********* 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 17 2543655096 -0.25 50 0.03249196962 1 0.6788306436 -0.01783379481 -0.6 14715.18682 0.197074726 6788.913874 -1.503379341 -386179.9757 2 3 5 6 7 8 9 -0.083575 -6.610698 8.333209 0.058884 -0.209739 0.381053 -2.305974 -6.237650 -56505.114816 -207.747771 -181178.794882 -189.903356 0.935053 -417.877125 -376.997664 -375.584941 -94.455136 -368.495507 -368.120042 -25.103746 -154.756729 -134.935653 -1325.243879 -135.510726 -128.394630 -475.784620 -5.327244 -3.723097 -107.253852 47.081826 47.073839 0.534011 89.220694 89.633555 -27.604037 93.464481 126.115497 -2183.058068 -5.327244 -5.337816 0.706844 47.081826 46.868358 14.272529 61.864978 65.384603 -235.323338 64.830153 80.519934 -1049.024148 -34.416118 -33.971915 -29.699576 7.762242 7.745197 1.139589 24.227707 24.626343 -26.652917 26.725534 35.936110 -615.822220 -368.495507 -366.725750 -59.163274 -135.510726 -134.359944 -38.470837 -104.621509 -94.337216 -343.805669 -101.457463 -90.346371 -371.445711 -5.327244 -3.820014 -50.386977 47.081826 47.236152 -5.159136 61.864978 83.701184 -729.988057 89.220694 89.773307 -18.473958 -5.327244 -3.649627 -56.083049 47.081826 46.493743 19.659709 64.830153 65.935590 -36.954954 89.220694 90.474222 -41.905655 -376.997664 -375.191358 -60.385122 -154.756729 -128.540580 -876.410316 -61.003265 -59.990351 -33.861872 -35.172609 -59.214778 803.733810 -368.495507 -135.510726 -104.621509 -101.457463 157.072225 93.464481 213.061927 427.430074 26.725534 402.917564 384.692934 510.523593 64.830153 197.429465 131.485093 474.857137 -376.997664 -154.756729 -61.003265 -35.172609 126.146651 146.849410 252.026251 294.540745 62.354200 307.385744 273.670209 251.805159 61.864978 395.346154 359.184299 216.060908 -5.327244 47.081826 89.220694 125.693156 -34.416118 7.762242 24.227707 36.851542 2 58 64045.41012 -0.25 50 0.03249196962 1 0.6869968383 0.04439801905 -0.5 6009.18072 0.1992468771 568.4397051 -1.675593949 36192.87525 2 3 5 6 7 8 9 0.007321 -2.727483 3.820413 0.028200 -0.010088 0.108446 -0.503131 -2.191360 1.703454 0.138982 1.796448 0.179975 1.006214 0.178455 -123.630187 -122.858696 4.518756 -113.290834 -112.759195 3.113902 -37.833223 -37.240817 3.469822 73.139165 76.298284 18.503501 91.007618 91.652060 3.774607 158.869602 159.289543 2.459672 190.986497 191.293974 1.800945 240.174652 240.249966 0.441125 91.007618 91.051770 0.258608 124.450809 124.760648 1.814780 158.869602 158.982674 0.662285 190.986497 179.764503 -65.729144 76.810826 77.170769 2.108249 143.136221 145.203023 12.105614 153.134711 153.227560 0.543835 173.431776 191.065315 103.282667 -113.290834 -112.020343 3.720743 -37.833223 -36.646864 3.474352 76.810826 76.153092 -1.926231 123.757363 125.043514 3.766601 91.007618 91.657284 1.902602 158.869602 159.357921 1.430085 190.986497 191.479062 1.442521 195.414644 226.255020 90.318687 91.007618 91.736603 2.134896 124.450809 125.072563 1.820859 158.869602 159.444806 1.684535 190.986497 191.728994 2.174467 -123.630187 -122.295832 3.907773 73.139165 71.459600 -4.918752 75.583339 77.171443 4.650899 76.810826 78.068780 3.684027 -113.290834 -37.833223 131.140901 123.757363 284.420150 296.927806 370.836220 409.440607 173.431776 485.502638 462.338280 591.969156 124.450809 290.762128 235.864990 556.278395 -123.630187 75.583339 73.139165 163.997211 240.174652 282.960515 427.164202 464.501502 153.134711 423.490693 384.380134 321.577458 195.414644 450.198077 473.256367 342.447852 91.007618 158.869602 190.986497 306.844341 