********* Eigenvalues for the 3+1 transverse lattice ********* Couplings: 0:mu^2 1:g^2 N 2:beta 3:lambda_1 4:lambda_2 5:lambda_3 6:lambda_4 7:lambda_5 8:tau_1 9:tau_2 10:kappa_S 11:kappa_A 12:mu_F 13:mu_0^2 14:mu_1^2 15:mu_2^2 16:mu_3^2 Use chi^2 fit with 40 criteria and tolerance 0.01. Overall scale from minimizing chi^2. 1/K^2 term used in all extrapolations. Parity doublets (charge,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 4 states (multiplet, charge, c^2 error for each) = (15, 1, 0.25 2 2 2) (15, -1, 0.25 2 2 2) (16, -1, 0.25 2 2 2) (16, 1, 0.25 2 2 2) Spectrum for P_perp a = (0,0), ( 0.25 0.25) using 4 states (multiplet, charge, c^2 error for each) = (17, 1, 0.25 2 2 2) (17, -1, 0.25 2 2 2) (18, -1, 0.25 2 2 2) (18, 1, 0.25 2 2 2). Ordinary spectra multiplets, 4 states, (charge,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) = (20/2,6) (20/2,8) (26/2,6) (32/2,6) (40/2,6) . Winding potential using (n,K,p) = ( 2 0,20/2,6) ( 2 0,20/2,8) ( 2 0,26/2,6) ( 2 0,32/2,6) ( 2 0,40/2,6) ( 3 0,20/2,5) ( 3 0,20/2,7) ( 3 0,26/2,5) ( 3 0,32/2,5) ( 3 0,40/2,5) ( 4 0,20/2,6) ( 4 0,20/2,8) ( 4 0,26/2,6) ( 4 0,32/2,6) ( 4 0,40/2,6) . Roundness of winding using (n,K,p) = ( 2 2,20/2,6) ( 2 2,20/2,8) ( 2 2,26/2,6) ( 2 2,32/2,6) ( 2 2,40/2,6) 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 0,60/2,2,3.75) ( 0 0,60/2,2,4.25) ( 0 0,100/2,2,4) ( 0 0,100/2,2,4.5) , 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 0,30/2,3,4) ( 1 0,30/2,5,4) ( 1 0,30/2,3,3.5) ( 1 0,60/2,3,4) ( 1 0,60/2,3,5) ( 1 0,100/2,3,5) ( 1 0,100/2,3,6) L=1.265-0.964*m and error 0.1; ( 1 0,30/2,3,4) ( 1 0,30/2,5,4) ( 1 0,30/2,3,3.5) ( 1 0,60/2,3,4) ( 1 0,60/2,3,5) ( 1 0,100/2,3,5) ( 1 0,100/2,3,6) L=5.058-3.856*m and error 0.1; ( 1 1,30/2,2,5.5) ( 1 1,30/2,4,5.5) ( 1 1,30/2,2,5) ( 1 1,30/2,2,5.5) ( 1 1,30/2,2,6.5) ( 1 1,100/2,2,6) ( 1 1,100/2,2,7) L=0+0*m and error 0.2; all in G^2 N units. p-extrapolation using n=( 1 0) and (K,p) = (24/2,5) (24/2,7) (24/2,9) . Result format: Fit info, # steps, chi^2, and p damping, scale G^2 N/sigma. The 17 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 22 81.88258399 -2.756749337 8.894655481 0 1 -0.2546928525 0.1616578358 -0.1404257494 1536.59326 -0.1231439098 757.144055 -1.10374949 -1.484784926 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.145645 -0.031769 -1.418906 0.140778 -0.085036 0.269211 1.238125 0.956028 0.527766 0.499257 0.769398 0.816707 1.162392 0.646859 10.879324 10.922541 0.895777 25.159863 25.094173 -1.36158 26.928683 26.938868 0.211099 29.703401 29.748617 0.937205 24.875673 24.892240 0.343384 41.097063 41.112227 0.314319 50.750059 50.772139 0.457677 52.005368 52.004435 -0.0193394 20.141551 20.148222 0.138281 24.875673 24.892094 0.34037 41.097063 41.101369 0.08925 49.630794 49.597248 -0.695336 29.703401 29.712191 0.182177 32.981207 32.980612 -0.0123399 43.471951 43.487010 0.312119 52.095342 52.078016 -0.359123 10.879324 10.965593 0.89407 25.159863 25.033701 -1.3075 29.703401 29.820576 1.21436 32.981207 32.980221 -0.0102154 24.875673 24.918676 0.445671 41.097063 41.118646 0.223684 49.630794 49.566057 -0.670916 50.750059 50.803117 0.549883 20.141551 20.154958 0.138947 24.875673 24.898452 0.236075 41.097063 