******* Eigenvalues for the 2+1 transverse lattice ******* Couplings: m^2, G^2 N, la_1/a, la_2/a, la_3/a, tau 0 1 2 3 4 5 Use chi^2 fit with 12 criteria, and tolerance 0.001. Overall scale from fitting lowest state to lattice value. 2 parity doublets with fractional errors 2 0.5. Spectrum for P_perp a = ( 0) ( 0.25) using (# states, o, multiplet, c^2 error for each) = (4, 1 & -1, 1 & 2, 0.5 2 0.5 0.5) (4, 1 & -1, 2 & 1, 0.5 0.5 0.5 0.5). Spectra extrapolated using (K,p) = (18/2,6) (18/2,8) (20/2,6) (20/2,8) (24/2,6) (32/2,6) . Winding potential using (n,K,p) = ( 2,20/2,4) ( 2,20/2,6) ( 2,24/2,4) ( 2,28/2,4) ( 3,21/2,5) ( 3,21/2,7) ( 3,23/2,5) ( 3,27/2,5) ( 4,20/2,6) ( 4,20/2,8) ( 4,22/2,6) ( 4,26/2,6) . Heavy potential determined using (n,K,p,K_max) = ( 0,-32/2,2,4) ( 0,-32/2,4,4) ( 0,-32/2,2,5) ( 0,-34/2,2,4) ( 0,-44/2,2,5) ( 0,-60/2,2,4) , L = 3 4 6 (all in G^2 N units); with relative error 0.25. Roundness determined using (n,K,p,K_max) = ( 1,-19/2,3,4) ( 1,-19/2,5,4) ( 1,-19/2,3,5) ( 1,-33/2,3,4) ( 1,-33/2,3,5) ( 1,-49/2,3,4) , L=3 and error 0.3 (all in G^2 N units). p-extrapolation using (n,K,p) = ( 1,19/2,3) ( 1,25/2,3) ( 1,39/2,3) ( 1,19/2,5) ( 1,25/2,5) ( 1,23/2,7) . Result format: fit info, # steps, chi^2, p damping, and scale g^2 N/(a sigma); the 6 couplings (G^2 N units) and which--if any--were fit; winding and longitudinal string tension fits; n=1 L=3 eigenvalue and derived value (G^2 N units); the rescaled spectrum for each P_perp*a and c^2 values. 1 3 181360.001459 -0.250000 -0.776112 0.032492 1.000000 -0.300000 -0.500000 10.000000 0.000000 5 -0.169319 -14.335718 14.873381 -0.164321 1.721515 -1.745269 0.695512 0.646273 16.524200 16.499380 -0.052186 12.174843 12.106137 -0.144461 9.350892 9.433217 0.173094 9.822626 9.778228 -0.093350 10.434445 10.413745 -0.043523 3.769561 3.736482 -0.069553 5.721193 5.713167 -0.016876 5.564774 5.550178 -0.030690 1 3 133772.594619 -0.250000 -0.903696 0.032492 1.000000 -0.300000 -0.450000 10.000000 0.000000 5 -0.115412 -12.122685 12.654914 -0.260201 3.123499 -4.995467 0.792147 0.673051 16.524200 16.498727 -0.042508 10.466652 10.394073 -0.121116 10.222449 10.295551 0.121989 8.933401 8.908275 -0.041930 9.333281 9.310992 -0.037195 1.887553 1.854121 -0.055790 4.305964 4.301847 -0.006872 4.397504 4.380273 -0.028755 1 3 95843.404262 -0.250000 -1.067714 0.032492 1.000000 -0.300000 -0.400000 10.000000 0.000000 5 -0.062279 -10.050369 10.630066 -0.120683 2.376068 -3.987739 0.860557 0.680930 16.524200 16.498252 -0.027607 8.641925 8.660711 0.019988 11.173820 11.157708 -0.017143 7.806236 7.785396 -0.022173 7.877083 7.852310 -0.026357 0.298467 0.269549 -0.030767 2.574019 2.570720 -0.003510 2.809684 2.789982 -0.020962 1 3 66560.121198 -0.250000 -1.281384 0.032492 1.000000 -0.300000 -0.350000 10.000000 -0.300000 5 -0.010189 -8.138495 8.814851 0.009807 1.319397 -2.287536 0.726385 0.585568 16.524200 16.498252 -0.005421 8.350365 8.378219 0.005819 10.570543 10.548874 -0.004527 6.362114 6.342804 -0.004034 5.895747 5.866523 -0.006105 -0.921371 -0.942648 -0.004445 0.433546 0.428591 -0.001035 0.615449 0.597667 -0.003715 1 4 44877.308188 -0.250000 -1.560883 0.032492 1.000000 -0.300000 -0.300000 10.000000 -0.394288 5 0.040722 -6.415082 7.228666 0.150318 0.366244 -0.786234 0.711066 0.559033 16.524200 16.499326 0.025297 8.082967 8.112169 -0.029699 9.885279 9.863256 0.022397 4.496589 4.477751 0.019158 3.172335 3.135442 0.037520 -1.879788 -1.890591 0.010987 -2.240904 -2.249008 0.008241 -2.255105 -2.261907 0.006917 1 5 29684.890386 -0.250000 -1.919977 0.032492 1.000000 -0.300000 -0.250000 10.000000 0.181629 5 0.090467 -4.915035 5.882757 0.220640 0.060999 -0.097936 1.036538 0.703015 16.524200 16.502451 0.060444 7.709905 7.736274 -0.073284 9.103026 9.077741 0.070271 2.093156 2.072746 0.056721 -0.391020 -0.437096 0.128051 -2.838641 -2.837622 -0.002833 -5.592762 -5.609294 0.045945 -5.757676 -5.740761 -0.047007 1 5 19785.472028 -0.250000 -2.353156 0.032492 1.000000 -0.300000 -0.200000 10.000000 -0.378639 5 0.139068 -3.672264 4.760492 0.238939 -0.162511 0.149710 0.799667 0.632239 16.524200 16.508421 0.082620 6.950439 6.969463 -0.099612 8.217692 8.044684 0.905863 -0.901291 -0.882727 -0.097201 -4.383380 -4.431177 0.250265 -4.425265 -4.419161 -0.031958 -9.690674 -9.687694 -0.015605 -9.679121 -9.666083 -0.068267 1 3 77082.157912 -0.250000 -2.809812 0.032492 1.000000 -0.300000 -0.150000 10.000000 -0.600000 5 0.186212 -2.705219 3.814884 0.236418 -0.232798 0.053084 0.676333 0.548599 16.524200 16.516021 0.068474 5.427024 5.436430 -0.078750 4.264327 4.218497 0.383671 -4.298393 -4.296205 -0.018318 -7.968565 -8.006205 0.315102 -7.236912 -7.235935 -0.008177 -13.628745 -13.602799 -0.217206 -14.238670 -14.240030 0.011387 1 8 10769.188017 -0.250000 -3.198026 0.032492 1.000000 -0.300000 -0.100000 10.000000 -0.783880 5 0.231013 -2.004890 3.012060 0.232322 -0.293935 -0.075879 0.561321 0.466680 16.524200 16.521736 0.029130 3.020559 3.022769 -0.026122 0.185863 0.181931 0.046472 -7.549094 -7.445673 -1.222502 -10.684961 -10.709766 0.293204 -10.832279 -10.837200 0.058168 -16.929579 -16.897181 -0.382961 -18.577898 -18.585247 0.086869 1 10 9295.834697 -0.250000 -3.442243 0.032492 1.000000 -0.300000 -0.050000 10.000000 -0.900000 5 0.272146 -1.533390 2.360985 0.228421 -0.323656 -0.172202 0.490207 0.425740 16.524200 16.523947 0.003794 0.157577 0.157303 0.004110 -2.113468 -2.102868 -0.158874 -8.880807 -8.880622 -0.002766 -12.423024 -12.437097 0.210941 -14.169480 -14.177084 0.113969 -19.054840 -19.023265 -0.473273 -21.924269 -21.935921 0.174652 1 10 8877.638237 -0.250000 -3.522844 0.032492 1.000000 -0.300000 0.000000 10.000000 -0.998923 5 0.308287 -1.233243 1.869091 0.224748 -0.349029 -0.255437 