********* 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 41 criteria and tolerance 0.01. Overall scale from minimizing chi^2. 1/K^2 term used in all extrapolations. Includes a fit to 1 eigenvalues from Teper. 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 39 207.601762 -2.143456304 4.086353587 0 1 0.521500869 0.02394401402 -0.1151235259 1432627.325 -0.01808908408 583167.9262 -0.1165972331 -0.2041636153 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 0.150646 -0.474114 -1.795490 0.291972 -0.650594 1.386310 0.269219 0.506615 0.640313 0.625077 1.152667 1.158628 0.957595 0.622360 -0.035687 -0.013681 0.216754 7.939096 7.947081 0.0786546 8.937417 8.896414 -0.403854 10.025521 10.046525 0.206874 10.108047 10.116882 0.0870192 16.041849 16.053688 0.11661 20.537874 20.547734 0.0971162 21.801227 21.795205 -0.0593069 8.893164 8.895167 0.0197283 10.108047 10.139189 0.306729 16.041849 16.034255 -0.0747972 19.932336 19.857774 -0.734388 10.025521 10.037866 0.121593 12.027145 12.022983 -0.040998 17.310905 17.325476 0.143518 20.724163 20.673524 -0.49876 -0.035687 0.008298 0.216616 8.937417 8.856982 -0.39612 10.025521 10.109283 0.412506 11.266786 11.157330 -0.539044 10.108047 10.139328 0.154049 16.041849 16.049508 0.037718 19.932336 19.885128 -0.232484 20.537874 20.591652 0.26484 8.893164 8.897583 0.0217658 10.108047 10.156314 0.2377 16.041849 16.042023 0.000856814 20.537874 20.693352 0.765684 7.939096 7.955867 0.0825931 10.025521 10.006017 -0.096052 11.323849 11.347987 0.118874 15.888198 15.896870 0.0427065 -0.035687 8.937417 11.266786 16.510863 27.953449 29.115551 28.896697 32.158613 20.724163 23.933819 29.668367 33.054535 8.893164 21.466909 22.365919 29.924522 7.939096 11.323849 15.888198 19.179861 21.801227 28.568685 27.875206 34.400670 12.027145 21.833552 30.133145 29.310447 19.932336 22.542565 30.141851 30.156952 10.108047 16.041849 20.537874 24.032236 10.025521 17.310905 21.021909 22.402120 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 1 95 120.8416389 -2.476224629 6.781296139 0.007919222016 1 0.3824656222 0.1373709283 -0.1845541594 1071246.361 -0.05724626629 436920.0055 -0.798662287 -1.009388966 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 0.161382 -0.363717 -0.680546 0.161780 0.026986 0.049743 1.108346 0.842273 0.585374 0.523985 0.897674 0.917062 1.023715 0.663175 7.732140 7.770636 0.674068 19.362324 19.356038 -0.110059 20.005994 19.996417 -0.167684 23.374150 23.378139 0.0698486 19.234015 19.247276 0.232213 31.946554 31.963348 0.294073 39.084003 39.104893 0.365779 41.207672 41.209595 0.033662 17.787196 17.785532 -0.0291467 19.234015 19.264877 0.540407 31.946554 31.952132 0.0976704 39.084003 39.406574 5.64824 23.374150 23.388259 0.247052 27.032639 27.030088 -0.0446628 34.952478 34.971876 0.339651 41.631247 41.623756 -0.131176 7.732140 7.809050 0.673347 20.005994 19.945231 -0.531976 23.374150 23.413510 0.3446 27.032639 27.025267 -0.0645461 19.234015 19.269102 0.307189 31.946554 31.968252 0.189971 39.084003 39.540653 3.99799 40.131850 39.685031 -3.91193 17.787196 17.784367 -0.0247685 19.234015 19.286656 0.460879 31.946554 31.969071 0.197139 39.084003 39.871680 6.89615 19.362324 19.392486 0.264073 23.374150 23.369587 -0.0399486 29.173500 29.169585 -0.0342806 33.839624 33.742746 -0.848179 7.732140 20.005994 27.395299 31.012141 52.062639 53.711421 51.858873 63.812129 44.630872 48.041236 56.424094 68.039997 17.787196 41.558488 43.003681 54.078288 19.362324 29.173500 33.839624 38.054257 41.207672 52.022699 53.189083 63.698827 27.032639 44.922296 58.446584 52.742740 40.131850 42.372144 55.458048 60.763743 19.234015 31.946554 39.084003 47.681338 23.374150 34.952478 41.631247 45.549319 2 20 276.6160198 -1.865184233 3.317531807 0.01800590693 1 0.7466533319 1.070814546 -0.4000713583 65742.30218 0.1260136806 31151.98187 -1.111429603 -0.8629836374 