********* 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 21 1117.398601 -7.661771025 8.75508891 0 1 -0.1783774396 -0.06394395242 -0.05083352092 116.4500954 -0.01326901624 39.29991539 -0.4404112743 -0.3517404219 2 3 4 5 6 7 8 9 0.186099 -0.362114 -0.380570 0.085192 0.393106 -0.510008 2.003179 1.079108 0.617785 0.604389 0.987788 0.850089 1.225995 0.752658 12.670000 12.694400 0.636088 16.981548 16.988006 0.168366 19.463746 19.459991 -0.097900 22.918307 22.882922 -0.922456 24.564903 24.585327 0.532442 45.510981 45.532570 0.562805 50.701397 50.717262 0.413581 52.997935 52.994549 -0.088271 24.564903 24.580211 0.399072 26.163021 26.164812 0.046688 45.510981 45.513156 0.056713 50.701397 50.708508 0.185373 22.918307 22.927040 0.227659 25.295291 25.287642 -0.199383 45.682791 45.699873 0.445321 49.098956 49.098191 -0.019965 12.670000 12.718780 0.635827 19.463746 19.456106 -0.099594 22.918307 22.875904 -0.552697 23.508881 23.526791 0.233446 24.564903 24.608659 0.570341 45.510981 45.534853 0.311161 50.701397 50.718010 0.216535 61.756175 66.509374 61.955633 24.564903 24.592569 0.360615 26.163021 26.166650 0.047296 45.510981 45.534606 0.307945 50.701397 50.730714 0.382122 16.981548 16.994649 0.170772 22.918307 22.907158 -0.145328 23.503245 23.506446 0.041724 37.007206 37.032253 0.326480 12.670000 19.463746 23.508881 31.563880 64.391413 72.876136 74.124229 95.973013 51.847590 69.385751 74.488709 78.638486 26.163021 52.795625 70.543981 77.810852 16.981548 23.503245 37.007206 43.951465 52.997935 68.622713 77.477935 92.652224 25.295291 70.619917 75.255511 78.761934 68.335136 61.756175 78.018822 78.623000 24.564903 45.510981 50.701397 65.760405 22.918307 45.682791 49.098956 63.294204 2 20 14.61051573 -1.246235226 10.93495274 0.001967542671 1 0.4073290257 -0.009436186153 -0.07682033988 225.6879118 0.07234282012 90.37516016 -0.631287677 -0.4969903246 2 3 4 5 6 7 8 9 0.180057 -0.863148 0.798516 0.094125 0.306409 -0.357725 1.189106 0.677125 0.589708 0.683498 0.918142 0.887620 1.076977 0.869542 12.670000 12.707609 1.184772 24.128879 24.152876 0.755977 24.510924 24.535220 0.765382 31.039674 31.008993 -0.966537 27.919538 27.943435 0.752829 53.876920 53.922027 1.420974 62.974263 63.008516 1.079062 68.167684 68.155124 -0.395695 27.919538 27.957237 1.187623 32.835467 32.861817 0.830108 53.876920 53.873470 -0.108701 62.974263 62.998559 0.765389 31.039674 31.065305 0.807452 36.303216 36.288872 -0.451859 59.513253 59.539537 0.828000 62.564149 62.578113 0.439909 12.670000 12.745233 1.185021 24.510924 24.558721 0.752876 31.039674 31.007951 -0.499682 32.208769 32.195705 -0.205774 27.919538 27.973961 0.857235 53.876920 53.913022 0.568658 62.974263 63.005330 0.489344 68.987166 68.991770 0.072514 27.919538 27.988318 1.083372 32.835467 32.888191 0.830479 53.876920 53.923975 0.741177 62.974263 63.058503 1.326897 24.128879 24.177595 0.767344 31.039674 31.061893 0.349981 32.286015 32.253145 -0.517750 46.419209 46.478271 0.930316 12.670000 24.510924 32.208769 40.106111 80.801120 83.647997 110.352644 107.749102 67.390301 86.906221 109.492617 110.928312 32.835467 67.372281 87.441153 93.362190 24.128879 32.286015 46.419209 56.373357 68.167684 81.145407 99.551673 112.181697 36.303216 86.632454 91.416825 102.522311 68.987166 86.837858 93.646117 105.339264 27.919538 53.876920 62.974263 76.611381 31.039674 59.513253 62.564149 70.796540 2 29 15.42933955 -1.173840623 10.13341747 0.007919222016 1 0.486209448 -0.03203773073 -0.08888792618 452.5604901 0.09409934055 206.0652447 -0.7226062936 -0.6217454002 2 3 4 5 6 7 8 9 0.194073 -0.896134 0.782248 0.100972 0.262943 -0.281687 1.339779 0.754232 0.599798 0.668153 0.900888 0.875169 1.129583 0.855790 12.670000 12.706299 1.142185 22.624258 22.651426 0.854890 22.806618 22.834285 0.870552 30.644125 30.629844 -0.449369 27.271838 27.294289 0.706439 53.050882 53.092002 1.293872 61.175824 61.213041 1.171057 66.647645 66.633171 -0.455455 27.271838 27.307307 1.116055 33.976145 34.004062 0.878432 53.050882 53.050455 -0.013423 61.175824 61.204816 0.912263 30.644125 30.670056 0.815956 35.978850 35.964420 -0.454058 58.742939 58.768535 0.805403 60.154397 60.170314 0.500846 12.670000 12.742624 1.142597 22.806618 22.860440 0.846775 30.644125 30.615031 -0.457735 30.905799 30.884479 -0.335421 27.271838 27.319988 0.757540 53.050882 53.085756 0.548676 61.175824 61.213419 0.591481 68.997544 69.102246 1.647283 27.271838 27.339551 1.065324 33.976145 34.031997 0.878712 53.050882 53.097242 0.729374 61.175824 61.268779 1.462461 22.624258 22.679467 0.868612 30.644125 30.698285 0.852106 30.946723 30.879902 -1.051292 45.164143 45.274365 1.734117 12.670000 22.806618 30.905799 39.496996 78.472170 80.509211 106.076281 115.524275 66.065163 88.665087 110.335167 113.254409 33.976145 66.610540 89.971106 92.646556 22.624258 30.946723 45.164143 52.221801 66.647645 78.399828 101.498702 105.181927 35.978850 84.898712 95.364098 94.784184 68.997544 88.299272 95.035866 95.054799 27.271838 53.050882 61.175824 76.931052 30.644125 58.742939 60.154397 66.156283 2 11 29.45473395 -1.228379936 9.088732157 0.01800590693 1 0.6004759605 -0.03103963355 -0.07736420642 50 0.1353960848 12.5 -0.8992109102 -0.8109590062 2 3 4 5 6 7 8 9 0.212328 -0.935705 0.752828 0.100030 0.235026 -0.236838 1.432775 0.857021 0.597446 0.614500 0.861099 0.814577 1.173600 0.787488 12.670000 12.698067 0.866611 23.304488 23.326278 0.672809 23.306215 23.331905 0.793232 29.126740 29.136505 0.301506 25.227117 25.243064 0.492370 50.399696 50.434963 1.088914 58.433319 58.471125 1.167314 63.850304 63.826126 -0.746528 25.227117 25.260902 1.043166 33.350070 33.379913 0.921454 50.399696 50.392075 -0.235304 58.433319 58.470700 1.154179 29.973124 29.994250 0.652291 34.528737 34.517042 -0.361111 56.168158 56.184229 0.496216 57.123126 57.146247 0.713894 12.670000 12.726169 0.867159 23.304488 23.358682 0.836667 29.126740 29.134718 0.123154 29.973124 29.924297 -0.753802 25.227117 25.263362 0.559560 50.399696 50.426011 0.406264 58.433319 58.466844 0.517570 66.251374 66.295968 0.688455 25.227117 25.290350 0.976205 33.350070 33.409765 0.921598 50.399696 50.428590 0.446076 58.433319 58.546483 1.747054 23.306215 23.346885 0.627882 29.160715 29.239760 1.220315 29.973124 29.887356 -1.324110 41.834238 41.863116 0.445835 12.670000 23.304488 29.126740 36.909432 74.269896 75.368329 100.998091 101.722422 63.281015 88.293483 111.101781 104.848146 33.350070 62.758721 83.409916 95.694719 23.306215 29.160715 41.834238 50.451733 63.850304 73.653446 97.114220 100.236689 34.528737 80.176189 96.939344 92.978809 66.251374 87.868920 91.729124 81.486206 25.227117 50.399696 58.433319 75.139395 29.973124 56.168158 57.123126 65.478448 2 20 21.65750316 -1.053819788 9.765653758 0.03249196962 1 0.7158250508 -0.06664943618 -0.1077657 197.2131732 0.1641942723 70.52359303 -0.9496511047 -0.8370762657 2 3 4 5 6 7 8 9 0.213582 -0.972286 0.707806 0.110696 0.197525 -0.186931 1.414064 0.824846 0.611188 0.671256 0.867757 0.862616 1.211637 0.874770 12.670000 12.705397 1.181273 22.241244 22.275984 1.159339 22.479501 