0.426746 0.384543 16.524200 16.524280 -0.001392 -2.475924 -2.476040 0.002002 -2.796184 -2.783027 -0.228619 -8.918509 -8.935598 0.296951 -13.224317 -13.230020 0.099098 -16.404786 -16.412091 0.126929 -19.931871 -19.905689 -0.454965 -23.862347 -23.877337 0.260478 1 8 9188.301978 -0.250000 -3.461893 0.032492 1.000000 -0.300000 0.050000 10.000000 -1.076326 5 0.338600 -1.044960 1.507348 0.221142 -0.363055 -0.327216 0.376206 0.345509 16.524200 16.524525 -0.006105 -4.311666 -4.313051 0.025975 -2.420458 -2.406798 -0.256208 -8.874891 -8.890928 0.300781 -13.244335 -13.243614 -0.013525 -16.959017 -16.961795 0.052104 -20.035609 -20.019694 -0.298504 -24.384599 -24.402890 0.343049 1 3 114694.960958 -0.250000 -0.975991 0.032492 1.000000 -0.250000 -0.500000 10.000000 -0.000000 5 -0.126249 -11.330636 12.041239 -0.202130 2.891476 -4.808139 0.827685 0.675622 16.524200 16.492402 -0.062689 11.065970 10.946186 -0.236150 8.267081 8.379557 0.221745 8.380830 8.336826 -0.086753 8.817469 8.789697 -0.054750 1.279122 1.244879 -0.067509 3.522802 3.517335 -0.010779 3.549889 3.527323 -0.044488 1 3 78701.258491 -0.250000 -1.178336 0.032492 1.000000 -0.250000 -0.450000 10.000000 -0.300000 5 -0.073244 -9.240270 10.007079 -0.034451 1.568783 -2.675114 0.700980 0.569231 16.524200 16.490110 -0.047075 8.173200 8.049882 -0.170289 9.701147 9.810967 0.151651 6.992296 6.959093 -0.045850 7.095636 7.062830 -0.045301 -0.207961 -0.235920 -0.038609 1.407907 1.400415 -0.010346 1.649062 1.627327 -0.030014 1 3 51272.625422 -0.250000 -1.460188 0.032492 1.000000 -0.250000 -0.400000 10.000000 -0.300000 5 -0.021331 -7.316328 8.178421 0.119244 0.634720 -1.157579 0.763764 0.604709 16.524200 16.487384 -0.018348 6.126106 6.142868 0.008354 10.066749 10.042607 -0.012032 5.119037 5.082799 -0.018060 4.676954 4.635517 -0.020651 -1.440907 -1.459724 -0.009378 -1.366053 -1.377211 -0.005561 -1.129749 -1.151273 -0.010727 1 3 31320.952242 -0.250000 -1.869072 0.032492 1.000000 -0.250000 -0.350000 10.000000 -0.300000 5 0.029562 -5.594180 6.570929 0.232733 -0.109749 0.110036 0.813347 0.628916 16.524200 16.484254 0.035315 5.022417 5.052791 -0.026853 9.191591 9.159669 0.028222 2.506104 2.448204 0.051188 1.267082 1.212698 0.048078 -2.726820 -2.734101 0.006437 -5.157027 -5.171834 0.013090 -5.319404 -5.339091 0.017404 1 3 17668.766694 -0.250000 -2.490509 0.032492 1.000000 -0.250000 -0.300000 10.000000 -0.525886 5 0.079737 -4.117038 5.183032 0.239430 -0.236500 0.126142 0.704012 0.542201 16.524200 16.481012 0.137225 3.706585 3.746781 -0.127718 7.678332 7.406630 0.863300 -1.354675 -1.410404 0.177072 -3.280673 -3.346146 0.208033 -4.884781 -4.884557 -0.000712 -10.644632 -10.663434 0.059740 -11.631379 -11.635887 0.014323 1 6 9083.234694 -0.250000 -3.483103 0.032492 1.000000 -0.250000 -0.250000 10.000000 -0.681705 5 0.129462 -2.924503 3.984121 0.235277 -0.267848 0.010457 0.628416 