********* 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 18 280.1407377 -7.735068011 3.149371067 0.03249196962 1 0 -0.03600509723 -0.1829124938 2273.242098 0.07499918867 1102.046419 0.9927284972 1.146175434 3 4 5 6 7 8 9 0.316879 -0.525638 0.271554 0.129260 0.216418 -0.257396 5.444172 2.043340 0.889479 0.361865 1.430639 0.770494 1.463825 0.437832 12.670000 12.681876 0.189623 12.981949 13.010000 0.447912 16.324265 16.331370 0.113451 17.144641 17.195603 0.813750 12.361386 12.370589 0.146942 27.094732 27.107648 0.206235 29.580104 29.779079 3.177142 30.508581 30.315462 -3.083627 12.361386 12.361386 0.000000 19.809359 19.809359 0.000000 27.094732 27.094732 0.000000 29.580104 29.580104 -0.000000 18.269864 18.269864 -0.000000 19.766670 19.766670 0.000000 27.556531 27.556531 -0.000000 29.572971 29.572971 0.000000 12.670000 12.694489 0.195515 16.324265 16.338472 0.113421 17.295998 17.292960 -0.024259 18.269864 18.258675 -0.089329 12.361386 12.368727 0.058605 27.094732 27.107389 0.101043 29.580104 29.588663 0.068332 31.204726 30.214569 -7.905181 12.361386 12.372450 0.088331 19.809359 19.809359 0.000000 27.094732 27.107908 0.105188 29.580104 29.782437 1.615378 12.981949 13.030418 0.386969 17.144641 17.227202 0.659148 18.269864 18.255176 -0.117260 18.550013 18.538011 -0.095825 12.670000 16.324265 17.295998 18.608710 32.594011 35.495461 41.494403 44.619526 31.140121 46.371082 48.477462 49.101160 19.809359 31.061384 41.152082 48.308649 12.981949 17.144641 18.550013 27.641669 30.508581 33.438126 42.322265 44.069378 19.766670 41.093437 44.532616 44.334065 35.385025 35.234529 46.139851 45.431123 12.361386 27.094732 29.580104 31.204726 18.269864 27.556531 29.572971 31.204726 2 59 158.393553 -7.238020331 3.366002514 0.03249196962 1 0.1 -0.05707336246 -0.1253938694 174.1757859 0.1453717755 82.10575231 -0.0992979664 -1.235722544 3 4 5 6 7 8 9 0.320759 -0.518238 0.250093 0.187020 0.120698 -0.149848 5.511172 2.079099 0.689743 0.463285 0.919695 0.979672 1.455833 0.569321 12.670000 12.681075 0.191327 13.285602 13.368164 1.426246 17.126966 17.310071 3.163109 17.598977 17.651589 0.908847 13.129088 13.137264 0.141239 28.572860 28.584502 0.201110 31.619658 31.779896 2.768088 32.385582 32.406816 0.366814 13.129088 13.129304 0.003719 21.953257 21.953455 0.003420 28.572860 28.573106 0.004254 31.619658 31.633257 0.234931 19.382327 19.382738 0.007091 20.432507 20.432188 -0.005508 28.302166 28.302205 0.000674 31.372203 31.372640 0.007543 12.670000 12.692368 0.193201 17.598977 17.558909 -0.346086 17.631789 17.668624 0.318166 19.372427 19.367226 -0.044925 13.129088 13.132564 0.030021 28.572860 28.584091 0.097009 31.619658 31.626725 0.061044 32.385582 32.409632 0.207727 13.129088 13.142394 0.114927 21.953257 21.953654 0.003422 28.572860 28.585397 0.108287 31.619658 31.812921 1.669295 13.285602 13.429262 1.240857 17.126966 17.486829 3.108285 18.054045 17.964916 -0.769847 19.382327 19.391632 0.080366 12.670000 17.631789 17.598977 19.372427 34.157893 38.035023 43.707320 48.164184 32.192022 48.568563 51.571480 49.707167 21.953257 32.969536 44.739111 51.077360 13.285602 17.126966 18.054045 29.569406 32.808828 35.137928 44.688243 47.911768 20.432507 43.201566 46.358184 50.978368 37.011957 38.487553 48.784650 47.416949 13.129088 28.572860 31.619658 32.385582 19.382327 28.302166 31.372203 33.997827 2 59 143.4838273 -7.140245586 3.673837208 0.03249196962 1 0.2 -0.0634424757 -0.1156810573 174.8658178 0.1750298282 80.35105715 0.0314690468 -1.097242848 3 4 5 6 7 8 9 0.307006 -0.497810 0.120523 0.191325 0.109461 -0.138585 5.202332 1.973300 0.689763 0.491351 0.937060 1.001798 1.433860 0.612102 12.670000 12.682424 0.224202 13.816373 13.849171 0.591882 18.388851 18.386134 -0.049044 18.418159 18.420872 0.048957 13.993820 14.002858 0.163104 30.200303 30.213321 0.234919 33.882822 33.904124 0.384411 34.693711 34.731665 0.684914 13.993820 13.994669 0.015329 23.651477 23.652296 0.014778 30.200303 30.201339 0.018698 33.882822 33.894876 0.217526 20.462648 20.464207 0.028126 21.575463 21.574258 -0.021752 29.764112 29.764228 0.002095 33.410215 33.412978 0.049863 12.670000 12.694980 0.225394 18.388851 18.383299 -0.050103 18.418159 18.423576 0.048874 20.347749 20.372505 0.223380 13.993820 13.996846 0.027305 30.200303 30.212973 0.114322 33.882822 33.894809 0.108156 34.693711 34.743015 0.444870 13.993820 14.010570 0.151136 23.651477 23.653115 0.014783 30.200303 30.215709 0.139006 33.882822 33.934265 0.464178 13.816373 13.876774 0.545006 18.522134 18.499644 -0.202924 18.893897 19.062874 1.524701 20.462648 20.471878 0.083283 12.670000 18.388851 18.418159 20.347749 36.359430 40.715183 46.860191 52.068773 34.215091 52.291316 55.662363 52.969202 23.651477 35.267052 48.368381 56.462454 13.816373 18.522134 18.893897 31.398713 35.062312 37.447154 47.836548 51.983719 21.575463 46.296112 49.540379 56.140713 39.389062 41.997438 52.509184 50.505679 13.993820 30.200303 33.882822 34.693711 20.462648 29.764112 33.410215 36.714594 5 100 91.60637641 -1.49383705 6.43473043 0.03249196962 1 0.3 -0.07917981068 -0.139711371 176.3313552 0.2589869707 80.33005351 0.791198303 -0.5071701052 3 4 5 6 7 8 9 0.240690 -0.753205 0.876585 0.156728 0.172133 -0.216016 4.545230 1.281890 0.701522 0.630959 1.033023 0.976042 1.412453 0.823462 12.670000 12.698091 0.696104 14.793105 14.830377 0.923602 25.318985 25.297626 -0.529287 25.397667 25.381758 -0.394230 22.250512 22.275615 0.622057 44.680457 44.709992 0.731904 54.985136 55.082097 2.402733 55.709148 55.637215 -1.782528 22.250512 22.252677 0.053642 40.010690 40.014248 0.088171 44.680457 44.680647 0.004720 54.985136 55.006581 0.531423 31.888326 31.893054 0.117169 34.209560 34.206430 -0.077566 44.015624 44.015311 -0.007752 52.599842 52.610454 0.262979 12.670000 12.726532 0.700443 25.318985 25.284949 -0.421712 30.147390 30.247620 1.241877 30.499513 30.530868 0.388498 22.250512 22.257830 0.090665 44.680457 44.711522 0.384899 54.985136 55.018766 0.416691 56.655980 56.698253 0.523778 22.250512 22.297737 0.585130 40.010690 40.017795 0.088036 44.680457 44.708812 0.351325 54.985136 55.137279 1.885094 14.793105 14.863982 0.878170 25.397667 25.357344 -0.499616 31.770708 31.937520 2.066831 31.888326 32.036719 1.838629 12.670000 25.318985 30.499513 30.147390 56.655980 65.198296 74.849978 86.559768 54.936154 81.492922 90.320138 88.238374 40.010690 57.864730 82.170412 87.360262 14.793105 25.397667 31.770708 47.981777 55.709148 58.817223 75.811623 88.715690 34.209560 75.884273 83.081487 89.002368 64.860059 71.090158 83.928184 83.392574 22.250512 44.680457 54.985136 58.872539 31.888326 44.015624 52.599842 61.908675 2 10 194.1840938 -7.467345304 3.496413533 0.03249196962 1 0.4 -0.05619295729 -0.0968878772 192.1731667 0.1478324792 73.44399575 -0.9370236797 -0.825061301 3 4 5 6 7 8 9 0.300987 -0.513915 -0.001389 0.109084 0.252868 -0.277441 4.192227 1.893806 0.695608 0.367887 0.979418 0.714551 1.361927 0.446515 12.670000 12.680849 0.182680 13.589875 13.597343 0.125759 14.588662 14.597361 0.146470 16.936643 16.928515 -0.136859 12.797579 