********* 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:zeta 11:kappa_S(9) 12:kappa_S(10) 13:kappa_S(11) 14:kappa_A(12) 15:kappa_A(13) 16:kappa_A(14) 17:mu_F(15) 18:mu_F(16) 19:mu_F(17) 20:mu_0^2(18) 21:mu_0^2(19) 22:mu_0^2(20) 23:mu_1^2(21) 24:mu_1^2(22) 25:mu_1^2(23) 26:mu_2^2(24) 27:mu_2^2(25) 28:mu_2^2(26) 29:mu_3^2(27) 30:mu_3^2(28) 31:mu_3^2(29) Use chi^2 fit with 40 criteria and tolerance 0.01. Overall scale from minimizing chi^2. 1/K^2 term used in all extrapolations. 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) = (20/2,6) (20/2,8) (24/2,6) (28/2,6) (32/2,6) (40/2,6) . Winding potential using (n,K,p) = ( 2 0,20/2,6) ( 2 0,20/2,8) ( 2 0,24/2,6) ( 2 0,28/2,6) ( 2 0,32/2,6) ( 2 0,40/2,6) ( 3 0,20/2,5) ( 3 0,20/2,7) ( 3 0,24/2,5) ( 3 0,28/2,5) ( 3 0,32/2,5) ( 3 0,40/2,5) ( 4 0,20/2,6) ( 4 0,20/2,8) ( 4 0,24/2,6) ( 4 0,28/2,6) ( 4 0,32/2,6) ( 4 0,40/2,6) . Roundness of winding using (n,K,p) = ( 2 2,20/2,6) ( 2 2,20/2,8) ( 2 2,24/2,6) ( 2 2,28/2,6) ( 2 2,32/2,6) ( 2 2,40/2,6) 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 0,60/2,2,3.75) ( 0 0,60/2,2,4.25) ( 0 0,100/2,2,4) ( 0 0,100/2,2,4.5) , 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 0,30/2,3,4) ( 1 0,30/2,5,4) ( 1 0,30/2,3,3.5) ( 1 0,60/2,3,4) ( 1 0,60/2,3,5) ( 1 0,100/2,3,5) ( 1 0,100/2,3,6) L=1.265-0.964*m and error 0.1; ( 1 0,30/2,3,4) ( 1 0,30/2,5,4) ( 1 0,30/2,3,3.5) ( 1 0,60/2,3,4) ( 1 0,60/2,3,5) ( 1 0,100/2,3,5) ( 1 0,100/2,3,6) L=5.058-3.856*m and error 0.1; ( 1 1,30/2,2,5.5) ( 1 1,30/2,4,5.5) ( 1 1,30/2,2,5) ( 1 1,30/2,2,5.5) ( 1 1,30/2,2,6.5) ( 1 1,100/2,2,6) ( 1 1,100/2,2,7) L=0+0*m and error 0.2; all in G^2 N units. p-extrapolation using n=( 1 0) and (K,p) = (24/2,5) (24/2,7) (24/2,9) . Result format: Fit info, # steps, chi^2, and p damping, scale G^2 N/sigma. The 32 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 87.95156146 -2.87030271 9.133554618 0 1 -0.1975105279 0.188096898 -0.1366182272 4377.50438 -0.1172104237 1110.901646 -1.161077082 -1.469942568 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.158799 -0.150514 -0.686810 0.138749 -0.096311 0.286815 1.613013 1.034024 0.533219 0.512757 0.780523 0.814319 1.147404 0.673590 15.709558 15.744146 0.802659 27.072266 27.036460 -0.830928 30.022707 30.026320 0.0838578 32.514545 32.537452 0.531604 26.205657 26.220358 0.341157 44.702400 44.714097 0.271446 53.854473 53.875234 0.481779 55.213506 55.214382 0.0203169 22.020623 22.024127 0.0813369 26.205657 26.215517 0.228819 44.702400 44.705727 0.0772185 53.254497 53.251543 -0.0685603 32.514545 32.519802 0.121992 35.751617 35.750790 -0.019177 46.560298 46.568971 0.201271 55.825841 55.818095 -0.179764 15.709558 15.778563 0.800678 27.072266 27.002658 -0.807682 32.514545 32.576180 0.715169 35.751617 35.750122 -0.0173373 26.205657 26.240411 0.40326 44.702400 44.718346 0.185024 53.470097 53.427433 -0.495046 53.854473 53.894204 0.461007 22.020623 22.027670 0.0817744 26.205657 26.219860 0.164799 44.702400 