********* 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 67 129050.0286 -7.653910142 8.033177484 0 1 1.439902991 0.03123228722 -0.6301952747 720183.571 0.3227661065 566.148482 -2.438874517 -3.886929377 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.018801 -2.538259 1.143826 0.074834 -0.535469 0.924960 -2.881011 -2.244874 0.190127 0.141497 0.002873 0.030597 0.766951 0.174890 -28.165643 -28.051895 0.274871 -22.432754 -22.332459 0.242363 -19.961856 -19.867690 0.22755 -16.233836 -16.144229 0.216533 3.713438 3.723321 0.0238812 10.763217 10.869189 0.256081 17.670962 17.722471 0.12447 23.289599 24.271184 2.37199 3.713438 4.296253 1.40837 4.961766 4.674111 -0.695115 10.763217 13.014581 5.4404 16.706374 14.350115 -5.69388 0.487255 0.583257 0.231989 17.935414 18.466618 1.28365 18.401599 18.743917 0.827209 20.202469 19.214052 -2.3885 -28.165643 -27.938370 0.274601 -19.961856 -19.773872 0.22713 0.487255 1.805459 1.59271 11.782202 10.388685 -1.68371 3.713438 4.155828 0.534516 10.763217 12.603436 2.22344 16.706374 14.621700 -2.5188 17.670962 17.865802 0.235414 3.713438 4.283600 0.688896 4.961766 4.498734 -0.559457 10.763217 11.069929 0.370584 17.670962 17.834912 0.198091 -22.432754 -22.229356 0.245755 -16.233836 -16.056689 0.214037 0.487255 0.536459 0.0594507 7.325769 7.407996 0.0993509 -28.165643 -19.961856 11.782202 15.972130 34.811894 35.991339 48.333126 50.855967 20.202469 42.445912 52.219912 57.192206 4.961766 40.267630 45.939295 54.279918 -22.432754 -16.233836 7.325769 12.206718 23.289599 41.208374 50.787989 50.834424 17.935414 44.311552 45.985623 56.425413 16.706374 31.931334 51.294143 53.614811 3.713438 10.763217 17.670962 24.356263 0.487255 18.401599 20.735427 21.841223 2 31 174462.8063 -7.653910142 8.033177484 0.001967542671 1 1.455347131 -0.2519199721 -0.2661706673 15510.178 0.570474864 557.7090332 1.813417289 -3.649873009 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.018801 -2.538259 1.143826 0.074834 -0.535469 0.924960 -2.881011 -2.244874 0.190127 0.141497 0.002873 0.030597 0.766951 0.174890 -28.165643 -28.051895 0.274871 -22.432754 -22.332459 0.242363 -19.961856 -19.867690 0.22755 -16.233836 -16.144229 0.216533 3.713438 3.723321 0.0238812 10.763217 10.869189 0.256081 17.670962 17.722471 0.12447 23.289599 24.271184 2.37199 3.713438 4.296253 1.40837 4.961766 4.674111 -0.695115 10.763217 13.014581 5.4404 16.706374 14.350115 -5.69388 0.487255 0.583257 0.231989 17.935414 18.466618 1.28365 18.401599 18.743917 0.827209 20.202469 19.214052 -2.3885 -28.165643 -27.938370 0.274601 -19.961856 -19.773872 0.22713 0.487255 1.805459 1.59271 11.782202 10.388685 -1.68371 3.713438 4.155828 0.534516 10.763217 12.603436 2.22344 16.706374 14.621700 -2.5188 17.670962 17.865802 0.235414 3.713438 4.283600 0.688896 4.961766 4.498734 -0.559457 10.763217 11.069929 0.370584 17.670962 17.834912 0.198091 -22.432754 -22.229356 0.245755 -16.233836 -16.056689 0.214037 0.487255 0.536459 0.0594507 7.325769 7.407996 0.0993509 -28.165643 -19.961856 11.782202 15.972130 34.811894 35.991339 48.333126 50.855967 20.202469 42.445912 52.219912 57.192206 4.961766 40.267630 45.939295 54.279918 -22.432754 -16.233836 7.325769 12.206718 23.289599 41.208374 50.787989 50.834424 17.935414 44.311552 45.985623 56.425413 16.706374 31.931334 51.294143 53.614811 3.713438 