********* 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 35 258644.42 -0.25 50 0.03249196962 1 0.9792323218 0.2163294909 0.03241982843 836.6022566 0 147.1787311 -2.014550788 -3.540647016 2 3 4 5 7 8 9 0.000343 -5.688387 9.299459 0.021428 -0.207032 0.290402 -4.821609 -4.523208 0.166594 0.026510 -0.137495 -0.046350 0.708622 0.042686 -253.545869 -252.936126 0.167479 -139.676790 -139.486261 0.052333 -132.108186 -131.705703 0.110551 -88.030926 -85.755729 0.624931 7.655981 7.963940 0.084587 56.319668 72.447638 4.429890 72.388494 74.598850 0.607121 127.529191 117.241952 -2.825609 -44.897721 -39.955083 1.357601 7.655981 3.768826 -1.067690 10.632499 66.590831 15.370147 56.319668 72.320370 4.394933 -33.562370 -29.006732 1.251303 10.722804 6.378058 -1.193377 30.912226 31.431420 0.142608 69.094698 71.525618 0.667704 -253.545869 -252.327486 0.167327 -132.108186 -131.078610 0.141397 -88.030926 -104.688345 -2.287657 -33.562370 -25.161290 1.153768 7.655981 8.501108 0.116066 56.319668 62.772173 0.886159 72.388494 72.668283 0.038425 103.073313 97.026109 -0.830497 -44.897721 -36.814870 1.110064 7.655981 1.452599 -0.851946 10.632499 67.353862 7.789865 56.319668 72.097130 2.166808 -139.676790 -139.250657 0.058523 10.722804 9.031103 -0.232331 30.912226 31.416447 0.069248 53.320775 51.851528 -0.201780 -253.545869 -132.108186 -88.030926 103.335456 127.529191 297.702125 300.509161 469.986156 81.581596 344.075232 515.660631 394.796171 -44.897721 92.705191 10.632499 341.486411 -139.676790 66.802649 53.320775 152.745772 135.321849 187.448093 284.488388 320.885945 -33.562370 192.881138 161.832407 267.878926 103.073313 175.422553 388.953214 266.989347 7.655981 72.388494 56.319668 265.110320 10.722804 30.912226 69.094698 138.799448 2 43 639102.0295 -0.25 50 0.03249196962 1 0.9450718129 0.3854668806 -0.1994517737 9098.18974 0.05 -3266.898175 -2.052538738 -2.960971052 2 3 4 5 7 8 9 0.017896 -5.200178 8.604989 0.022542 -0.175998 0.252973 -4.442330 -3.981383 0.218877 0.014103 0.026764 0.035700 0.713151 0.063981 -200.428704 -199.733585 9.952130 -63.935268 -64.384761 -6.435461 -57.699277 -57.512982 2.667210 -7.723045 12.053904 283.149676 18.512674 18.789208 3.959179 83.599977 83.741130 2.020921 93.369978 93.042335 -4.690915 163.004633 163.537163 7.624311 -44.185649 -38.833149 76.632584 18.512674 14.210964 -61.588263 46.455377 83.408875 529.069019 83.599977 100.521946 242.274485 -2.028763 -1.682803 4.953158 29.537589 29.647388 1.572013 81.267335 81.559588 4.184230 81.470258 120.279726 555.641222 -200.428704 -199.039854 9.942188 -63.935268 -66.253695 -16.596641 -2.028763 -1.338366 4.942262 17.721493 4.242316 -96.491744 18.512674 19.310309 5.709931 83.599977 83.752990 1.095361 93.369978 98.618376 37.571066 118.839546 114.541385 -30.768718 -44.185649 -35.506209 62.132453 18.512674 11.688422 -48.851946 46.455377 83.351538 264.124059 83.599977 92.571584 64.223956 -57.699277 -56.970303 5.218416 -7.723045 -4.869707 20.425845 29.537589 41.751607 87.435006 81.267335 81.376174 0.779131 -200.428704 -63.935268 17.721493 52.167461 170.091039 291.270158 332.864665 458.872851 81.470258 409.321721 554.590746 395.824813 -44.185649 129.672488 46.455377 377.274450 -57.699277 129.460229 -7.723045 143.113741 163.004633 222.250059 293.287386 342.528472 -2.028763 248.554402 188.396365 402.306364 118.839546 202.679247 417.250830 274.309320 18.512674 83.599977 93.369978 285.963250 29.537589 81.267335 83.296514 188.846187 2 58 26.67174177 -1.014183589 9.087325189 0.03249196962 1 0.6353193 -0.07273094693 -0.09943648645 426.8689968 0.1 171.1895069 -0.847203447 -0.7808082172 2 3 4 5 7 8 9 0.242290 -0.922614 0.632380 0.118097 0.204295 -0.201112 1.735744 1.094754 0.640215 0.704360 0.912171 0.910033 1.225023 0.919565 12.670000 12.710258 1.418217 24.670385 24.689852 0.685780 26.112103 26.119880 0.273981 32.080944 32.022424 -2.061550 27.588495 27.606492 0.634013 54.279685 54.309887 1.063970 62.854068 62.891421 1.315885 67.629335 67.612238 -0.602285 27.588495 27.623348 1.227825 36.938298 36.967256 1.020125 54.279685 54.274260 -0.191110 62.854068 62.879016 0.878881 32.619945 32.643573 0.832364 37.610383 37.596868 -0.476144 59.359559 59.380004 0.720250 61.701762 61.714192 0.437896 12.670000 12.750508 1.418077 26.112103 26.127566 0.272372 32.080944 32.042469 -0.677707 32.619945 32.633529 0.239256 27.588495 27.630787 0.744947 54.279685 54.307982 0.498441 62.854068 62.874730 0.363958 71.049805 71.101281 0.906707 27.588495 27.651900 1.116827 36.938298 36.996229 1.020401 54.279685 54.301012 0.375669 62.854068 62.956739 1.808466 24.670385 24.709428 0.687713 32.084708 32.028969 -0.981798 32.619945 32.674297 0.957350 45.283361 45.309268 0.456333 12.670000 26.112103 32.080944 40.343134 80.133971 79.321049 108.041211 102.808607 67.657825 97.635564 116.990627 110.592936 36.938298 67.205195 82.350654 110.013434 24.670385 32.084708 45.283361 54.853523 67.629335 79.138655 102.763530 106.866447 37.610383 87.410461 98.611636 102.195833 71.049805 97.660257 97.388315 89.233876 27.588495 54.279685 62.854068 78.609961 32.619945 59.359559 61.701762 72.435390 2 35 19.74429323 -1.054715405 9.297612264 0.03249196962 1 0.6902620969 -0.07745885053 -0.1051483609 112.5374959 0.15 44.50304912 -0.9240455367 -0.8392609812 2 3 4 5 7 8 9 0.221380 -0.945343 0.671489 0.112048 0.200511 -0.191694 1.553026 0.909631 0.618444 0.663183 0.876174 0.861763 1.218371 0.862730 12.670000 12.704227 1.127202 21.717546 21.743676 0.860517 21.776997 21.805646 0.943489 29.859096 29.863540 0.146354 27.121253 27.140381 0.629948 53.797207 53.831475 1.128560 60.967408 61.010669 1.424718 67.416552 67.395322 -0.699142 27.121253 27.156036 1.145516 37.242556 37.276062 1.103475 53.797207 53.795689 -0.049997 60.967408 61.001698 1.129261 31.462798 31.488706 0.853233 36.857524 36.843426 -0.464317 58.989111 59.009542 0.672826 59.761437 59.782878 0.706110 12.670000 12.738495 1.127875 21.776997 21.833014 0.922408 29.859096 29.860427 0.021927 31.462798 31.412276 -0.831911 27.121253 27.160616 0.648168 53.797207 53.828126 0.509120 60.967408 61.004482 0.610482 70.965173 71.005728 0.667790 27.121253 27.189737 1.127699 37.242556 37.309582 1.103687 53.797207 53.831699 0.567960 60.967408 61.082949 1.902541 21.717546 21.770808 0.877024 29.866687 29.883737 0.280757 31.462798 31.436559 -0.432067 44.572485 44.661265 1.461895 12.670000 21.776997 29.859096 39.896753 78.445193 78.793936 106.826422 101.465192 66.897602 98.006939 118.988661 110.564721 37.242556 66.791206 82.299273 113.956019 21.717546 29.866687 44.572485 52.686183 67.416552 77.437479 104.395847 105.983891 36.857524 89.824495 94.268737 107.873602 70.965173 97.803214 98.348528 86.828414 27.121253 53.797207 60.967408 78.446652 31.462798 59.761437 58.989111 70.445345 2 10 73.98391304 -1.404500586 6.640643266 0.03249196962 1 0.6774384651 -0.06819801631 -0.1011354581 50 0.2 12.5 -0.905222559 -0.8208443359 2 3 4 5 7 8 9 0.222105 -0.844493 0.577461 0.117157 0.204603 -0.205933 2.037851 1.004531 0.623203 0.530775 0.886070 0.795303 1.249629 0.676603 12.670000 12.693196 