********* 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 35 2383188.338 -0.25 50 0.03249196962 1 0.4079555203 -0.4422681198 -0.2919807252 39.92916212 0.075 -24.01627062 -0.4112190225 -2.126194874 2 3 4 5 7 8 9 0.001177 -14.638242 15.298321 0.020618 0.025392 0.402689 -6.626034 -12.716537 0.223457 0.265390 0.209617 0.207948 0.800391 0.241414 -949.830752 -949.615260 0.202876 -931.544384 -926.096721 5.128717 -745.249921 -718.973416 24.738088 -696.958145 -658.185211 36.502886 -399.167948 -398.582377 0.551288 -263.863594 -223.540709 37.962091 -226.224952 -216.795157 8.877706 -223.173823 -206.486372 15.710446 -399.167948 -399.152010 0.015005 -352.794708 -241.745365 104.547709 -226.224952 -177.251818 46.105892 -215.762526 -119.319294 90.796746 -469.869242 -469.795585 0.069344 -461.040336 -460.804211 0.222301 -398.655545 -454.947951 -52.996640 -397.197907 -397.026650 0.161230 -931.544384 -918.615370 6.086028 -745.249921 -695.454127 23.440193 -657.161108 -657.891412 -0.343773 -469.869242 -441.157201 13.515515 -399.167948 -398.564718 0.283956 -352.794708 -275.227616 36.512876 -226.224952 -238.781727 -5.910805 -223.173823 -217.350728 2.741084 -399.167948 -398.568136 0.282347 -263.863594 -194.908380 32.459038 -226.224952 -187.598142 18.182658 -215.762526 -119.529038 45.299641 -949.830752 -949.396522 0.204403 -696.958145 -696.177711 0.367371 -658.334547 -659.009645 -0.317786 -505.205662 -562.250700 -26.852604 -745.249921 -931.544384 -657.161108 -441.414625 -223.173823 -203.201299 -21.448622 -65.340439 -398.655545 60.717493 -35.437523 -24.191448 -72.161702 -178.212318 -33.649130 -106.097401 -949.830752 -658.334547 -696.958145 -505.205662 -206.552283 -194.796599 -263.863594 2.570107 -339.797469 -283.013968 -137.180216 -57.238623 -352.794708 134.363118 63.904209 72.691754 -399.167948 -119.552170 -215.762526 -226.224952 -397.197907 -469.869242 -461.040336 -325.090579 2 9 69.03874623 -1.028479906 10.63095532 0.03249196962 1 0.7058107897 0.007578736803 -0.06966437691 50 0.11 12.5 -0.9254947465 -0.7474911868 2 3 4 5 7 8 9 0.236471 -1.063162 0.837457 0.115381 0.197088 -0.191189 1.254851 0.933287 0.623792 0.770528 0.898650 0.949340 1.196263 1.014490 12.670000 12.715075 1.813046 33.759862 33.775490 0.628603 35.328942 35.289527 -1.585365 38.755008 38.876368 4.881415 29.919065 29.935723 0.670043 60.658341 60.694081 1.437551 73.601960 73.643140 1.656373 78.944233 78.915010 -1.175450 29.919065 29.967241 1.937784 39.552295 39.594326 1.690622 60.658341 60.636670 -0.871682 73.601960 73.624691 0.914310 38.879467 38.901248 0.876111 43.813762 43.803288 -0.421325 67.382697 67.399195 0.663566 73.992042 74.003794 0.472721 12.670000 12.760127 1.812570 35.328942 35.251239 -1.562712 38.755008 38.778266 0.467750 38.879467 38.957816 1.575712 29.919065 29.969896 1.022287 60.658341 60.682698 0.489848 73.601960 73.584726 -0.346598 79.410705 79.529335 2.385811 29.919065 29.997868 1.584832 39.552295 39.636360 1.690669 60.658341 60.662416 0.081944 73.601960 73.746248 2.901821 33.759862 33.791431 0.634893 38.879467 38.838545 -0.822988 39.844574 39.883500 0.782857 50.066146 50.118294 1.048763 12.670000 35.328942 38.755008 46.007463 94.130102 91.703363 128.700814 123.296204 78.863773 116.043648 132.026643 153.462428 39.552295 76.753972 92.404289 