********* 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 40 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 0,16/2,6) ( 2 0,16/2,4) ( 2 0,26/2,4) ( 3 0,17/2,7) ( 3 0,17/2,5) ( 3 0,25/2,5) ( 4 0,16/2,8) ( 4 0,16/2,6) ( 4 0,26/2,6) . Roundness of winding using (n,K,p) = ( 2 2,14/2,8) ( 2 2,14/2,6) ( 2 2,22/2,6) with error 1; in G^2 N units. Heavy potential determined using (n,K,p,K_max) = ( 0 0,-26/2,2,3.5) ( 0 0,-26/2,4,3.5) ( 0 0,-26/2,2,3) ( 0 0,-42/2,2,3.5) ( 0 0,-42/2,2,4.25) ( 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,-13/2,3,3.5) ( 1 0,-13/2,5,3.5) ( 1 0,-13/2,3,3) ( 1 0,-23/2,3,4) ( 1 0,-23/2,3,4.5) ( 1 0,-35/2,3,5) ( 1 0,-35/2,3,6) L=1.265-0.964*m and error 0.1; ( 1 0,-13/2,3,3.5) ( 1 0,-13/2,5,3.5) ( 1 0,-13/2,3,3) ( 1 0,-23/2,3,4) ( 1 0,-23/2,3,4.5) ( 1 0,-35/2,3,5) ( 1 0,-35/2,3,6) L=5.058-3.856*m and error 0.1; ( 1 1,-22/2,2,5) ( 1 1,-22/2,4,5) ( 1 1,-22/2,2,4.5) ( 1 1,-44/2,2,5) ( 1 1,-44/2,2,6) ( 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) = (13/2,3) (21/2,3) (45/2,3) (13/2,5) (27/2,5) (13/2,7) (15/2,7) . 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, 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. 1 60 68.24236423 -0.9090200107 8.548801997 0.03249196962 1 0.06 -0.1892453027 -0.1371415211 736.996197 -0.06136469569 338.2494765 -0.629796526 -0.7860218536 3 4 5 6 7 8 9 0.282541 -0.774051 0.968096 0.123145 0.242944 -0.259610 4.107812 1.607293 0.709698 0.762881 0.995134 0.977485 1.373341 0.993911 12.670000 12.695072 0.968941 14.260314 14.286164 0.999020 28.205056 28.201621 -0.132744 30.650113 30.670903 0.803464 31.938553 31.968499 1.157290 60.414838 60.444950 1.163701 64.522230 64.517832 -0.169944 65.298897 65.304481 0.215808 31.938553 31.939084 0.020534 40.072414 40.072725 0.012019 60.414838 60.415167 0.012715 64.522230 64.527446 0.201581 30.834316 30.835171 0.033012 34.518736 34.518049 -0.026567 56.907863 56.908285 0.016283 61.394287 61.395528 0.047964 12.670000 12.720686 0.979418 28.205056 28.198071 -0.134974 30.745278 30.695964 -0.952893 30.834316 30.846347 0.232464 31.938553 31.986147 0.919672 60.414838 60.455380 0.783405 64.522230 64.526750 0.087335 71.156460 71.152299 -0.080401 31.938553 31.951917 0.258228 40.072414 40.073037 0.012024 60.414838 60.435193 0.393319 64.522230 64.519328 -0.056078 14.260314 14.310096 0.961941 30.650113 30.649271 -0.016267 30.834316 30.804799 -0.570370 43.909094 43.975509 1.283334 12.670000 28.205056 30.745278 40.399400 77.170655 79.637113 99.166727 98.308104 64.461635 95.168600 103.843347 104.997476 40.072414 67.161995 90.990682 94.896452 14.260314 30.650113 43.909094 56.120285 65.298897 78.891268 95.464682 104.487126 34.518736 81.755623 101.019903 97.143774 79.657395 83.954572 101.431884 101.009762 31.938553 60.414838 64.522230 71.156460 30.834316 56.907863 61.394287 70.867563 2 9 70.26579334 -0.8384753089 8.9704442 0.03249196962 1 0.14 -0.1953999378 -0.1519337505 108.1216415 0.0267568197 36.08226657 -0.7123692921 -0.8651055423 3 4 5 6 7 8 9 0.270850 -0.784159 0.949343 0.118135 