******* 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 40 criteria and tolerance 0.01. Overall scale from fitting lowest state to lattice value. 4 parity doublets with fractional error 0.5 0.5 0.5 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 19 25147.297220 -1.433131 7.144234 0.000000 1.000000 0.210576 -0.021289 0.042190 3.224393 -0.013861 2.812583 -1.088388 2 3 4 5 6 7 8 0.248726 -0.790286 0.945032 0.176626 -0.579660 -0.320147 2.127549 1.317647 0.110438 0.238398 0.502989 0.451784 -23.662915 -23.107147 15.801190 12.280000 12.286269 0.178223 19.548864 19.532760 -0.457838 19.891711 19.892665 0.027106 20.185315 20.187264 0.055426 37.916346 37.935821 0.553680 45.890561 45.868835 -0.617694 46.108538 46.109409 0.024779 20.185315 20.200992 0.445725 21.302219 21.305724 0.099654 37.916346 37.883351 -0.938114 42.605649 42.633909 0.803455 20.779400 20.756200 -0.659605 20.848253 20.870904 0.644017 39.093742 39.090282 -0.098377 42.261119 42.250533 -0.300992 12.280000 12.292507 0.177795 19.891711 19.891688 -0.000334 20.779400 20.694495 -1.206979 20.848253 20.894172 0.652773 20.185315 20.204086 0.266843 37.916346 37.921172 0.068605 45.890561 45.839410 -0.727137 47.908977 47.963784 0.779111 20.185315 20.201721 0.233227 21.302219 21.309261 0.100112 37.916346 37.884817 -0.448203 42.605649 42.661819 0.798480 -23.662915 -22.557373 15.715976 19.548864 19.517512 -0.445677 20.779400 20.814479 0.498678 22.699478 22.700571 0.015541 12.280000 19.891711 22.811031 26.370384 55.384798 59.981216 61.577991 75.568122 42.261119 53.692455 62.002800 62.517443 21.302219 42.605649 53.147611 58.598774 -23.662915 19.548864 22.699478 34.127440 46.108538 56.871656 63.210375 64.645180 20.848253 52.632948 57.743347 61.257102 47.908977 54.132547 62.364150 62.429509 20.185315 37.916346 45.890561 49.118851 20.779400 39.093742 43.588171 45.722843 2 35 74.516053 -1.418650 7.051396 0.001968 1.000000 0.217043 0.001564 0.027502 2.958249 -0.049235 -0.139552 -1.657538 2 3 4 5 6 7 8 0.271465 -0.793202 0.931498 0.169490 -1.084655 -0.526830 2.432693 1.494954 -0.458206 -0.328446 0.070765 -0.106956 12.280000 12.307145 0.831378 21.798628 21.812861 0.435927 22.870517 22.945539 2.297723 24.542525 24.371578 -5.235652 21.318398 21.322710 0.132062 41.233098 41.251537 0.564729 49.609407 49.605048 -0.133515 49.703000 49.694895 -0.248243 21.318398 21.331914 0.413956 23.405451 23.409392 0.120708 41.233098 41.214817 -0.559904 46.820439 46.831987 0.353694 24.542525 24.569969 0.840527 24.764257 24.736894 -0.838040 42.897185 42.903242 0.185495 47.611167 47.519786 -2.798759 12.280000 12.334233 0.830500 21.798628 21.827128 0.436445 24.542525 24.423426 -1.823849 24.764257 24.751335 -0.197871 21.318398 21.341273 0.350292 41.233098 41.246510 0.205380 49.609407 49.574268 -0.538103 52.066935 52.063148 -0.057984 21.318398 21.331130 0.194962 23.405451 23.413342 0.120855 41.233098 41.220230 -0.197054 46.820439 46.843306 0.350177 22.870517 22.910348 0.609958 24.542525 24.439655 -1.575323 25.050006 25.099742 0.761641 26.590585 26.590272 -0.004793 12.280000 21.798628 24.974594 26.343123 60.025927 60.443422 71.740015 77.958287 47.611167 61.724462 69.835562 74.270860 23.405451 46.820439 59.637596 62.488596 22.870517 25.050006 26.590585 45.898258 49.703000 61.247661 69.237423 70.425251 24.764257 59.370220 63.623885 67.693881 52.066935 61.691433 62.257845 70.089854 21.318398 41.233098 49.609407 52.487250 24.542525 42.897185 47.784177 51.441290 2 18 45.532090 -1.066248 8.713914 0.007919 1.000000 0.322143 -0.039116 0.063587 5.290527 -0.046181 1.393385 -1.689585 