********* 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 20 27.31014225 -0.9163078862 9.95664953 0.03249196962 1 0.5799325088 -0.165 -0.08910508169 158.3325721 0.09810455832 62.23069566 -0.8842145368 -0.8729628651 2 4 5 6 7 8 9 0.238174 -0.901857 0.711601 0.108352 0.207797 -0.193416 1.991052 1.092482 0.633524 0.708571 0.887868 0.885764 1.238738 0.924231 12.670000 12.702604 1.237091 14.620269 14.639164 0.716921 15.534101 15.548570 0.548992 27.290370 27.289651 -0.027288 31.163223 31.185079 0.829247 58.600583 58.634455 1.285180 64.258379 64.296225 1.435967 70.266302 70.251442 -0.563843 31.163223 31.194241 1.176891 41.551048 41.577039 0.986158 58.600583 58.600499 -0.003220 64.258379 64.283670 0.959604 30.479141 30.503183 0.912220 35.912881 35.896728 -0.612854 59.726220 59.736783 0.400819 61.611345 61.635373 0.911675 12.670000 12.735206 1.237051 15.534101 15.563181 0.551692 27.290370 27.288233 -0.040540 30.479141 30.449452 -0.563244 31.163223 31.206125 0.813904 58.600583 58.629612 0.550709 64.258379 64.292428 0.645957 76.819205 76.845575 0.500271 31.163223 31.226094 1.192737 41.551048 41.603047 0.986489 58.600583 58.638985 0.728530 64.258379 64.349171 1.722439 14.620269 14.657657 0.709288 27.304650 27.295443 -0.174671 30.479141 30.481914 0.052607 48.616895 48.676424 1.129337 12.670000 15.534101 27.290370 43.696798 82.441751 83.707614 111.474177 110.918593 67.812855 101.856629 113.721301 109.644207 41.551048 70.264693 94.207614 113.716863 14.620269 27.304650 48.616895 54.964588 70.266302 82.009588 110.474739 113.367040 35.912881 90.314463 98.523508 114.581557 76.819205 102.048728 105.671400 88.063886 31.163223 58.600583 64.258379 80.384644 30.479141 61.611345 59.726220 69.736569 2 11 21.09715815 -1.040022157 8.995397371 0.03249196962 1 0.6523980134 -0.095 -0.1042396848 50 0.1282263252 12.5 -0.8905929069 -0.827351598 2 4 5 6 7 8 9 0.230200 -0.913649 0.636972 0.114154 0.203611 -0.196644 1.730468 1.007575 0.629102 0.667623 0.890893 0.872129 1.227256 0.868148 12.670000 12.704960 1.158285 20.719776 20.741653 0.724835 21.156256 21.178237 0.728271 29.124441 29.113611 -0.358818 27.042847 27.061803 0.628044 53.084624 53.116553 1.057891 59.854149 59.893625 1.307928 65.680405 65.662964 -0.577869 27.042847 27.075261 1.073950 36.870965 36.900264 0.970751 53.084624 53.083809 -0.026988 59.854149 59.883290 0.965478 30.714959 30.739492 0.812836 35.889688 35.875531 -0.469047 57.654138 57.669624 0.513078 58.279857 58.301969 0.732606 12.670000 12.739948 1.158758 21.156256 21.199531 0.716891 29.124441 29.120538 -0.064648 30.714959 30.673828 -0.681381 27.042847 27.081728 0.644102 53.084624 53.114218 0.490266 59.854149 59.887028 0.544670 69.763538 69.800855 0.618199 27.042847 27.106725 1.058206 36.870965 36.929580 0.971018 53.084624 53.117182 0.539367 59.854149 59.956692 1.698725 20.719776 20.764173 0.735478 29.124971 29.123648 -0.021915 30.714959 30.707017 -0.131570 43.596793 43.623657 0.445032 12.670000 21.156256 29.124441 38.976171 76.743494 77.079092 103.936554 98.654225 65.144917 95.020955 114.250991 105.079694 36.870965 65.372567 81.384112 109.335303 20.719776 29.124971 43.596793 51.962515 65.680405 75.907426 101.478782 103.583674 35.889688 86.450063 93.054090 103.797424 69.763538 95.006798 96.053652 84.640555 27.042847 53.084624 59.854149 75.993714 30.714959 58.279857 57.654138 68.843782 2 26 21.10716032 -1.089631693 8.973210047 0.03249196962 1 0.7009738285 -0.025 -0.1173034836 217.8297271 0.1460690827 92.59333697 -0.9047734147 -0.8017178563 2 4 5 6 7 