******* 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 1 (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=0.1. 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 43.31446972 -0.936967908 6.886492894 0.03249196962 1 0.595 -0.069 -0.207 19.86 0.098 3.508 -1.896 2 3 4 5 6 7 8 0.191109 -0.894020 0.518954 0.195715 -1.146727 -0.607405 1.439262 0.699719 -0.542969 -0.457842 -0.044088 -0.244013 5.734746 5.781855 0.991981 10.652454 10.684391 0.672485 12.099849 12.124937 0.528266 21.734455 21.688334 -0.971178 19.698534 19.724687 0.550703 36.385670 36.410311 0.518870 39.809848 39.841934 0.675644 45.178256 45.182690 0.093378 19.698534 19.718837 0.427513 25.498952 25.523557 0.518110 36.385670 36.403676 0.379153 39.809848 39.817774 0.166894 21.734455 21.760799 0.554730 27.360877 27.349842 -0.232371 40.455894 40.486444 0.643309 40.536822 40.538123 0.027394 5.734746 5.828986 0.992212 12.099849 12.150285 0.531012 21.734455 21.684288 -0.528188 23.474234 23.435109 -0.411931 19.698534 19.744157 0.480339 36.385670 36.420595 0.367707 39.809848 39.841775 0.336141 50.461082 50.452814 -0.087057 19.698534 19.745877 0.498450 25.498952 25.548181 0.518313 36.385670 36.435895 0.528790 39.809848 39.857936 0.506294 10.652454 10.716072 0.669803 21.734455 21.745546 0.116775 23.600540 23.556020 -0.468733 31.752634 31.783806 0.328202 5.734746 12.099849 23.474234 28.700350 54.043769 55.029168 70.982898 67.372060 48.752254 66.472285 69.252904 83.142425 25.498952 47.734192 52.809358 78.448501 10.652454 23.600540 31.752634 35.328666 45.178256 53.942471 68.974864 71.730938 27.360877 56.786647 62.938007 76.492685 50.461082 63.033054 70.164260 64.485924 19.698534 36.385670 39.809848 56.339786 21.734455 40.455894 40.536822 50.198863 2 18 39.69942507 -1.147492716 7.05005092 0.0517766953 1 0.7593660999 -0.07429959943 -0.1443947442 8.451757719 0.1555731485 1.806265761 -2.149890767 2 3 4 5 6 7 8 0.235573 -0.826614 0.256033 0.191905 -1.170322 -0.669166 1.779032 1.089975 -0.608152 -0.444069 -0.037679 -0.195213 8.900829 8.937995 0.987625 17.649155 17.669060 0.528932 18.207329 18.226012 0.496457 25.170499 25.177020 0.173284 21.432782 21.448760 0.424582 40.283289 40.307016 0.630497 46.042131 46.066237 0.640567 51.127398 51.123746 -0.097055 21.432782 21.455798 0.611613 29.793224 29.821432 0.749573 40.283289 40.287861 0.121489 46.042131 46.054595 0.331198 25.631457 25.653934 0.597275 30.261358 30.248789 -0.334005 44.966989 44.988467 0.570734 45.440298 45.447110 0.181023 8.900829 8.975186 0.987940 18.207329 18.244138 0.489059 25.170499 25.186584 0.213713 25.631457 25.622984 -0.112570 21.432782 21.465134 0.429841 40.283289 40.308352 0.332995 46.042131 46.064303 0.294589 53.825634 53.839257 0.180996 21.432782 21.478444 0.606687 29.793224 29.849652 0.749725 40.283289 40.314783 0.418436 46.042131 46.092818 0.673441 17.649155 17.689503 0.536080 25.183114 25.189737 0.087993 25.631457 25.610531 -0.278026 27.392066 27.538991 1.952100 8.900829 18.207329 25.170499 29.211941 59.687398 60.862498 77.679692 77.162817 51.985092 78.096657 77.966230 93.610504 29.793224 51.690253 63.113559 85.490109 17.649155 27.392066 25.183114 40.529979 51.127398 59.247925 75.634919 77.672801 30.261358 66.913143 61.832653 90.686086 53.825634 62.182177 74.361586 84.483774 21.432782 40.283289 46.042131 59.938292 25.631457 44.966989 45.440298 56.138727 2 10 31.19445377 -0.8535206415 5.860518032 0.07642881742 1 0.763 0.046 -0.273 13.576 0.041 3.88 -2.207 2 3 4 5 6 7 8 0.257619 -0.905511 0.163392 0.186233 -1.105554 -0.769597 1.683048 1.175864 -0.566739 -0.500942 -0.071302 -0.292269 6.447415 6.503706 1.359796 20.362405 20.400831 0.928245 22.066844 22.050598 -0.392463 24.977976 25.043679 1.587149 18.855457 18.873582 0.437842 35.450752 35.469123 0.443776 43.076127 43.094953 0.454772 45.716438 45.728474 0.290745 18.855457 18.877428 0.530758 25.337307 25.362739 0.614360 35.450752 35.466503 0.380471 43.076127 43.066158 -0.240815 26.548257 26.571237 0.555122 31.402607 31.395378 -0.174633 40.033290 40.059410 0.630983 45.571882 45.560789 -0.267955 6.447415 6.559970 1.359467 22.066844 22.033996 -0.396756 26.548257 26.583448 0.425054 27.399293 27.419087 0.239068 18.855457 18.895585 0.484675 35.450752 35.485328 0.417612 43.076127 43.079518 0.040957 48.815254 48.902172 1.049815 18.855457 18.895523 0.483930 25.337307 25.388181 0.614475 35.450752 35.484450 0.407013 43.076127 43.090698 0.175994 20.362405 20.439209 0.927652 24.977976 25.108155 1.572326 26.548257 26.535927 -0.148923 30.970808 30.968904 -0.023001 6.447415 22.066844 27.399293 31.131197 54.424898 56.766733 70.706829 68.658897 51.229949 73.898235 74.256111 81.177412 25.337307 48.237620 57.277547 70.120573 20.362405 24.977976 30.970808 38.459487 45.716438 56.002106 65.916499 69.602055 31.402607 59.051681 54.837364 84.454240 48.815254 58.333693 61.170534 80.714567 18.855457 35.450752 43.076127 51.738147 26.548257 40.033290 45.571882 51.684865