********* 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 0.25 (-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 10 75.75556429 -0.8958946804 7.479987858 0.03249196962 1 0.5600077032 -0.08278450812 -0.24268896 10.61907221 0.1096823369 2.034598746 0.03965971645 0.3185293312 2 3 4 5 6 7 8 9 0.204451 -1.066073 1.173892 0.185886 0.129453 -0.155834 2.064413 0.716270 0.646642 0.712075 0.901433 0.874206 1.204740 1.225732 1.199744 0.985984 10.126725 10.187599 1.489507 10.484720 10.611668 3.106235 12.670000 12.619049 -1.246692 26.539333 26.492051 -1.156938 22.679631 22.713983 0.840544 45.056524 45.091764 0.862271 46.542361 46.578655 0.888061 53.847420 53.853715 0.154036 22.679631 22.698453 0.460565 32.069685 32.090092 0.499350 45.056524 45.086386 0.730679 46.542361 46.551884 0.233024 26.539333 26.566835 0.672937 33.121804 33.110134 -0.285553 48.017915 48.056703 0.949092 48.908962 48.905092 -0.094690 10.126725 10.247418 1.476597 12.670000 12.731853 0.756735 26.539333 26.459627 -0.975154 28.373560 28.301163 -0.885731 22.679631 22.725265 0.558300 45.056524 45.103276 0.571976 46.542361 46.588406 0.563328 61.740248 61.732797 -0.091159 22.679631 22.740417 0.743677 32.069685 32.110531 0.499723 45.056524 45.139874 1.019736 46.542361 46.587730 0.555059 10.484720 10.575870 1.115157 26.539333 26.583068 0.535064 30.091340 30.005592 -1.049068 30.406744 30.491973 1.042716 12.670000 10.126725 28.373560 31.161733 62.196760 63.946986 84.118613 83.691918 58.153270 79.697371 95.490043 92.599065 32.069685 57.301351 70.062257 91.871568 10.484720 30.091340 30.406744 42.829110 53.847420 62.108133 83.924685 86.411593 33.121804 74.579801 86.331000 80.841132 61.740248 78.627443 83.709482 71.357057 22.679631 45.056524 46.542361 64.544620 26.539333 48.908962 48.017915 56.999121 2 10 51.32403215 -1.010456293 7.365754784 0.0517766953 1 0.8053638894 -0.08293719093 -0.1751274521 7.205644424 0.2276621744 1.525720612 -0.04196305763 0.387657513 2 3 4 5 6 7 8 9 0.228106 -1.072796 1.049493 0.191184 0.113877 -0.133476 2.055659 0.883242 0.641357 0.748505 0.914745 0.908053 1.257571 1.260861 1.213512 1.038205 12.670000 12.707634 1.011701 15.231807 15.265032 0.893202 15.579200 15.613037 0.909634 25.800684 25.865303 1.737138 22.254618 22.275037 0.548921 45.648121 45.679627 0.846976 48.771395 48.808087 0.986390 56.430658 56.423606 -0.189570 22.254618 22.277333 0.610641 33.787782 33.816056 0.760105 45.648121 45.667337 0.516592 48.771395 48.788791 0.467641 27.562340 27.587693 0.681562 32.601223 32.589143 -0.324747 48.754019 48.780504 0.711987 50.049241 50.059604 0.278594 12.670000 12.745291 1.012012 15.231807 15.297235 0.879445 25.903185 25.916154 0.174323 27.562340 27.718261 2.095807 22.254618 22.281347 0.359279 45.648121 45.689286 0.553325 48.771395 48.805690 0.460975 60.799093 60.821110 0.295940 22.254618 22.314207 0.800961 33.787782 33.844345 0.760287 45.648121 45.708223 0.807856 48.771395 48.843717 0.972110 15.579200 15.647542 0.918615 25.800684 25.830135 0.395852 25.836312 26.021695 2.491811 27.562340 27.511368 -0.685128 12.670000 15.231807 25.903185 28.959106 63.183055 64.847210 86.645284 83.082645 56.608072 87.434491 88.456147 113.265326 33.787782 56.623858 74.919370 98.641058 15.579200 25.836312 25.800684 44.198719 56.430658 62.514584 87.931434 86.964093 32.601223 79.451260 73.129768 101.998865 60.799093 76.740302 94.073902 75.496976 22.254618 45.648121 