2 3 4 5 6 7 8 0.294198 -0.941331 1.092195 0.159897 -0.922796 -0.719666 2.217000 1.548774 -0.372614 -0.104766 0.099535 0.188259 12.280000 12.299480 0.799007 23.919523 23.943831 0.997055 27.761958 27.765501 0.145327 28.787412 28.822076 1.421811 26.634932 26.638137 0.131451 49.876017 49.900372 0.998990 61.634004 61.602652 -1.285950 62.653776 62.660689 0.283564 26.634932 26.661027 1.070357 29.505765 29.515990 0.419428 49.876017 49.836374 -1.626039 57.807301 57.823776 0.675771 28.787412 28.811981 1.007754 29.107766 29.082012 -1.056369 51.516868 51.522463 0.229495 57.508657 57.453451 -2.264432 12.280000 12.319025 0.800369 27.761958 27.763658 0.034879 28.787412 28.631407 -3.199506 29.107766 29.110618 0.058493 26.634932 26.667262 0.663051 49.876017 49.882601 0.135039 62.653776 62.605739 -0.985183 63.244549 63.326837 1.687627 26.634932 26.661109 0.536855 29.505765 29.526217 0.419453 49.876017 49.839319 -0.752625 57.807301 57.839804 0.666594 23.919523 23.965792 0.948933 28.787412 28.803567 0.331307 28.979183 29.112303 2.730132 32.206285 32.214905 0.176788 12.280000 27.761958 31.352722 35.662999 75.402992 75.198097 99.151443 97.471048 57.508657 79.174012 92.698740 93.672763 29.505765 57.807301 76.404442 80.077083 23.919523 28.979183 32.206285 55.530815 61.634004 76.403311 87.225402 96.995304 29.107766 75.341088 79.084332 79.058537 63.244549 80.583256 79.483180 84.556454 26.634932 49.876017 62.653776 67.142498 28.787412 51.516868 59.539571 62.579100 2 102 25.800397 -1.065037 9.215910 0.018006 1.000000 0.647486 0.024308 -0.113940 4.713881 0.183963 0.584085 -1.426694 2 3 4 5 6 7 8 0.207247 -1.142415 1.331844 0.162389 -0.417564 -0.554517 1.397549 0.682038 0.156537 0.368190 0.550108 0.620587 12.280000 12.321035 1.254008 23.028196 23.061441 1.015945 23.472555 23.504962 0.990320 28.641425 28.691972 1.544701 24.259109 24.278181 0.582818 50.081062 50.121484 1.235273 57.420073 57.462162 1.286228 64.394715 64.374741 -0.610382 24.259109 24.290825 0.969221 33.075172 33.109306 1.043119 50.081062 50.088753 0.235040 57.420073 57.449518 0.899831 30.977003 31.003438 0.807859 36.136443 36.124276 -0.371804 57.247117 57.268739 0.660741 57.744268 57.766236 0.671337 12.280000 12.362181 1.255710 23.028196 23.092246 0.978665 30.015657 30.115350 1.523277 30.977003 30.913974 -0.963063 24.259109 24.293486 0.525266 50.081062 50.120053 0.595771 57.420073 57.464051 0.671969 66.865073 66.897491 0.495332 24.259109 24.326363 1.027613 33.075172 33.143443 1.043169 50.081062 50.138087 0.871334 57.420073 57.515915 1.464441 23.472555 23.539516 1.023135 28.641425 28.742222 1.540148 30.977003 31.011201 0.522547 31.974713 31.927044 -0.728363 12.280000 23.028196 30.015657 31.692861 73.397700 75.837481 100.844322 102.490157 64.758065 91.471684 110.116384 117.574974 33.075172 63.681886 79.303738 104.031429 23.472555 28.641425 31.974713 49.790736 64.394715 73.126127 98.648527 100.090171 36.136443 85.090044 97.883469 94.411254 66.865073 89.415751 93.309383 81.215394 24.259109 50.081062 57.420073 76.712453 30.977003 57.247117 57.744268 65.804368 2 10 22.258434 -1.101296 8.658309 0.032492 1.000000 0.753362 0.173911 -0.119360 18.711326 0.168729 4.412674 -3.177946 2 3 4 5 6 7 8 0.224234 -1.289343 1.487618 0.157485 -2.183401 -0.420323 1.100196 0.690483 -1.579483 -1.412415 -0.903655 -1.178859 12.280000 12.320508 1.258331 31.244585 31.272492 0.866898 32.550746 32.579711 0.899779 32.629953 32.662737 1.018381 22.125299 22.139357 0.436710 48.273816 48.304077 0.940049 58.056616 58.092843 1.125347 64.484081 64.464284 -0.614975 22.125299 22.160013 1.078341 