12.803999 0.108101 28.055733 28.068601 0.216666 29.533929 29.541891 0.134063 31.977979 31.973466 -0.075987 12.797579 12.801524 0.066427 20.295635 20.298720 0.051929 28.055733 28.063076 0.123636 29.533929 29.534445 0.008685 18.010292 18.014851 0.076774 19.214669 19.211178 -0.058791 28.311062 28.312610 0.026059 29.822244 29.828512 0.105534 12.670000 12.691733 0.182971 14.588662 14.605996 0.145931 16.936643 16.923855 -0.107663 17.955191 17.972572 0.146334 12.797579 12.802078 0.037882 28.055733 28.067407 0.098282 29.533929 29.545337 0.096041 32.194506 32.209586 0.126954 12.797579 12.813817 0.136710 20.295635 20.301807 0.051954 28.055733 28.084428 0.241583 29.533929 29.538796 0.040977 13.589875 13.604733 0.125095 16.942716 16.928989 -0.115565 18.010292 18.015614 0.044814 18.374694 18.388757 0.118397 12.670000 14.588662 16.936643 17.955191 34.378024 37.209170 44.592072 47.785080 31.226327 48.119954 52.435774 49.935293 20.295635 31.794984 43.377461 51.645560 13.589875 16.942716 18.374694 28.090896 31.977979 35.028762 45.322118 46.903207 19.214669 42.540451 43.781366 51.903061 34.801556 42.996613 44.489534 44.879934 12.797579 28.055733 29.533929 32.194506 18.010292 28.311062 29.822244 33.116857 2 10 168.8101858 -2.241518706 3.944038812 0.03249196962 1 0.5 -0.05619295729 -0.0968878772 192.1731667 0.1478324792 73.44399575 -0.9370236797 -0.825061301 3 4 5 6 7 8 9 0.281108 -0.665155 0.391577 0.109825 0.242071 -0.260140 3.420587 1.632655 0.675880 0.390828 0.953027 0.719654 1.320626 0.478888 12.670000 12.682889 0.228635 13.934465 13.944462 0.177349 13.955768 13.964375 0.152677 17.471795 17.466037 -0.102132 13.691418 13.698468 0.125060 29.209714 29.224367 0.259920 31.044433 31.056173 0.208275 33.968307 33.962718 -0.099153 13.691418 13.698558 0.126661 20.818315 20.824536 0.110356 29.209714 29.216776 0.125268 31.044433 31.048365 0.069768 18.431961 18.439098 0.126614 20.032180 20.027256 -0.087347 30.458312 30.462522 0.074678 30.968615 30.976707 0.143544 12.670000 12.695784 0.228697 13.934465 13.953948 0.172812 17.471795 17.462743 -0.080281 18.431961 18.422699 -0.082147 13.691418 13.698700 0.064588 29.209714 29.223815 0.125064 31.044433 31.058408 0.123957 35.603495 35.647909 0.393931 13.691418 13.712528 0.187235 20.818315 20.830762 0.110401 29.209714 29.238949 0.259298 31.044433 31.060962 0.146613 13.955768 13.973406 0.156435 17.474908 17.468243 -0.059112 18.431961 18.429122 -0.025178 20.328254 20.345195 0.150259 12.670000 13.934465 17.471795 19.163873 37.252292 39.463155 48.835678 51.067829 33.307853 48.541020 54.694017 51.862876 20.818315 33.657416 44.932011 52.375828 13.955768 17.474908 20.328254 29.136821 33.968307 37.588039 49.242044 50.271670 20.032180 45.284099 45.538672 52.522846 36.502635 47.804987 47.217012 43.897320 13.691418 29.209714 31.044433 35.603495 18.431961 30.458312 30.968615 35.363321 2 18 82.71058583 -1.283388488 6.27139061 0.03249196962 1 0.6 -0.08043918259 -0.1208367038 172.2548457 0.1248864787 81.56765461 -0.846635574 -0.9367286883 3 4 5 6 7 8 9 0.241780 -0.807309 0.505255 0.117948 0.214027 -0.218096 2.239390 1.190088 0.636644 0.533174 0.884257 0.803369 1.258543 0.678393 12.670000 12.694336 0.590405 16.422596 16.483546 1.478701 16.560250 16.580132 0.482353 23.308636 23.316008 0.178847 19.853253 19.867255 0.339704 39.987444 40.009840 0.543355 43.890415 43.916382 0.629990 48.327951 48.319688 -0.200475 19.853253 19.872001 0.454856 28.004588 28.021185 0.402665 39.987444 39.993845 0.155303 43.890415 43.905147 0.357413 24.056123 24.072977 