********* 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) = (20/2,8) (20/2,6) (24/2,6) (30/2,6) . 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 0,20/2,5) ( 3 0,20/2,7) ( 3 0,26/2,5) ( 3 0,34/2,5) ( 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 0,20/2,3,4) ( 1 0,20/2,5,4) ( 1 0,20/2,3,3.5) ( 1 0,34/2,3,4) ( 1 0,34/2,3,5) ( 1 0,70/2,3,5) ( 1 0,70/2,3,6) L=1.265-0.964*m and error 0.1; ( 1 0,20/2,3,4) ( 1 0,20/2,5,4) ( 1 0,20/2,3,3.5) ( 1 0,34/2,3,4) ( 1 0,34/2,3,5) ( 1 0,70/2,3,5) ( 1 0,70/2,3,6) 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) = (14/2,3) (36/2,3) (46/2,3) (14/2,5) (30/2,5) (14/2,7) (18/2,7) . 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. 2 76 84.36014962 -0.25 12.51620498 0 1 -0.05048601685 0.02385601416 -0.08744399953 2.480633569 -0.08244018241 0.2142310866 -1.91852861 -2.88041274 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.174778 -0.064861 -0.377886 0.096886 -0.378047 0.718308 2.535163 1.286124 0.408030 0.276955 0.386865 0.425752 1.109029 0.435978 27.964384 27.991646 0.954202 33.878483 33.892729 0.498632 34.438055 34.427159 -0.381361 37.804083 37.804893 0.0283696 38.270743 38.287145 0.574074 66.310530 66.313604 0.107601 70.415591 70.416312 0.0252551 70.888705 70.898683 0.349219 34.216310 34.216085 -0.00787557 38.270743 38.271562 0.0286435 66.310530 66.309736 -0.0277822 70.415591 70.464708 1.71915 37.804083 37.804329 0.00863264 40.301114 40.300686 -0.0149993 66.524062 66.527652 0.125652 68.047427 68.043017 -0.154379 27.964384 28.018774 0.951849 34.438055 34.416899 -0.370244 37.804083 37.807030 0.0515775 40.217844 40.209877 -0.139433 38.270743 38.302541 0.556477 66.310530 66.312797 0.0396897 70.415591 70.418959 0.0589441 70.888705 70.899598 0.190632 34.216310 34.215847 -0.008106 38.270743 38.273152 0.0421608 66.310530 66.312769 0.0391913 70.415591 70.448273 0.571956 33.878483 33.905605 0.47464 37.804083 37.801984 -0.0367318 37.991731 38.040038 0.845388 43.861637 43.867990 0.111175 27.964384 34.438055 40.217844 41.619699 81.515865 89.617788 91.351715 107.039006 73.193795 80.005393 81.164997 86.397846 34.216310 70.537726 74.417426 77.914224 33.878483 37.991731 43.861637 67.266237 71.469762 78.600008 91.089313 106.579024 40.301114 77.144355 81.406303 85.428286 76.845684 82.055689 85.087020 89.568656 38.270743 66.310530 70.415591 70.888705 37.804083 66.524062 68.047427 73.044325 2 12 105.6009949 -0.25 12.51620498 0.001967542671 1 0.3909839522 -0.01250282378 -0.06421231123 353.2492529 0.07049127522 160.6273835 -0.7123520719 -0.6519355869 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.174778 -0.064861 -0.377886 0.096886 -0.378047 0.718308 2.535163 1.286124 0.408030 0.276955 0.386865 0.425752 1.109029 0.435978 27.964384 27.991646 0.954202 33.878483 33.892729 0.498632 34.438055 34.427159 -0.381361 37.804083 37.804893 0.0283696 38.270743 38.287145 0.574074 66.310530 66.313604 0.107601 70.415591 70.416312 0.0252551 70.888705 70.898683 0.349219 34.216310 34.216085 -0.00787557 38.270743 38.271562 0.0286435 66.310530 66.309736 -0.0277822 70.415591 70.464708 1.71915 37.804083 37.804329 0.00863264 40.301114 40.300686 -0.0149993 66.524062 66.527652 0.125652 68.047427 68.043017 -0.154379 27.964384 28.018774 0.951849 34.438055 34.416899 -0.370244 37.804083 37.807030 0.0515775 40.217844 40.209877 -0.139433 38.270743 38.302541 0.556477 66.310530 66.312797 0.0396897 70.415591 70.418959 0.0589441 70.888705 70.899598 0.190632 34.216310 34.215847 -0.008106 38.270743 38.273152 0.0421608 66.310530 66.312769 0.0391913 70.415591 70.448273 0.571956 33.878483 33.905605 0.47464 37.804083 37.801984 -0.0367318 37.991731 38.040038 0.845388 43.861637 43.867990 0.111175 27.964384 34.438055 40.217844 41.619699 