********* 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 minimizing chi^2. 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) = (16/2,8) (16/2,6) (20/2,6) (26/2,6) . Winding potential using (n,K,p) = ( 2 0,20/2,4) ( 2 0,20/2,6) ( 2 0,24/2,4) ( 2 0,32/2,4) ( 3 0,19/2,5) ( 3 0,19/2,7) ( 3 0,25/2,5) ( 3 0,33/2,5) ( 4 0,18/2,6) ( 4 0,18/2,8) ( 4 0,24/2,6) ( 4 0,32/2,6) . Roundness of winding using (n,K,p) = ( 2 2,16/2,6) ( 2 2,16/2,8) ( 2 2,24/2,6) ( 2 2,28/2,6) with error 1; in G^2 N units. Heavy potential determined using (n,K,p,K_max) = ( 0 0,-40/2,2,4) ( 0 0,-40/2,4,4) ( 0 0,-40/2,2,3.5) ( 0 0,-50/2,2,3.75) ( 0 0,-50/2,2,4.25) ( 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,-19/2,3,4) ( 1 0,-19/2,5,4) ( 1 0,-19/2,3,3.5) ( 1 0,-33/2,3,4) ( 1 0,-33/2,3,5) ( 1 0,-69/2,3,5) ( 1 0,-69/2,3,6) L=1.265-0.964*m and error 0.1; ( 1 0,-19/2,3,4) ( 1 0,-19/2,5,4) ( 1 0,-19/2,3,3.5) ( 1 0,-33/2,3,4) ( 1 0,-33/2,3,5) ( 1 0,-69/2,3,5) ( 1 0,-69/2,3,6) L=5.058-3.856*m and error 0.1; ( 1 1,-34/2,2,5.5) ( 1 1,-34/2,4,5.5) ( 1 1,-34/2,2,5) ( 1 1,-48/2,2,5.5) ( 1 1,-48/2,2,6.5) ( 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) (35/2,3) (45/2,3) (13/2,5) (29/2,5) (13/2,7) (17/2,7) . 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 11 32.85754545 -7.476133493 11.74409182 0 1 -0.1798180011 -0.06597728403 -0.05285432603 4.131671084 -0.01594589623 0.9612626769 -0.4593008567 -0.396951357 2 3 4 5 6 7 8 9 0.179682 -0.379071 -0.397281 0.089619 0.339656 -0.413803 1.843605 1.008728 0.592802 0.719411 0.959964 0.917362 1.207667 0.911815 13.225889 13.259768 1.143880 18.074369 18.101130 0.903543 23.321047 23.314760 -0.212287 27.784608 27.738996 -1.540010 31.597432 31.626892 0.994676 57.674829 57.701396 0.897012 64.145818 64.163336 0.591480 67.078012 67.074030 -0.134462 31.597432 31.614199 0.566118 32.137180 32.142543 0.181074 57.674829 57.675127 0.010061 64.145818 64.146153 0.011327 27.784608 27.795388 0.363958 30.937636 30.927832 -0.331015 57.493480 57.513851 0.687792 62.174191 62.169398 -0.161856 13.225889 13.293633 1.143627 23.321047 23.308317 -0.214901 27.784608 27.728004 -0.955577 28.701327 28.722476 0.357025 31.597432 31.661258 1.077491 57.674829 57.700174 0.427876 64.145818 64.162785 0.286438 80.333906 80.447126 1.911343 31.597432 31.626033 0.482837 32.137180 32.147938 0.181614 57.674829 57.703160 0.478286 64.145818 64.164762 0.319807 18.074369 18.127709 0.900468 27.784608 27.771316 -0.224399 28.694209 28.696880 0.045087 33.561077 33.762886 3.406863 13.225889 23.321047 28.701327 38.007581 82.119288 88.857143 105.349798 115.711123 65.367835 93.630197 100.421505 105.668826 32.137180 66.327118 95.136414 103.186436 18.074369 28.694209 33.561077 56.704956 67.078012 86.658656 105.863549 109.290402 30.937636 94.895422 100.223289 103.772359 83.381905 87.839116 104.826774 103.746924 31.597432 57.674829 64.145818 80.333906 27.784608 57.493480 62.174191 77.003113 2 39 13.35771666 -2.212418668 12.02238135 0.001967542671 1 0.4286235989 0.01161817889 -0.06758574491 436.6795354 0.09711799423 181.7956756 -0.7951513785 -0.7015191923 2 3 4 5 6 7 8 9 0.171298 -0.850411 0.758890 0.084074 0.258734 -0.265164 1.072985 0.614835 0.540437 0.637754 0.838107 0.807071 1.051524 0.812669 12.224374 12.259212 1.147920 24.687222 24.709778 0.743216 24.700971 24.730433 0.970794 31.592866 31.563814 -0.957293 28.809220 28.832628 0.771326 54.412813 54.461878 1.616703 64.104886 64.134064 0.961420 70.415627 70.400383 -0.502301 28.809220 28.843147 1.117909 33.016752 33.051641 1.149638 54.412813 54.406666 -0.202555 64.104886 64.129106 0.798073 31.592866 31.618041 0.829513 36.810667 36.796511 -0.466461 60.663795 60.686660 0.753407 63.770032 63.787934 0.589892 12.224374 12.294073 1.148316 24.700971 24.758682 0.950800 31.592866 31.553852 -0.642773 32.467930 32.458420 -0.156676 28.809220 28.862923 0.884783 54.412813 54.445739 0.542459 64.104886 64.139870 0.576376 70.025191 70.103434 1.289080 28.809220 28.870251 1.005504 33.016752 33.086512 1.149325 54.412813 54.465521 0.868380 64.104886 64.174945 1.154248 24.687222 24.733432 0.761317 31.592866 31.624717 0.524745 32.563237 32.524185 -0.643391 50.478069 50.516128 0.627038 12.224374 24.700971 32.467930 42.615761 82.247061 87.191189 105.520560 121.861191 67.843733 93.149722 117.592387 115.705966 33.016752 69.193852 91.039561 95.421261 24.687222 32.563237 50.478069 54.063134 70.415627 83.110488 101.948951 107.493099 36.810667 83.999288 101.712801 93.509201 70.025191 92.114590 95.413843 91.130135 28.809220 54.412813 64.104886 78.684944 31.592866 60.663795 63.770032 69.815130 2 29 14.28109047 -1.792273428 11.17783782 0.007919222016 1 0.504034936 -0.004958577241 -0.07465097481 425.7069513 0.1175598006 195.6739757 -0.9083431627 -0.8642439384 2 3 4 5 6 7 8 9 0.187824 -0.862326 0.690837 0.091048 0.199166 -0.154301 1.250623 0.726618 0.551096 0.622162 0.816604 0.791821 1.101087 0.800403 12.573649 12.607517 1.137687 24.293109 24.322313 0.981021 24.302724 24.327837 0.843603 31.856327 31.859924 0.120847 28.457622 28.478969 0.717048 53.863540 53.908069 1.495788 62.980851 63.010517 0.996539 69.333697 69.317990 -0.527634 28.457622 28.490482 1.103799 34.621509 34.656735 1.183297 53.863540 53.858995 -0.152652 62.980851 63.005874 0.840572 31.872290 31.897253 0.838530 37.102821 37.088541 -0.479687 60.136858 60.158804 0.737177 62.154575 62.172540 0.603474 12.573649 12.641414 1.138165 24.293109 24.349874 0.953402 31.856327 31.836763 -0.328586 31.872290 31.843268 -0.487443 28.457622 28.505095 0.797339 53.863540 53.894682 0.523049 62.980851 63.015030 0.574074 71.974747 72.016660 0.703962 28.457622 28.518613 1.024376 34.621509 34.691957 1.183227 53.863540 53.912194 0.817181 62.980851 63.054457 1.236274 24.302724 24.353930 0.860045 31.872290 31.845028 -0.457885 31.911480 31.929576 0.303934 48.740557 48.893297 2.565386 12.573649 24.293109 31.856327 42.353660 80.695261 84.791992 106.698023 105.946419 69.205760 93.141259 119.095967 106.556773 34.621509 68.434475 85.490076 103.509535 24.302724 31.911480 48.740557 54.061258 69.333697 81.120170 103.656250 105.931228 37.102821 79.645432 107.889282 94.355267 