********* 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 34 1571948.027 -0.25 50 0.03249196962 1 0.7467091596 0.08676771798 0.01685290609 1102.326442 -0.3 398.1719906 -1.804954688 -3.686693648 2 3 4 5 7 8 9 -0.000929 -10.526175 13.469554 0.020329 -0.380391 0.470609 -9.874516 -8.849914 0.132377 -1.131892 -0.191170 -0.182165 0.555654 -4.645366 -576.367388 -575.569436 -0.593085 -359.774502 -358.064965 -1.270628 -345.292564 -347.841384 1.894432 -235.222457 -208.508647 -19.855269 -147.100152 -146.344909 -0.561341 -94.142768 -78.877016 -11.346401 -47.808305 -63.406307 11.593350 -44.401650 -21.748696 -16.837003 -217.845728 -230.849617 9.665252 -147.100152 -132.852016 -10.590049 -141.695646 -116.830377 -18.481325 -137.332316 -112.629562 -18.360534 -228.355338 -224.734661 -2.691100 -182.797620 -182.118122 -0.505043 -150.358539 -144.624681 -4.261740 -141.658437 -121.707374 -14.828799 -576.367388 -574.771734 -0.592992 -345.292564 -338.927941 -2.365280 -235.222457 -218.777219 -6.111532 -228.355338 -218.611723 -3.621013 -147.100152 -145.501398 -0.594144 -94.142768 -94.594338 0.167817 -89.441759 -90.128658 0.255272 -44.401650 -20.973443 -8.706608 -217.845728 -229.157951 4.203954 -147.100152 -137.343562 -3.625835 -141.695646 -133.388583 -3.087148 -137.332316 -67.600333 -25.914448 -359.774502 -356.522262 -1.208628 -182.797620 -159.804988 -8.544736 -170.354568 -157.929164 -4.617644 -150.358539 -80.589162 -25.928345 -576.367388 -345.292564 -206.429585 -235.222457 -44.401650 89.031422 204.404304 295.922182 -112.895998 218.481634 179.180354 281.347267 -217.845728 -137.332316 -141.695646 192.891540 -359.774502 -170.354568 25.271242 17.388204 -47.808305 63.372273 -6.252296 224.630082 -228.355338 -51.063326 121.768132 65.196552 -89.441759 60.583669 206.385368 95.330275 -147.100152 -21.655523 -94.142768 37.431524 -141.658437 -182.797620 -52.885947 -150.358539 2 51 1233902.744 -0.25 50 0.03249196962 1 0.7478028041 0.4675399524 -0.2303013408 31470.56476 -0.2 7637.455967 -2.13153852 -3.743412373 2 3 4 5 7 8 9 0.012000 -6.700141 10.037363 -0.021442 -0.149246 0.177723 -5.910120 -5.349474 0.107235 -0.237172 -0.375114 -0.274012 0.692977 -0.292388 -316.458788 -315.567387 8.557198 -103.027616 -101.254813 17.018409 -81.699770 -83.617978 -18.414247 -56.163942 12.996141 663.917038 -9.841302 -9.351416 4.702759 52.047725 52.150327 0.984948 54.073967 75.793925 208.505394 105.434843 83.714727 -208.506910 -93.514483 -89.858417 35.097194 -9.841302 -12.315588 -23.752442 1.809285 24.471056 217.546526 52.047725 47.297261 -45.603102 -63.839448 -46.592150 165.569133 8.674047 -8.008525 -160.147933 30.109963 29.762213 -3.338299 30.115138 30.758018 6.171458 -316.458788 -314.676905 8.552784 -81.699770 -83.058719 -6.522760 -63.839448 -39.927016 114.776258 -56.163942 -38.698825 83.830063 -9.841302 -8.585815 6.026155 52.047725 52.191284 0.689060 54.073967 52.342522 -8.310688 58.365923 60.341693 9.483418 -93.514483 -87.509863 28.821321 -9.841302 -13.759500 -18.806791 1.809285 41.038893 188.296517 52.047725 51.804606 -1.166939 -103.027616 -101.792669 5.927568 -46.698205 -16.238150 146.203912 8.674047 6.396592 -10.931460 30.109963 51.736657 103.805041 -316.458788 -81.699770 -56.163942 -13.711798 115.897685 271.506359 271.382537 390.965696 38.121345 376.597983 525.738596 295.551837 -93.514483 1.809285 64.146116 335.788651 -103.027616 110.417286 -46.698205 120.362902 105.434843 253.259135 161.954852 308.842309 -63.839448 182.464313 221.218874 262.335018 58.365923 265.989746 293.771785 267.264933 -9.841302 52.047725 54.073967 228.809494 8.674047 30.109963 30.115138 112.134367 2 9 104933770.5 -0.25 50 0.03249196962 1 0.70330315 -0.05619295729 -0.0968878772 192.1731667 -0.1 73.44399575 -0.9370236797 -0.825061301 2 3 4 5 7 8 9 0.164909 -5.691720 7.873694 0.114827 -0.100534 0.318558 -3.956929 -3.388233 0.539284 2.250013 0.781505 2.299538 0.821956 3.207822 -273.689113 -273.058863 83.147241 -33.581617 -29.009642 603.169221 -29.762202 -25.210476 600.497801 -22.061486 -21.014491 138.127490 47.164438 47.562660 52.536462 120.257919 120.349226 12.045822 155.964279 150.503764 -720.392004 181.741590 187.144102 712.739871 -1.810767 13.323480 1996.623328 47.164438 33.046967 -1862.482549 81.734634 120.132539 5065.739482 120.257919 146.717146 3490.699523 20.190327 20.331758 18.658705 25.070944 25.359617 38.083931 77.527453 77.911329 50.643720 114.489139 124.133886 1272.407407 -273.689113 -272.428956 83.124632 -29.762202 -22.789257 459.961588 3.606044 -10.692612 -943.192950 20.190327 25.671012 361.526509 47.164438 48.261619 72.374205 120.257919 120.352181 6.217869 154.534269 144.922584 -634.022791 155.964279 166.029057 663.910528 -1.810767 14.972696 1107.100183 47.164438 32.112923 -992.854347 81.734634 120.097896 2530.584580 120.257919 149.088093 1901.746341 -33.581617 -25.368710 541.754122 -22.061486 -20.175309 124.419313 20.190327 10.819057 -618.164093 77.527453 78.086475 36.875148 -273.689113 -29.762202 3.606044 72.369688 214.421273 352.766204 368.927440 482.733438 137.486893 349.831304 323.186520 484.172907 -1.810767 134.404707 81.734634 398.254944 -22.061486 -33.581617 154.105790 171.645650 181.741590 283.144179 362.554998 362.068308 25.070944 114.489139 356.698030 327.251037 154.534269 283.950069 350.602108 319.123585 47.164438 120.257919 155.964279 287.182842 20.190327 77.527453 166.583064 146.741938 2 17 840431.0563 -0.25 50 0.03249196962 1 0.6276610716 -0.01910298027 -0.4118692394 31512.70305 0 -11329.75424 -1.552422868 -3.154264953 2 3 4 5 7 8 9 0.086868 -3.448727 4.060407 0.021377 -0.000448 0.115244 -2.657959 -2.246231 0.361279 0.323237 0.164987 0.335590 0.914346 0.450592 -186.270909 -185.515081 52.525892 -82.713349 -82.218616 34.381201 -16.677279 -16.442738 16.299294 39.643247 39.191381 -31.402262 83.938395 84.410113 32.781804 148.503962 148.756292 17.535562 175.849113 176.169140 22.240087 203.790257 203.933145 9.929891 41.279478 42.326408 72.755830 83.938395 83.647759 -20.197563 147.722847 148.551290 57.572206 147.849185 148.993851 79.548016 39.643247 40.084547 30.667872 98.670811 98.951168 19.483241 141.868195 147.787570 411.364003 146.742886 157.662160 758.829453 -186.270909 -184.758428 52.554547 -16.677279 -16.206053 16.373801 39.643247 39.395604 -8.604916 98.670811 99.231481 19.481723 83.938395 84.944714 34.966812 147.722847 148.720260 34.657358 148.503962 149.837195 46.326160 175.849113 176.047427 6.890855 41.279478 43.316302 70.774008 83.938395 83.354080 -20.303324 147.849185 148.885100 35.995199 148.503962 176.323246 966.643524 -82.713349 -81.723924 34.379808 39.643247 39.875989 8.087143 103.280443 104.568908 44.770605 130.736308 130.881383 5.040955 -186.270909 -16.677279 102.049106 117.315275 293.071784 300.011849 371.020969 386.098934 141.868195 436.220844 434.850777 474.218407 41.279478 215.348455 147.849185 472.438103 -82.713349 130.736308 103.280443 137.487530 203.790257 303.575684 376.953714 399.225042 98.670811 242.700025 402.245604 308.048014 147.722847 385.205844 399.057011 349.347999 83.938395 148.503962 175.849113 254.490708 