G Selected Results
13/05/2014 22:38
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
1
Selected Results
Research Group Heim's Theory, IGW Innsbruck, 2003
Pay attention also to Heim,B. 1979/89/98, 1984
Ó IGW Innsbruck
Content
· Quantum Numbers of Basic States (N=0) 2
· Theoretical Data of Elementary Particles 3
with Mean Lives > 10-16 sec Calculated by B. Heim 1989
· Experimental Data of Elementary Particles 4
with Mean Lives > 10-16 sec
· Approximated Meson Resonances 5
· Approximated Baryon Resonances 6-8
· Numerical Evaluations of Different Equations 9-11
· Relative Deviations of the Theoretically Determined 12
Particle Masses from the Experimental Mean Values for
Different Values of the Gravity Constant
· Relative Deviations of the Theoretically Determined 13
Particle Lifetimes from the Corresponding Experimental
Mean Values
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
2
Table I
Quantum Numbers of Basic States (N=0)
Partikel k n m p s P Q eqx eC Â
e- ,e + 1 0 0 0 0 1 1 -1 0 0
0 0 e ,e 1 0 0 0 1 1 1 0 0 0
m - ,m + 1 11 6 11 6 1 1 -1 0 1
h,h 1 18 22 17 14 0 0 0 0 0
K + ,K - 1 17 26 30 28 1 0 1 1 1
K 0 ,K 0 1 18 5 5 2 1 0 0 1 1
p ± ,p m 1 12 9 2 3 2 0 ±1 0 0
p 0 ,p 0 1 12 3 6 4 2 0 0 0 0
L,L 2 1 3 0 -11 0 1 0 -1 0
W- ,W+ 2 4 4 -1 -15 0 3 -1 -3 0
p, p 2 0 0 0 0 1 1 1 0 0
n, n 2 0 0 -2 17 1 1 0 0 0
X- ,X+ 2 2 7 -17 2 1 1 -1 -2 1
X0 ,X0 2 2 6 -1 6 1 1 0 -2 1
S+ ,S- 2 2 -7 -12 10 2 1 1 -1 0
S0 ,S0 2 2 -7 -14 -2 2 1 0 -1 0
S- ,S+ 2 2 -6 -5 -8 2 1 -1 -1 0
o ++ ,o -- 2 2 1 9 4 3 3 2 0 0
o + ,o - 2 2 -1 -1 -6 3 3 1 0 0
o 0 ,o 0 2 2 -1 -10 2 3 3 0 0 0
o - ,o + 2 2 -1 -16 -15 3 3 -1 0 0
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
3
Tabelle II
Theoretical Data of Elementary Particles
with Mean Lives > 10-16 sec Calculated by B. Heim 1989
(J = spin, P = parity, I = isospin, S = strangeness, B = baryon number)
Type Symbol Mass
MeV
J P I S B Mean Life
10-8 sec
Photons g 0 1 -1 - - 0 ¥
ne 0.00381 ´ 10-6 1/2 - - - 0 ¥
nm 0.00537 1/2 - - - 0 ¥
nt 0.010752 1/2 - - - 0 ¥
n4 0.021059 1/2 - - - 0 ¥
n5 0.207001 1/2 - - - 0 ¥
e 0.51100343 1/2 ±1 - - 0 ¥
e0 0.51617049 1/2 1 - - 0 ¥
Leptons
m 105.65948493 1/2 ±1 - - 0 219.94237553
p± 139.56837088 0 -1 1 0 0 2.60282911
p0 134.96004114 0 -1 1 0 0 0.84016427 ´ 10-8
