********* 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 28 403488.413 -0.25 50 0 1 0.4687356835 0.1199937469 -0.3193866311 21576.32354 0.1571074162 1469.129401 -1.073779296 -76.76653171 2 3 4 5 6 7 8 9 0.007204 -2.157981 3.598212 0.037228 0.061408 0.110963 -1.099174 -1.650575 0.428597 0.245541 -23.431024 0.267299 -43.066830 0.322475 0.664284 0.303322 -86.791990 -86.280394 2.948274 -77.738309 -77.269735 2.700342 -66.428526 -65.910449 2.985627 -12.826601 -38.454483 -147.690831 57.331948 57.919530 3.386176 90.238201 90.655285 2.403611 114.462462 103.528182 -63.013123 121.974433 122.463835 2.820370 37.965968 39.073927 6.385049 57.331948 46.481677 -62.528986 81.850586 56.624679 -145.374291 90.238201 90.379842 0.816261 22.987913 23.367208 2.185836 82.099081 82.193989 0.546948 103.264570 103.246412 -0.104642 106.139054 104.565792 -9.066550 -77.738309 -76.772809 2.782037 -66.428526 -65.395417 2.976851 -12.826601 -21.392845 -24.683188 22.987913 -16.182741 -112.868212 57.331948 46.667251 -30.729772 90.238201 57.996991 -92.901375 114.462462 90.518007 -68.994706 121.974433 157.506547 102.383946 37.965968 40.083157 6.100570 57.331948 56.532578 -2.303342 81.850586 91.075554 26.581267 90.238201 103.168727 37.258642 -86.791990 -85.792779 2.879176 22.987913 -37.331291 -173.806663 24.132679 65.517207 119.247373 65.124103 83.487084 52.911979 -77.738309 -66.428526 -12.826601 25.954102 199.959667 114.462462 271.461918 395.790921 174.382334 217.353040 387.295578 381.605680 37.965968 81.850586 309.735482 136.342329 -86.791990 24.132679 83.415412 65.124103 156.506473 206.281090 246.194018 237.715590 82.099081 172.896420 279.643690 280.177874 140.193427 210.928719 256.776301 305.850112 57.331948 90.238201 121.974433 240.565538 22.987913 103.264570 106.139054 216.872165 2 10 96897.8669 -0.4770556535 50 0.001967542671 1 0.4755528091 0.02783528535 -0.2348740336 60.11839623 0.1079894521 21.3859735 -1.004881348 -0.72405263 2 3 4 5 6 7 8 9 0.096428 -1.415957 1.963441 0.042679 0.216662 -0.114021 -0.011953 -0.399101 0.519699 0.871975 0.566025 0.880603 0.793631 0.905841 0.912976 1.148607 -1.209146 -0.843568 28.201581 4.562248 5.007308 34.333095 9.383111 9.623629 18.554229 89.931827 89.700438 -17.849907 97.231791 97.530630 23.053161 180.155021 180.509798 27.368384 205.568510 205.834830 20.544619 242.873525 242.905180 2.441962 97.231791 97.347991 8.963963 104.072545 104.365662 22.611749 180.155021 180.356286 15.526094 205.568510 201.007629 -351.838221 93.189785 93.457246 20.632576 142.453701 142.460749 0.543714 217.040001 217.042324 0.179214 217.631011 217.772635 10.925273 -1.209146 -0.478163 28.194953 4.562248 5.262940 27.026621 93.189785 92.776648 -15.935241 126.624319 126.714056 3.461275 97.231791 97.725330 19.036407 180.155021 180.515404 13.900418 205.568510 201.004692 -176.032374 263.655104 258.434181 -201.377760 97.231791 97.572693 13.149023 104.072545 104.656437 22.521440 180.155021 180.905584 28.950192 205.568510 205.835082 10.282013 9.383111 10.053738 25.866948 89.931827 89.556204 -14.488251 93.189785 93.424694 9.060731 174.213292 175.035080 31.697429 -1.209146 4.562248 126.624319 144.939125 300.772408 263.655104 436.337298 483.717817 310.555648 295.454880 459.604623 507.707296 104.072545 227.265875 369.556995 367.644439 9.383111 89.931827 221.463104 174.213292 242.873525 302.484318 370.450639 406.553515 142.453701 322.654849 372.171891 428.758228 286.704217 290.676539 370.769493 411.316224 97.231791 180.155021 205.568510 356.535686 93.189785 217.631011 