******* Eigenvalues for the 3+1 transverse lattice ******* Couplings: m^2, G^2 N, t/a^2, la_1/a^2, la_2/a^2 0 1 2 3 4 la_3/a^2, la_4/a^2, la_5/a^2, tau 5 6 7 8 Use chi^2 fit with 39 criteria and tolerance 0.01. Overall scale from fitting lowest state to lattice value. Parity doublets (multi,o,state) with fractional error ( 5, 1,0) and ( 6, 1,0), error 0.5 ( 5,-1,0) and ( 6,-1,0), error 0.5 ( 7, 1,0) and ( 4,-1,0), 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 = (2,2) and (K,p) = (12/2,8) (12/2,6) (20/2,6) with error 0.3 (in G^2 N^2 units). Heavy potential determined using (n,K,p,K_max) = ( 0 0,-20/2,2,4) ( 0 0,-20/2,4,4) ( 0 0,-20/2,2,5) ( 0 0,-28/2,2,4) ( 0 0,-44/2,2,5) ( 0 0,-60/2,2,4) , L = 3.5 4.5 6 (all in G^2 N^2 units); with relative error=0.25. Roundness determined using (n,K,p,K_max) = ( 1 0,-13/2,3,4) ( 1 0,-13/2,5,4) ( 1 0,-13/2,3,5) ( 1 0,-23/2,3,4) ( 1 0,-23/2,3,5) ( 1 0,-29/2,3,4) , L=3.5 and error 0.3 ( 1 1,-20/2,2,4) ( 1 1,-20/2,4,4) ( 1 1,-20/2,2,5) ( 1 1,-30/2,2,4) ( 1 1,-44/2,2,5) ( 1 1,-60/2,2,4) , with L=3.5 and error 0.3 (all in G^2 N^2 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/(a^2 sigma); the 9 couplings (G^2 N units) and which--if any--were fit; winding and longitudinal string tension fits; the n=(2,2) winding eigenvalue and the n=(1,0) (1,1) longitudinal eigenvalues (G^2 N units) showing measured value and derived value for each. In each direction, the spectra for each P_perp*a and c^2 values. Finally come the states for the ordinary spectra. 2 42 1584.576020 -0.390792 -24.511494 0.000000 1.000000 0.175896 0.205926 -0.393814 7.112543 0.085156 2.852076 2.473957 2 3 4 5 6 7 8 0.026294 -1.285445 2.016606 0.156762 -1.189599 -0.615869 0.792634 -0.823015 -0.135545 -0.475670 0.073640 -0.244587 12.280000 11.976537 3.129372 9.551005 9.378395 1.779983 -24.723873 -24.833352 1.128973 -27.229054 -28.458722 12.680567 -40.752669 -41.055518 3.123042 -78.602432 -78.821638 2.260495 -107.793003 -107.866738 0.760374 -115.528305 -115.540351 0.124230 -40.752669 -40.757831 0.053236 -53.164254 -53.188376 0.248747 -78.602432 -78.616799 0.148157 -107.793003 -107.835291 0.436081 -54.259067 -54.290544 0.324601 -83.166542 -83.175694 0.094379 -99.209881 -99.210537 0.006768 -99.750139 -99.745389 -0.048992 12.280000 11.744563 2.760763 -24.723873 -24.938523 1.106759 -54.259067 -53.353608 -4.668631 -54.786699 -55.815603 5.305130 -40.752669 -41.034186 1.451532 -78.602432 -78.829520 1.170889 -107.793003 -107.846377 0.275201 -127.804114 -129.930229 10.962452 -40.752669 -41.087246 1.725115 -53.164254 -53.212664 0.249607 -78.602432 -78.842412 1.237362 -107.793003 -105.707283 -10.754172 9.551005 9.136403 2.137725 -27.229054 -29.665160 12.560797 -47.420867 -48.246740 4.258278 -54.259067 -54.290363 0.161367 12.280000 -24.723873 -54.786699 -67.667457 -128.101268 -134.779728 -179.219268 -211.894483 -158.333119 -163.410604 -220.071601 -275.313344 -53.164254 -152.139750 -144.239189 -167.371198 9.551005 -27.229054 -47.420867 -78.507077 -115.528305 -132.652277 -165.934712 -204.938953 -83.166542 -170.990759 -191.216187 -220.056187 -147.498506 -136.948863 -200.031864 -174.210744 -40.752669 -78.602432 -107.793003 -127.804114 -54.259067 -99.750139 -119.595855 -99.209881 2 68 108.906948 -1.145001 8.604062 0.001968 1.000000 -0.139848 -0.039730 -0.156516 4.969961 0.077753 0.506069 -2.137022 2 3 4 5 6 7 8 0.181708 -0.738100 0.938735 0.165102 -1.702645 -0.623063 3.157147 0.832909 -1.096640 -0.988529 -0.223740 -0.769130 12.280000 12.317578 0.940015 12.781100 12.823722 1.066181 25.423779 25.444593 0.520670 29.906852 29.964359 1.438539 25.450626 25.494765 1.104127 48.239504 48.286866 1.184737 57.690465 57.706122 0.391663 59.998672 60.002700 0.100757 25.450626 25.452790 0.054116 36.505274 36.507595 0.058061 48.239504 48.241866 0.059075 57.690465 57.709513 0.476492 30.771468 30.776306 0.121038 35.412212 35.409319 -0.072352 49.424531 49.424804 0.006849 56.963634 56.971286 0.191412 12.280000 12.358922 0.987113 25.423779 25.465337 0.519788 30.525728 30.566090 0.504820 30.771468 30.663707 -1.347814 25.450626 25.486297 0.446147 48.239504 48.286326 0.585616 57.690465 57.718960 0.356404 63.931395 63.895295 -0.451524 25.450626 25.507574 0.712277 36.505274 36.509919 0.058100 48.239504 48.292080 0.657587 57.690465 57.731275 0.510431 12.781100 12.862546 1.018680 29.906852 29.973645 0.835416 30.771468 30.705906 -0.820018 31.229660 31.231186 0.019090 12.280000 25.423779 30.525728 31.364678 63.931395 72.718324 85.695774 88.043643 62.542482 77.934331 86.539716 90.508174 36.505274 62.667021 84.610865 85.075727 12.781100 29.906852 31.229660 47.960194 59.998672 65.944317 88.628375 90.528477 35.412212 82.021587 86.536655 86.312801 74.707508 74.392754 81.459287 77.418478 25.450626 48.239504 57.690465 66.317029 30.771468 49.424531 56.963634 62.770334 2 35 82.817838 -1.074489 8.667260 0.007919 1.000000 0.322671 -0.038541 -0.177108 10.038382 0.129611 1.982824 -1.657000 2 3 4 5 6 7 8 0.184809 -0.880988 1.137505 0.159213 -0.835478 -0.679033 2.790394 0.739672 -0.291067 -0.154400 0.254458 0.064337 12.280000 12.321435 1.061934 13.024628 13.068677 1.128910 22.656711 22.692879 0.926940 31.116775 31.105603 -0.286314 25.454093 25.496612 1.089696 49.513230 49.563064 1.277177 56.336191 56.362590 0.676582 61.619110 61.624611 0.140982 25.454093 25.462060 0.204168 37.965828 37.975664 0.252086 49.513230 49.526613 0.342975 56.336191 56.358673 0.576172 31.612367 31.628352 0.409670 37.075371 37.066843 -0.218560 51.276745 51.277511 0.019637 57.986829 58.010826 0.614991 12.280000 12.364923 1.088231 22.656711 22.729024 0.926652 31.204233 31.292166 1.126791 31.612367 31.411897 -2.568883 25.454093 25.488307 0.438429 49.513230 49.565568 0.670673 56.336191 56.381712 0.583323 66.224723 66.210320 -0.184570 25.454093 25.520908 0.856187 37.965828 37.985512 0.252239 49.513230 49.587118 0.946826 56.336191 56.388133 0.665603 13.024628 13.110596 1.101617 31.116775 31.070043 -0.598827 31.612367 31.628178 0.202605 34.838989 34.906964 0.871047 12.280000 22.656711 31.204233 34.126190 66.224723 73.901342 88.233584 106.442286 64.581824 82.854494 96.224949 101.931822 37.965828 64.728453 89.903919 90.813244 13.024628 31.116775 34.838989 50.038437 