********* Eigenvalues for the 3+1 transverse lattice ********* Couplings: 0:mu^2 1:g^2 N 2:beta 3:lambda_1 4:lambda_2 5:lambda_3 6:lambda_4 7:lambda_5 8:tau_1 9:tau_2 10:kappa_S 11:kappa_A 12:mu_F 13:mu_0^2 14:mu_1^2 15:mu_2^2 16:mu_3^2 Use chi^2 fit with 40 criteria and tolerance 0.01. Overall scale from minimizing chi^2. Parity doublets (charge,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 4 states (multiplet, charge, c^2 error for each) = (15, 1, 0.25 2 2 2) (15, -1, 0.25 2 2 2) (16, -1, 0.25 2 2 2) (16, 1, 0.25 2 2 2) Spectrum for P_perp a = (0,0), ( 0.25 0.25) using 4 states (multiplet, charge, c^2 error for each) = (17, 1, 0.25 2 2 2) (17, -1, 0.25 2 2 2) (18, -1, 0.25 2 2 2) (18, 1, 0.25 2 2 2). Ordinary spectra multiplets, 4 states, (charge,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 0,18/2,7) ( 3 0,18/2,5) ( 3 0,26/2,5) ( 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 0,14/2,3,3.5) ( 1 0,14/2,5,3.5) ( 1 0,14/2,3,3) ( 1 0,24/2,3,4) ( 1 0,24/2,3,4.5) ( 1 0,36/2,3,5) ( 1 0,36/2,3,6) L=1.265-0.964*m and error 0.1; ( 1 0,14/2,3,3.5) ( 1 0,14/2,5,3.5) ( 1 0,14/2,3,3) ( 1 0,24/2,3,4) ( 1 0,24/2,3,4.5) ( 1 0,36/2,3,5) ( 1 0,36/2,3,6) 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) = (14/2,3) (22/2,3) (46/2,3) (14/2,5) (28/2,5) (14/2,7) (16/2,7) . Result format: Fit info, # steps, chi^2, and p damping, scale G^2 N/sigma. The 17 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 20 104.2882809 -7.773123274 12.64585014 0 1 -0.1855392676 0.4867288493 -0.2218701369 16391.09856 -0.1544536648 5838.981137 -2.016321431 -2.174321371 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.141553 -0.350119 0.093728 0.101580 -0.227256 0.420931 1.578076 0.794022 0.481882 0.358337 0.652735 0.538743 1.128351 0.518793 25.857655 25.873629 0.457498 41.907303 41.912000 0.134528 49.014440 49.027594 0.376741 52.356319 52.358733 0.069140 37.876668 37.893226 0.474243 58.471238 58.477214 0.171154 74.212171 74.215707 0.101279 75.292114 75.291271 -0.024157 27.946858 27.944902 -0.056037 37.876668 37.884607 0.227381 58.471238 58.441536 -0.850712 63.376092 63.390836 0.422289 52.356319 52.358163 0.052799 57.358524 57.359878 0.038769 59.028329 59.029978 0.047242 76.070836 76.079306 0.242596 25.857655 25.889560 0.456893 41.907303 41.917056 0.139665 52.356319 52.371806 0.221781 55.038172 55.032136 -0.086430 37.876668 37.907876 0.446920 58.471238 58.449706 -0.308357 63.376092 63.397560 0.307442 74.212171 74.227273 0.216274 27.946858 27.942873 -0.057068 37.876668 37.894397 0.253898 58.471238 58.454873 -0.234359 63.525737 63.539762 0.200846 49.014440 49.040398 0.371722 52.356319 52.350065 -0.089569 59.028329 58.983805 -0.637598 63.272653 63.299382 0.382772 25.857655 41.907303 55.038172 63.449251 83.691205 86.937851 92.846154 78.725995 81.555789 88.767332 95.746498 104.422883 27.946858 63.525737 77.496334 78.906029 49.014440 63.272653 71.473745 72.272115 75.292114 80.515097 89.519461 88.020922 57.358524 77.823663 97.992202 102.485192 63.376092 84.754996 81.174466 93.236578 37.876668 58.471238 74.212171 78.637859 52.356319 59.028329 76.070836 80.916302 2 12 106.5946382 -0.25 9.338354732 0.001967542671 1 0.05128983526 0.08588843657 -0.1282959758 1570.962466 -0.04986973483 746.0818937 -1.171488692 -1.458193253 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.165701 -0.044264 -0.378639 0.134722 0.013724 0.043809 