44.716027 0.15812 53.254497 53.248634 -0.068031 30.022707 30.028785 0.0705279 32.514545 32.507856 -0.0776046 41.374432 41.374432 -7.13736e-06 46.560298 46.510554 -0.577188 15.709558 27.072266 36.381034 42.315905 66.490343 68.779589 72.068355 84.751992 61.682794 63.845180 71.179591 81.201401 22.020623 53.254497 56.209980 63.147224 30.022707 41.374432 48.629450 52.158793 55.213506 63.209092 71.970148 84.157254 35.751617 59.244025 75.440364 76.851896 53.470097 64.974536 62.576534 75.579433 26.205657 44.702400 53.854473 58.133208 32.514545 46.560298 55.825841 59.768331 2 40 85.77340744 -2.422003581 7.771672184 0.001967542671 1 0.4526749069 0.2600010452 -0.2221522829 516107.7222 -0.00473899851 -238814.8328 0.03660596652 0.2421620745 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.135232 -0.486746 -0.575492 0.152930 0.608708 -1.258932 0.621465 0.523170 0.680079 0.679047 1.261785 1.252115 0.991114 0.915330 7.959138 8.002434 0.728044 22.075973 22.095480 0.328016 22.683973 22.685473 0.0252147 27.495703 27.456292 -0.662716 20.227307 20.241245 0.234391 34.266648 34.290559 0.402074 43.369514 43.393810 0.408555 46.838470 46.842075 0.0606216 18.210316 18.205297 -0.084399 20.227307 20.274119 0.787176 34.266648 34.273596 0.11684 43.319569 43.293056 -0.445828 27.495703 27.515713 0.336483 32.404682 32.401954 -0.04586 38.447755 38.469957 0.373333 48.883725 48.937333 0.901436 7.959138 8.045702 0.72781 22.683973 22.679738 -0.0356102 27.495703 27.455716 -0.336199 31.558011 31.724593 1.40058 20.227307 20.266562 0.330054 34.266648 34.293977 0.229775 43.319569 43.271743 -0.402113 43.369514 43.441518 0.605403 18.210316 18.201279 -0.0759812 20.227307 20.308619 0.683661 34.266648 34.299745 0.278274 43.369514 43.971539 5.06171 22.075973 22.122408 0.390418 27.495703 27.497009 0.0109841 33.835834 33.822388 -0.113045 38.447755 38.712721 2.22778 7.959138 22.683973 31.558011 36.234459 59.468993 61.880196 57.197110 75.585690 51.220749 57.020179 69.889374 76.565016 18.210316 46.441816 49.169126 56.335162 22.075973 33.835834 38.879522 41.354716 46.838470 61.026347 60.397253 70.380009 32.404682 53.404539 57.305082 70.967843 43.319569 46.532021 67.408055 68.791848 20.227307 34.266648 43.369514 56.443580 27.495703 38.447755 48.883725 53.542667 2 30 107.011728 -2.999274011 5.23243201 0.007919222016 1 0.2915529634 0.06137030907 -0.1246642037 262620.6729 0.007896282012 -125436.2951 -1.287568599 -1.979697008 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.187844 -0.218903 -0.370936 0.136942 -0.145570 0.374172 2.133058 1.237482 0.504807 0.350846 0.614868 0.642411 1.070940 0.410289 11.598343 11.614217 0.249639 16.096500 16.110058 0.213209 16.204067 16.207757 0.0580411 18.882726 18.858437 -0.38197 16.074890 16.082142 0.11405 28.179613 28.192125 0.196766 31.797947 31.805572 0.119915 33.849861 33.850784 0.0145172 16.074890 16.170103 1.49733 17.340550 17.255521 -1.33717 28.179613 28.183609 0.0628373 31.797947 31.804902 0.109377 