********* 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 42 criteria and tolerance 0.01. Overall scale from fitting lowest state to lattice value. Includes 1 nonstandard fit criteria (such as a specific lattice spacing). 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 0,14/2,6) ( 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=0.1. 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 0.1; 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 50.16192891 -0.9681201625 7.67334276 0.03249196962 1 0.6332096313 -0.004048704632 -0.22951899 50.31030442 0.1345058719 12.62538807 -0.733660211 -0.2408820916 2 3 4 5 6 7 8 9 0.214220 -1.071864 1.099021 0.123045 0.236897 -0.245295 1.799706 0.779272 0.635453 0.604826 0.797821 0.714827 1.069745 0.951532 1.176645 0.806066 12.670000 12.718607 1.278398 17.575447 17.601813 0.693438 17.621094 17.670377 1.296176 29.104740 29.052119 -1.383957 22.433757 22.460764 0.710304 46.126002 46.156149 0.792891 49.986799 50.028479 1.096202 56.704644 56.706013 0.036009 22.433757 22.457741 0.630812 31.502797 31.528309 0.670977 46.126002 46.150673 0.648870 49.986799 49.999779 0.341364 29.104740 29.133335 0.752072 35.294730 35.284087 -0.279912 51.484936 51.492426 0.196989 52.542912 52.573007 0.791522 12.670000 12.767240 1.278725 17.621094 17.698383 1.016374 29.104740 29.018132 -1.138918 32.484064 32.564652 1.059759 22.433757 22.474769 0.539329 46.126002 46.170943 0.590992 49.986799 50.029660 0.563631 62.102618 62.110839 0.108104 22.433757 22.494780 0.802479 31.502797 31.553848 0.671333 46.126002 46.190493 0.848073 49.986799 50.052959 0.870010 17.575447 17.649428 0.972866 29.104740 29.145913 0.541441 34.626023 34.584763 -0.542581 34.801414 34.801486 0.000940 12.670000 17.621094 32.484064 33.109492 65.902266 66.600240 89.283506 83.904157 61.005311 84.451206 93.356858 110.853276 31.502797 58.913039 70.257593 95.653249 17.575447 34.626023 34.801414 45.669741 56.704644 65.509441 87.514426 89.241449 35.294730 78.380148 88.642214 85.500566 62.102618 82.457487 84.914344 77.017069 22.433757 46.126002 49.986799 65.900892 29.104740 52.542912 51.484936 61.073364 2 12 52.27100889 -0.9701989718 6.99791388 0.0517766953 1 0.7510799228 -0.03602833268 -0.2216998675 23.36060482 0.1633643454 6.343519582 -0.8331818882 -0.2625390197 2 3 4 5 6 7 8 9 0.248673 -1.043148 0.921969 0.188816 0.119471 -0.138536 2.107138 1.061485 0.662234 0.738677 0.875795 0.897741 1.188456 1.248030 1.221225 1.023232 12.670000 12.712950 1.195869 19.060582 19.091058 0.848549 19.644260 19.674673 0.846803 28.904741 29.060597 4.339522 21.947954 21.968045 0.559395 45.238491 45.261806 0.649176 49.487108 49.523816 1.022067 55.546830 55.544870 -0.054594 21.947954 21.971903 0.666804 31.991682 32.016567 0.692880 45.238491 45.253780 0.425702 49.487108 49.502307 0.423187 28.904741 28.930037 0.704323 34.109714 34.098510 -0.311963 49.948477 49.955900 0.206661 50.999634 51.025294 0.714445 12.670000 12.755930 1.196281 19.644260 19.703205 0.820609 28.904741 28.941640 0.513688 30.723060 30.697549 -0.355151 21.947954 21.980929 0.459066 45.238491 45.274115 0.495951 49.487108 49.519811 0.455277 59.617130 59.660152 0.598938 21.947954 22.003087 0.767527 31.991682 32.041474 0.693181 45.238491 45.279959 0.577309 49.487108 49.557759 0.983559 19.060582 19.123365 0.874030 28.904741 29.042881 1.923130 30.803247 30.767268 -0.500887 33.255358 33.199019 -0.784324 12.670000 19.644260 31.342760 30.723060 64.320842 64.148713 86.713072 83.585568 57.881913 85.669090 91.528758 108.813319 31.991682 56.538350 71.694066 92.821548 19.060582 