2.605082 1.234011 0.562650 0.562636 0.841970 0.854906 1.096217 0.746120 24.622056 24.634855 0.316886 26.384326 26.383624 -0.017383 26.945771 26.958056 0.304145 29.344045 29.330706 -0.330251 28.816740 28.829165 0.307617 48.969547 48.972267 0.067333 51.249363 51.249013 -0.008670 52.715338 52.715978 0.015830 26.038840 26.038444 -0.009805 28.816740 28.817369 0.015569 48.969547 48.968942 -0.014992 51.249363 51.246742 -0.064896 29.799013 29.799134 0.002984 32.059245 32.059095 -0.003717 49.140287 49.140745 0.011322 51.361180 51.360753 -0.010569 24.622056 24.647697 0.317415 26.384326 26.383301 -0.012692 29.344045 29.318439 -0.316981 29.799013 29.824054 0.309983 28.816740 28.837247 0.253855 48.969547 48.969964 0.005162 51.249363 51.250728 0.016905 53.277414 53.270930 -0.080267 26.038840 26.038062 -0.009635 28.816740 28.822278 0.068562 48.969547 48.973302 0.046486 51.249363 51.242028 -0.090798 26.945771 26.969756 0.296906 29.799013 29.796757 -0.027929 34.817236 34.804116 -0.162421 49.140287 49.133389 -0.085398 24.622056 26.384326 29.344045 34.959514 59.238982 64.135798 68.001871 63.330645 55.011921 58.803114 60.880132 63.007471 26.038840 52.739668 55.027261 57.075832 26.945771 34.817236 50.228414 55.193923 52.715338 58.219056 65.269486 65.929710 32.059245 57.683701 61.178954 62.569946 55.222024 59.134365 62.896853 65.902360 28.816740 48.969547 51.249363 53.277414 29.799013 49.140287 51.361180 53.333664 1 67 84.18575565 -9.762227907 9.740554961 0.007919222016 1 0.1150469766 0.187011881 -0.311648554 9518.799799 -0.1896301303 3765.928167 -1.487075386 -2.369580444 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.137313 -0.399544 0.307499 0.122261 -0.164481 0.354114 1.806527 0.737397 0.486953 0.393023 0.590882 0.621121 1.064180 0.528974 16.834422 16.880943 0.995552 23.253257 23.244894 -0.178960 25.956539 25.984364 0.595463 32.463481 32.446639 -0.360423 29.907426 29.929116 0.464183 46.928616 46.936007 0.158170 51.541852 51.551210 0.200255 53.179658 53.164806 -0.317830 22.559004 22.558705 -0.006382 29.907426 29.909912 0.053216 46.928616 46.912459 -0.345772 49.459133 49.466989 0.168124 32.463481 32.464499 0.021780 38.133011 38.133463 0.009668 47.314719 47.314434 -0.006101 52.111298 52.114993 0.079072 16.834422 16.927573 0.996722 23.253257 23.237200 -0.171814 32.463481 32.441133 -0.239134 33.879803 33.894608 0.158414 29.907426 29.944610 0.397872 46.928616 46.918666 -0.106465 50.103954 50.114920 0.117342 51.541852 51.563407 0.230642 22.559004 22.558379 -0.006678 29.907426 29.918364 0.117042 46.928616 46.923816 -0.051368 49.459133 49.473574 0.154522 25.956539 26.011275 0.585677 32.463481 32.455388 -0.086598 44.922105 44.896440 -0.274620 47.314719 47.253677 -0.653157 16.834422 23.253257 33.879803 45.503198 60.226560 63.552317 64.860064 56.135731 58.799886 60.534548 65.205737 69.993487 22.559004 49.459133 52.868278 56.073887 25.956539 44.922105 48.142168 50.136646 53.179658 56.448027 63.751889 57.811014 38.133011 55.254581 63.578130 69.028365 50.103954 60.394376 65.714368 72.841781 29.907426 46.928616 51.541852 54.582363 32.463481 47.314719 52.111298 54.394244 2 12 142.0316076 -9.575588235 3.776583788 0.01800590693 1 0.5092963519 -0.0353246424 -0.1443702018 1570.962466 0.06676113425 746.0818937 -1.268005047 -1.411868608 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.190814 -0.305384 -0.239806 0.141323 -0.047473 0.160165 