) in view of the Levinson's theorem. We did not find X(3872) in the I = 1 channel in our simulation with exact isospin.
We performed the first lattice QCD search for manifestly exotic Zc(3900) [2]. During 2013, the experiments BESIII, Belle and CLEOc reported a discovery of Z+ (3900) in the decay to J/^ n+, while J and P are experimentally unknown. We simulated the most popular channel with JPC = 1+ and I = 1, and we did not find a candidate for Z+ (3900). Instead, we only found discrete scattering states DD * and J/^ n, which inevitably have to be present in a dynamical QCD. The possible reasons for not finding Z+ may be that its quantum numbers are not 1 + or that the employed interpolating fields were not diverse enough. A simulation with additional interpolating fields will be required for a more conclusive result.
The simulation of Kn scattering in p wave with I = 1/2 was aimed at calculating the scattering phase shift [3]. This was determined from each energy level using Luscher's relation, where we simulated scattering system with three choices of total momenta P = 0, ez, (ex+ey).TheBreitWignertypefitofthe resulting phase shift lead the mass and the decay width (or rather the K* —» Kn) coupling that agrees with the experimental values within the errors. This presents the first lattice determination of the K* (892) strong decay width.
References
1.	Sasa Prelovsek and Luka Leskovec, arXiv:1307.5172.
2.	Sasa Prelovsek and Luka Leskovec, arXiv:1308.2097.
3.	Sasa Prelovsek, Luka Leskovec, C.B. Lang and Daniel Mohler, Phys. Rev. D88 (2013) 054508, arXiv:1307.0736.