# 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

This work is supported by NSF grant PHY-0200060.

 E-mail: bvds@pitt.edu 