71.974747 92.306351 97.461872 88.990209 28.457622 53.863540 62.980851 80.261659 31.872290 60.136858 62.154575 71.491969 1 29 15.9934481 -1.577933099 10.53338729 0.01800590693 1 0.5753473285 -0.03528434272 -0.07929231256 463.0085279 0.1318320788 210.6092942 -0.9985792596 -1.008157113 2 3 4 5 6 7 8 9 0.210297 -0.839869 0.559247 0.097830 0.156937 -0.083795 1.543493 0.912414 0.569856 0.625497 0.810658 0.792861 1.153159 0.812975 13.724316 13.756731 1.148871 24.596074 24.618814 0.805963 24.629086 24.655323 0.929895 31.790850 31.801913 0.392106 28.953296 28.972498 0.680571 54.757005 54.796621 1.404068 63.374179 63.403057 1.023485 69.656760 69.641207 -0.551223 28.953296 28.984525 1.106813 37.190353 37.224528 1.211247 54.757005 54.752839 -0.147680 63.374179 63.398087 0.847359 32.876097 32.899938 0.844990 37.998745 37.984436 -0.507150 60.740647 60.761380 0.734811 61.868733 61.885160 0.582207 13.724316 13.789172 1.149319 24.629086 24.679530 0.893933 31.790850 31.784800 -0.107213 32.876097 32.836944 -0.693837 28.953296 28.994927 0.737742 54.757005 54.785733 0.509082 63.374179 63.404886 0.544170 72.740774 72.764184 0.414847 28.953296 29.012566 1.050320 37.190353 37.258709 1.211339 54.757005 54.799038 0.744860 63.374179 63.447674 1.302407 24.596074 24.643191 0.834973 31.805216 31.827752 0.399361 32.876097 32.843432 -0.578862 48.492748 48.587370 1.676824 13.724316 24.629086 31.790850 42.799191 80.811352 84.203434 106.503430 101.594525 69.253442 97.107592 114.387535 109.407583 37.190353 68.861814 80.064937 114.442349 24.596074 31.805216 48.492748 55.372536 69.656760 80.916285 103.920184 106.735249 37.998745 83.698877 97.366150 108.583553 72.740774 96.830346 98.634155 91.499778 28.953296 54.757005 63.374179 80.538607 32.876097 60.740647 61.868733 74.235830 2 30 18.77593979 -1.427599228 9.831757789 0.03249196962 1 0.6880169132 -0.0377660634 -0.09044574025 374.3195441 0.1578452064 143.0142141 -1.085570623 -1.093712135 2 3 4 5 6 7 8 9 0.223886 -0.852040 0.437353 0.106014 0.128639 -0.051916 1.589682 0.993718 0.584097 0.624344 0.808881 0.796639 1.187878 0.818214 13.070702 13.104239 1.181136 25.020723 25.041991 0.749019 25.240609 25.264596 0.844822 32.007177 32.019620 0.438249 27.944727 27.962001 0.608379 53.106271 53.141730 1.248829 61.874783 61.903275 1.003487 68.228449 68.213681 -0.520111 27.944727 27.976236 1.109698 37.532709 37.570005 1.313527 53.106271 53.101331 -0.173972 61.874783 61.898254 0.826641 33.235626 33.259741 0.849302 38.421847 38.407632 -0.500611 59.412625 59.431750 0.673571 60.661422 60.678494 0.601288 13.070702 13.137797 1.181498 25.240609 25.287872 0.832279 32.007177 32.001305 -0.103406 33.235626 33.198605 -0.651922 27.944727 27.983438 0.681685 53.106271 53.132582 0.463338 61.874783 61.902133 0.481622 70.461848 70.487339 0.448883 27.944727 28.003613 1.036947 37.532709 37.607307 1.313635 53.106271 53.140925 0.610250 61.874783 61.950291 1.329663 25.020723 25.063930 0.760857 32.024303 32.043877 0.344695 33.235626 33.208497 -0.477731 47.189237 47.206110 0.297123 13.070702 25.240609 32.007177 