******* Eigenvalues for the 3+1 transverse lattice ******* Couplings: m^2, G^2 N, t/a^2, la_1/a^2, la_2/a^2 0 1 2 3 4 la_3/a^2, la_4/a^2, la_5/a^2, tau 5 6 7 8 Use chi^2 fit with 39 criteria and tolerance 0.01. Overall scale from minimizing chi^2. Parity doublets (o,multi,state) with error for difference over average. ( 1, 5,0) and ( 1, 6,0), error 0.5 (-1, 5,0) and (-1, 6,0), error 0.5 ( 1, 7,0) and (-1, 4,0), error 0.5 Spectrum for P_perp a = (0,0), ( 0.25 0) using (# states, multiplet, o, c^2 error for each) = (4, 9 & 8, 1 & -1, 0.25 2 2 2) (4, 8 & 9, 1 & -1, 0.25 2 2 2) (4, 7 & 10, 1 & -1, 0.25 2 2 2) (4, 10 & 7, 1 & -1, 0.25 2 2 2) Spectrum for P_perp a = (0,0), ( 0.25 0.25) using (# states, multiplet, o, c^2 error for each) = (4, 11 & 12, 1 & -1, 0.25 2 2 2) (4, 12 & 11, 1 & -1, 0.25 2 2 2) (4, 14 & 13, 1 & -1, 0.25 2 2 2) (4, 13 & 14, 1 & -1, 0.25 2 2 2). Ordinary spectra multiplets, 4 states, (o,multiplet) = ( 1, 3) (-1, 3) ( 1, 4) (-1, 4) ( 1, 5) (-1, 5) ( 1, 6) (-1, 6) ( 1, 7) (-1, 7) . All spectra extrapolated using (K,p) = (16/2,8) (16/2,6) (20/2,6) (26/2,6) . Winding potential using (n,K,p) = ( 2 0,20/2,4) ( 2 0,20/2,6) ( 2 0,24/2,4) ( 2 0,32/2,4) ( 3 0,19/2,5) ( 3 0,19/2,7) ( 3 0,25/2,5) ( 3 0,33/2,5) ( 4 0,18/2,6) ( 4 0,18/2,8) ( 4 0,24/2,6) ( 4 0,32/2,6) . Roundness of winding using n = (2,2) and (K,p) = (16/2,6) (16/2,8) (24/2,6) (28/2,6) with error 2 (in G^2 N^2 units). Heavy potential determined using (n,K,p,K_max) = ( 0 0,-34/2,2,4) ( 0 0,-34/2,4,4) ( 0 0,-34/2,2,5) ( 0 0,-40/2,2,4) ( 0 0,-50/2,2,5) ( 0 0,-60/2,2,4) ( 0 0,-60/2,2,6) , L = 3 4 6 (all in G^2 N^2 units); with relative error=0.25. Roundness determined using (n,K,p,K_max) = ( 1 0,-17/2,3,4) ( 1 0,-17/2,5,4) ( 1 0,-17/2,3,5) ( 1 0,-33/2,3,4) ( 1 0,-33/2,3,5) ( 1 0,-55/2,3,4) ( 1 0,-55/2,3,6) , L=3 and error 0.5 ( 1 1,-30/2,2,4) ( 1 1,-30/2,4,4) ( 1 1,-30/2,2,5) ( 1 1,-40/2,2,4) ( 1 1,-50/2,2,5) ( 1 1,-60/2,2,4) ( 1 1,-60/2,2,6) , with L=3 and error 0.5 (all in G^2 N^2 units). p-extrapolation using n=( 1 0) and (K,p) = (13/2,3) (35/2,3) (13/2,5) (29/2,5) (13/2,7) (17/2,7) . Result format: fit info, # steps, chi^2, and p damping, scale g^2 N/(a^2 sigma); the 9 couplings (G^2 N units); which couplings -- if any -- were fit; winding and longitudinal string tension fits; the n=(2,2) winding eigenvalue and the n=(1,0) (1,1) longitudinal eigenvalues (G^2 N units) showing measured value and derived value for each. In each direction, the spectra for each P_perp*a and c^2 values. Finally come the states for the ordinary spectra. 2 10 31.83369023 -1.25609756 6.178074457 0.1453085056 1 1.260068 0.176086 -0.220545 10.799087 0.262786 1.781502 -2.450789 2 3 4 5 6 7 8 0.287015 -0.709983 -0.661935 0.187479 -0.945423 -0.584904 1.824647 1.503397 -0.358681 -0.238872 0.244061 -0.008306 11.958355 12.006612 1.369110 28.317936 28.333418 0.439240 28.553382 28.589703 1.030483 28.703195 28.706817 0.102776 20.248362 20.258429 0.285600 39.547752 39.565070 0.491337 50.852798 50.847542 -0.149110 53.931510 53.931800 0.008239 20.248362 20.272634 0.688638 31.944577 31.982282 1.069741 39.547752 39.552346 0.130344 50.852798 50.849038 -0.106679 33.799791 33.821450 0.614467 38.135810 38.124787 -0.312735 46.772204 46.790173 0.509806 51.971705 51.974416 0.076917 11.958355 12.054924 1.369896 28.317936 28.327830 0.140358 29.402820 29.423742 0.296791 33.799791 33.791646 -0.115551 20.248362 20.273241 0.352925 39.547752 39.568729 0.297580 50.852798 50.843418 -0.133058 53.120174 53.133922 0.195031 20.248362 20.292169 0.621430 31.944577 32.019987 1.069745 39.547752 39.570641 0.324700 50.852798 50.844322 -0.120236 28.553382 28.625698 1.025847 28.703195 28.731612 0.403122 