********* 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 11 50.91708566 -0.9092152296 6.108719182 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 1.422339 26.819460 26.827600 0.250626 27.961128 27.971908 0.331891 28.363122 28.403379 1.239446 21.205457 21.215520 0.309840 44.020920 44.035810 0.458466 52.593058 52.603405 0.318597 56.776303 56.762867 -0.413675 21.205457 21.233779 0.872004 33.841997 33.873920 0.982858 44.020920 44.021862 0.029005 52.593058 52.597402 0.133747 32.130935 32.150262 0.595036 35.814326 35.805644 -0.267317 49.880802 49.890721 0.305401 52.154523 52.165981 0.352761 12.670000 12.762439 1.423058 26.819460 26.835509 0.247068 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 -0.114411 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 0.556723 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 84.81338579 -0.82090354 5.202246183 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 1.144121 22.943926 22.965243 0.687496 31.586321 31.589923 0.116183 23.738554 23.757546 0.612487 47.306779 47.320190 0.432494 51.498568 51.484038 -0.468614 53.415861 53.460217 1.430499 23.738554 23.751717 0.424498 37.852877 37.864873 0.386885 47.306779 47.339278 1.048093 51.498568 51.495828 -0.088382 31.707649 31.726253 0.599975 37.348783 37.338603 -0.328294 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 0.495016 47.306779 47.355844 0.791177 51.498568 51.484395 -0.228544 53.415861 53.449140 0.536621 23.738554 23.772172 0.542104 37.852877 37.876882 0.387088 47.306779 47.350038 0.697556 51.498568 51.478266 -0.327384 17.365643 17.436740 1.146452 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 80.236116 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 77.545506 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 19 125.4557055 -1.00392376 5.007941367 0.25 1 1.718807972 0.2197835185 0.007362504244 6.993637943 0.2693113969 1.064955912 -0.005592468803 -0.5317882401 2 3 4 5 6 7 8 9 0.368152 -0.317836 -2.004553 0.216449 0.064657 -0.080237 2.342532 2.376807 0.775554 0.695951 0.939007 0.895959 1.323122 1.317364 1.367181 0.976113 12.670000 12.712351 1.249321 23.215704 23.253337 1.110128 23.309242 23.312368 0.092188 30.110282 30.244874 3.970293 18.300251 18.302313 0.060827 37.455665 37.477917 0.656421 47.122044 47.125071 0.089289 47.864751 47.854721 -0.295891 18.300251 18.328125 0.822237 30.219846 30.251962 0.947373 37.455665 37.456175 0.015061 47.122044 47.465454 10.130223 32.086904 32.085055 -0.054554 32.985123 32.988426 0.097448 42.220350 42.224619 0.125915 47.200202 47.156796 -1.280432 12.670000 12.754782 1.250488 23.309242 23.315273 0.088948 30.110282 29.914436 -2.888626 32.086904 32.079203 -0.113595 18.300251 18.315853 0.230116 37.455665 37.457426 0.025972 47.122044 47.152710 0.452314 47.471094 47.460355 -0.158386 18.300251 18.344500 0.652637 30.219846 30.284073 0.947313 37.455665 37.502767 0.694733 47.122044 47.680529 8.237354 23.215704 23.290625 1.105037 32.086904 32.109077 0.327035 32.414522 32.501799 1.287280 34.780171 34.853540 1.082140 12.670000 23.309242 30.110282 33.328576 56.500659 58.986824 79.499145 73.572775 48.932933 84.268867 108.929479 109.834240 30.219846 47.680538 61.121029 79.859911 23.215704 36.046794 32.414522 34.780171 51.190231 56.520356 68.943162 75.360828 32.985123 63.101663 69.982732 105.418701 47.471094 64.714683 65.771132 95.002871 18.300251 37.455665 47.864751 47.122044 32.086904 42.220350 47.200202 54.218778