22.504757 0.842850 30.862954 30.878449 0.517098 27.824191 27.844361 0.673128 55.500468 55.537527 1.236719 63.006933 63.054359 1.582718 70.154680 70.130652 -0.801867 27.824191 27.861410 1.242097 38.348868 38.386595 1.259042 55.500468 55.499313 -0.038542 63.006933 63.045293 1.280158 32.529532 32.557502 0.933428 38.280198 38.265676 -0.484621 61.130025 61.154056 0.801955 62.124391 62.146611 0.741528 12.670000 12.740839 1.182032 22.241244 22.308198 1.117200 30.862954 30.867814 0.081095 32.529532 32.470221 -0.989660 27.824191 27.865418 0.687918 55.500468 55.533867 0.557299 63.006933 63.048790 0.698425 73.527497 73.570030 0.709715 27.824191 27.897776 1.227847 38.348868 38.424331 1.259193 55.500468 55.538767 0.639053 63.006933 63.133624 2.113977 22.479501 22.532423 0.883072 30.881718 30.920128 0.640918 32.529532 32.481174 -0.806893 47.304212 47.333317 0.485650 12.670000 22.241244 30.862954 41.404635 81.408090 81.829962 111.373515 106.235973 69.648114 102.470804 121.933021 120.354995 38.348868 69.349058 85.278209 119.768700 22.479501 30.881718 47.304212 54.018121 70.154680 80.275194 109.105113 110.156040 38.280198 94.304015 97.341562 113.612525 73.527497 102.088667 102.458970 90.192999 27.824191 55.500468 63.006933 82.271015 32.529532 62.124391 61.130025 72.905616 2 11 29.11596973 -1.04396744 8.720529576 0.0517766953 1 0.8047884295 -0.08106672408 -0.07231883504 50 0.1646660674 12.5 -0.9487300165 -0.8650075065 2 3 4 5 6 7 8 9 0.255274 -0.940131 0.504020 0.127354 0.169500 -0.159602 1.710492 1.165066 0.640458 0.710966 0.895969 0.916739 1.257322 0.937437 12.670000 12.698914 1.029875 25.575673 25.591631 0.568390 26.488629 26.501102 0.444277 30.429135 30.422205 -0.246837 26.652142 26.664579 0.443003 53.485576 53.513529 0.995640 62.301516 62.343914 1.510112 67.801591 67.770592 -1.104133 26.652142 26.688213 1.284808 37.736268 37.770780 1.229277 53.485576 53.469519 -0.571923 62.301516 62.341720 1.431957 32.603816 32.622012 0.648130 37.007863 36.997791 -0.358743 59.200209 59.207861 0.272571 60.222321 60.250026 0.986791 12.670000 12.727844 1.030139 26.488629 26.513623 0.445118 30.429135 30.434849 0.101743 32.603816 32.586207 -0.313599 26.652142 26.685023 0.585585 53.485576 53.503483 0.318897 62.301516 62.322356 0.371132 69.250260 69.317587 1.199039 26.652142 26.716273 1.142113 37.736268 37.805301 1.229417 53.485576 53.491576 0.106852 62.301516 62.442286 2.506960 25.575673 25.607537 0.567481 30.429231 30.433262 0.071785 32.603816 32.629393 0.455512 43.607423 43.607457 0.000609 12.670000 26.488629 30.429135 38.991085 79.133760 77.857998 107.663215 102.987930 65.745224 103.807622 107.347712 131.088032 37.736268 65.669568 85.320912 113.460614 25.575673 30.429231 43.607423 54.443710 67.801591 77.536523 103.235388 105.541051 37.007863 90.729530 83.596290 117.968006 69.250260 88.418905 111.618245 90.499502 26.652142 53.485576 62.301516 77.467482 32.603816 59.200209 60.222321 72.402527 2 38 36.44149015 -0.9986512826 8.317435144 0.07642881742 1 0.9635552879 -0.04778704622 -0.1152279495 631.2203467 0.1973714639 91.78736596 -1.120582988 -1.030026197 2 3 4 5 6 7 8 9 0.260562 -0.947215 0.326966 0.127830 0.144350 -0.125211 1.637671 1.178153 0.646526 0.673171 0.873031 0.867812 1.290466 0.891021 12.670000 12.707056 1.284914 27.934971 27.957109 0.767631 29.074784 29.091021 0.563050 34.438197 34.496968 2.037925 25.817220 25.830583 0.463345 52.880905 52.905602 0.856359 61.762435 61.800978 1.336496 68.043908 68.119572 2.623709 25.817220 25.853955 1.273780 38.068752 38.107682 1.349893 