********* 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:kappa_S 11:kappa_A 12:mu_F 13:mu_0^2 14:mu_1^2 15:mu_2^2 16:mu_3^2 Use chi^2 fit with 40 criteria and tolerance 0.01. Overall scale from minimizing chi^2. 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) = (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 0,18/2,7) ( 3 0,18/2,5) ( 3 0,26/2,5) ( 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 0,14/2,3,3.5) ( 1 0,14/2,5,3.5) ( 1 0,14/2,3,3) ( 1 0,24/2,3,4) ( 1 0,24/2,3,4.5) ( 1 0,36/2,3,5) ( 1 0,36/2,3,6) L=1.265-0.964*m and error 0.1; ( 1 0,14/2,3,3.5) ( 1 0,14/2,5,3.5) ( 1 0,14/2,3,3) ( 1 0,24/2,3,4) ( 1 0,24/2,3,4.5) ( 1 0,36/2,3,5) ( 1 0,36/2,3,6) 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) = (14/2,3) (22/2,3) (46/2,3) (14/2,5) (28/2,5) (14/2,7) (16/2,7) . Result format: Fit info, # steps, chi^2, and p damping, scale G^2 N/sigma. The 17 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 49 5481599.676 -7.434801796 4.213173966 0 1 -1.714586604 -0.6105918718 0.1947159076 -185.9923174 0.1257410291 93.51078234 0.5323084906 13.97464428 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 -0.483501 9.344535 -43.718332 0.237351 -0.258435 0.600363 -3.902245 0.011733 0.380640 -6.982326 1.102124 0.865816 1.592705 -17.165103 -1790.522459 -1783.008058 -244.918370 -25.606052 -24.346442 -41.054719 -22.080944 -20.890415 -38.803125 -19.413390 -20.554073 37.178521 -6.334310 -3.088676 -105.785627 -6.061925 -2.270973 -123.559270 -4.894668 -1.456301 -112.067388 -4.344249 2.726400 -230.455067 -3.097588 -1.413626 -54.885701 -2.291074 -0.887054 -45.761516 -0.937965 -0.751484 -6.078016 -0.697889 3.354899 -132.093327 -12.115464 -12.115294 -0.005538 -4.432453 -4.435436 0.097245 -1.811950 -1.749329 -2.041034 -0.322349 -0.364128 1.361708 -25.606052 -23.988827 -26.355267 -19.413390 -19.570681 2.563303 -12.115464 -16.835466 76.919984 -8.150410 -10.573509 39.488278 -6.334310 -2.958783 -55.009625 -4.894668 -1.853193 -49.565703 -3.841879 -0.793499 -49.678239 -3.097588 2.984495 -99.117281 -6.061925 -1.365371 -76.537866 -4.344249 -0.959689 -55.156817 -3.097588 0.096669 -52.055523 -2.291074 3.488229 -94.182985 -1790.522459 -1775.554200 -243.931730 -22.080944 -22.052246 -0.467677 -14.161131 -14.182357 0.345917 -12.115464 -12.117492 0.033045 -25.606052 -19.413390 -8.150410 -6.168997 -1.199553 -6.334310 -3.841879 -4.894668 -1.811950 0.803917 7.446439 6.214605 0.720371 5.846664 7.459096 1.527968 -1790.522459 -22.080944 -14.161131 -10.603087 -1.493659 6.613192 -4.344249 -6.061925 -4.432453 1.422816 7.465868 2.489978 -0.697889 7.351366 1.937041 -0.937965 -3.097588 3.594454 -2.291074 2.742068 -12.115464 -0.322349 0.111907 1.464398 2 12 112.6039876 -0.25 8.405346326 0.001967542671 1 -0.1476657703 0.06864570615 -0.1203114222 1262.561216 -0.0378560403 506.5173228 -1.04425888 -1.254392203 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.166456 -0.034337 -0.476798 0.143636 0.034904 0.012561 2.371670 1.237708 0.580866 0.561274 0.897681 0.894532 1.155672 0.734092 