********* 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 40 criteria and tolerance 0.01. Overall scale from fitting lowest state to lattice value. 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 0,16/2,6) ( 2 0,16/2,4) ( 2 0,26/2,4) ( 3 0,17/2,7) ( 3 0,17/2,5) ( 3 0,25/2,5) ( 4 0,16/2,8) ( 4 0,16/2,6) ( 4 0,26/2,6) . Roundness of winding using (n,K,p) = ( 2 2,14/2,8) ( 2 2,14/2,6) ( 2 2,22/2,6) with error 1; in G^2 N units. Heavy potential determined using (n,K,p,K_max) = ( 0 0,-26/2,2,3.5) ( 0 0,-26/2,4,3.5) ( 0 0,-26/2,2,3) ( 0 0,-42/2,2,3.5) ( 0 0,-42/2,2,4.25) ( 0 0,-70/2,2,4) ( 0 0,-70/2,2,4.5) , 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,-13/2,3,3.5) ( 1 0,-13/2,5,3.5) ( 1 0,-13/2,3,3) ( 1 0,-23/2,3,4) ( 1 0,-23/2,3,4.5) ( 1 0,-35/2,3,5) ( 1 0,-35/2,3,6) L=1.265-0.964*m and error 0.1; ( 1 0,-13/2,3,3.5) ( 1 0,-13/2,5,3.5) ( 1 0,-13/2,3,3) ( 1 0,-23/2,3,4) ( 1 0,-23/2,3,4.5) ( 1 0,-35/2,3,5) ( 1 0,-35/2,3,6) L=5.058-3.856*m and error 0.1; ( 1 1,-22/2,2,5) ( 1 1,-22/2,4,5) ( 1 1,-22/2,2,4.5) ( 1 1,-44/2,2,5) ( 1 1,-44/2,2,6) ( 1 1,-70/2,2,6) ( 1 1,-70/2,2,7) L=0+0*m and error 0.2; all in G^2 N units. p-extrapolation using n=( 1 0) and (K,p) = (13/2,3) (21/2,3) (45/2,3) (13/2,5) (27/2,5) (13/2,7) (15/2,7) . 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, 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 11 77.51827811 -0.9272477994 7.747322082 0.03249196962 1 0 -0.1877430434 -0.1460443513 362.1229213 -0.04273520347 166.1078033 -0.5971954053 -0.7284104471 3 4 5 6 7 8 9 0.282162 -0.758383 0.938849 0.128339 0.239153 -0.261390 4.373511 1.616267 0.717135 0.724164 1.012875 0.965294 1.399287 0.941162 12.670000 12.691841 0.763893 13.218021 13.252355 1.200888 26.562299 26.558839 -0.120993 28.497040 28.472521 -0.857565 29.166629 29.194585 0.977805 55.365590 55.395318 1.039762 60.118461 60.114135 -0.151285 60.649932 60.652456 0.088270 29.166629 29.166629 -0.000002 38.198701 38.198701 0.000001 55.365590 55.365590 -0.000000 60.118461 60.118461 0.000000 29.407842 29.407842 -0.000000 32.861828 32.861828 -0.000000 52.696402 52.696402 0.000000 56.330133 56.330134 0.000001 12.670000 12.715252 0.791360 26.562299 26.555383 -0.120947 28.525459 28.493215 -0.563879 29.407842 29.408998 0.020219 29.166629 29.206577 0.698606 55.365590 55.400156 0.604488 60.118461 60.122338 0.067814 66.005456 66.005456 0.000000 29.166629 29.182597 0.279242 38.198701 38.198701 -0.000000 55.365590 55.390481 0.435289 60.118461 60.104942 -0.236411 13.218021 13.282981 1.136030 28.497040 28.461273 -0.625500 29.407842 29.409403 0.027301 39.557840 39.667438 1.916637 12.670000 26.562299 28.525459 38.198701 70.181060 73.416807 91.522094 90.039014 59.854547 87.385456 95.909036 97.728970 38.198701 62.487689 84.594413 89.343314 13.218021 28.497040 39.557840 51.994008 60.649932 71.753604 89.225997 94.741964 32.861828 76.620618 92.934988 89.041120 73.761084 77.278394 93.000311 96.202804 29.166629 55.365590 60.118461 66.005456 29.407842 52.696402 56.330133 66.005456 1 34 70.07901382 -0.8939801503 8.68081399 0.03249196962 1 0.05 -0.192813915 -0.1366979925 508.334369 -0.05529207298 221.1711536 -0.6446189357 -0.7961112301 3 4 5 6 7 8 9 0.282540 -0.777623 0.980356 0.121447 0.244083 -0.259356 4.176940 1.605237 0.708773 0.765228 0.992703 0.974469 1.377969 0.996845 12.670000 12.694069 0.944532 13.922495 13.945908 0.918815 28.508855 28.504581 -0.167698 30.753316 30.771477 0.712677 32.478406 32.508822 1.193617 61.303360 61.334462 1.220514 65.691293 65.685921 -0.210830 66.468355 66.473656 0.208040 32.478406 32.478766 0.014116 41.178345 41.178560 0.008453 