********* Eigenvalues for the 3+1 transverse lattice ********* Couplings: 0:mu^2 1:g^2 N 2:beta 3:lambda_1 4:lambda_2 5:lambda_3 6:lambda_4 7:lambda_5 8:tau_1 9:tau_2 10:kappa_S 11:kappa_A 12:mu_F 13:mu_0^2 14:mu_1^2 15:mu_2^2 16:mu_3^2 Use chi^2 fit with 40 criteria and tolerance 0.01. Overall scale from minimizing chi^2. Parity doublets (charge,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 4 states (multiplet, charge, c^2 error for each) = (15, 1, 0.25 2 2 2) (15, -1, 0.25 2 2 2) (16, -1, 0.25 2 2 2) (16, 1, 0.25 2 2 2) Spectrum for P_perp a = (0,0), ( 0.25 0.25) using 4 states (multiplet, charge, c^2 error for each) = (17, 1, 0.25 2 2 2) (17, -1, 0.25 2 2 2) (18, -1, 0.25 2 2 2) (18, 1, 0.25 2 2 2). Ordinary spectra multiplets, 4 states, (charge,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 0,18/2,7) ( 3 0,18/2,5) ( 3 0,26/2,5) ( 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 0,14/2,3,3.5) ( 1 0,14/2,5,3.5) ( 1 0,14/2,3,3) ( 1 0,24/2,3,4) ( 1 0,24/2,3,4.5) ( 1 0,36/2,3,5) ( 1 0,36/2,3,6) L=1.265-0.964*m and error 0.1; ( 1 0,14/2,3,3.5) ( 1 0,14/2,5,3.5) ( 1 0,14/2,3,3) ( 1 0,24/2,3,4) ( 1 0,24/2,3,4.5) ( 1 0,36/2,3,5) ( 1 0,36/2,3,6) 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) = (14/2,3) (22/2,3) (46/2,3) (14/2,5) (28/2,5) (14/2,7) (16/2,7) . Result format: Fit info, # steps, chi^2, and p damping, scale G^2 N/sigma. The 17 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. 1 39 133.4015349 -8.713831541 3.734299603 0 1 -0.2730124052 0.386912095 -0.3799041475 930352.951 -0.1360380007 319213.4952 -0.3987144515 -0.5658343718 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.104291 -0.357794 -0.068378 0.293266 -0.756401 1.638621 1.131267 0.467990 0.631015 0.693720 1.104663 1.083652 1.158255 0.704555 6.306326 6.323114 0.104611 10.302974 10.301528 -0.009011 11.132387 11.146739 0.089432 14.018378 13.938368 -0.498563 11.009930 11.017866 0.049452 16.852880 16.859202 0.039394 19.695697 19.699256 0.022181 20.715869 20.713669 -0.013708 8.266208 8.265465 -0.004629 11.009930 11.015132 0.032415 16.852880 17.020617 1.045213 17.216044 17.186032 -0.187018 14.131835 14.133887 0.012783 16.684227 16.686265 0.012696 17.355848 17.356626 0.004848 20.427871 20.427213 -0.004105 6.306326 6.339871 0.104516 10.302974 10.300821 -0.006707 14.018378 13.891419 -0.395557 14.131835 14.264998 0.414888 11.009930 11.024091 0.044121 16.852880 16.832984 -0.061990 17.216044 17.239518 0.073136 19.695697 19.707730 0.037493 8.266208 8.264665 -0.004806 11.009930 11.022094 0.037898 16.852880 17.032052 0.558235 17.377786 17.201097 -0.550500 11.132387 11.160393 0.087257 14.131835 14.131723 -0.000351 17.047289 16.990104 -0.178168 17.355848 17.740642 1.198880 6.306326 10.302974 14.018378 17.201080 23.348119 23.028899 25.645673 21.269992 22.186273 25.535644 26.971416 29.697176 8.266208 17.377786 21.667315 22.718753 11.132387 17.047289 19.669795 19.422206 20.715869 22.803708 23.761803 21.994435 16.684227 21.406410 27.578568 28.655109 17.216044 23.704853 24.421562 25.839390 11.009930 16.852880 19.695697 21.956899 14.131835 17.355848 20.427871 21.856479 2 12 115.7956701 -8.286317957 10.44350275 0.001967542671 1 0.03246857907 0.2448056187 -0.2076147858 10767.9697 -0.1061582912 4843.709277 -1.620811056 -1.996595401 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.149751 -0.166655 -0.092664 0.116638 -0.144914 0.303971 2.347312 1.019770 0.510578 0.419546 0.693389 0.642685 1.087925 0.574902 26.260913 26.263985 0.076869 29.121905 29.140012 0.453080 33.496860 33.513923 0.426958 37.394186 37.376590 -0.440292 31.945107 31.960743 0.391250 52.372654 52.373278 0.015604 58.910476 58.917067 0.164932 59.983263 59.983187 -0.001911 26.459945 26.459812 -0.003339 31.945107 31.945337 0.005756 52.372654 52.371926 -0.018225 57.291149 57.291544 0.009889 37.394186 37.394257 0.001784 41.377779 41.377746 -0.000831 52.406648 52.406873 0.005631 60.130587 60.128776 -0.045321 26.260913 26.267030 0.076527 29.121905 29.158289 0.455208 37.394186 37.354627 -0.494937 37.429770 37.465574 0.447957 31.945107 31.970859 0.322189 52.372654 52.372514 -0.001752 57.310695 57.311171 0.005953 58.910476 58.916436 0.074568 26.459945 26.459703 -0.003029 31.945107 31.950952 0.073122 52.372654 52.372698 0.000547 57.291149 57.291807 0.008228 33.496860 33.530773 0.424300 37.394186 37.389502 -0.058600 48.881728 48.863541 -0.227538 52.406648 52.405547 -0.013780 26.260913 29.121905 37.429770 49.210961 66.736816 73.785337 75.041857 61.098316 66.588072 66.549560 71.933229 75.522403 26.459945 57.291149 61.752066 61.640960 33.496860 48.881728 57.309648 57.809957 59.983263 64.282747 74.154150 68.262962 41.377779 64.167884 71.693934 75.420423 57.310695 66.505239 71.695180 80.554678 31.945107 52.372654 58.910476 60.494073 37.394186 52.406648 60.130587 62.953049 2 12 113.0692275 -8.762212981 8.65063896 0.007919222016 1 0.2780400938 0.1304202449 -0.2333791609 10767.9697 -0.03830511299 4843.709277 -1.528509264 -1.975281628 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.153355 -0.205107 -0.212286 0.124657 -0.138344 0.307619 1.950689 0.995195 0.524045 0.394561 0.696670 0.638361 1.060909 0.523078 18.771688 18.801592 0.634755 24.099480 24.124236 0.525472 24.274704 24.288392 0.290551 29.751045 29.653365 -2.073330 26.905685 26.919951 0.302804 43.428824 43.449006 0.428390 47.408948 47.403357 -0.118670 49.618090 49.619826 0.036835 25.139199 25.126730 -0.264660 26.905685 26.925471 0.419982 43.428824 43.419581 -0.196183 47.408948 47.362731 -0.980988 29.751045 29.755474 0.094010 33.620827 33.619595 -0.026148 45.400117 45.404341 0.089674 48.207940 48.200818 -0.151166 18.771688 18.831563 0.635450 24.274704 24.305444 0.326249 29.751045 29.570311 -1.918113 31.855207 32.004831 1.587950 26.905685 26.930295 0.261188 43.428824 43.423594 -0.055504 47.408948 47.404398 -0.048286 48.576095 48.616020 0.423726 25.139199 25.113999 -0.267441 26.905685 26.949536 0.465392 43.428824 43.458678 0.316840 47.408948 47.315274 -0.994151 24.099480 24.145556 0.489002 29.751045 29.752321 0.013543 36.605426 36.573797 -0.335675 44.683908 44.625607 -0.618744 18.771688 24.274704 31.855207 36.713963 56.965594 59.674741 62.481572 51.660111 52.552061 55.023416 60.531790 66.859066 25.139199 48.638014 51.422168 57.398908 