********* 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 11 98.99614655 -11.38740526 8.207602648 0 1 -0.3361550493 0.1809572375 -0.09942947991 5941.718319 -0.1257109718 2401.553189 -0.9856318668 -1.22262518 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.155408 -0.012240 -1.347726 0.144985 0.045459 -0.007673 1.309313 1.062555 0.561643 0.546940 0.883176 0.914725 1.184100 0.707206 10.884276 10.916972 0.667273 24.659197 24.567921 -1.86279 26.457648 26.457341 -0.00627409 27.336718 27.412437 1.54529 23.664938 23.676087 0.227535 37.281368 37.294910 0.276363 46.157702 46.165188 0.152779 46.991239 46.987968 -0.0667505 18.857483 18.859031 0.031593 23.664938 23.686161 0.433115 37.281368 37.265881 -0.31606 42.666265 42.654396 -0.242238 27.336718 27.344039 0.149413 29.154799 29.153192 -0.0327869 39.178051 39.189187 0.227272 45.746956 45.902589 3.17621 10.884276 10.949516 0.665723 24.659197 24.484930 -1.77826 27.336718 27.516862 1.83822 29.154799 29.151605 -0.0325865 23.664938 23.697649 0.333793 37.281368 37.279241 -0.0217047 42.666265 42.639806 -0.269997 46.157702 46.205195 0.484635 18.857483 18.860621 0.0320216 23.664938 23.696683 0.32393 37.281368 37.281253 -0.00117286 42.967358 42.951422 -0.16262 26.457648 26.456152 -0.0152661 27.336718 27.315321 -0.218344 34.141197 34.164390 0.23667 39.178051 39.183309 0.0536525 10.884276 24.659197 31.327871 36.990037 54.624731 63.439924 63.303170 65.631830 47.708222 52.682790 58.374455 69.104987 18.857483 42.967358 47.072292 54.411922 26.457648 34.141197 39.823928 43.537365 46.991239 53.175372 64.285062 68.381625 29.154799 46.506965 62.463854 64.396831 42.666265 55.827029 56.485066 57.714650 23.664938 37.281368 46.157702 50.844305 27.336718 39.178051 45.746956 49.535106 2 12 126.4499334 -11.38740526 8.207602648 0.001967542671 1 -0.0112217476 0.1022615784 -0.08665950019 5941.718319 -0.05099644467 2401.553189 -1.293279512 -1.577192798 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.155408 -0.012240 -1.347726 0.144985 0.045459 -0.007673 1.309313 1.062555 0.561643 0.546940 0.883176 0.914725 1.184100 0.707206 10.884276 10.916972 0.667273 24.659197 24.567921 -1.86279 26.457648 26.457341 -0.00627409 27.336718 27.412437 1.54529 23.664938 23.676087 0.227535 37.281368 37.294910 0.276363 46.157702 46.165188 0.152779 46.991239 46.987968 -0.0667505 18.857483 18.859031 0.031593 23.664938 23.686161 0.433115 37.281368 37.265881 -0.31606 42.666265 42.654396 -0.242238 27.336718 27.344039 0.149413 29.154799 29.153192 -0.0327869 39.178051 39.189187 0.227272 45.746956 45.902589 3.17621 10.884276 10.949516 0.665723 24.659197 24.484930 -1.77826 27.336718 27.516862 1.83822 29.154799 29.151605 -0.0325865 23.664938 23.697649 0.333793 37.281368 37.279241 -0.0217047 42.666265 42.639806 -0.269997 46.157702 46.205195 0.484635 18.857483 18.860621 0.0320216 23.664938 23.696683 0.32393 37.281368 37.281253 -0.00117286 42.967358 42.951422 -0.16262 26.457648 26.456152 -0.0152661 27.336718 27.315321 -0.218344 34.141197 34.164390 0.23667 39.178051 39.183309 0.0536525 10.884276 24.659197 31.327871 36.990037 54.624731 63.439924 63.303170 65.631830 47.708222 52.682790 58.374455 69.104987 18.857483 42.967358 47.072292 54.411922 26.457648 34.141197 39.823928 43.537365 46.991239 53.175372 64.285062 68.381625 29.154799 46.506965 62.463854 64.396831 42.666265 55.827029 56.485066 57.714650 23.664938 37.281368 46.157702 50.844305 27.336718 39.178051 45.746956 49.535106 2 12 77.2604158 -0.25 8.349449522 0.007919222016 1 0.270510428 0.03648985991 -0.08089210899 5941.718319 0.01046974966 2401.553189 -1.52887185 -1.86439673 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.189700 -0.066619 -0.555551 0.128522 -0.213673 0.475846 2.366679 1.381537 0.525897 0.402134 0.687129 0.631510 1.072951 0.539826 20.247291 20.262010 0.373002 26.047468 26.054805 0.185938 26.065998 26.075764 0.247491 28.725042 28.700457 -0.623039 26.254282 26.262769 0.215081 44.805277 44.822188 0.428552 49.730652 49.725543 -0.12946 51.963013 51.965019 0.0508352 26.254282 26.304717 1.27815 27.522313 27.481075 -1.04505 44.805277 44.802998 -0.0577653 49.730652 49.714082 -0.419907 28.725042 28.730876 0.147865 30.517729 30.513239 -0.113799 46.903418 46.913045 0.243973 49.577358 49.575744 -0.0409115 20.247291 20.276698 0.372618 26.065998 26.083014 0.215606 28.725042 28.686722 -0.485547 30.517729 30.508204 -0.120698 26.254282 26.271277 0.215348 44.805277 44.810652 0.068097 49.730652 49.737457 0.086227 53.607299 53.616182 0.112557 26.254282 26.353069 1.25174 27.522313 27.441848 -1.01958 44.805277 44.829186 0.302947 49.730652 49.677646 -0.671638 26.047468 26.064622 0.217354 28.725042 28.726273 0.0156015 30.987331 30.973530 -0.174868 46.663405 46.522376 -1.78699 20.247291 26.065998 30.986770 34.034524 61.014257 62.838196 66.132422 76.481300 52.463120 55.070378 63.290617 66.608207 27.522313 51.004071 54.465433 63.412398 26.047468 30.987331 46.663405 50.363441 51.963013 62.113221 63.820792 76.538182 30.517729 55.336311 62.969885 67.041388 53.607299 61.145791 63.435166 60.521250 26.254282 44.805277 49.730652 56.224634 28.725042 46.903418 49.577358 53.061236 2 12 189.5893038 -0.25 8.349449522 0.01800590693 1 0.5095713065 -0.01640064532 -0.08229097655 5941.718319 0.05869415654 2401.553189 -1.691827089 -2.084111813 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.189700 -0.066619 -0.555551 0.128522 -0.213673 0.475846 2.366679 1.381537 0.525897 0.402134 0.687129 0.631510 1.072951 0.539826 20.247291 20.262010 0.373002 26.047468 26.054805 0.185938 26.065998 26.075764 0.247491 28.725042 28.700457 -0.623039 26.254282 26.262769 0.215081 44.805277 44.822188 0.428552 49.730652 49.725543 -0.12946 51.963013 51.965019 0.0508352 26.254282 26.304717 1.27815 27.522313 27.481075 -1.04505 44.805277 44.802998 -0.0577653 49.730652 49.714082 -0.419907 28.725042 28.730876 0.147865 30.517729 30.513239 -0.113799 46.903418 46.913045 0.243973 49.577358 49.575744 -0.0409115 20.247291 20.276698 0.372618 26.065998 26.083014 0.215606 28.725042 28.686722 -0.485547 30.517729 30.508204 -0.120698 26.254282 26.271277 0.215348 44.805277 44.810652 0.068097 49.730652 49.737457 0.086227 53.607299 53.616182 0.112557 26.254282 26.353069 1.25174 27.522313 27.441848 -1.01958 44.805277 44.829186 0.302947 49.730652 49.677646 -0.671638 26.047468 26.064622 0.217354 28.725042 28.726273 0.0156015 30.987331 30.973530 -0.174868 46.663405 46.522376 -1.78699 20.247291 26.065998 30.986770 34.034524 61.014257 62.838196 66.132422 76.481300 52.463120 55.070378 63.290617 66.608207 27.522313 51.004071 54.465433 63.412398 26.047468 30.987331 46.663405 50.363441 51.963013 62.113221 63.820792 76.538182 30.517729 55.336311 62.969885 67.041388 53.607299 61.145791 63.435166 60.521250 26.254282 44.805277 49.730652 56.224634 28.725042 46.903418 49.577358 53.061236 1 56 33.57804313 -7.684737254 9.802556427 0.03249196962 1 0.9390060253 -0.08900090298 -0.06240938859 9210111.122 0.2081072534 3826170.655 -1.982983021 -2.56772725 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.240698 -0.935222 0.476687 0.117103 -0.327739 0.634226 1.287977 1.049948 0.474734 0.378361 0.499693 0.530330 1.036718 