61.303360 61.303486 0.004947 65.691293 65.695177 0.152409 31.351924 31.352521 0.023443 35.044451 35.043967 -0.018994 57.735391 57.735627 0.009242 62.025662 62.026529 0.033994 12.670000 12.718827 0.958062 28.508855 28.500238 -0.169070 30.855013 30.871132 0.316265 31.351924 31.302399 -0.971753 32.478406 32.525419 0.922454 61.303360 61.343103 0.779801 65.691293 65.696029 0.092924 72.566942 72.563913 -0.059436 32.478406 32.492949 0.285355 41.178345 41.178776 0.008457 61.303360 61.326078 0.445759 65.691293 65.683607 -0.150823 13.922495 13.968025 0.893369 30.753316 30.740914 -0.243344 31.351924 31.332814 -0.374954 44.539082 44.584408 0.889372 12.670000 28.508855 30.855013 41.377589 78.091966 80.959574 101.025052 99.659908 65.319459 96.191975 105.494742 106.928486 41.178345 68.313995 93.439843 96.117501 13.922495 30.753316 44.539082 56.945975 66.468355 79.838067 97.507124 105.825508 35.044451 82.944374 102.511603 98.459038 81.011124 85.426818 102.654072 103.482605 32.478406 61.303360 65.691293 72.566942 31.351924 57.735391 62.025662 72.383490 2 27 68.7962038 -0.8664359731 9.001381256 0.03249196962 1 0.1 -0.2013803516 -0.1350675858 387.2873935 -0.02179613344 169.5364767 -0.6942061056 -0.8309778189 3 4 5 6 7 8 9 0.281017 -0.779542 0.965409 0.117035 0.245413 -0.257095 4.197436 1.589270 0.703771 0.765767 0.982305 0.962358 1.376275 0.997097 12.670000 12.689894 0.805153 12.911196 12.938582 1.108379 28.992262 29.001798 0.385966 30.764756 30.743232 -0.871143 33.687264 33.718434 1.261555 63.301678 63.334524 1.329358 68.408548 68.409610 0.042998 70.043788 70.047611 0.154708 33.687264 33.688468 0.048755 45.023996 45.024807 0.032826 63.301678 63.301730 0.002118 68.408548 68.418288 0.394224 33.279811 33.282006 0.088838 37.013452 37.011657 -0.072655 59.783354 59.783504 0.006075 63.590197 63.593247 0.123436 12.670000 12.712542 0.860903 28.992262 29.011245 0.384147 30.806356 30.773974 -0.655299 33.279811 33.258791 -0.425370 33.687264 33.729508 0.854877 63.301678 63.337713 0.729222 68.408548 68.420846 0.248870 77.468530 77.454480 -0.284311 33.687264 33.709775 0.455538 45.023996 45.025619 0.032835 63.301678 63.331424 0.601957 68.408548 68.417788 0.186999 12.911196 12.962502 1.038228 30.764756 30.730530 -0.692619 33.279811 33.280363 0.011179 45.905948 45.961351 1.121149 12.670000 28.992262 30.806356 44.383713 80.079913 84.567320 104.855281 105.806723 67.765133 98.896943 109.938921 111.089476 45.023996 71.767477 100.459484 101.469372 12.911196 30.764756 45.905948 59.200964 70.043788 81.756803 104.292164 108.700639 37.013452 87.144821 106.806734 101.382064 83.971470 86.954643 108.437518 107.896440 33.687264 63.301678 68.408548 77.468530 33.279811 59.783354 63.590197 77.248530 2 10 68.39043146 -0.8766583336 8.546439334 0.03249196962 1 0.15 -0.1944095162 -0.1483665358 367.7977579 0.009137445076 164.2479479 -0.7060254262 -0.8650953831 3 4 5 6 7 8 9 0.273115 -0.772895 0.916851 0.117860 0.243124 -0.255916 4.182649 1.526629 0.699213 0.729355 0.972659 0.938018 1.375506 0.947062 12.577874 12.604805 1.005769 12.670000 12.698121 1.050224 28.038300 28.055533 0.643600 29.768891 29.730956 -1.416712 31.793070 31.824736 1.182621 59.776592 59.810512 1.266791 65.839112 65.845619 0.243004 67.920476 67.924208 0.139394 31.793070 31.795184 0.078948 44.703680 44.705309 0.060828 59.776592 59.776623 0.001171 65.839112 65.853809 0.548870 33.249037 33.253116 0.152327 37.157710 37.154500 -0.119894 57.083008 57.083022 0.000539 61.416947 61.422249 0.197994 12.670000 12.716054 0.859981 28.038300 28.072698 0.642329 29.768891 29.730850 -0.710346 33.249037 33.217679 -0.585570 31.793070 31.830326 