0.241987 -0.255013 4.321075 1.501312 0.698968 0.755175 0.972732 0.956940 1.384857 0.983319 12.556790 12.580146 0.907930 12.670000 12.699028 1.128427 30.607170 30.622008 0.576826 30.952097 30.914762 -1.451380 33.381040 33.415354 1.333951 62.293390 62.330193 1.430688 70.420326 70.426392 0.235836 72.175521 72.179017 0.135875 33.381040 33.382754 0.066623 48.391929 48.393356 0.055462 62.293390 62.293545 0.006017 70.420326 70.433980 0.530806 35.705216 35.708774 0.138310 39.757950 39.755159 -0.108485 59.567406 59.567331 -0.002903 64.983452 64.987732 0.166376 12.670000 12.719452 0.961216 30.607170 30.636742 0.574793 30.959566 30.919864 -0.771700 35.705216 35.677755 -0.533779 33.381040 33.417398 0.706693 62.293390 62.330021 0.711992 70.420326 70.437276 0.329465 79.260499 79.345732 1.656685 33.381040 33.416745 0.694013 48.391929 48.394784 0.055485 62.293390 62.330658 0.724384 70.420326 70.442714 0.435172 12.556790 12.611980 1.072737 30.952097 30.910862 -0.801498 35.705216 35.704651 -0.010994 45.534075 45.565677 0.614240 12.670000 30.607170 30.959566 44.025476 79.260499 85.755015 104.005150 110.053940 69.835338 100.148981 111.183997 115.093937 48.391929 74.256498 102.751723 109.985596 12.556790 30.952097 45.534075 60.334795 72.175521 80.707045 104.658939 113.748098 39.757950 92.100556 108.727188 103.219350 85.428554 87.972918 110.319936 111.503717 33.381040 62.293390 70.420326 79.522262 35.705216 59.567406 64.983452 80.298628 2 10 63.43074483 -0.8726188989 9.083387407 0.03249196962 1 0.22 -0.1930923017 -0.1504024004 109.9296083 0.0280703823 37.06577931 -0.7302205073 -0.8902237751 3 4 5 6 7 8 9 0.265282 -0.785287 0.897695 0.116424 0.239772 -0.249204 3.937477 1.449184 0.690450 0.747203 0.958009 0.945595 1.359277 0.972407 12.532980 12.556339 0.900621 12.670000 12.698963 1.116647 27.994107 28.020286 1.009316 30.695948 30.655986 -1.540745 33.239632 33.273578 1.308786 62.589043 62.625109 1.390494 68.184262 68.198500 0.548937 71.643684 71.647267 0.138137 33.239632 33.244059 0.170710 47.358475 47.362079 0.138953 62.589043 62.588411 -0.024371 68.184262 68.206464 0.855971 34.933670 34.941926 0.318302 39.307121 39.300772 -0.244772 59.763255 59.762876 -0.014604 64.391983 64.402614 0.409895 12.670000 12.719242 0.949255 27.994107 28.046417 1.008392 30.695948 30.655735 -0.775216 34.933670 34.890202 -0.837947 33.239632 33.278258 0.744612 62.589043 62.624563 0.684739 68.184262 68.213063 0.555202 79.485488 79.324171 -3.109757 33.239632 33.277770 0.735201 47.358475 47.365686 0.139016 62.589043 62.624308 0.679808 68.184262 68.228302 0.848975 12.532980 12.588253 1.065522 30.696881 30.656437 -0.779640 34.933670 34.933587 -0.001594 45.959015 45.992137 0.638517 12.670000 27.994107 30.695948 44.013213 79.656902 85.412101 104.815381 109.532700 69.719214 101.235706 109.413471 115.039437 47.358475 73.793172 101.864439 109.646772 12.532980 30.696881 45.959015 59.556887 71.643684 80.954094 105.298960 113.112949 39.307121 92.110393 105.092241 106.600034 84.374983 89.510311 108.000316 106.953076 33.239632 62.589043 