Chiral Corrections to Nucleon Two- and Three-Point Correlation Functions

Abstract

We consider multi-particle contributions to nucleon two- and three-point functions from the perspective of chiral dynamics. Lattice nucleon interpolating operators, which have definite chiral transformation properties, can be mapped into chiral perturbation theory. Using the most common of such operators, we determine pion-nucleon and pion-delta couplings to nucleon two- and three-point correlation functions at leading order in the low-energy expansion. The couplings of pions to nucleons and deltas in two-point functions are consistent with simple phase-space considerations, in accordance with the Lehmann spectral representation. An argument based on available phase space on a torus is utilized to derive the scaling of multiple-pion couplings. While multi-pion states are indeed suppressed, this suppression scales differently with particle number compared to that in infinite volume. For nucleon three-point correlation functions, we investigate the axial-vector current at vanishing momentum transfer. The effect of pion-nucleon and pion-delta states on the extraction of the nucleon axial charge is assessed. We show that couplings to finite volume multi-particle states could potentially lead to overestimation of the axial charge. Hence pion-nucleon excited states cannot explain the trend seen in lattice QCD calculations of the nucleon axial charge.

18 pages, 3 figures, v.2 comparison with arXiv:1503.03649 added, v.3 phase-space argument corrected

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Cited by in corpus (20)

• Nucleon axial structure from lattice QCD
• Iso-vector axial form factors of the nucleon in two-flavour lattice QCD
• Nucleon axial, scalar, and tensor charges using lattice QCD at the physical pion mass
• $N\pi$-state contamination in lattice calculations of the nucleon axial form factors
• Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors
• The pion-nucleon sigma term from lattice QCD
• Nucleon-pion-state contribution in lattice calculations of the nucleon charges $g_A,g_T$ and $g_S$
• Nucleon-pion-state contribution to nucleon two-point correlation functions
• Low energy scattering phase shifts for meson-baryon systems
• Axial form factors of the octet baryons in a covariant quark model
• On the effect of excited states in lattice calculations of the nucleon axial charge
• Chiral perturbation theory and nucleon-pion-state contaminations in lattice QCD
• Toward $N$ to $N\pi$ matrix elements from lattice QCD
• Excited states in nucleon structure calculations
• $N\pi$-state contamination in lattice calculations of the nucleon electromagnetic form factors
• Three-particle $N\pi \pi$ state contribution to the nucleon two-point function in lattice QCD
• Detailed analysis of excited state systematics in a lattice QCD calculation of $g_A$
• Excited-state effects in nucleon structure on the lattice using hybrid interpolators
• Nucleon form factors and couplings with $N_{\mathrm{f}}=2+1$ Wilson fermions
• Nucleon-pion-state contributions in the determination of the nucleon axial charge