********* 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 30985498.04 -0.25 50 0.03249196962 1 0.7087662944 -0.02201074633 -0.07425181828 50 0 12.5 -1.366911069 -1.23529159 2 3 4 5 7 8 9 0.200535 -2.845875 4.077538 0.061777 0.041376 0.071719 -0.896115 -0.731902 0.550942 1.429448 0.727935 1.453766 0.958028 1.999824 -85.715099 -85.259860 73.033175 87.258508 87.293438 5.603777 91.142629 91.426431 45.529788 92.220401 93.106333 142.128456 111.463844 111.635899 27.602526 206.805730 206.968722 26.148442 267.098661 266.257783 -134.900312 289.576194 290.490029 146.604819 106.087249 106.538777 72.437759 111.463844 111.706210 38.882443 200.129891 206.663232 1048.131515 206.805730 267.590483 9751.582260 116.056099 116.161966 16.984087 134.427184 134.495926 11.028196 211.660800 211.896813 37.863274 273.288901 272.506776 -125.474805 -85.715099 -84.805106 72.994248 91.142629 91.763333 49.789187 98.357730 102.434242 326.993514 116.056099 111.942616 -329.959094 111.463844 112.016752 44.351029 206.805730 206.939664 10.743363 267.098661 266.932942 -13.292965 281.561486 282.344135 62.779417 106.087249 106.985853 72.080717 111.463844 111.743155 22.404687 200.129891 206.715628 528.268618 206.805730 264.522902 4629.727995 87.258508 87.344898 6.929732 92.220401 99.310594 568.733092 116.056099 109.605760 -517.407763 211.660800 211.322131 -27.165993 -85.715099 98.357730 91.142629 205.831440 337.674150 404.748340 543.125207 490.121586 279.028627 417.813559 462.151402 597.676101 106.087249 282.837145 200.129891 502.773599 87.258508 92.220401 220.793213 232.997065 289.576194 376.946877 459.993982 492.222984 134.427184 290.831321 420.071321 447.738198 281.561486 385.571050 447.100426 409.235578 111.463844 206.805730 267.098661 387.862519 116.056099 211.660800 273.288901 315.859942 2 10 173286.3234 -0.5086119649 50 0.03249196962 1 0.6876968103 -0.04416457489 -0.08829726599 50 0.05 12.5 -1.187355549 -1.089822155 2 3 4 5 7 8 9 0.223918 -1.484867 1.572150 0.077337 0.178323 -0.131365 0.532446 0.502998 0.588792 2.004526 0.798599 2.033517 1.128009 2.762131 -0.749702 -0.421063 58.870680 120.851849 120.867378 2.781661 140.126396 139.060217 -190.989684 148.972385 149.381742 73.330159 132.904326 133.025935 21.784234 253.259369 253.422365 29.198106 318.654577 318.760666 19.004234 336.147279 336.134022 -2.374835 132.904326 133.169072 47.425182 157.958300 158.204726 44.143557 253.259369 253.166558 -16.625640 318.654577 318.366631 -51.581010 151.357080 151.489045 23.639563 178.369317 178.326938 -7.591551 273.458709 273.622447 29.331120 321.622589 321.432458 -34.059062 -0.749702 -0.092714 58.844660 140.126396 138.088133 -182.561730 148.972385 150.755776 159.733574 151.357080 151.759575 36.050381 132.904326 133.283867 33.994414 253.259369 253.390809 11.772705 318.654577 318.180657 -42.447733 341.392248 342.360183 86.695386 132.904326 133.297394 35.205995 157.958300 158.450825 44.114200 253.259369 253.270412 0.989036 318.654577 318.787188 11.877671 120.851849 120.890663 3.476486 149.189671 148.645343 -48.754007 151.357080 152.261515 81.007820 235.548126 235.634582 7.743668 -0.749702 140.126396 148.972385 211.029014 416.533998 406.404228 585.978308 534.598455 339.211189 489.378355 554.179748 652.341283 157.958300 333.068287 355.858561 560.706826 120.851849 149.189671 235.548126 270.016001 336.147279 413.485202 517.495301 556.962519 178.369317 402.537429 508.725362 506.017380 341.392248 482.838036 490.526519 463.211359 132.904326 253.259369 318.654577 419.145850 151.357080 273.458709 