24.099480 36.605426 44.683908 47.678865 49.618090 57.071528 60.259601 52.235954 33.620827 52.354424 61.132707 65.726668 48.576095 58.304701 62.419329 66.414638 26.905685 43.428824 47.408948 53.410959 29.751045 45.400117 48.207940 51.326871 2 12 91.27831175 -9.721262102 6.042135308 0.01800590693 1 0.4852912285 0.03900344622 -0.2576725541 10767.9697 0.01640947589 4843.709277 -1.428862762 -1.947091764 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.166619 -0.409199 -0.021794 0.134021 -0.120975 0.285930 1.673993 0.921028 0.541841 0.348229 0.709412 0.626870 1.057829 0.428457 10.901678 10.929395 0.446465 14.891882 14.896258 0.070495 14.898686 14.936922 0.615889 20.527657 20.477684 -0.804953 19.252875 19.263140 0.165352 29.660764 29.685556 0.399343 33.285298 33.272051 -0.213378 35.148335 35.446131 4.796816 19.252875 19.341141 1.421762 19.849474 19.774487 -1.207864 29.660764 29.655162 -0.090246 33.285298 33.231175 -0.871791 20.527657 20.537430 0.157421 23.722317 23.718542 -0.060810 32.158035 32.164298 0.100883 33.324175 33.306015 -0.292520 10.901678 10.957216 0.447298 14.898686 14.941354 0.343645 20.527657 20.442406 -0.686601 23.722317 23.713104 -0.074196 19.252875 19.273008 0.162148 29.660764 29.654008 -0.054415 33.285298 33.279773 -0.044490 34.343235 34.396955 0.432656 19.252875 19.425844 1.393069 19.849474 19.703678 -1.174223 29.660764 29.708675 0.385870 33.285298 33.160635 -1.004019 14.891882 14.934449 0.342830 20.527657 20.533444 0.046610 23.875076 23.845285 -0.239930 28.839066 28.856821 0.142995 10.901678 14.898686 23.887372 26.150892 41.428127 42.721704 42.952284 38.517166 35.745430 38.962156 44.410166 48.466938 19.849474 34.846141 37.344279 44.407517 14.891882 23.875076 28.839066 31.731795 35.442417 43.005668 43.006826 35.148335 23.722317 36.729527 43.821692 48.527790 34.343235 41.881412 45.177134 45.619385 19.252875 29.660764 33.285298 38.867399 20.527657 32.158035 33.324175 35.794785 2 12 190.3838888 -9.420399121 1.697262195 0.03249196962 1 0.6536526686 -0.02889837652 -0.2805752854 10767.9697 0.05768806722 4843.709277 -1.320890834 -1.911514786 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.187392 -0.627943 0.234477 0.146185 -0.104324 0.259404 1.576641 0.900506 0.565864 0.285173 0.732039 0.601083 1.077988 0.297224 2.719702 2.728775 0.046170 3.931129 3.942649 0.058623 3.947097 3.950438 0.017005 5.958569 5.945034 -0.068878 5.619760 5.622556 0.014227 8.446859 8.455538 0.044166 9.723433 9.718213 -0.026564 10.473822 10.475459 0.008333 5.619760 5.921004 1.532990 6.311225 6.015714 -1.503814 8.446859 8.445787 -0.005456 9.723433 9.707685 -0.080141 5.958569 5.963350 0.024326 7.005554 7.003382 -0.011052 9.320522 9.323046 0.012843 9.615761 9.609633 -0.031185 2.719702 2.737889 0.046277 3.931129 3.946505 0.039124 5.958569 5.938119 -0.052035 6.633485 6.623576 -0.025213 5.619760 5.625890 0.015597 8.446859 8.445020 -0.004681 9.723433 9.722398 -0.002634 10.149403 10.166924 0.044581 5.619760 5.945654 0.829217 6.311225 5.996347 -0.801185 8.446859 8.464768 0.045568 9.723433 9.683456 -0.101720 3.947097 3.961452 0.036527 5.958569 5.961655 0.007851 6.625641 6.615537 -0.025709 