29.908556 29.946723 1.185611 48.273816 48.266017 -0.242254 58.056616 58.081623 0.776836 33.687731 33.709561 0.678124 37.697050 37.689218 -0.243293 55.386441 55.396001 0.296962 61.473465 61.497208 0.737549 12.280000 12.361053 1.258911 31.244585 31.300198 0.863783 32.550746 32.608505 0.897108 33.687731 33.652325 -0.549922 22.125299 22.161163 0.557036 48.273816 48.299731 0.402520 58.056616 58.071786 0.235624 63.578942 63.649816 1.100809 22.125299 22.186993 0.958221 29.908556 29.984883 1.185503 48.273816 48.292925 0.296805 58.056616 58.162624 1.646516 32.629953 32.694538 1.003121 33.013564 33.063095 0.769317 33.687731 33.695602 0.122261 37.797823 37.789513 -0.129078 12.280000 31.244585 32.550746 37.487032 75.019160 74.293920 103.769155 103.288450 66.055226 100.963393 116.718814 129.809814 29.908556 62.415392 76.332869 105.754856 33.013564 32.629953 37.797823 53.812121 64.484081 73.537820 94.444127 100.669838 37.697050 83.087654 90.378509 107.504584 63.578942 83.957531 103.575044 84.507611 22.125299 48.273816 58.056616 73.177472 33.687731 55.386441 61.473465 67.149248 2 10 30.604216 -0.992173 8.320727 0.051777 1.000000 0.859310 -0.001673 -0.068023 7.774506 0.193752 1.197623 -1.891760 2 3 4 5 6 7 8 0.265724 -1.148425 1.044841 0.161482 -0.689625 -0.494376 1.686083 1.107976 -0.071255 0.115038 0.378721 0.370671 12.280000 12.312606 1.153467 30.734623 30.773241 1.366165 30.884037 30.910797 0.946657 30.964968 30.986600 0.765238 24.368807 24.379271 0.370185 50.634009 50.661064 0.957073 59.732859 59.774376 1.468723 65.642460 65.611198 -1.105940 24.368807 24.404232 1.253216 34.910516 34.946899 1.287094 50.634009 50.616220 -0.629320 59.732859 59.772597 1.405783 32.738485 32.754628 0.571076 36.557370 36.549575 -0.275767 57.088292 57.091131 0.100412 59.190308 59.223847 1.186495 12.280000 12.345262 1.154372 30.964968 31.008155 0.763885 31.202686 31.272374 1.232664 31.409625 31.409279 -0.006136 24.368807 24.398098 0.518099 50.634009 50.649810 0.279482 59.732859 59.750249 0.307608 65.433806 65.511209 1.369120 24.368807 24.431290 1.105210 34.910516 34.983282 1.287107 50.634009 50.636872 0.050636 59.732859 59.874302 2.501881 30.734623 30.811646 1.362393 30.884037 30.937291 0.941963 31.508999 31.584122 1.328780 32.738485 32.661897 -1.354689 12.280000 30.964968 31.202686 31.409625 75.936237 74.726978 103.839221 101.662001 63.988290 101.744755 108.583563 134.226102 34.910516 62.796609 82.482919 108.052278 30.734623 30.884037 31.508999 53.336951 65.642460 74.227093 98.119188 100.883447 36.557370 85.892442 80.086264 116.254987 65.433806 86.022769 104.079686 89.095272 24.368807 50.634009 59.732859 73.444390 32.738485 57.088292 59.190308 68.926957 2 34 101.716067 -1.374343 4.066397 0.076429 1.000000 0.749151 0.225395 -0.123579 4.793873 0.097729 1.486252 -0.017670 2 3 4 5 6 7 8 0.336516 -0.867754 0.535868 0.246843 -0.170127 0.301828 3.068329 1.891356 1.135868 0.943238 1.646078 1.085825 11.293674 11.371556 1.705179 12.280000 12.303241 0.508853 19.398266 19.397204 -0.023254 22.408780 22.413669 0.107032 14.129987 14.134821 0.105845 31.436974 31.448121 0.244055 37.401804 37.414220 0.271843 37.706082 37.707027 0.020699 14.129987 14.143005 0.285019 21.467975 21.478958 0.240454 31.436974 31.437267 0.006405 37.401804 37.418737 0.370728 24.109983 24.117602 0.166806 25.666021 25.662054 -0.086847 34.775445 34.780758 0.116326 38.329192 38.328061 -0.024763 12.280000 12.326300 0.506861 19.398266 19.396064 -0.024099 22.427559 22.403532 -0.263029 24.109983 24.129215 0.210542 14.129987 14.141655 0.127736 31.436974 31.450054 0.143181 