8 9 0.221622 -0.967376 0.685467 0.116595 0.198210 -0.193557 1.450261 0.891280 0.620971 0.662544 0.886015 0.874403 1.213722 0.862353 12.670000 12.708527 1.225883 24.571930 24.597645 0.818218 25.082533 25.108126 0.814315 32.359572 32.350301 -0.295013 25.762977 25.781297 0.582940 52.251632 52.283742 1.021707 60.266178 60.307715 1.321637 66.328169 66.309256 -0.601797 25.762977 25.798322 1.124650 35.311034 35.344884 1.077056 52.251632 52.249412 -0.070635 60.266178 60.297798 1.006123 32.359572 32.385613 0.828566 37.561279 37.548335 -0.411870 58.770712 58.789985 0.613217 59.897890 59.918800 0.665320 12.670000 12.747079 1.226267 25.082533 25.133236 0.806647 32.359572 32.322758 -0.585687 32.413955 32.401917 -0.191522 25.762977 25.802851 0.634368 52.251632 52.282485 0.490843 60.266178 60.298008 0.506395 68.848423 68.895699 0.752123 25.762977 25.830450 1.073444 35.311034 35.378747 1.077258 52.251632 52.280551 0.460074 60.266178 60.378828 1.792176 24.571930 24.623634 0.822569 32.359572 32.431149 1.138729 32.680860 32.584376 -1.534983 43.299446 43.397202 1.555219 12.670000 25.082533 32.413955 38.741807 77.548898 77.148632 105.564071 100.770546 66.928573 97.195956 108.873401 124.370439 35.311034 65.665507 80.028884 110.125115 24.571930 32.680860 43.299446 53.211252 66.328169 76.380398 100.840209 104.049878 37.561279 88.496111 94.699635 103.067954 68.848423 96.415470 95.388748 87.568990 25.762977 52.251632 60.266178 77.069695 32.359572 58.770712 59.897890 70.458129 1 90 24.38378497 -1.123222438 8.504622982 0.03249196962 1 0.6942549892 0.045 -0.1535093957 825.8533281 0.1356558378 11.24799625 -0.8677522412 -0.7712601937 2 4 5 6 7 8 9 0.215986 -0.986661 0.715923 0.122935 0.193588 -0.193050 1.352873 0.830714 0.622686 0.650580 0.893703 0.884517 1.211736 0.846210 12.670000 12.715347 1.332736 25.606117 25.631063 0.733158 26.437306 26.459133 0.641471 32.757109 32.763926 0.200351 23.963834 23.982977 0.562601 49.801528 49.831377 0.877235 57.964821 58.003857 1.147278 63.745541 63.734110 -0.335959 23.963834 23.997379 0.985883 32.735638 32.768205 0.957138 49.801528 49.805168 0.106953 57.964821 57.987924 0.678991 32.757109 32.784036 0.791396 37.942692 37.931420 -0.331271 56.524650 56.544382 0.579927 59.758160 59.775161 0.499647 12.670000 12.760700 1.332835 26.437306 26.480984 0.641843 32.757109 32.691968 -0.957242 35.838196 35.942259 1.529206 23.963834 24.004551 0.598335 49.801528 49.836340 0.511550 57.964821 57.992555 0.407552 65.871382 65.918909 0.698404 23.963834 24.028504 0.950329 32.735638 32.800787 0.957357 49.801528 49.833711 0.472917 57.964821 58.060470 1.405559 25.606117 25.656041 0.733625 32.757109 32.895029 2.026740 37.852333 37.844868 -0.109697 39.413025 39.283699 -1.900456 12.670000 26.437306 35.838196 36.201381 74.923108 74.020507 102.008930 98.509903 66.190015 95.312019 108.100557 132.496649 32.735638 63.624228 76.446141 104.508825 25.606117 39.413025 37.852333 52.331155 63.745541 73.763545 95.515192 100.112155 37.942692 84.446064 95.746934 96.751580 65.871382 92.122225 92.397882 84.947110 23.963834 49.801528 57.964821 72.953775 32.757109 56.524650 59.758160 67.647407 2 18 269.7806277 -1.648653868 7.417372081 0.03249196962 1 0.7535760685 0.115 -0.1086201546 57.58500849 0.2009511252 17.08656011 -0.7854348478 -0.6788413829 2 4 5 6 7 8 9 0.211215 -0.990413 0.739356 0.138789 0.175941 -0.183865 1.278269 0.791724 0.611771 0.621338 0.898009 0.911175 1.212500 0.806889 12.670000 12.698098 0.704317 24.937054 24.956308 0.482622 25.252468 25.269052 0.415712 