33.799791 33.792038 -0.109988 36.926408 36.923175 -0.045857 11.958355 29.402820 28.317936 36.784136 62.629810 63.416164 77.409443 74.798752 57.592688 74.086938 92.745482 106.465663 31.944577 54.634553 67.439144 74.515774 28.553382 28.703195 36.926408 51.278471 53.931510 62.080446 73.699386 75.551044 38.135810 64.255404 74.636432 68.274961 53.120174 68.774353 73.680712 66.626924 20.248362 39.547752 54.129557 50.852798 33.799791 46.772204 51.971705 59.645502 2 67 39.22723035 -2.832330267 6.0504173 0.1921681542 1 0.8108652901 0.1208098836 -0.1847742634 6.032613704 0.1009379378 0.425941243 -3.25681977 2 3 4 5 6 7 8 0.540146 -0.290426 -0.831162 0.206458 -1.644749 -0.474202 6.894302 3.926844 -0.858993 -0.625694 0.095564 -0.274301 30.606322 30.630789 1.279337 31.467849 31.491485 1.235934 44.475429 44.485629 0.533340 52.851611 52.879923 1.480434 30.538207 30.544403 0.323981 66.146776 66.151611 0.252862 69.895572 69.906461 0.569368 77.205738 77.214758 0.471636 30.538207 30.548204 0.522759 55.017139 55.027283 0.530388 66.146776 66.157204 0.545305 69.895572 69.902160 0.344475 56.687460 56.697986 0.550412 59.556152 59.548402 -0.405262 74.971825 74.983553 0.613283 78.867210 78.866088 -0.058700 30.606322 30.655264 1.279570 44.475429 44.495781 0.532105 52.851611 52.864262 0.330752 56.687460 56.646082 -1.081815 30.538207 30.548434 0.267375 66.146776 66.154964 0.214092 69.895572 69.912323 0.437952 77.205738 77.212354 0.172975 30.538207 30.560367 0.579374 55.017139 55.037429 0.530481 66.146776 66.169114 0.584024 69.895572 69.913746 0.475149 31.467849 31.515045 1.233947 52.917268 52.937089 0.518230 56.687460 56.724040 0.956396 57.288000 57.297019 0.235800 30.606322 44.475429 52.851611 58.008580 90.088434 90.805353 104.471597 104.196345 82.509538 112.458620 116.706471 125.468613 55.017139 80.123497 95.824200 111.220963 31.467849 52.917268 57.288000 60.341393 79.770003 89.989304 101.771402 103.850267 59.556152 94.224873 101.411134 110.259849 83.592925 97.554635 98.963068 109.333494 30.538207 66.146776 69.895572 77.205738 56.687460 74.971825 78.867210 83.293366 2 60 49.28339542 -1.085544406 4.049603443 0.25 1 1.395536386 0.3177310879 -0.4138441734 8.397982232 0.09877213053 1.657395499 -1.931791338 2 3 4 5 6 7 8 0.391982 -0.428848 -1.619871 0.204880 -0.520562 -0.292996 3.136192 2.504523 0.284148 0.209589 0.855325 0.374600 11.950864 12.003922 1.347583 19.570593 19.616861 1.175094 22.532481 22.536064 0.090978 27.325485 27.337582 0.307241 16.842967 16.851069 0.205765 33.106357 33.119032 0.321917 40.281749 40.283710 0.049794 41.825552 41.825263 -0.007336 16.842967 16.859378 0.416797 27.895306 27.918044 0.577496 33.106357 33.127131 0.527594 40.281749 40.285129 0.085842 31.692457 31.708360 0.403922 35.348651 35.342386 -0.159111 38.802268 38.820695 0.468029 44.405353 44.391928 -0.340960 11.950864 12.056977 1.347525 22.532481 22.539547 0.089728 27.922032 27.855184 -0.848901 31.692457 31.741994 0.629075 16.842967 16.862303 0.245549 33.106357 33.137007 0.389216 40.281749 40.282222 0.006001 41.825552 41.814141 -0.144903 16.842967 16.872650 0.376939 27.895306 27.940789 0.577576 33.106357 33.143216 0.468067 40.281749 40.291331 0.121685 19.570593 19.662621 1.168661 27.325485 27.351171 0.326181 31.692457 31.792525 1.270764 34.934060 34.927065 -0.088836 11.950864 22.532481 27.922032 35.776610 49.593087 53.678907 57.763014 60.695748 49.482308 67.506952 66.387511 65.683031 27.895306 45.868922 52.944936 64.733589 19.570593 27.325485 34.934060 37.544388 43.598539 51.757374 56.632470 59.174833 35.348651 50.095092 60.298499 62.456526 44.056958 53.621392 59.690119 61.887471 16.842967 33.106357 40.281749 41.825552 31.692457 38.802268 44.405353 50.078390