61.619110 67.720983 90.430186 96.144849 37.075371 86.414289 89.793721 95.109210 70.513136 83.168002 82.658695 93.443898 25.454093 49.513230 56.336191 71.702648 31.612367 51.276745 57.986829 62.597564 2 86 57.017804 -1.016523 8.404357 0.018006 1.000000 0.372260 -0.112615 -0.167708 5.858440 0.067726 -0.035901 -2.433310 2 3 4 5 6 7 8 0.220835 -0.918626 1.098873 0.160285 -0.526452 -0.777421 2.685293 0.985412 0.019987 0.172077 0.506136 0.412105 12.271820 12.309943 1.132076 12.280000 12.313100 0.982925 17.494617 17.535972 1.228066 28.684225 28.692843 0.255935 26.627334 26.662121 1.033018 51.853382 51.893006 1.176657 53.653632 53.681493 0.827353 60.388363 60.392453 0.121469 26.627334 26.640568 0.392993 36.816415 36.828422 0.356542 51.853382 51.874934 0.639993 53.653632 53.665321 0.347118 29.409951 29.429903 0.592499 34.928202 34.916318 -0.352879 52.546737 52.542112 -0.137352 54.444963 54.477324 0.960976 12.280000 12.352866 1.081895 17.494617 17.577334 1.228170 28.684225 28.681101 -0.046373 29.409951 29.280456 -1.922709 26.627334 26.669474 0.625680 51.853382 51.892294 0.577757 53.653632 53.700705 0.698925 68.333357 68.253462 -1.186259 26.627334 26.681293 0.801163 36.816415 36.840444 0.356782 51.853382 51.936753 1.237866 53.653632 53.685474 0.472780 12.271820 12.341398 1.033080 28.702956 28.700248 -0.040218 29.409951 29.369516 -0.600373 34.802439 34.814991 0.186375 12.280000 17.494617 28.684225 31.355936 68.333357 72.600027 90.987736 104.037301 62.387816 83.982644 94.361734 100.421065 36.816415 63.173611 86.614335 89.941577 12.271820 28.702956 34.802439 48.877292 60.388363 69.120619 91.598580 94.470266 34.928202 82.334166 89.342422 88.863384 69.335746 84.252764 79.009981 91.742516 26.627334 51.853382 53.653632 69.526280 29.409951 52.546737 54.444963 62.210943 2 67 40.908834 -0.926301 8.085826 0.032492 1.000000 0.542127 -0.074610 -0.244019 9.265654 0.099090 1.139061 -1.458716 2 3 4 5 6 7 8 0.210465 -1.031822 1.104286 0.155316 -0.393108 -0.812002 2.160157 0.789933 0.125733 0.239792 0.570401 0.457616 12.280000 12.319177 1.066742 12.833536 12.893713 1.638531 14.734592 14.782147 1.294844 29.692730 29.633461 -1.613807 24.879321 24.915837 0.994286 49.801069 49.836888 0.975297 51.368276 51.408778 1.102828 59.105961 59.113115 0.194779 24.879321 24.899296 0.543890 35.082356 35.103181 0.567042 49.801069 49.833425 0.881011 51.368276 51.377519 0.251676 29.692730 29.721406 0.780793 36.781212 36.769026 -0.331800 52.961663 53.003066 1.127354 54.314430 54.310157 -0.116332 12.280000 12.372018 1.252754 14.734592 14.840976 1.448338 29.692730 29.596884 -1.304883 32.421558 32.438835 0.235211 24.879321 24.928545 0.670155 49.801069 49.850168 0.668445 51.368276 51.418626 0.685475 67.671715 67.656059 -0.213140 24.879321 24.943149 0.868973 35.082356 35.124037 0.567466 49.801069 49.888195 1.186151 51.368276 51.417246 0.666688 12.833536 12.928955 1.299048 29.692730 29.731800 0.531897 33.835052 33.801135 -0.461749 33.857083 33.857106 0.000319 12.280000 14.734592 32.421558 33.253830 68.444003 70.195856 92.168499 90.214956 64.074351 87.510864 104.076291 102.603283 35.082356 