0.547389 15.977811 15.998167 0.480362 16.334871 16.350372 0.365822 22.138977 22.136086 -0.068227 19.938605 19.951841 0.312357 40.694564 40.722580 0.661162 44.669222 44.698843 0.699016 50.165708 50.150073 -0.368978 19.938605 19.958051 0.458913 29.228829 29.249617 0.490566 40.694564 40.703976 0.222128 44.669222 44.686610 0.410327 24.341171 24.357852 0.393656 27.809079 27.799608 -0.223507 43.892639 43.911636 0.448311 44.084611 44.095786 0.263726 12.670000 12.716405 0.547548 15.977811 16.017551 0.468906 22.138977 22.132349 -0.078210 24.341171 24.316227 -0.294316 19.938605 19.956835 0.215103 40.694564 40.723385 0.340080 44.669222 44.696840 0.325874 53.276958 53.292893 0.188028 19.938605 19.985775 0.556574 29.228829 29.270413 0.490660 40.694564 40.740428 0.541176 44.669222 44.732667 0.748610 16.334871 16.366784 0.376558 22.142792 22.144479 0.019902 24.341171 24.326792 -0.169655 32.092530 32.113603 0.248651 12.670000 15.977811 22.138977 28.684216 56.031192 58.366564 76.122812 75.489860 49.130730 73.072402 86.771849 81.544152 29.228829 49.537136 64.059791 84.582355 16.334871 22.142792 32.092530 38.833040 50.165708 55.893688 77.556646 76.146765 27.809079 68.806648 64.392736 85.338715 53.276958 72.831828 73.088435 62.994034 19.938605 40.694564 44.669222 56.892487 24.341171 44.084611 43.892639 52.272963 2 10 66.94720626 -1.488172241 7.094702299 0.03249196962 1 0.6986793502 -0.05936120705 -0.09713011646 50 0.25 12.5 -0.910760097 -0.800545535 2 3 4 5 7 8 9 0.209522 -0.850562 0.646426 0.119915 0.198868 -0.201356 2.115051 0.906415 0.615343 0.550914 0.880336 0.814049 1.257131 0.705752 12.670000 12.699563 0.703117 16.411305 16.426311 0.356896 17.662102 17.673625 0.274045 22.548980 22.542280 -0.159360 20.918958 20.933817 0.353395 43.079125 43.112566 0.795377 47.137357 47.170586 0.790309 53.400862 53.383407 -0.415141 20.918958 20.936863 0.425856 31.925749 31.948084 0.531211 43.079125 43.096592 0.415449 47.137357 47.149823 0.296484 26.014906 26.031821 0.402295 29.483311 29.474125 -0.218473 45.705297 45.713325 0.190946 47.141288 47.167306 0.618809 12.670000 12.729117 0.703012 17.662102 17.684871 0.270769 22.559981 22.549790 -0.121200 26.014906 26.020590 0.067584 20.918958 20.933068 0.167800 43.079125 43.117402 0.455197 47.137357 47.164019 0.317063 57.113036 57.122069 0.107426 20.918958 20.970425 0.612040 31.925749 31.970415 0.531171 43.079125 43.142507 0.753736 47.137357 47.196848 0.707461 16.411305 16.441564 0.359836 22.548980 22.543462 -0.065629 26.014906 26.004962 -0.118265 34.000811 34.024878 0.286197 12.670000 17.662102 22.559981 30.129524 58.232587 62.194963 79.668131 83.936683 51.888718 78.765406 91.909058 89.146065 31.925749 52.712040 70.269144 91.912945 16.411305 22.548980 34.000811 40.840121 53.400862 58.595342 81.054504 82.486975 29.483311 74.530454 69.855448 92.104991 57.113036 78.387293 78.702166 66.054320 20.918958 43.079125 47.137357 60.632862 26.014906 45.705297 47.141288 54.835499 2 10 51.78433079 -1.432803284 8.365511123 0.03249196962 1 0.7507291054 -0.03415708535 -0.08898820066 50 0.3 12.5 -0.9951044511 -0.8322693502 2 3 4 5 7 8 9 0.191536 -0.900987 0.747269 0.114900 0.195338 -0.194798 1.872717 0.724711 0.594064 0.583301 0.849642 0.815552 1.246605 0.752626 12.670000 12.708151 0.978061 18.503778 18.519483 0.402611 21.131709 21.129224 -0.063714 24.998836 24.998988 0.003908 23.420869 23.438170 0.443523 48.559448 48.601032 1.066069 53.889092 53.935782 1.196968 61.345594 61.320286 -0.648796 23.420869 23.441285 0.523393 36.393246 36.423111 0.765633 