20.430646 20.445690 0.336773 23.812704 23.827444 0.329963 23.848278 23.845169 -0.069585 26.420925 26.382844 -0.852485 25.908634 25.919589 0.245254 43.084527 43.094687 0.227423 45.961742 45.953586 -0.182571 47.239255 47.241294 0.045627 23.730168 23.727319 -0.063776 25.908634 25.913468 0.108231 43.084527 43.080695 -0.085785 45.961742 45.943856 -0.400396 26.420925 26.422058 0.025355 28.358622 28.357855 -0.017159 43.910482 43.913478 0.067061 45.840646 45.837678 -0.066426 20.430646 20.460769 0.337165 23.848278 23.850811 0.028353 26.420925 26.350888 -0.783923 27.560055 27.619743 0.668082 25.908634 25.927485 0.211000 43.084527 43.084238 -0.003241 45.961742 45.961745 0.000040 48.666688 48.658171 -0.095335 23.730168 23.724442 -0.064089 25.908634 25.921387 0.142751 43.084527 43.097969 0.150456 45.961742 45.911164 -0.566115 23.812704 23.833342 0.231002 26.420925 26.419560 -0.015285 30.303385 30.287480 -0.178030 43.910482 43.849236 -0.685518 20.430646 23.848278 27.560055 30.424289 53.262022 57.520588 61.427460 55.138301 48.920559 51.136162 54.638549 58.320891 23.730168 46.984406 48.544833 52.867211 23.812704 30.303385 44.369192 48.045917 47.239255 52.805264 58.701613 56.929005 28.358622 50.260922 55.535939 57.244591 48.666688 54.084380 56.254286 59.032193 25.908634 43.084527 45.961742 48.772764 26.420925 43.910482 45.840646 47.711471 2 29 83.23419647 -9.963903787 9.909704447 0.007919222016 1 0.06665684768 0.07485119468 -0.2869147126 4587635.016 -0.1783436366 2018051.428 -1.515377013 -2.505935987 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.142899 -0.432393 0.382641 0.119397 -0.203517 0.419575 1.998408 0.758632 0.476327 0.372226 0.555377 0.585152 1.081329 0.508217 14.526847 14.571608 1.014171 22.302796 22.330994 0.638894 23.372501 23.368932 -0.080864 29.397801 29.375848 -0.497410 30.464208 30.487745 0.533280 48.103167 48.108803 0.127702 51.064582 51.075361 0.244214 52.464418 52.454892 -0.215846 23.370028 23.369989 -0.000886 30.464208 30.465080 0.019765 48.103167 48.097757 -0.122574 50.405772 50.400728 -0.114274 29.397801 29.398266 0.010538 34.797761 34.797792 0.000688 48.282782 48.282373 -0.009264 50.517041 50.517229 0.004274 14.526847 14.616604 1.016836 23.372501 23.365365 -0.080839 29.397801 29.365172 -0.369652 30.600698 30.617711 0.192739 30.464208 30.504121 0.452159 48.103167 48.101753 -0.016012 51.064582 51.079418 0.168077 52.381156 52.387532 0.072230 23.370028 23.369936 -0.001042 30.464208 30.472841 0.097799 48.103167 48.106094 0.033160 50.405772 50.395609 -0.115126 22.302796 22.358779 0.634218 29.397801 29.388763 -0.102391 39.405699 39.375235 -0.345119 46.348576 46.336357 -0.138426 14.526847 23.372501 30.600698 39.960734 59.500330 63.972496 64.060372 53.885757 56.687334 59.154692 62.492118 66.092700 23.370028 50.405772 53.035513 54.356281 22.302796 39.405699 46.348576 49.752785 52.464418 55.658893 61.185199 53.793453 34.797761 55.024160 59.692318 65.573923 52.381156 59.350755 65.273948 71.940898 30.464208 48.103167 51.064582 52.985337 29.397801 48.282782 50.517041 