******* Eigenvalues for the 3+1 transverse lattice ******* Couplings: m^2, G^2 N, t/a^2, la_1/a^2, la_2/a^2 0 1 2 3 4 la_3/a^2, la_4/a^2, la_5/a^2, tau 5 6 7 8 Use chi^2 fit with 39 criteria and tolerance 0.01. Overall scale from minimizing chi^2. Parity doublets (o,multi,state) with error for difference over average. ( 1, 5,0) and ( 1, 6,0), error 0.5 (-1, 5,0) and (-1, 6,0), error 0.5 ( 1, 7,0) and (-1, 4,0), error 0.5 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) = (16/2,8) (16/2,6) (20/2,6) (26/2,6) . 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 0,19/2,5) ( 3 0,19/2,7) ( 3 0,25/2,5) ( 3 0,33/2,5) ( 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 = (2,2) and (K,p) = (16/2,6) (16/2,8) (24/2,6) (28/2,6) with error 0.3 (in G^2 N^2 units). Heavy potential determined using (n,K,p,K_max) = ( 0 0,-34/2,2,4) ( 0 0,-34/2,4,4) ( 0 0,-34/2,2,5) ( 0 0,-40/2,2,4) ( 0 0,-50/2,2,5) ( 0 0,-60/2,2,4) ( 0 0,-60/2,2,6) , L = 3 4 6 (all in G^2 N^2 units); with relative error=0.25. Roundness determined using (n,K,p,K_max) = ( 1 0,-17/2,3,4) ( 1 0,-17/2,5,4) ( 1 0,-17/2,3,5) ( 1 0,-33/2,3,4) ( 1 0,-33/2,3,5) ( 1 0,-55/2,3,4) ( 1 0,-55/2,3,6) , L=3 and error 0.3 ( 1 1,-30/2,2,4) ( 1 1,-30/2,4,4) ( 1 1,-30/2,2,5) ( 1 1,-40/2,2,4) ( 1 1,-50/2,2,5) ( 1 1,-60/2,2,4) ( 1 1,-60/2,2,6) , with L=3 and error 0.3 (all in G^2 N^2 units). p-extrapolation using n=( 1 0) and (K,p) = (13/2,3) (35/2,3) (13/2,5) (29/2,5) (13/2,7) (17/2,7) . Result format: fit info, # steps, chi^2, and p damping, scale g^2 N/(a^2 sigma); the 9 couplings (G^2 N units) and which--if any--were fit; winding and longitudinal string tension fits; the n=(2,2) winding eigenvalue and the n=(1,0) (1,1) longitudinal eigenvalues (G^2 N units) showing measured value and derived value for each. In each direction, the spectra for each P_perp*a and c^2 values. Finally come the states for the ordinary spectra. 2 10 33.51335311 -1.256097575 6.178074217 0.1453085056 1 1.260068 0.176086 -0.220545 10.799087 0.262786 1.781502 -2.450789 2 3 4 5 6 7 8 0.287015 -0.709983 -0.661935 0.187479 -0.945423 -0.584904 1.824647 1.503397 -0.358681 -0.238872 0.244061 -0.008307 11.958354 12.006611 1.369111 28.317935 28.333417 0.439241 28.553381 28.589702 1.030483 28.703194 28.706816 0.102776 20.248361 20.258428 0.285600 39.547750 39.565068 0.491336 50.852796 50.847540 -0.149110 53.931508 53.931798 0.008239 20.248361 20.272634 0.688637 31.944575 31.982281 1.069743 39.547750 39.552344 0.130343 50.852796 50.849036 -0.106679 33.799790 33.821448 0.614466 38.135809 38.124786 -0.312735 46.772202 46.790171 0.509807 51.971703 51.974414 0.076917 11.958354 12.054923 1.369896 28.317935 28.327829 0.140358 29.402819 29.423741 0.296791 33.799790 33.791644 -0.115551 20.248361 20.273240 0.352925 39.547750 39.568728 0.297579 50.852796 50.843416 -0.133059 53.120171 53.133920 0.195031 20.248361 20.292168 0.621429 31.944575 32.019986 1.069746 39.547750 39.570640 0.324699 50.852796 50.844320 -0.120236 28.553381 28.625697 1.025847 28.703194 28.731611 0.403122 33.799790 33.792037 -0.109988 36.926407 36.923174 -0.045857 11.958354 29.402819 28.317935 36.784134 62.629808 63.416162 77.409440 74.798749 57.592685 74.086935 92.745478 106.465659 31.944575 54.634551 67.439142 74.515771 28.553381 28.703194 36.926407 51.278469 53.931508 62.080443 73.699383 75.551041 38.135809 64.255402 