********* Eigenvalues for the 3+1 transverse lattice ********* Couplings: m^2, G^2 N, beta, la_1, la_2, la_3, la_4, 0 1 2 3 4 5 6 la_5, tau_1, tau_2 (2-9 divided by a^2) 7 8 9 Use chi^2 fit with 40 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 0.25 (-1, 5,0) and (-1, 6,0), error 0.25 ( 1, 7,0) and (-1, 4,0), error 0.25 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,K,p) = ( 2 2,16/2,6) ( 2 2,16/2,8) ( 2 2,24/2,6) ( 2 2,28/2,6) with error 1; in G^2 N units. Heavy potential determined using (n,K,p,K_max) = ( 0 0,-40/2,2,4) ( 0 0,-40/2,4,4) ( 0 0,-40/2,2,3.5) ( 0 0,-50/2,2,3.75) ( 0 0,-50/2,2,4.25) ( 0 0,-70/2,2,4) ( 0 0,-70/2,2,4.5) , L = 3.577-2.726*m 5.058-3.856*m 7.154-5.452*m (all in G^2 N units); relative scale error=0.1. Roundness determined using (n,K,p,K_max) = ( 1 0,-19/2,3,4) ( 1 0,-19/2,5,4) ( 1 0,-19/2,3,3.5) ( 1 0,-33/2,3,4) ( 1 0,-33/2,3,5) ( 1 0,-69/2,3,5) ( 1 0,-69/2,3,6) L=1.265-0.964*m and error 0.1; ( 1 0,-19/2,3,4) ( 1 0,-19/2,5,4) ( 1 0,-19/2,3,3.5) ( 1 0,-33/2,3,4) ( 1 0,-33/2,3,5) ( 1 0,-69/2,3,5) ( 1 0,-69/2,3,6) L=5.058-3.856*m and error 0.1; ( 1 1,-34/2,2,5.5) ( 1 1,-34/2,4,5.5) ( 1 1,-34/2,2,5) ( 1 1,-48/2,2,5.5) ( 1 1,-48/2,2,6.5) ( 1 1,-70/2,2,6) ( 1 1,-70/2,2,7) L=0+0*m and error 0.2; all in G^2 N units. p-extrapolation using n=( 1 0) and (K,p) = (13/2,3) (35/2,3) (45/2,3) (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/sigma. The 10 couplings (G^2 N units); which couplings -- if any -- were fit. Winding potential and heavy souce potential fits. Roundness of winding potential, 1 values, and roundness of heavy source potential, 3 values, (G^2 N units) showing measured value and derived value for each. The rescaled spectrum for each P_perp*a and c^2 values. Finally come the states for the ordinary spectra. 2 48 90.07550124 -1.050872918 4.569788962 0.1072401379 1 1.1740687 0.01840094341 -0.09087995142 39.97962091 0.2394010712 17.49537346 0.02020551666 -0.6040448371 2 3 4 5 6 7 8 9 0.262871 -0.913168 -0.208384 0.211170 0.049775 -0.057332 1.150358 1.163751 0.673029 0.560931 0.960487 0.978783 1.238567 0.732177 4.165274 4.186640 0.410655 16.543316 16.700810 3.027064 17.830452 17.750117 -1.544048 18.137719 18.408293 5.200481 13.467309 13.473302 0.115192 25.043504 25.057351 0.266140 32.726929 32.733390 0.124197 35.042574 35.037862 -0.090565 13.467309 13.487458 0.387271 19.673064 19.703024 0.575836 25.043504 25.035095 -0.161624 32.726929 32.742493 0.299149 18.889547 18.900245 0.205624 21.511933 21.506191 -0.110365 29.047543 29.056990 0.181562 32.417548 32.417986 0.008430 4.165274 4.207957 0.410185 17.830452 17.831823 0.013172 18.553610 18.637233 0.803627 18.889547 18.836311 -0.511600 13.467309 13.488147 0.200259 25.043504 25.049451 0.057148 32.726929 32.724746 -0.020976 33.712026 34.061132 3.354949 13.467309 13.498757 0.302222 19.673064 19.732972 0.575717 25.043504 25.048522 0.048222 32.726929 32.774009 0.452447 16.543316 16.699707 1.502930 18.137719 18.342191 1.964997 18.366573 18.639053 2.618567 18.889547 18.920287 0.295415 4.165274 17.830452 19.622975 18.553610 40.977987 41.732497 52.727034 50.601738 35.312794 46.249070 71.484686 64.190370 19.673064 34.467256 44.853613 44.813104 18.137719 16.543316 18.366573 30.358395 35.042574 40.642572 49.815610 51.348271 21.511933 42.842618 44.512209 48.633720 33.712026 45.865097 44.378239 