62.911100 76.751752 99.657449 12.833536 33.835052 33.857083 47.515379 59.105961 68.421550 91.739434 94.321174 36.781212 81.521988 95.148240 87.859228 67.671715 86.191819 91.352039 79.359570 24.879321 49.801069 51.368276 70.063617 29.692730 54.314430 52.961663 63.734197 5 100 26.429819 -0.958450 7.293168 0.051777 1.000000 0.736052 -0.040684 -0.112741 9.561634 0.111659 1.940532 -1.982974 2 3 4 5 6 7 8 0.287021 -1.050202 0.901323 0.156967 -0.798037 -0.659176 2.167193 1.358629 -0.223636 -0.100305 0.259178 0.127893 12.280000 12.319130 1.310569 25.567872 25.597327 0.986531 27.209736 27.211813 0.069553 30.683252 30.727407 1.478859 23.384688 23.397662 0.434541 47.397588 47.420202 0.757399 55.325692 55.355568 1.000609 59.358371 59.345954 -0.415868 23.384688 23.413646 0.969893 32.951583 32.976766 0.843440 47.397588 47.394365 -0.107929 55.325692 55.339680 0.468466 30.820917 30.840099 0.642443 34.775747 34.765268 -0.350951 52.211572 52.227129 0.521031 55.372036 55.379645 0.254835 12.280000 12.358285 1.310986 27.209736 27.213736 0.066978 30.820917 30.873778 0.885213 31.144562 31.143611 -0.015917 23.384688 23.416118 0.526339 47.397588 47.421725 0.404204 55.325692 55.334482 0.147191 61.344496 61.407131 1.048907 23.384688 23.437113 0.877926 32.951583 33.001961 0.843647 47.397588 47.412351 0.247225 55.325692 55.404039 1.312010 25.567872 25.626739 0.985821 30.683252 30.770971 1.468965 30.820917 30.782056 -0.650779 31.007561 31.040771 0.556148 12.280000 27.209736 31.607473 31.144562 69.926229 68.434554 93.766544 90.332997 59.705308 90.103106 97.128327 112.196534 32.951583 58.612767 74.536491 95.373630 25.567872 30.683252 31.007561 49.439842 59.358371 68.772185 88.206541 91.959161 34.775747 78.270935 73.599176 101.751235 61.344496 77.969285 93.665733 80.541121 23.384688 47.397588 55.325692 65.756254 30.820917 52.211572 55.372036 63.311003 5 100 42.409431 -0.937726 6.040147 0.076429 1.000000 0.716338 0.001518 -0.163326 12.928868 0.011827 2.939927 -1.571862 2 3 4 5 6 7 8 0.333204 -0.973347 0.649888 0.176114 -0.444290 -0.460555 2.698671 1.773524 0.286757 0.332541 0.736652 0.544459 12.280000 12.326387 1.493730 26.251751 26.289737 1.223202 29.505426 29.494069 -0.365728 29.544639 29.553126 0.273316 21.566793 21.579172 0.398621 43.658979 43.676947 0.578584 52.107473 52.122490 0.483568 54.224449 54.245915 0.691226 21.566793 21.590252 0.755406 30.560312 30.578463 0.584482 43.658979 43.667352 0.269605 52.107473 52.086719 -0.668311 31.157899 31.175007 0.550924 34.646968 34.638231 -0.281341 47.712569 47.733393 0.670552 53.430245 53.406072 -0.778405 12.280000 12.372761 1.493536 29.544639 29.440055 -1.683883 29.657221 29.644531 -0.204317 31.157899 31.298258 2.259900 21.566793 21.598025 0.502865 43.658979 43.689124 0.485363 52.107473 52.099059 -0.135478 56.575550 56.608208 0.525826 21.566793 21.607216 0.650838 30.560312 30.596624 0.584653 43.658979 43.681603 0.364264 52.107473 52.105176 -0.036992 26.251751 26.327616 1.221485 29.505426 29.537223 0.511949 31.157899 31.125535 -0.521093 33.500627 33.537351 0.591280 12.280000 29.544639 29.657221 33.701585 63.591813 64.458106 