********* 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 41 criteria and tolerance 0.01. Overall scale from fitting lowest state to lattice value. 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) = (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=0.2. 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 0.2; 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 67 21.64428548 -0.9682382099 7.716717484 0.03249196962 1 0.618757128 -0.0488635492 -0.1792262244 11.14294286 0.1186053731 1.296265757 -0.5569628502 -0.308517491 2 3 4 5 6 7 8 9 0.230266 -1.038658 1.049993 0.141775 0.224470 -0.249202 1.979647 0.934722 0.644404 0.682156 0.798945 0.802123 1.069437 1.066522 1.186757 0.919323 12.280000 12.327295 1.344607 17.628805 17.662738 0.964749 18.464670 18.495163 0.866955 28.892909 28.857327 -1.011623 23.373032 23.397654 0.700017 47.150865 47.179279 0.807832 51.252718 51.291558 1.104243 57.456929 57.455656 -0.036209 23.373032 23.397372 0.692014 32.499171 32.522788 0.671416 47.150865 47.169921 0.541780 51.252718 51.266607 0.394876 28.892909 28.919795 0.764369 34.583577 34.571171 -0.352714 51.560365 51.565924 0.158049 52.737752 52.767939 0.858235 12.280000 12.374619 1.345022 18.464670 18.526236 0.875185 28.892909 28.812243 -1.146689 31.029880 31.046727 0.239483 23.373032 23.412764 0.564812 47.150865 47.190796 0.567631 51.252718 51.291027 0.544576 62.808128 62.819613 0.163261 23.373032 23.431265 0.827797 32.499171 32.546428 0.671757 47.150865 47.205695 0.779418 51.252718 51.319530 0.949746 17.628805 17.696091 0.956491 28.892909 28.963742 1.006909 32.733675 32.723924 -0.138605 32.820527 32.764594 -0.795095 12.280000 18.464670 31.029880 31.669713 66.920169 67.566954 90.151593 85.211357 60.420668 84.062618 98.020144 100.833987 32.499171 59.168119 71.545867 95.579866 17.628805 32.820527 32.733675 46.373143 57.456929 66.490911 88.319962 90.288647 34.583577 77.755929 88.525692 86.219521 62.808128 82.981201 85.440728 76.784259 23.373032 47.150865 51.252718 66.808614 28.892909 52.737752 51.560365 61.872623 2 29 21.60688017 -0.9802355471 7.247115159 0.0517766953 1 0.7667343904 -0.0701581166 -0.1164752194 7.842397704 0.156458423 1.634073327 -0.6068530858 -0.3003015025 2 3 4 5 6 7 8 9 0.272798 -1.038033 0.898708 0.149576 0.198437 -0.218184 2.159532 1.256690 0.660132 0.706965 0.820488 0.828851 1.104134 1.101659 1.213616 0.958363 12.280000 12.314134 1.079718 21.988086 22.022812 1.098447 23.064194 23.082167 0.568515 28.033202 28.093913 1.920423 22.916661 22.930081 0.424494 46.578718 46.602140 0.740877 52.760565 52.793958 1.056276 57.885086 57.870271 -0.468636 22.916661 22.943726 0.856099 33.035002 33.060941 0.820520 46.578718 46.577100 -0.051197 52.760565 52.784675 0.762646 29.083066 29.102944 0.628799 33.195840 33.184870 -0.347008 51.673718 51.689401 0.496071 51.680514 51.695334 0.468785 12.280000 12.348315 1.080463 23.064194 23.099840 0.563783 28.919369 28.885589 -0.534266 29.083066 29.215580 2.095837 22.916661 22.944464 0.439728 46.578718 46.602394 0.374461 52.760565 52.784171 0.373347 60.301465 60.346390 0.710530 22.916661 22.969834 0.840973 33.035002 33.086894 0.820737 46.578718 46.598652 0.315265 52.760565 52.850578 1.423647 21.988086 22.057254 1.093953 28.033202 28.153968 1.910039 28.145087 28.164293 0.303763 29.083066 29.052656 -0.480963 12.280000 23.064194 28.919369 29.448954 67.036460 66.567324 90.416649 87.369964 57.456363 88.039685 91.801165 110.507154 33.035002 57.056546 73.805413 95.570762 21.988086 28.033202 28.145087 47.133239 57.885086 