********* 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 10 569640861.6 -0.25 50 0.03249196962 1 0.70330315 -0.5 -0.0968878772 192.1731667 0.1478324792 73.44399575 -0.9370236797 -0.825061301 2 4 5 6 7 8 9 0.118096 -13.579969 12.884578 0.149484 -1.092427 1.624094 -6.920721 -11.024632 0.160591 1.575581 0.415432 1.649197 0.628328 2.606821 -1127.103875 -1127.130392 -2.505218 -1126.380684 -1126.393564 -1.216844 -902.640537 -699.670347 19175.897924 -802.013774 -657.928075 13612.701719 -423.913193 -423.848265 6.134233 -395.384276 -321.070351 7020.913907 -354.544434 -310.672837 4144.831686 -354.448808 -277.626158 7257.929401 -469.169379 -423.794369 4286.868705 -423.913193 -316.712851 10127.905098 -319.867940 -274.098590 4324.124653 -309.185731 -236.310530 6884.988452 -651.248264 -651.049913 18.739474 -628.216636 -628.164125 4.961065 -593.157772 -593.274200 -10.999691 -543.601560 -543.578801 2.150273 -1126.380684 -1126.405140 -1.155266 -802.013774 -658.187408 6794.100435 -657.665798 -600.471638 2701.749889 -651.248264 -590.771881 2856.796202 -469.169379 -446.792282 1057.054072 -423.913193 -423.744185 7.983656 -395.384276 -333.565200 2920.222651 -354.448808 -294.696506 2822.591932 -423.913193 -423.714189 9.400621 -354.544434 -304.675524 2355.718194 -319.867940 -295.960730 1129.333890 -314.972411 -229.220765 4050.754448 -1127.103875 -1127.156602 -2.490701 -902.640537 -900.045131 122.602320 -699.677269 -699.667449 0.463881 -651.248264 -611.497179 1877.770166 -1126.380684 -657.665798 -601.266374 -802.013774 -395.384276 -354.448808 -39.316035 -90.216248 -593.157772 -62.417232 -177.070036 -194.411666 -177.102364 -309.185731 -276.929080 -92.727704 -1127.103875 -699.677269 -902.640537 -585.542337 -314.972411 -354.544434 -166.636031 -207.978929 -493.475370 -486.095986 -321.013183 -166.317565 -469.169379 -1.576691 -73.656877 -77.214242 -423.913193 -227.571310 -319.867940 -274.158570 -543.601560 -651.248264 -628.216636 -315.010904 2 76 2183850.967 -0.25 50 0.03249196962 1 0.9536044707 -0.4 -0.1641075653 480.1532459 0.1620413873 -60.94910673 -1.812563108 -4.055893831 2 4 5 6 7 8 9 0.000738 -9.355254 9.250560 0.020627 -0.564158 0.601115 -8.427735 -8.193031 0.026953 -0.183209 -0.397312 -0.338352 0.560818 -0.211597 -737.324120 -737.215570 0.064083 -735.240327 -735.254796 -0.008542 -549.978966 -526.897882 13.626098 -527.170627 -487.044994 23.688479 -302.267703 -301.207786 0.625730 -256.872954 -207.896680 28.913525 -203.418330 -203.182499 0.139225 -203.173143 -176.359976 15.829362 -343.104221 -330.741772 7.298268 -302.267703 -224.344461 46.002593 -237.944190 -207.571361 17.930836 -203.173143 -175.927655 16.084586 -427.232810 -426.991490 0.142465 -382.279114 -382.198151 0.047797 -350.467816 -350.196290 0.160297 -329.226032 -329.543157 -0.187217 -737.324120 -737.217114 0.031586 -549.978966 -526.625227 6.893531 -527.170627 -483.188355 12.982638 -483.154482 -427.474610 16.435523 -343.104221 -334.357252 2.581921 -302.267703 -279.441382 6.737848 -256.872954 -208.135581 14.386244 -203.418330 -202.397095 0.301447 -302.267703 -226.770363 22.285221 -237.944190 -206.602560 9.251388 -203.173143 -174.464840 8.474085 -199.767116 -170.938208 8.509685 -735.240327 -735.159235 0.023937 -520.138788 -512.793281 2.168239 -487.715251 -486.385563 0.392496 -427.232810 -436.578557 -2.758667 -737.324120 -527.170627 -483.154482 -549.978966 -256.872954 -203.418330 132.141606 -39.524973 -329.226032 -88.975598 51.250177 -57.535009 -187.553866 -237.944190 -131.696539 -28.229117 -735.240327 -487.715251 -520.138788 -243.379925 -199.767116 -109.467953 -150.746871 -97.035042 -311.070162 -310.326854 -197.552005 46.494641 -343.104221 78.933033 -104.016255 42.301934 -176.812564 -203.173143 -179.266323 -302.267703 -427.232810 -382.279114 -350.467816 -143.618360 1 26 424629.9992 -0.25 50 0.03249196962 1 0.7150311743 -0.3 -0.09642351564 5559.52073 0.158160682 2675.616137 -1.625288786 -2.532325289 2 4 5 6 7 8 9 0.119930 -3.016806 4.147130 0.021482 -0.078160 0.196834 -0.686905 -1.538974 0.375530 0.305895 0.293572 0.316461 0.961101 0.455926 -279.242651 -279.209272 3.202553 -273.381485 -273.404469 -2.205188 -120.947247 -120.730100 20.834001 -103.213692 -103.121093 8.884381 104.336638 104.578627 23.217455 127.642540 127.794380 14.568178 127.663843 128.046586 36.721845 127.817851 128.384250 54.342628 104.336638 104.434791 9.417200 108.696240 108.987919 27.984900 122.122177 124.311705 210.072279 127.642540 127.748556 10.171635 -42.411060 -42.261747 14.325694 8.062847 7.960596 -9.810344 42.877701 43.000007 11.734499 49.450789 49.509962 5.677277 -273.381485 -273.420007 -1.847989 -120.947247 -120.513225 20.820932 -103.213692 -103.040110 8.327106 -42.411060 -42.651855 -11.551410 104.336638 104.720108 18.395843 122.122177 109.442379 -608.275720 127.642540 127.766542 5.948636 127.663843 128.005135 16.372438 104.336638 104.635563 14.340050 108.696240 109.278660 27.939868 127.642540 128.022487 18.226814 127.663843 128.197289 25.590474 -279.242651 -279.182020 2.908610 -101.337903 -101.337442 0.022080 -100.754933 -100.957584 -9.721614 -42.411060 -42.487376 -3.661026 -273.381485 -120.947247 -103.213692 -34.153301 223.500838 127.830976 311.088206 421.084713 87.686560 239.936871 291.793138 314.549420 108.696240 164.027930 202.343113 340.196723 -279.242651 -101.337903 -100.754933 124.200609 165.829569 217.113998 213.670675 307.085712 8.062847 136.299264 191.555049 333.387831 122.122177 314.110782 249.947815 376.088765 104.336638 127.817851 127.642540 127.663843 -42.411060 49.450789 42.877701 184.636841 2 9 3536909.628 -0.4638515982 81.02549334 0.03249196962 1 0.70330315 -0.2 -0.0968878772 192.1731667 0.1478324792 73.44399575 -0.9370236797 -0.825061301 2 4 5 6 7 8 9 0.178952 -1.323573 1.385465 0.108275 0.120324 -0.049325 0.754529 0.281227 0.586356 3.832005 0.836673 3.860080 1.134878 5.367791 -41.110883 -40.814338 68.797050 -23.896623 -23.744890 35.201256 12.670000 12.807156 31.819523 106.038818 106.181732 33.155230 216.118841 216.341504 51.656679 377.604415 377.945707 79.177986 411.648307 412.006444 83.085958 471.243536 471.086076 -36.529950 216.118841 216.413429 68.342880 271.382596 271.739448 82.787796 377.604415 377.599137 -1.224484 411.648307 411.909753 60.654135 148.144714 148.390172 56.944944 206.534239 206.394569 -32.402803 365.353769 365.555667 46.839360 392.034421 392.181413 34.101601 -41.110883 -40.515270 69.089590 12.670000 12.943435 31.717711 106.038818 106.184099 16.852257 148.144714 147.790153 -41.128261 216.118841 216.573169 52.700866 377.604415 377.848265 28.285999 411.648307 412.000401 40.842047 522.878602 495.107166 -3221.416361 216.118841 216.699876 67.398596 271.382596 272.096125 82.767584 377.604415 378.031129 49.497733 411.648307 412.513523 100.362902 -23.896623 -23.595916 34.881259 106.658822 106.643567 -1.769603 148.144714 148.153779 1.051521 286.166280 284.932651 -143.097895 12.670000 -41.110883 106.038818 309.877732 565.433200 571.040798 722.798869 907.190784 445.593209 674.484581 784.955933 746.390612 271.382596 470.045954 