h 548.80002432 0 -1 0 0 0 0.00233820 ´ 10-8
K± 493.71425074 0 -1 1/2 ±1 0 1.23709835
K0 497.72299959 0 -1 1/2 1 0 5.17900027
Mesons
K0 497.72299959 0 -1 1/2 -1 0 0.00887666
p 938.27959246 1/2 1 1/2 0 1 ¥
n 939.57336128 1/2 1 1/2 0 1 917.33526856 ´ 10 8
L 1115.59979064 1/2 1 0 0 1 0.02578198
S+ 1189.37409717 1/2 1 1 1 1 0.00800714
S- 1197.30443002 1/2 1 1 1 1 0.01481729
S0 1192.47794854 1/2 1 1 1 1 0.42908026 ´ 10-10
X- 1321.29326013 1/2 1 1/2 -2 1 0.01653050
X0 1314.90206200 1/2 1 1/2 -2 1 0.02961947
W- 1672.17518902 3/2 1 0 -3 1 0.01317650
o++,o--- 1232.91663788 3/2 1 3/2 0 1 5.99071759 ´ 10-16
o+,o-- 1234.60981181 3/2 1 3/2 0 1 5.72954997 ´ 10-16
o-,o + 1229.99529979 3/2 1 3/2 0 1 6.74230244 ´ 10-16
Baryons
o0,o 0 1237.06132359 3/2 1 3/2 0 1 5.08526841 ´ 10-16
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
4
Tabelle III
Experimental Data of Elementary Particles
with Mean Lives > 10-16 sec
(J = spin, P = parity, I = isospin, S = strangeness, B = baryon number)
Type Symbol Mass/MeV
(PDG,CERN 2002)
J P I S B Mean Life
10-8 sec
Photons g 0 1 -1 - - 0 ¥
ne £ 5 ´ 10-8 1/2 - - - 0 ¥
nm < 0.17 1/2 - - - 0 ¥
nt <18.2 1/2 - - - 0 ¥
e 0.51099907±0.00000015 1/2 ±1 - - 0 ¥
Leptons
m 105.658389±0.000034 1/2 ±1 - - 0 219.703±0.004
p± 139.57018±0.000351 0 -1 1 0 0 2.6033±0.0005
p0 134.9766±0.0006 0 -1 1 0 0 (0.84±0.06)´10-8
h 547.30±0.12 0 -1 0 0 0
K± 493.677±0.016 0 -1 1/2 ±1 0 1.2384±0.0024
K0 497.672±0.031 0 -1 1/2 1 0 5.2±0.5(Rohlf1994)
Mesons
K0 497.672±0.031 0 -1 1/2 -1 0 0.0089±0.0002 ( " )
p 938.27231±0.00026 1/2 1 1/2 0 1 ¥
n 939.56563±0.00028 1/2 1 1/2 0 1 (886.7±1.9)´10 8
L 1115.683±0.006 1/2 1 0 0 1 0.02632±0.0002
S+ 1189.37±0.07 1/2 1 1 1 1 0.00799±0.00004
S- 1197.449±0.03 1/2 1 1 1 1 0.01479±0.00011
S0 1192.642±0.024 1/2 1 1 1 1 (7.4±0.7)´10-12
X- 1321.32±0.13 1/2 1 1/2 -2 1 0.01639±0.00015
X0 1314.9±0.6 1/2 1 1/2 -2 1 0.029±0.0009
W- 1672.45±0.29 3/2 1 0 -3 1 0.00822±0.00012
D++ »1232 3/2 1 3/2 0 1
D+ »1232 3/2 1 3/2 0 1
D0 »1232 3/2 1 3/2 0 1
Baryons
D- »1232 3/2 1 3/2 0 1
The data are taken from the Particle Data Group homepage https://pdg.lbl.gov , CERN, (2002),
except for the life times of K0 and K0 , which are taken from J.W. Rohlf 1994: Modern Physics
from a to Z0, New York: John Wiley & Sons.