0.500314 16.524200 16.478655 0.328599 1.875231 1.921030 -0.330434 -0.779539 -0.920680 1.018313 -7.218710 -7.108819 -0.792846 -8.975164 -9.040494 0.471344 -9.643529 -9.649504 0.043109 -19.158608 -19.185766 0.195939 -21.010061 -20.977139 -0.237526 1 9 4285.309653 -0.250000 -5.134803 0.032492 1.000000 -0.250000 -0.200000 10.000000 -0.843275 5 0.178513 -2.035497 2.951112 0.231052 -0.316630 -0.103792 0.536920 0.510752 16.524200 16.479757 0.651808 -1.233161 -1.188156 -0.660047 -11.875852 -11.942180 0.972771 -16.831563 -16.691980 -2.047130 -16.710924 -16.771409 0.887085 -19.376283 -19.395935 0.288224 -33.236742 -33.307493 1.037632 -35.372960 -35.265832 -1.571150 1 11 1919.982417 -0.250000 -7.874955 0.032492 1.000000 -0.250000 -0.150000 10.000000 -0.986637 5 0.225841 -1.434309 2.119419 0.227509 -0.369936 -0.194003 0.450564 0.680842 16.524200 16.488468 1.016776 -7.307946 -7.273361 -0.984149 -27.682517 -27.722475 1.137049 -28.537273 -28.553842 0.471490 -28.543845 -28.601179 1.631494 -37.369111 -37.402415 0.947690 -58.236356 -58.187726 -1.383828 -56.936121 -56.924765 -0.323164 3 14 1173.768304 -0.250000 -11.905779 0.032492 1.000000 -0.250000 -0.100000 10.000000 -1.116618 5 0.269702 -1.067258 1.530767 0.224532 -0.426357 -0.264709 0.367809 1.078196 16.524200 16.504968 0.988088 -18.765839 -18.749902 -0.818809 -48.893273 -48.915525 1.143233 -46.730570 -46.756361 1.325040 -45.737021 -45.789785 2.710803 -66.373991 -66.417802 2.250855 -91.405219 -91.301312 -5.338376 -92.956666 -92.989031 1.662825 1 5 10047.333366 -0.422869 -32.007001 0.032492 1.000000 -0.250000 -0.050000 10.000000 -0.252285 5 0.311609 -0.765350 0.957595 0.237026 -0.076401 0.104469 0.965596 4.223567 16.524200 16.511542 2.019973 -77.819148 -77.814017 -0.818881 -146.486646 -146.530213 6.952381 -150.948427 -150.973992 4.079573 -127.312099 -127.390239 12.469355 -206.616526 -206.701692 13.590648 -253.635880 -253.403153 -37.138276 -269.399322 -269.526300 20.262955 4 4 296238.664310 -0.571053 -69.504983 0.032492 1.000000 -0.250000 0.000000 10.000000 0.000000 5 0.343510 -0.662288 0.747361 0.236039 -0.041367 0.080421 1.053969 9.602071 16.524200 16.522484 0.655492 -204.148230 -204.153377 1.966370 -326.772177 -326.868860 36.933698 -347.352053 -347.389432 14.279185 -281.934774 -282.003940 26.421849 -485.112273 -485.240079 48.822898 -553.370772 -552.943133 -163.362355 -608.257880 -608.791990 204.035134 4 4 3425152.759094 -0.668774 -73.244216 0.032492 1.000000 -0.250000 0.050000 10.000000 -0.000000 5 0.369221 -0.617400 0.643085 0.236024 -0.040968 0.079671 1.053179 10.489107 16.524200 16.518618 2.415389 -240.561133 -240.565007 1.676398 -345.353282 -345.452454 42.911068 -369.257468 -369.254700 -1.197541 -300.124412 -300.111039 -5.786244 -535.889458 -535.967985 33.977914 -578.135556 -577.762659 -161.349697 -655.253881 -657.355925 909.540382 1 4 67897.372433 -0.250000 -1.268698 0.032492 1.000000 -0.200000 -0.500000 10.000000 -0.300000 5 -0.082619 -8.670539 9.597082 0.025313 1.240640 -2.169710 0.728179 0.587375 16.524200 16.482316 -0.070243 9.351141 9.160743 -0.319317 7.143867 7.304620 0.269598 6.319156 6.264921 -0.090958 6.456698 6.416212 -0.067899 -0.486534 -0.513068 -0.044501 0.529683 0.519890 -0.016424 0.554946 0.530037 -0.041775 1 4 42180.784525 -0.250000 -1.610147 0.032492 1.000000 -0.200000 -0.450000 10.000000 -0.420268 5 -0.030695 -6.747797 7.756273 0.194573 0.071759 -0.312874 0.705229 0.548135 16.524200 16.476841 -0.037450 5.064593 4.932483 -0.104468 8.951428 9.053222 0.080494 4.034552 3.960359 -0.058670 3.675266 3.622345 -0.041849 -1.781605 -1.798058 -0.013010 -2.803157 -2.818382 -0.012039 -2.803331 -2.826133 -0.018031 1 5 23899.633740 -0.250000 -2.140370 0.032492 1.000000 -0.200000 -0.400000 10.000000 0.237221 5 0.020347 -5.038883 6.121052 0.223213 0.041811 -0.074162 1.057085 0.690315 16.524200 16.469157 0.038353 2.251651 2.247758 0.002713 8.477237 8.459003 0.012705 0.634828 0.212143 0.294523 -0.272262 -0.341330 0.048126 -3.525532 -3.531849 0.004402 -7.680825 -7.701220 0.014211 -8.278722 -8.299628 0.014567 1 3 11875.359079 -0.250000 -3.042641 0.032492 1.000000 -0.200000 -0.350000 10.000000 -0.600000 5 0.071009 -3.592673 4.677772 0.236197 -0.230214 0.050444 0.679093 0.520033 16.524200 16.457611 0.230187 -0.991943 -0.960917 -0.107252 2.563580 2.320339 0.840850 -4.986319 -4.895820 -0.312841 -5.667714 -5.747172 0.274675 -7.257395 -7.264979 0.026216 -15.582961 -15.608406 0.087961 -17.821750 -17.830956 0.031823 1 9 4861.755617 -0.250000 -4.818992 0.032492 1.000000 -0.200000 -0.300000 10.000000 -0.833715 5 0.121718 -2.452062 3.401280 0.231200 -0.312348 -0.100429 0.541106 0.453543 16.524200 16.437880 0.810103 -6.356264 -6.295908 -0.566429 -10.092147 -10.225706 1.253440 -15.057850 -14.706197 -3.300242 -13.827737 -13.911664 0.787649 -16.528009 -16.554331 0.247026 -30.651810 -30.686311 0.323794 -35.770067 -35.728200 -0.392921 1 11 1514.054133 -0.250000 -9.472571 0.032492 1.000000 -0.200000 -0.250000 10.000000 -1.010334 5 0.172253 -1.634638 2.319280 0.227444 -0.386534 -0.201723 0.434093 0.697461 16.524200 16.393070 3.423397 -19.203538 -19.097002 -2.781321 -35.890441 -36.013373 3.209362 -34.812136 -34.858242 1.203703 -32.361390 -32.466917 2.754970 -43.140897 -43.204797 1.668233 -69.559744 -69.626699 1.747985 -78.975293 -78.824788 -3.929207 1 12 707269.016849 -0.296744 -68.159379 0.032492 1.000000 -0.200000 -0.200000 10.000000 -1.123675 5 0.224260 -1.046451 1.383342 0.227077 -0.418097 -0.198304 0.395539 6.936882 16.524200 15.868161 160.445119 -179.988414 -179.429007 -136.811996 -317.156864 -317.503844 84.859494 -336.550121 -337.174646 152.737850 -254.746400 -255.238708 120.401790 -386.748501 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