41.761216 79.108991 81.591849 103.791709 103.330722 67.975601 100.096938 101.154153 128.242430 37.532709 67.512734 80.606955 114.107396 25.020723 32.024303 47.189237 54.257275 68.228449 78.756850 101.137399 103.481487 38.421847 86.063601 81.633884 120.134106 70.461848 84.575178 106.433843 96.961798 27.944727 53.106271 61.874783 80.612582 33.235626 59.412625 60.661422 73.524242 2 67 21.14397298 -1.238894832 9.439747355 0.0517766953 1 0.8583785306 -0.03683371639 -0.1011665016 62.42699646 0.2123650507 18.84721656 -1.205198517 -1.189366451 2 3 4 5 6 7 8 9 0.220942 -0.917026 0.333033 0.110884 0.103662 -0.032108 1.269714 0.892136 0.580782 0.602100 0.781764 0.774381 1.196887 0.794344 9.517227 9.552398 1.173647 23.486985 23.509532 0.752397 23.884527 23.909539 0.834654 30.165356 30.180935 0.519860 26.259424 26.275552 0.538207 49.430425 49.464037 1.121636 58.757190 58.785725 0.952210 65.740501 65.726191 -0.477526 26.259424 26.293503 1.137228 36.463616 36.510652 1.569607 49.430425 49.422398 -0.267865 58.757190 58.783103 0.864715 31.908413 31.934099 0.857146 37.487277 37.472946 -0.478213 56.486275 56.503441 0.572843 57.693985 57.715092 0.704367 9.517227 9.587597 1.174118 23.884527 23.934500 0.833789 30.165356 30.162884 -0.041241 31.908413 31.870837 -0.626950 26.259424 26.298817 0.657287 49.430425 49.452951 0.375850 58.757190 58.783880 0.445319 66.406828 66.438000 0.520093 26.259424 26.320485 1.018811 36.463616 36.557683 1.569526 49.430425 49.459056 0.477718 58.757190 58.838362 1.354357 23.486985 23.532126 0.753182 30.200215 30.218562 0.306118 31.908413 31.886913 -0.358724 44.772548 44.802693 0.502968 9.517227 23.884527 30.165356 39.878090 76.198986 78.102206 100.326973 99.028735 65.474011 102.728420 103.468639 111.288057 36.463616 64.943153 80.497975 103.873083 23.486985 30.200215 44.772548 50.897303 65.740501 75.319568 97.842771 99.039964 37.487277 85.009097 77.574549 120.534143 66.406828 78.952526 94.067344 111.790050 26.259424 49.430425 58.757190 77.974068 31.908413 56.486275 57.693985 71.743824 2 38 25.27942199 -1.066638143 8.151888524 0.07642881742 1 0.9621379023 -0.04816088182 -0.1372380555 111.6269914 0.2076011633 22.36387504 -1.147318734 -1.185153687 2 3 4 5 6 7 8 9 0.242956 -0.871067 0.057396 0.129730 0.092410 -0.038558 1.467571 1.079757 0.619169 0.620222 0.821986 0.820398 1.235426 0.822813 8.937266 8.977813 1.284878 22.854333 22.877609 0.737577 23.770443 23.788045 0.557769 30.136790 30.181964 1.431507 24.386824 24.402108 0.484307 45.604414 45.630917 0.839837 54.487369 54.512072 0.782814 60.483655 60.481743 -0.060601 24.386824 24.417972 0.987013 34.963386 35.006233 1.357762 45.604414 45.602075 -0.074134 54.487369 54.503004 0.495482 31.033389 31.059471 0.826486 36.450189 36.435935 -0.451689 51.996964 52.017104 0.638208 54.251551 54.263710 0.385300 8.937266 9.018364 1.284941 23.770443 23.805636 0.557610 30.136790 30.123496 -0.210639 31.033389 30.996263 -0.588246 24.386824 24.423892 0.587313 45.604414 45.627389 0.364015 54.487369 54.506715 0.306540 61.287538 61.341314 0.852058 24.386824 24.442639 