41.113698 0.172399 49.644571 49.632410 -0.126028 26.928683 26.942548 0.143687 29.703401 29.691134 -0.127139 37.728225 37.894078 1.71885 43.471951 43.348212 -1.2824 10.879324 25.159863 34.337594 39.936576 63.386957 64.103728 69.222934 80.408019 56.758917 60.283827 67.139414 79.394804 20.141551 49.644571 53.189110 60.860795 26.928683 37.728225 44.367131 48.798877 52.005368 60.174820 68.405153 79.175129 32.981207 54.626454 72.944342 73.236889 49.630794 59.349767 61.897788 72.564395 24.875673 41.097063 50.750059 56.658132 29.703401 43.471951 52.095342 55.736609 1 39 65.18503272 -2.438267522 10.22595504 0.001967542671 1 0.3828033402 0.2305046045 -0.2406620893 349835.6311 -0.04815808088 143070.1472 -1.671159074 -2.291408068 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.132362 -0.414075 -0.586578 0.113866 -0.273892 0.590123 0.772095 0.571495 0.438805 0.322700 0.492882 0.521545 1.000560 0.437360 10.554307 10.615318 1.32129 28.041928 28.076885 0.757044 28.723027 28.701597 -0.464102 35.555876 35.521556 -0.743253 27.234673 27.256516 0.473046 45.716690 45.743418 0.578849 56.443585 56.480453 0.79843 60.442113 60.450316 0.177632 23.620540 23.626742 0.134315 27.234673 27.274421 0.860795 45.716690 45.731845 0.32822 56.258074 56.180811 -1.67324 35.555876 35.577761 0.473936 42.179934 42.180901 0.0209354 50.396853 50.424400 0.59657 62.974894 62.970833 -0.0879505 10.554307 10.676227 1.32018 28.723027 28.687654 -0.38303 35.555876 35.529802 -0.282345 40.373011 40.446708 0.798012 27.234673 27.289530 0.594008 45.716690 45.756216 0.428003 56.258074 56.184470 -0.796994 56.443585 56.539048 1.03369 23.620540 23.633426 0.139535 27.234673 27.302532 0.73479 45.716690 45.759323 0.461646 56.443585 56.675134 2.50726 28.041928 28.104991 0.682853 35.555876 35.555879 2.96458e-05 45.406296 45.389598 -0.180804 50.396853 50.516088 1.2911 10.554307 28.723027 40.373011 47.342198 76.882212 79.067592 74.539722 96.531863 66.957845 74.579969 86.846586 101.485303 23.620540 59.184916 64.425352 79.733812 28.041928 45.406296 50.843910 54.904870 60.442113 76.878156 78.200685 95.316202 42.179934 68.099841 86.552943 80.356293 56.258074 61.895029 83.837247 89.576638 27.234673 45.716690 56.443585 71.286731 35.555876 50.396853 62.974894 68.301385 2 30 107.011728 -2.999274011 5.23243201 0.007919222016 1 0.2915529634 0.06137030907 -0.1246642037 262620.6729 0.007896282012 -125436.2951 -1.287568599 -1.979697008 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.187844 -0.218903 -0.370936 0.136942 -0.145570 0.374172 2.133058 1.237482 0.504807 0.350846 0.614868 0.642411 1.070940 0.410289 11.598343 11.614217 0.249639 16.096500 16.110058 0.213209 16.204067 16.207757 0.0580411 18.882726 18.858437 -0.38197 16.074890 16.082142 0.11405 28.179613 28.192125 0.196766 31.797947 31.805572 0.119915 33.849861 33.850784 0.0145172 16.074890 16.170103 1.49733 17.340550 17.255521 -1.33717 28.179613 28.183609 0.0628373 31.797947 31.804902 0.109377 18.882726 18.889211 0.101984 20.928394 20.924455 -0.0619476 30.220863 30.230744 0.155395 32.700492 32.700565 0.00115716 11.598343 11.630058 0.249376 16.204067 16.219391 0.1205 18.882726 18.846064 -0.288276 20.928394 20.919677 -0.0685425 16.074890 16.089429 0.114322 