3+1 transverse lattice: baryons

Calculations of baryons states using the transverse lattice method. During the summer of 2003, two Geneva College students, Joe Berg and Justin Lambright, worked on the baryon calculation; see a summary of activities, PDF format, and Postscript

Assignment of multiplets associated with the 2 dimensional lattice

Multiplets are as follows:

In the following P_1 and P_2 are reflections, R is a 90° rotation, and E is the identity.
Note that: P_2 = P_1 R^2 and R^2 = P_1 P_2.
A blank means that the state remains indefinite under the associated symmetry.

  group   |             Multiplet number                        
  element | 0    19   20   21   22   23   24   25   26
 ---------|---------------------------------------------
  E       | 1    1    1    1    1    1    1    1    1
  P_1     |          
  P_2     |                          z^2  z^6
  R^2     |      z^6  z^2  z^2  z^6            
          |                                                         
  P_1 R   |                                    z^2  z^6
  R       |      z^7  z    z^5  z^3
  R^3     |      z^5  z^3  z^7  z
  P_1 R^3 |          
 -------------------------------------------------------
  J_z     |      1/2  -1/2 3/2  -3/2

  where z = exp(i pi/4)

  The multiplets have the following use:

  23       P_perp = (c,0),   P_2 = +1
  24       P_perp = (c,0),   P_2 = -1
  25       P_perp = (c,c), P_1 R = +1
  26       P_perp = (c,c), P_1 R = -1

Starting couplings are from the m₀²=1.0 datum from lll_10.out

First result: lll_01.out (pretty stinky) Wrong glue couplings.
Try again: lll_02.out (still pretty bad) Wrong glue couplings.
It looks like we were using the wrong mass shifts. Try mass shifts based only on particle truncation minus number of particles in the state. lll_03.out
There are two possible truncations, here are raw results for an ordinary truncation and raw results for truncation on each leg. In the ordinary truncation, mass shifts are assigned based on the distance from the truncation. For the truncation on each leg, mass shifts are based on the number of particles in that leg.
Try again with different starting couplings: blll_04.out (rerunning on cluster). Raw data output for the delta: J_z=1/2 and J_z=3/2. Raw data output for the nucleon: J_z=1/2 and J_z=3/2.

This work is supported by NSF grant PHY-0200060.

E-mail: bvds@pitt.edu