53.865367 2 12 80.71700854 -9.643231995 6.555589111 0.01800590693 1 0.4468114494 0.05367453178 -0.2430870049 5562.964623 0.01421308257 2635.9574 -1.407036916 -1.903203927 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.169035 -0.328628 -0.137258 0.135604 -0.108417 0.264610 1.831430 1.006494 0.546663 0.378662 0.721284 0.657721 1.068228 0.477881 12.953107 12.980523 0.486090 17.160449 17.164602 0.073624 17.166833 17.205112 0.678683 22.776295 22.723198 -0.941418 20.988497 20.999084 0.187704 32.917558 32.941834 0.430414 36.675254 36.662430 -0.227372 38.900784 38.905495 0.083524 20.988497 21.070455 1.453113 21.672427 21.602403 -1.241513 32.917558 32.913229 -0.076748 36.675254 36.630711 -0.789745 22.776295 22.784939 0.153249 26.001352 25.997785 -0.063243 35.431962 35.439052 0.125710 36.825770 36.812100 -0.242371 12.953107 13.008041 0.486984 17.166833 17.209043 0.374193 22.776295 22.683599 -0.821754 26.001352 25.992110 -0.081925 20.988497 21.008524 0.177542 32.917558 32.913246 -0.038226 36.675254 36.672774 -0.021986 38.204467 38.250651 0.409424 20.988497 21.150691 1.437850 21.672427 21.535453 -1.214274 32.917558 32.964241 0.413841 36.675254 36.566247 -0.966346 17.160449 17.203028 0.377456 22.776295 22.781230 0.043752 26.446447 26.416849 -0.262389 32.621882 32.635971 0.124901 12.953107 17.166833 26.459168 28.139971 45.504058 47.081314 48.274594 42.176238 39.799246 42.600914 48.621488 53.249974 21.672427 38.515730 40.893397 48.477372 17.160449 26.446447 32.621882 35.568818 38.900784 47.011719 47.463694 39.762180 26.001352 40.765022 48.085642 53.194045 38.204467 46.144774 49.536150 50.005199 20.988497 32.917558 36.675254 42.989678 22.776295 35.431962 36.825770 39.732276 2 12 184.0480131 -9.524016852 1.798195232 0.03249196962 1 0.656492777 0.03394311086 -0.2739415607 7928.214096 0.05208241661 3819.257984 -1.33154823 -1.974644426 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.189312 -0.563105 0.100774 0.148733 -0.099685 0.249661 1.595864 0.963987 0.561058 0.285958 0.716480 0.615903 1.076923 0.290520 3.147599 3.156919 0.050765 4.836170 4.846140 0.054307 4.844166 4.848878 0.025660 6.724104 6.709344 -0.080396 5.963701 5.966419 0.014808 9.120936 9.129289 0.045495 10.534121 10.529166 -0.026989 11.345574 11.348036 0.013409 5.963701 6.241440 1.512765 6.656280 6.384528 -1.480159 9.120936 9.118825 -0.011499 10.534121 10.516703 -0.094873 6.724104 6.728762 0.025369 7.788388 7.786441 -0.010608 10.072110 10.074748 0.014367 10.571649 10.564621 -0.038282 3.147599 3.166286 0.050892 4.836170 4.851182 0.040884 6.724104 6.701140 -0.062541 7.669555 7.660604 -0.024377 5.963701 5.969852 0.016752 9.120936 9.118320 -0.007125 10.534121 10.531836 -0.006222 10.956033 10.975728 0.053637 5.963701 6.306734 0.934202 6.656280 6.324597 -0.903293 9.120936 9.136923 0.043537 10.534121 10.492818 -0.112483 4.844166 4.858467 0.038946 6.724104 6.727029 0.007964 7.653544 7.644797 -0.023822 8.716085 8.724995 0.024265 3.147599 4.836170 7.669555 9.108854 13.163744 13.978725 14.235120 12.827396 11.320023 12.505019 