321.622589 366.943159 2 17 107.0120482 -0.9145616973 11.30214306 0.03249196962 1 0.6630748179 -0.0603785168 -0.0997362931 349.686203 0.1 123.4144007 -0.9795397617 -0.9103238238 2 3 4 5 7 8 9 0.234713 -1.005230 0.748166 0.103236 0.208128 -0.195349 1.440385 0.965993 0.620499 0.749534 0.867276 0.903007 1.206903 0.982325 12.670000 12.723996 2.291798 30.201207 30.224340 0.981838 32.414509 32.414106 -0.017098 38.946741 39.056179 4.644977 33.134654 33.157577 0.972940 65.049894 65.087630 1.601662 76.660090 76.707042 1.992817 82.408928 82.386933 -0.933583 33.134654 33.182221 2.018905 43.652451 43.693102 1.725392 65.049894 65.039470 -0.442430 76.660090 76.689051 1.229213 39.269641 39.300105 1.293030 45.624261 45.608140 -0.684246 71.482481 71.507992 1.082795 75.859188 75.873582 0.610940 12.670000 12.777970 2.291338 32.414509 32.413588 -0.019545 38.946741 39.054926 2.295902 39.269641 39.155087 -2.431064 33.134654 33.192744 1.232785 65.049894 65.083782 0.719170 76.660090 76.677674 0.373150 85.796133 85.875788 1.690442 33.134654 33.217529 1.758775 43.652451 43.733767 1.725688 65.049894 65.070808 0.443840 76.660090 76.792955 2.819667 30.201207 30.247810 0.989010 38.964725 39.048829 1.784873 39.269641 39.192720 -1.632408 55.863337 55.881941 0.394821 12.670000 32.414509 38.946741 49.355928 98.639587 96.622982 133.827086 126.365719 82.813720 119.542799 139.168210 144.145625 43.652451 81.773457 98.117330 135.413201 30.201207 38.964725 55.863337 66.410582 82.408928 97.037093 125.499216 131.486811 45.624261 105.964696 122.469447 123.398657 85.796133 119.353295 118.701475 109.698402 33.134654 65.049894 76.660090 97.230585 39.269641 71.482481 75.859188 88.379628 2 10 35.97947267 -1.14435867 8.147565309 0.03249196962 1 0.6740962067 -0.06659025148 -0.1027906815 50 0.15 12.5 -0.9619274274 -0.8894881101 2 3 4 5 7 8 9 0.227983 -0.907400 0.614827 0.107759 0.209514 -0.203708 1.711526 0.993314 0.619300 0.594486 0.869602 0.804564 1.227591 0.765339 12.670000 12.699402 0.873817 20.790197 20.810097 0.591417 20.814928 20.840418 0.757543 27.645624 27.657040 0.339275 24.170953 24.186939 0.475106 48.427823 48.457612 0.885339 54.789987 54.826905 1.097191 60.404557 60.385860 -0.555665 24.170953 24.200360 0.873974 33.538993 33.566754 0.825050 48.427823 48.426997 -0.024562 54.789987 54.819211 0.868546 28.900736 28.922512 0.647198 33.444943 33.432831 -0.359955 53.249355 53.267219 0.530894 53.732150 53.750170 0.535571 12.670000 12.728840 0.874358 20.814928 20.864083 0.730440 27.645624 27.646735 0.016518 28.900736 28.854996 -0.679684 24.170953 24.203019 0.476497 48.427823 48.455058 0.404718 54.789987 54.821629 0.470200 63.451968 63.486638 0.515195 24.170953 24.229692 0.872866 33.538993 33.594527 0.825244 48.427823 48.458425 0.454751 54.789987 54.888416 1.462661 20.790197 20.831754 0.617539 27.657326 27.679669 0.332009 28.900736 28.869591 -0.462808 39.382921 39.406959 0.357192 12.670000 20.814928 27.645624 35.148981 69.908081 70.460718 94.833414 90.301824 59.944662 87.667782 104.473958 100.370460 33.538993 59.747811 74.219888 100.752708 20.790197 27.657326 39.382921 48.053536 60.404557 69.127884 92.690340 94.139876 33.444943 80.710258 83.247107 96.408307 63.451968 87.475842 87.413324 78.101380 24.170953 48.427823 54.789987 69.760030 28.900736 53.732150 53.249355 63.835953 2 10 71.11953496 -1.385782605 6.758125175 0.03249196962 1 0.6815650872 -0.06686209952 -0.1032386493 50 0.2 12.5 -0.9160548245 -0.8346234995 2 3 4 5 7 8 9 0.220334 -0.851556 0.584485 0.115965 0.204834 -0.205289 1.992445 