********* 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 92.63921768 -1.354321987 11.11209763 0 1 0.3126500461 0.03566193024 -0.08846833087 40 0.03702830116 10 -0.3895991247 -0.281915355 2 3 4 5 6 7 8 9 0.161818 -0.789583 0.740610 0.105339 0.358093 -0.491342 1.075408 0.597538 0.592428 0.741685 0.965062 0.996354 1.024769 0.946273 12.670000 12.715293 1.303088 25.128481 25.152153 0.681039 26.140337 26.151239 0.313663 31.259800 31.223325 -1.049377 26.879991 26.907554 0.792987 52.232156 52.275941 1.259712 61.491975 61.525034 0.951117 66.299978 66.294849 -0.147567 26.879991 26.915120 1.010662 29.414394 29.434985 0.592404 52.232156 52.234467 0.066490 61.491975 61.028619 -13.330880 31.259800 31.284814 0.719674 36.402775 36.390142 -0.363466 57.539013 57.567958 0.832754 63.543657 63.529719 -0.400985 12.670000 12.760576 1.302940 26.140337 26.161677 0.306971 31.259800 31.231962 -0.400453 34.834674 34.838696 0.057850 26.879991 26.941538 0.885351 52.232156 52.274916 0.615112 61.491975 60.984992 -7.293017 71.491520 71.559547 0.978568 26.879991 26.943802 0.917932 29.414394 29.455625 0.593120 52.232156 52.281462 0.709283 61.491975 61.522141 0.433937 25.128481 25.176439 0.689882 31.259800 31.264886 0.073170 35.377924 35.362482 -0.222139 44.402260 44.449092 0.673681 12.670000 26.140337 34.834674 39.135120 79.631101 82.626353 101.855856 105.051436 75.613343 74.492646 101.588708 110.439060 29.414394 61.982934 83.246098 88.598681 25.128481 35.377924 44.402260 56.164786 66.299978 80.462483 101.511347 96.957148 36.402775 80.509519 87.198986 100.782242 75.922731 71.491520 96.894931 97.211125 26.879991 52.232156 61.491975 79.452260 31.259800 57.539013 63.543657 70.585655 1 56 13.95884966 -1.257951129 10.90937117 0.001967542671 1 0.4108676937 -0.01682535803 -0.07337518499 108.0151938 0.07800290308 44.56770216 -0.6397261616 -0.5051349625 2 3 4 5 6 7 8 9 0.180101 -0.859530 0.795173 0.092970 0.306720 -0.356665 1.209864 0.680674 0.588228 0.677410 0.915038 0.879593 1.078074 0.860964 12.670000 12.704981 1.099682 23.280508 23.306608 0.820505 23.493822 23.520783 0.847566 30.470400 30.448253 -0.696213 27.932008 27.955393 0.735150 53.615495 53.661220 1.437443 62.488637 62.522360 1.060131 67.736871 67.723571 -0.418114 27.932008 27.969175 1.168414 32.993990 33.020212 0.824324 53.615495 53.612225 -0.102808 62.488637 62.513710 0.788210 30.470400 30.495482 0.788514 35.683989 35.669597 -0.452412 59.173111 59.199050 0.815438 61.547651 61.562413 0.464078 12.670000 12.739989 1.100104 23.493822 23.546756 0.832041 30.470400 30.439186 -0.490617 31.104679 31.088974 -0.246854 27.932008 27.984675 0.827837 53.615495 53.650757 0.554249 62.488637 62.521595 0.518049 68.490019 68.487110 -0.045728 27.932008 28.000462 1.075983 32.993990 33.046456 0.824676 53.615495 53.664957 0.777460 62.488637 62.571066 1.295640 23.280508 23.333367 0.830858 30.470400 30.508580 0.600127 31.152408 31.102800 -0.779747 45.435542 45.558195 1.927889 12.670000 23.493822 31.104679 39.824724 80.006065 83.230089 109.168050 107.574296 66.205894 86.369248 107.551940 109.853630 32.993990 66.988416 87.167746 93.252113 23.280508 31.152408 45.435542 56.881440 67.736871 80.425935 99.376925 110.831852 35.683989 86.239751 91.079201 101.210082 68.490019 86.432276 94.179246 105.082793 27.932008 53.615495 62.488637 75.745999 30.470400 59.173111 61.547651 71.554684 2 47 15.16074382 -1.142207138 10.28237001 0.007919222016 1 0.4664277841 -0.06004003256 -0.07932246395 185.4328002 0.08566137353 77.9531642 -0.7144667883 -0.6264536298 2 3 