0.695692 59.776592 59.811014 0.642779 65.839112 65.857607 0.345358 75.179052 75.109739 -1.294295 31.793070 31.823382 0.566026 44.703680 44.706939 0.060850 59.776592 59.810049 0.624764 65.839112 65.862940 0.444939 12.577874 12.640810 1.175219 29.769139 29.731118 -0.709976 33.249037 33.248323 -0.013336 43.538574 43.613401 1.397251 12.670000 28.038300 29.768891 42.044584 75.858411 81.191643 99.437271 103.369171 66.076178 95.558287 104.876970 108.204886 44.703680 69.897132 96.612026 102.145227 12.577874 29.769139 43.538574 57.016823 67.920476 77.288879 99.700632 106.619410 37.157710 86.422805 103.317848 97.270969 80.648961 82.725707 105.042103 103.810271 31.793070 59.776592 65.839112 75.179052 33.249037 57.083008 61.416947 75.225615 2 10 63.11060806 -0.8825613476 8.83887556 0.03249196962 1 0.2 -0.1946272955 -0.1467913418 369.6893701 0.01986599702 163.627996 -0.7270424883 -0.8833004416 3 4 5 6 7 8 9 0.269593 -0.777876 0.897017 0.116177 0.241669 -0.251819 4.003971 1.490992 0.693293 0.736330 0.962570 0.937564 1.363175 0.956898 12.557525 12.584868 1.042491 12.670000 12.697620 1.053066 27.673552 27.697017 0.894629 30.085658 30.048431 -1.419331 32.554226 32.586464 1.229130 61.365670 61.400031 1.310076 66.740970 66.753036 0.460030 69.811548 69.814935 0.129170 32.554226 32.557948 0.141897 45.982363 45.985291 0.111630 61.365670 61.365168 -0.019128 66.740970 66.760750 0.754129 33.980025 33.986945 0.263819 38.089760 38.084360 -0.205891 58.485139 58.484989 -0.005720 62.818946 62.827868 0.340157 12.670000 12.716018 0.877252 27.673552 27.720431 0.893662 30.085658 30.048030 -0.717311 33.980025 33.940083 -0.761430 32.554226 32.591867 0.717551 61.365670 61.399989 0.654240 66.740970 66.766328 0.483394 77.364118 77.261376 -1.958585 32.554226 32.588519 0.653729 45.982363 45.988221 0.111674 61.365670 61.399013 0.635622 66.740970 66.779255 0.729823 12.557525 12.620352 1.197688 30.086715 30.048987 -0.719219 33.980025 33.979734 -0.005560 44.915091 44.990406 1.435743 12.670000 27.673552 30.085658 43.101736 77.890991 83.358466 102.346522 106.447970 67.789628 98.485217 106.842930 111.724335 45.982363 71.783895 99.367270 105.867604 12.557525 30.086715 44.915091 58.255658 69.811548 79.230632 102.712965 109.986862 38.089760 89.233977 104.875415 101.171450 82.341701 85.192075 107.510934 104.509372 32.554226 61.365670 66.740970 77.364118 33.980025 58.485139 62.818946 77.518966 2 35 23.95109234 -1.243882127 10.36268529 0.03249196962 1 0.8 -0.03235856928 -0.09756637699 371.4468475 0.2402262055 163.6837805 -1.088908584 -0.9087856329 3 4 5 6 7 8 9 0.190372 -1.014407 0.785790 0.101245 0.197132 -0.185847 1.137151 0.606793 0.578947 0.628088 0.817202 0.803693 1.202530 0.815451 12.670000 12.703735 1.064819 22.083896 22.124504 1.281755 22.851760 22.878604 0.847306 30.397475 30.404469 0.220772 27.500255 27.519494 0.607251 56.234586 56.279251 1.409828 63.950057 64.008883 1.856780 72.923316 72.886087 -1.175106 27.500255 27.537897 1.188145 39.207796 39.254672 1.479613 56.234586 56.238048 0.109275 63.950057 63.997290 1.490864 33.150627 33.178875 0.891604 38.919199 38.906310 -0.406823 62.671235 62.706444 1.111343 63.731937 63.752210 0.639928 12.670000 12.737505 1.065370 22.083896 22.163523 1.256682 30.397475 30.401414 0.062172 33.150627 33.109410 -0.650501 27.500255 27.535054 0.549191 56.234586 56.275941 0.652679 63.950057 64.006345 0.888346 75.309899 75.344254 0.542182 27.500255 27.579288 1.247307 39.207796 39.301524 1.479238 56.234586 56.289272 0.863058 63.950057 64.098377 2.340809 22.851760 22.906715 0.867306 30.444343 30.508040 1.005277 33.150627 33.072536 -1.232451 48.843634 