7.855554 7.866905 0.028883 2.719702 3.931129 6.633485 8.450019 12.171687 12.520074 13.047374 11.850592 10.352672 11.373962 13.506122 14.114600 6.311225 10.349896 11.274452 13.687421 3.947097 6.625641 7.855554 8.853428 10.473822 12.879254 12.609619 11.370533 7.005554 10.895093 13.153713 13.578533 10.149403 11.886681 13.447822 13.217655 5.619760 8.446859 9.723433 11.439463 5.958569 9.320522 9.615761 10.466047 2 65 49.26983666 -9.380422551 6.608860525 0.0517766953 1 1.084527478 -0.1105524272 -0.2199619137 562466.8902 0.1885118828 269504.9424 -1.239413534 -1.686110215 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.239735 -1.185398 0.985417 0.165163 -0.094920 0.231187 1.143741 0.855660 0.601125 0.534723 0.802717 0.821964 1.070256 0.711423 6.605810 6.640872 0.888811 15.610537 15.638406 0.706491 16.019320 16.048651 0.743550 23.800111 23.752892 -1.197014 22.626486 22.632889 0.162322 32.122859 32.163657 1.034239 40.453696 40.410134 -1.104319 44.449222 44.473126 0.605951 22.626486 22.671804 1.148819 28.917835 28.910668 -0.181678 32.122859 32.111155 -0.296685 40.292100 40.285636 -0.163865 24.231145 24.267214 0.914339 28.648230 28.625647 -0.572492 36.100697 36.107143 0.163411 38.967251 38.920016 -1.197393 6.605810 6.676163 0.891729 16.019320 16.076841 0.729081 23.834918 23.803140 -0.402785 24.231145 24.222839 -0.105277 22.626486 22.652939 0.335289 32.122859 32.097305 -0.323891 40.292100 40.403288 1.409313 40.453696 40.414554 -0.496127 22.626486 22.680017 0.678500 28.917835 28.927199 0.118688 32.122859 32.211860 1.128084 40.453696 40.097786 -4.511161 15.610537 15.667383 0.720525 23.800111 23.745134 -0.696840 24.231145 24.279319 0.610606 25.751877 25.807105 0.700020 6.605810 16.019320 23.834918 37.842580 48.074676 48.409320 55.192351 54.813137 40.194080 45.501241 56.724038 59.963786 28.917835 42.648732 48.064088 55.455469 15.610537 23.800111 25.751877 33.804494 44.449222 51.741110 49.157001 54.837594 28.648230 45.107188 52.492582 56.326831 40.292100 44.188239 57.831204 52.476677 22.626486 32.122859 40.453696 47.982490 24.231145 36.100697 38.967251 42.607743 2 12 66.83075002 -8.939576923 6.521716707 0.07642881742 1 0.8655973916 -0.08839531533 -0.3223463624 10767.9697 0.09670792046 4843.709277 -1.074587307 -1.814948158 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.250808 -0.717886 0.194146 0.180933 -0.073990 0.184070 2.201154 1.312845 0.639750 0.597852 0.809020 0.894922 1.196717 0.801588 13.569095 13.610052 1.071893 19.181857 19.220764 1.018232 19.194286 19.222089 0.727635 28.937921 28.882642 -1.446700 24.545401 24.554414 0.235884 38.597299 38.632053 0.909555 44.665269 44.646200 -0.499054 48.391252 48.404398 0.344066 24.545401 24.552813 0.193979 32.130293 32.147786 0.457824 38.597299 38.601205 0.102208 44.665269 44.630014 -0.922681 28.937921 28.962101 0.632833 33.676837 33.663543 -0.347920 42.667061 42.685250 0.476022 44.258980 44.248408 -0.276684 13.569095 13.651244 1.074975 19.181857 19.250928 0.903835 28.937921 28.858873 -1.034381 30.810295 30.764061 -0.604993 24.545401 24.565391 0.261575 38.597299 38.600908 0.047221 44.665269 44.670513 0.068621 50.372830 