********* 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 42 criteria and tolerance 0.01. Overall scale from fitting lowest state to lattice value. Includes 1 nonstandard fit criteria (such as a specific lattice spacing). 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 0,14/2,6) ( 2 0,14/2,4) ( 2 0,22/2,4) ( 3 0,15/2,7) ( 3 0,15/2,5) ( 3 0,23/2,5) ( 4 0,14/2,8) ( 4 0,14/2,6) ( 4 0,22/2,6) . Roundness of winding using (n,K,p) = ( 2 2,12/2,8) ( 2 2,12/2,6) ( 2 2,20/2,6) with error 1; in G^2 N units. Heavy potential determined using (n,K,p,K_max) = ( 0 0,-20/2,2,3) ( 0 0,-20/2,4,3) ( 0 0,-20/2,2,4.5) ( 0 0,-32/2,2,3) ( 0 0,-32/2,2,4.5) ( 0 0,-60/2,2,3) ( 0 0,-60/2,2,4.5) , L = 3 4 6 (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) ( 1 0,-13/2,5,3) ( 1 0,-13/2,3,4.5) ( 1 0,-23/2,3,3) ( 1 0,-23/2,3,4.5) ( 1 0,-29/2,3,3) ( 1 0,-29/2,3,4.5) L=0 and error 0.1; ( 1 0,-13/2,3,3) ( 1 0,-13/2,5,3) ( 1 0,-13/2,3,4.5) ( 1 0,-23/2,3,3) ( 1 0,-23/2,3,4.5) ( 1 0,-29/2,3,3) ( 1 0,-29/2,3,4.5) L=2.5 and error 0.1; ( 1 0,-13/2,3,3) ( 1 0,-13/2,5,3) ( 1 0,-13/2,3,4.5) ( 1 0,-23/2,3,3) ( 1 0,-23/2,3,4.5) ( 1 0,-29/2,3,3) ( 1 0,-29/2,3,4.5) L=5 and error 0.1; ( 1 1,-20/2,2,3) ( 1 1,-20/2,4,3) ( 1 1,-20/2,2,4.5) ( 1 1,-30/2,2,3) ( 1 1,-44/2,2,4.5) ( 1 1,-60/2,2,3) ( 1 1,-60/2,2,4.5) L=0 and error 0.1; 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) (23/2,5) (11/2,7) (13/2,7) . 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, 4 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 21 102.8961942 -0.8890647396 7.62610075 0.03249196962 1 0.5604361586 -0.0827869489 -0.2428080622 10.61409467 0.1097280507 2.041015026 0.04151463554 0.3240308435 2 3 4 5 6 7 8 9 0.203216 -1.071085 1.183166 0.185896 0.129560 -0.156129 2.049525 0.702539 0.646173 0.723218 0.901824 0.883018 1.205512 1.231812 1.198661 1.001233 10.237256 10.304889 1.677018 10.477508 10.557164 1.975143 12.670000 12.663306 -0.165995 26.962540 26.913780 -1.209048 23.075941 23.111318 0.877220 45.811989 45.848194 0.897716 47.302091 47.339103 0.917748 54.774519 54.781122 0.163742 23.075941 23.095126 0.475725 32.620245 32.641153 0.518413 45.811989 45.842584 0.758628 47.302091 47.311898 0.243173 26.962540 26.990733 0.699080 33.718532 33.706676 -0.293976 48.855927 48.896001 0.993665 49.728676 49.724308 -0.108321 10.237256 10.374068 1.696187 12.670000 12.720620 0.627580 26.962540 26.880937 -1.011715 28.885633 28.811051 -0.924664 23.075941 23.122870 0.581827 45.811989 45.859950 0.594613 47.302091 47.349259 0.584786 62.866567 62.859879 -0.082915 23.075941 23.138211 0.772029 32.620245 32.662091 0.518804 45.811989 45.897528 1.060507 47.302091 47.348334 0.573317 10.477508 10.571219 1.161815 26.962540 27.006597 0.546213 30.638324 30.553868 -1.047083 30.944883 31.030095 1.056455 12.670000 10.237256 28.885633 31.720445 63.289423 65.069235 85.634934 85.271984 59.234584 81.122445 97.246296 94.377123 32.620245 58.350236 71.278401 93.598260 10.477508 30.638324 30.944883 43.446853 54.774519 63.196952 85.438839 87.999694 33.718532 75.918855 88.030532 82.174027 62.866567 80.022532 85.275039 72.613606 23.075941 45.811989 47.302091 65.762112 26.962540 49.728676 48.855927 57.917074 2 38 69.32168856 -0.9637941653 8.981591805 0.0517766953 1 0.8302797445 -0.09153679973 -0.1916247836 6.48815451 0.2521375707 1.177401624 -0.3596181343 0.3328854685 2 3 4 5 6 7 8 9 0.206798 -1.138710 1.210624 0.173016 0.152166 -0.171070 1.882576 0.667002 0.629024 0.816945 0.892750 0.944974 1.232696 1.242690 1.200783 1.121922 12.670000 12.719100 1.459161 14.696734 14.735831 1.161885 15.184297 15.227585 1.286427 28.746064 28.817099 2.111024 26.195428 26.224273 0.857223 53.215474 53.258986 1.293107 56.448933 56.494195 1.345095 66.496729 66.490534 -0.184079 26.195428 26.221553 0.776378 40.308150 40.345144 1.099385 53.215474 53.244990 0.877169 56.448933 56.468794 0.590226 31.542039 31.575170 0.984613 38.056311 38.041758 -0.432485 57.154666 57.194536 1.184871 57.738712 57.745496 0.201623 12.670000 12.768649 1.465832 15.184297 15.270053 1.274251 28.817217 28.869676 0.779491 31.542039 31.664599 1.821120 