********* 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 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 0.5 (-1, 5,0) and (-1, 6,0), error 0.5 ( 1, 7,0) and (-1, 4,0), error 0.5 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=0.2. 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 0.2; 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) (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 20 47.12969602 -1.401261778 10.11798014 0 1 -0.1730069918 -0.06739594464 -0.05833567132 3.897655234 -0.01136425081 1.055571647 -0.1469570838 0.1837884385 2 3 4 5 6 7 8 9 0.195624 -0.617371 0.499931 0.114313 0.385264 -0.505158 2.014807 1.010115 0.585763 0.783949 0.804118 0.872697 1.103980 1.077046 1.203483 1.028908 12.280000 12.310874 0.977757 15.156776 15.202546 1.449492 20.895888 20.897021 0.035891 25.476412 25.425323 -1.617947 28.287561 28.313917 0.834684 51.449221 51.474801 0.810088 55.985922 56.007956 0.697819 59.507022 59.505303 -0.054418 28.287561 28.302611 0.476619 29.763350 29.768489 0.162735 51.449221 51.454110 0.154805 55.985922 55.988329 0.076232 25.476412 25.488450 0.381240 28.617843 28.608742 -0.288196 51.300908 51.317766 0.533894 54.819797 54.820811 0.032101 12.280000 12.341740 0.977626 20.895888 20.898049 0.034213 25.476412 25.418208 -0.921627 26.095928 26.112921 0.269086 28.287561 28.340358 0.836019 51.449221 51.479609 0.481178 55.985922 56.005928 0.316795 67.389225 67.837216 7.093750 28.287561 28.317569 0.475170 29.763350 29.773644 0.163001 51.449221 51.479617 0.481298 55.985922 56.015023 0.460808 15.156776 15.247466 1.436036 25.476412 25.455970 -0.323681 26.101884 26.102972 0.017229 26.212184 26.421133 3.308626 12.280000 20.895888 26.095928 33.652196 71.346526 77.005405 84.811799 103.257069 58.394477 72.394714 77.835439 82.249981 29.763350 58.901147 71.695830 79.955409 15.156776 26.101884 26.212184 49.679724 59.507022 72.688436 86.011542 97.654909 28.617843 71.130404 76.588248 82.785178 71.444137 68.883897 82.233496 83.863893 28.287561 51.449221 55.985922 67.389225 25.476412 51.300908 54.819797 61.579308 2 66 30.47998401 -1.111661459 10.00734442 0.001967542671 1 -0.2881949368 -0.05824953178 -0.1413953492 5.431003743 0.06648625036 0.4077905267 -0.3804819868 -0.3017740793 2 3 4 5 6 7 8 9 0.163799 -0.705595 0.593912 0.110515 0.323494 -0.370932 2.063712 0.679034 0.593735 0.679515 0.727845 0.771569 1.010795 0.976966 1.284960 0.891744 11.675237 11.721994 1.226310 12.280000 12.311897 0.836571 16.302568 16.349674 1.235457 29.084933 29.027717 -1.500604 27.616997 27.662505 1.193542 51.846824 51.898639 1.358975 55.719825 55.752474 0.856307 62.584321 62.589689 0.140773 27.616997 27.631272 0.374391 35.483397 35.495849 0.326580 51.846824 51.873979 0.712215 55.719825 55.731498 0.306144 29.084933 29.106739 0.571903 35.245492 35.233339 -0.318746 53.724681 53.725179 0.013048 56.807801 56.841365 0.880282 12.280000 12.354723 0.979877 16.302568 16.396862 1.236536 29.084933 29.008646 -1.000388 29.678031 29.636036 -0.550712 27.616997 27.670124 0.696692 51.846824 51.897982 0.670863 55.719825 55.775658 0.732172 70.831567 70.864758 0.435258 27.616997 27.683525 0.872423 35.483397 35.508323 0.326872 51.846824 51.953436 1.398069 55.719825 55.752482 0.428255 11.675237 11.757738 1.081881 29.084933 29.090439 0.072205 29.689444 29.641839 -0.624267 36.164561 36.204759 0.527137 12.280000 16.302568 29.678031 33.772782 70.831567 77.652683 95.204462 101.218700 64.231468 80.983545 92.592671 98.394917 35.483397 65.757922 84.326907 88.128944 11.675237 29.689444 36.164561 49.902908 