18.882726 18.889211 0.101984 20.928394 20.924455 -0.0619476 30.220863 30.230744 0.155395 32.700492 32.700565 0.00115716 11.598343 11.630058 0.249376 16.204067 16.219391 0.1205 18.882726 18.846064 -0.288276 20.928394 20.919677 -0.0685425 16.074890 16.089429 0.114322 28.179613 28.190648 0.08677 31.797947 31.810371 0.0976942 35.200537 35.203418 0.0226464 16.074890 16.250118 1.37783 17.340550 17.185622 -1.21821 28.179613 28.201401 0.17132 31.797947 31.814185 0.127682 16.096500 16.115622 0.150352 18.882726 18.884187 0.0114896 21.512409 21.500232 -0.0957507 28.639223 28.993566 2.78621 11.598343 16.204067 21.408886 22.579879 41.010535 41.555784 42.597013 51.381746 35.900067 36.872770 43.968155 48.308355 17.340550 34.259752 35.952731 43.805914 16.096500 21.512409 29.043878 28.639223 33.849861 42.148743 41.677592 51.798314 20.928394 37.369774 43.761783 46.378984 35.200537 37.617320 42.170807 45.147733 16.074890 28.179613 31.797947 37.649999 18.882726 30.220863 32.700492 35.578785 2 11 235.2777341 -2.749427294 0.5814634467 0.01800590693 1 0.4737611485 0.02953318691 -0.09962541523 4377.50438 0.06644441079 1110.901646 -1.635653399 -1.988847142 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.207525 -0.329256 -0.468895 0.122195 -0.230641 0.506968 1.887977 1.272334 0.516413 0.346599 0.620612 0.436603 1.076255 1.168475 1.103346 1.105004 0.00320223 1.793193 1.794228 0.0019984 1.799598 1.800890 0.00249396 2.116236 2.114260 -0.00381465 1.804593 1.805237 0.00124356 3.062836 3.064802 0.00379609 3.646263 3.646810 0.00105531 3.907096 3.907051 -8.62614e-05 1.804593 1.728229 -0.147436 2.090793 2.169364 0.151697 3.062836 3.062892 0.000108582 3.646263 3.648218 0.00377333 2.116236 2.117460 0.00236396 2.363968 2.363137 -0.00160476 3.380928 3.382312 0.00267226 3.665544 3.665884 0.000656354 1.103346 1.106666 0.00320532 1.799598 1.802112 0.00242624 2.116236 2.114111 -0.00205184 2.265514 2.264507 -0.000971847 1.804593 1.806277 0.00162539 3.062836 3.064102 0.00122274 3.646263 3.647609 0.00129937 4.024954 4.025951 0.000962557 1.804593 1.750161 -0.0525456 2.090793 2.149247 0.0564284 3.062836 3.065577 0.00264599 3.646263 3.649612 0.00323271 1.793193 1.795315 0.00204853 2.116236 2.116877 0.000618817 2.260313 2.259126 -0.00114617 3.049832 3.154690 0.101224 1.103346 1.799598 2.265514 2.804460 4.563145 5.219380 4.909065 5.698946 4.015616 4.137982 5.402725 5.480215 2.090793 3.929264 4.255074 5.108344 1.793193 2.260313 3.159579 3.049832 3.907096 4.705125 5.334557 5.954897 2.363968 4.335798 5.200497 4.926211 4.024954 4.053191 5.222604 5.304134 1.804593 3.062836 3.646263 4.566790 2.116236 3.380928 3.665544 4.229239 2 11 194.3598285 -2.534459085 4.147291177 0.03249196962 1 0.6461257957 -0.00338979826 -0.09776984643 4377.50438 0.1058364024 1110.901646 -1.709120459 -2.06538317 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.225930 -0.457713 -0.652176 0.122084 -0.218095 0.472337 1.653889 1.268203 0.526545 0.266614 0.614520 0.465054 