********* 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:zeta 11:kappa_S(9) 12:kappa_S(10) 13:kappa_S(11) 14:kappa_A(12) 15:kappa_A(13) 16:kappa_A(14) 17:mu_F(15) 18:mu_F(16) 19:mu_F(17) 20:mu_0^2(18) 21:mu_0^2(19) 22:mu_0^2(20) 23:mu_1^2(21) 24:mu_1^2(22) 25:mu_1^2(23) 26:mu_2^2(24) 27:mu_2^2(25) 28:mu_2^2(26) 29:mu_3^2(27) 30:mu_3^2(28) 31:mu_3^2(29) 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) (24/2,6) (28/2,6) (32/2,6) (40/2,6) . Winding potential using (n,K,p) = ( 2 0,20/2,6) ( 2 0,20/2,8) ( 2 0,24/2,6) ( 2 0,28/2,6) ( 2 0,32/2,6) ( 2 0,40/2,6) ( 3 0,20/2,5) ( 3 0,20/2,7) ( 3 0,24/2,5) ( 3 0,28/2,5) ( 3 0,32/2,5) ( 3 0,40/2,5) ( 4 0,20/2,6) ( 4 0,20/2,8) ( 4 0,24/2,6) ( 4 0,28/2,6) ( 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 2,24/2,6) ( 2 2,28/2,6) ( 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 32 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 82.28446395 -2.759430215 8.888259618 0 1 -0.2542230945 0.1620003782 -0.139734519 1537.140659 -0.1231826608 756.8971785 -1.102493015 -1.485336785 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 0.146138 -0.033794 -1.403571 0.140865 -0.084347 0.267881 1.246454 0.959860 0.527747 0.500264 0.769262 0.817951 1.162245 0.648288 10.970024 11.012977 0.89268 25.187313 25.121969 -1.35801 26.985833 26.995201 0.194697 29.722379 29.767464 0.936988 24.885690 24.902124 0.341532 41.119363 41.134438 0.313302 50.763084 50.785071 0.456933 52.008607 52.007540 -0.0221773 20.163994 20.170573 0.136723 24.885690 24.901987 0.3387 41.119363 41.123620 0.0884845 49.608415 49.575282 -0.688591 29.722379 29.731076 0.180742 32.977103 32.976484 -0.0128667 43.481218 43.496122 0.309749 52.081674 52.064387 -0.359259 10.970024 11.055764 0.890951 25.187313 25.061790 -1.30435 29.722379 29.839020 1.21205 32.977103 32.976091 -0.01051 24.885690 24.928364 0.443435 41.119363 41.140770 0.222446 49.608415 49.544525 -0.6639 50.763084 50.815621 0.545917 20.163994 20.177224 0.13747 24.885690 24.908275 0.234691 41.119363 41.135875 0.171589 49.611938 49.600012 -0.123923 26.985833 26.998546 0.132102 29.722379 29.710214 -0.126407 37.749601 37.903372 1.59788 43.481218 43.360831 -1.25097 10.970024 25.187313 34.341951 39.937288 63.318593 64.010472 69.194577 80.449540 56.721763 60.245385 67.071334 79.269350 20.163994 49.611938 53.167528 60.798011 26.985833 37.749601 44.426734 48.800462 52.008607 60.115938 68.363560 79.115628 32.977103 54.581936 72.861943 73.132749 49.608415 59.568822 61.701517 72.376613 24.885690 41.119363 50.763084 56.613170 29.722379 43.481218 52.081674 55.721780 2 12 209.3099707 -2.759430215 8.888259618 0.001967542671 1 0.05128983526 0.08588843657 -0.1282959758 1570.962466 -0.04986973483 746.0818937 -1.171488692 -1.458193253 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 0.146138 -0.033794 -1.403571 0.140865 -0.084347 0.267881 1.246454 0.959860 0.527747 0.500264 0.769262 0.817951 1.162245 0.648288 10.970024 11.012977 0.89268 25.187313 25.121969 -1.35801 26.985833 26.995201 0.194697 29.722379 29.767464 0.936988 24.885690 24.902124 0.341532 41.119363 41.134438 0.313302 50.763084 50.785071 0.456933 52.008607 52.007540 -0.0221773 20.163994 20.170573 0.136723 24.885690 24.901987 0.3387 41.119363 41.123620 0.0884845 49.608415 49.575282 -0.688591 29.722379 29.731076 0.180742 32.977103 32.976484 -0.0128667 43.481218 43.496122 0.309749 52.081674 52.064387 -0.359259 10.970024 11.055764 0.890951 25.187313 25.061790 -1.30435 29.722379 29.839020 1.21205 32.977103 32.976091 -0.01051 24.885690 24.928364 0.443435 41.119363 41.140770 0.222446 49.608415 49.544525 -0.6639 50.763084 50.815621 0.545917 20.163994 20.177224 0.13747 24.885690 24.908275 0.234691 41.119363 41.135875 0.171589 49.611938 49.600012 -0.123923 26.985833 26.998546 0.132102 29.722379 29.710214 -0.126407 37.749601 37.903372 1.59788 43.481218 43.360831 -1.25097 10.970024 25.187313 34.341951 39.937288 63.318593 64.010472 69.194577 80.449540 56.721763 60.245385 67.071334 79.269350 20.163994 49.611938 53.167528 60.798011 26.985833 37.749601 44.426734 48.800462 52.008607 60.115938 68.363560 79.115628 32.977103 54.581936 72.861943 73.132749 49.608415 59.568822 61.701517 72.376613 24.885690 41.119363 50.763084 56.613170 29.722379 43.481218 52.081674 55.721780 2 11 123.9145695 -2.759430215 8.888259618 0.007919222016 1 0.3011124807 0.01801528854 -0.1346305717 1570.962466 0.01419058522 746.0818937 -1.235078327 -1.428012162 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 0.146138 -0.033794 -1.403571 0.140865 -0.084347 0.267881 1.246454 0.959860 0.527747 0.500264 0.769262 0.817951 1.162245 0.648288 10.970024 11.012977 0.89268 25.187313 25.121969 -1.35801 26.985833 26.995201 0.194697 29.722379 29.767464 0.936988 24.885690 24.902124 0.341532 41.119363 41.134438 0.313302 50.763084 50.785071 0.456933 52.008607 52.007540 -0.0221773 20.163994 20.170573 0.136723 24.885690 24.901987 0.3387 41.119363 41.123620 0.0884845 49.608415 49.575282 -0.688591 29.722379 29.731076 0.180742 32.977103 32.976484 -0.0128667 43.481218 43.496122 0.309749 52.081674 52.064387 -0.359259 10.970024 11.055764 0.890951 25.187313 25.061790 -1.30435 29.722379 29.839020 1.21205 32.977103 32.976091 -0.01051 24.885690 24.928364 0.443435 41.119363 41.140770 0.222446 49.608415 49.544525 -0.6639 50.763084 50.815621 0.545917 20.163994 20.177224 0.13747 24.885690 24.908275 0.234691 41.119363 41.135875 0.171589 49.611938 49.600012 -0.123923 26.985833 26.998546 0.132102 29.722379 29.710214 -0.126407 37.749601 37.903372 1.59788 43.481218 43.360831 -1.25097 10.970024 25.187313 34.341951 39.937288 63.318593 64.010472 69.194577 80.449540 56.721763 60.245385 67.071334 79.269350 20.163994 49.611938 53.167528 60.798011 26.985833 37.749601 44.426734 48.800462 52.008607 60.115938 68.363560 79.115628 32.977103 54.581936 72.861943 73.132749 49.608415 59.568822 61.701517 72.376613 24.885690 41.119363 50.763084 56.613170 29.722379 43.481218 52.081674 55.721780 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 2 31 56.09762893 -2.448244458 9.479078562 0.0517766953 1 0.5553927126 -0.06218848666 -0.09575376838 2603.679294 0.07337942127 1101.782583 -1.777430274 -2.244371066 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 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 67 41.41948808 -2.448244458 9.479078562 0.1072401379 1 0.9875232035 0.02959759127 -0.09965159425 1460.344932 0.1138726952 697.7717191 -1.610672245 -1.780781601 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 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