A new approach for Delta form factors

Abstract

Abstract.We discuss a new approach to reducing excited state contributions from two-and three-point correlation functions in lattice simulations. For the purposes of this talk, we focus on the ∆(1232) resonance and discuss how this new method reduces excited state contamination from two-point functions and mention how this will be applied to three-point functions to extract hadronic form factors. 11.15.Ha,12.38.Gc,13.40.Gp,14.20.Gk The calculation of the electromagnetic form factors for mesons and baryons is crucial to understanding the structure of hadronic states in QCD. However, they are notoriously difficult to both measure experimentally as well as calculate theoretically due to the complications that arise from the strong interactions. In the case of the ∆(1232) resonance, the form factors themselves are not currently experimentally accessible, although two of the form factors in the static limit are known (the charge) or measured to some degree (the magnetic dipole moment). For the nucleon, experimental results do exist for the form factors as a function of the momentum transfer. This makes a calculation of the nucleon form factors both a check of methodology as well as of QCD, and allows us to be confident that lattice results for the ∆ form factors are reasonable. PACS:The electromagnetic form factors of the ∆ are encoded in the matrix elementwhere u α is a Rarita-Schwinger vector-spinor describing the external ∆, and J µ = ∑ qq γ µ q is the vector current. The Lorentz structure of Γ is given, for example, in [1], and has four form factors F * 1,2,3,4 (Q 2 ) that are functions of Q 2 = −(p ′ − p) 2 alone. These form factors give rise, in the limit Q 2 → 0, to the electric charge, magnetic dipole moment, electric quadrupole moment, and magnetic octupole moment of the ∆.Of these moments, the charge is of course known, and from the PDG [2], we havewhere we have added all of the errors (including theoretical) in quadrature just to get an idea for how well these are determined experimentally. Thus, it is essential even for this simple quantity to have a well-determined lattice result. Some unquenched results were obtained using the form factor approach in [3] and using a background field technique [4], but there are several difficulties that arise in these different methods. For this work, we will focus on the difficulties with the form factor approach. These are determined by calculating the 3-point correlator:where FT is the Fourier Transform of the correlator, and χ is some appropriate interpolating operator for the ∆. In the large time limit t f ≫ t ≫ t i :Here we have schematically written this so that Z contains various overlap factors of the form 0|χ|∆ as well as other kinematic factors that are known. The dots denote contributions from excited states that are generally ignored.

Statistics of baryon correlation functions in lattice QCD

“…In addition, this method also has similarities to the generalized pencil-of-functions method introduced to LQCD in Ref. [56], where correlation functions involving shifted source and sink times are combined in a variational basis. In the generalized pencil-of-functions approach, shifted source and sink times have primarily been investigated to reduce excited-state contamination rather than StN improvement.…”

Baryon-baryon interactions and spin-flavor symmetry from lattice quantum chromodynamics

“…(15), it is clear that a linear combination of the two correlation functions can be used to remove the excited-state contamination of the lowest lying state at earlier times. Various realizations of this approach are the Matrix Prony [90,91] and the GPoF [92][93][94] methods. Alternatively, a correlated χ-squared function can be formed to fit directly to single or two-exponential forms, with the correlations both in time and between the different source and sink structures accounted for.…”

Construction and Analysis of Two Baryon Correlation functions

“…In the above I have generalized the method to the case of a matrix of correlators as well as established the connection to the creation and annihilation operators of the underlying quantum field theory. This connection allows for use of the obtained eigenvectors and projection operators with the analysis of three point functions for extracting hadronic matrix elements [9].…”