********* 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. 2 51 37.18636325 -1.044178923 8.457201745 0.03249196962 1 0.6570811128 0.0640199677 -0.3 178.0607273 0.1553042973 55.31762552 -0.8297634451 -0.921292102 2 3 5 6 7 8 9 0.164132 -0.970639 0.722306 0.125917 0.185313 -0.180519 1.278380 0.432704 0.603008 0.587891 0.844339 0.851296 1.222811 0.758189 12.670000 12.731233 1.359953 16.813942 16.946299 2.939591 17.182085 17.154340 -0.616192 31.452837 31.456043 0.071204 23.069101 23.104581 0.787982 48.461118 48.498360 0.827121 52.265954 52.316101 1.113747 60.402568 60.409823 0.161130 23.069101 23.094306 0.559775 32.517798 32.549059 0.694280 48.461118 48.497752 0.813616 52.265954 52.278084 0.269403 31.452837 31.486844 0.755267 39.323867 39.316381 -0.166248 55.834255 55.844161 0.220022 56.724683 56.757564 0.730266 12.670000 12.792473 1.360029 16.813942 16.923557 1.217252 31.452837 31.393106 -0.663302 35.185146 35.250817 0.729261 23.069101 23.118835 0.552280 48.461118 48.519683 0.650343 52.265954 52.320566 0.606451 66.882144 66.885446 0.036666 23.069101 23.140820 0.796420 32.517798 32.580356 0.694682 48.461118 48.550071 0.987794 52.265954 52.335640 0.773845 17.182085 17.281688 1.106071 31.452837 31.608668 1.730460 39.104552 39.045137 -0.659797 39.175564 39.072002 -1.150036 12.670000 16.813942 35.185146 38.098275 70.325044 71.243408 96.573812 89.803143 66.787505 94.686163 105.205137 130.598800 32.517798 64.018511 75.116044 105.420765 17.182085 39.175564 39.104552 48.024569 60.402568 70.102930 94.855127 96.438914 39.323867 85.495085 99.055830 92.195092 66.882144 89.963754 92.644846 83.809210 23.069101 48.461118 52.265954 71.446097 31.452837 56.724683 55.834255 65.309646 2 18 30.49123249 -1.058288818 8.445647904 0.03249196962 1 0.6697596803 0.01046140327 -0.24 81.67030343 0.1547261802 30.73884959 -0.8200953076 -0.8868292413 2 3 5 6 7 8 9 0.181493 -0.949981 0.684714 0.125585 0.188636 -0.184869 1.398830 0.587556 0.611568 0.611649 0.860334 0.866152 1.224231 0.791328 12.670000 12.724051 1.325617 17.693604 17.750034 1.383966 17.929177 17.963790 0.848892 30.905238 30.859375 -1.124824 23.731471 23.762019 0.749216 48.984594 49.020049 0.869552 53.276761 53.323663 1.150280 61.050013 61.051462 0.035538 23.731471 23.758760 0.669285 33.413216 33.444433 0.765600 48.984594 49.013415 0.706847 53.276761 53.292086 0.375846 30.905238 30.938446 0.814428 37.920367 37.909318 -0.270998 55.180286 55.192058 0.288691 56.479855 56.511325 0.771821 12.670000 12.778136 1.326034 17.693604 17.786346 1.137263 30.905238 30.805609 -1.221716 35.022083 35.121938 1.224474 23.731471 23.777325 0.562300 48.984594 49.036793 0.640098 53.276761 53.325382 0.596224 66.734533 66.745769 0.137784 23.731471 23.801363 0.857058 33.413216 33.475680 0.765965 48.984594 49.060721 0.933518 53.276761 53.352140 0.924349 17.929177 18.018302 1.092902 30.905238 30.983229 0.956365 37.087268 37.107515 0.248282 37.569004 37.527083 -0.514068 12.670000 17.693604 35.022083 35.574859 70.844990 71.661682 96.795427 90.828209 65.839453 92.250893 102.441142 124.099527 33.413216 63.482441 75.656668 105.113101 17.929177 37.569004 37.087268 48.077556 61.050013 70.348175 95.234998 96.452219 37.920367 85.146441 96.723443 92.849038 66.734533 89.640898 92.099723 83.463420 23.731471 48.984594 53.276761 71.885013 30.905238 56.479855 55.180286 65.536255 3 27 25.32177923 -1.069361358 8.766599159 0.03249196962 1 0.6938953891 -0.02360234501 -0.18 448.8710516 0.1609194377 150.0197443 -0.8735564629 -0.8576817747 2 3 5 6 7 