217.040001 267.480617 2 38 267.3605648 -1.017776644 13.95441276 0.007919222016 1 0.5541589714 0.08680046582 -0.2186982975 510.5770444 0.2170911116 173.353321 -0.8881733557 -0.6548020234 2 3 4 5 6 7 8 9 0.132132 -1.163853 1.577475 0.085272 0.267709 -0.251186 1.110239 0.090384 0.547641 0.650725 0.619155 0.705508 0.858003 0.839790 1.069306 0.844392 12.670000 12.762523 2.729542 19.539840 19.603714 1.884347 23.158751 23.221277 1.844584 41.814531 41.736758 -2.294391 32.049752 32.110285 1.785785 65.125772 65.216272 2.669839 75.401664 75.463161 1.814250 86.741123 86.751687 0.311635 32.049752 32.078240 0.840413 44.889911 44.937741 1.411034 65.125772 65.188616 1.853971 75.401664 75.412135 0.308911 41.814531 41.864622 1.477745 52.748597 52.735747 -0.379100 76.690086 76.711396 0.628653 81.099273 81.327910 6.745057 12.670000 12.855339 2.733855 23.158751 23.282456 1.824720 41.814531 41.709173 -1.554088 48.719027 48.852840 1.973808 32.049752 32.110804 0.900544 65.125772 65.239827 1.682364 75.401664 75.478083 1.127233 87.539391 87.247860 -4.300236 32.049752 32.166992 1.729345 44.889911 44.985588 1.411287 65.125772 65.318142 2.837552 75.401664 75.466870 0.961825 19.539840 19.668591 1.899144 41.814531 41.863716 0.725500 50.116335 50.093981 -0.329740 50.233971 50.516890 4.173207 12.670000 23.158751 48.719027 49.973622 96.315814 109.188887 132.483333 164.296013 84.155845 136.280311 166.371035 179.271620 44.889911 91.530464 122.819428 137.511866 19.539840 50.116335 50.233971 88.447390 86.741123 99.008844 138.517746 139.220093 52.748597 122.076455 142.980350 133.037612 87.539391 127.830548 136.243262 108.118749 32.049752 65.125772 75.401664 104.831056 41.814531 76.690086 81.288541 81.099273 2 21 41.00329997 -0.9977239387 8.359580887 0.01800590693 1 0.5689568263 0.04587997542 -0.2250167494 78.54304964 0.1395976019 32.11559859 -0.5703178052 -0.2237411628 2 3 4 5 6 7 8 9 0.185046 -1.088911 1.236197 0.128782 0.243420 -0.263339 1.465251 0.545981 0.602189 0.633295 0.760002 0.747315 1.025654 0.993813 1.124676 0.846568 12.670000 12.720239 1.243450 17.083081 17.136855 1.330933 17.440217 17.477593 0.925086 29.237655 29.182744 -1.359075 22.333660 22.364299 0.758333 46.149684 46.188584 0.962786 50.683899 50.727169 1.070945 57.754756 57.757163 0.059577 22.333660 22.358084 0.604490 30.337910 30.365183 0.675038 46.149684 46.179568 0.739627 50.683899 50.696202 0.304500 29.237655 29.268021 0.751593 35.904088 35.894479 -0.237813 53.233150 53.243972 0.267857 53.380944 53.410546 0.732652 12.670000 12.770516 1.243905 17.083081 17.173241 1.115760 29.237655 29.138804 -1.223300 32.973236 33.076648 1.279749 22.333660 22.378159 0.550682 46.149684 46.201825 0.645254 50.683899 50.733707 0.616379 62.314840 62.444746 1.607629 22.333660 22.399365 0.813106 30.337910 30.392486 0.675397 46.149684 46.234874 1.054241 50.683899 50.744852 0.754308 17.440217 17.531785 1.133175 29.237655 29.288809 0.633051 35.038782 35.081154 0.524370 36.072262 36.112660 0.499936 12.670000 17.083081 32.973236 34.645901 66.867522 68.845822 91.361751 92.026155 60.686779 86.018447 102.015215 110.985692 30.337910 60.300612 74.832828 91.565189 17.440217 35.038782 36.072262 44.150143 57.754756 66.971632 89.636754 91.634610 35.904088 78.125647 90.493243 85.038923 62.314840 81.373060 87.247797 77.123823 22.333660 46.149684 50.683899 68.331651 29.237655 53.380944 53.233150 60.351055 2 57 40.32966962 -0.9854029064 7.537670802 0.03249196962 1 0.6543456166 0.005041750817 -0.2269415059 90.12159745 0.153060515 36.87525431 -0.4899565938 -0.2054946415 2 3 4 5 6 7 8 9 0.210446 -1.084159 1.126604 0.149083 0.207874 -0.232330 1.753831 0.740237 0.629857 0.656196 0.797856 0.789556 1.071239 1.075967 1.172580 0.889406 12.670000 12.715742 1.160942 16.993595 17.039523 1.165678 17.208729 17.243431 0.880768 28.458141 28.448577 -0.242730 21.724774 21.750636 0.656378 44.942437 44.973527 0.789066 48.790593 48.830905 1.023156 55.594349 55.594609 0.006594 21.724774 21.748263 0.596161 30.809622 30.835703 0.661964 44.942437 44.966891 0.620656 48.790593 48.803973 0.339593 28.458141 28.486292 0.714488 34.449206 34.438887 -0.261898 50.297424 50.308310 0.276285 51.389945 51.416411 0.671720 12.670000 12.761516 1.161351 16.993595 17.072814 1.005305 28.458141 28.372545 -1.086231 31.799430 31.882754 1.057392 21.724774 21.762970 0.484713 44.942437 44.987251 0.568699 48.790593 48.832681 0.534106 60.615295 60.624732 0.119749 21.724774 21.785335 0.768531 30.809622 30.861810 0.662286 44.942437 45.008508 0.838457 48.790593 48.855464 0.823228 17.208729 17.290244 1.034448 28.458141 28.576613 1.503428 33.172184 33.230386 0.738592 33.807750 33.751954 -0.708065 12.670000 16.993595 31.799430 32.188250 64.176588 65.156223 87.246966 82.076206 59.546994 83.050854 91.633095 110.079598 30.809622 57.508482 69.041870 94.319289 17.208729 33.807750 33.172184 44.480756 55.594349 63.810720 86.046337 87.058636 34.449206 77.015198 86.095675 85.080411 60.615295 81.037205 83.160900 75.303676 21.724774 44.942437 48.790593 64.563702 28.458141 51.389945 50.297424 59.642772 2 11 347.730585 -1.024955262 6.271781835 0.0517766953 1 0.7512111576 0.006667730694 -0.2208371035 61.86096362 0.1670423706 22.24564226 -0.5957891754 -0.2317902355 2 3 4 5 6 7 8 9 0.247064 -1.035867 0.910347 0.151790 0.195265 -0.216351 2.126549 1.054439 0.659659 0.599057 0.831596 0.747681 1.121895 1.052926 1.224043 0.815387 12.670000 12.707702 0.934728 18.742942 18.768590 0.635866 18.931395 18.962439 0.769662 27.043201 28.434818 34.501667 19.480832 19.498401 0.435573 41.006562 41.027802 0.526594 44.966192 44.999207 0.818517 50.548715 50.547716 -0.024780 19.480832 19.501748 0.518559 28.799594 28.822011 0.555756 41.006562 41.021443 0.368937 44.966192 44.979745 0.336015 27.043201 27.065432 0.551150 31.668152 31.659045 -0.225777 46.043427 46.052072 0.214340 46.587634 46.608657 0.521223 12.670000 12.745435 0.935108 18.931395 18.989504 0.720330 27.043201 27.389545 4.293366 28.668793 28.336142 -4.123628 19.480832 19.508442 0.342258 41.006562 41.039423 0.407354 44.966192 44.996239 0.372466 53.878041 53.977365 1.231245 19.480832 19.530218 0.612202 28.799594 28.844446 0.555993 41.006562 41.045826 0.486723 44.966192 45.028836 0.776546 18.742942 18.798146 0.684313 27.043201 27.078489 0.437431 29.424951 29.388671 -0.449737 30.773229 30.828093 0.680103 12.670000 18.931395 28.668793 29.192762 58.148199 58.203199 78.396539 76.554506 53.006034 78.672246 85.330016 105.482189 28.799594 51.330253 65.649629 83.744335 18.742942 30.773229 29.424951 41.500665 50.548715 57.483410 76.624244 77.552706 31.668152 68.631683 66.021235 90.159205 53.878041 67.216110 82.475382 68.615334 19.480832 41.006562 44.966192 55.996301 27.043201 46.587634 46.043427 53.842441 2 11 167.2757803 -0.9913432318 6.069774658 0.07642881742 1 0.8891271189 -0.003761199917 -0.2139156169 61.86096362 0.1963280409 22.24564226 -0.4051262455 -0.3069904088 2 3 4 5 6 7 8 9 0.270702 -1.010381 0.687082 0.179085 0.140082 -0.159640 2.242455 1.241119 0.680379 0.655090 0.847824 0.821767 1.160148 1.172163 1.254677 0.904157 12.670000 