Lattice operators for scattering of particles with spin

Abstract

We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give the consistent operators for PN, PV, VN and NN scattering, where P, V and N denote pseudoscalar, vector and nucleon. Explicit expressions for operators are given for all irreducible representations at lowest two relative momenta. Each hadron has a good helicity in the first method. The hadrons are in a certain partial wave L with total spin S in the second method. These enable the physics interpretations of the operators obtained from the general projection method. The correct transformation properties of the operators in all three methods are proven. The total momentum of two hadrons is restricted to zero since parity is a good quantum number in this case.

arXiv comment29 pages, updated to match the version published by JHEP. The relation between partial-wave and helicity operators is now provided (Eq. 4.13) and proved (Appendix D). Discussions on the applicability of the constructed operators and higher partial-waves have been extended

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Cited by in corpus (16)

• Signature of a doubly charm tetraquark pole in $D{D}^{\ast }$ scattering on the lattice
• $P$-wave $\pi \pi$ scattering and the $\rho$ resonance from lattice QCD
• Dynamically-coupled partial-waves in $\rho \pi$ isospin-2 scattering from lattice QCD
• Nucleon-$J/\psi$ and nucleon-${\eta }_c$ scattering in $P_c$ pentaquark channels from LQCD
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: The $\rho$-resonance
• P-wave nucleon-pion scattering amplitude in the $\Delta (1232)$ channel from lattice QCD
• Toward $N$ to $N\pi$ matrix elements from lattice QCD
• Light and strange vector resonances from lattice QCD at physical quark masses
• Investigation of pion-nucleon contributions to nucleon matrix elements
• Lattice study of $cc\bar{u}\bar{s}$ tetraquark channel in $D^{(\ast )}{D}_s^{(\ast )}$ scattering
• Physical-mass calculation of $\rho (770)$ and $K^{\ast }(892)$ resonance parameters via $\pi \pi$ and $K\pi$ scattering amplitudes from lattice QCD
• Charmoniumlike Channels $1^{+}$ with Isospin $1$ from Lattice and Effective Field Theory
• Decay properties of light $1^{-+}$ hybrids
• Construction of general $N$-body lattice operators with arbitrary momenta
• Operators for scattering of particles with spin
• $J/\psi$ -nucleon scattering in $P_c^{+}$ pentaquarks channel