76.810826 191.142385 213.093850 143.136221 2 76 18791.22895 -0.3336592304 50 0.03249196962 1 0.9007762383 0.09625951691 -0.4 863.3724834 0.3454475005 -30.53422498 -1.869670015 -4.075864523 2 3 5 6 7 8 9 0.001263 -1.991045 2.717788 0.020065 0.040925 0.015901 -0.835202 -1.641216 0.194309 0.090393 -0.230340 0.138825 1.011182 0.097679 -65.242389 -64.742100 0.505585 -63.318888 -62.853514 0.470300 -25.735850 -25.227281 0.513953 64.862226 119.508768 55.225053 82.547689 82.955764 0.412396 155.824893 156.202990 0.382099 185.735122 186.117033 0.385954 243.947364 243.932032 -0.015494 82.547689 82.589216 0.041967 112.886184 113.358467 0.477282 155.824893 155.973542 0.150223 185.735122 185.940816 0.207872 77.627076 77.970895 0.347459 136.124527 136.283005 0.160156 144.304173 151.404719 7.175715 172.131682 202.678601 30.870301 -65.242389 -64.229871 0.511618 -25.735850 -24.721017 0.512788 77.627076 76.712715 -0.462021 121.192379 121.261282 0.034816 82.547689 82.938213 0.197329 155.824893 156.348093 0.264369 185.735122 186.127136 0.198082 221.592813 228.128868 3.302624 82.547689 83.058531 0.258125 112.886184 113.826980 0.475378 155.824893 156.357814 0.269281 185.735122 186.504697 0.388861 -63.318888 -62.397830 0.465404 64.862226 38.079714 -13.533021 77.627076 106.700075 14.690389 144.304173 189.821604 22.999649 -65.242389 -25.735850 130.518200 121.192379 275.468306 288.481362 414.733561 457.445186 172.131682 499.402929 505.850499 689.597378 112.886184 269.319304 281.812828 556.420192 -63.318888 64.862226 195.820156 200.018916 243.947364 278.796726 447.152564 442.784594 136.124527 416.956590 325.541392 442.203750 221.592813 427.853702 457.477187 305.926070 82.547689 155.824893 185.735122 285.248393 77.627076 202.816626 208.908200 144.304173 2 17 15761.33989 -0.536884101 31.00768301 0.03249196962 1 0.7038940398 -0.06183261889 -0.3 483.6382303 0.1559715476 208.652727 -1.189571866 -1.818365253 2 3 5 6 7 8 9 0.113249 -1.357418 1.399803 0.077933 0.153009 -0.094185 0.407444 -0.276447 0.499690 0.961692 0.569794 1.026128 1.153186 1.296701 -1.682125 -1.399147 15.899283 4.250173 4.440882 10.715121 12.670000 12.911323 13.558883 78.175510 77.937881 -13.351355 76.487512 76.673867 10.470494 146.089977 146.275062 10.399107 153.704504 153.879411 9.827298 187.342265 187.380071 2.124173 76.487512 76.584667 5.458742 101.929608 102.087727 8.883989 146.089977 146.234551 8.122962 153.704504 153.760602 3.151910 78.175510 78.348713 9.731515 112.493385 112.464560 -1.619585 161.049343 161.222408 9.723773 168.700470 169.074306 21.004209 -1.682125 -1.192722 13.748716 12.670000 13.158188 13.714591 78.175510 77.884004 -8.189232 91.883934 91.630111 -7.130616 76.487512 76.751382 7.412856 146.089977 146.342061 7.081746 153.704504 153.908745 5.737723 203.310037 204.205015 25.142458 76.487512 76.791382 8.536583 101.929608 102.246005 8.888498 146.089977 146.496640 11.424312 153.704504 153.960844 7.201320 4.250173 4.701842 12.688664 78.175510 78.343278 4.713096 93.863884 93.447042 -11.710280 102.972931 102.869212 -2.913783 12.670000 -1.682125 91.883934 120.623209 223.250768 225.382251 300.549409 328.534426 192.252444 302.897846 350.269872 367.150349 101.929608 205.210860 221.261367 365.533601 4.250173 93.863884 129.666678 102.972931 187.342265 220.431407 316.387131 317.289477 112.493385 269.896750 321.887374 276.802008 203.310037 290.656227 312.077778 242.491330 76.487512 146.089977 153.704504 230.716192 78.175510 169.067210 161.049343 168.700470 2 17 51.97587425 -0.9552517205 10.03742785 