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Register a new userNucleon-Nucleon Scattering Parameters in the Limit of SU(3) Flavor Symmetry
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The scattering lengths and effective ranges that describe low-energy nucleon-nucleon scattering are calculated in the limit of SU(3)-flavor symmetry at the physical strange-quark mass with Lattice Quantum Chromodynamics. The calculations are performed with an isotropic clover discretization of the quark action in three volumes with spatial extents of L sim 3.4 fm, 4.5fm and 6.7 fm, and with a lattice spacing of b sim 0.145 fm. With determinations of the energies of the two-nucleon systems (both of which contain bound states at these up and down quark masses) at rest and moving in the lattice volume, Luschers method is used to determine the low-energy phase shifts in each channel, from which the scattering length and effective range are obtained. The scattering parameters, in the 1S0 channel are found to be m_pi a^(1S0) = 9.50^{+0.78}_{-0.69}^{+1.10}_{-0.80} and m_pi r^(1S0) = {4.61^{+0.29}_{-0.31}^{+0.24}_{-0.26}, and in the 3S1 channel are m_pi a^(3S1) = 7.45^{+0.57}_{-0.53}^{+0.71}_{-0.49} and m_pi r^(3S1) = 3.71^{+0.28}_{-0.31}^{+0.28}_{-0.35}. These values are consistent with the two-nucleon system exhibiting Wigners supermultiplet symmetry, which becomes exact in the limit of large-N_c. In both spin channels, the phase shifts change sign at higher momentum, near the start of the t-channel cut, indicating that the nuclear interactions have a repulsive core even at the SU(3)-symmetric point.
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The binding energies of a range of nuclei and hypernuclei with atomic number A <= 4 and strangeness |s| <= 2, including the deuteron, di-neutron, H-dibaryon, 3He, Lambda 3He, Lambda 4He, and Lambda Lambda 4He, are calculated in the limit of flavor-SU(3) symmetry at the physical strange quark mass with quantum chromodynamics (without electromagnetic interactions). The nuclear states are extracted from Lattice QCD calculations performed with n_f=3 dynamical light quarks using an isotropic clover discretization of the quark-action in three lattice volumes of spatial extent L ~ 3.4 fm, 4.5 fm and 6.7 fm, and with a single lattice spacing b ~ 0.145 fm.
The origin of the low-lying nature of the $N$*(1440), or Roper resonance, has been the subject of significant interest for many years, including several investigations using lattice QCD. The majority of lattice studies have not observed a low-lying excited state energy level in the region of the Roper resonance. However, it has been claimed that chiral symmetry could play an important role in our understanding of this resonance. The purpose of this study is to systematically examine the role of chiral symmetry in the low-lying nucleon spectrum by directly comparing the clover and overlap fermion actions. To ensure any differences in results are attributable to the choice of fermion action, simulations are performed on the same set of gauge field configurations at matched pion masses. Correlation matrix techniques are employed to determine the excitation energy of the first positive-parity excited state for each action. The clover and overlap actions show a remarkable level of agreement. We do not find any evidence that fermion action chiral symmetry plays a significant role in understanding the Roper resonance on the lattice.
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Previous extrapolations of lattice QCD results for the nucleon mass to the physically relevant region of small quark masses, using chiral effective field theory, are extended and expanded in several directions. A detailed error analysis is performed. An approach with explicit delta(1232) degrees of freedom is compared to a calculation with only pion and nucleon degrees of freedom. The role of the delta(1232) for the low-energy constants of the latter theory is elucidated. The consistency with the chiral perturbation theory analysis of pion-nucleon scattering data is examined. It is demonstrated that this consistency can indeed be achieved if the delta(1232) dominance of the P-wave pion-nucleon low-energy constant c3 is accounted for. Introduction of the delta(1232) as an explicit propagating degree of freedom is not crucial in order to describe the quark-mass dependence of the nucleon mass, in contrast to the situation with spin observables of the nucleon. The dependence on finite lattice volume is shown to yield valuable additional constraints. What emerges is a consistent and stable extrapolation scheme for pion masses below 0.6 GeV.
We present the first lattice-QCD calculation of the nucleon isovector unpolarized parton distribution functions (PDFs) at the physical-continuum limit using Large-Momentum Effective Theory (LaMET). The lattice results are calculated using ensembles with multiple sea pion masses with the lightest one around 135~MeV, 3 lattice spacings $ain[0.06,0.12]$~fm, and multiple volumes with $M_pi L$ ranging 3.3 to 5.5. We perform a simultaneous chiral-continuum extrapolation to obtain RI/MOM renormalized nucleon matrix elements with various Wilson-link displacements in the continuum limit at physical pion mass. Then, we apply one-loop perturbative matching to the quasi-PDFs to obtain the lightcone PDFs. We find the lattice-spacing dependence to be much larger than the dependence on pion mass and lattice volume for these LaMET matrix elements. Our physical-continuum limit unpolarized isovector nucleon PDFs are found to be consistent with global-PDF results.
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