********* 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 41 criteria and tolerance 0.01. Overall scale from minimizing chi^2. 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) = (16/2,8) (16/2,6) (20/2,6) (26/2,6) . Winding potential using (n,K,p) = ( 2 0,20/2,4) ( 2 0,20/2,6) ( 2 0,24/2,4) ( 2 0,32/2,4) ( 3 0,19/2,5) ( 3 0,19/2,7) ( 3 0,25/2,5) ( 3 0,33/2,5) ( 4 0,18/2,6) ( 4 0,18/2,8) ( 4 0,24/2,6) ( 4 0,32/2,6) . Roundness of winding using (n,K,p) = ( 2 2,16/2,6) ( 2 2,16/2,8) ( 2 2,24/2,6) ( 2 2,28/2,6) with error 1; in G^2 N units. Heavy potential determined using (n,K,p,K_max) = ( 0 0,-34/2,2,3) ( 0 0,-34/2,4,3) ( 0 0,-34/2,2,4.5) ( 0 0,-50/2,2,3) ( 0 0,-50/2,2,4.5) ( 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,-17/2,3,3) ( 1 0,-17/2,5,3) ( 1 0,-17/2,3,4.5) ( 1 0,-33/2,3,3) ( 1 0,-33/2,3,4.5) ( 1 0,-55/2,3,3) ( 1 0,-55/2,3,4.5) L=0 and error 0.1; ( 1 0,-17/2,3,3) ( 1 0,-17/2,5,3) ( 1 0,-17/2,3,4.5) ( 1 0,-33/2,3,3) ( 1 0,-33/2,3,4.5) ( 1 0,-55/2,3,3) ( 1 0,-55/2,3,4.5) L=2.5 and error 0.1; ( 1 0,-17/2,3,3) ( 1 0,-17/2,5,3) ( 1 0,-17/2,3,4.5) ( 1 0,-33/2,3,3) ( 1 0,-33/2,3,4.5) ( 1 0,-55/2,3,3) ( 1 0,-55/2,3,4.5) L=5 and error 0.1; ( 1 1,-30/2,2,3) ( 1 1,-30/2,4,3) ( 1 1,-30/2,2,4.5) ( 1 1,-40/2,2,3) ( 1 1,-50/2,2,4.5) ( 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) (35/2,3) (45/2,3) (13/2,5) (29/2,5) (13/2,7) (17/2,7) . 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 10 43712.49936 -0.25 3.829860579 0 1 0.4615471413 0.02857154732 -0.235374258 61.86096362 0.1055338636 22.24564226 -0.9962373144 -0.07384778996 2 3 4 5 6 7 8 9 0.008330 -1.991315 2.107968 0.036202 -0.075870 0.320664 -1.859765 -1.661176 0.426149 0.854136 0.581142 0.142544 0.867949 0.169556 0.516305 0.590692 -7.817941 -7.783556 0.017552 -7.341294 -7.302791 0.019654 -7.250910 -7.224773 0.013342 -3.045134 -5.331619 -1.167169 3.695126 3.726796 0.016166 5.163254 4.391035 -0.394190 5.423484 5.199693 -0.114237 6.753610 6.769987 0.008360 0.183847 1.803200 0.826622 3.489618 1.827475 -0.848464 3.695126 2.126936 -0.800505 5.163254 5.163942 0.000351 -0.850682 -0.818303 0.016528 2.934587 2.951439 0.008602 4.351847 4.255262 -0.049303 5.890593 4.334067 -0.794551 -7.817941 -7.749193 0.017547 -7.341294 -7.275797 0.016717 -0.850682 -0.859002 -0.002124 -0.659817 0.027299 0.175374 3.695126 1.832312 -0.475450 5.163254 3.762631 -0.357484 5.199066 4.183340 -0.259246 5.423484 5.171840 -0.064228 0.183847 1.817883 0.417059 3.489618 2.159759 -0.339423 3.695126 5.228920 0.391474 5.163254 6.774803 0.411319 -7.250910 -7.186893 0.016339 -3.045134 -5.325481 -0.582018 -0.850682 1.343616 0.560055 3.708893 3.706117 -0.000708 -7.817941 -7.341294 0.350600 -0.659817 13.346769 5.423484 18.516377 18.586362 7.455403 12.827516 15.374243 22.179420 0.183847 3.489618 16.023031 15.433289 -7.250910 -3.045134 4.455334 3.708893 8.381896 13.222107 11.114318 12.844013 