1.095832 0.291683 6.419136 6.431611 0.187014 12.475313 12.485262 0.149161 12.616517 12.628391 0.178024 15.232571 15.234634 0.0309388 13.043001 13.047268 0.0639735 21.620994 21.636886 0.238265 26.784198 26.789296 0.0764356 28.786066 28.784880 -0.0177774 13.043001 13.025004 -0.269809 15.890923 15.932332 0.620801 21.620994 21.618776 -0.0332409 26.784198 26.805399 0.317849 15.232571 15.243719 0.16714 17.477017 17.469423 -0.11384 24.339408 24.350972 0.173374 26.593927 26.598930 0.0749915 6.419136 6.444143 0.187446 12.616517 12.640409 0.179095 15.232571 15.190682 -0.313997 15.670209 15.695779 0.191676 13.043001 13.057282 0.107055 21.620994 21.629471 0.0635433 26.784198 26.795520 0.084873 29.437683 28.507863 -6.96991 13.043001 13.011412 -0.236787 15.890923 15.963685 0.545417 21.620994 21.639523 0.138897 26.784198 26.822864 0.289843 12.475313 12.494834 0.146328 15.232571 15.292894 0.452181 15.628130 15.566921 -0.458818 21.521432 21.755544 1.7549 6.419136 12.616517 15.670209 20.604596 33.255596 35.200880 42.261718 41.610039 29.419592 30.619969 41.195192 42.619585 15.890923 29.194483 32.541304 37.138129 12.475313 15.628130 21.773304 21.521432 28.786066 33.998810 42.959311 40.963885 17.477017 32.807757 34.505066 41.137907 29.790728 29.437683 40.262541 39.837689 13.043001 21.620994 26.784198 33.728671 15.232571 24.339408 26.593927 32.048868 1 58 46.33943527 -2.585029871 11.12388405 0.0517766953 1 0.7160454212 -0.05872471784 -0.05024358428 2549633.693 0.1436478277 442080.2252 -2.074773831 -2.57669355 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.273459 -0.439091 -0.692756 0.101678 -0.257088 0.512414 2.240682 1.661986 0.520488 0.430554 0.516813 0.542809 1.161271 0.641656 21.790490 21.811273 1.01153 37.770774 37.789520 0.912395 37.931067 37.955717 1.19976 43.080387 43.068467 -0.580167 38.022399 38.029856 0.362916 64.198393 64.240693 2.05877 79.560368 79.561617 0.060766 84.477182 84.471926 -0.255815 38.022399 38.031753 0.45526 50.299644 50.348796 2.39228 64.198393 64.184842 -0.659582 79.560368 79.619398 2.87301 45.101553 45.121582 0.974793 50.319383 50.303592 -0.768544 71.025988 71.048577 1.09944 76.932985 76.940542 0.367775 21.790490 21.832215 1.01541 37.931067 37.980319 1.19857 43.080580 43.081276 0.0169518 45.101553 45.084221 -0.421803 38.022399 38.050720 0.689194 64.198393 64.214931 0.402447 79.560368 79.581013 0.502387 86.132477 86.030763 -2.47524 38.022399 38.028532 0.149239 50.299644 50.397406 2.37909 64.198393 64.238510 0.976259 79.560368 79.636929 1.86313 37.770774 37.807586 0.895851 43.080387 43.080694 0.00746328 45.101553 45.102076 0.0127088 57.552819 57.604223 1.25096 21.790490 37.931067 43.080580 56.302706 95.586949 104.625838 118.440493 125.855149 82.837240 92.816511 116.525042 127.936270 50.299644 84.103065 100.280423 109.019410 37.770774 43.080387 57.552819 69.641989 84.477182 97.938014 118.893902 120.638962 50.319383 99.765012 102.161711 113.850122 86.132477 90.964587 111.242588 115.942585 