0.03249196962 1 0.67306899 -0.02622254608 -0.2 5095.34973 0.136126344 2044.437017 -0.9189310045 -1.001203701 2 3 5 6 7 8 9 0.194113 -0.981239 0.717858 0.112215 0.197326 -0.185865 1.324736 0.661401 0.604183 0.667655 0.832594 0.864513 1.213905 0.869410 12.670000 12.731404 1.914247 21.674716 21.713053 1.195129 22.051833 22.098288 1.448223 35.220490 35.161562 -1.837035 28.465552 28.497956 1.010190 57.428759 57.467058 1.193951 63.665561 63.719290 1.674975 71.889621 71.886397 -0.100507 28.465552 28.502021 1.136919 38.966673 39.004899 1.191683 57.428759 57.450938 0.691434 63.665561 63.688386 0.711560 35.220490 35.259269 1.208907 42.957718 42.942598 -0.471377 64.606909 64.617967 0.344723 65.477321 65.516791 1.230439 12.670000 12.792839 1.914722 22.051833 22.137976 1.342724 35.220490 35.141455 -1.231924 38.063624 38.007954 -0.867736 28.465552 28.522058 0.880779 57.428759 57.481745 0.825909 63.665561 63.716453 0.793259 77.730579 77.757934 0.426389 28.465552 28.546854 1.267274 38.966673 39.043154 1.192131 57.428759 57.496539 1.056503 63.665561 63.767132 1.583203 21.674716 21.758157 1.300613 35.220490 35.260590 0.625051 38.721228 38.617919 -1.610311 48.610619 48.664364 0.837724 12.670000 22.051833 38.063624 43.008570 84.541450 84.419293 115.260573 107.928462 75.992268 106.841070 118.516721 140.877407 38.966673 73.942045 87.437662 122.998386 21.674716 38.721228 48.610619 56.434959 71.889621 83.536988 111.778879 114.527135 42.957718 98.162855 112.610671 108.701750 77.730579 104.771957 107.507914 96.992679 28.465552 57.428759 63.665561 85.568160 35.220490 65.477321 64.606909 76.736170 2 19 21.1105122 -1.041440602 9.403521437 0.03249196962 1 0.6850866073 -0.07205935741 -0.1 1361.38261 0.1392130213 561.5881828 -0.916796375 -0.826031015 2 3 5 6 7 8 9 0.226441 -0.950074 0.671417 0.112687 0.201123 -0.193056 1.553599 0.945377 0.621898 0.678230 0.882599 0.874490 1.217059 0.883726 12.670000 12.705452 1.207826 23.242929 23.265159 0.757386 23.580436 23.604775 0.829217 30.856189 30.859149 0.100867 27.533290 27.551851 0.632365 54.599262 54.632847 1.144219 62.473936 62.516813 1.460812 68.562897 68.540740 -0.754871 27.533290 27.569433 1.231361 37.525075 37.558733 1.146688 54.599262 54.594345 -0.167496 62.473936 62.509084 1.197473 32.221632 32.246970 0.863265 37.550231 37.536354 -0.472798 60.581088 60.601056 0.680300 60.632253 60.653127 0.711168 12.670000 12.740926 1.208201 23.580436 23.628427 0.817508 30.856189 30.857505 0.022427 32.221632 32.177305 -0.755101 27.533290 27.573978 0.693102 54.599262 54.628338 0.495308 62.473936 62.507636 0.574079 71.825806 71.872283 0.791726 27.533290 27.602025 1.170880 37.525075 37.592403 1.146908 54.599262 54.627489 0.480847 62.473936 62.593866 2.042983 23.242929 23.288028 0.768246 30.863131 30.879848 0.284757 32.221632 32.198766 -0.389518 46.400875 46.416236 0.261675 12.670000 23.580436 30.856189 40.684030 80.204376 80.116028 109.046290 103.157003 68.062019 99.547264 119.524655 114.008867 37.525075 67.804247 83.251219 114.869073 23.242929 30.863131 46.400875 54.200031 68.562897 79.101987 105.507808 108.015318 37.550231 90.627523 96.553946 108.219195 71.825806 99.398669 99.436794 89.036270 27.533290 54.599262 62.473936 80.007565 32.221632 60.581088 60.632253 72.311325 2 10 70.54110189 -1.259433994 8.381912778 0.03249196962 1 0.70330315 -0.05619295729 0 192.1731667 0.1478324792 73.44399575 -0.9370236797 -0.825061301 2 3 5 6 7 8 9 0.256075 -0.939990 0.631916 0.114192 0.203801 -0.202168 1.682862 1.187601 0.619304 0.657764 0.880627 0.865421 