2.934587 7.119841 13.715638 19.718260 5.199066 13.039382 8.793393 15.453551 3.695126 5.163254 6.753610 11.366946 -0.850682 4.351847 5.890593 6.156104 -2 19 468.6512622 -0.6366444298 7.862314749 0.001967542671 1 0.4361996386 0.07502971886 -0.2454345027 1529.797819 0.08533079239 731.7590762 0.2683604664 0.9311299316 2 3 4 5 6 7 8 9 0.083650 -1.115842 1.114244 0.173112 0.115192 -0.127732 -0.107623 -0.307364 0.511304 0.452670 0.867953 0.662424 1.282479 1.042807 0.885282 0.632177 -1.348784 -1.289314 0.625797 3.842734 3.896070 0.561248 4.540156 4.581047 0.430293 15.115024 15.052141 -0.661707 14.707803 14.751088 0.455485 27.167216 27.211862 0.469806 30.866468 30.909324 0.450966 36.528176 36.539295 0.117001 14.329954 14.378071 0.506323 14.707803 14.719341 0.121406 27.167216 27.192655 0.267698 30.866468 30.607516 -2.724925 15.115024 15.150074 0.368830 22.202857 22.205714 0.030057 31.746229 31.403155 -3.610135 32.504669 32.537775 0.348368 -1.348784 -1.229807 0.625995 4.540156 4.628971 0.467296 15.115024 15.033133 -0.430865 20.872764 20.940644 0.357147 14.707803 14.785446 0.408516 27.167216 27.213534 0.243703 30.866468 30.916098 0.261126 31.706606 31.607152 -0.523274 14.329954 14.425704 0.503781 14.707803 14.740515 0.172109 27.167216 27.260818 0.492481 30.866468 30.919556 0.279318 3.842734 3.941699 0.520699 15.115024 15.142645 0.145325 21.211483 21.358394 0.772961 21.908565 21.911451 0.015185 -1.348784 4.540156 20.872764 23.579493 45.937228 47.558041 57.270519 62.575317 36.439774 57.980328 66.886573 72.926296 14.329954 34.907120 51.885898 55.624555 3.842734 21.908565 21.211483 26.997857 36.528176 46.391431 54.991277 59.681180 22.202857 40.074680 65.051518 59.460380 31.706606 55.871479 56.533805 49.499231 14.707803 27.167216 30.866468 37.345295 15.115024 32.504669 34.248925 31.746229 2 13 17.70067822 -1.477226715 11.17239628 0.007919222016 1 0.4941932815 -0.0435257309 -0.06242650333 177.4594688 0.1057716792 77.01523082 -0.8205027395 -0.7510636479 2 3 4 5 6 7 8 9 0.192084 -0.865091 0.692538 0.095940 0.187260 -0.119756 1.269118 0.758149 0.577567 0.632582 0.634309 0.692944 0.879001 0.841569 1.046677 0.834334 10.905502 10.936384 1.060380 21.623407 21.646298 0.786019 21.796838 21.819650 0.783280 28.371336 28.363653 -0.263807 28.823496 28.844529 0.722189 53.116922 53.160143 1.484072 61.992059 62.020643 0.981487 67.816302 67.799101 -0.590643 28.823496 28.857218 1.157877 34.472648 34.506969 1.178454 53.116922 53.106859 -0.345542 61.992059 62.019656 0.947578 29.717209 29.740208 0.789724 34.810022 34.796199 -0.474621 58.341476 58.361890 0.700964 59.834750 59.851984 0.591736 10.905502 10.967289 1.060775 21.796838 21.841952 0.774537 28.371336 28.368234 -0.053261 29.717209 29.684923 -0.554281 28.823496 28.873144 0.852366 53.116922 53.143346 0.453653 61.992059 62.022937 0.530126 70.636395 70.694146 0.991478 28.823496 28.883399 1.028424 34.472648 34.541284 