85.706229 80.868468 56.668693 86.316394 88.519013 110.963736 30.560312 54.618579 69.977337 84.013359 26.251751 29.505426 33.500627 47.458137 54.224449 64.459979 78.507594 82.926605 34.646968 70.421746 68.865241 92.649188 56.575550 74.489925 68.063228 90.002110 21.566793 43.658979 52.107473 57.280901 31.157899 47.712569 53.430245 58.864896 2 58 46.622174 -0.934479 5.435862 0.107240 1.000000 0.831783 -0.030554 -0.204996 10.195881 0.034678 1.773425 -1.360561 2 3 4 5 6 7 8 0.355318 -0.887521 0.321706 0.192360 -0.314440 -0.267199 3.063004 1.995239 0.549322 0.547022 1.014411 0.748396 12.280000 12.327147 1.457000 24.198144 24.233021 1.077796 27.133857 27.108263 -0.790925 27.780657 27.780544 -0.003502 20.643780 20.655345 0.357379 41.972286 41.987323 0.464705 50.752831 50.786434 1.038447 51.718254 51.723559 0.163955 20.643780 20.665063 0.657698 30.743219 30.760865 0.545333 41.972286 41.982928 0.328870 50.752831 50.766193 0.412952 30.397485 30.414666 0.530967 33.983363 33.974612 -0.270434 45.802735 45.822145 0.599839 50.765034 50.748733 -0.503773 12.280000 12.374298 1.457059 27.133857 27.063832 -1.081999 28.288383 28.305738 0.268165 30.397485 30.461099 0.982955 20.643780 20.670910 0.419190 41.972286 42.000884 0.441886 50.752831 50.772911 0.310273 51.923910 51.910990 -0.199645 20.643780 20.682332 0.595691 30.743219 30.778524 0.545523 41.972286 41.995115 0.352746 50.752831 50.826753 1.142226 24.198144 24.267919 1.078144 27.780657 27.800304 0.303588 30.397485 30.370754 -0.413028 32.461346 32.485184 0.368348 12.280000 28.288383 27.133857 32.558602 60.321003 60.895952 80.515845 75.542603 53.962115 85.869491 83.736095 107.863444 30.743219 52.266355 67.361409 77.366183 24.198144 27.780657 32.461346 45.185289 51.718254 60.892743 74.632612 78.198932 33.983363 67.319756 68.802374 88.124001 54.184348 71.650166 66.238129 87.720645 20.643780 41.972286 50.752831 51.923910 30.397485 45.802735 50.765034 56.038619 2 35 106.006285 -1.312030 3.187057 0.145309 1.000000 0.798827 0.481080 -0.311313 8.801926 -0.032445 2.346571 -1.184404 2 3 4 5 6 7 8 0.377831 -0.711843 0.038222 0.223850 -0.311903 0.111264 3.712270 2.315587 0.799215 0.613689 1.348081 0.712244 12.280000 12.307887 0.537300 13.791650 13.837866 0.890419 17.464684 17.467742 0.058918 21.478216 21.449567 -0.551986 12.309328 12.314844 0.106271 27.836203 27.843981 0.149857 31.527086 31.530343 0.062742 32.665401 32.667043 0.031625 12.309328 12.318107 0.169140 19.253527 19.261252 0.148823 27.836203 27.845520 0.179507 31.527086 31.534907 0.150670 23.586303 23.591370 0.097628 25.333757 25.333126 -0.012166 30.666547 30.671897 0.103082 33.846770 33.840280 -0.125049 12.280000 12.333181 0.512314 17.464684 17.470718 0.058125 21.478216 21.425022 -0.512439 23.586303 23.626589 0.388092 12.309328 12.321171 0.114092 27.836203 27.852778 0.159676 31.527086 31.532535 0.052488 32.665401 32.663181 -0.021390 12.309328 12.326070 0.161287 19.253527 19.268980 0.148862 27.836203 27.853876 0.170254 31.527086 31.543720 0.160239 13.791650 13.885932 0.908252 21.611349 21.622835 0.110649 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