604.938277 838.897376 -23.896623 106.658822 296.527699 286.166280 471.243536 556.332598 788.742698 789.465908 206.534239 586.946941 681.912605 820.618530 522.878602 675.481444 720.073494 678.122581 216.118841 377.604415 411.648307 530.255905 148.144714 392.034421 365.353769 417.432079 2 27 21.72647207 -1.007901632 9.598297881 0.03249196962 1 0.6734451402 -0.1 -0.1128146522 4265.589878 0.1428887894 2082.896624 -0.9283443294 -0.8803187387 2 4 5 6 7 8 9 0.217965 -0.941985 0.686997 0.109617 0.201302 -0.189336 1.590558 0.887613 0.616595 0.665813 0.866824 0.856601 1.220979 0.866099 12.670000 12.706240 1.213081 19.475551 19.507552 1.071169 19.713771 19.743718 1.002421 29.342416 29.332865 -0.319719 28.226331 28.248178 0.731281 55.258493 55.294504 1.205414 61.738852 61.782976 1.476980 68.626091 68.608011 -0.605214 28.226331 28.260871 1.156192 38.655847 38.689255 1.118305 55.258493 55.261581 0.103369 61.738852 61.770134 1.047111 31.395921 31.423984 0.939358 37.221519 37.205927 -0.521921 59.300338 59.318364 0.603394 60.899937 60.924803 0.832369 12.670000 12.742519 1.213730 19.475551 19.534567 0.987734 29.342416 29.338940 -0.058181 31.395921 31.345159 -0.849600 28.226331 28.268567 0.706893 55.258493 55.293019 0.577850 61.738852 61.778689 0.666742 73.259584 73.294506 0.584478 28.226331 28.296904 1.181164 38.655847 38.722680 1.118570 55.258493 55.302025 0.728574 61.738852 61.847745 1.822523 19.713771 19.775440 1.032138 29.343575 29.344770 0.020010 31.395921 31.381671 -0.238507 47.046817 47.166055 1.995662 12.670000 19.475551 29.342416 41.355765 79.880552 80.569650 108.770837 104.739948 68.135560 99.673729 120.229656 110.783925 38.655847 68.481317 85.145114 116.498853 19.713771 29.343575 47.046817 52.573039 68.626091 78.965304 107.341925 108.488561 37.221519 91.288871 97.169451 110.471041 73.259584 99.528688 101.482933 87.358703 28.226331 55.258493 61.738852 80.067116 31.395921 60.899937 59.300338 70.381939 1 26 21.81654517 -1.121516738 9.069435028 0.03249196962 1 0.725004358 0 -0.1214499383 1357.214449 0.1615596226 253.1934285 -0.9374342868 -0.8119233895 2 4 5 6 7 8 9 0.214755 -0.993041 0.722930 0.115080 0.196702 -0.191542 1.321489 0.815366 0.612762 0.652301 0.874659 0.862244 1.208214 0.848495 12.670000 12.708709 1.206292 25.246752 25.270727 0.747134 25.575453 25.604956 0.919411 32.780327 32.769697 -0.331257 25.391636 25.409898 0.569100 52.150384 52.183427 1.029739 60.374340 60.417395 1.341759 66.849579 66.829355 -0.630271 25.391636 25.427817 1.127523 34.965747 35.002079 1.132220 52.150384 52.148207 -0.067835 60.374340 60.408107 1.052304 32.780327 32.807079 0.833683 38.028759 38.016263 -0.389418 59.194479 59.212628 0.565575 60.484594 60.508616 0.748613 12.670000 12.747444 1.206700 25.575453 25.633827 0.909562 32.780327 32.735334 -0.701059 33.162230 33.154528 -0.120015 25.391636 25.431316 0.618283 52.150384 52.182001 0.492659 60.374340 60.408437 0.531298 68.862428 68.911333 0.762021 25.391636 25.460860 1.078630 34.965747 35.038420 1.132364 52.150384 52.180482 0.468983 60.374340 60.491827 1.830656 25.246752 25.295292 0.756330 32.780327 32.858472 1.217639 33.864742 33.755291 -1.705429 43.956065 43.989738 0.524692 12.670000 25.575453 33.162230 38.803734 77.884015 77.533028 106.488709 102.497058 67.597559 98.853760 111.383547 129.382227 34.965747 65.964648 80.518076 111.409733 25.246752 33.864742 43.956065 53.569211 66.849579 76.640160 101.482284 104.661367 38.028759 89.169147 95.213563 105.319232 68.862428 96.830130 96.769343 88.414255 25.391636 52.150384 