1.178354 53.116922 53.156673 0.682462 61.992059 62.071580 1.365247 21.623407 21.669374 0.789192 28.374700 28.380505 0.099654 29.717209 29.704334 -0.221039 48.426966 48.534144 1.840063 10.905502 21.796838 28.371336 42.036981 79.640782 83.355315 104.894425 105.460290 66.662998 89.848425 111.529566 105.076369 34.472648 66.817979 86.622891 98.638899 21.623407 28.374700 48.426966 51.467713 67.816302 80.017507 102.476230 103.790087 34.810022 77.293624 105.640631 91.202255 70.636395 90.060815 93.285304 88.396173 28.823496 53.116922 61.992059 77.327012 29.717209 58.341476 59.834750 67.637242 2 39 22.47180089 -1.572966564 10.47598849 0.01800590693 1 0.6851569107 0.07576779499 -0.08731529669 134.0420324 0.1643876832 35.52827472 -0.9736469364 -0.7931468011 2 3 4 5 6 7 8 9 0.173479 -1.113455 0.942094 0.105077 0.142465 -0.068689 0.464842 0.392136 0.556535 0.585210 0.610362 0.657217 0.855859 0.829424 1.014469 0.779732 5.908164 5.947783 1.152014 23.363447 23.385989 0.655471 23.929878 23.950943 0.612496 29.677479 29.654875 -0.657255 23.514384 23.533504 0.555967 45.996779 46.037754 1.191477 56.888207 56.917895 0.863241 63.710457 63.692261 -0.529089 23.514384 23.553044 1.124151 28.634957 28.689893 1.597408 45.996779 45.979610 -0.499209 56.888207 56.917582 0.854142 29.677479 29.704150 0.775556 35.045647 35.033552 -0.351709 53.200057 53.217492 0.506965 58.463126 58.487821 0.718072 5.908164 5.987414 1.152203 23.929878 23.972040 0.612986 29.677479 29.648923 -0.415168 30.855203 30.859525 0.062834 23.514384 23.569036 0.794573 45.996779 46.017897 0.307046 56.888207 56.909504 0.309623 62.985136 63.038802 0.780256 23.514384 23.575385 0.886875 28.634957 28.744751 1.596276 45.996779 46.023321 0.385892 56.888207 56.983906 1.391354 23.363447 23.408523 0.655361 29.677479 29.714651 0.540450 31.926143 31.880401 -0.665038 44.623041 44.654649 0.459554 5.908164 23.929878 30.855203 38.941026 75.312147 77.143919 101.112133 95.664060 64.669917 95.015415 100.062732 120.711396 28.634957 62.486259 68.565471 109.955410 23.363447 31.926143 44.623041 49.595975 63.710457 74.581125 94.897183 99.311800 35.045647 76.910253 86.143597 108.948728 62.985136 82.271400 99.045589 87.033818 23.514384 45.996779 56.888207 78.172083 29.677479 53.200057 58.463126 68.417671 2 30 38.09971781 -1.289334416 8.208554152 0.03249196962 1 0.6467941838 0.02098792552 -0.2055618352 59.58122667 0.1411251555 23.00904488 -0.7288968752 -0.2598458368 2 3 4 5 6 7 8 9 0.197698 -0.856006 0.466904 0.138627 0.137437 -0.092536 1.521050 0.783941 0.626942 0.618043 0.791610 0.729793 1.132226 0.980645 1.133323 0.835044 11.464313 11.513043 1.265283 19.307166 19.340543 0.866624 19.691319 19.725797 0.895240 29.651223 29.614784 -0.946148 23.084131 23.108854 0.641943 44.884370 44.915027 0.796011 50.496573 50.531294 0.901536 56.907753 56.909015 0.032770 23.084131 23.107663 0.611001 31.163851 31.194240 0.789046 44.884370 