48.927656 1.326045 12.670000 22.083896 30.397475 41.928164 82.457971 84.612828 114.805378 117.776645 71.401603 108.962428 120.305188 141.351924 39.207796 71.007631 90.314593 128.336645 22.851760 30.444343 48.843634 53.351415 72.923316 81.648469 115.445375 112.502602 38.919199 100.231758 93.959936 129.189864 75.309899 106.817099 108.148892 91.931681 27.500255 56.234586 63.950057 85.937257 33.150627 63.731937 62.671235 74.120646 1 35 24.58630337 -1.65788948 10.83581899 0.03249196962 1 0.85 0.03120959276 -0.09078478384 379.7735365 0.282467117 158.2739348 -1.179585092 -0.9120809467 3 4 5 6 7 8 9 0.179041 -1.060317 0.856917 0.096608 0.201159 -0.194890 0.886625 0.479122 0.562549 0.615124 0.798640 0.781803 1.196172 0.797519 12.670000 12.705975 1.116703 26.008982 26.038335 0.911166 26.139767 26.163455 0.735272 33.602122 33.625498 0.725628 27.092552 27.110147 0.546147 57.214751 57.261976 1.465897 66.232544 66.297198 2.006906 76.040472 75.996783 -1.356159 27.092552 27.131691 1.214891 39.024949 39.078637 1.666522 57.214751 57.216195 0.044815 66.232544 66.286369 1.670789 35.105959 35.133707 0.861316 40.670045 40.659150 -0.338214 66.062785 66.101740 1.209189 66.309214 66.327892 0.579784 12.670000 12.741972 1.117041 26.008982 26.066538 0.893304 33.602122 33.671291 1.073530 35.105959 35.126380 0.316947 27.092552 27.125093 0.505043 57.214751 57.257326 0.660777 66.232544 66.298945 1.030570 76.807304 76.840397 0.513616 27.092552 27.173565 1.257351 39.024949 39.132276 1.665758 57.214751 57.269295 0.846540 66.232544 66.392997 2.490307 26.139767 26.188212 0.751882 34.171365 34.171113 -0.003907 35.105959 35.112841 0.106806 49.642596 49.679655 0.575168 12.670000 26.008982 33.602122 42.058502 85.158282 88.159992 119.901854 131.932927 74.405502 117.273008 127.389634 159.151541 39.024949 73.165526 94.820146 135.126493 26.139767 34.171365 49.642596 56.382180 76.040472 84.701426 119.740301 116.707074 40.670045 103.311904 95.285252 142.582088 76.807304 103.677746 122.543481 98.083469 27.092552 57.214751 66.232544 90.158781 35.105959 66.309214 66.062785 78.717626 2 42 38.65137561 -7.704260591 11.40035494 0.03249196962 1 0.9 0.06245335539 -0.0737703635 395.3704661 0.3116668596 182.0506771 -1.25519489 -0.9883266253 3 4 5 6 7 8 9 0.150608 -0.135366 -2.771749 0.091730 0.201658 -0.196662 0.824932 0.723028 0.536319 0.576503 0.752634 0.739987 1.183660 0.744170 12.670000 12.707542 1.031345 31.046725 31.057399 0.293224 31.151814 31.144349 -0.205092 38.911373 38.992309 2.223448 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40.290111 50.273053 70.719908 81.719849 92.700841 128.278563 128.197167 45.143055 110.476364 142.812219 159.741076 81.775248 135.914127 137.349948 118.972322 26.795715 59.585869 72.679625 96.572041 39.662747 70.571144 73.713649 90.784920 2 10 585.7279032 -7.417120898 14.30214604 0.03249196962 1 0.95 0.1217690426 -0.06499508697 398.0635529 0.3879171744 154.3287187 -1.384256 -1.038894621 3 4 5 6 7 8 9 0.124884 -0.115807 -2.898233 0.084678 0.201811 -0.200833 0.597085 0.520987 0.506145 0.600814 0.707849 0.737115 1.177368 0.778972 12.670000 12.731912 1.769302 37.466739 37.504619 1.082537 38.246408 38.146890 -2.844005 49.150339 49.954463 22.980091 30.937752 30.956215 0.527644 70.816845 70.884215 1.925298 87.339087 87.403017 1.826994 99.010982 98.981300 -0.848243 30.937752 30.993770 1.600879 52.548099 52.607488 1.697199 70.816845 70.840157 0.666217 87.339087 87.386108 1.343767 49.150339 49.177129 0.765607 55.129842 55.118068 -0.336471 85.239205 85.263743 0.701246 90.831565 90.817397 -0.404896 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