0.561965 7.329615 7.351545 0.827886 21.376886 21.405192 1.06862 22.586160 22.603371 0.649755 27.372518 27.366042 -0.244476 30.116072 30.122178 0.230494 44.481966 44.528096 1.74149 58.555003 58.528445 -1.00257 63.223172 63.236090 0.487674 30.116072 30.147270 1.17774 37.416052 37.450049 1.28342 44.481966 44.467187 -0.557922 58.105597 58.105972 0.0141656 30.394066 30.420560 1.00017 35.982977 35.963047 -0.752399 49.588146 49.610051 0.826956 55.876182 55.878124 0.0733013 7.329615 7.373111 0.821015 22.586160 22.622556 0.687008 27.395776 27.405184 0.177583 30.394066 30.410835 0.316535 30.116072 30.153159 0.700034 44.481966 44.477756 -0.0794705 58.105597 58.092941 -0.238888 58.555003 58.620528 1.23684 30.116072 30.149264 0.62652 37.416052 37.488832 1.37376 44.481966 44.549368 1.27226 58.555003 58.639215 1.58956 21.376886 21.432935 1.05797 27.372518 27.378745 0.117529 30.394066 30.406384 0.232511 36.210414 36.254525 0.832609 7.329615 22.586160 27.395776 51.050702 70.819897 85.722890 87.437948 89.014968 57.343628 62.126270 79.159848 89.991796 37.416052 62.708238 68.328584 82.313390 21.376886 27.372518 36.210414 48.499291 63.223172 74.923341 92.486879 94.102330 35.982977 66.624290 76.230678 84.019134 58.105597 61.945330 84.410030 81.335395 30.116072 44.481966 58.555003 70.209781 30.394066 49.588146 55.876182 62.437737 2 29 28.57602916 -8.079444341 8.048375532 0.0517766953 1 0.8261159086 -0.06615208202 -0.1125534693 1790847.499 0.05125040869 761558.3982 -1.576961645 -2.061058367 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.263033 -0.751853 -0.054634 0.139496 -0.190077 0.404185 1.623853 1.345584 0.564133 0.498839 0.675807 0.698263 1.101465 0.693476 9.113040 9.145005 1.08271 24.130681 24.153183 0.762188 25.044278 25.052432 0.27617 29.628792 29.624720 -0.137927 26.999831 27.008174 0.282613 42.158925 42.186747 0.942406 52.868604 52.873900 0.179381 56.061026 56.059532 -0.0506046 26.999831 27.035306 1.20162 31.993430 32.011379 0.607987 42.158925 42.133278 -0.868689 52.868604 52.906309 1.27714 29.628792 29.655241 0.895858 33.805962 33.788450 -0.593139 46.562256 46.582846 0.697412 51.945242 51.928709 -0.560002 9.113040 9.176955 1.08247 25.044278 25.063253 0.321358 29.628792 29.646460 0.299228 29.935963 29.915972 -0.338567 26.999831 27.035358 0.601681 42.158925 42.151036 -0.133608 52.868604 52.839023 -0.500985 55.172583 55.254432 1.38618 26.999831 27.043068 0.732268 31.993430 32.038307 0.76004 42.158925 42.171975 0.221027 52.868604 52.951591 1.40547 24.130681 24.172892 0.714886 29.628792 29.665824 0.627162 29.919080 29.883383 -0.604564 40.116567 40.117669 0.0186567 9.113040 25.044278 29.935963 44.306262 66.190562 71.440040 77.558507 81.544900 55.089214 59.189496 76.893280 80.065807 31.993430 55.918725 61.352702 71.469286 24.130681 29.919080 40.116567 45.607849 56.061026 68.555228 80.476214 83.281004 33.805962 60.126675 67.583052 77.270942 55.172583 58.616764 76.884412 73.848873 26.999831 42.158925 52.868604 63.954680 29.628792 46.562256 51.945242 60.044735 2 12 54.33801236 -8.079444341 8.048375532 0.07642881742 1 0.9584307248 -0.09282041651 -0.134250509 5941.718319 0.1184137027 2401.553189 -1.70808177 -2.308582939 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.263033 -0.751853 -0.054634 0.139496 -0.190077 0.404185 1.623853 1.345584 0.564133 0.498839 0.675807 0.698263 1.101465 0.693476 9.113040 9.145005 1.08271 24.130681 24.153183 0.762188 25.044278 25.052432 0.27617 29.628792 29.624720 -0.137927 26.999831 27.008174 0.282613 42.158925 42.186747 0.942406 52.868604 52.873900 0.179381 56.061026 