********* 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 0.25 (-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 29 85.39492861 -1.2192767 9.564109881 0 1 -0.2148413075 0.06801309251 -0.2272950312 11.87290939 0.03794724288 4.188340243 -0.4509407619 -0.4535866801 2 3 4 5 6 7 8 9 0.111290 -0.649256 0.510163 0.090489 0.339045 -0.363553 1.451541 0.304833 0.554141 0.513816 0.650434 0.616143 0.920427 0.814468 1.199840 0.666779 11.423246 11.502252 1.345479 12.670000 12.729457 1.012558 13.624803 13.671551 0.796134 27.522886 27.424219 -1.680309 22.647473 22.705498 0.988172 45.269285 45.330115 1.035943 48.080304 48.117026 0.625398 54.846757 54.859118 0.210517 22.647473 22.658630 0.190005 26.721465 26.731618 0.172902 45.269285 45.294923 0.436622 48.080304 48.095937 0.266235 27.522886 27.539848 0.288867 35.686285 35.682702 -0.061011 52.248797 52.262642 0.235792 52.252798 52.268264 0.263387 12.670000 12.785843 0.986415 13.624803 13.719019 0.802257 27.522886 27.353142 -1.445385 30.854452 31.004814 1.280347 22.647473 22.718244 0.602615 45.269285 45.326849 0.490164 48.080304 48.150391 0.596798 60.030396 60.045349 0.127327 22.647473 22.715148 0.576255 26.721465 26.741805 0.173199 45.269285 45.384731 0.983035 48.080304 48.114781 0.293581 11.423246 11.582471 1.355816 27.522886 27.532959 0.085770 29.142134 29.487246 2.938670 37.638245 37.625963 -0.104586 12.670000 13.624803 30.854452 34.748128 64.059342 66.972221 87.994285 84.716060 72.449927 66.155199 87.562362 101.344284 26.721465 58.122048 72.077524 76.046911 11.423246 29.142134 37.638245 41.474668 54.846757 66.324823 86.264072 84.238286 35.686285 75.600903 81.126494 84.834491 66.545272 64.952422 84.594144 71.728794 22.647473 45.269285 48.080304 60.030396 27.522886 52.252798 52.248797 57.033242 2 11 126.7340314 -1.244120854 10.71492672 0.001967542671 1 -0.3421106843 0.07688264715 -0.2517688947 13.45909968 0.1058909412 2.560350251 0.04234944975 0.7932335736 2 3 4 5 6 7 8 9 0.113754 -0.726309 0.510360 0.163734 0.180851 -0.218451 1.441454 0.247520 0.561565 0.712119 0.886341 0.850641 1.145210 1.155566 1.274637 0.974921 12.670000 12.735442 1.276240 13.312107 13.381822 1.359566 16.391757 16.456454 1.261699 32.748316 32.640811 -2.096541 25.637377 25.699554 1.212572 51.392887 51.465574 1.417521 57.020362 57.063928 0.849618 65.066468 65.082257 0.307926 25.637377 25.653218 0.308935 33.681807 33.701657 0.387117 51.392887 51.432296 0.768536 57.020362 57.037135 0.327093 32.748316 32.776962 0.558660 42.279599 42.272506 -0.138340 59.829595 59.839534 0.193814 62.371031 62.402542 0.614524 12.670000 12.804174 1.308323 16.391757 16.520445 1.254828 32.748316 32.574480 -1.695061 36.229822 36.402097 1.679843 25.637377 25.704388 0.653427 51.392887 51.472390 0.775222 57.020362 57.096190 0.739390 73.716017 74.440178 7.061263 25.637377 25.726542 0.869443 33.681807 33.721558 0.387612 51.392887 51.537482 1.409938 57.020362 57.065009 0.435344 13.312107 13.448898 1.333835 32.748316 32.768931 0.201017 38.529712 38.576331 0.454582 40.444400 40.617866 1.691466 12.670000 16.391757 36.229822 41.581949 73.981532 81.128957 100.034766 108.062515 77.968227 87.908994 114.754222 128.683945 33.681807 69.397392 92.848880 94.806702 13.312107 38.529712 40.444400 57.643041 65.066468 76.097747 100.641125 102.585918 42.279599 91.734071 98.912755 108.571270 80.757851 78.839959 97.537540 89.628547 25.637377 51.392887 57.020362 