33.255358 30.803247 45.157230 55.546830 63.492479 84.773366 86.016249 34.109714 76.062654 72.202359 98.237751 59.617130 74.988630 90.817123 75.070000 21.947954 45.238491 49.487108 62.534287 28.904741 50.999634 49.948477 59.728718 2 10 143.0154271 -0.9389767146 6.778814108 0.07642881742 1 0.8905679728 -0.01248205081 -0.2163150187 23.63807043 0.1752110567 6.196949392 -0.1071617173 -0.01562034817 2 3 4 5 6 7 8 9 0.270787 -1.040452 0.724062 0.195314 0.104925 -0.122291 2.129546 1.216354 0.680745 0.759230 0.895761 0.921097 1.239543 1.280087 1.245296 1.054766 12.670000 12.715030 1.322540 23.165437 23.192381 0.791318 23.784845 23.811007 0.768359 30.739662 31.412702 19.767091 21.865329 21.881886 0.486278 45.598623 45.618291 0.577649 51.238481 51.272972 1.013014 57.022754 57.093399 2.074823 21.865329 21.891723 0.775183 32.817374 32.845622 0.829636 45.598623 45.608530 0.290985 51.238481 51.254336 0.465684 30.739662 30.764245 0.721979 35.602039 35.591696 -0.303785 51.662136 51.681880 0.579897 52.192177 52.203235 0.324777 12.670000 12.760084 1.322872 23.784845 23.836100 0.752670 30.739662 30.736177 -0.051185 31.403585 31.422298 0.274797 21.865329 21.895842 0.448086 45.598623 45.630404 0.466699 51.238481 51.264134 0.376717 59.626182 59.685106 0.865301 21.865329 21.920730 0.813560 32.817374 32.873888 0.829909 45.598623 45.626001 0.402046 51.238481 51.313020 1.094612 23.165437 23.220542 0.809212 30.739662 30.749103 0.138631 32.382265 32.350713 -0.463338 32.810305 32.888879 1.153846 12.670000 23.784845 31.403585 32.356196 66.244495 64.869551 89.264022 85.639571 58.874093 93.033138 96.449391 124.569183 32.817374 57.152354 76.282670 93.816533 23.165437 32.810305 32.382265 46.785996 57.022754 64.903604 85.724389 87.398219 35.602039 76.615319 73.573268 103.679659 59.626182 78.548251 79.046921 92.386524 21.865329 45.598623 51.238481 62.165129 30.739662 51.662136 52.192177 60.876555 2 11 40.277294 -0.929747941 6.231728169 0.1072401379 1 1.047691707 0.01509896306 -0.2246728997 23.63807043 0.2000105803 6.196949392 -0.111838015 -0.0541969195 2 3 4 5 6 7 8 9 0.293280 -0.979683 0.390674 0.201078 0.092852 -0.109140 2.239789 1.415395 0.703934 0.739114 0.920427 0.911378 1.292847 1.287734 1.277583 1.029671 12.670000 12.714493 1.301065 26.745800 26.772714 0.787034 26.794887 26.830263 1.034485 28.961202 28.968270 0.206696 20.873221 20.886419 0.385955 43.781031 43.797361 0.477530 51.289714 51.327835 1.114754 55.547138 55.537802 -0.273024 20.873221 20.899648 0.772783 32.342070 32.371042 0.847211 43.781031 43.787864 0.199817 51.289714 51.343679 1.578055 31.116504 31.138520 0.643808 35.375292 35.366277 -0.263623 49.673322 49.687919 0.426870 51.491648 51.502584 0.319822 12.670000 12.759003 1.301325 26.745800 26.799080 0.779016 28.961202 28.975395 0.207513 31.116504 31.097914 -0.271800 20.873221 20.899855 0.389424 43.781031 43.808392 0.400061 51.289714 51.346574 0.831355 56.918770 56.938933 0.294811 20.873221 20.925839 0.769341 32.342070 32.400029 0.847429 43.781031 43.800078 0.278498 51.289714 51.418481 1.882721 26.794887 26.866199 1.042678 29.338303 29.390509 0.763310 31.116504 31.117968 0.021401 32.611722 32.595370 -0.239087 12.670000 26.745800 28.961202 32.596186 64.489044 62.529570 86.665821 81.794884 56.854725 95.910249 93.009808 120.840951 32.342070 54.984695 72.948596 77.727848 26.794887 29.338303 32.611722 45.985607 55.547138 62.896784 82.026235 84.071151 35.375292 73.430885 74.513864 100.921599 56.918770 77.858384 67.032392 101.781482 20.873221 43.781031 51.289714 57.439727 31.116504 49.673322 51.491648 59.021433