39.643247 157.427755 199.573120 146.742886 2 25 210.9715386 -0.8771366872 12.3570642 0.03249196962 1 0.6688940935 -0.06258079068 -0.09992714445 989.7872316 0.1 475.1170295 -1.045371384 -0.9777417282 2 3 4 5 7 8 9 0.232228 -1.030493 0.786874 0.094897 0.211426 -0.194624 1.361337 0.925688 0.612331 0.753789 0.846421 0.885605 1.201647 0.987489 12.670000 12.729959 2.752968 32.085877 32.120095 1.571103 34.670363 34.667812 -0.117105 41.693263 41.829865 6.272016 35.907688 35.933168 1.169928 70.248882 70.290163 1.895398 83.010488 83.062069 2.368294 89.268080 89.243988 -1.106206 35.907688 35.960726 2.435218 47.039558 47.085331 2.101647 70.248882 70.236503 -0.568401 83.010488 83.041755 1.435582 42.122835 42.156571 1.548966 49.156444 49.138882 -0.806347 77.185202 77.213379 1.293742 82.111969 82.127405 0.708711 12.670000 12.789893 2.752408 34.670363 34.665146 -0.119768 41.693263 41.883889 4.376250 42.122835 41.930663 -4.411721 35.907688 35.973115 1.502032 70.248882 70.285274 0.835459 83.010488 83.028393 0.411036 92.887059 92.977340 2.072607 35.907688 35.999283 2.102768 47.039558 47.131117 2.101937 70.248882 70.270505 0.496398 83.010488 83.156809 3.359128 32.085877 32.152303 1.524966 41.710456 41.794443 1.928112 42.122835 42.048520 -1.706055 60.416038 60.631574 4.948096 12.670000 34.670363 41.693263 53.707554 107.166963 104.750939 145.657645 136.968312 89.687721 129.583944 151.465609 156.248826 47.039558 88.594235 105.797985 147.339144 32.085877 41.710456 60.416038 71.605713 89.268080 105.337079 136.363729 142.982876 49.156444 114.461252 133.358434 133.761025 92.887059 129.376091 128.899325 118.948877 35.907688 70.248882 83.010488 105.964582 42.122835 77.185202 82.111969 95.690834 2 10 61.55724743 -1.338795632 7.183385915 0.03249196962 1 0.70330315 -0.05619295729 -0.0968878772 192.1731667 0.2 73.44399575 -0.9370236797 -0.825061301 2 3 4 5 7 8 9 0.219109 -0.880275 0.600804 0.114469 0.203161 -0.201837 1.809057 0.947696 0.616437 0.550726 0.877069 0.797047 1.236305 0.705044 12.670000 12.692993 0.579030 17.561973 17.586965 0.629385 18.111932 18.128785 0.424402 23.779761 23.785827 0.152753 21.058166 21.071593 0.338141 42.972843 43.002202 0.739353 47.853461 47.887345 0.853314 53.628681 53.609046 -0.494460 21.058166 21.081371 0.584376 30.416475 30.441158 0.621596 42.972843 42.978150 0.133659 47.853461 47.877565 0.607013 25.767260 25.785405 0.456967 29.550988 29.541051 -0.250241 46.809143 46.829045 0.501184 47.360672 47.374495 0.348108 12.670000 12.716008 0.579307 17.561973 17.610273 0.608168 23.779761 23.776630 -0.039424 25.767260 25.737103 -0.379722 21.058166 21.079629 0.270252 42.972843 43.001115 0.355992 47.853461 47.884836 0.395065 56.328613 56.351259 0.285152 21.058166 21.110001 0.652682 30.416475 30.465848 0.621683 42.972843 43.013733 0.514874 47.853461 47.934579 1.021403 18.111932 18.147194 0.444000 23.789177 23.802180 0.163731 25.767260 25.743150 -0.303584 34.954620 34.986438 0.400633 12.670000 17.561973 23.779761 30.898290 60.419178 62.330205 82.385904 80.996721 52.596739 78.361369 91.482585 91.210362 30.416475 52.706604 67.507263 90.609183 18.111932 23.789177 34.954620 41.578864 53.628681 60.068221 83.332852 81.495557 29.550988 73.079470 69.165327 91.088973 56.328613 78.076115 77.777145 67.878972 21.058166 42.972843 47.853461 61.187260 25.767260 47.360672 46.809143 55.971999 2 10 77.15948252 -1.469752544 8.661553321 0.03249196962 1 0.70330315 -0.05619295729 -0.0968878772 192.1731667 0.3 73.44399575 -0.9370236797 -0.825061301 2 3 4 5 7 8 9 0.193419 -0.882289 0.801012 0.119851 0.195001 -0.196917 2.243118 0.765189 0.603751 0.620217 0.862581 0.855164 1.268782 0.804103 12.670000 12.710209 1.077793 17.406890 17.423895 0.455823 22.989091 22.987889 -0.032224 25.493899 25.486601 -0.195635 25.046494 25.067910 0.574068 51.498075 51.542405 1.188254 56.858632 56.903794 1.210581 64.354244 64.334354 -0.533153 25.046494 25.063848 0.465186 40.121869 40.148729 0.719968 51.498075 51.524721 0.714235 56.858632 56.869579 0.293437 31.603107 31.622708 0.525412 35.529811 35.519808 -0.268140 53.163899 53.168617 0.126490 57.692329 57.734356 1.126528 12.670000 12.750399 1.077548 22.989091 22.986764 -0.031184 25.606106 25.593162 -0.173479 31.603107 31.662528 0.796393 25.046494 25.058303 0.158278 51.498075 51.554354 0.754267 56.858632 56.886139 0.368672 68.588168 69.150706 7.539402 25.046494 25.112298 0.881934 40.121869 40.175540 0.719328 51.498075 51.583623 1.146555 56.858632 56.933275 1.000399 17.406890 17.440977 0.456847 25.493899 25.476819 -0.228919 31.603107 31.600487 -0.035110 41.725339 41.764118 0.519735 12.670000 22.989091 25.606106 36.344059 68.588168 76.956052 93.073011 107.601530 62.333210 96.804543 111.065674 109.943975 40.121869 64.096671 88.375442 114.303729 17.406890 25.493899 41.725339 54.582371 64.354244 69.963841 96.301420 102.043331 35.529811 92.644803 87.441238 112.603581 70.179526 96.089794 97.355152 79.439101 25.046494 51.498075 56.858632 73.398074 31.603107 53.163899 57.692329 65.203733 2 76 83.66525971 -7.106222093 10.99894022 0.03249196962 1 0.813814512 0.008546824166 -0.05758866355 22167.03523 0.4 -574.7830039 -1.185163752 -0.9139937383 2 3 4 5 7 8 9 0.159981 -0.296609 -1.684684 0.101520 0.202695 -0.204645 1.851282 0.772650 0.557089 0.617698 0.791736 0.798673 1.249277 0.801415 12.670000 12.728486 1.646597 25.615149 25.618602 0.097225 31.925633 31.837642 -2.477283 32.328287 32.303367 -0.701585 28.533799 28.556265 0.632497 61.623638 61.681019 1.615495 71.793216 71.850437 1.610979 79.429874 79.412408 -0.491719 28.533799 28.558183 0.686501 50.077103 50.111911 0.979975 61.623638 61.664246 1.143269 71.793216 71.793518 0.008489 40.689384 40.707198 0.501545 44.572766 44.563704 -0.255129 65.626251 65.636059 0.276127 75.306078 75.307612 0.043170 12.670000 12.786898 1.645564 31.925633 31.758248 -2.356262 33.940883 33.934315 -0.092456 40.689384 41.037919 4.906306 28.533799 28.539841 0.085054 61.623638 61.708992 1.201515 71.793216 71.811437 0.256493 85.008070 85.264711 3.612717 28.533799 28.621550 1.235263 50.077103 50.146583 0.978059 61.623638 61.734118 1.555211 71.793216 71.860434 0.946215 25.615149 25.622676 0.105966 32.328287 32.267555 -0.854919 40.689384 40.876885 2.639448 52.205399 52.094226 -1.564981 12.670000 31.925633 33.940883 46.332118 85.008070 109.348721 107.472993 167.750326 78.212094 152.882320 157.510897 169.031884 50.077103 80.677431 122.042851 166.420057 25.615149 32.328287 52.205399 88.316602 79.429874 90.682189 121.876622 130.595516 44.572766 117.445126 120.555056 177.679012 86.973872 137.210706 138.603639 119.640289 28.533799 61.623638 71.793216 92.944382 40.689384 65.626251 75.306078 94.902660 2 43 46634.17442 -0.4790503116 50 0.03249196962 1 0.6815635259 -0.07534409417 -0.06081273728 188.7949603 0.5 -5.923090561 -1.875200037 -1.924662567 2 3 4 5 7 8 9 0.087797 -1.789263 2.966301 0.020923 0.169404 -0.147693 2.144821 -0.716096 0.428463 0.470277 0.467268 0.482978 1.244660 0.600727 -54.115797 -53.936369 12.602649 -46.867996 -46.757861 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