1.941755 1.191153 0.588093 0.315540 0.848158 0.668412 1.065405 0.350890 7.050855 7.062297 0.131924 9.608441 9.616095 0.088244 9.662917 9.671243 0.096002 12.280786 12.265858 -0.172114 12.144806 12.149452 0.053570 18.715640 18.729722 0.162359 21.254846 21.240216 -0.168689 22.439088 22.446032 0.080064 12.144806 12.272391 1.471054 13.218244 13.098147 -1.384716 18.715640 18.713163 -0.028567 21.254846 21.202034 -0.608924 12.280786 12.286607 0.067123 13.513178 13.509146 -0.046498 19.906146 19.910427 0.049354 20.604980 20.597221 -0.089456 7.050855 7.073797 0.132257 9.662917 9.678077 0.087396 12.280786 12.258936 -0.125961 12.607988 12.595485 -0.072083 12.144806 12.154799 0.057611 18.715640 18.712078 -0.020534 21.254846 21.249108 -0.033080 21.952827 21.978062 0.145483 12.144806 12.375438 1.329598 13.218244 13.002040 -1.246415 18.715640 18.743776 0.162201 21.254846 21.133768 -0.698017 9.608441 9.625083 0.095938 12.280786 12.284550 0.021705 12.601366 12.587615 -0.079271 17.921930 17.938586 0.096023 7.050855 9.662917 12.607988 17.003950 26.032014 26.870288 27.217529 24.843296 21.910712 22.988518 27.113360 27.851651 13.218244 21.765781 23.537350 27.944093 9.608441 12.601366 17.921930 19.783557 22.439088 27.399967 27.505294 23.017908 13.513178 23.022709 26.698779 28.528882 21.952827 25.583689 27.013239 28.374150 12.144806 18.715640 21.254846 24.046090 12.280786 19.906146 20.604980 22.308944 2 12 196.3066789 -9.533503455 1.672469174 0.03249196962 1 0.6751164286 -0.07375746079 -0.157741533 1570.962466 0.1076113598 746.0818937 -1.268982104 -1.410344977 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.213562 -0.475326 -0.052082 0.151422 -0.080847 0.217556 1.903430 1.226659 0.607730 0.284330 0.858063 0.639182 1.087565 0.283701 2.898004 2.904159 0.035171 4.321230 4.325531 0.024582 4.392443 4.396167 0.021279 5.774958 5.763067 -0.067952 5.595266 5.597146 0.010744 8.500310 8.507725 0.042375 9.915264 9.907351 -0.045220 10.578749 10.582926 0.023872 5.595266 5.865846 1.546312 6.600330 6.334570 -1.518772 8.500310 8.499281 -0.005877 9.915264 9.890705 -0.140352 5.826448 5.830516 0.023247 6.484629 6.481762 -0.016387 9.125232 9.127431 0.012565 9.550861 9.546887 -0.022708 2.898004 2.910345 0.035264 4.392443 4.399545 0.020292 5.777899 5.769856 -0.022981 5.826448 5.821419 -0.014371 5.595266 5.599890 0.013211 8.500310 8.498457 -0.005294 9.915264 9.912450 -0.008039 10.282831 10.296069 0.037828 5.595266 5.849580 0.726676 6.600330 6.354883 -0.701344 8.500310 8.515620 0.043748 9.915264 9.856211 -0.168738 4.321230 4.330057 0.025222 5.774958 5.759892 -0.043048 5.826448 5.837322 0.031071 7.860307 7.870853 0.030135 2.898004 4.392443 5.777899 8.673673 12.074924 12.854888 13.205278 12.207176 10.255560 10.666114 12.896543 13.646290 6.600330 10.248831 11.284238 13.719762 4.321230 5.774958 7.860307 8.942925 10.578749 12.845135 13.287688 11.832535 6.484629 10.942205 12.898007 13.462772 10.282831 11.510473 13.064703 13.230093 5.595266 8.500310 9.915264 11.412502 5.826448 9.125232 9.550861 10.459202 2 48 46.71315582 -9.048213093 6.79882144 0.0517766953 1 0.9255540976 -0.06069435614 -0.2698300162 5185.455993 0.1899764074 2161.887365 -1.28538792 -1.791512503 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.222691 -0.843632 0.555160 0.163657 -0.104597 0.246950 1.693483 1.007290 0.599651 0.520839 0.781115 0.804705 1.114853 0.692393 10.209193 10.252325 1.044859 