********* 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 10 136.5594262 -1.152315916 8.727313889 0.03249196962 1 0.4309730233 0.469792689 -0.475 50 -0.0008460879276 12.5 -0.7146898877 -0.7166763249 2 3 5 6 7 8 9 0.141043 -1.076480 1.091512 0.145267 0.158188 -0.159067 0.814576 0.188304 0.589942 0.613967 0.864649 0.921751 1.209358 0.797220 12.670000 12.739345 1.365738 27.179077 27.234113 1.083927 27.363581 27.436223 1.430674 34.225502 34.225306 -0.003867 20.919323 20.954323 0.689322 47.580077 47.600346 0.399196 54.756530 54.808885 1.031121 58.798784 58.811818 0.256698 20.919323 20.932132 0.252260 24.033420 24.054879 0.422631 47.580077 47.611484 0.618565 54.756530 54.756026 -0.009941 35.973041 35.986988 0.274686 44.365977 44.383099 0.337207 53.462451 53.465211 0.054363 64.046934 64.043911 -0.059548 12.670000 12.808615 1.365003 27.179077 27.282080 1.014318 34.225502 34.222954 -0.025090 35.973041 35.822006 -1.487301 20.919323 20.974453 0.542881 47.580077 47.628308 0.474952 54.756530 54.801179 0.439678 63.771373 63.835223 0.628760 20.919323 20.959851 0.399097 24.033420 24.076349 0.422742 47.580077 47.635011 0.540960 54.756530 54.815706 0.582728 27.363581 27.516062 1.501550 35.618639 35.612123 -0.064175 35.973041 35.986988 0.137343 51.340395 53.253616 18.840303 12.670000 27.179077 34.225502 38.436562 73.847658 72.024835 101.651015 96.012220 71.278925 113.558042 136.149975 117.503786 24.033420 63.616893 70.358633 104.790358 27.363581 35.618639 53.149358 51.340395 58.798784 74.651915 92.363577 99.956780 44.365977 86.003456 95.598550 113.763199 63.771373 95.925417 93.148665 83.293616 20.919323 47.580077 54.756530 71.224557 35.973041 53.462451 64.046934 67.463814 1 45 41.44301214 -1.113090415 8.37187796 0.03249196962 1 0.5506143922 0.3194596056 -0.425 87.14817411 0.0899903302 4.125946693 -0.8824863114 -0.9069688574 2 3 5 6 7 8 9 0.150305 -1.034738 0.899674 0.126566 0.178951 -0.175513 0.977839 0.280158 0.586286 0.561088 0.827214 0.834919 1.214034 0.721669 12.670000 12.739084 1.390898 22.487484 22.546696 1.192136 23.270929 23.326901 1.126900 33.707593 33.779627 1.450275 21.058608 21.093178 0.696003 46.926581 46.951732 0.506370 52.656358 52.710340 1.086832 58.547077 58.559663 0.253404 21.058608 21.077519 0.380736 27.186185 27.212110 0.521964 46.926581 46.961677 0.706587 52.656358 52.662615 0.125957 33.981636 34.004568 0.461705 42.200447 42.205916 0.110104 54.092422 54.108832 0.330380 61.219370 61.223890 0.091002 12.670000 12.808151 1.390718 23.270929 23.381989 1.118008 33.707593 33.705674 -0.019322 33.981636 33.902483 -0.796810 21.058608 21.109896 0.516300 46.926581 46.978703 0.524691 52.656358 52.710002 0.540009 63.741478 63.873533 1.329354 21.058608 21.114342 0.561049 27.186185 27.238060 0.522209 46.926581 46.994699 0.685719 52.656358 52.723279 0.673669 22.487484 22.606890 1.202018 33.981636 34.007229 0.257635 37.757045 37.756547 -0.005004 46.055129 46.141159 0.866035 12.670000 23.270929 33.707593 40.852737 70.765427 70.391319 97.696156 95.564458 68.337898 104.574791 123.837750 116.474263 27.186185 63.452470 70.793226 103.015037 22.487484 37.757045 46.055129 50.659095 58.547077 71.198566 91.045100 97.207436 42.200447 83.513490 101.406830 98.672919 63.741478 92.571644 91.030933 81.822510 21.058608 46.926581 52.656358 69.538945 33.981636 54.092422 61.219370 64.241204 1 68 35.81391827 -1.170022813 9.019038966 0.03249196962 1 0.6455539646 0.3131995403 -0.375 68.61336393 0.1567796544 25.17457961 -1.01853936 -0.9566279809 2 3 5 6 7 8 9 0.145238 -1.084437 0.969879 0.117321 0.181814 -0.176289 0.749615 0.198701 0.567588 0.556015 0.798290 0.801700 1.201207 0.715830 12.670000 12.738590 1.437553 24.507797 24.552536 0.937672 24.526642 24.586656 1.257802 35.129089 35.166481 0.783675 21.711749 21.744249 0.681155 48.714801 48.746645 0.667387 55.552853 55.604378 1.079898 62.735277 62.745706 0.218571 21.711749 21.734939 0.486021 28.745140 28.779380 0.717627 48.714801 48.748780 0.712145 55.552853 55.563482 0.222763 35.129089 35.157242 0.590052 43.084125 43.087621 0.073264 57.099601 57.115946 0.342553 63.852186 63.863757 0.242504 12.670000 12.807199 1.437742 24.507797 24.625476 1.233184 35.129089 35.050412 -0.824476 35.156968 35.176208 0.201617 21.711749 21.760523 0.511108 48.714801 48.769739 0.575710 55.552853 55.606519 0.562380 66.812198 66.883380 0.745936 21.711749 21.774437 0.656923 28.745140 28.813641 0.717835 48.714801 48.791259 0.801220 55.552853 55.623393 0.739210 24.526642 24.619275 0.970728 35.129089 35.153921 0.260220 37.754852 37.882529 1.337958 46.577396 46.532363 -0.471912 12.670000 24.507797 35.156968 44.476654 74.293647 74.790308 103.741565 102.101661 70.741015 111.204955 132.121387 124.689868 28.745140 66.331701 76.341443 111.622984 24.526642 37.754852 46.577396 52.852278 62.735277 74.522024 97.004542 103.164475 43.084125 87.992184 103.119151 111.113588 66.812198 93.791578 102.186635 86.661901 21.711749 48.714801 55.552853 74.534576 35.129089 57.099601 63.852186 67.475456 2 29 42.9818683 -1.141218602 8.01669633 0.03249196962 1 0.597376198 0.2378927919 -0.325 71.60736677 0.0909939794 2.673152835 -0.8097718598 -0.7947335512 2 3 5 6 7 8 9 0.180629 -1.002679 0.798888 0.132408 0.181372 -0.183593 1.157164 0.542218 0.611422 0.603760 0.876705 0.881174 1.215314 0.781266 12.670000 12.732922 1.457823 24.449097 24.492295 1.000860 25.559332 25.596209 0.854390 33.224318 33.527413 7.022345 21.325171 21.352276 0.627990 46.443135 46.468569 0.589271 53.407422 53.451880 1.030057 58.792508 58.799050 0.151584 21.325171 21.348963 0.551235 28.129598 28.156405 0.621101 46.443135 46.468554 0.588923 53.407422 53.415761 0.193224 33.496597 33.521334 0.573116 40.117602 40.116690 -0.021129 53.279247 53.298774 0.452421 59.852855 59.858186 0.123524 12.670000 12.795830 1.457667 25.559332 25.631748 0.838889 33.224318 33.234764 0.121007 33.496597 33.459897 -0.425148 21.325171 21.371325 0.534667 46.443135 46.490660 0.550543 53.407422 53.445894 0.445675 62.590147 62.633207 0.498822 21.325171 21.380850 0.645003 28.129598 28.183234 0.621340 46.443135 46.497203 0.626344 53.407422 53.474489 0.776939 24.449097 24.536978 1.018048 33.496597 33.520672 0.278894 37.257512 37.254010 -0.040567 42.706345 42.673458 -0.380979 12.670000 25.559332 33.224318 42.737862 70.578305 69.422842 96.366308 93.599302 66.726929 97.322915 114.130581 117.128343 28.129598 61.736148 70.524514 98.641439 24.449097 37.257512 42.706345 50.509218 58.792508 70.198706 88.783774 94.980257 40.117602 80.371027 97.598171 93.936528 62.590147 89.051769 88.040001 80.085862 21.325171 46.443135 53.407422 67.684600 33.496597 53.279247 59.852855 63.635230 1 66 31.42741616 -1.063787043 8.137560467 0.03249196962 1 0.6407993467 0.05968507766 -0.275 136.0658844 0.1346302181 5.028945848 -0.7862748897 -0.8510520152 2 3 5 6 7 8 9 0.182167 -0.943066 0.664229 0.129696 0.187447 -0.187267 1.405259 0.597302 0.618350 0.608178 0.874747 0.877126 1.226304 0.786367 12.670000 12.728171 1.379719 19.222262 19.268414 1.094636 19.454617 19.495865 0.978314 31.374722 31.399112 0.578497 