8 9 0.196597 -0.953602 0.683937 0.119653 0.193121 -0.187151 1.418796 0.704663 0.613044 0.629841 0.866861 0.860261 1.219561 0.816819 12.670000 12.716173 1.273245 19.587023 19.639186 1.438427 19.902968 19.924117 0.583191 31.147079 31.107105 -1.102310 24.862495 24.887904 0.700687 50.657864 50.692980 0.968364 56.126333 56.171452 1.244190 63.574782 63.567551 -0.199413 24.862495 24.893310 0.849760 34.786227 34.819527 0.918274 50.657864 50.675572 0.488326 56.126333 56.148485 0.610854 31.147079 31.178908 0.877704 37.435777 37.422313 -0.371268 56.503879 56.518813 0.411807 57.731881 57.760898 0.800175 12.670000 12.762390 1.273857 19.587023 19.666778 1.099646 31.147079 31.081189 -0.908488 32.454647 32.421380 -0.458691 24.862495 24.905044 0.586669 50.657864 50.702706 0.618286 56.126333 56.170204 0.604883 68.115704 68.140148 0.337038 24.862495 24.932449 0.964516 34.786227 34.852848 0.918562 50.657864 50.718482 0.835796 56.126333 56.215999 1.236305 19.902968 19.969782 0.921226 31.147079 31.197945 0.701327 33.051386 32.951906 -1.371624 42.433905 42.477439 0.600238 12.670000 19.587023 32.454647 37.600613 73.632403 74.303387 100.549344 95.335178 66.135319 94.235996 104.866606 122.624822 34.786227 64.592876 78.159327 108.627264 19.902968 33.051386 42.433905 49.622604 63.574782 72.857025 98.749564 99.780469 37.435777 87.269440 94.998248 99.620066 68.115704 92.741191 94.252774 84.468692 24.862495 50.657864 56.126333 74.833020 31.147079 57.731881 56.503879 67.431772 2 17 42.9125662 -1.005308462 10.23606152 0.03249196962 1 0.705447628 -0.02416816531 -0.12 571.5495301 0.1360301077 201.0288916 -0.936149531 -0.8405278271 2 3 5 6 7 8 9 0.219079 -1.011153 0.749767 0.112593 0.197849 -0.189087 1.307443 0.835202 0.615233 0.712627 0.872443 0.898267 1.204590 0.932831 12.670000 12.717553 1.706195 27.463930 27.491099 0.974829 28.402691 28.425950 0.834564 36.139794 36.113770 -0.933749 28.992092 29.013721 0.776059 58.467961 58.504084 1.296093 68.061189 68.108395 1.693744 74.704375 74.683964 -0.732334 28.992092 29.034411 1.518417 39.161207 39.201595 1.449109 58.467961 58.463715 -0.152347 68.061189 68.095801 1.241878 36.139794 36.170420 1.098859 42.198474 42.183835 -0.525252 65.733875 65.756239 0.802431 67.928664 67.951434 0.816959 12.670000 12.765114 1.706351 28.402691 28.449011 0.830995 36.139794 36.103838 -0.645049 36.453622 36.443211 -0.186775 28.992092 29.041700 0.889973 58.467961 58.502622 0.621811 68.061189 68.093579 0.581077 77.393532 77.454083 1.086286 28.992092 29.070391 1.404693 39.161207 39.241994 1.449320 58.467961 58.497105 0.522852 68.061189 68.190664 2.322796 27.463930 27.518509 0.979144 36.139794 36.186071 0.830214 36.725802 36.668568 -1.026782 50.070670 50.092701 0.395230 12.670000 28.402691 36.453622 44.011576 88.136709 86.988840 120.236228 114.123434 75.649850 109.683026 123.701692 141.335024 39.161207 74.074341 89.064448 124.474049 27.463930 36.725802 50.070670 59.759709 74.704375 86.613171 113.745573 118.170559 42.198474 99.214190 108.837738 114.521920 77.393532 108.692143 107.647229 99.244072 28.992092 58.467961 68.061189 87.637792 36.139794 65.733875 67.928664 79.566128 2 9 26.08528221 -1.081217182 9.3863364 0.03249196962 1 0.6918586637 -0.06345403659 -0.06 50 0.1340465699 12.5 -0.9679229883 -0.8489054881 2 3 5 6 7 8 9 0.241018 -0.959476 0.673656 0.108539 0.206253 -0.199217 1.575429 1.052871 0.620292 0.678172 0.877327 0.863628 1.213923 0.883009 12.670000 12.699003 1.049809 26.098563 26.114424 0.574091 26.992865 27.004257 0.412345 30.870574 30.862687 -0.285481 27.544280 27.557893 0.492740 54.727549 54.759579 1.159369 64.317858 64.359980 1.524688 69.366377 69.332952 -1.209842 27.544280 27.582355 1.378196 37.213152 37.246528 1.208081 54.727549 54.708445 -0.691489 64.317858 64.363212 1.641678 32.676480 32.694440 0.650079 37.161335 37.151195 -0.367027 60.295694 60.304895 0.333058 62.260143 62.287115 0.976291 12.670000 12.728019 1.050032 26.992865 27.015670 0.412735 30.870574 30.875628 0.091465 32.676480 32.660171 -0.295172 27.544280 27.581618 0.675762 54.727549 54.746252 0.338494 64.317858 64.338158 0.367397 71.155515 71.221475 1.193756 27.544280 27.610308 1.194993 37.213152 37.279911 1.208217 54.727549 54.734800 0.131241 64.317858 64.467702 2.711907 26.098563 26.130262 0.573693 30.870629 30.874868 0.076712 32.676480 32.681281 0.086887 45.252916 45.276642 0.429394 12.670000 26.992865 30.870574 40.299651 81.502072 80.780527 110.749638 105.618336 67.619462 100.443120 117.219726 118.217346 37.213152 67.447989 83.371672 114.242046 26.098563 30.870629 45.252916 55.718740 69.366377 80.214840 105.341946 109.101176 37.161335 90.519990 94.084271 109.563859 71.155515 100.078429 99.199593 90.509614 27.544280 54.727549 64.317858 80.507288 32.676480 60.295694 62.260143 73.539658 2 10 73.51203583 -1.282954011 8.199233946 0.03249196962 1 0.7030483607 -0.06692978634 0 50 0.1566661468 12.5 -0.8862246536 -0.7759871729 2 3 5 6 7 8 9 0.255365 -0.921625 0.607694 0.119997 0.198680 -0.198607 1.740647 1.197257 0.623212 0.666474 0.893376 0.887679 1.219801 0.867922 12.670000 12.678869 0.297113 23.509226 23.517687 0.283451 23.815008 23.821523 0.218268 26.628470 26.634037 0.186495 24.222760 24.228530 0.193317 48.454837 48.482477 0.925973 57.531584 57.577612 1.541963 61.511472 61.457603 -1.804667 24.222760 24.255052 1.081810 33.147997 33.175838 0.932711 48.454837 48.422897 -1.070014 57.531584 57.633127 3.401784 28.597319 28.599413 0.070155 31.490175 31.490406 0.007744 52.935534 52.927500 -0.269142 54.601184 54.648252 1.576798 12.670000 12.687744 0.297214 23.815008 23.827743 0.213317 26.656505 26.705915 0.827650 28.597319 28.560562 -0.615692 24.222760 24.245741 0.384954 48.454837 48.458465 0.060785 57.531584 57.547894 0.273197 61.872458 61.938022 1.098219 24.222760 24.275886 0.889892 33.147997 33.203681 0.932729 48.454837 48.442710 -0.203125 57.531584 57.762774 3.872527 23.509226 23.526434 0.288238 26.628470 26.640141 0.195498 28.597319 28.596998 -0.005380 39.420153 39.440946 0.348298 12.670000 23.815008 26.656505 35.077606 71.376675 71.329033 97.092816 93.679079 57.761283 89.089901 102.893921 102.630068 33.147997 58.351922 74.654189 100.547162 23.509226 26.628470 39.420153 49.692132 61.511472 70.353831 92.902897 95.646545 31.490175 80.748244 75.044437 101.942772 61.872458 85.136895 90.418012 79.089278 24.222760 48.454837 57.531584 69.557237 28.597319 52.935534 54.601184 64.522980 2 27 131.1941855 -2.240583696 5.7994368 0.03249196962 1 0.6774006266 -0.01457136078 0.06 44.92111237 0.1582699221 10.39965513 -0.2777288938 -0.194063853 2 3 5 6 7 8 9 0.284165 -0.823296 0.453011 0.178786 0.130883 -0.154515 2.212361 1.506652 0.685446 0.669893 1.070148 1.057991 1.243276 0.877204 12.670000 12.668940 -0.027946 20.747304 20.757035 0.256590 20.871302 20.876111 0.126822 23.118993 23.193516 1.965018 17.862022 17.862125 0.002715 37.017216 37.035992 0.495092 44.167350 44.204922 0.990696 46.697909 46.643770 -1.427537 17.862022 17.882807 0.548051 25.026952 25.043198 0.428362 37.017216 36.986472 -0.810642 43.481981 43.557660 