68.184262 79.485488 34.933670 59.763255 64.391983 79.700123 2 10 50.45264485 -0.9313029257 8.998337739 0.03249196962 1 0.3 -0.1880498382 -0.1463685143 111.737575 0.03320081377 38.04929205 -0.7456519473 -0.8928434714 3 4 5 6 7 8 9 0.258664 -0.787856 0.826107 0.115632 0.235495 -0.241454 3.498452 1.384721 0.681518 0.728196 0.945821 0.928439 1.332992 0.946570 12.575198 12.597272 0.822075 12.670000 12.699088 1.083264 24.293463 24.325696 1.200392 29.756417 29.718672 -1.405626 32.162749 32.194972 1.199975 61.763218 61.798356 1.308550 63.743152 63.763209 0.746956 69.383306 69.386405 0.115386 32.162749 32.171120 0.311721 44.968699 44.975369 0.248414 61.763218 61.764248 0.038369 63.743152 63.767289 0.898879 33.285568 33.299112 0.504379 37.942182 37.932069 -0.376596 58.732983 58.731178 -0.067227 62.101543 62.120620 0.710451 12.670000 12.718380 0.900853 24.293463 24.357912 1.200068 29.756417 29.718741 -0.701528 33.285568 33.237159 -0.901400 32.162749 32.202883 0.747294 61.763218 61.792576 0.546659 63.743152 63.783800 0.756879 77.849793 77.715116 -2.507731 32.162749 32.203828 0.764899 44.968699 44.982046 0.248532 61.763218 61.805803 0.792953 63.743152 63.791155 0.893844 12.575198 12.629006 1.001933 29.757489 29.719474 -0.707855 33.285568 33.286480 0.016970 45.360467 45.395326 0.649098 12.670000 24.293463 29.756417 42.906932 78.277565 82.960982 103.415073 106.476892 67.997698 100.113418 105.501896 112.781829 44.968699 71.490137 98.251127 107.148544 12.575198 29.757489 45.360467 57.253759 69.383306 79.310486 103.599481 110.049994 37.942182 90.239809 97.577778 107.059006 80.970641 94.562387 96.814433 104.434734 32.162749 61.763218 63.743152 77.849793 33.285568 58.732983 62.101543 75.987554 2 18 36.33086653 -0.9645232547 9.23867979 0.03249196962 1 0.38 -0.1851315424 -0.1336806477 105.7988154 0.03922700292 42.71171954 -0.7722761181 -0.8756060196 3 4 5 6 7 8 9 0.254380 -0.803803 0.762090 0.113827 0.229766 -0.230304 3.007167 1.326499 0.671412 0.726387 0.934936 0.920290 1.303426 0.944907 12.670000 12.698536 1.073002 12.834282 12.861615 1.027761 21.054111 21.086061 1.201408 29.158148 29.125132 -1.241467 32.037890 32.067527 1.114425 61.790072 61.819049 1.089567 62.315300 62.345551 1.137499 69.125153 69.126247 0.041120 32.037890 32.052219 0.538797 43.563786 43.574770 0.413036 61.790072 61.809262 0.721566 62.315300 62.321286 0.225080 32.161002 32.179962 0.712913 37.090568 37.076678 -0.522294 59.764886 59.752319 -0.472555 60.923054 60.959679 1.377177 12.670000 12.719249 0.925929 21.054111 21.118017 1.201510 29.158239 29.126417 -0.598301 32.161002 32.118374 -0.801461 32.037890 32.080549 0.802039 61.790072 61.818495 0.534370 62.315300 62.357818 0.799380 78.374122 78.362524 -0.218045 32.037890 32.083196 0.851802 43.563786 43.585765 0.413236 61.790072 61.857857 1.274428 62.315300 62.345205 0.562245 12.834282 12.896024 1.160815 29.158148 29.126301 -0.598757 32.161002 32.163856 0.053657 45.666091 45.772583 2.002173 12.670000 21.054111 29.158239 43.136436 79.507943 82.939093 105.665640 106.748979 67.748594 