4 5 6 7 8 9 0.198056 -0.881161 0.768211 0.099635 0.265116 -0.282149 1.426727 0.799314 0.602706 0.676234 0.903313 0.876811 1.133538 0.866300 12.670000 12.704664 1.129476 21.481548 21.507842 0.856774 21.743761 21.768388 0.802425 29.707598 29.719298 0.381233 28.154219 28.176791 0.735480 53.922167 53.963215 1.337516 61.829799 61.865981 1.178930 67.151875 67.137228 -0.477252 28.154219 28.189162 1.138551 34.889996 34.916558 0.865484 53.922167 53.920634 -0.049947 61.829799 61.858450 0.933561 30.231861 30.256844 0.814041 35.502406 35.487660 -0.480498 59.050890 59.076612 0.838113 59.964101 59.978528 0.470101 12.670000 12.739354 1.129901 21.743761 21.791841 0.783306 29.707598 29.714965 0.120033 30.231861 30.178896 -0.862889 28.154219 28.202602 0.788242 53.922167 53.955482 0.542776 61.829799 61.866509 0.598078 69.865174 69.970276 1.712299 28.154219 28.220889 1.086170 34.889996 34.943137 0.865774 53.922167 53.967718 0.742120 61.829799 61.920749 1.481752 21.481548 21.534866 0.868659 29.714593 29.751715 0.604794 30.231861 30.182088 -0.810883 45.420889 45.533271 1.830912 12.670000 21.743761 29.707598 40.103077 79.153342 81.455706 106.487238 117.471727 66.488025 88.264374 107.718330 112.402242 34.889996 67.106450 90.657009 94.183332 21.481548 29.714593 45.420889 51.893203 67.151875 79.223419 102.472665 106.296996 35.502406 87.799651 94.046150 94.697401 69.865174 89.102539 94.439035 100.892075 28.154219 53.922167 61.829799 76.493828 30.231861 59.050890 59.964101 66.972825 2 11 19.07651632 -1.114092623 10.28604437 0.01800590693 1 0.5995972328 -0.05585487327 -0.08052230361 50 0.1324210124 12.5 -0.8931419294 -0.7803424232 2 3 4 5 6 7 8 9 0.207678 -0.954393 0.787765 0.099107 0.231270 -0.227821 1.363915 0.805498 0.598219 0.662038 0.865937 0.843138 1.169429 0.853896 12.670000 12.702283 1.103408 23.214320 23.244463 1.030237 23.269405 23.292796 0.799497 30.550616 30.561322 0.365901 28.434660 28.454261 0.669931 55.818425 55.858880 1.382729 64.363726 64.407522 1.496880 70.535220 70.509300 -0.885920 28.434660 28.473214 1.317710 37.242550 37.277008 1.177747 55.818425 55.811300 -0.243508 64.363726 64.404916 1.407837 32.044987 32.070167 0.860640 37.484802 37.470787 -0.479013 61.928982 61.949727 0.709029 62.230849 62.255156 0.830786 12.670000 12.734609 1.104136 23.214320 23.273723 1.015160 30.550616 30.556256 0.096373 32.044987 31.994413 -0.864274 28.434660 28.478518 0.749506 55.818425 55.848866 0.520234 64.363726 64.403736 0.683743 73.855954 73.906017 0.855546 28.434660 28.507135 1.238551 37.242550 37.311475 1.177896 55.818425 55.854531 0.617032 64.363726 64.489781 2.154211 23.269405 23.316978 0.813010 30.558930 30.585178 0.448551 32.044987 32.010685 -0.586191 47.163706 47.196772 0.565071 12.670000 23.214320 30.550616 41.375802 82.427484 83.648259 112.161227 116.188178 69.695664 97.306594 120.735336 116.969741 37.242550 69.651336 94.883173 104.715054 23.269405 30.558930 47.163706 53.897978 70.535220 81.728810 108.732857 111.629753 37.484802 87.859964 109.094611 102.428743 73.855954 96.981375 102.708545 91.447084 28.434660 55.818425 64.363726 82.852477 32.044987 61.928982 62.230849 70.498762 2 20 21.15604785 -1.062435849 9.480622399 0.03249196962 1 0.70330315 -0.05619295729 -0.0968878772 192.1731667 0.1478324792 73.44399575 -0.9370236797 -0.825061301 2 3 4 5 6 7 8 9 0.224458 -0.967432 0.689918 0.111891 0.200314 -0.192344 1.471192 0.914470 0.617772 0.675894 0.877970 0.870234 1.212685 0.880779 12.670000 12.704925 1.189125 24.380741 24.404270 0.801131 24.735776 24.761476 0.875043 