********* 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 9 2408.163631 -0.7151633794 23.1974447 0.03249196962 1 0.5698580825 -0.2 -0.09431340785 50 0.09664070213 12.5 -0.8076994742 -0.8737621797 2 4 5 6 7 8 9 0.223093 -1.006854 0.953127 0.116139 0.186800 -0.162057 1.813391 0.897034 0.624542 1.450887 0.875468 1.542741 1.223604 1.975941 12.004346 12.039422 2.904423 12.670000 12.692635 1.874259 22.121932 22.208625 7.178465 50.219496 50.241225 1.799260 71.120060 71.179872 4.952624 129.154314 129.237272 6.869197 138.117323 138.202199 7.027995 153.520380 153.494995 -2.101954 71.120060 71.188594 5.674826 93.071887 93.132782 5.042258 129.154314 129.165885 0.958115 138.117323 138.165037 3.950886 60.221232 60.280344 4.894678 73.735932 73.695302 -3.364288 125.671900 125.710927 3.231555 131.855675 131.895214 3.273948 12.670000 12.715859 1.898622 22.121932 22.294943 7.162934 50.219496 50.217031 -0.102046 60.221232 60.150603 -2.924157 71.120060 71.229557 4.533350 129.154314 129.224360 2.900052 138.117323 138.202412 3.522818 171.849846 171.800463 -2.044534 71.120060 71.267366 6.098688 93.071887 93.193718 5.043998 129.154314 129.272849 4.907542 138.117323 138.295001 7.356177 12.004346 12.074205 2.892269 50.292393 50.270494 -0.906646 60.221232 60.227502 0.259610 107.522764 107.712709 7.864013 12.670000 22.121932 50.219496 97.831320 180.955683 185.095640 241.218829 263.901612 146.009560 223.797551 244.453621 238.527324 93.071887 154.607899 214.125723 250.568972 12.004346 50.292393 109.879555 107.522764 153.520380 180.154208 245.968131 253.799802 73.735932 192.182743 216.232986 260.490375 171.849846 223.888850 231.821035 206.409721 71.120060 129.154314 138.117323 174.149770 60.221232 131.855675 125.671900 140.816622 2 44 21.37002391 -0.9895136749 9.292414673 0.03249196962 1 0.6216532225 -0.13 -0.09209573102 241.4985882 0.1143848412 105.492553 -0.879967785 -0.8328078473 2 4 5 6 7 8 9 0.236032 -0.901992 0.651887 0.112031 0.205755 -0.196094 1.856532 1.067752 0.632877 0.683868 0.894085 0.877877 1.232310 0.890305 12.670000 12.702848 1.152741 18.376486 18.401011 0.860658 18.909712 18.926258 0.580657 27.872372 27.862609 -0.342609 28.518586 28.537822 0.675054 54.830229 54.862457 1.130973 61.295979 61.334263 1.343499 66.952996 66.935465 -0.615193 28.518586 28.550406 1.116677 38.462752 38.490294 0.966506 54.830229 54.827885 -0.082266 61.295979 61.324562 1.003051 30.278793 30.302163 0.820112 35.433284 35.418664 -0.513062 57.987759 58.001277 0.474375 59.058942 59.081029 0.775096 12.670000 12.735719 1.153144 18.909712 18.942471 0.574795 27.872372 27.870221 -0.037743 30.278793 30.246655 -0.563911 28.518586 28.558211 0.695282 54.830229 54.858054 0.488235 61.295979 61.328058 0.562879 71.882398 71.917693 0.619303 28.518586 28.581093 1.096782 38.462752 38.517851 0.966791 54.830229 54.862080 0.558883 61.295979 61.395793 1.751389 18.376486 18.424989 0.851053 27.877684 27.869688 -0.140299 30.278793 30.279968 0.020619 45.289259 45.408267 2.088168 12.670000 18.909712 27.872372 40.778928 78.430422 79.072577 106.089421 102.238370 65.456166 96.712237 112.276001 105.625817 38.462752 66.662512 85.798955 109.977641 18.376486 27.877684 45.289259 52.682623 66.952996 77.752828 104.304509 106.496038 35.433284 87.066631 93.822696 107.668182 71.882398 96.917096 98.921790 85.127567 28.518586 54.830229 61.295979 77.274088 30.278793 59.058942 57.987759 68.563037 1 35 19.79324579 -1.071279984 9.110319053 0.03249196962 1 0.6894809891 -0.06 -0.09936150348 110.709696 0.1424544752 43.90892567 -0.9114288512 -0.8085788379 2 4 5 6 7 8 9 0.227410 -0.948436 0.664230 0.114112 0.200900 -0.194593 1.553826 0.953875 0.623218 0.668617 0.887271 0.871894 1.217337 0.870337 12.670000 12.704483 1.143074 23.551649 23.576282 0.816539 24.007342 24.031046 0.785735 30.727469 30.742804 0.508307 26.617760 26.635256 0.579951 53.147963 53.180421 1.075931 61.035042 61.076562 1.376334 66.926712 66.904569 -0.734000 26.617760 26.652987 1.167735 36.384707 36.417529 1.087993 53.147963 53.142568 -0.178830 61.035042 61.069622 1.146282 31.822027 31.846295 0.804451 36.905687 36.892549 -0.435502 59.139239 59.157572 0.607710 59.532343 59.553616 0.705142 12.670000 12.738995 1.143546 24.007342 24.054339 0.778931 30.727469 30.731722 0.070486 31.822027 31.775724 -0.767434 26.617760 26.656541 0.642768 53.147963 53.175949 0.463851 61.035042 61.066951 0.528862 69.796899 69.843669 0.775174 26.617760 26.684437 1.105122 36.384707 36.450363 1.088197 53.147963 53.174083 0.432915 61.035042 61.152923 1.953793 23.551649 23.601094 0.819505 30.746186 30.781740 0.589279 31.822027 31.781409 -0.673216 43.748600 43.839837 1.512180 12.670000 24.007342 30.727469 39.314154 78.202002 78.057357 106.300305 100.856349 66.538790 97.280981 114.040493 115.226701 36.384707 66.062377 81.127566 111.600902 23.551649 30.746186 43.748600 53.241115 66.926712 77.105208 102.480853 105.129928 36.905687 88.675511 93.843644 105.326660 69.796899 97.056049 96.572332 87.280793 26.617760 53.147963 61.035042 78.020730 31.822027 59.139239 59.532343 70.909206 1 49 22.39480755 -1.133779576 9.05143988 0.03249196962 1 0.728762087 0.01 -0.1218770318 605.1238282 0.1628100108 61.99809709 -0.940625215 -0.8078135581 2 4 5 6 7 8 9 0.214193 -0.999893 0.733257 0.115318 0.196286 -0.191521 1.293956 0.805311 0.611886 0.651244 0.874393 0.862117 1.206983 0.847135 12.670000 12.708949 1.208206 25.623120 25.646926 0.738455 26.004768 26.033741 0.898746 32.923983 32.916548 -0.230635 25.203029 25.221038 0.558653 51.975315 52.008211 1.020432 60.350391 60.393220 1.328582 66.818179 66.797836 -0.631033 25.203029 25.239352 1.126760 34.698976 34.735605 1.136249 51.975315 51.972695 -0.081270 60.350391 60.384129 1.046565 32.923983 32.950584 0.825162 38.118942 38.106717 -0.379241 59.089128 59.106509 0.539138 60.695958 60.720530 0.762212 12.670000 12.747923 1.208596 26.004768 26.062329 0.892766 32.923983 32.877889 -0.714933 33.553053 33.539031 -0.217488 25.203029 25.242587 0.613551 51.975315 52.006679 0.486462 60.350391 60.383710 0.516790 68.617469 68.667793 0.780532 25.203029 25.272154 1.072135 34.698976 34.772243 1.136382 51.975315 52.004496 0.452602 60.350391 60.468165 1.826691 25.623120 25.671076 0.743801 32.923983 33.009281 1.322969 34.695955 34.567901 -1.986118 43.320108 43.365977 0.711432 12.670000 26.004768 33.553053 38.591073 77.850888 77.432828 106.518839 102.894310 67.644374 99.091028 112.189726 130.784818 34.698976 65.857856 80.379255 111.176354 25.623120 34.695955 43.320108 53.691780 66.818179 76.579929 101.180958 104.578506 38.118942 88.893530 95.331717 105.344279 68.617469 96.131914 97.326396 88.447731 25.203029 51.975315 60.350391 77.380481 32.923983 59.089128 60.695958 70.656549 2 28 23.43368908 -1.241306669 9.382827549 0.03249196962 1 0.7682827185 0.08 -0.1400799221 48.56677875 0.1928357508 16.75283777 -1.018412602 -0.8381960092 2 4 5 6 7 8 9 0.197359 -1.057407 0.833920 0.111507 0.194524 -0.189758 1.012085 0.625707 0.592767 0.630945 0.846784 0.835918 1.197017 0.819657 12.670000 12.712920 1.271655 27.205482 27.226822 0.632279 27.582691 27.617514 1.031752 34.369487 