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
5
Table IV
Approximated Meson Resonances
(k=1)
Partikel P N(N)± KB(KB)± Theoretische Masse in
MeV
e 0 49 10 691,7094
w(783) 0 64 51 783,9033
h´(958) 0 144 28 956,8400
S * (993) 0 170 -1 992,6142
F(1019) 0 153 63 1019,6306
f (1270) 0 253 26 1274,5452
D(1285) 0 255 27 1286,1728
E(1420) 0 272 82 1414,1873
f ' (1514) 0 323 2 1517,8602
w(1675) 0 342 71 1664,0125
* (892)
- K 1 23(11)- 29(3) 891,1955(892,2211)
(1240) A K 1 83(69) 6(15) 1241,1180(1239,9767)
K* (1420) 1 98(101) 25(23) 1420,2213(1414,4956)
L(1770) 1 161(164) 65(11) 1775,2145(1764,9862)
p(770) 2 8(5) 30(34) 769,9833(769,3101)
d (970) 2 39(21) 19(5) 976,4931(973,6704)
(1100) 1 A 2 76(48) 41(5) 1106,9780(1106,7462)
B(1235) 2 93(79) 27(10) 1239,5340(1239,1994)
(1310) 2 A 2 127(86) 22(59) 1310,4695(1309,6730)
(1540) 1 F 2 182(145) 37(4) 1539,5100(1537,9095)
p' (1600) 2 215(156) 43(29) 1604,8640(1605,1008)
(1640) 3 A 2 221(160) 4(7) 1637,2669(1634,2138)
g(1680) 2 228(165) 28(5) 1686,0154(1678,6425)
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
6
Table Va
Approximated Baryon Resonances
(k=2)
Partikel P N(N)± KB(K)± theoretische Masse in MeV
N(1470) 1 13(12) 10(38) 1470,4888(1480,1770)
N(1520) 1 14(13) 29(8) 1509,6087(1515,7293)
N(1535) 1 18(17) -2(8) 1533,9788(1535,3254)
N(1670) 1 23(22) 8(0) 1657,9536(1679,5754)
N(1688) 1 24(23) -23(11) 1694,3687(1719,4898)
N(1700) 1 25(27) 63(-12) 1734,6717(1751,2494)
N(1770) 1 26(24) 14(65) 1771,8218(1769,0721)
N(1780) 1 31(29) -9(0) 1784,3644(1782,2884)
N(1810) 1 32(30) 38(40) 1808,3795(1808,5253)
N(1990) 1 37(35) 60(50) 1974,9129(1989,7028)
N(2000) 1 42(39) -3(-37) 2011,0552(2001,9706)
N(2040) 1 44(41) 7(30) 2044,8079(2034,6322)
N(2100) 1 40(44) 78(25) 2107,8085(2120,5890)
N(2190) 1 49(46) -14(21) 2200,5168(2195,5259)
N(2220) 1 50(47) 66(43) 2244,1911(2245,4563)
N(2650) 1 73(69) 2(-9) 2653,5304(2652,4071)
N(3030) 1 90(85) 41(54) 3036,2404(3033,5279)
N(3245) 1 95(90) 61(28) 3234,0166(3231,8730)
N(3690) 1 119(113) 3(4) 3689,8085(3684,1957)
N(3755) 1 113(115) 37(31) 3751,7230(3728,0808)
L(1330) 0 25 10 1329,8831
L(1405) 0 22 79 1403,3999
L(1520) 0 37 36 1516,3419
L(1670) 0 54 4 1669,9762
L(1690) 0 55 61 1693,2832
L(1750) 0 58 25 1754,7613
L(1815) 0 70 -10 1815,4961
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
7
Table Vb
Approximated Baryon Resonances
(k=2 continuation)
Partikel P N(N)± KB(K)± Theoretische Masse in MeV
L(1830) 0 71 11 1830,4081
L(1860) 0 73 -5 1864,6313
L(1870) 0 74 1 1884,4529
L(2010) 0 87 17 2010,5372
L(2020) 0 88 18 2018,1998
L(2100) 0 94 0 2095,9533
L(2110) 0 84 34 2113,6593
L(2350) 0 116 30 2344,7465
L(2585) 0 136 5 2591,7184