28.179613 28.190648 0.08677 31.797947 31.810371 0.0976942 35.200537 35.203418 0.0226464 16.074890 16.250118 1.37783 17.340550 17.185622 -1.21821 28.179613 28.201401 0.17132 31.797947 31.814185 0.127682 16.096500 16.115622 0.150352 18.882726 18.884187 0.0114896 21.512409 21.500232 -0.0957507 28.639223 28.993566 2.78621 11.598343 16.204067 21.408886 22.579879 41.010535 41.555784 42.597013 51.381746 35.900067 36.872770 43.968155 48.308355 17.340550 34.259752 35.952731 43.805914 16.096500 21.512409 29.043878 28.639223 33.849861 42.148743 41.677592 51.798314 20.928394 37.369774 43.761783 46.378984 35.200537 37.617320 42.170807 45.147733 16.074890 28.179613 31.797947 37.649999 18.882726 30.220863 32.700492 35.578785 2 57 30.02227566 -2.448244458 9.479078562 0.01800590693 1 0.5627179068 0.03312387817 -0.1050565025 2187.649264 0.03820850964 1018.080029 -1.593983909 -1.900638289 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.198480 -0.458942 -0.802592 0.123072 -0.228114 0.503193 1.184252 1.028578 0.515014 0.425156 0.637840 0.616191 1.040714 0.591163 10.513266 10.550700 1.12685 26.612763 26.630531 0.534846 27.606570 27.609870 0.0993432 31.535391 31.512573 -0.686863 27.732864 27.745240 0.372545 45.379801 45.411402 0.951263 56.798399 56.817535 0.576032 60.543612 60.536037 -0.228035 27.732864 27.766975 1.02682 29.932059 29.955449 0.704092 45.379801 45.367060 -0.383531 56.798399 56.877039 2.36726 31.535391 31.560669 0.760939 36.224434 36.209892 -0.437765 50.605035 50.632367 0.822766 57.643454 57.672781 0.882809 10.513266 10.588163 1.12729 27.606570 27.606741 0.00257428 31.535391 31.544285 0.133869 34.387441 34.382929 -0.0679121 27.732864 27.776439 0.655855 45.379801 45.395107 0.230375 56.798399 56.883453 1.28017 60.124625 60.078935 -0.687685 27.732864 27.778194 0.682273 29.932059 29.983018 0.767004 45.379801 45.401526 0.326987 56.798399 56.987809 2.85087 26.612763 26.654441 0.627302 31.535391 31.531211 -0.062913 34.318614 34.325256 0.0999727 46.355808 46.354757 -0.0158138 10.513266 27.606570 34.387441 44.950599 73.684507 80.930704 78.293313 91.313376 61.469422 64.759472 85.802362 89.757154 29.932059 61.834322 63.879785 76.801310 26.612763 34.318614 46.355808 49.837522 60.543612 75.751723 83.391775 93.822523 36.224434 65.449948 79.505887 79.783485 60.124625 61.679098 83.930430 84.852041 27.732864 45.379801 56.798399 70.841632 31.535391 50.605035 57.643454 66.004438 2 48 82.41562195 -2.448244458 9.479078562 0.03249196962 1 0.8667231126 0.1089537809 -0.1450426846 31718.64654 0.3177797202 1294.138006 -1.594412188 -1.782851633 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.198480 -0.458942 -0.802592 0.123072 -0.228114 0.503193 1.184252 1.028578 0.515014 0.425156 0.637840 0.616191 1.040714 0.591163 10.513266 10.550700 1.12685 26.612763 26.630531 0.534846 27.606570 27.609870 0.0993432 31.535391 31.512573 -0.686863 27.732864 27.745240 0.372545 45.379801 45.411402 0.951263 56.798399 56.817535 0.576032 60.543612 60.536037 -0.228035 27.732864 27.766975 1.02682 29.932059 29.955449 0.704092 45.379801 45.367060 -0.383531 56.798399 56.877039 2.36726 31.535391 31.560669 0.760939 36.224434 36.209892 -0.437765 50.605035 50.632367 0.822766 57.643454 57.672781 