34.446773 2.289864 24.601460 24.620147 0.553683 52.297177 52.332196 1.037553 61.192611 61.238113 1.348170 68.647778 68.627497 -0.600899 24.601460 24.638821 1.106952 34.047671 34.089651 1.243805 52.297177 52.296989 -0.005595 61.192611 61.227614 1.037085 34.369487 34.398268 0.852735 39.754057 39.743025 -0.326869 60.529478 60.544985 0.459446 63.073386 63.102688 0.868156 12.670000 12.755896 1.272486 27.582691 27.652151 1.029007 34.369487 34.457259 1.300282 37.256729 37.245420 -0.167531 24.601460 24.641550 0.593903 52.297177 52.331956 0.515215 61.192611 61.230479 0.560980 69.494484 69.547381 0.783638 24.601460 24.673501 1.067239 34.047671 34.131631 1.243796 52.297177 52.332028 0.516288 61.192611 61.313609 1.792501 27.205482 27.248606 0.638849 34.369487 34.523199 2.277127 38.095750 38.078434 -0.256519 41.132631 41.110142 -0.333158 12.670000 27.582691 37.507224 37.256729 79.433313 79.295463 109.828657 109.497520 70.095919 105.045501 120.757017 143.744182 34.047671 67.382272 82.562926 115.532967 27.205482 41.132631 38.095750 55.244100 68.647778 78.129149 103.601664 107.293127 39.754057 90.811489 98.050954 112.988169 69.494484 94.793969 105.787164 91.062399 24.601460 52.297177 61.192611 79.362473 34.369487 60.529478 63.073386 72.003703 2 9 186.3858732 -1.3851415 8.781197314 0.03249196962 1 0.7490775688 0.15 -0.1267892353 50 0.1651385798 12.5 -0.9959281303 -0.7960272555 2 4 5 6 7 8 9 0.204943 -1.078801 0.887457 0.116349 0.193219 -0.192896 0.980725 0.671673 0.596365 0.626057 0.858957 0.847274 1.195621 0.813011 12.670000 12.710939 1.178801 29.621402 29.644745 0.672149 30.265104 30.287687 0.650251 34.102885 34.993263 25.637817 22.774639 22.789814 0.436960 49.325481 49.356320 0.887972 59.073251 59.110591 1.075195 65.484030 65.465243 -0.540940 22.774639 22.810195 1.023830 30.969810 31.007803 1.093985 49.325481 49.319731 -0.165570 59.073251 59.099314 0.750467 34.102885 34.126293 0.674028 38.444896 38.436147 -0.251922 56.604750 56.615906 0.321209 62.265343 62.288924 0.679002 12.670000 12.751899 1.179106 30.265104 30.310965 0.660267 34.102885 34.071633 -0.449929 34.957102 35.029595 1.043693 22.774639 22.812003 0.537941 49.325481 49.353681 0.405992 59.073251 59.091953 0.269255 65.061127 65.128121 0.964530 22.774639 22.838750 0.923019 30.969810 31.045795 1.093970 49.325481 49.347546 0.317666 59.073251 59.180030 1.537315 29.621402 29.667665 0.666047 34.102885 34.128011 0.361744 38.277920 38.263876 -0.202197 39.190187 39.203763 0.195451 12.670000 30.265104 34.957102 37.876178 76.301734 75.511684 105.333158 104.475132 67.255623 102.051017 117.652942 132.916057 30.969810 63.741156 77.965596 107.790097 29.621402 39.190187 38.277920 54.433350 65.484030 74.847551 96.351947 102.395722 38.444896 84.760346 93.954160 107.233872 65.061127 86.688169 103.984441 86.149919 22.774639 49.325481 59.073251 74.399606 34.102885 56.604750 62.265343 68.434490 1 18 20.91223025 -1.525832034 9.396691318 0.03249196962 1 0.7598186247 0.22 -0.1227893317 67.27974335 0.1656278753 19.11496853 -1.082113797 -0.7972331182 2 4 5 6 7 8 9 0.194870 -1.146243 1.024647 0.110431 0.194586 -0.193748 0.720180 0.540794 0.582148 0.623076 0.842123 0.827208 1.185101 0.809375 12.670000 12.713554 1.276044 34.050906 34.080956 0.880406 35.050240 35.083410 0.971804 35.499579 35.527727 0.824680 23.060831 23.075931 0.442398 51.032429 51.064934 0.952347 62.071495 62.108952 1.097417 69.171067 69.151381 -0.576742 23.060831 23.098493 1.103402 30.774401 30.817406 1.259979 51.032429 51.023513 -0.261210 62.071495 62.093466 0.643731 36.338913 