********* 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 21 104.268357 -0.8903568857 7.610640525 0.03249196962 1 0.5600077032 -0.08278450812 -0.24268896 10.61907221 0.1096823369 2.034598746 0.03965971645 0.3185293312 2 3 4 5 6 7 8 9 0.203390 -1.070011 1.181570 0.185886 0.129439 -0.155818 2.054142 0.704802 0.646314 0.722058 0.901070 0.882063 1.204403 1.231091 1.199031 0.999630 10.254004 10.321999 1.684002 10.485204 10.566200 2.005998 12.670000 12.661203 -0.217886 26.932462 26.883582 -1.210580 23.040788 23.076071 0.873830 45.749336 45.785467 0.894855 47.235244 47.272145 0.913903 54.691022 54.697604 0.163015 23.040788 23.059906 0.473481 32.578577 32.599399 0.515692 45.749336 45.779848 0.755693 47.235244 47.245030 0.242359 26.932462 26.960557 0.695830 33.669776 33.657945 -0.293020 48.788752 48.828727 0.990035 49.649734 49.645359 -0.108344 10.254004 10.391801 1.706387 12.670000 12.719130 0.608392 26.932462 26.850985 -1.008958 28.847438 28.773014 -0.921620 23.040788 23.087561 0.579200 45.749336 45.797167 0.592316 47.235244 47.282312 0.582851 62.768497 62.761621 -0.085156 23.040788 23.102889 0.769017 32.578577 32.620252 0.516080 45.749336 45.834694 1.057018 47.235244 47.281322 0.570599 10.485204 10.578617 1.156761 26.932462 26.975901 0.537922 30.586301 30.501363 -1.051815 30.918018 31.003447 1.057894 12.670000 10.254004 28.847438 31.665638 63.183325 64.966797 85.483075 85.120081 59.136121 80.993405 97.072168 94.211425 32.578577 58.256467 71.179313 93.430146 10.485204 30.586301 30.918018 43.406860 54.691022 63.093560 85.289384 87.850148 33.669776 75.803884 87.859092 82.062180 62.768497 79.896864 85.130605 72.502543 23.040788 45.749336 47.235244 65.639261 26.932462 49.649734 48.788752 57.845868 2 65 51.88500981 -1.012764577 7.35690937 0.0517766953 1 0.8053638894 -0.08293719093 -0.1751274521 7.205644424 0.2276621744 1.525720612 -0.04196305763 0.387657513 2 3 4 5 6 7 8 9 0.227250 -1.073177 1.053889 0.191186 0.113869 -0.133469 2.061060 0.876558 0.641120 0.746320 0.914508 0.906307 1.257364 1.259656 1.214125 1.035200 12.670000 12.707855 1.012605 15.109992 15.143176 0.887656 15.433460 15.467255 0.904010 25.744239 25.814104 1.868851 22.217239 22.237822 0.550579 45.582880 45.614633 0.849373 48.654263 48.690829 0.978133 56.346239 56.339446 -0.181702 22.217239 22.239753 0.602232 33.793206 33.821410 0.754442 45.582880 45.602577 0.526891 48.654263 48.671352 0.457117 27.527870 27.553243 0.678730 32.572811 32.560757 -0.322441 48.702352 48.729273 0.720132 49.917869 49.927775 0.264974 12.670000 12.745744 1.013067 15.109992 15.175362 0.874318 25.852829 25.866229 0.179222 27.527870 27.670094 1.902225 22.217239 22.243842 0.355807 45.582880 45.624512 0.556823 48.654263 48.688482 0.457673 60.766443 60.787899 0.286977 22.217239 22.276880 0.797690 33.793206 33.849627 0.754621 45.582880 45.643971 0.817082 48.654263 48.725791 0.956674 15.433460 15.501689 0.912546 25.744239 25.773076 0.385683 25.783702 25.969749 2.488342 27.527870 27.477328 -0.675986 12.670000 15.109992 25.852829 28.900928 63.022439 64.749503 86.449196 83.063641 56.539190 87.343412 88.306445 113.188108 33.793206 56.568135 74.914438 98.590741 15.433460 25.783702 25.744239 44.056843 56.346239 62.372129 87.711492 86.936419 32.572811 79.418683 73.125515 101.898533 60.766443 76.734594 93.934240 75.346852 22.217239 45.582880 48.654263 65.017458 27.527870 