Electric Polarizability of Charged Pions from nHYP Four-Point Functions

Abstract

Understanding a hadron's electric and magnetic polarizabilities allows one to access internal structural information. Traditionally, the external field two-point function method has been used to calculate polarizabilities. However, recent work has demonstrated the effectiveness of using four-point functions for computing polarizabilities of charged and neutral hadrons. Our previous study on the electric polarizability of the charged pion used a quenched Wilson action on a lattice with pion mass from 1100 MeV to 370 MeV. In this work, we employ a number of improvements, including a dynamical action (nHYP), smaller pion masses (220 MeV and 315 MeV), and a variable lattice size in order to extrapolate to infinite volume. Preliminary results are presented.

Figures (10)

• Figure 1: Topological diagram of the four-point function for the charged pion. Time moves from right to left. The four-momentum conservation is $p_2 = p_1 + q_1 + q_2$.
• Figure 2: All possible diagrams corresponding to the $\pi^+$ four-point function.
• Figure 3: Normalized four-point functions for diagrams (left to right) (a), (b), and (c) as a function of current separation. Black, blue, magenta, cyan, and green data points represent momenta (0,0,0), (0,0,1), (0,1,1), (1,1,1), and (0,0,2), respectively. The quark zero-momentum wall sources are at $t_0 = 6$ and $t_3 = 41$, with a fixed current insertion at $t_1 = 17$, as indicated by the vertical lines. The diagrams correspond only to Ensemble 1.
• Figure 4: Elastic fits for Ensembles 1, 2, and 3 ($m_\pi = 315$ MeV). The colored curves are the computer-generated fits and the black points represent the raw data. Note that the fits are made on the sum of diagrams (a) and (b) only.
• Figure 5: Form factors for Ensembles 1, 2, and 3 ($m_\pi = 315$ MeV). A z-expansion fit with 2 parameters was used.