36.361984 0.675940 40.494995 40.487485 -0.220031 58.707661 58.717939 0.301137 66.522822 66.545444 0.662758 12.670000 12.757121 1.276233 34.050906 34.111786 0.891823 35.499579 35.555452 0.818479 36.338913 36.307440 -0.461049 23.060831 23.100999 0.588421 51.032429 51.059840 0.401550 62.071495 62.081219 0.142456 67.549394 67.632602 1.218919 23.060831 23.126204 0.957650 30.774401 30.860396 1.259750 51.032429 51.052328 0.291502 62.071495 62.179756 1.585928 35.050240 35.117134 0.979926 36.338913 36.351425 0.183297 38.342812 38.346111 0.048317 41.605164 41.600390 -0.069935 12.670000 34.050906 35.499579 41.262068 80.697396 79.776200 112.228814 112.104599 71.159280 111.353508 128.906179 138.093828 30.774401 66.784814 81.732675 114.760248 35.050240 38.342812 41.605164 58.009420 69.171067 78.984261 100.912671 108.563242 40.494995 88.875824 97.935616 117.873503 67.549394 90.190830 112.628047 91.262342 23.060831 51.032429 62.071495 78.864028 36.338913 58.707661 66.522822 72.122060 2 11 40.9883626 -1.777625326 8.819930048 0.03249196962 1 0.7332956313 0.29 -0.1202238531 50 0.1554625435 12.5 -0.994174461 -0.7999345134 2 4 5 6 7 8 9 0.191640 -1.145274 1.054600 0.122804 0.183210 -0.185863 0.683671 0.519669 0.576463 0.629617 0.835381 0.866775 1.186296 0.819731 12.670000 12.710406 1.092729 31.650773 31.666038 0.412829 32.872881 32.875055 0.058792 34.918790 34.949036 0.817955 21.195797 21.208844 0.352842 47.801998 47.831706 0.803417 58.474713 58.507330 0.882094 65.167472 65.151340 -0.436274 21.195797 21.228705 0.889954 27.915097 27.953865 1.048437 47.801998 47.793615 -0.226707 58.474713 58.489645 0.403826 35.098051 35.117360 0.522210 38.544510 38.538652 -0.158431 54.798567 54.807278 0.235579 63.479500 63.496477 0.459135 12.670000 12.750822 1.092874 31.650773 31.680780 0.405751 34.918790 34.978907 0.812896 35.098051 35.073545 -0.331373 21.195797 21.231350 0.480741 47.801998 47.826292 0.328508 58.474713 58.480517 0.078482 63.154022 63.232603 1.062566 21.195797 21.252173 0.762313 27.915097 27.992615 1.048202 47.801998 47.820466 0.249721 58.474713 58.563867 1.205545 32.872881 32.877283 0.059521 35.098051 35.103877 0.078776 36.841156 36.897694 0.764509 40.824511 40.824777 0.003602 12.670000 34.918790 31.650773 40.638631 75.951279 75.344739 105.562954 105.813392 67.444894 107.767129 124.045404 127.856801 27.915097 62.666456 77.215898 108.039131 36.841156 32.872881 40.824511 55.658999 65.167472 74.420185 94.088120 102.144448 38.544510 83.298423 90.453840 115.482468 63.154022 85.226347 101.351831 91.097013 21.195797 47.801998 58.474713 73.798053 35.098051 54.798567 63.479500 67.872652 2 10 47.43513164 -1.963508393 8.35839337 0.03249196962 1 0.7066611485 0.36 -0.112750652 50 0.1426798424 12.5 -0.9767879552 -0.8093884054 2 4 5 6 7 8 9 0.188022 -1.142822 1.086900 0.127102 0.178427 -0.183108 0.649083 0.497218 0.569715 0.611134 0.826134 0.867057 1.186671 0.794170 12.670000 12.706672 0.922130 30.290287 30.297218 0.174287 31.047199 31.052608 0.136017 33.863589 33.890138 0.667594 19.665541 19.676712 0.280902 45.133752 45.160928 0.683320 55.474360 55.502476 0.706970 61.797313 61.788971 -0.209756 19.665541 19.693968 0.714792 25.430832 25.465834 0.880124 45.133752 45.125126 -0.216912 55.474360 55.488919 0.366068 33.996601 34.012347 0.395935 36.782288 36.777835 -0.111973 51.448473 51.455552 0.178014 60.748866 60.761772 0.324499 12.670000 12.743352 0.922213 30.290287 30.303190 0.162224 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48.160227 57.878958 30.377402 43.177748 52.564966 55.200744