0.984174 0.620749 0.532665 0.880790 0.792325 1.247324 0.679319 12.670000 12.693779 0.566526 16.099417 16.120877 0.511280 16.496047 16.512145 0.383508 22.475878 22.474920 -0.022813 20.194076 20.207710 0.324822 41.189739 41.218268 0.679714 45.260714 45.291170 0.725621 50.871998 50.856194 -0.376526 20.194076 20.214142 0.478078 29.541172 29.562715 0.513257 41.189739 41.199246 0.226500 45.260714 45.278751 0.429737 24.629076 24.646365 0.411902 28.209353 28.199638 -0.231453 44.478876 44.498123 0.458553 44.746810 44.758498 0.278484 12.670000 12.717573 0.566710 16.099417 16.141239 0.498202 22.475878 22.469198 -0.079573 24.629076 24.602286 -0.319128 20.194076 20.213157 0.227299 41.189739 41.219202 0.350982 45.260714 45.289161 0.338872 54.009295 54.025950 0.198403 20.194076 20.242431 0.576026 29.541172 29.584266 0.513352 41.189739 41.236174 0.553152 45.260714 45.326321 0.781531 16.496047 16.529275 0.395818 22.481037 22.484308 0.038966 24.629076 24.612711 -0.194942 32.617102 32.638620 0.256325 12.670000 16.099417 22.475878 29.111462 56.899042 59.191622 77.368053 76.671644 49.905448 74.159399 88.186913 83.040037 29.541172 50.257976 64.834929 85.935577 16.496047 22.481037 32.617102 39.240239 50.871998 56.729958 78.838806 77.226248 28.209353 69.793695 65.419071 86.623132 54.009295 73.896161 74.179038 63.937335 20.194076 41.189739 45.260714 57.799156 24.629076 44.746810 44.478876 52.963773 2 10 65.79611272 -1.481583853 7.148937608 0.03249196962 1 0.6985467559 -0.05983995404 -0.09915412385 50 0.25 12.5 -0.9147431937 -0.809960497 2 3 4 5 7 8 9 0.208525 -0.852341 0.651151 0.119400 0.199160 -0.201339 2.109779 0.897253 0.614323 0.551652 0.877511 0.812830 1.257068 0.706789 12.670000 12.700089 0.717684 16.370977 16.386396 0.367777 17.677858 17.689882 0.286778 22.687426 22.680526 -0.164578 21.060916 21.076150 0.363354 43.344152 43.378007 0.807490 47.405349 47.438793 0.797690 53.742304 53.725125 -0.409729 21.060916 21.078903 0.429015 32.157947 32.180499 0.537898 43.344152 43.362135 0.428919 47.405349 47.417724 0.295164 26.169076 26.186328 0.411502 29.697083 29.687743 -0.222779 45.974767 45.982733 0.189998 47.444321 47.470659 0.628226 12.670000 12.730171 0.717591 17.677858 17.701628 0.283478 22.698814 22.688064 -0.128203 26.169076 26.173105 0.048054 21.060916 21.075336 0.171969 43.344152 43.383154 0.465123 47.405349 47.432236 0.320654 57.541994 57.550791 0.104915 21.060916 21.112988 0.621003 32.157947 32.203047 0.537855 43.344152 43.408667 0.769394 47.405349 47.464945 0.710734 16.370977 16.402061 0.370704 22.687426 22.681681 -0.068523 26.169076 26.158860 -0.121837 34.253684 34.277916 0.288988 12.670000 17.677858 22.698814 30.343771 58.598308 62.598138 80.187919 84.534842 52.271256 79.286584 92.610501 89.720040 32.157947 53.096984 70.746574 92.610166 16.370977 22.687426 34.253684 41.161457 53.742304 58.962941 81.578957 83.096433 29.697083 75.091879 70.335021 92.792948 57.541994 78.903918 79.293880 66.463507 21.060916 43.344152 47.405349 61.076257 26.169076 45.974767 47.444321 55.129874 2 10 53.55657597 -1.446165655 8.307624159 0.03249196962 1 0.7250412128 -0.04552381506 -0.09053710506 50 0.3 12.5 -0.9579925349 -0.8154991025 2 3 4 5 7 8 9 0.194274 -0.884130 0.761326 0.118291 0.194890 -0.196094 2.086395 0.765226 0.601089 0.595540 0.861020 0.834237 1.258762 0.769585 12.670000 12.708256 0.987897 17.815598 17.830792 0.392339 21.715130 21.711250 -0.100202 24.749415 24.746015 -0.087792 23.736109 23.754587 0.477164 49.069277 49.111122 1.080571 54.222736 54.267460 1.154899 