50.422499 0.649946 24.545401 24.556364 0.143450 32.130293 32.167547 0.487498 38.597299 38.673372 0.995453 44.665269 44.552684 -1.473241 19.194286 19.258708 0.843000 28.937921 28.955836 0.234426 30.780013 30.728825 -0.669824 37.554182 37.587901 0.441232 13.569095 19.181857 30.810295 41.255338 54.312443 61.338369 60.342258 63.867587 50.989771 51.670713 65.679604 68.131236 32.130293 49.276482 55.280398 61.647869 19.194286 30.780013 37.554182 39.647964 48.391252 56.897394 61.639453 64.097804 33.676837 54.154890 59.882190 64.197575 50.372830 51.915650 64.814346 62.357431 24.545401 38.597299 44.665269 55.889256 28.937921 42.667061 44.258980 51.537325 2 11 132.9404069 -8.871049845 4.428542533 0.1072401379 1 0.9013715922 -0.07478623986 -0.3411756858 10767.9697 0.09151090948 4843.709277 -0.9325347252 -1.751513872 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.295013 -0.584952 -0.140171 0.197762 -0.050121 0.121403 2.915658 1.757634 0.690983 0.508225 0.863326 0.865504 1.290581 0.658297 12.398784 12.427645 0.603295 16.689866 16.719899 0.627802 16.718744 16.735077 0.341409 23.486845 23.444321 -0.888910 18.112716 18.118072 0.111962 30.160964 30.182010 0.439954 34.440529 34.430774 -0.203922 37.131644 37.141844 0.213205 18.112716 18.105905 -0.142373 25.358171 25.379901 0.454253 30.160964 30.165528 0.095412 34.440529 34.424143 -0.342536 23.486845 23.501856 0.313785 26.801401 26.792718 -0.181498 33.191865 33.206311 0.301975 34.483905 34.479611 -0.089758 12.398784 12.456711 0.605438 16.689866 16.737803 0.501022 23.486845 23.423540 -0.661651 25.063799 25.030553 -0.347479 18.112716 18.123860 0.116479 30.160964 30.166608 0.058992 34.440529 34.446154 0.058795 39.659330 40.516655 8.960622 18.112716 18.099464 -0.138502 25.358171 25.401084 0.448521 30.160964 30.207705 0.488532 34.440529 34.383319 -0.597947 16.718744 16.763596 0.468787 23.486845 23.495741 0.092978 25.038480 25.003965 -0.360744 27.147474 27.165856 0.192125 12.398784 16.689866 25.063799 29.448784 41.571396 46.226486 47.903750 51.178676 39.476797 41.962316 52.352765 54.107197 25.358171 38.219446 44.902233 45.938573 16.718744 25.038480 27.147474 31.108528 37.131644 43.185572 49.149391 49.902655 26.801401 44.601464 44.359765 48.961343 39.659330 41.197615 46.994101 51.682772 18.112716 30.160964 34.440529 43.819483 23.486845 33.191865 34.483905 40.873480 2 12 162.5553398 -9.018718706 3.364098549 0.1453085056 1 0.8816420158 -0.02662741713 -0.3585127406 10767.9697 0.06664522001 4843.709277 -0.7743987451 -1.675565804 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.350961 -0.324832 -0.678329 0.213443 -0.034748 0.074885 4.011336 2.398065 0.752908 0.466042 0.928382 0.859562 1.411034 0.593403 13.277069 13.298753 0.409636 16.887430 16.917936 0.576287 16.922570 16.926085 0.066411 21.808150 21.771540 -0.691579 15.101841 15.105220 0.063836 27.151516 27.164030 0.236409 30.359085 30.354800 -0.080939 32.356377 32.364412 0.151785 15.101841 15.096048 -0.109435 22.479577 22.493901 0.270602 27.151516 27.155581 0.076800 30.359085 30.351824 -0.137162 21.808150 21.816814 0.163661 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