49.917869 48.702352 60.559095 2 76 44.14652367 -0.951659175 6.333180588 0.07642881742 1 0.8347637881 0.03187481423 -0.294875563 19.814336 0.1506472787 4.98862931 0.1222352436 -0.004998060414 2 3 4 5 6 7 8 9 0.263140 -1.031616 0.730773 0.197810 0.105978 -0.131365 2.225758 1.164854 0.688646 0.708178 0.905842 0.884818 1.249774 1.263440 1.260995 0.986209 12.670000 12.721546 1.374423 21.374565 21.411013 0.971877 22.258366 22.289021 0.817386 29.658844 29.665499 0.177458 20.659717 20.679216 0.519920 43.578195 43.595570 0.463309 48.153054 48.189309 0.966700 53.713146 53.774749 1.642591 20.659717 20.682338 0.603178 31.046203 31.070624 0.651166 43.578195 43.596947 0.500027 48.153054 48.163672 0.283105 30.196282 30.220723 0.651695 35.549931 35.541894 -0.214304 49.482336 49.505036 0.605263 50.496166 50.502478 0.168311 12.670000 12.773106 1.374628 22.258366 22.318134 0.796825 29.658844 29.672387 0.180553 30.196282 30.173357 -0.305643 20.659717 20.691920 0.429329 43.578195 43.614966 0.490236 48.153054 48.182493 0.392476 57.407083 57.410340 0.043420 20.659717 20.711774 0.694033 31.046203 31.095068 0.651464 43.578195 43.613628 0.472396 48.153054 48.217133 0.854311 21.374565 21.449034 0.992838 30.196282 30.205067 0.117119 30.303075 30.380889 1.037426 33.931047 33.894610 -0.485781 12.670000 22.258366 29.658844 33.876241 62.801105 61.461071 84.104737 80.875674 57.640068 88.743213 92.806288 116.564876 31.046203 55.205044 72.191630 88.961921 21.374565 30.303075 33.931047 44.653324 53.713146 61.770473 80.611712 82.820249 35.549931 72.855013 70.060098 99.833700 57.407083 74.310236 74.418160 88.396873 20.659717 43.578195 48.153054 58.268517 30.196282 49.482336 50.496166 57.623775 2 40 41.74066726 -0.9298037996 6.017391396 0.1072401379 1 1.010299347 0.06377601078 -0.237912886 66.60646779 0.156974588 19.07312956 0.06414892733 -0.08995752766 2 3 4 5 6 7 8 9 0.303343 -0.997822 0.428975 0.203371 0.091524 -0.111766 2.265959 1.482544 0.711021 0.731806 0.922326 0.908865 1.293723 1.292840 1.281602 1.020865 12.670000 12.716571 1.360108 28.096671 28.129351 0.954438 28.500248 28.531140 0.902221 28.592485 28.613535 0.614769 20.364479 20.377359 0.376181 42.730707 42.746737 0.468160 51.905507 51.953173 1.392087 54.451197 54.446516 -0.136704 20.364479 20.390482 0.759437 31.111975 31.139018 0.789804 42.730707 42.739269 0.250057 51.905507 51.969500 1.868945 31.470924 31.491774 0.608940 35.543993 35.536082 -0.231046 48.275617 48.291686 0.469293 52.022522 52.025257 0.079870 12.670000 12.763133 1.359991 28.500248 28.499831 -0.006080 28.592485 28.634060 0.607104 31.470924 31.469807 -0.016317 20.364479 20.392216 0.405034 42.730707 42.759142 0.415229 51.905507 51.966124 0.885163 54.884334 54.844202 -0.586027 20.364479 20.414505 0.730520 31.111975 31.166076 0.790018 42.730707 42.751554 0.304426 51.905507 52.068782 2.384251 28.096671 28.162909 0.967261 30.366102 30.368397 0.033512 31.470924 31.464398 -0.095305 33.994649 33.991653 -0.043743 12.670000 28.592485 28.500248 34.022367 63.789729 61.718709 85.354824 79.973192 56.583293 94.160650 92.173005 115.823823 31.111975 54.198952 70.720130 76.679926 28.096671 30.366102 33.994649 45.889839 54.451197 62.422734 79.223756 82.694140 35.543993 71.202232 72.452142 99.012786 55.685562 75.796096 66.915896 98.138046 20.364479 42.730707 51.905507 54.884334 31.470924 48.275617 52.022522 58.056461