********* 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 41 criteria and tolerance 0.01. Overall scale from fitting lowest state to lattice value. 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) = (12/2,8) (12/2,6) (14/2,6) (18/2,6) . Winding potential using (n,K,p) = ( 2 0,14/2,6) ( 2 0,14/2,4) ( 2 0,22/2,4) ( 3 0,15/2,7) ( 3 0,15/2,5) ( 3 0,23/2,5) ( 4 0,14/2,8) ( 4 0,14/2,6) ( 4 0,22/2,6) . Roundness of winding using (n,K,p) = ( 2 2,12/2,8) ( 2 2,12/2,6) ( 2 2,20/2,6) with error 1; in G^2 N units. Heavy potential determined using (n,K,p,K_max) = ( 0 0,-20/2,2,3) ( 0 0,-20/2,4,3) ( 0 0,-20/2,2,4.5) ( 0 0,-32/2,2,3) ( 0 0,-32/2,2,4.5) ( 0 0,-60/2,2,3) ( 0 0,-60/2,2,4.5) , L = 3 4 6 (all in G^2 N units); relative scale error=0.1. Roundness determined using (n,K,p,K_max) = ( 1 0,-13/2,3,3) ( 1 0,-13/2,5,3) ( 1 0,-13/2,3,4.5) ( 1 0,-23/2,3,3) ( 1 0,-23/2,3,4.5) ( 1 0,-29/2,3,3) ( 1 0,-29/2,3,4.5) L=0 and error 0.1; ( 1 0,-13/2,3,3) ( 1 0,-13/2,5,3) ( 1 0,-13/2,3,4.5) ( 1 0,-23/2,3,3) ( 1 0,-23/2,3,4.5) ( 1 0,-29/2,3,3) ( 1 0,-29/2,3,4.5) L=2.5 and error 0.1; ( 1 0,-13/2,3,3) ( 1 0,-13/2,5,3) ( 1 0,-13/2,3,4.5) ( 1 0,-23/2,3,3) ( 1 0,-23/2,3,4.5) ( 1 0,-29/2,3,3) ( 1 0,-29/2,3,4.5) L=5 and error 0.1; ( 1 1,-20/2,2,3) ( 1 1,-20/2,4,3) ( 1 1,-20/2,2,4.5) ( 1 1,-30/2,2,3) ( 1 1,-44/2,2,4.5) ( 1 1,-60/2,2,3) ( 1 1,-60/2,2,4.5) L=0 and error 0.1; all in G^2 N units. p-extrapolation using n=( 1 0) and (K,p) = (13/2,3) (21/2,3) (45/2,3) (13/2,5) (23/2,5) (11/2,7) (13/2,7) . 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, 4 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 11 50.80625583 -0.9092152375 6.108719181 0.1453085056 1 1.249802166 -0.002865019972 -0.1904018266 11.13327209 0.2451368356 1.704690865 -0.4095520523 -0.2113940006 2 3 4 5 6 7 8 9 0.315011 -0.850257 -0.141513 0.195607 0.100615 -0.115386 2.326799 1.652139 0.725812 0.737612 0.924529 0.903428 1.309918 1.267468 1.304898 1.025262 12.670000 12.716196 1.422340 26.819460 26.827600 0.250626 27.961128 27.971908 0.331891 28.363122 28.403379 1.239447 21.205457 21.215520 0.309839 44.020920 44.035810 0.458465 52.593058 52.603405 0.318594 56.776303 56.762867 -0.413675 21.205457 21.233779 0.872004 33.841997 33.873920 0.982858 44.020920 44.021862 0.029004 52.593058 52.597402 0.133746 32.130935 32.150262 0.595035 35.814326 35.805644 -0.267321 49.880802 49.890721 0.305402 52.154523 52.165981 0.352762 12.670000 12.762439 1.423058 26.819460 26.835509 0.247069 29.508463 29.530867 0.344903 32.130935 32.125705 -0.080519 21.205457 21.229040 0.363053 44.020920 44.042291 0.329001 52.593058 52.585626 -0.114413 56.857023 56.886654 0.456157 21.205457 21.258637 0.818683 33.841997 33.905852 0.983004 44.020920 44.031353 0.160611 52.593058 52.629221 0.556722 27.961128 27.982840 0.334235 28.363122 28.443444 1.236505 32.130935 32.113534 -0.267880 32.321026 32.331569 0.162301 12.670000 29.508463 26.819460 32.306893 65.506334 63.386775 88.261012 82.212259 56.624857 84.390942 112.232345 124.968026 33.841997 55.104846 73.371720 83.754720 28.363122 27.961128 32.321026 50.337779 56.776303 63.665667 82.860076 84.866908 35.814326 74.209618 77.833759 104.951889 56.857023 77.885360 73.002850 104.526646 21.205457 44.020920 57.129678 52.593058 32.130935 49.880802 52.154523 60.228818 2 11 84.80063145 -0.8209035403 5.202246178 0.1921681542 1 0.8202312568 -0.2818631883 -0.4016507405 31.16946395 -0.002980689269 5.19849575 0.09585595049 -0.9073021121 2 3 4 5 6 7 8 9 0.387457 -0.705829 -0.112384 0.212265 0.074871 -0.092755 4.561887 2.379783 0.848338 0.733582 0.958044 0.920563 1.308862 1.323763 1.520590 1.026683 12.670000 12.723722 1.732563 17.365643 17.401119 1.144122 22.943926 22.965243 0.687496 31.586321 31.589923 0.116183 23.738554 23.757546 0.612486 47.306779 47.320190 0.432494 51.498568 51.484038 -0.468614 53.415861 53.460217 1.430500 23.738554 23.751717 0.424495 37.852877 37.864873 0.386884 47.306779 47.339278 1.048093 51.498568 51.495828 -0.088383 31.707649 31.726253 0.599975 37.348783 37.338603 -0.328295 47.877968 47.887000 0.291308 52.267604 52.279143 0.372154 12.670000 12.777588 1.734884 22.943926 22.986302 0.683325 31.586321 31.593547 0.116529 31.707649 31.652534 -0.888744 23.738554 23.769252 0.495015 47.306779 47.355844 0.791176 51.498568 51.484395 -0.228544 53.415861 53.449140 0.536622 23.738554 23.772172 0.542103 37.852877 37.876882 0.387088 47.306779 47.350038 0.697555 51.498568 51.478266 -0.327384 17.365643 17.436740 1.146453 31.707649 31.689740 -0.288796 32.569981 32.580111 0.163349 33.200330 33.180744 -0.315838 12.670000 22.943926 31.586321 33.215519 62.151383 63.500304 80.236115 76.760083 57.230815 81.237356 99.456405 103.361037 37.852877 57.155667 73.794051 80.664808 17.365643 32.569981 33.200330 45.732367 53.625438 62.922613 77.545505 81.799201 37.348783 74.258028 75.605054 78.453445 61.397586 75.510296 76.329793 78.177604 23.738554 47.306779 53.415861 51.498568 31.707649 47.877968 52.267604 60.101144 2 20 106.0673258 -1.016736594 4.77538231 0.25 1 1.701117967 0.2494168049 -0.04515257517 6.828465099 0.2714627672 1.053125645 0.3210060796 -0.1805178998 2 3 4 5 6 7 8 9 0.366233 -0.326210 -1.944676 0.214030 0.073037 -0.093513 2.429104 2.360568 0.778996 0.659209 0.995124 0.866419 1.401990 1.292887 1.377609 0.924891 12.670000 12.713635 1.221003 21.878511 21.917290 1.085116 22.470815 22.471885 0.029943 29.202939 29.516418 8.771912 17.581523 17.584309 0.077953 36.617434 36.653503 1.009320 45.265138 45.268898 0.105215 45.494862 45.470762 -0.674367 17.581523 17.607530 0.727738 29.230737 29.260737 0.839463 36.617434 36.643104 0.718305 45.265138 45.488220 6.242359 31.336828 31.340372 0.099176 32.447356 32.446569 -0.022027 41.019170 41.024243 0.141970 45.617147 45.591085 -0.729272 12.670000 12.757329 1.221838 22.470815 22.472749 0.027064 29.202939 29.028609 -2.439090 31.336828 31.472222 1.894325 17.581523 17.596629 0.211351 36.617434 36.628860 0.159868 45.265138 45.305649 0.566800 45.494862 45.491381 -0.048701 17.581523 17.623984 0.594085 29.230737 29.290735 0.839440 36.617434 36.732929 1.615922 45.265138 45.304540 0.551276 21.878511 21.955747 1.080621 31.088359 31.069811 -0.259503 31.336828 31.467330 1.825882 33.688025 33.748809 0.850438 12.670000 22.470815 29.202939 33.170575 54.623460 56.396531 76.098095 70.676760 47.599901 81.812656 104.148224 107.083405 29.230737 46.266562 58.901298 77.249124 21.878511 35.168955 31.088359 33.688025 49.229912 54.374802 66.230301 72.225353 32.447356 60.793435 68.269129 101.275477 46.053774 62.487713 63.147259 91.757364 17.581523 36.617434 45.494862 45.265138 31.336828 41.019170 45.617147 52.073236