14.839748 15.826896 6.656280 11.195431 12.137037 14.743476 4.844166 7.653544 8.716085 9.920924 11.345574 13.905350 14.114749 12.326186 7.788388 11.882551 14.483661 14.442949 10.956033 12.880345 14.778279 14.315954 5.963701 9.120936 10.534121 12.671433 6.724104 10.072110 10.571649 11.563213 2 47 45.55962782 -9.369954152 6.903648624 0.0517766953 1 0.9512419514 0.1401678041 -0.3340921541 45626.48396 0.1750495074 19441.14541 -1.438535821 -1.966143731 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.212016 -0.853742 0.528960 0.160528 -0.129210 0.282729 1.468508 0.908506 0.584132 0.492464 0.737980 0.767697 1.103589 0.655337 12.588568 12.634563 1.077148 22.873800 22.904079 0.709094 23.108835 23.142410 0.786302 31.855151 31.798189 -1.333997 23.953446 23.961978 0.199811 36.801188 36.841209 0.937256 44.993731 44.964840 -0.676588 49.762608 49.781496 0.442344 23.953446 23.999377 1.075658 30.419709 30.408281 -0.267622 36.801188 36.797641 -0.083050 44.993731 44.915822 -1.824531 31.855151 31.885311 0.706302 37.127367 37.115578 -0.276077 42.414935 42.428408 0.315513 45.955897 45.930341 -0.598493 12.588568 12.680809 1.080092 23.108835 23.171279 0.731189 31.855151 31.784283 -0.829832 36.686351 36.760632 0.869798 23.953446 23.975910 0.263045 36.801188 36.792284 -0.104258 44.993731 44.984168 -0.111979 47.044988 47.131445 1.012361 23.953446 24.017717 0.752580 30.419709 30.419520 -0.002217 36.801188 36.887745 1.013542 44.993731 44.794277 -2.335499 22.873800 22.939156 0.765287 31.855151 31.872600 0.204322 35.464283 35.507039 0.500656 36.127930 36.114773 -0.154059 12.588568 23.108835 36.686351 42.277968 54.294113 60.971083 62.630258 61.869363 49.484211 55.882008 70.396403 67.915396 30.419709 49.794092 54.472420 61.451672 22.873800 36.127930 35.464283 40.544158 49.762608 57.792931 60.822745 63.114159 37.127367 54.401822 58.038702 66.968835 47.044988 51.558144 63.248357 64.922916 23.953446 36.801188 44.993731 58.043419 31.855151 42.414935 45.955897 52.630098 2 10 49.77634596 -9.104879651 7.284320648 0.07642881742 1 0.8214137817 -0.1286861836 -0.239004814 37998.08153 0.05808031917 18835.57169 -1.397047044 -2.060778167 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.269182 -0.602115 -0.084355 0.159501 -0.130435 0.282687 2.331233 1.540799 0.623324 0.565369 0.752962 0.797795 1.198211 0.774948 15.450297 15.486677 1.141341 22.326863 22.372112 1.419591 22.400944 22.415255 0.448979 31.119337 31.078516 -1.280688 27.541265 27.549700 0.264648 43.621359 43.652283 0.970171 50.308814 50.288506 -0.637119 53.665146 53.680687 0.487596 27.541265 27.558728 0.547868 35.251327 35.258928 0.238475 43.621359 43.615720 -0.176934 50.308814 50.267846 -1.285303 31.119337 31.142180 0.716653 35.197924 35.182969 -0.469180 47.143803 47.161859 0.566477 49.176496 49.164467 -0.377379 15.450297 15.523336 1.145724 22.326863 22.385162 0.914512 31.119337 31.058146 -0.959867 31.900854 31.858095 -0.670737 27.541265 27.562291 0.329832 43.621359 43.617595 -0.059045 50.308814 50.310809 0.031288 56.141593 56.186845 0.709849 