65.971644 87.663717 89.190052 33.195840 77.734802 72.395835 100.235524 60.301465 75.904515 94.422738 77.138957 22.916661 46.578718 52.760565 64.977001 29.083066 51.680514 51.673718 61.775391 2 57 24.70812797 -0.9339632269 6.524101031 0.07642881742 1 0.8257895672 -0.07875413137 -0.1665972628 14.84440385 0.1281657361 4.241797545 -0.483566631 -0.2969928299 2 3 4 5 6 7 8 9 0.299470 -0.981630 0.643311 0.170477 0.160727 -0.182674 2.477285 1.494540 0.698532 0.718205 0.868701 0.861841 1.180716 1.178376 1.267304 0.985299 12.280000 12.320860 1.277298 22.648611 22.682926 1.072716 24.202850 24.213527 0.333750 29.405297 29.483253 2.436940 22.273338 22.287269 0.435497 45.244217 45.262595 0.574508 51.422717 51.451350 0.895064 55.813933 55.821692 0.242554 22.273338 22.298481 0.785979 32.855261 32.878770 0.734891 45.244217 45.249052 0.151148 51.422717 51.433608 0.340462 29.685020 29.705935 0.653830 33.925008 33.913913 -0.346843 49.812681 49.830582 0.559594 51.496375 51.502612 0.194974 12.280000 12.361725 1.277370 24.202850 24.223846 0.328163 29.685020 29.723374 0.599490 29.999091 29.987803 -0.176428 22.273338 22.302269 0.452199 45.244217 45.270840 0.416116 51.422717 51.438557 0.247583 58.564948 58.691327 1.975320 22.273338 22.322556 0.769279 32.855261 32.902295 0.735148 45.244217 45.264090 0.310611 51.422717 51.485554 0.982155 22.648611 22.716846 1.066525 29.405297 29.559401 2.408662 29.685020 29.664963 -0.313492 29.924032 29.930343 0.098630 12.280000 24.202850 30.958179 29.999091 65.387708 63.914293 87.270104 83.642302 56.597165 89.092744 91.770315 107.832178 32.855261 55.760485 74.061142 90.967841 22.648611 29.405297 29.924032 46.283115 55.813933 64.228689 83.374094 85.867029 33.925008 74.693569 72.165806 96.896216 58.564948 76.510794 76.199012 90.182583 22.273338 45.244217 51.422717 60.756019 29.685020 49.812681 51.496375 59.992433 2 21 44.59155323 -0.8607392267 6.421705751 0.1072401379 1 0.9174406036 0.003033688249 -0.1938037679 46.18864072 0.05814430559 13.52392586 -0.2727109059 -0.3496377262 2 3 4 5 6 7 8 9 0.335834 -0.999251 0.450438 0.193975 0.109051 -0.126207 2.495339 1.743723 0.732957 0.797008 0.904164 0.950533 1.250227 1.297834 1.295236 1.105949 12.280000 12.333131 1.833335 30.873843 30.898934 0.865811 31.553428 31.561511 0.278915 33.237916 33.188199 -1.715531 22.974204 22.987342 0.453347 46.499523 46.517976 0.636757 58.408928 58.449025 1.383574 58.966707 58.974110 0.255446 22.974204 23.003072 0.996127 33.802825 33.828402 0.882548 46.499523 46.508750 0.318393 58.408928 58.427784 0.650639 34.089033 34.109724 0.713972 38.143661 38.134218 -0.325837 51.391085 51.413861 0.785925 57.611412 57.588235 -0.799745 12.280000 12.386227 1.832743 31.553428 31.560100 0.115117 33.237916 33.140772 -1.676020 34.089033 34.214207 2.159634 22.974204 23.007914 0.581602 46.499523 46.531106 0.544901 58.408928 58.420494 0.199544 59.325467 59.311274 -0.244870 22.974204 23.024485 0.867499 33.802825 33.853992 0.882781 46.499523 46.523413 0.412184 58.408928 58.515043 1.830799 30.873843 30.924813 0.879392 33.388295 33.409638 0.368242 34.089033 34.045491 -0.751225 36.315733 36.363789 0.829107 12.280000 33.237916 31.553428 36.499964 68.613717 69.769093 93.396266 86.711945 61.334181 99.496318 97.571372 125.591794 33.802825 59.051493 76.513364 86.717567 30.873843 33.388295 36.315733 50.650454 58.966707 69.419702 85.427875 90.132782 38.143661 76.582659 76.996917 103.569867 60.673965 81.587521 74.129534 103.471571 22.974204 46.499523 58.408928 59.325467 34.089033 51.391085 57.611412 64.130888