127.643244 33.759862 39.844574 50.066146 65.025205 78.944233 92.245029 117.466870 124.804003 43.813762 102.709250 112.037491 118.873243 79.410705 110.036337 115.888724 105.002754 29.919065 60.658341 73.601960 91.444692 38.879467 67.382697 73.992042 84.066808 2 17 29.27587722 -1.046815841 10.02197383 0.03249196962 1 0.7148724732 -0.03798142641 -0.09078397784 342.1060866 0.145 121.9174522 -0.9581868914 -0.8259915001 2 3 4 5 7 8 9 0.225681 -1.002716 0.736235 0.110481 0.199903 -0.191317 1.358481 0.894765 0.614992 0.700377 0.874604 0.883736 1.205306 0.915369 12.670000 12.707795 1.367726 27.331175 27.353769 0.817669 28.046234 28.067729 0.777864 33.916232 33.933406 0.621505 28.493757 28.511546 0.643769 57.272199 57.307437 1.275175 67.036599 67.082648 1.666441 73.267482 73.239034 -1.029495 28.493757 28.535381 1.506330 38.592585 38.631767 1.417931 57.272199 57.259656 -0.453913 67.036599 67.078276 1.508244 34.850929 34.876248 0.916237 40.235598 40.222565 -0.471657 64.060542 64.076157 0.565071 65.924357 65.951799 0.993076 12.670000 12.745602 1.367954 28.046234 28.089156 0.776645 33.916232 33.930679 0.261399 34.850929 34.804828 -0.834171 28.493757 28.537875 0.798280 57.272199 57.299049 0.485823 67.036599 67.065756 0.527572 75.255118 75.319551 1.165865 28.493757 28.568470 1.351869 38.592585 38.670956 1.418057 57.272199 57.290811 0.336753 67.036599 67.179846 2.591935 27.331175 27.376427 0.818798 33.965730 34.076235 1.999494 34.850929 34.742707 -1.958188 48.970458 48.987459 0.307632 12.670000 28.046234 33.916232 42.886154 86.086353 85.177434 117.519796 111.996947 72.761370 107.053157 120.745905 135.369857 38.592585 71.787213 87.520203 121.920842 27.331175 33.965730 48.970458 58.466866 73.267482 84.578140 111.522391 115.474930 40.235598 96.874891 102.441614 114.790866 75.255118 106.229190 105.243782 96.343882 28.493757 57.272199 67.036599 85.798968 34.850929 64.060542 65.924357 77.716719 2 18 1582999326 -0.25 50 0.03249196962 1 0.3404901466 -0.5589012215 -0.2903345092 47.74368118 0.18 -5.768321623 -0.6268949426 362332.187 2 3 4 5 7 8 9 -0.063308 -24.580517 25.003745 -0.016776 -1.248753 0.871753 -12.946366 -21.961516 -0.383799 -157.080051 -0.151109 -139.235635 0.571483 -316.541685 -1574.758175 -1574.181905 -29.186171 -1571.192402 -1571.553301 18.278314 -1201.222421 -1201.521590 15.151933 -1200.906711 -1201.063630 7.947425 -960.642303 -960.342340 -15.192113 -728.268617 -724.922821 -169.453430 -724.219537 -714.223886 -506.246438 -713.058317 -711.226155 -92.792883 -960.642303 -960.638252 -0.205139 -713.058317 -713.055436 -0.145936 -708.417715 -617.204276 -4619.656882 -611.482086 -611.770579 14.611200 -941.213578 -962.775355 1092.032186 -938.193607 -880.592524 -2917.303041 -891.420426 -879.987979 -579.015362 -879.635684 -860.088398 -990.004912 -1571.192402 -1571.004936 -4.747255 -1201.222421 -1201.684900 11.711526 -1096.942578 -1096.138196 -20.369634 -941.213578 -836.602744 -2649.095189 -960.642303 -960.296399 -8.759446 -728.268617 -714.374769 -351.838575 -713.058317 -712.012663 -26.479459 -708.417715 -611.533822 -2453.423244 -960.642303 -960.380055 -6.640992 -724.219537 -714.067796 -257.075922 -713.058317 -707.996368 -128.185441 -675.113796 -603.194070 -1821.247288 -1574.758175 -1574.514829 -6.162342 -1200.906711 -1201.356426 