37.401804 37.416508 0.160963 37.706082 37.700656 -0.059391 14.129987 14.154017 0.263066 21.467975 21.489946 0.240524 31.436974 31.446816 0.107742 37.401804 37.445679 0.480305 11.293674 11.448705 1.697165 22.408780 22.419057 0.112507 24.109983 24.116190 0.067949 27.136024 27.184214 0.527551 12.280000 19.398266 22.427559 26.177625 45.012936 44.419717 58.678573 56.904113 40.156707 64.378753 63.395012 76.164386 21.467975 38.033592 48.604625 60.657953 11.293674 22.408780 27.834294 27.136024 38.988226 44.442160 54.067204 57.271349 25.666021 48.970672 51.711168 66.739157 39.332369 52.472783 48.182700 63.012718 14.129987 31.436974 37.401804 37.706082 24.109983 34.775445 38.329192 40.656487 2 29 185.185469 -1.396630 3.636078 0.107240 1.000000 0.806600 -0.021715 -0.038878 1.958835 0.133151 1.458153 -2.951597 2 3 4 5 6 7 8 0.421798 -0.644756 0.018542 0.181153 -1.634444 -0.229428 4.504941 2.731949 -0.798563 -0.923927 -0.036516 -0.805507 -0.017747 0.091540 2.681804 12.280000 12.284677 0.114766 18.581612 18.570072 -0.283186 22.068082 22.069146 0.026091 14.948467 14.950736 0.055699 32.673049 32.682227 0.225203 36.248833 36.252643 0.093483 37.383112 37.392127 0.221220 14.948467 14.959134 0.261770 24.326537 24.334741 0.201303 32.673049 32.668673 -0.107406 36.248833 36.260169 0.278161 23.453030 23.456828 0.093211 24.533655 24.531048 -0.063954 35.148021 35.149516 0.036681 36.671995 36.677603 0.137621 12.280000 12.289328 0.114453 18.581612 18.558526 -0.283256 22.068082 22.070191 0.025876 22.980143 22.978722 -0.017441 14.948467 14.954766 0.077292 32.673049 32.680189 0.087601 36.248833 36.254156 0.065304 37.383112 37.381663 -0.017777 14.948467 14.968037 0.240122 24.326537 24.342949 0.201357 32.673049 32.675567 0.030894 36.248833 36.273755 0.305779 -0.017747 0.199819 2.669436 22.514806 22.509009 -0.071127 23.453030 23.509769 0.696167 23.669135 23.678477 0.114614 12.280000 18.581612 22.068082 22.980143 43.981623 43.767386 56.139178 54.704176 37.743599 57.196136 62.854202 69.331503 24.326537 37.505351 49.034549 54.920975 -0.017747 22.514806 24.038275 23.669135 38.801232 43.521712 53.894132 55.272522 24.533655 48.732047 50.552570 59.282312 39.626369 51.318912 48.046418 62.512580 14.948467 32.673049 36.248833 37.383112 23.453030 35.148021 36.671995 39.976142 2 43 27.474240 -0.899001 7.340383 0.145309 1.000000 1.393819 0.076151 -0.162262 404.385474 0.338429 175.860000 -2.263832 2 3 4 5 6 7 8 0.272637 -0.949505 -0.047747 0.179121 -0.873139 -0.000849 1.528643 1.225619 -0.025525 0.056402 0.477921 0.282441 12.280000 12.318217 1.223708 30.008653 30.027586 0.606250 31.658040 31.680058 0.705025 34.470818 34.508649 1.211359 22.629875 22.640195 0.330432 47.502600 47.520510 0.573474 57.984105 57.999152 0.481815 64.070302 64.043264 -0.865738 22.629875 22.664537 1.109882 35.993667 36.040792 1.508926 47.502600 47.495724 -0.220187 57.984105 57.982203 -0.060901 34.902985 34.923599 0.660061 38.655562 38.647908 -0.245099 55.348658 55.350271 0.051642 57.289208 57.320482 1.001369 12.280000 12.356437 1.223758 30.008653 30.046337 0.603322 34.470818 34.545862 1.201456 34.653957 34.650297 -0.058589 22.629875 22.656108 0.419995 47.502600 47.521630 0.304667 57.984105 57.971871 -0.195867 62.036532 62.074642 0.610138 22.629875 22.693609 1.020379 35.993667 36.087903 1.508720 47.502600 47.505835 0.051785 57.984105 58.021004 0.590763 31.658040 31.698527 0.648194 34.828979 34.804496 -0.391980 34.902985 34.923446 0.327582 37.229972 37.290242 0.964927 12.280000 34.470818 30.008653 34.653957 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