Construction of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mi>b</mml:mi><mml:mover accent="true"><mml:mi>u</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mover accent="true"><mml:mi>d</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math> tetraquark states on lattice with NRQCD bottom and HISQ up and down quarks
Protick Mohanta, Subhasish Basak
Abstract
We construct $bb\overline{u}\overline{d}$ states on lattice using non relativistic QCD (NRQCD) action for bottom and highly improved staggered quark (HISQ) action for the light up/down quarks. The NRQCD-HISQ tetraquark operators are constructed for ``bound'' $[bb][\overline{u}\overline{d}]$ and ``molecular'' $[b\overline{u}][b\overline{d}]$ states. Corresponding to these different operators, two different appropriately tuned light quark masses are needed to obtain the desired spectra. We explain this requirement of different ${m}_{u/d}$ in the light of relativized quark model involving Hartree-Fock calculation. The mass spectra of double bottom tetraquark states are obtained on MILC ${N}_{f}=2+1$ Asqtad lattices at three different lattice spacings. Variational analysis has been carried out to obtain the relative contribution of bound and molecular states to the energy eigenstates.