22.863626 22.894301 0.727563 47.905958 47.937143 0.739667 52.371993 52.419868 1.135514 59.491155 59.495861 0.111629 22.863626 22.889296 0.608866 31.819512 31.848175 0.679829 47.905958 47.935632 0.703828 52.371993 52.384776 0.303194 31.374722 31.405916 0.739874 38.460712 38.452477 -0.195325 55.348580 55.380814 0.764539 55.731226 55.738657 0.176233 12.670000 12.786362 1.379956 19.454617 19.544126 1.061500 31.374722 31.364048 -0.126593 34.455568 34.473506 0.212730 22.863626 22.910437 0.555147 47.905958 47.957056 0.605982 52.371993 52.420533 0.575641 65.035516 65.046831 0.134194 22.863626 22.929567 0.782006 31.819512 31.876869 0.680200 47.905958 47.976354 0.834838 52.371993 52.444578 0.860800 19.222262 19.307561 1.011574 31.374722 31.491617 1.386272 38.249693 38.197715 -0.616408 38.517601 38.438030 -0.943649 12.670000 19.454617 34.455568 37.476677 69.739706 69.992466 95.016566 89.772185 65.591357 91.623053 101.935190 125.628354 31.819512 62.454828 73.261146 101.198431 19.222262 38.517601 38.249693 48.327416 59.491155 69.352973 91.847625 94.676430 38.460712 82.686266 95.137262 91.266258 65.035516 87.866182 89.589498 81.613742 22.863626 47.905958 52.371993 69.283156 31.374722 55.348580 55.731226 64.151772 2 9 30.14334184 -1.046171964 8.699321025 0.03249196962 1 0.6725224968 0.006892573462 -0.225 50 0.1490088395 12.5 -0.83822421 -0.8727949056 2 3 5 6 7 8 9 0.187928 -0.953741 0.681369 0.123415 0.190810 -0.186415 1.389430 0.634854 0.613952 0.627844 0.865554 0.870208 1.221566 0.814066 12.670000 12.724761 1.432420 19.449319 19.480472 0.814891 19.472933 19.526374 1.397886 31.860992 31.808683 -1.368293 24.544505 24.573980 0.770994 50.517007 50.551769 0.909281 55.473717 55.521450 1.248577 63.114899 63.114421 -0.012501 24.544505 24.573900 0.768908 34.273590 34.306005 0.847891 50.517007 50.542444 0.665354 55.473717 55.491258 0.458827 31.860992 31.894652 0.880449 38.811229 38.799394 -0.309561 57.174399 57.185140 0.280944 58.096140 58.129509 0.872851 12.670000 12.779562 1.432939 19.472933 19.560631 1.146985 31.860992 31.763308 -1.277589 35.886859 35.983009 1.257528 24.544505 24.591364 0.612853 50.517007 50.567508 0.660484 55.473717 55.521457 0.624386 68.447482 68.464783 0.226270 24.544505 24.615449 0.927862 34.273590 34.338448 0.848259 50.517007 50.586688 0.911339 55.473717 55.556017 1.076385 19.449319 19.530770 1.065279 31.860992 31.925046 0.837739 38.459687 38.458299 -0.018157 38.525043 38.466900 -0.760441 12.670000 19.472933 35.886859 36.416957 73.521887 73.996989 100.312674 94.147823 67.569372 94.904421 105.527468 127.213277 34.273590 65.232633 77.657812 107.890537 19.449319 38.525043 38.459687 50.024719 63.114899 72.877469 97.922308 99.783489 38.811229 87.326919 99.370000 95.805922 68.447482 92.438747 94.485211 85.905491 24.544505 50.517007 55.473717 74.156163 31.860992 58.096140 57.174399 67.712258 1 26 24.68037107 -1.060950488 8.729257993 0.03249196962 1 0.6831140924 -0.02722676737 -0.175 520.8510776 0.151390763 185.9427369 -0.8582897103 -0.843294424 2 3 5 6 7 8 9 0.202143 -0.946615 0.669576 0.120646 0.194143 -0.189194 1.463779 0.754227 0.618067 0.639159 0.875317 0.869905 1.220901 0.829684 12.670000 12.716142 1.302732 20.375565 20.420894 1.279777 20.452096 20.476235 0.681528 31.289235 31.249166 -1.131271 25.022595 25.047338 0.698583 50.836294 50.870051 0.953071 56.531271 56.575592 1.251310 63.646163 63.638800 -0.207884 25.022595 25.053660 0.877056 34.801214 34.833557 0.913140 50.836294 50.851857 0.439393 56.531271 56.553537 0.628614 31.289235 31.320363 