38.022399 64.198393 79.560368 94.660431 45.101553 71.025988 76.932985 94.390875 2 67 32.0961939 -2.640154481 11.18099712 0.07642881742 1 0.7507955792 -0.08032221076 -0.04336979498 1891118.956 0.1370251959 686354.6488 -2.129855211 -2.528319718 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.322389 -0.397237 -0.785295 0.101138 -0.217238 0.432756 2.914445 2.083713 0.570651 0.500066 0.578877 0.598929 1.240864 0.738990 28.422723 28.441531 1.08476 44.561233 44.581502 1.16902 44.650052 44.664890 0.855744 50.235622 50.234328 -0.0746604 41.878626 41.884708 0.350809 73.272717 73.312882 2.31648 89.701270 89.701290 0.00119837 94.411505 94.404878 -0.382172 41.878626 41.893801 0.875236 58.982052 59.021247 2.26054 73.272717 73.257041 -0.90407 89.701270 89.750277 2.82644 52.637233 52.654010 0.967571 57.597758 57.583936 -0.797124 80.291192 80.310363 1.10569 86.368741 86.375446 0.386696 28.422723 28.460506 1.08956 44.561233 44.601691 1.16669 50.248936 50.258817 0.284962 52.637233 52.616846 -0.587912 41.878626 41.901831 0.669189 73.272717 73.287994 0.440546 89.701270 89.719828 0.535156 93.577893 93.589296 0.328818 41.878626 41.897967 0.557743 58.982052 59.060699 2.26794 73.272717 73.305714 0.951549 89.701270 89.756988 1.60677 44.650052 44.679085 0.837219 50.235622 50.238172 0.0735268 52.637233 52.634964 -0.0654376 62.414089 62.382481 -0.911476 28.422723 44.561233 50.248936 60.043298 106.153521 114.965252 129.141585 144.521236 91.661581 109.304522 132.281217 145.379358 58.982052 93.599599 116.936585 120.584911 44.650052 50.235622 62.414089 77.775555 94.411505 108.444049 130.202640 131.846503 57.597758 115.965595 112.567768 120.523713 93.577893 110.049951 119.094713 133.755898 41.878626 73.272717 89.701270 104.282469 52.637233 80.291192 86.368741 104.068152 2 12 102.1413047 -2.456127017 5.68644574 0.1072401379 1 0.9978531898 -0.03487187311 -0.1290024477 4377.50438 0.1506395238 1110.901646 -1.637320694 -1.961756426 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.340019 -0.573735 -1.131722 0.145291 -0.089099 0.215620 2.558113 2.004951 0.646605 0.474531 0.758941 0.685908 1.287717 0.638192 12.907155 12.930585 0.72484 25.325298 25.343801 0.572414 25.673336 25.693381 0.620089 30.220371 30.607325 11.9708 21.867456 21.872216 0.147253 38.433547 38.453853 0.628178 48.611569 48.625447 0.429343 51.522402 51.518928 -0.107472 21.867456 21.878012 0.326573 31.811809 31.841648 0.923084 38.433547 38.429067 -0.138614 48.611569 48.634796 0.718573 30.220371 30.240023 0.607943 34.505830 34.491531 -0.442333 44.095592 44.113943 0.567703 48.368534 48.377615 0.280921 12.907155 12.954148 0.726889 25.673336 25.714287 0.633431 30.220371 30.199461 -0.32344 30.686922 30.681372 -0.0858457 21.867456 21.885612 0.280844 38.433547 38.445754 0.188816 48.611569 48.628749 0.26574 50.359915 50.361778 0.0288093 21.867456 21.880011 0.194207 31.811809 31.871690 0.926239 38.433547 38.452568 0.294209 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