0.882809 10.513266 10.588163 1.12729 27.606570 27.606741 0.00257428 31.535391 31.544285 0.133869 34.387441 34.382929 -0.0679121 27.732864 27.776439 0.655855 45.379801 45.395107 0.230375 56.798399 56.883453 1.28017 60.124625 60.078935 -0.687685 27.732864 27.778194 0.682273 29.932059 29.983018 0.767004 45.379801 45.401526 0.326987 56.798399 56.987809 2.85087 26.612763 26.654441 0.627302 31.535391 31.531211 -0.062913 34.318614 34.325256 0.0999727 46.355808 46.354757 -0.0158138 10.513266 27.606570 34.387441 44.950599 73.684507 80.930704 78.293313 91.313376 61.469422 64.759472 85.802362 89.757154 29.932059 61.834322 63.879785 76.801310 26.612763 34.318614 46.355808 49.837522 60.543612 75.751723 83.391775 93.822523 36.224434 65.449948 79.505887 79.783485 60.124625 61.679098 83.930430 84.852041 27.732864 45.379801 56.798399 70.841632 31.535391 50.605035 57.643454 66.004438 1 58 46.33943527 -2.585029871 11.12388405 0.0517766953 1 0.7160454212 -0.05872471784 -0.05024358428 2549633.693 0.1436478277 442080.2252 -2.074773831 -2.57669355 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.273459 -0.439091 -0.692756 0.101678 -0.257088 0.512414 2.240682 1.661986 0.520488 0.430554 0.516813 0.542809 1.161271 0.641656 21.790490 21.811273 1.01153 37.770774 37.789520 0.912395 37.931067 37.955717 1.19976 43.080387 43.068467 -0.580167 38.022399 38.029856 0.362916 64.198393 64.240693 2.05877 79.560368 79.561617 0.060766 84.477182 84.471926 -0.255815 38.022399 38.031753 0.45526 50.299644 50.348796 2.39228 64.198393 64.184842 -0.659582 79.560368 79.619398 2.87301 45.101553 45.121582 0.974793 50.319383 50.303592 -0.768544 71.025988 71.048577 1.09944 76.932985 76.940542 0.367775 21.790490 21.832215 1.01541 37.931067 37.980319 1.19857 43.080580 43.081276 0.0169518 45.101553 45.084221 -0.421803 38.022399 38.050720 0.689194 64.198393 64.214931 0.402447 79.560368 79.581013 0.502387 86.132477 86.030763 -2.47524 38.022399 38.028532 0.149239 50.299644 50.397406 2.37909 64.198393 64.238510 0.976259 79.560368 79.636929 1.86313 37.770774 37.807586 0.895851 43.080387 43.080694 0.00746328 45.101553 45.102076 0.0127088 57.552819 57.604223 1.25096 21.790490 37.931067 43.080580 56.302706 95.586949 104.625838 118.440493 125.855149 82.837240 92.816511 116.525042 127.936270 50.299644 84.103065 100.280423 109.019410 37.770774 43.080387 57.552819 69.641989 84.477182 97.938014 118.893902 120.638962 50.319383 99.765012 102.161711 113.850122 86.132477 90.964587 111.242588 115.942585 38.022399 64.198393 79.560368 94.660431 45.101553 71.025988 76.932985 94.390875 1 49 31.834014 -2.448244458 9.479078562 0.07642881742 1 0.7548959906 -0.0801511735 -0.04253468797 5049.306346 0.1383156146 2229.637051 -2.141892323 -2.55348201 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.198480 -0.458942 -0.802592 0.123072 -0.228114 0.503193 1.184252 1.028578 0.515014 0.425156 0.637840 0.616191 1.040714 0.591163 10.513266 10.550700 1.12685 26.612763 26.630531 0.534846 27.606570 27.609870 0.0993432 31.535391 31.512573 -0.686863 27.732864 27.745240 0.372545 45.379801 45.411402 0.951263 56.798399 56.817535 0.576032 60.543612 60.536037 -0.228035 27.732864 27.766975 1.02682 29.932059 29.955449 0.704092 