0.878824 37.457152 37.443579 -0.383197 56.817480 56.830923 0.379551 57.740600 57.770060 0.831756 12.670000 12.762323 1.303272 20.375565 20.449617 1.045362 31.289235 31.226940 -0.879388 32.582095 32.551693 -0.429179 25.022595 25.065448 0.604939 50.836294 50.879151 0.604994 56.531271 56.573450 0.595415 68.100836 68.126964 0.368837 25.022595 25.091405 0.971351 34.801214 34.865921 0.913444 50.836294 50.891911 0.785112 56.531271 56.621345 1.271523 20.452096 20.516935 0.915301 31.289235 31.334912 0.644801 33.084322 32.994522 -1.267662 42.511406 42.552307 0.577381 12.670000 20.375565 32.582095 37.713141 73.999473 74.418646 100.788803 95.247907 66.140594 94.025902 104.997682 121.323135 34.801214 64.620076 78.032561 107.955729 20.452096 33.084322 42.511406 50.224266 63.646163 73.188281 98.393382 100.068995 37.457152 86.848667 95.494132 98.627479 68.100836 92.655738 94.020586 84.692276 25.022595 50.836294 56.531271 74.712335 31.289235 57.740600 56.817480 67.763035 2 18 23.29856061 -1.03043144 9.704253672 0.03249196962 1 0.7022239622 -0.05349352088 -0.125 338.5193033 0.1518609798 121.5598802 -0.9231638571 -0.8500480182 2 3 5 6 7 8 9 0.213686 -0.973038 0.703223 0.113213 0.197389 -0.188192 1.412023 0.824356 0.614217 0.679299 0.869374 0.875765 1.212297 0.885951 12.670000 12.711534 1.378054 23.262766 23.289922 0.901003 23.407200 23.440671 1.110508 32.713262 32.749747 1.210520 27.769235 27.791102 0.725495 55.606193 55.642203 1.194764 63.195009 63.241615 1.546336 70.210775 70.192167 -0.617412 27.769235 27.806589 1.239331 38.076420 38.113503 1.230364 55.606193 55.608151 0.064944 63.195009 63.228634 1.115652 33.267758 33.297784 0.996199 39.259402 39.244439 -0.496441 62.068518 62.089006 0.679784 62.495259 62.520310 0.831160 12.670000 12.753104 1.378639 23.407200 23.471771 1.071186 32.713262 32.713315 0.000879 33.267758 33.205876 -1.026594 27.769235 27.813658 0.736938 55.606193 55.642200 0.597326 63.195009 63.235184 0.666488 73.806080 73.848985 0.711768 27.769235 27.843282 1.228383 38.076420 38.150600 1.230596 55.606193 55.646037 0.660976 63.195009 63.313315 1.962624 23.262766 23.319386 0.939299 32.783295 32.793135 0.163232 33.267758 33.245112 -0.375697 47.403286 47.425400 0.366843 12.670000 23.407200 32.713262 41.535981 81.953604 81.950564 111.817607 105.819601 70.746315 102.696896 119.368233 125.128354 38.076420 69.920154 85.060620 118.874985 23.262766 32.783295 47.403286 55.022615 70.210775 80.786923 108.450693 110.620040 39.259402 94.117556 100.828084 110.654780 73.806080 102.054992 102.482505 91.708489 27.769235 55.606193 63.195009 82.699247 33.267758 62.495259 62.068518 74.024568 2 10 22.86018478 -1.080448921 9.25400937 0.03249196962 1 0.6911455606 -0.0622511239 -0.075 50 0.1368180857 12.5 -0.9411083714 -0.8142441651 2 3 5 6 7 8 9 0.235992 -0.953568 0.667293 0.110819 0.204213 -0.197582 1.571955 1.017781 0.623170 0.674156 0.886398 0.866906 1.215519 0.877678 12.670000 12.701114 1.087169 25.116185 25.134786 0.649936 25.838469 25.855169 0.583530 30.721563 30.716028 -0.193375 27.126834 27.141844 0.524486 54.013476 54.045560 1.121096 62.907527 62.949011 1.449538 68.277800 68.249103 -1.002710 27.126834 27.163672 1.287175 36.833445 36.866491 1.154674 54.013476 53.999795 -0.478038 62.907527 62.948060 1.416313 32.291386 32.311981 0.719611 36.989819 36.978276 -0.403308 59.741223 59.753891 0.442656 61.052388 61.077359 0.872567 12.670000 12.732246 1.087499 25.838469 25.871853 0.583247 30.721563 30.724702 0.054849 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