100.870421 105.869599 113.034713 43.563786 70.891817 97.343743 107.303170 12.834282 29.158148 45.666091 56.469642 69.125153 80.215295 105.270252 110.430325 37.090568 89.237037 96.896743 109.044182 79.492599 101.152241 90.782866 103.899985 32.037890 61.790072 62.315300 78.374122 32.161002 59.764886 60.923054 73.587757 2 34 28.32180006 -0.9531834754 9.771654148 0.03249196962 1 0.46 -0.1838840944 -0.07420913252 3934.510062 0.04262979428 1836.677658 -0.8544655006 -0.8412849885 3 4 5 6 7 8 9 0.270529 -0.814815 0.660864 0.106215 0.227287 -0.220079 2.588676 1.432025 0.662213 0.737089 0.928356 0.905889 1.270642 0.960112 12.670000 12.697709 1.171979 15.684637 15.694573 0.420285 20.748337 20.754594 0.264639 29.816761 29.810383 -0.269771 33.023831 33.043301 0.823535 61.742321 61.769671 1.156824 67.339787 67.369596 1.260789 71.583680 71.573800 -0.417875 33.023831 33.047694 1.009354 43.039372 43.055690 0.690186 61.742321 61.740841 -0.062580 67.339787 67.353593 0.583922 31.767719 31.786281 0.785124 36.085089 36.070903 -0.600015 62.080874 62.100978 0.850343 63.076696 63.079359 0.112648 12.670000 12.725365 1.170871 20.748337 20.760875 0.265161 29.869180 29.844493 -0.522087 31.767719 31.770457 0.057909 33.023831 33.064325 0.856386 61.742321 61.768536 0.554406 67.339787 67.362625 0.482977 79.223462 79.244517 0.445268 33.023831 33.070012 0.976659 43.039372 43.072019 0.690411 61.742321 61.767800 0.538833 67.339787 67.403719 1.352043 15.684637 15.704014 0.409789 29.816761 29.808535 -0.173968 31.767719 31.773936 0.131492 49.446164 49.476185 0.634907 12.670000 20.748337 29.869180 44.890475 84.564038 85.973412 112.798290 109.233804 68.136840 104.090823 109.649277 112.599880 43.039372 71.459831 98.663635 109.937664 15.684637 29.816761 49.446164 58.319737 71.583680 84.830931 110.853895 115.054973 36.085089 89.044307 98.666231 113.435755 79.223462 104.205211 106.161894 92.742860 33.023831 61.742321 67.339787 80.719323 31.767719 62.080874 63.076696 73.686129 2 11 30.85232747 -1.02403561 8.119355941 0.03249196962 1 0.54 -0.1427967707 -0.1210780004 117.1614752 0.0824858559 40.99983027 -0.8223854263 -0.8402306747 3 4 5 6 7 8 9 0.241045 -0.841902 0.621964 0.115321 0.214580 -0.210993 2.231622 1.164207 0.650187 0.640149 0.914077 0.860406 1.257494 0.827277 12.670000 12.704822 1.090407 15.438601 15.460365 0.681533 16.698483 16.714437 0.499597 26.111970 26.088599 -0.731853 26.157764 26.179006 0.665165 50.343216 50.370005 0.838897 54.350165 54.382300 1.006271 59.685012 59.679431 -0.174750 26.157764 26.180755 0.719962 35.395614 35.414459 0.590102 50.343216 50.352251 0.282931 54.350165 54.364060 0.435093 27.803945 27.825982 0.690081 32.571377 32.557143 -0.445722 51.813193 51.815654 0.077053 53.436197 53.462948 0.837666 12.670000 12.739644 1.090419 16.698483 16.731975 0.524392 26.111970 26.092964 -0.297580 27.803945 27.772133 -0.498080 26.157764 26.195175 0.585750 50.343216 50.373339 0.471645 54.350165 54.380629 0.476964 65.848464 65.861658 0.206583 26.157764 26.208845 0.799787 35.395614 35.433321 0.590371 50.343216 