56.059532 -0.0506046 26.999831 27.035306 1.20162 31.993430 32.011379 0.607987 42.158925 42.133278 -0.868689 52.868604 52.906309 1.27714 29.628792 29.655241 0.895858 33.805962 33.788450 -0.593139 46.562256 46.582846 0.697412 51.945242 51.928709 -0.560002 9.113040 9.176955 1.08247 25.044278 25.063253 0.321358 29.628792 29.646460 0.299228 29.935963 29.915972 -0.338567 26.999831 27.035358 0.601681 42.158925 42.151036 -0.133608 52.868604 52.839023 -0.500985 55.172583 55.254432 1.38618 26.999831 27.043068 0.732268 31.993430 32.038307 0.76004 42.158925 42.171975 0.221027 52.868604 52.951591 1.40547 24.130681 24.172892 0.714886 29.628792 29.665824 0.627162 29.919080 29.883383 -0.604564 40.116567 40.117669 0.0186567 9.113040 25.044278 29.935963 44.306262 66.190562 71.440040 77.558507 81.544900 55.089214 59.189496 76.893280 80.065807 31.993430 55.918725 61.352702 71.469286 24.130681 29.919080 40.116567 45.607849 56.061026 68.555228 80.476214 83.281004 33.805962 60.126675 67.583052 77.270942 55.172583 58.616764 76.884412 73.848873 26.999831 42.158925 52.868604 63.954680 29.628792 46.562256 51.945242 60.044735 2 12 86.70917599 -8.079444341 8.048375532 0.1072401379 1 1.007111734 -0.08692145748 -0.1704658318 5941.718319 0.1057822614 2401.553189 -1.53026267 -2.216352277 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.263033 -0.751853 -0.054634 0.139496 -0.190077 0.404185 1.623853 1.345584 0.564133 0.498839 0.675807 0.698263 1.101465 0.693476 9.113040 9.145005 1.08271 24.130681 24.153183 0.762188 25.044278 25.052432 0.27617 29.628792 29.624720 -0.137927 26.999831 27.008174 0.282613 42.158925 42.186747 0.942406 52.868604 52.873900 0.179381 56.061026 56.059532 -0.0506046 26.999831 27.035306 1.20162 31.993430 32.011379 0.607987 42.158925 42.133278 -0.868689 52.868604 52.906309 1.27714 29.628792 29.655241 0.895858 33.805962 33.788450 -0.593139 46.562256 46.582846 0.697412 51.945242 51.928709 -0.560002 9.113040 9.176955 1.08247 25.044278 25.063253 0.321358 29.628792 29.646460 0.299228 29.935963 29.915972 -0.338567 26.999831 27.035358 0.601681 42.158925 42.151036 -0.133608 52.868604 52.839023 -0.500985 55.172583 55.254432 1.38618 26.999831 27.043068 0.732268 31.993430 32.038307 0.76004 42.158925 42.171975 0.221027 52.868604 52.951591 1.40547 24.130681 24.172892 0.714886 29.628792 29.665824 0.627162 29.919080 29.883383 -0.604564 40.116567 40.117669 0.0186567 9.113040 25.044278 29.935963 44.306262 66.190562 71.440040 77.558507 81.544900 55.089214 59.189496 76.893280 80.065807 31.993430 55.918725 61.352702 71.469286 24.130681 29.919080 40.116567 45.607849 56.061026 68.555228 80.476214 83.281004 33.805962 60.126675 67.583052 77.270942 55.172583 58.616764 76.884412 73.848873 26.999831 42.158925 52.868604 63.954680 29.628792 46.562256 51.945242 60.044735 2 21 93.15694351 -7.787266281 5.060840922 0.1453085056 1 1.027018984 -0.06577009631 -0.2156762069 6722.356327 0.07236667129 2161.822876 -1.09477977 -1.996661964 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.388763 -0.508231 -0.667923 0.191331 -0.033235 0.089017 3.596487 2.518380 0.714169 0.621586 0.833236 0.899619 1.377750 0.840529 15.832650 15.862227 0.93105 26.300613 26.326112 0.802694 26.595400 26.604510 0.286795 31.724755 31.760319 1.11953 22.341355 22.345735 0.137892 39.487727 39.503986 0.511834 47.724978 47.732310 0.230806 50.347100 50.352162 0.159346 22.341355 22.342301 0.0297731 33.260621 33.286070 0.801139 39.487727 39.487863 0.00429011 47.724978 47.725207 0.00718768 31.795284 31.816665 0.673065 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