0.884351 34.963386 35.049082 1.357794 45.604414 45.629816 0.402473 54.487369 54.548336 0.965999 22.854333 22.900951 0.738634 30.432004 30.421453 -0.167173 31.033389 31.060342 0.427046 40.872948 40.854036 -0.299655 8.937266 23.770443 30.136790 36.842693 70.638454 71.516713 91.664745 89.375819 61.267385 97.984530 98.853802 96.712018 34.963386 60.498680 77.575073 79.010065 22.854333 30.432004 40.872948 47.354940 60.483655 69.713548 88.460310 90.390506 36.450189 77.512996 74.381120 107.627000 61.287538 76.542554 76.650027 112.242482 24.386824 45.604414 54.487369 69.739162 31.033389 51.996964 54.251551 66.689980 2 11 31.87016203 -1.117961513 6.617426049 0.1072401379 1 1.009994691 -0.00729168206 -0.1435818867 60.68327765 0.1625519907 9.60935071 -0.7883196908 -0.7342659374 2 3 4 5 6 7 8 9 0.302685 -0.738809 -0.335260 0.173065 0.079422 -0.058371 2.149276 1.640765 0.711792 0.715051 0.989383 0.978495 1.307684 0.959147 11.638391 11.678089 1.272231 28.580774 28.603828 0.738830 29.699697 29.695135 -0.146197 31.694031 31.726034 1.025623 22.471365 22.482008 0.341075 42.864923 42.884319 0.621607 53.725683 53.748356 0.726648 56.126554 56.125292 -0.040444 22.471365 22.497534 0.838667 33.457612 33.490048 1.039525 42.864923 42.865024 0.003243 53.725683 53.747341 0.694092 32.287836 32.307590 0.633073 36.405749 36.394481 -0.361132 48.358862 48.378809 0.639265 53.281059 53.276016 -0.161594 11.638391 11.717770 1.271970 29.699697 29.690804 -0.142496 31.694031 31.711866 0.285783 32.287836 32.321245 0.535338 22.471365 22.500185 0.461804 42.864923 42.885249 0.325708 53.725683 53.741396 0.251797 56.513814 56.556391 0.682259 22.471365 22.516162 0.717819 33.457612 33.522492 1.039635 42.864923 42.883668 0.300365 53.725683 53.799625 1.184855 28.580774 28.627392 0.747011 32.287836 32.224337 -1.017517 32.868793 32.931891 1.011074 34.152584 34.141041 -0.184965 11.638391 29.699697 31.694031 32.982767 65.645030 66.475977 82.872427 80.232474 57.726334 78.091137 104.596373 96.176378 33.457612 56.297918 71.775111 72.761789 28.580774 34.152584 32.868793 46.330040 56.126554 65.433721 78.634999 81.364261 36.405749 69.227065 72.673932 81.535085 56.513814 74.008639 72.951396 92.787734 22.471365 42.864923 53.725683 58.711788 32.287836 48.358862 53.281059 61.655646 2 11 49.89301563 -1.234769612 6.07368105 0.1453085056 1 1.24391 0.13023 -0.169091 43.0093 0.231558 6.79892 -0.526116 -0.515096 2 3 4 5 6 7 8 9 0.306867 -0.690667 -0.709571 0.200533 0.050126 -0.041225 1.979583 1.675570 0.736267 0.736583 1.027995 1.028129 1.331271 0.995635 12.080028 12.119168 1.167206 29.111051 29.127320 0.485167 29.798282 29.774422 -0.711520 31.119114 31.133813 0.438339 20.465635 20.474175 0.254692 39.659440 39.676480 0.508150 50.991592 50.988008 -0.106867 53.852191 53.852696 0.015071 20.465635 20.490638 0.745621 32.022469 32.058573 1.076658 39.659440 39.659425 -0.000452 50.991592 50.992027 0.012993 33.380803 33.399442 0.555853 37.183470 37.173228 -0.305401 46.308405 46.325295 0.503662 51.817462 51.814202 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