44.903251 0.490258 50.496573 50.508028 0.297435 29.651223 29.679878 0.744028 35.768180 35.755998 -0.316297 51.365295 51.395257 0.777955 52.291952 52.298641 0.173688 11.464313 11.561798 1.265597 19.691319 19.756888 0.851252 29.651223 29.577715 -0.954328 33.743228 33.800294 0.740863 23.084131 23.126321 0.547737 44.884370 44.924526 0.521328 50.496573 50.533101 0.474227 61.218829 61.214176 -0.060409 23.084131 23.138507 0.705933 31.163851 31.224646 0.789268 44.884370 44.943126 0.762804 50.496573 50.552250 0.722832 19.307166 19.377214 0.909389 29.651223 29.710377 0.767957 35.268709 35.352350 1.085870 35.488746 35.446997 -0.542010 11.464313 19.691319 33.743228 34.086557 66.550992 68.380809 86.990227 86.831312 61.311785 85.454983 87.615282 110.922393 31.163851 58.895361 68.089043 95.608526 19.307166 35.488746 35.268709 45.736391 56.907753 66.481250 84.725361 87.058948 35.768180 74.359228 72.709745 100.801156 61.218829 74.565770 86.910875 82.287865 23.084131 44.884370 50.496573 67.348588 29.651223 51.365295 52.291952 61.991304 1 39 29.48133856 -1.258558566 8.257650718 0.0517766953 1 0.8130939055 0.01102718387 -0.1072144006 87.71519508 0.1562871945 -1.228872157 -0.9332334551 -0.8386832766 2 3 4 5 6 7 8 9 0.242430 -0.883718 0.294080 0.135765 0.119543 -0.066172 1.525310 1.092481 0.645362 0.655263 0.720560 0.753675 1.003813 0.984203 1.145622 0.888675 10.858232 10.897214 1.248635 25.905701 25.925110 0.621662 26.947316 26.953265 0.190567 31.882753 31.888190 0.174170 24.133735 24.148218 0.463887 46.316783 46.344058 0.873610 55.828604 55.851663 0.738597 60.784579 60.777260 -0.234435 24.133735 24.164172 0.974913 33.114520 33.151545 1.185923 46.316783 46.312098 -0.150076 55.828604 55.840240 0.372704 31.882753 31.905377 0.724666 36.542708 36.530473 -0.391902 52.319448 52.338601 0.613493 56.547982 56.555877 0.252857 10.858232 10.936189 1.248498 26.947316 26.959290 0.191772 31.882753 31.896989 0.227993 34.511270 34.533002 0.348039 24.133735 24.170854 0.594463 46.316783 46.339648 0.366186 55.828604 55.839964 0.181939 61.666149 61.704661 0.616793 24.133735 24.186463 0.844457 33.114520 33.188573 1.185971 46.316783 46.339165 0.358452 55.828604 55.886433 0.926139 25.905701 25.944617 0.623248 31.882753 31.936198 0.855946 34.585263 34.486518 -1.581411 38.824729 38.869906 0.723532 10.858232 26.947316 34.562174 34.511270 71.574713 72.192909 92.669950 90.756000 62.167867 94.323742 97.029733 100.331181 33.114520 60.472624 73.984332 97.441217 25.905701 34.585263 38.824729 49.323580 60.784579 70.899811 87.998625 91.274473 36.542708 77.135667 71.613606 109.093720 61.666149 74.479664 81.635177 103.511245 24.133735 46.316783 55.828604 69.625262 31.882753 52.319448 56.547982 65.934352 2 38 53.70794617 -1.661310016 6.013680298 0.07642881742 1 0.9015537741 0.1122084281 -0.133064238 27.94252277 0.1873963102 -8.946559638 0.250628024 -0.21487434 2 3 4 5 6 7 8 9 0.272426 -0.771303 -0.017403 0.205005 0.060147 -0.063980 1.999166 1.405927 0.677151 0.683233 0.863705 0.866833 1.240100 1.259568 1.214346 0.955737 11.970375 12.013958 1.142404 25.182602 25.301188 3.108426 26.307815 26.354984 1.236425 26.991984 27.016783 0.650039 18.849597 18.858357 0.229635 37.764827 37.783248 0.482845 45.825915 45.839886 0.366212 49.405483 49.404852 -0.016535 18.849597 18.870247 0.541306 27.766984 27.793556 0.696525 37.764827 37.763876 -0.024939 45.825915 45.835791 0.258873 28.869637 28.885484 0.415379 32.114497 32.105621 -0.232685 43.181597 43.193975 0.324442 47.180129 47.185799 0.148617 11.970375 12.057007 1.135411 25.182602 25.219579 0.484625 26.307815 26.400825 1.219015 28.869637 28.863582 -0.079360 18.849597 18.871024 0.280831 37.764827 37.782129 0.226760 45.825915 45.838746 0.168162 49.514395 49.694679 2.362850 18.849597 18.886996 0.490168 27.766984 27.820133 0.696594 37.764827 37.782494 0.231542 45.825915 45.860717 0.456116 26.991984 27.041641 0.650813 28.756590 28.733021 -0.308906 28.869637 28.869820 0.002389 30.818904 30.814007 -0.064193 11.970375 26.307815 25.182602 30.799712 57.372199 58.048622 72.453447 71.093643 51.265937 76.816788 83.306479 89.122773 27.766984 49.095548 62.294401 63.065887 26.991984 28.756590 30.818904 41.513772 49.405483 56.876158 68.954518 71.181281 32.114497 60.669915 62.773082 79.066682 49.514395 64.715063 61.506005 84.673302 18.849597 37.764827 45.825915 52.458150 28.869637 43.181597 47.180129 53.115198 2 21 38.76037422 -1.237652207 7.206820714 0.1072401379 1 1.058013636 -0.007311681748 -0.1764913569 65.84387633 0.2444961456 19.01948223 -0.9546986354 -0.5119687473 2 3 4 5 6 7 8 9 0.276934 -0.706763 -0.352942 0.158541 0.081965 -0.037025 2.132499 1.464594 0.701241 0.673480 0.845242 0.793975 1.199264 1.071012 1.242980 0.925397 13.779068 13.818682 1.264984 27.639798 27.662370 0.720778 27.863985 27.889715 0.821624 34.302065 34.338881 1.175624 23.850509 23.863347 0.409969 46.180115 46.201744 0.690678 54.911090 54.932339 0.678542 60.214372 60.210322 -0.129354 23.850509 23.876078 0.816511 36.906076 36.942185 1.153099 46.180115 46.184949 0.154381 54.911090 54.927454 0.522540 34.302065 34.326328 0.774773 39.294556 39.280787 -0.439700 52.976854 52.996280 0.620320 54.982006 54.991921 0.316632 13.779068 13.858312 1.265253 27.863985 27.914122 0.800499 34.302065 34.281832 -0.323061 34.321804 34.355724 0.541575 23.850509 23.877486 0.430737 46.180115 46.205148 0.399697 54.911090 54.937864 0.427482 61.066092 61.089749 0.377719 23.850509 23.900364 0.796009 36.906076 36.978304 1.153244 46.180115 46.208018 0.445519 54.911090 54.959483 0.772665 27.639798 27.686518 0.745945 34.302065 34.314386 0.196718 34.632245 34.601452 -0.491653 36.787712 36.813409 0.410291 13.779068 27.863985 34.321804 34.569038 69.195578 70.340585 87.508098 85.649235 61.800425 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