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 0.044603 -0.901716 -1.984599 0.188337 -0.080318 0.193832 -1.435427 -0.792966 0.477515 0.316256 0.805152 0.827153 1.007712 0.301918 0.120742 0.139755 0.045015 11.819836 11.486752 -0.788594 12.166049 12.138902 -0.0642727 12.476928 12.498280 0.0505522 5.726152 5.729590 0.00813833 11.664820 11.675737 0.0258469 18.481227 18.489308 0.0191322 20.383227 20.385861 0.00623504 3.630612 3.671566 0.0969596 5.726152 5.710495 -0.0370689 11.664820 11.663754 -0.00252304 18.481227 20.584972 4.98073 13.462034 13.471791 0.0230997 15.891147 15.893511 0.00559626 17.858690 17.865819 0.0168786 22.719308 21.432942 -3.04554 0.120742 0.158796 0.0450471 12.476928 12.473472 -0.00409074 13.021237 12.997056 -0.0286249 13.462034 13.335155 -0.150197 5.726152 5.741603 0.0182905 11.664820 11.671237 0.00759607 18.481227 18.501639 0.0241634 19.597080 19.591221 -0.00693604 3.630612 3.698387 0.0802299 5.726152 5.700551 -0.0303062 11.664820 11.677176 0.0146269 18.481227 21.178366 3.19281 11.819836 11.553616 -0.315145 12.166049 12.159376 -0.00789994 13.462034 13.776212 0.371917 15.891147 15.522282 -0.436655 0.120742 12.476928 13.021237 16.012402 26.329737 25.496107 33.957871 37.343941 33.152403 31.284469 37.672703 40.805001 3.630612 24.337743 21.419659 23.096763 12.166049 11.819836 20.601088 20.525872 20.383227 26.921191 25.770005 33.139452 17.858690 22.719308 35.612136 34.858937 20.588177 19.597080 25.120091 31.117931 5.726152 11.664820 18.481227 24.214284 13.462034 15.891147 26.567181 29.339978 2 12 261.3921616 -2.553828228 3.581199231 0.03249196962 1 0.6177612249 -0.005162961477 -0.07138649268 2880.884843 0.08016376382 1298.390329 -1.880839895 -2.245494561 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 0.235986 -0.430358 -0.710143 0.109876 -0.264964 0.545086 1.735292 1.368763 0.513554 0.226106 0.565986 0.367171 1.096671 0.226916 5.741770 5.751094 0.126077 11.487146 11.494216 0.0955999 11.676733 11.684301 0.102328 13.247213 13.286942 0.537209 11.371677 11.374922 0.0438753 18.954448 18.966997 0.169681 23.565773 23.569677 0.0527801 25.027286 25.024189 -0.0418738 11.371677 11.341806 -0.403911 13.633940 13.683367 0.668336 18.954448 18.948744 -0.077127 23.565773 23.594188 0.384209 13.247213 13.254879 0.103666 14.863023 14.857520 -0.0744181 21.094557 21.102386 0.105852 23.286450 23.290629 0.0565131 5.741770 5.760455 0.126322 11.676733 11.692082 0.103771 13.247213 13.192474 -0.370084 13.476999 13.522647 0.308621 11.371677 11.383816 0.0820678 18.954448 18.959038 0.0310324 23.565773 23.572617 0.046266 25.638948 24.493942 -7.74128 11.371677 11.326141 -0.307869 13.633940 13.712998 0.534502 18.954448 18.963310 0.0599099 23.565773 23.618161 0.354188 11.487146 11.500857 0.092695 13.247213 13.339613 0.624707 13.452257 13.359703 -0.625748 18.741557 18.721575 -0.135097 5.741770 11.676733 13.476999 18.101095 29.217637 30.546835 36.358610 36.083051 25.206647 26.625261 35.379427 36.336423 13.633940 25.029629 27.945022 31.872264 11.487146 13.452257 18.741557 19.375462 25.027286 29.791427 36.645967 34.521709 14.863023 28.081743 30.030914 35.423345 25.774640 25.638948 34.666404 34.739921 11.371677 18.954448 23.565773 28.879285 13.247213 21.094557 23.286450 27.595327 2 20 60.93895273 -2.3661165 9.256272845 0.0517766953 1 0.9490070095 0.02549745994 -0.08806677208 34897.47678 0.2315867594 13919.24343 -1.89699892 -2.072547332 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 0.243812 -0.695806 -0.855691 0.119125 -0.196496 0.415800 1.274690 1.147732 0.533856 0.450715 0.622889 0.608503 1.120525 0.637816 11.295046 11.322925 1.00668 28.702110 28.732324 1.091 29.739267 29.773403 1.23261 35.869329 35.846582 -0.821345 28.630554 28.637174 0.239035 47.363882 47.405817 1.51423 62.690536 62.698942 0.303562 68.060832 68.057696 -0.113231 28.630554 28.637983 0.268239 38.270636 38.335573 2.34479 47.363882 47.356911 -0.251723 62.690536 62.738613 1.73602 36.275313 36.303125 1.00427 42.968527 42.948304 -0.73021 55.771268 55.803257 1.15511 62.547809 62.565022 0.621553 11.295046 11.351036 1.01086 29.739267 29.806755 1.21845 36.267606 36.264292 -0.0598394 36.275313 36.267585 -0.139515 28.630554 28.663116 0.587886 47.363882 47.382292 0.33239 62.690536 62.721582 0.560529 67.236270 67.107594 -2.32316 28.630554 28.626905 -0.0658773 38.270636 38.400314 2.34126 47.363882 47.414196 0.908383 62.690536 62.767147 1.38317 28.702110 28.761794 1.07757 35.869329 35.830853 -0.694664 36.275313 36.335714 1.0905 47.508133 47.426488 -1.47405 11.295046 29.739267 36.267606 44.764191 76.730351 85.231893 95.135792 107.682016 70.661281 74.059792 106.221935 109.121209 38.270636 69.544434 83.142242 87.847531 28.702110 35.869329 47.508133 49.719163 68.060832 78.608595 95.511179 95.059346 42.968527 84.180575 78.022573 92.404447 67.236270 71.566701 85.510526 102.424252 28.630554 47.363882 62.690536 78.204870 36.275313 55.771268 62.547809 80.189600 1 56 34.99324178 -2.336977525 9.269584325 0.07642881742 1 0.9069054469 -0.1233454572 -0.07563964821 172157.176 0.1398497016 66308.0547 -1.838889801 -2.209171385 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 0.296431 -0.570170 -1.249605 0.120477 -0.170828 0.363961 1.933470 1.645081 0.576979 0.519735 0.643117 0.660981 1.200245 0.740054 12.805167 12.829269 1.05964 27.995664 28.016813 0.929821 28.454921 28.475842 0.919784 35.280544 35.281453 0.0399715 32.385330 32.393017 0.337937 53.159032 53.193540 1.51714 68.118148 68.133211 0.662234 71.949628 71.941768 -0.345566 32.385330 32.402032 0.734282 43.755864 43.807205 2.25717 53.159032 53.140014 -0.836121 68.118148 68.180621 2.74664 36.968312 36.991655 1.02626 43.214922 43.197226 -0.778017 59.583375 59.606547 1.01872 64.968766 64.984709 0.700946 12.805167 12.853612 1.06494 28.454921 28.496861 0.921942 35.305776 35.323768 0.395518 36.968312 36.943652 -0.542101 32.385330 32.420178 0.766045 53.159032 53.168418 0.206333 68.118148 68.143044 0.547267 71.002547 70.980324 -0.488514 32.385330 32.399513 0.311776 43.755864 43.858725 2.26112 53.159032 53.179883 0.458355 68.118148 68.238881 2.654 27.995664 28.037126 0.911433 35.280544 35.287783 0.159125 36.968312 36.965776 -0.0557531 48.253829 48.288223 0.756052 12.805167 28.454921 35.305776 48.232138 83.389030 88.923552 102.543805 111.887608 71.259247 82.017612 104.250396 115.610779 43.755864 73.076675 89.429107 94.285595 27.995664 35.280544 48.253829 57.507704 71.949628 84.591191 102.081176 102.740338 43.214922 88.270063 85.618750 95.645612 71.002547 82.240763 92.548092 107.771445 32.385330 53.159032 68.118148 81.622769 36.968312 59.583375 64.968766 83.473912 2 12 61.13098909 -2.495040079 6.83176777 0.1072401379 1 0.9551207121 -0.04742752676 -0.1127629643 2880.884843 0.1443605436 1298.390329 -1.733947497 -2.102699039 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 0.347501 -0.533847 -1.067891 0.137859 -0.101726 0.237451 2.764038 2.112676 0.640625 0.526073 0.729499 0.704066 1.295475 0.725130 16.694224 16.719633 0.965163 31.021511 31.041941 0.776023 31.338043 31.360583 0.856183 36.621836 36.712173 3.43143 26.648454 26.653748 0.201105 47.095247 47.119304 0.913802 59.093800 59.108094 0.542963 62.432889 62.428385 -0.171071 26.648454 26.660745 0.466863 38.923528 38.956442 1.25021 47.095247 47.089085 -0.23403 59.093800 59.120823 1.02645 36.621836 36.643070 0.806551 41.377629 41.361723 -0.604215 53.541785 53.561757 0.758608 58.443776 58.453457 0.367739 16.694224 16.745192 0.968006 31.338043 31.383971 0.872289 36.621836 36.597487 -0.462442 36.742854 36.737245 -0.106534 26.648454 26.668431 0.379404 47.095247 47.109038 0.26193 59.093800 59.112539 0.355896 61.186271 61.189782 0.0666764 26.648454 26.663719 0.289914 38.923528 38.989587 1.25463 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