48.771395 65.103859 27.562340 50.049241 48.754019 60.658904 2 11 44.13858015 -0.9542839246 6.300698934 0.07642881742 1 0.8347637881 0.03187481423 -0.294875563 19.814336 0.1506472787 4.98862931 0.1222352436 -0.004998060414 2 3 4 5 6 7 8 9 0.263990 -1.029527 0.727237 0.197813 0.105964 -0.131336 2.234703 1.173296 0.688900 0.705772 0.906121 0.882956 1.250042 1.262189 1.261533 0.982908 12.670000 12.721055 1.358720 21.390266 21.426336 0.959945 22.263633 22.293902 0.805550 29.518538 29.525389 0.182337 20.573935 20.593186 0.512323 43.404534 43.421829 0.460288 47.992847 48.028732 0.954999 53.504197 53.572288 1.812098 20.573935 20.596454 0.599317 30.925747 30.949995 0.645320 43.404534 43.422963 0.490445 47.992847 48.003439 0.281887 30.089512 30.113737 0.644704 35.386758 35.378719 -0.213963 49.268493 49.290908 0.596529 50.306365 50.312719 0.169121 12.670000 12.772125 1.358927 22.263633 22.322655 0.785372 29.518538 29.532467 0.185343 30.089512 30.066479 -0.306488 20.573935 20.605803 0.424060 43.404534 43.440940 0.484442 47.992847 48.021909 0.386704 57.143795 57.147302 0.046666 20.573935 20.625627 0.687839 30.925747 30.974265 0.645613 43.404534 43.439526 0.465622 47.992847 48.056511 0.847146 21.390266 21.463956 0.980561 30.089512 30.098145 0.114869 30.186872 30.262214 1.002540 33.768440 33.732513 -0.478059 12.670000 22.263633 29.518538 33.715062 62.542566 61.212051 83.739020 80.528467 57.365290 88.350133 92.341303 116.026206 30.925747 54.952047 71.869243 88.564344 21.390266 30.186872 33.768440 44.501129 53.504197 61.515727 80.245481 82.451149 35.386758 72.511374 69.786147 99.312723 57.143795 74.031067 73.966199 88.053884 20.573935 43.404534 47.992847 57.989771 30.089512 49.268493 50.306365 57.377296 2 12 40.90330802 -0.9315195162 5.998378997 0.1072401379 1 1.010299347 0.06377601078 -0.237912886 66.60646779 0.156974588 19.07312956 0.06414892733 -0.08995752766 2 3 4 5 6 7 8 9 0.303850 -0.996314 0.426425 0.203371 0.091511 -0.111734 2.271625 1.487786 0.711149 0.730156 0.922468 0.907568 1.293873 1.291955 1.281956 1.018586 12.670000 12.716236 1.348322 28.092221 28.124624 0.944931 28.396776 28.439666 1.250737 28.585881 28.606684 0.606624 20.310479 20.323239 0.372116 42.623411 42.639400 0.466290 51.837153 51.884431 1.378682 54.316149 54.311369 -0.139399 20.310479 20.336405 0.756051 31.035627 31.062551 0.785151 42.623411 42.631792 0.244420 51.837153 51.900778 1.855411 31.396382 31.417086 0.603750 35.437919 35.430019 -0.230360 48.145445 48.161385 0.464809 51.889969 51.892661 0.078514 12.670000 12.762464 1.348207 28.396776 28.396188 -0.008575 28.585881 28.626971 0.599120 31.396382 31.395793 -0.008595 20.310479 20.338031 0.401737 42.623411 42.651622 0.411341 51.837153 51.896994 0.872527 54.671378 54.631719 -0.578258 20.310479 20.360295 0.726363 31.035627 31.089490 0.785362 42.623411 42.644041 0.300812 51.837153 51.999600 2.368603 28.092221 28.157887 0.957469 30.258083 30.260379 0.033473 31.396382 31.389681 -0.097719 33.888364 33.885741 -0.038249 12.670000 28.585881 28.396776 33.916486 63.619765 61.562193 85.119005 79.759296 56.411394 93.893012 91.881940 115.490627 31.035627 54.041345 70.518890 76.437504 28.092221 30.258083 33.888364 45.788268 54.316149 62.257821 78.997776 82.461794 35.437919 70.993594 72.273890 98.690060 55.525182 75.570811 66.766876 97.832431 20.310479 42.623411 51.837153 54.671378 31.396382 48.145445 51.889969 57.900485