81.515865 89.617788 91.351715 107.039006 73.193795 80.005393 81.164997 86.397846 34.216310 70.537726 74.417426 77.914224 33.878483 37.991731 43.861637 67.266237 71.469762 78.600008 91.089313 106.579024 40.301114 77.144355 81.406303 85.428286 76.845684 82.055689 85.087020 89.568656 38.270743 66.310530 70.415591 70.888705 37.804083 66.524062 68.047427 73.044325 2 12 194.6124487 -0.25 12.51620498 0.007919222016 1 0.5231479107 -0.03043728016 -0.06878036918 308.8254528 0.1179545436 136.0173874 -0.8333810675 -0.7597176587 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.174778 -0.064861 -0.377886 0.096886 -0.378047 0.718308 2.535163 1.286124 0.408030 0.276955 0.386865 0.425752 1.109029 0.435978 27.964384 27.991646 0.954202 33.878483 33.892729 0.498632 34.438055 34.427159 -0.381361 37.804083 37.804893 0.0283696 38.270743 38.287145 0.574074 66.310530 66.313604 0.107601 70.415591 70.416312 0.0252551 70.888705 70.898683 0.349219 34.216310 34.216085 -0.00787557 38.270743 38.271562 0.0286435 66.310530 66.309736 -0.0277822 70.415591 70.464708 1.71915 37.804083 37.804329 0.00863264 40.301114 40.300686 -0.0149993 66.524062 66.527652 0.125652 68.047427 68.043017 -0.154379 27.964384 28.018774 0.951849 34.438055 34.416899 -0.370244 37.804083 37.807030 0.0515775 40.217844 40.209877 -0.139433 38.270743 38.302541 0.556477 66.310530 66.312797 0.0396897 70.415591 70.418959 0.0589441 70.888705 70.899598 0.190632 34.216310 34.215847 -0.008106 38.270743 38.273152 0.0421608 66.310530 66.312769 0.0391913 70.415591 70.448273 0.571956 33.878483 33.905605 0.47464 37.804083 37.801984 -0.0367318 37.991731 38.040038 0.845388 43.861637 43.867990 0.111175 27.964384 34.438055 40.217844 41.619699 81.515865 89.617788 91.351715 107.039006 73.193795 80.005393 81.164997 86.397846 34.216310 70.537726 74.417426 77.914224 33.878483 37.991731 43.861637 67.266237 71.469762 78.600008 91.089313 106.579024 40.301114 77.144355 81.406303 85.428286 76.845684 82.055689 85.087020 89.568656 38.270743 66.310530 70.415591 70.888705 37.804083 66.524062 68.047427 73.044325 2 12 114.9288443 -0.25 12.51620498 0.01800590693 1 0.6004759605 -0.03103963355 -0.07736420642 1615.461127 0.1353960848 730.1603311 -0.8992109102 -0.8109590062 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.174778 -0.064861 -0.377886 0.096886 -0.378047 0.718308 2.535163 1.286124 0.408030 0.276955 0.386865 0.425752 1.109029 0.435978 27.964384 27.991646 0.954202 33.878483 33.892729 0.498632 34.438055 34.427159 -0.381361 37.804083 37.804893 0.0283696 38.270743 38.287145 0.574074 66.310530 66.313604 0.107601 70.415591 70.416312 0.0252551 70.888705 70.898683 0.349219 34.216310 34.216085 -0.00787557 38.270743 38.271562 0.0286435 66.310530 66.309736 -0.0277822 70.415591 70.464708 1.71915 37.804083 37.804329 0.00863264 40.301114 40.300686 -0.0149993 66.524062 66.527652 0.125652 68.047427 68.043017 -0.154379 27.964384 28.018774 0.951849 34.438055 34.416899 -0.370244 37.804083 37.807030 0.0515775 40.217844 40.209877 -0.139433 38.270743 38.302541 0.556477 66.310530 66.312797 0.0396897 70.415591 70.418959 0.0589441 70.888705 70.899598 0.190632 34.216310 34.215847 -0.008106 38.270743 38.273152 0.0421608 66.310530 66.312769 0.0391913 70.415591 70.448273 0.571956 33.878483 33.905605 0.47464 37.804083 37.801984 -0.0367318 37.991731 38.040038 0.845388 43.861637 43.867990 0.111175 27.964384 34.438055 40.217844 41.619699 81.515865 89.617788 91.351715 107.039006 73.193795 80.005393 81.164997 86.397846 34.216310 70.537726 74.417426 77.914224 33.878483 37.991731 43.861637 67.266237 71.469762 78.600008 91.089313 106.579024 40.301114 77.144355 81.406303 85.428286 76.845684 82.055689 85.087020 89.568656 38.270743 66.310530 70.415591 70.888705 37.804083 