X(1530) 1 4(2) 9(5) 1531,5487(1534,7628)
X(1630) 1 7(4) 30(20) 1621,5840(1661,1690)
X(1820) 1 16(10) 35(9) 1828,9065(1810,8367)
X(1940) 1 19(13) 59(27) 1944,8454((1945,2579)
X(2030) 1 25(19) -4(-3) 2027,8157(2037,5528)
X(2250) 1 31(24) 65(-4) 2247,4841(2241,9080)
X(2500) 1 42(35) 42(13) 2481,8202(2517,9008)
D(1650) 3 44 11 1651,0807
D(1670) 3 48 44 1678,6242
D(1690) 3 71 0 1690,0383
D(1890) 3 124 1 1887,9876
D(1900) 3 125 56 1900,8602
D(1910) 3 129 -27 1915,2764
D(1950) 3 134 59 1949,2695
D(1960) 3 137 38 1965,3571
D(2160) 3 211 33 2153,9221
D(2420) 3 302 12 2422,5186
D(2850) 3 419 63 2856,6694
D(3230) 3 572 34 3229,6911
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
8
Table Vc
Approximated Baryon Resonances
(k=2 continuation)
Partikel P (N)+N(N)- (KB)+KB(KB)- Theoretische Masse in MeV
S(1385) 2 (13)+6(13)- (11)+59(22)- (1383)+1382(1386)-
S(1440) 2 (16)8(16) (9)71(-5) (1441)1434(1441)
S(1480) 2 (18)20(18) (64)12(52) (1492)1490(1489)
S(1620) 2 (32)35(32) (18)10(20) (1624)1622(1616)
S(1670) 2 (34)27(35) (8)15(-23) (1664)1660 (1678)
S(1690) 2 (35)38(36) (-10)43(57) (1691)1683((1705)
S(1750) 2 (43)41(38) (-25)34(5) (1752)1747(1750)
S(1765) 2 (45)49(46) (9)10(-2) (1769)1766(1770)
S(1840) 2 (50)45(51) (19)11(47) (1847)1844(1848)
S(1880) 2 (42)57(43) (65)61(7) (1884)1887(1885)
S(1915) 2 (53)59(54) (28)16(24) (1909)1923(1908)
S(1940) 2 (54)60(55) (23)44(-10) (1932)1951(1931)
S(2000) 2 (63)70(64) (8)1(-45) (2003)2012(2002)
S(2030) 2 (66)72(59) (21)12(5) (2035)2031(2031)
S(2070) 2 (68)75(69) (2)38(40) (2066)2071(2064)
S(2080) 2 (69)76(70) (9)29(10) (2083)2089(2074)
S(2100) 2 (70)77(71) (31)52(6) (2103)2106(2093)
S(2250) 2 (76)84(78) (-12)33(35) (2243)2250(2252)
S(2455) 2 (94)104(85) (18)56(3) (2444)2458(2455)
S(2620) 2 (110)121(103) (27)-12(26) (2624)2625(2621)
S(3000) 2 (136)150(140) (-85)38(12) (2994)3001(3003)
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
9
Tables VI
Numerical Evaluations of the Equations V and VIII (chapter E)
symbol numerical value symbol numerical value
h 0,98998964 J 7,93991266
h1,1 0,98756399 J1,1 7,92534503
h1,2 0,98516776 J1,2 7,91095114
h2,2 0,84242385 J2,2 7,04779227
a+ 0,01832211 a- 0,00812835
Numerical Evaluations of the Equations
X and B23,B24,B28 (chapter E+F)
k Qn Qm Qp Qs B H A
1 3 3 2 1 27 9 2787,59025432
2 24 31 34 15 26 104 14727,57867072
Table VII
Numerical Evaluations of the Equations
IX and B8,B9,B10,B13 (chapter E+F)
Ni(k,q ) numerical value Ni(k,q ) numerical value
N1(1,1 ) 0,99688127 N4(1,1 ) 4
N1(1,0 ) 1 N4(1,0 ) 4
N1(2,1 ) 0,99627809 N4(2,1 ) 4
N1(2,0 ) 1 N4(2,0 ) 2
N1(2,2 ) 0,95891826 N4(2,2 ) 6
N2(1,1) 0,67506174 N5(1,1) 1,15773470
N2(1,0) 0,66666667 N5(1,0) 1,15773470