73.716017 32.748316 59.829595 62.371031 63.102045 2 11 67.82519976 -1.022918936 8.449703873 0.007919222016 1 0.3823473864 0.17836064 -0.3410673126 2768.364926 0.08444060389 -356.0879983 0.07585124883 0.4439032469 2 3 4 5 6 7 8 9 0.135324 -1.039434 1.277800 0.172173 0.163201 -0.200343 1.248177 0.202884 0.573360 0.633920 0.840384 0.799767 1.112054 1.142827 1.091265 0.874473 12.670000 12.725147 1.008920 14.493392 14.586554 1.704413 14.817540 14.844636 0.495724 28.718687 28.818218 1.820939 20.287989 20.332985 0.823215 43.559574 43.604315 0.818538 46.572372 46.618914 0.851494 53.369157 53.382460 0.243388 20.287989 20.302408 0.263806 25.565646 25.584224 0.339877 43.559574 43.597275 0.689749 46.572372 46.578534 0.112725 28.718687 28.740994 0.408115 37.176844 37.176878 0.000624 50.883908 50.907104 0.424375 53.403820 53.407317 0.063968 12.670000 12.780183 1.007905 14.493392 14.617415 1.134513 28.718687 28.716171 -0.023015 31.116147 31.102976 -0.120485 20.287989 20.344679 0.518575 43.559574 43.615497 0.511558 46.572372 46.638776 0.607432 56.276816 56.044802 -2.122376 20.287989 20.350218 0.569248 25.565646 25.602839 0.340220 43.559574 43.668492 0.996336 46.572372 46.611280 0.355913 14.817540 14.934129 1.066512 28.718687 28.745561 0.245831 35.409539 35.424350 0.135488 40.294842 40.278723 -0.147450 12.670000 14.493392 31.116147 35.998111 62.859050 65.922301 86.455279 93.962698 59.517626 87.177907 103.097364 109.401469 25.565646 56.136183 78.537888 76.900413 14.817540 35.409539 40.294842 43.476252 53.369157 64.275434 84.788739 86.860804 37.176844 74.294921 88.906972 90.992235 56.276816 78.471890 83.872838 74.211168 20.287989 43.559574 46.572372 61.962104 28.718687 50.883908 53.403820 57.215832 2 10 212.836659 -0.8762589199 10.70332757 0.01800590693 1 0.3970642585 -0.1178895788 -0.1773631553 14.92429551 0.06290829772 1.108947459 0.0307695015 0.9761637746 2 3 4 5 6 7 8 9 0.208321 -0.995056 1.218736 0.178404 0.147534 -0.177300 2.326370 0.823857 0.641320 0.982789 0.996747 1.094267 1.323825 1.369287 1.187450 1.354426 12.436239 12.508152 2.565534 12.670000 12.689842 0.707895 18.121234 18.176460 1.970214 33.994519 33.966079 -1.014616 32.875637 32.923971 1.724383 62.839230 62.889148 1.780844 64.528535 64.567717 1.397852 73.381246 73.388213 0.248563 32.875637 32.895611 0.712617 44.059636 44.077766 0.646794 62.839230 62.871011 1.133827 64.528535 64.541309 0.455743 34.336702 34.366118 1.049446 42.030483 42.013978 -0.588818 64.059492 64.048188 -0.403272 65.546762 65.597198 1.799330 12.670000 12.761363 1.629713 18.121234 18.231679 1.970093 33.994519 33.955623 -0.693824 34.336702 34.236747 -1.782972 32.875637 32.939388 1.137198 62.839230 62.891016 0.923755 64.528535 64.589984 1.096119 83.119764 83.264222 2.576813 32.875637 32.948591 1.301344 44.059636 44.095922 0.647270 62.839230 62.950790 1.989989 64.528535 64.570760 0.753205 12.436239 12.528399 1.643933 34.004458 34.045618 0.734205 34.336702 34.239819 -1.728175 48.656808 48.681549 0.441338 12.670000 18.121234 33.994519 43.953140 84.609425 89.041382 110.597688 133.477215 76.811462 102.635382 116.657910 124.336651 44.059636 77.596107 105.438315 110.683816 12.436239 34.004458 48.656808 57.749836 73.381246 85.405238 112.610940 115.755757 42.030483 100.844841 108.571662 109.362570 83.718186 104.233012 99.448716 112.308313 32.875637 62.839230 64.528535 83.119764 34.336702 64.059492 65.546762 73.566931