52.880905 52.871600 -0.322672 61.762435 61.788973 0.920244 34.438197 34.460601 0.776875 39.084506 39.073488 -0.382044 59.545922 59.555868 0.344878 61.130988 61.155326 0.843916 12.670000 12.744107 1.284848 29.074784 29.107502 0.567264 34.438197 34.478900 0.705700 34.464284 34.594474 2.257195 25.817220 25.850694 0.580358 52.880905 52.902990 0.382888 61.762435 61.779681 0.299015 68.729474 68.952183 3.861254 25.817220 25.883935 1.156682 38.068752 38.146619 1.350026 52.880905 52.889761 0.153539 61.762435 61.874045 1.935068 27.934971 27.979100 0.765092 34.438197 34.654596 3.751867 37.890252 37.881248 -0.156104 39.236981 39.027231 -3.636583 12.670000 29.074784 34.464284 37.243267 79.224364 77.028665 108.071702 103.253303 66.974722 111.215641 113.422377 142.206466 38.068752 65.892796 89.786949 108.794711 27.934971 37.890252 39.236981 54.944676 68.043908 77.171711 102.653247 104.783710 39.084506 90.427191 86.311924 122.332212 68.729474 93.252559 95.143364 109.460326 25.817220 52.880905 61.762435 75.427882 34.438197 59.545922 61.130988 72.454460 2 29 35.68033307 -1.052498571 6.313871063 0.1072401379 1 1.069443599 -0.002399241499 -0.144075724 112.5411493 0.1968792034 17.29744757 -0.8179134534 -0.8163233507 2 3 4 5 6 7 8 9 0.294596 -0.840465 -0.036160 0.169747 0.100031 -0.088355 2.051433 1.511780 0.701997 0.678807 0.964442 0.950755 1.349162 0.904470 12.670000 12.705105 1.044760 28.951537 28.981692 0.897448 29.239731 29.257713 0.535150 29.435934 29.539558 3.083888 21.133559 21.143304 0.290019 43.978113 43.995199 0.508484 54.695347 54.728687 0.992205 56.336223 56.332660 -0.106050 21.133559 21.162007 0.846613 32.513310 32.542937 0.881734 43.978113 43.975422 -0.080092 54.695347 54.771926 2.279028 31.100868 31.118570 0.526802 34.595987 34.587430 -0.254673 49.462701 49.472341 0.286874 52.311872 52.322558 0.318042 12.670000 12.740199 1.044585 29.239731 29.275615 0.533969 29.435934 29.448943 0.193578 31.100868 31.106087 0.077653 21.133559 21.158071 0.364746 43.978113 43.997883 0.294179 54.695347 54.745954 0.753040 56.336223 56.295405 -0.607380 21.133559 21.185422 0.771734 32.513310 32.572576 0.881891 43.978113 43.987278 0.136385 54.695347 54.864733 2.520514 28.951537 29.012289 0.904011 31.100868 31.075192 -0.382074 31.204697 31.228451 0.353467 32.326457 32.300588 -0.384936 12.670000 29.239731 29.435934 31.227854 65.594589 63.567098 88.382297 83.229370 56.273904 96.584087 93.556805 121.987574 32.513310 54.810695 73.365142 79.598341 28.951537 32.326457 31.204697 46.897519 56.515169 63.923466 82.723847 85.390886 34.595987 73.626207 75.250498 100.749758 56.686417 77.854539 68.554244 102.930825 21.133559 43.978113 54.695347 56.336223 31.100868 49.462701 52.311872 59.853154 2 11 61.15551283 -1.128602283 5.340781703 0.1453085056 1 1.24391 0.13023 -0.169091 50 0.231558 12.5 -0.526116 -0.515096 2 3 4 5 6 7 8 9 0.310317 -0.767859 -0.405700 0.199066 0.061852 -0.054759 2.067692 1.663967 0.742746 0.662844 1.037673 0.977975 1.388670 0.886405 12.670000 12.704895 0.925337 26.174270 26.165787 -0.224945 26.834353 26.840053 0.151143 27.860813 27.874619 0.366102 18.171653 18.179001 0.194833 38.554864 38.568224 0.354254 46.802136 46.814148 0.318527 50.205268 50.213886 0.228534 18.171653 18.196844 0.667991 28.974342 29.002278 0.740808 38.554864 38.554346 -0.013737 46.802136 46.809836 0.204174 29.922325 29.936562 0.377519 32.570008 32.564008 -0.159099 43.867525 43.875269 0.205350 47.645755 47.649941 0.110990 12.670000 12.739800 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