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.
- Charge conjugation: C = R^2 O, where O is orientation reversal
- A blank means that the state remains indefinite under the associated symmetry.

group | Multiplet number element | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ---------|--------------------------------------------------------- E | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 P_1 | 1 -1 1 -1 1 -1 1 -1 P_2 | 1 -1 1 -1 -1 1 1 -1 1 -1 R^2 | 1 -1 1 1 1 1 -1 -1 1 1 1 -1 1 -1 | P_1 R | 1 -1 -1 1 1 1 -1 -1 1 -1 R | 1 1 -1 -1 R^3 | 1 1 -1 -1 P_1 R^3 | 1 -1 -1 1 1 -1 -1 1 ------------------------------------------------------------------- J_z^P_1 | 0+ 0- 2+ 2- 1+ 1- The multiplets have the following use: 9, 8 P_perp = (c,0), P_2 = +1 7, 10 P_perp = (c,0), P_2 = -1 11,12 P_perp = (c,c), P_1 R = +1 14,13 P_perp = (c,c), P_1 R = -1 15 n = (c,0) P_2 = +1 16 n = (c,0) P_2 = -1 17 n = (c,c) P_1 R = +1 18 n = (c,c) P_1 R = -1

To produce these results, we wrote lots of C-code. This code is linked to standard packages BLAS, LAPACK, and (optionally) ARPACK along with some other standard routines, and a parallel lanczos solver.

The due to finite-`K` errors, the couplings
that produce the best Lorentz covariance are slightly shifted
for different methods:

- Improved matrix elements, anti-periodic boundary conditions (this is what we used to obtain our glueball results in the past).
- Anti-periodic boundary conditions, plain DLCQ.
- Periodic boundary conditions, plain DLCQ. Since
convergence in
`K`is so poor, we resort to a 1/`K`extrapolation.- Entire trajectory: ytraj_1_10.out
- Re-run entire trajectory: ytraj_1_21.out
- Re-run entire trajectory: ytraj_1_31.out
- Re-run entire trajectory: ytraj_1_41.out
- Re-run entire trajectory: ytraj_1_51.out
- Using above runs, lowest chi^2 for each mass: ytraj_1_composite.out
- Re-run entire trajectory: ytraj_1_61.out

- BIG basis, periodic boundary conditions, plain DLCQ. Since
convergence in
`K`is so poor, we resort to a 1/`K`extrapolation. Some spectra are printed incorrectly although chi^{2}and couplings are OK.- Entire trajectory: ttraj_1_10.out
- Rerun with slightly larger
`K`and different starting couplings: ttraj_1_20.out - Rerun using fit to above as starting points: ttraj_1_30.out (generally poor)
- Rerun using ytraj_1_* composite data as starting points: ttraj_1_40.out
- Rerun using ttraj_1_* composite data as starting points: ttraj_1_50.out
- Composite best chi
^{2}of the above: ttraj_1_composite.out

- 2003 BIG basis, with
`K`up to 20 and periodic boundary conditions, plain DLCQ. Since convergence in`K`is so poor, we resort to a 1/`K`extrapolation.- First try:
ttraj_2_10.out and
ttraj_2_11.out.
Some spectra are printed
incorrectly although chi
^{2}and couplings are OK. - Second try:
ttraj_2_20.out. Some spectra
are printed incorrectly, although the couplings and
chi
^{2}are ok. - Third try: ttraj_2_30.out.
- Fourth try: ttraj_2_40.out.
- Fifth try, fitting to teper's 0
^{++}mass: ttraj_2_45.out. - Best chi
^{2}for each mass: ttraj_2_composite.out.

- First try:
ttraj_2_10.out and
ttraj_2_11.out.
Some spectra are printed
incorrectly although chi

- K_convergence_dlcq.ps: K convergence of a two link state, winding=(2,0), for various DLCQ methods. The coupling constants are from the best fit data ytraj_1_composite.out.
- spectrum_even.ps (LaTeX source) spectrum from the best fit datum in ytraj_1_composite.out.
- ttraj_spectrum.ps (LaTeX source) spectrum from the best fit datum in ttraj_1_composite.out.

- dense_spectrum_6.out
- dense_spectrum_8.out
- dense_spectrum_10.out
- full_spectrum_12.out; less than the full number of states in a sector.

- dense_6_0.out dense_8_0.out dense_10_0.out full_12_0.out
- dense_6_1.out dense_8_1.out dense_10_1.out full_12_1.out
- dense_6_2.out dense_8_2.out dense_10_2.out full_12_2.out
- dense_6_3.out dense_8_3.out dense_10_3.out full_12_3.out
- dense_6_4.out dense_8_4.out dense_10_4.out full_12_4.out
- dense_6_5.out dense_8_5.out dense_10_5.out full_12_5.out
- dense_6_6.out dense_8_6.out dense_10_6.out full_12_6.out
- dense_6_7.out dense_8_7.out dense_10_7.out full_12_7.out
- dense_6_8.out dense_8_8.out dense_10_8.out full_12_8.out (some sectors missing)
- dense_6_9.out dense_8_9.out dense_10_9.out full_12_9.out (some sectors missing)
- dense_6_10.out dense_8_10.out dense_10_10.out full_12_10.out (some sectors missing)

E-mail: bvds@pitt.edu |