N2( 2,1) 0,67670370 N5( 2,1) 1,73247496
N2(2,0) 0,66666667 N5(2,0) 1,15773470
N2(2,2) 0,79136728 N5(2,2) 76,73214581
N3(1,1) 1,95731764 N6(1,1) 0.00000164
N3(1,0) 2 N6(1,0) 0,00000164
N3(2,1) 2,59881924 N6(2,1) 0,02518725
N3(2,0) 2,71828183 N6(2,0) -0.10493009
N3(2,2) 2,12190443 N6(2,2) 0,15580107
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
10
Table VIII
Numerical Evaluations of the Equations
B22,B29,B30,B31 (Chapter F)
Particle a1 a2 a3 WN=0
e- 35 11 89,96774158 38,70294226
e0 34 28 77,11059862 38,51308957
m 1 23 7,26891022 2830,2632345
p± 25 0 95,62488526 3514,46294316
K+ 16 31 7,26891022 8857,95769020
p0 22 2 -0,03225806 3419,16217346
K0 22 17 98,29474138 9332,35821820
h 28 33 48,65020426 9905,00599107
p 0 23 84,22944059 14792,56308050
S+ 21 30 26,15371691 18124,03136129
S- 21 47 94,49556347 18183,30294347
X- 26 25 15,61504747 18998, 73451193
W- 47 3 69,73881899 23157,61451004
o++ 23 27 82,92386515 18115,38391620
o+ 23 22 22,64335811 18467,56082305
o- 21 27 69,73881899 18448,51703290
n 0 36 101,15000035 14828,61089116
L 13 45 -0,033333333 16827,97671482
S0 21 46 83,86257747 18179,59733741
X0 26 22 71,62409771 18990,08927597
o0 23 39 93,76289283 18508,94119539
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
11
Table IX
Numerical Evaluations of the Equations
XXXV and B48,B49 (Chapter E+F)
Particle Y j L(N)
e- ,e + -408,54063248 0 1021
0 0 e ,e -53,97104336 0 1373
m - ,m + 1086,93016693 2,57120915 2340
h,h 0,26273140×10-8 5,06612007 3236
K + ,K - 184,84508008 -40,78574065 3258
K 0 147,94249859 -12,73395842 3166
K 0 0,25356917 -12,73395842 3166
p ± ,p m 17,08389288 -2,32863274 1485
p 0 ,p 0 3,70004027×10-8 -5,12094079 1833
L,L 0.06178705 0 1964
W- ,W+ 0,09369559 -137,03604095 2062
p, p 17,31698079 9,28034058 1841
n, n 1228,02191382 11,16885467 1932
X- ,X+ 0,10666692 23,44132266 2247
X0 ,X0 0,20184712 90,44612205 2382
S+ ,S- 0,04603481 -6,00947753 5785
S0 ,S0 211,63404729×10-8 11,78154008 6375
S- ,S+ 0.06836890 -2,01125294 5991
o ++ ,o -- 14,72282381×10-16 -1364,07751672 35510
o + ,o - 11,51525605×10-16 -623,74523006 5115
o 0 ,o 0 10,13617609×10-16 -985,00227539 5551
o - ,o + 10,19390807×10-16 -548,14408156 5102
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
12
Relative Deviations of the Theoretically Determined Particle
Masses from the Experimental Meanvalues for
Different Values of the Gravity Constant Gv
Introduction to Heim's Mass Formula
Ó IGW Innsbruck, 2003
13
Relative Deviations of the Theoretically Determined Particle Lifetimes
from the Corresponding Experimental Mean Values
Heim 1989, ? : an experimental value could not be found at the PDG data set,
Heim 1998, measuring uncertainty