0.408880 27.594995 27.584916 -0.244517 42.830007 42.838801 0.213342 43.612235 43.628651 0.398275 12.670000 12.718703 0.590787 16.560250 16.598864 0.468406 23.308636 23.303505 -0.062243 24.056123 24.016600 -0.479425 19.853253 19.876821 0.285892 39.987444 40.011775 0.295142 43.890415 43.915178 0.300384 51.879762 51.895533 0.191309 19.853253 19.895205 0.508901 28.004588 28.037796 0.402831 39.987444 40.020585 0.402013 43.890415 43.946225 0.676999 16.422596 16.534393 1.356136 23.323752 23.328357 0.055856 24.056123 24.033230 -0.277698 28.931494 29.713707 9.488531 12.670000 16.560250 23.308636 28.419963 55.453987 56.564910 74.247101 71.449948 48.368857 69.652554 82.571795 76.362899 28.004588 48.418661 61.095329 78.606739 16.422596 23.323752 28.931494 39.463635 48.327951 55.206832 73.391231 74.519544 27.594995 64.582415 67.141321 75.894912 51.879762 69.503347 70.139863 62.573533 19.853253 39.987444 43.890415 54.889637 24.056123 43.612235 42.830007 51.617138 2 27 20.02181344 -1.060065661 9.346364416 0.03249196962 1 0.7 -0.06774836509 -0.1086115316 1073.807581 0.1552061319 472.0779266 -0.93456378 -0.844032745 3 4 5 6 7 8 9 0.218479 -0.955048 0.681896 0.111603 0.199819 -0.190820 1.498312 0.878020 0.615607 0.659975 0.872034 0.857966 1.215947 0.858438 12.670000 12.704914 1.140715 22.136076 22.167316 1.020669 22.214825 22.238857 0.785162 30.339848 30.354534 0.479809 27.012975 27.032358 0.633253 53.839550 53.874287 1.134886 61.114137 61.158329 1.443846 67.738036 67.716588 -0.700731 27.012975 27.048304 1.154254 37.164518 37.199171 1.132195 53.839550 53.838509 -0.034039 61.114137 61.149045 1.140525 31.735889 31.762494 0.869245 37.211604 37.197511 -0.460445 59.371369 59.392690 0.696573 60.087330 60.108990 0.707674 12.670000 12.739865 1.141307 22.136076 22.196026 0.979327 30.339848 30.344090 0.069290 31.735889 31.679904 -0.914559 27.012975 27.052754 0.649816 53.839550 53.871356 0.519577 61.114137 61.152278 0.623063 71.126216 71.167406 0.672872 27.012975 27.082645 1.138120 37.164518 37.233837 1.132391 53.839550 53.875042 0.579778 61.114137 61.231676 1.920107 22.214825 22.265236 0.823495 30.356421 30.392726 0.593076 31.735889 31.689926 -0.750830 45.792553 45.825136 0.532277 12.670000 22.136076 30.339848 40.095648 78.760358 79.070180 107.401950 102.019963 67.402936 98.695861 117.806584 114.746552 37.164518 67.088248 82.472950 114.689252 22.214825 30.356421 45.792553 52.887950 67.738036 77.707160 104.832170 106.387619 37.211604 90.605266 94.769348 108.418275 71.126216 98.376665 98.714737 87.485422 27.012975 53.839550 61.114137 79.185776 31.735889 60.087330 59.371369 70.929300 2 9 92844.89397 -0.5619988057 50 0.03249196962 1 0.8 -0.05619295729 -0.0968878772 192.1731667 0.1478324792 73.44399575 -0.9370236797 -0.825061301 3 4 5 6 7 8 9 0.190402 -1.469182 1.497580 0.115651 0.139786 -0.094322 0.217742 0.241231 0.579521 2.661843 0.830657 2.708724 1.116575 3.705102 -0.662264 -0.415495 37.588360 90.977109 91.106704 19.740174 100.277281 100.284916 1.162960 122.378027 122.079071 -45.537487 122.210670 122.323028 17.114646 239.210702 239.384529 26.477626 288.389905 288.635758 37.448777 320.765719 320.617442 -22.585789 122.210670 122.463329 38.485406 151.661196 151.958170 45.235536 239.210702 239.076891 -20.382301 288.389905 288.599605 31.941946 131.106996 131.256425 22.761214 162.057785 162.006533 -7.806658 268.298489 268.375352 11.707877 283.460313 283.609706 22.755675 -0.662264 -0.168834 37.580029 100.277281 100.293493 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