66.524062 68.047427 73.044325 2 56 30.99935177 -7.673516029 8.678759592 0.03249196962 1 0.9168912451 -0.01786345717 -0.1077112368 2903.678485 0.1708952772 -614.4995047 -1.766339593 -2.241450263 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.232117 -0.951506 0.472020 0.130508 -0.263195 0.535889 1.167438 0.964429 0.504869 0.424785 0.589112 0.614150 1.032273 0.599156 7.538327 7.564716 0.850568 21.931186 21.964164 1.06293 22.982648 23.017179 1.11299 28.627394 28.627990 0.019219 26.553182 26.560360 0.231346 40.204036 40.243401 1.26879 52.282258 52.274632 -0.245814 56.943553 56.947479 0.12654 26.553182 26.590724 1.21004 31.927134 31.952649 0.822421 40.204036 40.187236 -0.541505 52.282258 52.343575 1.97635 29.195137 29.226840 1.02184 34.475662 34.454865 -0.670329 45.860623 45.883538 0.738585 51.399160 51.425389 0.845432 7.538327 7.590932 0.847766 22.982648 23.053351 1.13945 28.803837 28.803427 -0.00661016 29.195137 29.182145 -0.20938 26.553182 26.590299 0.598177 40.204036 40.198649 -0.0868161 52.282258 52.267950 -0.230596 52.517383 52.591787 1.1991 26.553182 26.593410 0.648308 31.927134 31.990580 1.0225 40.204036 40.255242 0.825228 52.282258 52.415388 2.1455 21.931186 21.996007 1.04465 28.627394 28.636387 0.144931 29.195137 29.202680 0.121562 36.511913 36.538193 0.423517 7.538327 22.982648 28.803837 44.672382 64.571653 77.180883 75.314759 81.035251 52.764412 58.880213 77.214545 82.823420 31.927134 57.037607 61.119887 73.075446 21.931186 28.627394 36.511913 43.961859 56.943553 67.897273 84.582529 82.770233 34.475662 60.341128 67.445199 77.414297 52.517383 56.593704 77.116561 73.391542 26.553182 40.204036 52.282258 64.241138 29.195137 45.860623 51.399160 58.837501 2 56 27.27247306 -7.667556331 8.873869738 0.0517766953 1 0.8324909106 -0.03811118578 -0.08896850124 6053.93793 0.07863477069 2647.96996 -1.800863741 -2.308056378 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.267987 -0.685738 -0.112908 0.127663 -0.233661 0.469049 1.775889 1.444045 0.544868 0.467357 0.612953 0.634810 1.107815 0.667915 12.624188 12.651045 1.02189 29.349092 29.372938 0.90734 30.088468 30.108979 0.780442 34.484556 34.485390 0.0317243 30.043989 30.051417 0.282642 47.618846 47.650271 1.19573 59.973005 59.972909 -0.00365882 63.639940 63.638436 -0.0572491 30.043989 30.074490 1.16055 36.585369 36.609730 0.926932 47.618846 47.590354 -1.08407 59.973005 60.007452 1.3107 34.564206 34.589130 0.948342 38.686732 38.669005 -0.674479 52.854351 52.872765 0.700651 58.943718 58.932468 -0.428073 12.624188 12.677865 1.0212 30.088468 30.131718 0.822813 34.520675 34.514526 -0.116981 34.564206 34.555380 -0.167912 30.043989 30.077428 0.636172 47.618846 47.609717 -0.173674 59.973005 59.948594 -0.464415 62.274070 62.351161 1.46664 30.043989 30.082315 0.729152 36.585369 36.638348 1.00791 47.618846 47.634592 0.299581 59.973005 60.024513 0.97993 29.349092 29.394604 0.865861 34.484556 34.501431 0.321042 34.564206 34.549159 -0.286268 45.937495 45.923718 -0.262088 12.624188 30.088468 34.520675 49.229593 73.891576 80.668000 87.029661 92.369129 62.318424 66.730991 87.312928 91.144229 36.585369 62.941829 69.677762 80.177467 29.349092 34.484556 45.937495 50.540563 63.639940 76.604205 90.082339 92.965446 38.686732 68.697216 75.586663 87.499386 62.274070 65.871785 84.588627 83.931566 30.043989 47.618846 59.973005 71.927140 34.564206 52.854351 58.943718 68.483506 1 93 35.44936834 -7.667556331 8.873869738 0.07642881742 1 0.7916137285 -0.1179795174 -0.04460185423 160.6552891 0.06584087387 59.8051532 -2.154917946 -2.769467652 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.267987 -0.685738 -0.112908 0.127663 -0.233661 0.469049 1.775889 1.444045 0.544868 0.467357 0.612953 0.634810 1.107815 0.667915 