********* 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 42 criteria and tolerance 0.01. Overall scale from fitting lowest state to lattice value. Includes 1 nonstandard fit criteria (such as a specific lattice spacing). 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 21 61.79771654 -0.9102712194 6.096971974 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 0.315382 -0.849094 -0.143688 0.195610 0.100625 -0.115409 2.330562 1.655999 0.725886 0.736686 0.924612 0.902700 1.310018 1.266980 1.305130 1.023985 12.670000 12.715971 1.414331 26.789712 26.797878 0.251249 27.937910 27.948525 0.326590 28.353171 28.392921 1.222963 21.171066 21.181054 0.307275 43.952811 43.967681 0.457473 52.509849 52.520380 0.324003 56.690752 56.677222 -0.416256 21.171066 21.199339 0.869826 33.789998 33.821835 0.979489 43.952811 43.953620 0.024891 52.509849 52.514467 0.142085 32.084073 32.103278 0.590865 35.746639 35.737988 -0.266160 49.795689 49.805500 0.301852 52.077086 52.088533 0.352176 12.670000 12.761988 1.415053 26.789712 26.805808 0.247602 29.476231 29.498196 0.337889 32.084073 32.079142 -0.075845 21.171066 21.194540 0.361086 43.952811 43.974024 0.326314 52.509849 52.502597 -0.111552 56.755016 56.784798 0.458135 21.171066 21.224106 0.815906 33.789998 33.853681 0.979633 43.952811 43.963095 0.158194 52.509849 52.546732 0.567373 27.937910 27.959302 0.329080 28.353171 28.432485 1.220091 32.084073 32.066177 -0.275285 32.256250 32.267436 0.172072 12.670000 29.476231 26.789712 32.242348 65.402105 63.289520 88.114197 82.081378 56.517464 84.213864 112.059481 124.735684 33.789998 55.005408 73.242870 83.631911 28.353171 27.937910 32.256250 50.241389 56.690752 63.565192 82.714435 84.723981 35.746639 74.075651 77.684725 104.754125 56.755016 77.741916 72.903253 104.278163 21.171066 43.952811 57.040252 52.509849 32.084073 49.795689 52.077086 60.129921 2 75 84.90288656 -0.8169308363 5.255196785 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 0.385961 -0.710965 -0.103648 0.212264 0.074877 -0.092772 4.545228 2.363766 0.847993 0.739467 0.957652 0.925160 1.308487 1.326880 1.519484 1.034842 12.670000 12.724466 1.767564 17.381712 17.417839 1.172429 23.048639 23.070571 0.711762 31.890002 31.893540 0.114814 23.952789 23.972145 0.628152 47.701163 47.714645 0.437535 52.009145 51.992091 -0.553425 53.830983 53.878465 1.540924 23.952789 23.966082 0.431378 38.178741 38.190894 0.394399 47.701163 47.733728 1.056829 52.009145 52.006162 -0.096791 31.959924 31.978780 0.611919 37.695332 37.685071 -0.332992 48.276777 48.285883 0.295516 52.719852 52.731627 0.382133 12.670000 12.779084 1.770038 23.048639 23.092242 0.707528 31.890002 31.897003 0.113602 31.959924 31.904449 -0.900156 23.952789 23.983999 0.506419 47.701163 47.750621 0.802529 52.009145 51.992798 -0.265254 53.830983 53.867183 0.587395 23.952789 23.986885 0.553253 38.178741 38.203059 0.394607 47.701163 47.744300 0.699969 52.009145 51.985487 -0.383872 17.381712 17.454105 1.174680 31.959924 31.942396 -0.284410 32.900716 32.910676 0.161611 33.499612 33.478894 -0.336178 12.670000 23.048639 31.890002 33.515490 62.690328 64.052740 80.956361 77.448520 57.775965 81.937454 100.561269 104.254554 38.178741 57.688030 74.482085 81.362502 17.381712 32.900716 33.499612 46.092508 54.078763 63.468630 78.241169 82.559137 37.695332 74.963317 76.334292 79.125051 61.971690 76.209556 77.069535 78.821624 23.952789 47.701163 53.830983 52.009145 31.959924 48.276777 52.719852 60.646403 2 39 125.7587809 -1.013875747 4.836793557 0.25 1 1.695808366 0.2285890778 0.00500555168 7.280374948 0.2496406132 1.047206761 -0.8757623394 -1.32767186 2 3 4 5 6 7 8 9 0.374715 -0.310775 -1.993544 0.188653 0.102541 -0.118381 2.450497 2.437752 0.780580 0.621121 0.822470 0.803039 1.142053 1.178409 1.376154 0.864196 12.670000 12.711295 1.197509 22.901723 22.905453 0.108175 23.122728 23.154929 0.933785 29.760059 29.796166 1.047066 17.896133 17.898176 0.059240 36.887334 36.916058 0.832964 46.177985 46.178489 0.014636 46.341619 46.324811 -0.487413 17.896133 17.922973 0.778322 29.572275 29.602518 0.876994 36.887334 36.895902 0.248480 46.177985 46.349843 4.983660 31.582318 31.580802 -0.043987 32.447240 32.450198 0.085778 41.347148 41.351999 0.140696 46.225782 46.179899 -1.330555 12.670000 12.752717 1.199338 22.901723 22.908964 0.104992 29.760059 29.551768 -3.020075 31.582318 31.609123 0.388642 17.896133 17.911283 0.219659 36.887334 36.889481 0.031136 46.177985 46.209316 0.454283 46.341619 46.344985 0.048803 17.896133 17.938728 0.617593 29.572275 29.632758 0.876963 36.887334 36.963718 1.107518 46.177985 46.317233 2.019016 23.122728 23.186801 0.929017 31.582318 32.112835 7.692145 32.707744 32.271775 -6.321258 34.645430 34.614802 -0.444091 12.670000 22.901723 29.760059 32.865940 55.015504 57.883532 77.304314 71.385684 47.948655 81.985876 105.639233 107.019286 29.572275 46.668316 59.634199 77.715168 23.122728 34.685737 32.707744 34.645430 49.977811 55.302562 67.130528 73.399719 32.447240 61.455871 68.276757 102.111627 46.491115 63.085916 64.111953 92.385057 17.896133 36.887334 46.341619 46.177985 31.582318 41.347148 46.225782 53.004985