60.374340 77.573620 32.780327 59.194479 60.484594 70.757762 2 36 82.65657359 -1.824472192 5.856806084 0.03249196962 1 0.6789890439 0.1 -0.07958681485 192.8237498 0.1539952797 72.32735488 -0.5040171558 -0.5867836358 2 4 5 6 7 8 9 0.244880 -0.881618 0.571603 0.162655 0.155844 -0.175735 1.834485 1.148869 0.646433 0.602822 0.955029 0.974256 1.235961 0.779652 12.670000 12.689690 0.451841 22.818150 22.851442 0.763964 23.152954 23.141120 -0.271562 25.280839 25.607716 7.500976 17.144728 17.152160 0.170558 36.887209 36.907152 0.457639 43.229504 43.252811 0.534823 47.010674 46.993579 -0.392284 17.144728 17.165522 0.477183 24.193460 24.212130 0.428445 36.887209 36.880934 -0.143995 43.229504 43.249580 0.460675 25.280839 25.292275 0.262437 27.652438 27.646386 -0.138890 41.433854 41.438930 0.116464 44.454771 44.470536 0.361756 12.670000 12.709390 0.451949 23.152954 23.179368 0.303065 25.280839 25.234022 -0.537164 25.568586 25.641837 0.840454 17.144728 17.162552 0.204518 36.887209 36.902741 0.178215 43.229504 43.241755 0.140555 47.224100 47.263420 0.451146 17.144728 17.183356 0.443207 24.193460 24.230810 0.428546 36.887209 36.899035 0.135695 43.229504 43.302336 0.835653 22.818150 22.834850 0.191605 25.280839 25.319047 0.438393 26.877331 26.864250 -0.150087 28.120601 28.122111 0.017327 12.670000 23.152954 25.568586 26.640870 53.873654 54.194759 72.740867 72.378217 47.310390 70.394125 77.766569 94.850851 24.193460 45.468220 57.722200 73.889246 22.818150 28.120601 26.877331 40.135171 47.010674 53.290199 68.024749 71.507780 27.652438 60.136751 63.534955 76.048092 47.224100 61.928461 71.847015 60.236933 17.144728 36.887209 43.229504 50.966194 25.280839 41.433854 44.454771 48.633966 2 51 21.24157508 -1.426387994 9.024187509 0.03249196962 1 0.7384427077 0.2 -0.1183512293 192.7344121 0.1427442842 67.97172448 -1.023337978 -0.7672252488 2 4 5 6 7 8 9 0.204228 -1.121654 0.979026 0.114848 0.193231 -0.192840 0.851196 0.634545 0.594244 0.632401 0.861641 0.846834 1.188924 0.822172 12.670000 12.712798 1.262031 33.042661 33.058880 0.478272 33.092966 33.123362 0.896304 35.466563 35.503313 1.083692 22.847325 22.862011 0.433051 50.009643 50.040568 0.911899 60.850272 60.884604 1.012397 67.191648 67.174076 -0.518163 22.847325 22.884350 1.091780 30.408334 30.447717 1.161295 50.009643 50.001002 -0.254805 60.850272 60.866394 0.475407 35.574980 35.596810 0.643696 39.549466 39.541887 -0.223466 57.163694 57.175538 0.349239 64.811813 64.827817 0.471918 12.670000 12.755590 1.261926 33.042661 33.076560 0.499803 35.466563 35.512286 0.674133 35.574980 35.578199 0.047454 22.847325 22.887238 0.588465 50.009643 50.036726 0.399312 60.850272 60.851761 0.021958 65.990783 66.076893 1.269591 22.847325 22.910837 0.936409 30.408334 30.487091 1.161182 50.009643 50.027283 0.260086 60.850272 60.949402 1.461565 33.092966 33.153926 0.898790 35.574980 35.587892 0.190368 39.390235 39.383695 -0.096435 40.375682 40.379106 0.050489 12.670000 33.042661 35.466563 40.233791 78.829857 77.568690 109.068086 107.407691 69.308297 106.570245 123.524061 134.038113 30.408334 65.100424 79.151283 109.879432 33.092966 39.390235 40.375682 56.795320 67.191648 77.167457 97.776400 105.375382 39.549466 86.151353 97.087152 110.035867 65.990783 88.079548 107.724530 88.401033 22.847325 50.009643 60.850272 76.233246 35.574980 57.163694 64.811813 70.462214 2 11 59.02415887 -2.170505208 7.327895128 0.03249196962 1 0.70330315 0.3 -0.0968878772 192.1731667 0.1478324792 73.44399575 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