Compared results of different implementations of the 1982 Heim mass formulas =========================================================================== Data input: ---------------------- GPROG 06 (Pascal) Pi = 3.14159265358979E+0000 base of natural logarithm: ebn = 2.71828182845905E+0000 plancks constant/2Pi: hq = 1.05457159600000E-0034 [Ws*s] speed of light : c = 2.99792458000000E+0008 [m/s] gravitational constant: gam = 6.67331980000000E-0011 [m**3/(kg*s*s) Vacuum wave resistance: Rg = 3.76730313461000E+0002 [Ohm] Fine structure constant: alfa = 7.29735253328589E-0003 "strong" constant: beta = 9.99985890199089E-0001 Conversion kg - MeV : fakMeV = 5.60958920000000E+0029 [MeV/kg] Length unit:s0 = 1.00000000000000E+0000 [m] Derived constants: ----------------- Geometrical shortening: eta = 9.89989640819342E-0001 Geometrical shortening: theta = 7.93991266691442E+0000 Geometrical shortening: xi = 1.61803398874989E+0000 Elementary charge: eq = 1.60216459374958E-0019 [As] Mass element amu = 2.25898458329390E-0031 [kg] Geometrical shortening: alfp Geometrical shortening: alfm Pascal 0.6 1.83221150779746E-0002 8.12834494443715E-0003 Pascal 0.61 1.83221150781647E-0002 8.12834494462534E-0003 FORTRAN 1982 .183221150781649D-01 .812834494462544D-02 Excel v.06 1,83221150781649E-02 8,12834494462544E-03 Accuracy of numer types used: ---------+----------+------------- FORTRAN | double | 15 digits Excel | ? | 15 digits Pascal | extended | 19-20 digits results -----------------------------+------------+------------------------------------------------------------------------------------+-------------------------------------+----------------------+ | | Absolute values | Errors related to empirical values |Errors between FORTRAN and | Empirical | GPROG FORTRAN | GPROG 0.6 Pascal | GPROG 0.61 Pascal | Excel v0.6 | Fortran |Pascal 06 | Excel | Pascal0.6 |Pascal 0.61 | CERN 2002 | | | changed reamining | | [%] |[%] | [%] | [%] | [%] | # Name (kPQkap)x qx Cs | Mean value | | | reals to extended | | | | | | | -----------------------------+------------+---------------+----------------------+----------------------+----------------------+-----------+------------+------------+-----------+----------| 01 eta (1000) 1 0 0 | 547,3 | 5,4880235E+02 | 5,48802349198685E+02 | 5,48802349204379E+02 | 5,48802349204388E+02 |-0,2745021 | -0,2745020 | -0,2745020 | 0,000000 | 0,000000| 02 e0 (1110) 1 0 0 | | 5,0687877E-01 | 5,06878771052940E-01 | 5,06878771058145E-01 | 4,97591675307314E-01 | | | | | | 03 e- (1110) 2 -1 0 | 0,51099907 | 5,1099885E-01 | 5,10998846697922E-01 | 5,01711750952360E-01 | 5,10965496282392E-01 | 0,0000431 | 0,0000437 | 0,0065702 | -0,000001 | -1,851083| 04 my (1111) 1 -1 0 | 105,658389 | 1,0565854E+02 | 1,05658535754895E+02 | 1,05658535756002E+02 | 1,05658465699639E+02 |-0,0001429 | -0,0001389 | -0,0000726 | -0,000004 | -0,000004| 05 K+- (1101) 1 1 1 | 493,677 | 4,9367795E+02 | 4,93677949365270E+02 | 4,93677949370403E+02 | 4,93678410571596E+02 |-0,0001924 | -0,0001923 | -0,0002857 | 0,000000 | 0,000000| 06 K0 (1101) 2 0 1 | 497,672 | 4,9766955E+02 | 4,97669554452197E+02 | 4,97669554457361E+02 | 4,97669554457370E+02 | 0,0004923 | 0,0004914 | 0,0004914 | 0,000001 | 0,000001| 07 pi0 (1200) 2 0 0 | 134,9766 | 1,3496154E+02 | 1,34961535383459E+02 | 1,34961535384859E+02 | 1,34961535384861E+02 | 0,0111575 | 0,0111609 | 0,0111609 | -0,000003 | -0,000003| 08 pi+- (1200) 1 1 0 | 139,57018 | 1,3956581E+02 | 1,39565808464920E+02 | 1,39565808466381E+02 | 1,39565784170503E+02 | 0,0031310 | 0,0031321 | 0,0031495 | -0,000001 | -0,000001| 09 Lambda (2010) 1 0 -1 | 1115,683 | 1,1155909E+03 | 1,11558164043715E+03 | 1,11558164044872E+03 | 1,11559092754449E+03 | 0,0082550 | 0,0090850 | 0,0082526 | -0,000830 | -0,000830| 10 om (2030) 1 -1 -3 | | 1,6722020E+03 | 1,67220204591898E+03 | 1,67220204593635E+03 | 1,67220204593638E+03 | | | | | | 11 p (2110) 1 1 0 | 938,27231 | 9,3827207E+02 | 9,38272070116816E+02 | 9,38272070126560E+02 | 9,38271921776457E+02 | 0,0000256 | 0,0000256 | 0,0000414 | 0,000000 | 0,000000| 12 n (2110) 2 0 0 | 939,56563 | 9,3956549E+02 | 9,39565492307344E+02 | 9,39565492317092E+02 | 9,39565492317108E+02 | 0,0000149 | 0,0000147 | 0,0000147 | 0,000000 | 0,000000| 13 xi0 (2111) 1 0 -2 | 1314,9 | 1,3147744E+03 | 1,31477442763082E+03 | 1,31477442764446E+03 | 1,31477442764448E+03 | 0,0095521 | 0,0095500 | 0,0095500 | 0,000002 | 0,000002| 14 xi- (2111) 2 -1 -2 | 1321,32 | 1,3213061E+03 | 1,32130610341039E+03 | 1,32130610342411E+03 | 1,32127776723429E+03 | 0,0010520 | 0,0010517 | 0,0031963 | 0,000000 | 0,000000| 15 sig+ (2210) 1 1 -1 | 1189,37 | 1,1893545E+03 | 1,18936382537436E+03 | 1,18936382538672E+03 | 1,18935477594549E+03 | 0,0013032 | 0,0005192 | 0,0012800 | 0,000784 | 0,000784| 16 sig0 (2210) 2 0 -1 | 1192,642 | 1,1924268E+03 | 1,19243607312886E+03 | 1,19243607314124E+03 | 1,19242678604550E+03 | 0,0180440 | 0,0172664 | 0,0180451 | 0,000778 | 0,000778| 17 sig- (2210) 3 -1 -1 | 1197,449 | 1,1972755E+03 | 1,19728481036347E+03 | 1,19728481037591E+03 | 1,19727576093468E+03 | 0,0144891 | 0,0137116 | 0,0144673 | 0,000778 | 0,000778| 18 o-- (2310) 4 -2 0 | 1672,45 | 1,5340925E+03 | 1,50171945227284E+03 | 1,50171945228843E+03 | 1,53408849518099E+03 | 8,2727436 | 10,2084097 | 8,2729830 | -2,155732 | -2,155732| 19 o- (2310) 3 -1 0 | | 1,5309707E+03 | 1,64836678371277E+03 | 1,64836678372988E+03 | 1,53097046329979E+03 | | | | 7,121964 | 7,121964| 20 o0 (2310) 2 0 0 | | 1,5491707E+03 | 1,53485268022499E+03 | 1,53485268024091E+03 | 1,54912425125759E+03 | | | | -0,932860 | -0,932860| 21 o+ (2310) 1 1 0 | | 1,5399516E+03 | 1,52720846719356E+03 | 1,52720846720944E+03 | 1,53995131215791E+03 | | | | -0,834407 | -0,834407| 22 delt++ (2330) 1 2 0 | | 1,2302550E+03 | 1,23029214432023E+03 | 1,23029214433299E+03 | 1,23024902906903E+03 | | | | 0,003019 | 0,003019| 23 delt+ (2330) 2 1 0 | | 1,2299804E+03 | 1,22979459514165E+03 | 1,22979459515443E+03 | 1,22976641967070E+03 | | | | -0,015109 | -0,015109| 24 delt (2330) 3 0 0 | | 1,2311277E+03 | 1,23126696760208E+03 | 1,23126696761485E+03 | 1,23112766117861E+03 | | | | 0,011311 | 0,011311| 25 delt- (2330) 4 -1 0 | | 1,2356698E+03 | 1,23568837876626E+03 | 1,23568837877910E+03 | 1,23566943556094E+03 | | | | 0,001504 | 0,001504| ------------------------------------------------------------------------------------------------ Different allocations of protosimplexes in omicrons (2310) because of different intermediate result w2 Ground level -- x=1 qx=1 -------------------------- Q1 Q2 Q3 Q4 K1 K2 K3 K4 w2 Pascal 06 24 31 34 15 28 8 3 1 4.83286841258744E-0001 Corrected K3, n3, K4, n4. This resonance is not allowed! FORTRAN 24 31 34 15 28 16 9 11 Excel 06 24 31 34 15 28 16 9 11 0,496854522 Ground level -- x=2 qx= ------------------------- Q1 Q2 Q3 Q4 K1 K2 K3 K4 Pascal 06 24 31 34 15 28 10 5 24 FORTRAN 24 31 34 15 28 17 15 23 ### undefined ik4 via 3 in Gstruc : Excel 06 24 31 34 15 28 17 15 18 Corrected value of K3, n3, K4, n4. This resonance is not allowed! Ground level ---x=3 qx=-1 ---------------------------- Q1 Q2 Q3 Q4 K1 K2 K3 K4 Pascal 06 24 31 34 15 27 46 40 51 Corrected value of K3, n3, K4, n4. This resonance is not allowed! FORTRAN 24 31 34 15 28 11 12 6 Excel 06 24 31 34 15 28 11 12 6 Ground level ---x=4 qx=-2 ---------------------------- Q1 Q2 Q3 Q4 K1 K2 K3 K4 Pascal 06 24 31 34 15 28 20 20 6 FORTRAN 24 31 34 15 28 25 32 21 Excel 06 24 31 34 15 28 25 32 21 ---------------------------------------------------------------------------------------- 1. The error in the computation of strangeness of xi is absent here that happend in the 1982 DESY code. I used the equations given in the 1982 paper. 2. There is an interesting variance in omicrons, when using Pascal. I don't know whether Pascal has more accuracy because of 20 digits used. At this point we need further investigation with a mathematical orientated programming language. 3. Resonance limits calculated in excel and pascal are 100% identical (besides - of course - the omicrons mentioned). Interesting enough these limits are in many cases significantly smaller than the limits Burkhard Heim has published in "Elementary structures", vol 2. This may be a result of number types used. You find the limits in the excel worksheet and in the file gprogout.dat. The Pascal version calculates resonances up to N=180. 4. As noted before I skipped the special truncation rule for values >x.99 This rule was mentioned in the 1982 paper and in "Elementary structures", vol 2.