12.706773 0.966749 21.046359 21.066222 0.522210 21.308613 21.335447 0.705447 28.016821 28.715485 18.367570 19.640246 19.654660 0.378959 41.439892 41.457864 0.472474 46.101493 46.132370 0.811732 51.591788 52.132037 14.202924 19.640246 19.662848 0.594204 29.960373 29.985064 0.649113 41.439892 41.449270 0.246553 46.101493 46.116726 0.400471 28.016821 28.038194 0.561865 32.270968 32.261823 -0.240421 46.822883 46.834001 0.292283 47.074634 47.091819 0.451772 12.670000 12.743573 0.967101 21.308613 21.360631 0.683763 28.016821 27.999936 -0.221950 28.700488 28.730775 0.398119 19.640246 19.665130 0.327096 41.439892 41.468256 0.372833 46.101493 46.126254 0.325477 53.908938 53.937420 0.374390 19.640246 19.689410 0.646256 29.960373 30.009772 0.649332 41.439892 41.466199 0.345801 46.101493 46.168444 0.880050 21.046359 21.088034 0.547819 28.016821 28.032045 0.200106 29.356239 29.320991 -0.463335 30.672980 30.761443 1.162834 12.670000 21.308613 28.700488 29.267853 59.340210 58.560700 79.921931 77.263309 53.025255 84.253570 86.706025 112.312363 29.960373 51.548802 69.031950 83.591560 21.046359 30.672980 29.356239 42.405933 51.591788 58.234320 77.573359 78.224238 32.270968 69.238397 67.325338 93.336371 53.908938 71.477366 69.913073 84.155074 19.640246 41.439892 46.101493 55.735150 28.016821 47.074634 46.822883 54.775631 2 40 36.32591495 -0.9324244488 7.303394895 0.1072401379 1 1.193400746 0.083101877 -0.2310101095 76.07596096 0.3289346882 24.04021233 -0.8642782112 -0.5507131472 2 3 4 5 6 7 8 9 0.242486 -1.071851 0.535241 0.159254 0.149996 -0.158668 1.560362 0.934941 0.659963 0.678617 0.791932 0.811295 1.114413 1.105088 1.224409 0.928775 12.670000 12.713295 1.226775 26.946499 26.998757 1.480744 28.270692 28.294024 0.661116 31.157452 31.190704 0.942201 21.637604 21.652678 0.427142 46.635009 46.655478 0.579986 54.039471 54.067825 0.803409 61.042366 61.025628 -0.474259 21.637604 21.667255 0.840177 34.227669 34.269529 1.186105 46.635009 46.641850 0.193828 54.039471 54.094406 1.556606 32.830532 32.856522 0.736443 37.566447 37.558393 -0.228196 54.119296 54.146098 0.759462 54.919073 54.930898 0.335044 12.670000 12.756639 1.227487 26.946499 27.031774 1.208161 31.157452 31.223565 0.936675 32.830532 32.759742 -1.002930 21.637604 21.664294 0.378139 46.635009 46.666660 0.448411 54.039471 54.099695 0.853229 61.392541 61.418045 0.361332 21.637604 21.700391 0.889552 34.227669 34.311388 1.186102 46.635009 46.657982 0.325469 54.039471 54.146447 1.515606 28.270692 28.337245 0.942910 32.830532 32.860737 0.427941 33.992390 34.021048 0.406012 34.325479 34.275346 -0.710270 12.670000 26.946499 31.157452 34.008307 69.254818 67.976986 95.883449 96.399144 61.504159 107.931810 109.751480 136.711972 34.227669 59.306690 80.640716 88.307749 28.270692 33.992390 34.325479 48.824204 61.042366 67.384809 93.484537 91.072903 37.566447 82.097374 83.987486 123.067652 61.392541 86.905709 70.961731 119.455712 21.637604 46.635009 54.039471 64.770309 32.830532 54.919073 54.119296 63.883931 2 11 44.09468901 -0.9056052878 6.151917419 0.1453085056 1 1.274473596 -0.03290033385 -0.1945765174 61.86096362 0.2781541745 22.24564226 0.1275988113 -0.5171047534 2 3 4 5 6 7 8 9 0.302307 -0.839089 -0.157083 0.207810 0.084036 -0.104829 2.277591 1.559732 0.718869 0.755955 0.868347 0.933178 1.247717 1.321145 1.300289 1.056188 12.670000 12.707282 1.109363 27.543047 27.574424 0.933682 28.621079 28.631395 0.306968 28.691562 28.718320 0.796225 21.088013 21.098540 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