31.489116 31.505226 0.548530 27.350946 27.368805 0.608065 54.692968 54.726997 1.158608 63.021944 63.065996 1.499887 69.235487 69.210672 -0.844900 27.350946 27.388316 1.272366 37.360049 37.395550 1.208755 54.692968 54.685868 -0.241747 63.021944 63.060183 1.301979 32.714048 32.739122 0.853734 37.986512 37.973182 -0.453873 61.042762 61.060714 0.611235 61.459053 61.483170 0.821142 12.670000 12.739877 1.189589 24.735776 24.786752 0.867813 31.489116 31.494835 0.097364 32.714048 32.666131 -0.815736 27.350946 27.391330 0.687502 54.692968 54.721173 0.480166 63.021944 63.055797 0.576326 71.922520 71.972931 0.858208 27.350946 27.421033 1.193156 37.360049 37.431062 1.208929 54.692968 54.718606 0.436459 63.021944 63.149847 2.177426 24.380741 24.428120 0.806586 31.509718 31.551595 0.712915 32.714048 32.668106 -0.782123 46.079568 46.119222 0.675060 12.670000 24.735776 31.489116 40.671582 80.893427 80.667207 110.235875 104.613931 68.706068 100.845148 117.176579 121.515663 37.360049 68.166604 83.611723 115.960397 24.380741 31.509718 46.079568 54.821068 69.235487 79.677113 106.172907 108.845728 37.986512 91.926776 96.548449 109.618814 71.922520 100.564043 99.870021 90.238187 27.350946 54.692968 63.021944 80.974003 32.714048 61.042762 61.459053 73.194705 2 11 24.13152998 -1.06099118 8.502642263 0.0517766953 1 0.8209652375 -0.06049699822 -0.09817395281 50 0.1751773935 12.5 -0.9989484598 -0.9151652788 2 3 4 5 6 7 8 9 0.245516 -0.946295 0.513102 0.122768 0.172506 -0.161652 1.642051 1.081970 0.633778 0.668181 0.879802 0.873923 1.256923 0.876838 12.670000 12.702411 1.082558 25.066117 25.086201 0.670821 25.763747 25.783967 0.675352 30.777132 30.795234 0.604633 25.673744 25.687858 0.471437 52.102654 52.130462 0.928790 60.158098 60.199544 1.384317 66.162979 66.138536 -0.816409 25.673744 25.708545 1.162395 36.668498 36.703307 1.162630 52.102654 52.093348 -0.310805 60.158098 60.193612 1.186186 32.310079 32.331733 0.723287 36.949815 36.938410 -0.380943 58.285405 58.297271 0.396311 58.771870 58.797229 0.846997 12.670000 12.734846 1.082942 25.763747 25.804206 0.675676 30.777132 30.780341 0.053594 32.310079 32.277022 -0.552046 25.673744 25.707022 0.555756 52.102654 52.125419 0.380182 60.158098 60.184306 0.437667 67.808401 67.868666 1.006432 25.673744 25.738301 1.078126 36.668498 36.738125 1.162787 52.102654 52.116957 0.238870 60.158098 60.283266 2.090332 25.066117 25.106248 0.670206 30.803091 30.823675 0.343751 32.310079 32.344471 0.574363 42.399594 42.366768 -0.548205 12.670000 25.763747 30.777132 37.820868 76.913592 75.852508 104.782290 100.553599 65.031773 101.778541 106.965208 129.493640 36.668498 64.476344 83.614807 110.974723 25.066117 30.803091 42.399594 53.070370 66.162979 75.365139 100.785176 102.613616 36.949815 88.652504 81.646486 116.947450 67.808401 86.385644 109.299104 88.425244 25.673744 52.102654 60.158098 75.354654 32.310079 58.285405 58.771870 70.532622 2 47 34.96816202 -0.9923163742 8.629737615 0.07642881742 1 0.9762055015 -0.04976286858 -0.1216910507 54.50017115 0.2093907269 17.51604602 -1.17837166 -1.077597823 2 3 4 5 6 7 8 9 0.253733 -0.954827 0.337574 0.122212 0.146107 -0.124886 1.571079 1.117230 0.638729 0.663192 0.856026 0.846224 1.287636 0.877094 12.670000 12.708702 1.355905 28.305076 28.322737 0.618717 29.017272 29.039537 0.780043 35.110868 35.193178 2.883655 26.498787 26.513184 0.504382 54.340164 54.365994 0.904937 63.082723 63.124348 1.458323 69.978338 70.023809 1.593023 26.498787 26.536611 1.325147 39.190496 39.231873 1.449594 54.340164 54.331576 -0.300896 63.082723 63.113395 1.074573 35.110868 35.135098 0.848858 40.058199 40.046528 -0.408874 61.457111 61.467831 0.375564 62.280741 62.308086 0.957994 12.670000 12.747423 1.356227 29.017272 29.061674 0.777796 35.110868 35.180911 1.226955 35.170348 35.441079 4.742429 26.498787 26.533429 0.606839 54.340164 54.363913 0.416003 63.082723 63.105469 0.398442 70.787496 70.999917 3.721017 26.498787 26.568587 1.222700 39.190496 39.273256 1.449711 54.340164 54.351037 0.190459 63.082723 63.202985 2.106653 28.305076 28.340934 0.628119 35.110868 35.214911 1.822529 35.235035 35.304652 1.219501 41.594739 41.491523 -1.808068 12.670000 29.017272 35.170348 37.708007 81.260904 79.136497 111.178770 106.649340 68.853619 114.754592 117.074604 146.804268 39.190496 67.779897 92.608297 111.750056 28.305076 41.594739 35.235035 56.118171 69.978338 79.119814 106.276347 107.683183 40.058199 93.474454 88.832192 126.815880 70.787496 95.872031 99.256720 112.174688 26.498787 54.340164 63.082723 77.990738 35.110868 61.457111 62.280741 74.546134 2 20 30.43439037 -1.004886887 6.874591599 0.1072401379 1 1.083865656 -0.004344122122 -0.1545179607 109.6733472 0.2003587249 31.5021133 -0.9925019422 -1.002026841 2 3 4 5 6 7 8 9 0.286213 -0.874907 0.008860 0.155708 0.107376 -0.088413 1.890480 1.415904 0.683801 0.675536 0.915029 0.913550 1.340062 0.900251 12.670000 12.709817 1.253499 30.280527 30.310964 0.958209 30.503006 30.522782 0.622594 31.982670 31.990947 0.260563 22.646964 22.658257 0.355502 46.939374 46.957995 0.586217 57.947827 57.985469 1.185021 60.630138 60.612784 -0.546327 22.646964 22.678474 0.991964 34.653712 34.687377 1.059834 46.939374 46.937182 -0.069017 57.947827 58.041980 2.964081 33.043143 33.063511 0.641204 37.002790 36.993347 -0.297264 52.966235 52.977475 0.353864 55.992490 56.004322 0.372481 12.670000 12.749622 1.253315 30.503006 30.542497 0.621619 31.982670 31.998995 0.256965 33.043143 33.048385 0.082517 22.646964 22.675089 0.442700 46.939374 46.961700 0.351426 57.947827 58.012152 1.012520 60.833111 60.877065 0.691866 22.646964 22.704434 0.904613 34.653712 34.721053 1.059996 46.939374 46.950067 0.168321 57.947827 58.147996 3.150812 30.280527 30.342042 0.968299 33.043143 33.017200 -0.408370 33.240717 33.263372 0.356604 34.815722 34.806636 -0.143030 12.670000 30.503006 31.982670 33.273457 70.524461 68.215844 95.435741 89.713573 60.527518 104.410797 100.998687 132.074805 34.653712 58.880275 78.986750 85.265138 30.280527 34.815722 33.240717 49.990729 60.630138 68.662392 89.235881 92.095755 37.002790 79.360594 80.426043 109.323509 60.833111 83.934087 73.084404 111.792518 22.646964 46.939374 57.947827 61.564864 33.043143 52.966235 55.992490 64.377664 2 11 50.37235095 -0.9968561765 6.025751287 0.1453085056 1 1.224105734 0.03732316724 -0.1686371402 50 0.20336059 12.5 -0.7362189248 -0.7583883552 2 3 4 5 6 7 8 9 0.316789 -0.790243 -0.377912 0.186480 0.070641 -0.055439 2.101663 1.696828 0.734269 0.709064 0.995125 0.980123 1.385051 0.953506 12.670000 12.711091 1.254996 28.469532 28.470890 0.041487 29.763827 29.748364 -0.472291 31.785853 31.800357 0.442965 20.966338 20.975371 0.275878 43.410695 43.426070 0.469613 52.862430 52.872709 0.313934 56.644819 56.635365 -0.288750 20.966338 20.995675 0.896000 33.006295 33.037642 0.957419 43.410695 43.410789 0.002873 52.862430 52.867406 0.151974 32.652481 32.669787 0.528561 35.957653 35.949837 -0.238741 48.969625 48.981556 0.364391 53.214531 53.213364 -0.035646 12.670000 12.752171 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