45.379801 45.367060 -0.383531 56.798399 56.877039 2.36726 31.535391 31.560669 0.760939 36.224434 36.209892 -0.437765 50.605035 50.632367 0.822766 57.643454 57.672781 0.882809 10.513266 10.588163 1.12729 27.606570 27.606741 0.00257428 31.535391 31.544285 0.133869 34.387441 34.382929 -0.0679121 27.732864 27.776439 0.655855 45.379801 45.395107 0.230375 56.798399 56.883453 1.28017 60.124625 60.078935 -0.687685 27.732864 27.778194 0.682273 29.932059 29.983018 0.767004 45.379801 45.401526 0.326987 56.798399 56.987809 2.85087 26.612763 26.654441 0.627302 31.535391 31.531211 -0.062913 34.318614 34.325256 0.0999727 46.355808 46.354757 -0.0158138 10.513266 27.606570 34.387441 44.950599 73.684507 80.930704 78.293313 91.313376 61.469422 64.759472 85.802362 89.757154 29.932059 61.834322 63.879785 76.801310 26.612763 34.318614 46.355808 49.837522 60.543612 75.751723 83.391775 93.822523 36.224434 65.449948 79.505887 79.783485 60.124625 61.679098 83.930430 84.852041 27.732864 45.379801 56.798399 70.841632 31.535391 50.605035 57.643454 66.004438 2 11 41.13835841 -2.486412705 7.485021768 0.1072401379 1 0.9693536776 0.0204072559 -0.09558755502 3001.62308 0.1117905621 1359.332191 -1.648715278 -1.819325638 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.352662 -0.563378 -1.180065 0.145524 -0.088035 0.213219 2.600015 2.110406 0.660353 0.620317 0.796569 0.799006 1.285116 0.860673 18.060294 18.090230 1.26436 37.668292 37.686214 0.756962 38.517361 38.531232 0.585841 41.756839 41.712954 -1.85345 28.912709 28.917977 0.222476 51.651066 51.676030 1.05438 66.291801 66.309136 0.732162 69.280697 69.270484 -0.431342 28.912709 28.927437 0.62203 41.396343 41.435021 1.63354 51.651066 51.635445 -0.659754 66.291801 66.328299 1.54149 41.756839 41.777426 0.869518 46.492426 46.477313 -0.638297 59.194064 59.212317 0.770894 66.593253 66.604278 0.46566 18.060294 18.120258 1.2663 38.517361 38.542748 0.536117 41.756839 41.747637 -0.19432 43.113336 43.114309 0.0205469 28.912709 28.936654 0.505646 51.651066 51.660165 0.192146 66.291801 66.298960 0.151175 66.910292 66.931271 0.443027 28.912709 28.928846 0.340759 41.396343 41.473919 1.63819 51.651066 51.660228 0.193492 66.291801 66.387561 2.02221 37.668292 37.705762 0.791269 41.756839 41.725715 -0.657262 42.538583 42.564872 0.555144 42.907754 42.932624 0.52518 18.060294 38.517361 43.113336 43.170729 80.251599 83.198853 95.868830 101.393111 71.675732 84.801659 109.933535 110.426343 41.396343 69.930452 88.300279 85.543031 37.668292 42.907754 42.538583 57.653093 69.280697 80.753490 92.049596 97.185967 46.492426 77.220224 89.284817 92.937651 66.910292 83.906219 84.858497 95.966826 28.912709 51.651066 66.291801 70.017141 41.756839 59.194064 66.593253 77.364368 2 49 56.27160837 -2.448244458 9.479078562 0.1453085056 1 1.252473799 -0.01285882917 -0.3410730989 1656.424111 0.1306108859 738.6348871 -0.7573425426 -1.217352712 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.198480 -0.458942 -0.802592 0.123072 -0.228114 0.503193 1.184252 1.028578 0.515014 0.425156 0.637840 0.616191 1.040714 0.591163 10.513266 10.550700 1.12685 26.612763 26.630531 0.534846 27.606570 27.609870 0.0993432 31.535391 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