60.057176 13.467309 25.043504 32.726929 38.635982 18.889547 29.047543 32.417548 38.811929 2 39 31.83225906 -0.8598217205 6.87551073 0.1453085056 1 1.381126953 -0.006764472674 -0.1948535865 12.30080671 0.3076560823 2.279476223 -1.206659192 -1.302373229 2 3 4 5 6 7 8 9 0.245344 -0.876532 -0.595915 0.156288 0.034333 0.016134 0.932598 1.011730 0.640044 0.589340 0.804542 0.810746 1.243331 0.790401 4.165211 4.214584 1.332576 25.055184 25.086711 0.850906 26.088463 26.119321 0.832861 26.334444 26.364930 0.822821 20.565753 20.578465 0.343111 36.977762 36.998335 0.555247 48.675720 48.705491 0.803515 52.748240 52.747055 -0.031971 20.565753 20.595742 0.809410 31.310876 31.362761 1.400370 36.977762 36.977876 0.003086 48.675720 48.731095 1.494575 28.805033 28.832178 0.732626 34.269469 34.255686 -0.372005 44.116312 44.137417 0.569601 47.822120 47.829443 0.197633 4.165211 4.263954 1.332524 25.055184 25.118022 0.847994 27.145337 27.134675 -0.143877 28.755814 28.753885 -0.026032 20.565753 20.600289 0.466066 36.977762 36.996437 0.252010 48.675720 48.724555 0.659029 51.362577 51.488239 1.695801 20.565753 20.616649 0.686846 31.310876 31.414612 1.399911 36.977762 37.000565 0.307719 48.675720 48.798292 1.654098 26.088463 26.149523 0.823998 26.334444 26.395866 0.828888 28.691602 28.713049 0.289428 28.805033 28.776529 -0.384661 4.165211 25.055184 27.145337 28.755814 61.422468 62.594508 78.660688 75.153532 54.661737 67.325163 106.505517 102.227347 31.310876 53.288664 68.782689 71.533427 26.334444 26.088463 28.691602 40.482818 52.748240 60.661585 75.344541 76.667759 34.269469 64.971441 71.884827 62.863385 51.362577 69.395357 71.313366 75.149144 20.565753 36.977762 48.675720 57.652684 28.805033 44.116312 47.822120 59.756237 -2 10 137.0460918 -1.961302944 7.008591008 0 1 0.3689085924 0.04179866664 -0.07575883236 50 0.07317431175 12.5 -0.6282192014 -0.490700441 2 3 4 5 6 7 8 9 0.145100 -0.878954 0.876070 0.086533 0.301898 -0.359389 0.679738 0.391353 0.527079 0.435885 0.866246 0.733969 0.983353 0.533417 4.957994 4.982142 0.392916 12.716701 12.730874 0.230598 12.969303 12.982943 0.221942 16.451263 16.428761 -0.366143 15.085655 15.101667 0.260546 28.535577 28.564851 0.476325 34.104220 34.121760 0.285396 37.644113 37.637753 -0.103477 15.085655 15.104099 0.300110 15.741290 15.764429 0.376500 28.535577 28.531736 -0.062492 34.104220 33.397126 -11.505202 16.451263 16.467055 0.256952 19.557190 19.549704 -0.121806 31.883848 31.898878 0.244545 34.876620 34.877380 0.012366 4.957994 5.006297 0.392976 12.969303 12.996367 0.220180 16.451263 16.429311 -0.178595 17.959872 17.960062 0.001545 15.085655 15.124203 0.313611 28.535577 28.555864 0.165048 34.104220 33.825707 -2.265863 35.506553 35.802124 2.404629 15.085655 15.116143 0.248036 15.741290 15.787465 0.375662 28.535577 28.566061 0.248008 34.104220 34.138236 0.276741 12.716701 12.745282 0.232522 16.451263 16.460005 0.071119 18.164830 18.154342 -0.085325 27.193358 27.215272 0.178277 4.957994 12.969303 17.959872 22.502990 44.712527 47.315640 59.496789 60.379413 36.277126 49.175617 61.110761 65.241552 15.741290 35.117216 48.374620 49.963846 12.716701 18.164830 27.193358 29.135582 37.644113 45.276266 51.436166 63.597475 19.557190 46.556398 50.262049 56.663617 35.506553 48.599125 50.211832 49.811181 15.085655 28.535577 34.104220 40.235314 16.451263 31.883848 34.876620 35.954074