27.541265 27.567382 0.409693 35.251327 35.271551 0.317247 43.621359 43.677754 0.884626 50.308814 50.186455 -1.919392 22.400944 22.459225 0.914222 31.119337 31.147779 0.446151 31.895375 31.835911 -0.932783 41.968056 42.010284 0.662403 15.450297 22.326863 31.900854 45.530028 61.112785 67.949380 68.530934 71.671162 54.745902 57.395505 70.482655 73.567717 35.251327 53.651134 60.725061 68.351891 22.400944 31.895375 41.968056 44.304960 53.665146 63.791747 70.061962 71.156118 35.197924 59.227074 66.318237 70.086556 56.141593 57.952246 71.583902 68.991798 27.541265 43.621359 50.308814 61.534360 31.119337 47.143803 49.176496 56.932742 2 11 98.50276386 -8.759288452 5.335730856 0.1072401379 1 0.9533021314 -0.1131319213 -0.3557856176 20228.99226 0.09830611755 9750.568781 -0.9425853121 -1.681989874 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.292031 -0.704270 0.002652 0.196074 -0.050713 0.124779 2.732998 1.632311 0.693443 0.585609 0.877212 0.910024 1.280816 0.779434 13.616507 13.653267 0.916475 18.418231 18.455632 0.932461 18.455880 18.479462 0.587911 27.365051 27.314108 -1.270056 21.736203 21.743039 0.170432 35.513817 35.541446 0.688819 40.778800 40.765922 -0.321056 44.145252 44.157440 0.303854 21.736203 21.726799 -0.234460 30.442837 30.472234 0.732895 35.513817 35.519764 0.148261 40.778800 40.757073 -0.541683 27.365051 27.385758 0.516252 31.613278 31.601371 -0.296874 39.172405 39.190598 0.453572 40.599425 40.593309 -0.152476 13.616507 13.690272 0.919520 18.418231 18.480385 0.774789 27.365051 27.291040 -0.922589 28.963671 28.920827 -0.534079 21.736203 21.750792 0.181865 35.513817 35.520591 0.084441 40.778800 40.786017 0.089972 47.090391 47.252152 2.016436 21.736203 21.717534 -0.232713 30.442837 30.500892 0.723692 35.513817 35.575788 0.772495 40.778800 40.703232 -0.941999 18.455880 18.515353 0.741367 27.365051 27.379584 0.181167 28.939051 28.892377 -0.581827 32.555171 32.557279 0.026273 13.616507 18.418231 28.963671 35.065387 49.302211 55.170868 56.774443 60.105740 46.790474 49.211354 61.739908 64.119516 30.442837 45.471309 53.064306 55.127760 18.455880 28.939051 32.555171 36.241533 44.145252 51.337622 58.273336 58.432140 31.613278 52.455506 52.867509 58.164317 47.090391 48.347601 55.875636 61.666810 21.736203 35.513817 40.778800 51.878997 27.365051 39.172405 40.599425 48.650404 2 13 115.3333111 -8.863029652 4.747518371 0.1453085056 1 0.938967997 -0.1210019785 -0.3291059662 24618.21 0.05026764128 12001.97987 -0.9059424461 -1.83522371 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.358261 -0.472661 -0.492970 0.203897 -0.036127 0.087529 3.732347 2.331802 0.739195 0.600858 0.892286 0.916245 1.392216 0.805047 16.586210 16.617034 0.838815 21.711923 21.753720 1.137435 21.754993 21.760768 0.157166 28.805203 28.759262 -1.250220 21.237650 21.242398 0.129221 37.103009 37.120510 0.476253 41.905854 41.900034 -0.158387 44.552568 44.563462 0.296457 21.237650 21.227961 -0.263663 31.219160 31.242930 0.646873 37.103009 37.105346 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