Two-nucleon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi></mml:math>-wave interactions at the SU(3) flavor-symmetric point with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>≈</mml:mo><mml:msubsup><mml:mi>m</mml:mi><mml:mi>s</mml:mi><mml:mtext>phys</mml:mtext></mml:msubsup></mml:mrow></mml:math>: A first lattice QCD calculation with the stochastic Laplacian Heaviside method
Ben Hörz, Dean Howarth, Enrico Rinaldi, Andrew D. Hanlon, Chia Cheng Chang, Christopher Körber, Evan Berkowitz, John Bulava, M. A. Clark, Wayne Tai Lee, Colin Morningstar, Amy Nicholson, Pavlos Vranas, André Walker-Loud
Abstract
We report on the first application of the stochastic Laplacian Heaviside method for computing multiparticle interactions with lattice QCD to the two-nucleon system. Like the Laplacian Heaviside method, this method allows for the construction of interpolating operators which can be used to construct a set of positive-definite two-nucleon correlation functions, unlike nearly all other applications of lattice QCD to two nucleons in the literature. It also allows for a variational analysis in which optimal linear combinations of the interpolating operators are formed that couple predominantly to the eigenstates of the system. Utilizing such methods has become of paramount importance to help resolve the discrepancy in the literature on whether two nucleons in either isospin channel form a bound state at pion masses heavier than physical, with the discrepancy persisting even in the SU(3)-flavor-symmetric point with all quark masses near the physical strange quark mass. This is the first in a series of papers aimed at resolving this discrepancy. In the present work, we employ the stochastic Laplacian Heaviside method without a hexaquark operator in the basis at a lattice spacing of $a\ensuremath{\approx}0.086$ fm, lattice volume of $L=48a\ensuremath{\approx}4.1$ fm and pion mass ${m}_{\ensuremath{\pi}}\ensuremath{\approx}714$ MeV. With this setup, the observed spectrum of two-nucleon energy levels strongly disfavors the presence of a bound state in either the deuteron or dineutron channel.