74.636429 68.274958 53.120171 68.774350 73.680709 66.626922 20.248361 39.547750 54.129555 50.852796 33.799790 46.772202 51.971703 59.645500 2 76 80.02156432 -1.131075912 3.838178428 0.1921681542 1 1.014048168 0.001213210749 -0.2698755973 4.366204395 0.006906898549 1.049811391 -1.166127756 2 3 4 5 6 7 8 0.438680 -0.429108 -1.053351 0.222707 -0.266643 -0.087862 4.302947 2.948661 0.713488 0.586751 1.248979 0.757399 11.691405 11.730910 1.064246 13.217295 13.274187 1.532647 20.901195 20.903073 0.050590 24.911415 24.918320 0.186026 17.304781 17.311936 0.192746 34.507393 34.517882 0.282557 39.538790 39.542762 0.107009 41.393928 41.390768 -0.085137 17.304781 17.317312 0.337574 27.882110 27.895638 0.364450 34.507393 34.519432 0.324308 39.538790 39.545440 0.179170 28.355306 28.368122 0.345264 31.288692 31.281393 -0.196636 38.067034 38.083441 0.442023 42.318916 42.303127 -0.425329 11.691405 11.769134 1.046989 20.901195 20.904919 0.050158 25.883012 25.803808 -1.066874 28.355306 28.418293 0.848433 17.304781 17.321669 0.227477 34.507393 34.529696 0.300409 39.538790 39.545639 0.092256 41.393928 41.384732 -0.123869 17.304781 17.327257 0.302751 27.882110 27.909172 0.364523 34.507393 34.530171 0.306809 39.538790 39.553163 0.193613 13.217295 13.331961 1.544538 24.911415 24.926226 0.199500 28.355306 28.487604 1.782036 30.417599 30.316866 -1.356859 11.691405 20.901195 25.883012 30.721879 48.238693 51.415877 57.284227 59.892652 45.380055 62.195374 65.273216 72.614762 27.882110 43.748183 52.619935 60.193244 13.217295 24.911415 30.417599 30.816001 42.344496 50.095074 56.330678 58.490480 31.288692 50.891687 56.900654 57.128211 44.230851 54.173750 56.582036 57.980126 17.304781 34.507393 39.538790 41.393928 28.355306 38.067034 42.318916 46.877813 2 44 60.03538799 -0.7482830443 3.468824561 0.25 1 1.300096986 0.2322462085 -0.4941604208 8.44489048 -0.05492553675 2.258347075 -2.208977024 2 3 4 5 6 7 8 0.378204 -0.679106 -1.333820 0.184865 -0.654886 -0.598813 2.490743 2.179801 -0.023423 -0.137041 0.461009 -0.009103 5.853087 5.910972 1.215046 15.177917 15.243302 1.372478 18.985360 18.990282 0.103316 21.011229 21.022959 0.246219 14.351886 14.361547 0.202791 26.403309 26.413507 0.214053 34.569423 34.574431 0.105134 34.658199 34.631338 -0.563835 14.351886 14.367534 0.328461 21.960108 21.980774 0.433791 26.403309 26.420596 0.362872 34.569423 34.576870 0.156333 25.334397 25.350299 0.333809 28.973965 28.970071 -0.081737 31.191252 31.212713 0.450503 36.545347 36.525605 -0.414404 5.853087 5.968794 1.214391 18.985360 18.995218 0.103462 22.553571 22.412148 -1.484289 25.334397 25.453282 1.247751 14.351886 14.375840 0.251404 26.403309 26.429485 0.274724 34.569423 34.578381 0.094023 34.658199 34.628562 -0.311059 14.351886 14.378541 0.279751 21.960108 22.001445 0.433843 26.403309 26.432093 0.302092 34.569423 34.572134 0.028454 15.177917 15.307874 1.363954 21.011229 21.035626 0.256055 25.334397 25.480700 1.535507 28.509987 28.451280 -0.616153 5.853087 18.985360 22.553571 29.283171 40.505803 45.875784 47.428434 52.591136 41.664024 55.627752 54.822885 55.160224 21.960108 38.306930 44.026462 50.749392 15.177917 21.011229 28.509987 30.658417 35.358285 43.937013 47.172087 50.013731 28.973965 41.898238 50.907390 48.804972 36.699248 45.165603 50.685040 49.365069 14.351886 26.403309 34.569423 34.658199 25.334397 31.191252 36.545347 42.384955