10.763217 17.670962 24.356263 0.487255 18.401599 20.735427 21.841223 2 39 85.13831738 -7.697236436 5.29499186 0.007919222016 1 0.9926124593 0.01375246882 -0.1423871926 48009.56724 0.2460818136 508.8902036 0.4114783138 0.1212049822 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.182631 -1.324113 1.213844 0.217287 0.085894 -0.214639 0.297424 0.288663 0.653126 0.556219 1.201720 1.181211 0.927174 0.714169 -0.060052 -0.037663 0.346412 7.319698 7.350310 0.473648 8.943805 8.962718 0.292637 12.819226 12.841500 0.344629 13.591733 13.596071 0.0671283 19.281522 19.312089 0.472947 26.579213 26.575845 -0.0521073 29.675933 29.944336 4.15285 13.591733 13.655637 0.988749 15.276143 15.256176 -0.308937 19.281522 19.285320 0.0587596 24.454837 24.467108 0.189859 13.490433 13.516811 0.408121 17.859582 17.845178 -0.222863 22.847042 23.048393 3.11539 24.665580 24.496593 -2.61465 -0.060052 -0.015483 0.344795 8.943805 8.982584 0.300003 13.490433 13.505905 0.119695 13.679086 13.679040 -0.000358872 13.591733 13.621905 0.233422 19.281522 19.286778 0.0406636 24.454837 24.477969 0.178951 26.579213 26.597073 0.13817 13.591733 13.622149 0.235304 15.276143 15.312561 0.281745 19.281522 19.345448 0.494543 26.579213 27.303233 5.60118 7.319698 7.380629 0.471376 12.819226 12.863656 0.343718 13.490433 13.447445 -0.332568 13.804836 13.855823 0.394449 -0.060052 8.943805 13.679086 22.738379 33.549423 39.962169 42.841129 43.789727 24.665580 31.736654 40.966205 42.210913 15.276143 30.202232 31.777471 40.190419 7.319698 12.819226 13.804836 22.820642 29.675933 36.052065 43.882619 45.400872 17.859582 30.933319 37.122023 39.301560 24.454837 29.167378 40.601458 39.902386 13.591733 19.281522 26.579213 30.296775 13.490433 22.847042 27.095687 28.352542 2 30 342.0327874 -7.697236436 5.29499186 0.01800590693 1 0.401850008 -0.0187740809 0.8229904089 -138.7060685 0.5223551598 328.6857531 -1.771541775 -2.270905263 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.182631 -1.324113 1.213844 0.217287 0.085894 -0.214639 0.297424 0.288663 0.653126 0.556219 1.201720 1.181211 0.927174 0.714169 -0.060052 -0.037663 0.346412 7.319698 7.350310 0.473648 8.943805 8.962718 0.292637 12.819226 12.841500 0.344629 13.591733 13.596071 0.0671283 19.281522 19.312089 0.472947 26.579213 26.575845 -0.0521073 29.675933 29.944336 4.15285 13.591733 13.655637 0.988749 15.276143 15.256176 -0.308937 19.281522 19.285320 0.0587596 24.454837 24.467108 0.189859 13.490433 13.516811 0.408121 17.859582 17.845178 -0.222863 22.847042 23.048393 3.11539 24.665580 24.496593 -2.61465 -0.060052 -0.015483 0.344795 8.943805 8.982584 0.300003 13.490433 13.505905 0.119695 13.679086 13.679040 -0.000358872 13.591733 13.621905 0.233422 19.281522 19.286778 0.0406636 24.454837 24.477969 0.178951 26.579213 26.597073 0.13817 13.591733 13.622149 0.235304 15.276143 15.312561 0.281745 19.281522 19.345448 0.494543 26.579213 27.303233 5.60118 7.319698 7.380629 0.471376 12.819226 12.863656 0.343718 13.490433 13.447445 -0.332568 13.804836 13.855823 0.394449 -0.060052 8.943805 13.679086 22.738379 33.549423 39.962169 42.841129 43.789727 24.665580 31.736654 40.966205 42.210913 15.276143 30.202232 31.777471 40.190419 7.319698 12.819226 13.804836 22.820642 29.675933 36.052065 43.882619 45.400872 17.859582 30.933319 37.122023 39.301560 24.454837 29.167378 