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Register a new userRole of chiral symmetry in the nucleon excitation spectrum
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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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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.
We study hadron correlators upon artificial restoration of the spontaneously broken chiral symmetry. In a dynamical lattice simulation we remove the lowest lying eigenmodes of the Dirac operator from the valence quark propagators and study evolution of the hadron masses obtained. All mesons and baryons in our study, except for a pion, survive unbreaking the chiral symmetry and their exponential decay signals become essentially better. From the analysis of the observed spectroscopic patterns we conclude that confinement still persists while the chiral symmetry is restored. All hadrons fall into different chiral multiplets. The broken U(1)_A symmetry does not get restored upon unbreaking the chiral symmetry. We also observe signals of some higher symmetry that includes chiral symmetry as a subgroup. Finally, from comparison of the Delta - N splitting before and after unbreaking of the chiral symmetry we conclude that both the color-magnetic and the flavor-spin quark-quark interactions are of equal importance.
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 a precise lattice QCD calculation of the contribution to the neutron-proton mass splitting arising from strong isospin breaking, $m_n-m_p|_{QCD}=2.32pm0.17$ MeV. We also determine $m_{Xi^-} - m_{Xi^0}|_{QCD} = 5.44pm0.31$ MeV. The calculation is performed at three values of the pion mass, with several values of the quark mass splitting and multiple lattice volumes, but only a single lattice spacing and an estimate of discretization errors. The calculations are performed on the anisotropic clover-Wilson ensembles generated by the Hadron Spectrum Collaboration. The omega-baryon mass is used to set the scale $a_t^{-1}=6111pm127$ MeV, while the kaon masses are used to determine the value of the light-quark mass spitting. The nucleon mass splitting is then determined as a function of the pion mass. We observe, for the first time, conclusive evidence for non-analytic light quark mass dependence in lattice QCD calculations of the baryon spectrum. When left as a free parameter, the fits prefer a nucleon axial coupling of $g_A=1.24(56)$. To highlight the presence of this chiral logarithm in the nucleon mass splitting, we also compute the isospin splitting in the cascade-baryon system which is less sensitive to chiral dynamics. Finally, we update the best lattice QCD determination of the CP-odd pion-nucleon coupling that would arise from a non-zero QCD theta-term, $bar{g}_0 / (sqrt{2}f_pi) = (14.7pm1.8pm1.4) cdot 10^{-3} bar{theta}$. The original lattice QCD correlation functions, analysis results and extrapolated quantities are packaged in HDF5 files made publicly available including a simple Python script to access the numerical results, construct effective mass plots along with our analysis results, and perform the extrapolations of various quantities determined in this work.
We investigate general properties of the eigenvalue spectrum for improved staggered quarks. We introduce a new chirality operator $[gamma_5 otimes 1]$ and a new shift operator $[1 otimes xi_5]$, which respect the same recursion relation as the $gamma_5$ operator in the continuum. Then we show that matrix elements of the chirality operator sandwiched between two eigenstates of the staggered Dirac operator are related to those of the shift operator by the Ward identity of the conserved $U(1)_A$ symmetry of staggered fermion actions. We perform a numerical study in quenched QCD using HYP staggered quarks to demonstrate the Ward identity. We introduce a new concept of leakage patterns which collectively represent the matrix elements of the chirality operator and the shift operator sandwiched between two eigenstates of the staggered Dirac operator. The leakage pattern provides a new method to identify zero modes and non-zero modes in the Dirac eigenvalue spectrum. This method is as robust as the spectral flow method but requires much less computing power. Analysis using a machine learning technique confirms that the leakage pattern is universal, since the staggered Dirac eigenmodes on normal gauge configurations respect it. In addition, the leakage pattern can be used to determine a ratio of renormalization factors as a by-product. We conclude that it might be possible and realistic to measure the topological charge $Q$ using the Atiya-Singer index theorem and the leakage pattern of the chirality operator in the staggered fermion formalism.
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