48.559448 48.582159 0.582230 53.889092 53.902904 0.354096 29.591000 29.610269 0.493984 33.480369 33.471124 -0.237017 51.826620 51.835436 0.225996 54.448881 54.483833 0.896047 12.670000 12.746276 0.977736 21.131709 21.126719 -0.063962 25.101303 25.097188 -0.052744 29.591000 29.677862 1.113430 23.420869 23.434182 0.170644 48.559448 48.609784 0.645223 53.889092 53.920189 0.398610 65.413002 65.423927 0.140043 23.420869 23.483059 0.797177 36.393246 36.452941 0.765194 48.559448 48.637542 1.001037 53.889092 53.968589 1.019025 18.503778 18.535450 0.405986 24.998836 24.993702 -0.065799 29.591000 29.583628 -0.094505 39.364935 39.389424 0.313912 12.670000 21.131709 25.101303 34.119607 66.235952 73.210076 90.409998 103.279704 59.467893 92.581949 102.065883 112.557122 36.393246 60.363683 81.999706 108.773382 18.503778 24.998836 39.364935 50.712068 61.345594 67.229057 93.608015 95.865722 33.480369 86.701753 80.923352 109.616798 65.413002 89.391782 93.973253 75.673366 23.420869 48.559448 53.889092 70.490883 29.591000 51.826620 54.448881 62.353617 1 43 46.09104405 -7.134707607 10.83438056 0.03249196962 1 0.8728073833 0.03470054971 -0.08521591704 157.1490375 0.35 -23.50615347 -1.212305233 -0.9640211644 2 3 4 5 7 8 9 0.151940 -0.285114 -1.971701 0.096848 0.200859 -0.198099 1.207319 0.683946 0.544376 0.577884 0.766892 0.756307 1.209443 0.746115 12.670000 12.721774 1.363676 26.503082 26.516439 0.351811 28.308557 28.277301 -0.823238 34.736103 34.715396 -0.545406 26.640877 26.659785 0.498015 58.229383 58.283023 1.412827 68.401072 68.460110 1.555006 77.633958 77.602878 -0.818620 26.640877 26.677588 0.966938 44.484370 44.523778 1.037959 58.229383 58.259043 0.781218 68.401072 68.427382 0.692989 38.424554 38.447893 0.614721 43.433391 43.420647 -0.335637 66.419582 66.438357 0.494507 70.628534 70.639741 0.295196 12.670000 12.773500 1.363034 28.308557 28.246308 -0.819784 35.038532 35.049989 0.150884 38.424554 38.611868 2.466823 26.640877 26.662119 0.279750 58.229383 58.301194 0.945709 68.401072 68.439016 0.499703 80.993723 81.041046 0.623220 26.640877 26.730949 1.186194 44.484370 44.563177 1.037850 58.229383 58.323853 1.244117 68.401072 68.517409 1.532094 26.503082 26.530861 0.365836 34.736103 34.679357 -0.747318 38.424554 38.531000 1.401837 50.519641 50.472783 -0.617095 12.670000 28.308557 35.038532 44.331403 85.346432 98.874045 114.249825 159.486962 76.734497 148.004041 151.266245 181.454699 44.484370 77.632224 117.868975 162.620568 26.503082 34.736103 50.519641 78.769989 77.633958 87.995142 121.897421 122.723381 43.433391 109.251069 130.060413 159.166173 80.993723 133.624731 130.415506 115.225362 26.640877 58.229383 68.401072 91.385974 38.424554 66.419582 70.628534 88.960531 2 44 95.63874667 -8.012348582 12.10182396 0.03249196962 1 0.8656173264 0.01629681356 -0.04247606813 69.48454314 0.4 2.805136154 -1.327285761 -1.019070534 2 3 4 5 7 8 9 0.154150 -0.277107 -1.893939 0.085829 0.211993 -0.212615 1.483140 0.719348 0.535409 0.586808 0.746895 0.732689 1.226228 0.757082 12.670000 12.730316 1.800317 28.403867 28.406199 0.069599 33.380578 33.272174 -3.235641 33.975905 33.957307 -0.555117 30.106741 30.126353 0.585377 65.256688 65.318893 1.856668 76.650124 76.735052 2.534928 85.713482 85.666470 -1.403225 30.106741 30.139245 0.970187 51.986118 52.028761 1.272813 65.256688 65.295758 1.166143 76.650124 76.675307 0.751668 42.603743 42.621233 0.522016 46.818317 46.810650 -0.228862 71.275457 71.290394 0.445839 79.740649 79.734967 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