12.624188 12.651045 1.02189 29.349092 29.372938 0.90734 30.088468 30.108979 0.780442 34.484556 34.485390 0.0317243 30.043989 30.051417 0.282642 47.618846 47.650271 1.19573 59.973005 59.972909 -0.00365882 63.639940 63.638436 -0.0572491 30.043989 30.074490 1.16055 36.585369 36.609730 0.926932 47.618846 47.590354 -1.08407 59.973005 60.007452 1.3107 34.564206 34.589130 0.948342 38.686732 38.669005 -0.674479 52.854351 52.872765 0.700651 58.943718 58.932468 -0.428073 12.624188 12.677865 1.0212 30.088468 30.131718 0.822813 34.520675 34.514526 -0.116981 34.564206 34.555380 -0.167912 30.043989 30.077428 0.636172 47.618846 47.609717 -0.173674 59.973005 59.948594 -0.464415 62.274070 62.351161 1.46664 30.043989 30.082315 0.729152 36.585369 36.638348 1.00791 47.618846 47.634592 0.299581 59.973005 60.024513 0.97993 29.349092 29.394604 0.865861 34.484556 34.501431 0.321042 34.564206 34.549159 -0.286268 45.937495 45.923718 -0.262088 12.624188 30.088468 34.520675 49.229593 73.891576 80.668000 87.029661 92.369129 62.318424 66.730991 87.312928 91.144229 36.585369 62.941829 69.677762 80.177467 29.349092 34.484556 45.937495 50.540563 63.639940 76.604205 90.082339 92.965446 38.686732 68.697216 75.586663 87.499386 62.274070 65.871785 84.588627 83.931566 30.043989 47.618846 59.973005 71.927140 34.564206 52.854351 58.943718 68.483506 2 12 83.46687884 -7.667556331 8.873869738 0.1072401379 1 1.009994691 -0.00729168206 -0.1435818867 60.68327765 0.1625519907 9.60935071 -0.7883196908 -0.7342659374 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.267987 -0.685738 -0.112908 0.127663 -0.233661 0.469049 1.775889 1.444045 0.544868 0.467357 0.612953 0.634810 1.107815 0.667915 12.624188 12.651045 1.02189 29.349092 29.372938 0.90734 30.088468 30.108979 0.780442 34.484556 34.485390 0.0317243 30.043989 30.051417 0.282642 47.618846 47.650271 1.19573 59.973005 59.972909 -0.00365882 63.639940 63.638436 -0.0572491 30.043989 30.074490 1.16055 36.585369 36.609730 0.926932 47.618846 47.590354 -1.08407 59.973005 60.007452 1.3107 34.564206 34.589130 0.948342 38.686732 38.669005 -0.674479 52.854351 52.872765 0.700651 58.943718 58.932468 -0.428073 12.624188 12.677865 1.0212 30.088468 30.131718 0.822813 34.520675 34.514526 -0.116981 34.564206 34.555380 -0.167912 30.043989 30.077428 0.636172 47.618846 47.609717 -0.173674 59.973005 59.948594 -0.464415 62.274070 62.351161 1.46664 30.043989 30.082315 0.729152 36.585369 36.638348 1.00791 47.618846 47.634592 0.299581 59.973005 60.024513 0.97993 29.349092 29.394604 0.865861 34.484556 34.501431 0.321042 34.564206 34.549159 -0.286268 45.937495 45.923718 -0.262088 12.624188 30.088468 34.520675 49.229593 73.891576 80.668000 87.029661 92.369129 62.318424 66.730991 87.312928 91.144229 36.585369 62.941829 69.677762 80.177467 29.349092 34.484556 45.937495 50.540563 63.639940 76.604205 90.082339 92.965446 38.686732 68.697216 75.586663 87.499386 62.274070 65.871785 84.588627 83.931566 30.043989 47.618846 59.973005 71.927140 34.564206 52.854351 58.943718 68.483506 2 57 82.8536894 -7.667556331 8.873869738 0.1453085056 1 1.290676899 0.2079933294 -0.1669680323 14.5899588 0.2554160961 2.889320866 1.425967844 -1.446613638 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.267987 -0.685738 -0.112908 0.127663 -0.233661 0.469049 1.775889 1.444045 0.544868 0.467357 0.612953 0.634810 1.107815 0.667915 12.624188 12.651045 1.02189 29.349092 29.372938 0.90734 30.088468 30.108979 0.780442 34.484556 34.485390 0.0317243 30.043989 30.051417 0.282642 47.618846 47.650271 1.19573 59.973005 59.972909 -0.00365882 63.639940 63.638436 -0.0572491 30.043989 30.074490 1.16055 36.585369 36.609730 0.926932 47.618846 47.590354 -1.08407 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