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Volume 256 - 34th annual International Symposium on Lattice Field Theory (LATTICE2016) - Hadron Spectroscopy and Interactions
Luescher's finite volume test for two-baryon systems with attractive interactions
S. Aoki,* T. Doi, T. Iritani for HAL QCD Collaboration
*corresponding author
Full text: pdf
Pre-published on: 2016 December 27
Published on: 2017 March 24
For the attractive interaction,
the L¥"uscher's finite volume formula gives the phase shift at negative squared moment $k^2<0$ for the ground state in the finite volume, which corresponds to the analytic continuation of the phase shift at $k^2<0$ in the infinite volume.
Using this fact, we reexamine behaviors of phase shifts at $k^2 <0$ obtained directly from plateaux of effective energy shifts in previous lattice studies for two nucleon systems on various volumes.
We have found that data, based on which existences of the bound states are claimed, show singular behaviors of the phase shift at $k^2<0$, which seem incompatible with smooth behaviors predicted by the effective range expansion.
This, together with the fake plateau problem for the determination of the energy shift,
brings a serious doubt on existences of the $NN$ bound states claimed in previous lattice studies
at heavier pion masses.
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