40.601458 39.902386 13.591733 19.281522 26.579213 30.296775 13.490433 22.847042 27.095687 28.352542 2 86 276.3578546 -7.697236436 5.29499186 0.03249196962 1 0.1897842884 0.3397511906 0.7625417719 -292.7073507 0.4198812424 235.5894858 -1.611412484 -2.266839374 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.182631 -1.324113 1.213844 0.217287 0.085894 -0.214639 0.297424 0.288663 0.653126 0.556219 1.201720 1.181211 0.927174 0.714169 -0.060052 -0.037663 0.346412 7.319698 7.350310 0.473648 8.943805 8.962718 0.292637 12.819226 12.841500 0.344629 13.591733 13.596071 0.0671283 19.281522 19.312089 0.472947 26.579213 26.575845 -0.0521073 29.675933 29.944336 4.15285 13.591733 13.655637 0.988749 15.276143 15.256176 -0.308937 19.281522 19.285320 0.0587596 24.454837 24.467108 0.189859 13.490433 13.516811 0.408121 17.859582 17.845178 -0.222863 22.847042 23.048393 3.11539 24.665580 24.496593 -2.61465 -0.060052 -0.015483 0.344795 8.943805 8.982584 0.300003 13.490433 13.505905 0.119695 13.679086 13.679040 -0.000358872 13.591733 13.621905 0.233422 19.281522 19.286778 0.0406636 24.454837 24.477969 0.178951 26.579213 26.597073 0.13817 13.591733 13.622149 0.235304 15.276143 15.312561 0.281745 19.281522 19.345448 0.494543 26.579213 27.303233 5.60118 7.319698 7.380629 0.471376 12.819226 12.863656 0.343718 13.490433 13.447445 -0.332568 13.804836 13.855823 0.394449 -0.060052 8.943805 13.679086 22.738379 33.549423 39.962169 42.841129 43.789727 24.665580 31.736654 40.966205 42.210913 15.276143 30.202232 31.777471 40.190419 7.319698 12.819226 13.804836 22.820642 29.675933 36.052065 43.882619 45.400872 17.859582 30.933319 37.122023 39.301560 24.454837 29.167378 40.601458 39.902386 13.591733 19.281522 26.579213 30.296775 13.490433 22.847042 27.095687 28.352542 2 67 274.8920663 -7.697236436 5.29499186 0.0517766953 1 0.5726567189 0.2513942609 0.5465241088 -65.50463303 0.3129831711 312.6325138 -1.490899146 -2.424670056 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.182631 -1.324113 1.213844 0.217287 0.085894 -0.214639 0.297424 0.288663 0.653126 0.556219 1.201720 1.181211 0.927174 0.714169 -0.060052 -0.037663 0.346412 7.319698 7.350310 0.473648 8.943805 8.962718 0.292637 12.819226 12.841500 0.344629 13.591733 13.596071 0.0671283 19.281522 19.312089 0.472947 26.579213 26.575845 -0.0521073 29.675933 29.944336 4.15285 13.591733 13.655637 0.988749 15.276143 15.256176 -0.308937 19.281522 19.285320 0.0587596 24.454837 24.467108 0.189859 13.490433 13.516811 0.408121 17.859582 17.845178 -0.222863 22.847042 23.048393 3.11539 24.665580 24.496593 -2.61465 -0.060052 -0.015483 0.344795 8.943805 8.982584 0.300003 13.490433 13.505905 0.119695 13.679086 13.679040 -0.000358872 13.591733 13.621905 0.233422 19.281522 19.286778 0.0406636 24.454837 24.477969 0.178951 26.579213 26.597073 0.13817 13.591733 13.622149 0.235304 15.276143 15.312561 0.281745 19.281522 19.345448 0.494543 26.579213 27.303233 5.60118 7.319698 7.380629 0.471376 12.819226 12.863656 0.343718 13.490433 13.447445 -0.332568 13.804836 13.855823 0.394449 -0.060052 8.943805 13.679086 22.738379 33.549423 39.962169 42.841129 43.789727 24.665580 31.736654 40.966205 42.210913 15.276143 30.202232 31.777471 40.190419 7.319698 12.819226 13.804836 22.820642 29.675933 36.052065 43.882619 45.400872 17.859582 30.933319 37.122023 