29.172072 30.388119 30.482093 19.922650 19.934176 0.288897 43.137810 43.164861 0.678071 50.621534 50.654799 0.833829 56.367479 56.347405 -0.503173 19.922650 19.950358 0.694530 28.070374 28.100185 0.747269 43.137810 43.133879 -0.098543 50.621534 50.649280 0.695492 29.172072 29.190494 0.461779 32.727471 32.719422 -0.201749 49.567196 49.574786 0.190256 52.338857 52.363135 0.608551 12.670000 12.726232 0.704777 25.252468 25.297592 0.565549 29.172072 29.083824 -1.106030 30.325120 30.447613 1.535240 19.922650 19.947820 0.315462 43.137810 43.161060 0.291394 50.621534 50.647842 0.329732 56.372557 56.415958 0.543957 19.922650 19.975964 0.668193 28.070374 28.130001 0.747317 43.137810 43.160770 0.287770 50.621534 50.714938 1.170657 24.937054 24.963679 0.333699 29.172072 29.215457 0.543766 31.765572 31.736271 -0.367234 33.585469 33.609304 0.298734 12.670000 25.252468 30.325120 31.056043 64.359599 64.993528 88.531947 89.962924 56.987272 86.576056 97.421313 115.880045 28.070374 54.599638 68.850259 92.871165 24.937054 33.585469 31.765572 46.543137 56.367479 63.571604 83.466419 86.677726 32.727471 73.273790 76.215002 96.178840 56.372557 74.150436 89.552110 73.304411 19.922650 43.137810 50.621534 63.244292 29.172072 49.567196 52.338857 58.441275 2 18 20.86046766 -1.454078313 9.190070752 0.03249196962 1 0.7568354351 0.185 -0.1184472529 50.67222136 0.1628608939 12.41374978 -1.044445646 -0.7848600678 2 4 5 6 7 8 9 0.201028 -1.119825 0.967359 0.112856 0.194179 -0.193350 0.834767 0.609320 0.589921 0.629871 0.853384 0.839225 1.188975 0.818638 12.670000 12.712199 1.247364 32.698510 32.722488 0.708781 32.830933 32.862752 0.940534 35.562635 35.595994 0.986090 23.149481 23.164381 0.440441 50.670206 50.702150 0.944259 61.337297 61.374686 1.105188 68.109024 68.088628 -0.602911 23.149481 23.187027 1.109823 31.131542 31.172701 1.216630 50.670206 50.661184 -0.266680 61.337297 61.361190 0.706258 35.581405 35.604308 0.677023 39.773926 39.765817 -0.239690 58.169767 58.180239 0.309550 65.144758 65.167852 0.682636 12.670000 12.754411 1.247575 32.698510 32.747335 0.721610 35.562635 35.553225 -0.139077 35.581405 35.629065 0.704411 23.149481 23.188779 0.580806 50.670206 50.697240 0.399558 61.337297 61.348417 0.164349 66.898680 66.978468 1.179239 23.149481 23.215087 0.969630 31.131542 31.213851 1.216495 50.670206 50.689146 0.279930 61.337297 61.447657 1.631087 32.830933 32.894533 0.939992 35.581405 35.596015 0.215939 39.220457 39.220079 -0.005588 40.217249 40.211043 -0.091724 12.670000 32.698510 35.562635 39.880563 79.469237 78.500224 110.164107 109.574383 69.852387 107.783501 124.542136 136.999682 31.131542 65.877499 80.610143 112.333203 32.830933 39.220457 40.217249 56.921960 68.109024 77.811566 99.622170 106.684897 39.773926 87.621721 96.881130 113.521082 66.898680 89.079640 109.818006 89.552742 23.149481 50.670206 61.337297 77.502592 35.581405 58.169767 65.144758 71.089366 1 27 20.92440399 -1.665003605 9.694333841 0.03249196962 1 0.770900773 0.255 -0.122804189 100.3649093 0.1773551685 36.66077286 -1.130825707 -0.814071455 2 4 5 6 7 8 9 0.186862 -1.175399 1.086430 0.107391 0.195121 -0.194616 0.582898 0.455299 0.571262 0.615221 0.826395 0.812612 1.180858 0.798727 12.670000 12.713630 1.264558 35.454798 35.491827 1.073227 35.499462 35.529739 0.877551 36.977468 37.012815 1.024516 22.999780 23.014789 0.435027 51.572504 51.606002 0.970918 62.995962 63.034521 1.117606 70.657838 70.637369 -0.593266 22.999780 23.037482 1.092734 30.524488 30.570353 1.329347 51.572504 51.562691 -0.284414 