50.384593 0.647842 54.350165 54.411346 0.957905 15.438601 15.480458 0.655367 26.112662 26.092580 -0.314437 27.803945 27.807164 0.050394 40.319366 40.353265 0.530759 12.670000 16.698483 26.111970 36.640743 69.708923 70.933997 93.447148 91.175163 59.296633 86.364399 97.739883 94.695425 35.395614 60.516641 79.312875 95.636202 15.438601 26.112662 40.319366 48.047874 59.685012 69.539539 92.281529 94.911674 32.571377 77.476910 86.157052 94.008240 65.848464 86.457704 89.225955 76.329252 26.157764 50.343216 54.350165 68.964083 27.803945 53.436197 51.813193 62.405794 2 27 21.47533811 -1.021331755 8.826295955 0.03249196962 1 0.62 -0.09971265872 -0.1009905593 639.3158441 0.1038829215 285.7540813 -0.8352385764 -0.7843752046 3 4 5 6 7 8 9 0.240666 -0.894711 0.611926 0.118074 0.205170 -0.201482 1.853986 1.107105 0.641717 0.687294 0.913079 0.898178 1.232624 0.895296 12.670000 12.706834 1.251866 21.443180 21.465140 0.746369 22.488867 22.502285 0.456021 29.612769 29.592130 -0.701445 27.164745 27.183124 0.624631 52.989336 53.018976 1.007367 60.129276 60.165774 1.240477 65.159291 65.144113 -0.515866 27.164745 27.196284 1.071929 36.590430 36.616906 0.899839 52.989336 52.987139 -0.074678 60.129276 60.154160 0.845725 30.804597 30.827802 0.788682 35.749299 35.735405 -0.472202 57.607729 57.629399 0.736498 58.151979 58.163693 0.398101 12.670000 12.743671 1.251922 22.488867 22.515752 0.456858 29.612769 29.600391 -0.210344 30.804597 30.781017 -0.400709 27.164745 27.204376 0.673476 52.989336 53.017480 0.478256 60.129276 60.155931 0.452961 69.349139 69.388405 0.667269 27.164745 27.224958 1.023224 36.590430 36.643399 0.900120 52.989336 53.016063 0.454184 60.129276 60.224092 1.611254 21.443180 21.486613 0.738082 29.612774 29.600406 -0.210188 30.804597 30.810053 0.092723 43.876791 43.937434 1.030527 12.670000 22.488867 29.612769 39.227180 76.728856 76.683097 103.372978 97.914925 64.746473 93.954059 112.058586 103.342772 36.590430 64.983954 81.291135 106.271084 21.443180 29.612774 43.876791 52.354795 65.159291 75.975708 99.997780 103.015004 35.749299 84.476852 93.866338 100.762124 69.349139 94.083778 94.938000 84.810282 27.164745 52.989336 60.129276 75.089849 30.804597 57.607729 58.151979 69.213032 2 12 20.51002514 -1.068638642 9.3512454 0.03249196962 1 0.7 -0.07380661512 -0.09505330489 120.7774086 0.1545798749 42.96685575 -0.9438648547 -0.8292815717 3 4 5 6 7 8 9 0.223020 -0.951688 0.676287 0.110463 0.201136 -0.192094 1.528324 0.917011 0.617208 0.661397 0.876404 0.855928 1.216169 0.860256 12.670000 12.701922 1.065177 22.443694 22.466635 0.765529 22.461236 22.488999 0.926417 29.756426 29.757894 0.048990 27.139351 27.157174 0.594731 53.934564 53.968875 1.144884 61.509671 61.553497 1.462411 67.862310 67.837523 -0.827100 27.139351 27.174912 1.186617 37.264216 37.298486 1.143521 53.934564 53.929475 -0.169808 61.509671 61.547621 1.266315 31.584205 31.608749 0.818996 36.810424 36.796994 -0.448145 59.401159 59.424375 0.774687 59.937415 59.956304 0.630311 12.670000 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