1.995510 23.227473 23.211165 -0.429987 24.282414 24.297902 0.408395 40.261700 40.245241 -0.433994 42.484024 42.576981 2.451096 12.670000 12.667851 -0.028326 20.871302 20.883026 0.154577 23.227473 23.253171 0.338803 23.574421 23.580434 0.079275 17.862022 17.871239 0.121518 37.017216 37.013284 -0.051831 44.167350 44.444065 3.648210 46.063389 45.844453 -2.886437 17.862022 17.894562 0.429013 25.026952 25.059445 0.428390 37.017216 36.997317 -0.262349 43.481981 43.624457 1.878400 20.747304 20.764730 0.229736 23.118993 23.114008 -0.065717 23.227473 23.275495 0.633126 28.069493 28.038060 -0.414414 12.670000 20.871302 23.574421 25.166478 53.304280 53.832213 71.749645 71.508014 43.213124 67.718251 71.394918 82.583471 25.026952 43.481981 57.802328 72.750001 20.747304 23.118993 28.069493 39.500126 46.697909 52.777132 68.002213 70.727366 24.282414 59.440385 58.160247 74.081313 46.063389 60.806060 70.328111 59.042075 17.862022 37.017216 44.167350 50.925097 23.227473 40.261700 42.484024 48.041271 2 10 246.1813895 -7.57645368 5.908888191 0.03249196962 1 0.7309760427 -0.05555754821 0.12 50 0.247632208 12.5 -0.5183832557 -0.5974561756 2 3 5 6 7 8 9 0.267347 -0.270206 -1.608174 0.162685 0.152218 -0.170086 2.359965 1.667550 0.627913 0.627585 0.931476 0.986799 1.244998 0.815775 12.670000 12.661573 -0.212993 16.464722 16.474332 0.242885 16.478941 16.481821 0.072804 22.298459 22.153766 -3.657192 17.694019 17.690175 -0.097171 37.242725 37.263278 0.519488 44.652750 44.697583 1.133185 46.969753 46.893691 -1.922506 17.694019 17.713561 0.493931 26.761747 26.776386 0.370002 37.242725 37.208322 -0.869567 43.538469 43.682201 3.632907 22.357452 22.293946 -1.605152 22.669188 22.731517 1.575390 39.632990 39.617665 -0.387342 41.264941 41.249191 -0.398103 12.670000 12.653102 -0.213548 16.464722 16.480396 0.198079 22.357452 22.015903 -4.316422 22.402199 22.672416 3.414944 17.694019 17.693337 -0.008618 37.242725 37.235388 -0.092726 44.652750 44.669685 0.214023 46.641130 46.674026 0.415733 17.694019 17.726085 0.405236 26.761747 26.791032 0.370094 37.242725 37.222273 -0.258472 43.538469 43.604793 0.838186 16.478941 16.488043 0.115027 22.298459 22.261491 -0.467198 22.357452 22.391832 0.434495 28.249967 28.269768 0.250243 12.670000 16.464722 22.402199 26.270771 52.167516 54.922286 71.387093 82.307023 41.264941 79.389976 86.831412 76.694388 26.761747 43.538469 66.690513 85.488375 16.478941 22.298459 28.249967 39.686305 46.969753 52.768305 71.249346 71.102789 22.669188 61.631587 62.475630 87.825637 46.641130 69.256658 75.378592 62.251600 17.694019 37.242725 44.652750 50.430791 22.357452 39.632990 41.902202 50.429873 1 59 120.4212784 -7.234883067 5.861232817 0.03249196962 1 0.6936510446 -0.05539226393 0.18 52.33594108 0.3052744244 19.27468385 -0.311974086 -0.1516374369 2 3 5 6 7 8 9 0.281084 -0.268263 -1.413495 0.178638 0.127446 -0.149639 2.820740 1.803723 0.665340 0.670357 1.056617 1.056377 1.271543 0.878444 12.670000 12.670540 0.014236 14.894568 14.898525 0.104316 16.176386 16.184702 0.219213 22.799764 22.761115 -1.018786 17.982477 17.975543 -0.182783 38.460950 38.481218 0.534269 45.259036 45.262772 0.098479 47.098802 47.075822 -0.605743 17.982477 17.997024 0.383461 28.108217 28.119830 0.306108 38.460950 38.431272 -0.782304 43.456329 43.467897 0.304936 22.188996 22.227076 1.003791 22.799764 22.759607 -1.058538 39.109478 39.103576 -0.155568 40.287091 40.274332 -0.336329 12.670000 12.671104 0.014557 16.176386 16.192044 0.206378 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