62.584321 72.549385 98.179719 98.073043 35.245492 84.327253 90.406972 90.326859 75.459136 76.115829 91.276669 91.921035 27.616997 51.846824 55.719825 72.766130 29.084933 53.724681 56.807801 70.619798 2 49 14.67358372 -0.9964012838 9.839613992 0.007919222016 1 0.4742632111 -0.05834621608 -0.1400782167 13.28868186 0.1195935875 2.345056097 -0.5928012604 -0.4492963063 2 3 4 5 6 7 8 9 0.179506 -1.040468 1.289693 0.106534 0.280253 -0.288953 1.549038 0.556794 0.587629 0.655068 0.699280 0.738674 0.960658 0.929399 1.095682 0.859332 12.280000 12.324292 1.251720 12.619967 12.662981 1.215578 13.112465 13.148541 1.019510 27.811206 27.821133 0.280554 26.252684 26.287929 0.996060 49.939318 49.990754 1.453606 54.827551 54.867025 1.115540 62.216557 62.215139 -0.040084 26.252684 26.278822 0.738687 34.294068 34.320290 0.741049 49.939318 49.970475 0.880518 54.827551 54.838711 0.315384 27.909423 27.940968 0.891483 34.488871 34.473093 -0.445889 54.486166 54.502057 0.449078 54.852085 54.880842 0.812684 12.280000 12.368762 1.254223 12.619967 12.703392 1.178802 27.811206 27.800494 -0.151358 27.909423 27.828522 -1.143133 26.252684 26.302167 0.699212 49.939318 49.995724 0.797030 54.827551 54.877303 0.702999 64.325541 64.442216 1.648638 26.252684 26.326080 1.037103 34.294068 34.346538 0.741409 49.939318 50.047875 1.533936 54.827551 54.878055 0.713630 13.112465 13.187025 1.053549 27.852563 27.860536 0.112649 27.909423 27.870167 -0.554683 40.469339 40.529060 0.843866 12.280000 12.619967 27.811206 36.164477 71.438940 75.958522 93.433941 117.751451 61.586436 85.095758 101.591133 108.657828 34.294068 64.427380 88.052817 91.095013 13.112465 27.852563 40.469339 52.896833 62.216557 72.020284 96.686822 97.478880 34.488871 84.463313 91.225793 92.182129 64.325541 86.480623 88.646517 101.005208 26.252684 49.939318 54.827551 69.802702 27.909423 54.486166 54.852085 65.877427 2 28 21.31601536 -0.9271888576 9.20987085 0.01800590693 1 0.4254186022 -0.1146574925 -0.1607646449 15.4369137 0.07319907112 -2.269700558 -0.6057623085 -0.5302174727 2 3 4 5 6 7 8 9 0.213585 -0.990847 1.185197 0.113160 0.272474 -0.283720 2.239186 0.865986 0.637037 0.687469 0.744705 0.773587 1.007393 0.972315 1.179145 0.906500 12.280000 12.317828 1.190566 12.329340 12.367816 1.210972 14.843609 14.885734 1.325819 28.665328 28.660748 -0.144151 28.093745 28.130485 1.156341 53.805627 53.845701 1.261253 55.837160 55.872736 1.119709 63.257892 63.261168 0.103126 28.093745 28.113424 0.619376 37.523826 37.541311 0.550326 53.805627 53.833521 0.877908 55.837160 55.845676 0.268043 29.394732 29.420994 0.826533 35.671558 35.656444 -0.475672 55.705755 55.747798 1.323258 55.851012 55.844000 -0.220694 12.280000 12.364101 1.323474 14.843609 14.928261 1.332152 28.665328 28.650592 -0.231894 29.394732 29.302098 -1.457761 28.093745 28.144540 0.799348 53.805627 53.849727 0.693979 55.837160 55.885860 0.766377 71.608619 71.525710 -1.304719 28.093745 28.155859 0.977480 37.523826 37.558820 0.550693 53.805627 53.897319 1.442926 55.837160 55.876443 0.618182 12.329340 12.397413 1.071237 28.671992 28.668426 -0.056118 29.394732 29.357442 -0.586823 42.807375 42.815535 0.128407 12.280000 14.843609 28.665328 36.495469 73.032404 76.535008 96.159636 114.199926 65.446452 87.878921 100.784423 107.204568 37.523826 66.158738 90.689053 94.574853 12.329340 28.671992 42.807375 49.016122 63.257892 73.556761 97.680505 99.886120 35.671558 85.542346 95.429936 91.803779 71.608619 88.741679 89.687849 92.288835 28.093745 53.805627 55.837160 72.174914 29.394732 55.851012 55.705755 62.832807