17.499417 17.527644 0.683791 18.365852 18.389459 0.571862 27.128062 27.145058 0.411732 23.728702 23.737276 0.207723 35.238826 35.280338 1.005603 42.807173 42.770095 -0.898220 46.839998 46.859647 0.475993 23.728702 23.773228 1.078625 30.874809 30.860294 -0.351636 35.238826 35.243150 0.104749 42.807173 42.727606 -1.927479 27.128062 27.158145 0.728763 31.747850 31.730404 -0.422617 39.427341 39.438906 0.280162 41.915912 41.897387 -0.448752 10.209193 10.295613 1.046744 18.365852 18.411632 0.554489 27.128062 27.107570 -0.248202 27.906989 27.853115 -0.652533 23.728702 23.750182 0.260173 35.238826 35.236386 -0.029553 42.807173 42.799232 -0.096184 45.045658 45.116259 0.855142 23.728702 23.798641 0.847132 30.874809 30.860986 -0.167429 35.238826 35.337002 1.189136 42.807173 42.586645 -2.671110 17.499417 17.557346 0.701650 27.128062 27.181572 0.648138 27.830543 27.758108 -0.877348 30.858613 30.934449 0.918554 10.209193 18.365852 27.906989 40.799255 50.965485 54.808472 59.640791 57.494653 45.460576 48.887058 61.397341 64.953297 30.874809 46.521983 51.761246 59.792855 17.499417 27.830543 30.858613 37.140464 46.839998 54.403218 55.780991 59.822692 31.747850 50.116204 57.873265 59.285953 45.045658 48.358335 61.033223 57.736244 23.728702 35.238826 42.807173 51.779762 27.128062 39.427341 41.915912 46.988865 2 57 39.69398236 -9.180373479 7.563874923 0.07642881742 1 0.76809841 -0.1692461589 -0.1857716652 49854.19434 0.02426983029 24828.43378 -1.547566329 -2.239030657 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.280322 -0.531459 -0.246649 0.148495 -0.166355 0.340103 2.430894 1.680288 0.611141 0.528937 0.712160 0.733464 1.201923 0.734706 15.880884 15.914083 1.126294 22.903951 22.929273 0.859073 22.963928 22.988224 0.824247 30.912199 30.946653 1.168860 28.683755 28.691760 0.271583 45.567465 45.594481 0.916504 52.273980 52.254324 -0.666836 55.087284 55.102457 0.514725 28.683755 28.712611 0.978958 35.931338 35.925961 -0.182424 45.567465 45.554409 -0.442923 52.273980 52.230872 -1.462461 30.912199 30.932793 0.698634 34.342464 34.327499 -0.507695 48.251991 48.268106 0.546683 50.491023 50.478944 -0.409787 15.880884 15.947544 1.130730 22.963928 23.003966 0.679149 30.912199 30.868313 -0.744429 30.976108 30.940954 -0.596306 28.683755 28.704935 0.359266 45.567465 45.559264 -0.139108 52.273980 52.273502 -0.008117 57.990367 58.038021 0.808336 28.683755 28.727813 0.747345 35.931338 35.929399 -0.032895 45.567465 45.605335 0.642362 52.273980 52.151894 -2.070909 22.903951 22.955543 0.875134 30.912199 30.912751 0.009355 30.976025 30.950573 -0.431737 43.499920 43.555070 0.935498 15.880884 22.963928 30.976108 46.263632 63.643324 69.752069 71.634437 73.417569 54.828004 59.185229 70.233878 74.021273 35.931338 54.454524 61.920480 70.448125 22.903951 30.976025 43.499920 46.429290 55.087284 66.220994 72.402802 72.739651 34.342464 60.321597 68.102494 69.973197 57.990367 60.142587 72.783184 72.055893 28.683755 45.567465 52.273980 62.334198 30.912199 48.251991 50.491023 58.148510 2 56 98.56749724 -8.678295519 5.149387628 0.1072401379 1 0.9511099567 -0.0773283664 -0.412850594 8437.647236 0.1209403565 3655.724334 -0.7290905206 -1.437938054 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.279549 -0.730019 0.118290 0.210061 -0.040558 0.093812 2.751778 1.521160 0.710374 0.597659 0.931472 0.960682 1.287035 0.792613 13.452365 13.492002 0.912910 17.658699 