11.388286 -1120.623707 -1120.566355 -1.452346 -975.173133 -933.812647 -1047.385427 -1571.192402 -1201.222421 -1096.942578 -787.906672 -728.268617 -602.891560 -507.500127 -479.161412 -891.420426 -180.116509 -535.862754 -402.582618 -510.827044 -373.389141 -366.585185 -241.397391 -1574.758175 -1200.906711 -1120.623707 -975.173133 -724.219537 -579.572462 -675.113796 -662.219361 -690.485423 -796.605653 -517.885439 -414.371201 -708.417715 -224.572084 -213.206157 -192.452627 -960.642303 -713.058317 -573.233363 -611.482086 -879.635684 -860.367502 -938.193607 -941.213578 5 100 212302110 -1 50 0.03249196962 1 0.252398771 -1.724179947 -0.2566677085 16547.8932 0.215 109.1330787 11.7268316 69869.55637 2 3 4 5 7 8 9 -0.007183 -102.384312 53.257925 -2.471167 -1.194492 -12.728936 -81.365536 -95.784535 -13.861922 -16.766409 -14.313824 -16.019978 -2.659345 -35.914401 -6786.705861 -6786.663728 -0.242104 -6785.844029 -6785.877329 0.191356 -5880.752327 -5880.317899 -2.496359 -5877.632304 -5878.052597 2.415132 -6133.142914 -6133.128505 -0.082802 -5787.851004 -5787.873547 0.129537 -5244.866723 -5241.215436 -20.981410 -5244.170472 -4960.856634 -1628.007504 -6133.142914 -6133.142877 -0.000213 -5787.851004 -5787.850965 -0.000221 -4971.040047 -4981.901107 62.410953 -4700.228817 -4766.389358 380.178595 -5176.481183 -5150.934046 -146.801621 -5150.897504 -5123.433213 -157.818174 -5123.436019 -4983.294987 -805.293005 -5017.285728 -4937.754251 -457.012060 -6785.844029 -6785.875370 0.090049 -5880.752327 -5880.714189 -0.109578 -5434.686308 -5434.531715 -0.444169 -5293.102213 -5285.394948 -22.144144 -6133.142914 -6133.137463 -0.015661 -5787.851004 -5787.877520 0.076186 -5244.866723 -4954.716653 -833.645288 -4971.040047 -4948.180461 -65.679068 -6133.142914 -6133.119473 -0.067351 -5787.851004 -5787.869497 0.053133 -5244.170472 -4957.688272 -823.106938 -4971.040047 -4957.215670 -39.719540 -6786.705861 -6786.690375 -0.044493 -5877.632304 -5877.642259 0.028604 -5466.529929 -5437.522818 -83.341843 -5437.703009 -5273.477854 -471.843851 -6785.844029 -5880.752327 -5434.686308 -5293.102213 -5244.866723 -4787.508820 -4686.914291 -4415.536707 -4926.654050 -4404.200687 -4484.002295 -4253.090056 -4684.524572 -4162.275536 -4202.222583 -4163.021946 -6786.705861 -5877.632304 -5437.703009 -5466.529929 -5244.170472 -4799.660157 -4712.202563 -4412.782637 -4804.915249 -4596.315023 -4425.267354 -4176.570468 -4700.228817 -4071.625950 -4207.398223 -4208.554604 -6133.142914 -5787.851004 -4657.997910 -4971.040047 -5123.436019 -5150.897504 -5017.285728 -5176.481183 2 70 589892700.7 -1 50 0.03249196962 1 -1.065005747 -2.703487966 -0.4327354594 -9.063635605 0.25 -10.2140451 4.659918721 46500.69071 2 3 4 5 7 8 9 -0.003591 -195.347918 96.048697 -0.192528 -24.732343 -6.397707 -157.262967 -183.370559 -27.656012 -7.786851 -28.383505 -27.360255 -6.449115 -17.955285 -12091.987941 -12091.934688 -0.152987 -12033.772673 -12034.585299 2.334550 -10421.611947 -10419.898631 -4.922091 -10405.200217 -10406.755410 4.467829 -11231.170697 -11231.165321 -0.015445 -10294.186571 -10294.197965 0.032734 -9597.869801 -9595.853466 -5.792620 -9597.203012 -9558.949239 -109.897185 -11231.170697 -11231.170349 -0.000999 -10294.186571 -10294.186335 -0.000677 -9362.788753 -9376.274525 38.742540 -9026.006899 -9026.008125 0.003522 -9508.102907 -9522.589914 41.618935 -9471.532296 -9508.020480 104.824920 -9291.352450 -9192.815484 -283.081495 -9157.941212 -9079.128846 -226.415763 -12033.772673 -12035.377607 2.305364 -10421.611947 -10421.267131 -0.495302 -10353.156379 -10353.270654 0.164147 -9522.127094 -9530.237813 11.650422 -11231.170697 -11231.168125 -0.003694 -10294.186571 -10294.201694 0.021724 -9597.869801 -9557.572368 -57.884152 -9362.788753 -9103.126111 -372.985347 -11231.170697 -11231.161825 -0.012743 -10294.186571 -10294.193762 0.010330 -9597.203012 -9558.948672 -54.949407 -9362.788753 -9100.056533 -377.394559 -12091.987941 -12091.882032 -0.152130 -10405.200217 -10405.231789 0.045351 -10354.899434 -10354.594073 -0.438628 -9577.596907 -9588.476625 15.627875 -12033.772673 -10421.611947 -10353.156379 -9522.127094 -9597.869801 -8929.107961 -8898.784984 -8825.331718 -9026.883558 -8714.243359 -8495.240820 -8266.846400 -8799.585127 -8293.389703 -8209.177356 -8591.322554 -12091.987941 -10405.200217 -10354.899434 -9577.596907 -9597.203012 -8952.291244 -8867.888099 -8861.872639 -9055.295232 -8686.923575 -8254.236384 -8017.056139 -8810.056431 -8223.817493 -8231.173256 -8411.130603 -11231.170697 -10294.186571 -9026.006899 -9362.788753 -9508.102907 -9471.532296 -9157.941212 -9291.352450 5 101 81170397.09 -1 50 0.03249196962 1 0.02105633986 -1.280785256 -0.05026962727 61854.66721 0.285 -1393.012706 7.706579017 56779.52492 2 3 4 5 7 8 9 0.000727 -59.437491 26.595428 -1.359338 -0.652043 -6.292954 -47.073234 -56.107244 -7.723150 -6.637783 -8.015261 -8.237605 -1.025788 -6.544216 -4447.007283 -4446.817953 0.110166 -4446.156116 -4446.344792 -0.109787 -3867.642165 -3865.907364 1.009441 -3859.722146 -3861.455607 -1.008661 -3867.138762 -3867.135694 0.001785 -3673.848066 -3673.883558 -0.020652 -3255.315317 -3243.056933 7.132870 -3251.792345 -3115.971737 79.030876 -3867.138762 -3867.138761 0.000000 -3673.848066 -3673.848066 0.000000 -2949.456437 -2966.225256 -9.757389 -2885.401895 -2871.253217 8.232789 -3272.983304 -3197.954357 43.657612 -3215.894749 -3164.282040 30.032244 -3205.241667 -3150.647485 31.767094 -3164.281760 -3132.842400 18.293838 -4446.156116 -3384.215476 308.959370 -3867.642165 -3060.472954 234.836564 -3336.674435 -2409.671115 269.700915 -3272.983304 -1930.260829 390.649604 -3867.138762 -3867.156566 -0.005180 -3673.848066 -3673.878921 -0.008977 -3251.792345 -3116.216011 39.444370 -2949.456437 -2977.178526 -8.065422 -3867.138762 -3867.114825 0.006964 -3673.848066 -3673.888183 -0.011672 -3255.315317 -3107.562423 42.986999 -2949.456437 -2989.320280 -11.597925 -4447.007283 -4447.000018 0.002114 -3859.722146 -3859.782293 -0.017499 -3607.086706 -3358.375138 72.359760 -3272.983304 -3231.636083 12.029496 -4446.156116 -3867.642165 -3223.589682 -3336.674435 -3251.792345 -2922.894238 -2768.297918 -2447.196573 -3123.243411 -2372.948853 -2743.446251 -2538.998911 -2885.401895 -2287.234616 -2506.372461 -2412.199322 -4447.007283 -3859.722146 -3226.008659 -3607.086706 -3255.315317 -2936.428351 -2835.284891 -2380.018059 -2937.760455 -2942.111286 -2593.770399 -2495.287851 -2871.010459 -2245.924788 -2439.984218 -2537.013023 -3867.138762 -3673.848066 -2841.730314 -2949.456437 -3164.281760 -3215.894749 -3205.241667 -3272.983304