39.301560 24.454837 29.167378 40.601458 39.902386 13.591733 19.281522 26.579213 30.296775 13.490433 22.847042 27.095687 28.352542 1 30 274.4598982 -7.697236436 5.29499186 0.07642881742 1 1.091530103 0.1562293758 0.06576769174 188.8592794 0.1941177919 447.4574011 -1.284179044 -2.458960355 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.182631 -1.324113 1.213844 0.217287 0.085894 -0.214639 0.297424 0.288663 0.653126 0.556219 1.201720 1.181211 0.927174 0.714169 -0.060052 -0.037663 0.346412 7.319698 7.350310 0.473648 8.943805 8.962718 0.292637 12.819226 12.841500 0.344629 13.591733 13.596071 0.0671283 19.281522 19.312089 0.472947 26.579213 26.575845 -0.0521073 29.675933 29.944336 4.15285 13.591733 13.655637 0.988749 15.276143 15.256176 -0.308937 19.281522 19.285320 0.0587596 24.454837 24.467108 0.189859 13.490433 13.516811 0.408121 17.859582 17.845178 -0.222863 22.847042 23.048393 3.11539 24.665580 24.496593 -2.61465 -0.060052 -0.015483 0.344795 8.943805 8.982584 0.300003 13.490433 13.505905 0.119695 13.679086 13.679040 -0.000358872 13.591733 13.621905 0.233422 19.281522 19.286778 0.0406636 24.454837 24.477969 0.178951 26.579213 26.597073 0.13817 13.591733 13.622149 0.235304 15.276143 15.312561 0.281745 19.281522 19.345448 0.494543 26.579213 27.303233 5.60118 7.319698 7.380629 0.471376 12.819226 12.863656 0.343718 13.490433 13.447445 -0.332568 13.804836 13.855823 0.394449 -0.060052 8.943805 13.679086 22.738379 33.549423 39.962169 42.841129 43.789727 24.665580 31.736654 40.966205 42.210913 15.276143 30.202232 31.777471 40.190419 7.319698 12.819226 13.804836 22.820642 29.675933 36.052065 43.882619 45.400872 17.859582 30.933319 37.122023 39.301560 24.454837 29.167378 40.601458 39.902386 13.591733 19.281522 26.579213 30.296775 13.490433 22.847042 27.095687 28.352542 2 30 276.2281288 -7.697236436 5.29499186 0.1072401379 1 1.217925551 -0.1432112643 -0.2392899627 671.1055108 0.02436495537 672.1077236 -1.026872398 -2.290829313 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.182631 -1.324113 1.213844 0.217287 0.085894 -0.214639 0.297424 0.288663 0.653126 0.556219 1.201720 1.181211 0.927174 0.714169 -0.060052 -0.037663 0.346412 7.319698 7.350310 0.473648 8.943805 8.962718 0.292637 12.819226 12.841500 0.344629 13.591733 13.596071 0.0671283 19.281522 19.312089 0.472947 26.579213 26.575845 -0.0521073 29.675933 29.944336 4.15285 13.591733 13.655637 0.988749 15.276143 15.256176 -0.308937 19.281522 19.285320 0.0587596 24.454837 24.467108 0.189859 13.490433 13.516811 0.408121 17.859582 17.845178 -0.222863 22.847042 23.048393 3.11539 24.665580 24.496593 -2.61465 -0.060052 -0.015483 0.344795 8.943805 8.982584 0.300003 13.490433 13.505905 0.119695 13.679086 13.679040 -0.000358872 13.591733 13.621905 0.233422 19.281522 19.286778 0.0406636 24.454837 24.477969 0.178951 26.579213 26.597073 0.13817 13.591733 13.622149 0.235304 15.276143 15.312561 0.281745 19.281522 19.345448 0.494543 26.579213 27.303233 5.60118 7.319698 7.380629 0.471376 12.819226 12.863656 0.343718 13.490433 13.447445 -0.332568 13.804836 13.855823 0.394449 -0.060052 8.943805 13.679086 22.738379 33.549423 39.962169 42.841129 43.789727 24.665580 31.736654 40.966205 42.210913 15.276143 30.202232 31.777471 40.190419 7.319698 12.819226 13.804836 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