1.216224 0.855074 12.670000 12.680747 0.369078 25.104688 25.112626 0.272624 25.555467 25.559963 0.154390 27.663255 27.669098 0.200689 24.639413 24.645509 0.209341 49.379834 49.407768 0.959320 59.087221 59.133115 1.576114 63.008850 62.955013 -1.848879 24.639413 24.673508 1.170886 33.496172 33.525135 0.994673 49.379834 49.346102 -1.158443 59.087221 59.192817 3.626440 29.531327 29.533331 0.068813 32.477249 32.477668 0.014386 54.038562 54.030793 -0.266811 56.496297 56.539681 1.489928 12.670000 12.691491 0.369021 25.555467 25.564236 0.150568 27.729757 27.766427 0.629655 29.531327 29.509808 -0.369501 24.639413 24.664754 0.435139 49.379834 49.383187 0.057577 59.087221 59.086293 -0.015924 63.115791 63.201273 1.467819 24.639413 24.694429 0.944691 33.496172 33.554100 0.994691 49.379834 49.365041 -0.254023 59.087221 59.339703 4.335428 25.104688 25.120769 0.276133 27.663255 27.675784 0.215149 29.531327 29.534609 0.056366 40.874662 40.906558 0.547698 12.670000 25.555467 27.729757 36.243006 73.489488 73.008354 99.964987 96.711507 59.469501 91.288983 103.335969 108.785379 33.496172 59.766075 75.983402 102.372992 25.104688 27.663255 40.874662 51.191972 63.008850 72.314607 94.626352 98.205216 32.477249 82.280437 77.896642 103.147494 63.115791 86.520548 92.994669 81.515439 24.639413 49.379834 59.087221 71.980309 29.531327 54.038562 56.496297 66.233526 2 10 335.3202646 -1.579954012 7.555715392 0.03249196962 1 0.70330315 -0.05619295729 0.1 192.1731667 0.1478324792 73.44399575 -0.9370236797 -0.825061301 2 3 5 6 7 8 9 0.283030 -0.898234 0.541115 0.116689 0.204864 -0.208162 1.902881 1.433649 0.618434 0.640918 0.880255 0.862019 1.221217 0.831589 12.670000 12.659602 -0.355775 21.396485 21.408519 0.411732 21.760063 21.767700 0.261317 26.611871 26.655944 1.507978 22.514750 22.512409 -0.080112 45.168871 45.192326 0.802515 55.541003 55.635013 3.216660 57.791664 57.664428 -4.353477 22.514750 22.544827 1.029116 30.421752 30.445141 0.800259 45.168871 45.111223 -1.972514 53.049182 53.636977 20.111985 26.611871 26.563344 -1.660417 27.818515 27.863802 1.549553 48.500618 48.462140 -1.316541 51.959005 52.029948 2.427369 12.670000 12.649146 -0.356769 21.760063 21.775364 0.261770 26.611871 26.595380 -0.282138 27.818515 27.599930 -3.739546 22.514750 22.527954 0.225895 45.168871 45.150588 -0.312797 55.541003 55.578637 0.643840 56.339141 56.387404 0.825668 22.514750 22.556978 0.722439 30.421752 30.468525 0.800179 45.168871 45.119041 -0.852497 53.049182 53.192625 2.454013 21.396485 21.420514 0.411087 26.611871 26.617011 0.087933 27.748763 27.740041 -0.149217 36.756695 36.789235 0.556696 12.670000 21.760063 27.843855 32.812275 67.279431 66.853221 91.483630 87.851496 51.959005 84.146429 92.150474 97.780963 30.421752 53.049182 70.210837 92.173616 21.396485 27.748763 36.756695 47.850819 57.791664 66.288119 85.714412 89.774286 27.818515 74.236246 70.569385 92.068205 56.339141 75.409275 88.052011 74.097099 22.514750 45.168871 55.541003 64.429665 26.611871 48.500618 52.099222 59.278865 2 18 171.4551039 -7.234043407 6.792807271 0.03249196962 1 0.7536618752 -0.03619238865 0.2 3469.57297 0.3436203099 1413.139047 0.1132486131 0.4460384399 2 3 5 6 7 8 9 0.260090 -0.179198 -1.891988 0.192321 0.106429 -0.138097 2.458503 1.665024 0.696353 0.766932 1.201894 1.153067 1.253326 1.020464 12.670000 12.669480 -0.014702 16.066383 16.068933 0.072086 17.246592 17.260301 0.387535 25.095891 25.149882 1.526188 19.667378 19.658704 -0.245216 42.242121 42.266070 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