61.514262 61.491874 -0.578117 23.736109 23.754464 0.473984 37.462519 37.489858 0.705983 49.069277 49.093890 0.635591 54.222736 54.233738 0.284090 30.001665 30.020335 0.482144 33.763306 33.753991 -0.240547 51.424325 51.430891 0.169566 54.917290 54.954878 0.970659 12.670000 12.746487 0.987577 21.715130 21.707460 -0.099039 24.849523 24.841819 -0.099465 30.001665 30.085140 1.077803 23.736109 23.747843 0.151503 49.069277 49.121234 0.670844 54.222736 54.250603 0.359807 65.961425 66.052809 1.179915 23.736109 23.798110 0.800529 37.462519 37.517160 0.705506 49.069277 49.150101 1.043563 54.222736 54.296065 0.946795 17.815598 17.846164 0.394650 24.749415 24.737782 -0.150195 30.001665 29.999491 -0.028068 39.330704 39.354965 0.313256 12.670000 21.715130 24.849523 34.279732 65.961425 73.530897 89.655492 102.961000 59.533163 92.603845 104.562096 108.105428 37.462519 60.853290 83.382879 108.927703 17.815598 24.749415 39.330704 51.543648 61.514262 67.142069 92.855123 96.736239 33.763306 87.643822 82.431395 108.427835 66.302037 90.830161 93.357557 75.776245 23.736109 49.069277 54.222736 70.323564 30.001665 51.424325 54.917290 62.485675 2 37 47.46929777 -2.067791598 10.97606187 0.03249196962 1 0.846453776 0.0131775048 -0.07559792394 68.98223407 0.35 6.413093266 -1.17614773 -0.922831745 2 3 4 5 7 8 9 0.168506 -0.995494 0.863562 0.100037 0.200291 -0.198025 1.253025 0.460499 0.556324 0.621336 0.788643 0.796134 1.221110 0.806641 12.670000 12.720581 1.496809 23.736285 23.755204 0.559848 26.532488 26.498707 -0.999662 30.564476 30.581058 0.490705 27.855601 27.875125 0.577763 58.471643 58.526849 1.633684 66.694394 66.772136 2.300590 76.574208 76.527061 -1.395205 27.855601 27.884965 0.868961 42.825484 42.875053 1.466871 58.471643 58.496202 0.726746 66.694394 66.721414 0.799608 35.691087 35.715365 0.718469 40.624172 40.615279 -0.263157 64.852849 64.867699 0.439428 67.650219 67.693184 1.271436 12.670000 12.771112 1.496081 26.532488 26.466285 -0.979562 31.074626 31.102576 0.413550 35.691087 35.980706 4.285286 27.855601 27.872780 0.254181 58.471643 58.537314 0.971681 66.694394 66.748507 0.800670 79.917808 79.936032 0.269638 27.855601 27.936315 1.194267 42.825484 42.924515 1.465281 58.471643 58.565297 1.385724 66.694394 66.827949 1.976124 23.736285 23.774452 0.564729 30.564476 30.574919 0.154523 35.691087 35.732267 0.609313 50.863263 50.808579 -0.809128 12.670000 26.532488 31.074626 41.641221 82.941679 96.353251 111.465008 142.250905 74.199383 120.407556 122.187273 158.807749 42.825484 74.462682 102.169491 141.576586 23.736285 30.564476 50.863263 65.651146 76.574208 84.800937 119.930490 120.350074 40.624172 108.474480 100.090293 146.244348 79.917808 105.353200 128.667117 95.781860 27.855601 58.471643 66.694394 90.229765 35.691087 64.852849 67.650219 77.867313 2 20 162.0013259 -7.523039204 11.52988835 0.03249196962 1 0.8149386883 0.0005661556003 -0.05541452186 56.2977644 0.4 9.388508797 -1.243063327 -0.9327777512 2 3 4 5 7 8 9 0.159082 -0.292441 -1.710237 0.094365 0.208822 -0.210269 1.848884 0.766438 0.554435 0.610341 0.785146 0.773834 1.249122 0.790199 12.670000 12.730751 1.782880 26.030988 26.033301 0.067885 32.971794 32.949262 -0.661235 33.057946 32.961105 -2.841999 29.877924 29.901739 0.698910 64.266676 64.326913 1.767784 74.953088 75.012885 1.754875 82.875681 82.857382 -0.537005 29.877924 29.903264 0.743655 52.503390 52.540423 1.086824 64.266676 64.309001 1.242132 74.953088 74.953782 0.020377 42.186461 42.204925 0.541869 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