62.995962 63.018748 0.660434 37.092232 37.115318 0.669104 41.194129 41.187179 -0.201422 59.538654 59.547677 0.261538 68.060066 68.085117 0.726088 12.670000 12.757277 1.264821 35.454798 35.528955 1.074678 35.499462 35.559512 0.870238 37.092232 37.043063 -0.712556 22.999780 23.040082 0.584059 51.572504 51.599405 0.389849 62.995962 63.007337 0.164843 68.442701 68.527503 1.228951 22.999780 23.064931 0.944159 30.524488 30.616191 1.328969 51.572504 51.593095 0.298406 62.995962 63.106324 1.599365 36.977468 37.044983 0.978436 37.092232 37.105462 0.191723 37.705407 37.741212 0.518899 42.928791 42.922464 -0.091693 12.670000 35.454798 35.499462 42.503252 82.163444 81.522250 114.814728 115.976849 72.608793 116.005173 134.037888 140.483014 30.524488 67.908909 83.567252 118.515545 37.705407 36.977468 42.928791 59.209940 70.657838 80.413492 102.947694 111.031615 41.194129 90.732720 97.960436 125.206736 68.442701 92.028013 114.457765 95.433521 22.999780 51.572504 62.995962 80.836401 37.092232 59.538654 68.060066 73.400976 2 9 46.68480528 -2.012717601 8.284087552 0.03249196962 1 0.7222941102 0.325 -0.09624452442 50 0.1448303596 12.5 -1.088675718 -0.7963448651 2 4 5 6 7 8 9 0.194800 -1.132007 1.049920 0.114956 0.192318 -0.196487 0.718300 0.557635 0.575558 0.579455 0.835296 0.812178 1.188167 0.748728 12.670000 12.704692 0.895732 30.155678 30.161555 0.151738 31.005475 31.009458 0.102855 33.657421 33.774520 3.023478 19.853895 19.864428 0.271965 45.193909 45.221139 0.703081 55.492283 55.520931 0.739689 61.734760 61.720173 -0.376623 19.853895 19.883676 0.768952 25.951014 25.985854 0.899562 45.193909 45.182730 -0.288636 55.492283 55.511079 0.485304 33.657421 33.672561 0.390927 36.345224 36.340285 -0.127535 51.496436 51.503371 0.179062 60.256959 60.270239 0.342866 12.670000 12.739386 0.895770 30.155678 30.165801 0.130686 33.657421 33.651566 -0.075592 33.748393 33.800201 0.668829 19.853895 19.884947 0.400887 45.193909 45.213260 0.249827 55.492283 55.510099 0.230005 59.365293 59.423746 0.754634 19.853895 19.903484 0.640194 25.951014 26.020677 0.899340 45.193909 45.206775 0.166106 55.492283 55.570270 1.006806 31.005475 31.015036 0.123433 33.657421 33.659117 0.021890 35.629137 35.670251 0.530785 39.092395 39.098739 0.081896 12.670000 33.748393 30.155678 39.008989 71.803083 71.434106 99.576703 100.091444 63.603634 103.049995 117.361299 119.973101 25.951014 58.873187 73.320199 101.623314 35.629137 31.005475 39.092395 53.440774 61.734760 70.382843 88.276618 96.285004 36.345224 78.334483 83.197956 111.884958 59.365293 81.043643 90.568972 90.645098 19.853895 45.193909 55.492283 69.342716 33.657421 51.496436 60.256959 64.229756 2 10 152.5768458 -2.121517926 7.51018978 0.03249196962 1 0.6805098193 0.395 -0.0636280747 50 0.1190754072 12.5 -1.121491795 -0.7966923382 2 4 5 6 7 8 9 0.197454 -1.103853 1.042717 0.113156 0.195313 -0.202204 0.780820 0.606116 0.573298 0.535024 0.833125 0.780058 1.191143 0.686512 12.670000 12.697638 0.655765 28.786947 28.776437 -0.249369 29.256131 29.255443 -0.016322 30.988995 31.010572 0.511952 17.907668 17.915171 0.178032 41.423810 41.447191 0.554754 51.135245 51.155370 0.477497 56.553027 56.638340 2.024192 17.907668 17.931944 0.575988 22.947121 22.975766 0.679654 41.423810 41.410455 -0.316876 51.135245 51.761363 14.855672 31.593847 31.603428 0.227321 33.272765 33.269485 -0.077830 46.667455 46.672330 0.115655 55.413632 55.428343 0.349051 12.670000 12.725269 0.655678 28.786947 28.756974 -0.355579 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