26.195428 26.229121 0.500644 53.215474 53.274483 0.876821 56.448933 56.490912 0.623759 72.604642 72.623550 0.280944 26.195428 26.271758 1.134186 40.308150 40.382145 1.099485 53.215474 53.302340 1.290742 56.448933 56.535011 1.279024 14.696734 14.775209 1.166055 28.746064 28.764725 0.277278 30.463667 30.667601 3.030247 31.542039 31.495796 -0.687124 12.670000 15.184297 28.817217 33.205774 73.785630 76.453618 102.359912 100.700278 66.899377 104.129083 104.971519 136.798837 40.308150 67.178505 89.355908 120.002323 14.696734 30.463667 28.746064 47.585346 66.496729 73.066262 103.769450 104.864317 38.056311 95.912376 86.843436 123.279706 72.604642 92.918615 111.542241 87.558946 26.195428 53.215474 56.448933 78.527917 31.542039 57.738712 57.154666 69.673637 2 85 41.68302799 -0.952849181 6.564221147 0.07642881742 1 0.8804752179 0.000677297323 -0.2530512908 15.49278694 0.1830641551 4.351784003 0.2121443504 0.08951585412 2 3 4 5 6 7 8 9 0.261320 -1.035531 0.731579 0.196077 0.114241 -0.145355 2.154665 1.146480 0.680689 0.728878 0.912854 0.899987 1.264196 1.270803 1.251296 1.014099 12.670000 12.717200 1.295447 21.670183 21.708148 1.041985 22.019939 22.051609 0.869191 28.777925 28.856759 2.163654 21.123828 21.142029 0.499528 44.427274 44.446421 0.525493 49.039305 49.075235 0.986144 55.134325 55.197224 1.726308 21.123828 21.148041 0.664547 32.008127 32.035038 0.738591 44.427274 44.442301 0.412423 49.039305 49.053833 0.398735 30.056988 30.082035 0.687435 35.180316 35.170793 -0.261354 50.335677 50.344587 0.244537 50.642599 50.665060 0.616459 12.670000 12.764421 1.295736 22.019939 22.082052 0.852374 29.943767 29.959541 0.216474 30.056988 30.041522 -0.212248 21.123828 21.154188 0.416628 44.427274 44.461918 0.475413 49.039305 49.068879 0.405844 58.327699 58.346897 0.263463 21.123828 21.178316 0.747730 32.008127 32.061969 0.738876 44.427274 44.460922 0.461752 49.039305 49.110241 0.973455 21.670183 21.746875 1.052441 28.777925 28.933584 2.136097 30.056988 30.069933 0.177635 32.382553 32.344568 -0.521263 12.670000 22.019939 29.943767 32.330585 63.825094 62.791014 86.011531 82.898218 57.740532 90.556718 94.181700 120.894872 32.008127 55.844752 74.318934 91.555685 21.670183 28.777925 32.382553 45.237997 55.134325 62.653074 83.335033 84.419136 35.180316 74.744720 71.819590 101.584862 58.327699 76.189624 77.013904 89.753318 21.123828 44.427274 49.039305 60.140638 30.056988 50.642599 50.335677 58.930105 2 49 40.83316387 -0.9290931832 6.059390174 0.1072401379 1 1.016609896 0.0683079228 -0.2376635647 66.53364902 0.1606733733 19.02497966 0.1102626769 -0.1027765444 2 3 4 5 6 7 8 9 0.301640 -1.003649 0.436832 0.203203 0.093234 -0.115173 2.231174 1.464077 0.709242 0.734869 0.918391 0.911362 1.289271 1.294545 1.278804 1.025115 12.670000 12.716710 1.365985 28.357760 28.390780 0.965644 28.519342 28.549338 0.877203 28.790166 28.812108 0.641674 20.400923 20.413826 0.377339 42.853165 42.869318 0.472380 52.175675 52.223688 1.404083 54.712906 54.707917 -0.145892 20.400923 20.427197 0.768355 31.169815 31.197354 0.805355 42.853165 42.861550 0.245227 52.175675 52.241650 1.929369 31.599207 31.620169 0.613037 35.679141 35.671286 -0.229731 48.475329 48.491214 0.464535 52.238318 52.241532 0.094007 12.670000 12.763412 1.365879 28.519342 28.518463 -0.012855 28.790166 28.833517 0.633880 31.599207 31.597416 -0.026186 20.400923 20.428771 0.407193 42.853165 42.881598 0.415754 52.175675 52.237354 0.901873 55.104383 55.063229 -0.601753 20.400923 20.451425 0.738439 31.169815 31.224908 0.805564 42.853165 42.873909 0.303320 52.175675 52.342477 2.438987 28.357760 28.424676 0.978440 30.396186 30.398054 0.027316 31.599207 31.593038 -0.090192 34.150210 34.146996 -0.046991 12.670000 28.790166 28.519342 34.173702 64.076198 61.978097 85.814189 80.416360 56.826707 94.784682 92.873353 116.325646 31.169815 54.404644 71.019410 76.813780 28.357760 30.396186 34.150210 46.072314 54.712906 62.675281 79.607244 83.104924 35.679141 71.530465 72.795266 99.729797 55.869238 76.150476 67.165994 98.823112 20.400923 42.853165 52.175675 55.104383 31.599207 48.475329 52.238318 58.296646