17.686909 0.649739 17.766405 17.802732 0.836683 27.208516 27.151595 -1.311000 20.959184 20.966522 0.169016 34.375079 34.405146 0.692498 39.348689 39.335712 -0.298893 42.924783 42.936192 0.262777 20.959184 20.950057 -0.210208 29.746372 29.774718 0.652861 34.375079 34.385418 0.238131 39.348689 39.328448 -0.466194 27.208516 27.229028 0.472431 31.810589 31.799933 -0.245432 38.280113 38.297434 0.398935 39.587408 39.583191 -0.097122 13.452365 13.531844 0.915277 17.766405 17.832168 0.757324 27.208516 27.124313 -0.969685 29.483518 29.437826 -0.526197 20.959184 20.973323 0.162825 34.375079 34.386330 0.129569 39.348689 39.356759 0.092931 46.314799 46.425655 1.276629 20.959184 20.942522 -0.191872 29.746372 29.802324 0.644337 34.375079 34.446324 0.820453 39.348689 39.274821 -0.850673 17.658699 17.722136 0.730546 27.208516 27.220740 0.140771 29.431663 29.386570 -0.519290 31.574215 31.567820 -0.073641 13.452365 17.766405 29.483518 33.596920 47.623036 53.608486 54.930607 58.300178 46.458462 48.119289 61.107939 63.227139 29.746372 44.777152 51.972912 53.605716 17.658699 29.431663 31.574215 35.238100 42.924783 49.659730 56.456710 56.577957 31.810589 51.635595 51.532130 57.246680 46.314799 46.716986 54.176656 60.527921 20.959184 34.375079 39.348689 51.090857 27.208516 38.280113 39.587408 47.574967 2 11 105.5101431 -9.127174982 5.122562159 0.1453085056 1 0.8507976573 -0.05324967878 -0.2567129115 1570.962466 0.1354421572 746.0818937 -0.8885773624 -1.579965316 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.371339 -0.172546 -0.902569 0.208654 -0.037434 0.082522 4.499799 2.685348 0.761823 0.665689 0.950508 0.972259 1.434141 0.902376 21.750151 21.777564 0.834335 27.150912 27.172522 0.657685 27.454315 27.469618 0.465745 33.604020 33.565947 -1.158769 23.128195 23.132219 0.122490 42.369417 42.389821 0.620997 47.409568 47.392059 -0.532889 50.305271 50.320682 0.469040 23.128195 23.120981 -0.219554 35.743711 35.761294 0.535144 42.369417 42.377221 0.237524 47.409568 47.389177 -0.620626 33.604020 33.615388 0.345991 36.421649 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38.750019 38.748167 -0.081448 44.455820 44.454156 -0.073197 27.612499 27.614472 0.086759 58.146189 58.142892 -0.145039 58.233300 58.237383 0.179553 63.290299 63.295693 0.237285 27.612499 27.609349 -0.138537 45.764072 45.770584 0.286429 58.146189 58.131031 -0.666694 58.233300 58.241293 0.351547 47.003864 47.007267 0.149666 48.767626 48.764747 -0.126645 61.181074 61.189570 0.373676 64.063005 64.061003 -0.088015 37.044129 37.077291 0.729295 38.750019 38.745312 -0.103515 44.455820 44.464682 0.194882 47.003864 46.959837 -0.968246 27.612499 27.616029 0.077637 58.146189 58.133292 -0.283638 58.233300 58.244851 0.254029 63.290299 63.298937 0.189963 27.612499 27.606828 -0.124723 45.764072 45.777048 0.285373 58.146189 58.122534 -0.520232 58.233300 58.247139 0.304336 37.480696 37.519884 0.861812 44.457313 44.474197 0.371301 47.003864 47.002874 -0.021786 49.624364 49.607853 -0.363111 37.044129 38.750019 44.455820 49.610592 73.660937 75.137436 82.533662 84.111530 66.608657 85.350036 82.877247 83.573379 45.764072 65.148842 77.288341 82.162231 37.480696 44.457313 49.624364 61.610622 64.601203 74.322189 81.337388 82.982411 48.767626 77.431717 80.363613 87.699949 69.832094 79.454722 78.956993 87.131306 27.612499 58.146189 58.233300 63.290299 47.003864 61.181074 64.063005 67.262516