On similarity between all-known elementary particles and resonances mass spectrum and

nuclei atomic weights

A. G. Syromyatnikov, Saint Petersburg state university

In this work I give generalization of discovering [1] of the simple fact of proportionality between all elementary particles masses and 24 resonance masses [2-4] in one side and nuclei masses in another side with some constant coefficient to all-known elementary particles and resonances mass (see list [4]).

In that unexpected repeating of the whole by a fragments spectrum in 3 cases for particles and in 11 cases for resonances fit took admissible doubling of this calculated dilatation coefficient by means an ion electric charge doubling (in possibility processes of their electroproduction on a threshold of spin shock-waves (see [5]) forming [1] in accelerated beams of ions of some stable chemical elements). Consideration of all known resonances from particles list⁴ according to underlying pages show that a number of this cases electric charge doubling more 55 percent. Fundamentally in this case that W⁺ boson of electroweak interaction in recalculating on mass directly join to a border of chemical elements stability through Bi – 209.

If so it be on more number of resonances then there mass spectrum are defined by chemical elements mass spectrum, relation charge to mass of electron, speed of light in vacuum and calculated threshold value spin shock-wave. Chemical elements (CE) masses are defined by a dilaton quark – lepton X – structure jump features [1].

Below on table 1 all discovered 46 elementary particles and in table 2 all 121 resonances group in some multyplets for every ion kind on that occur their electroproduction as in [1].

Table 1.

CE	Num- ber of particles in multyplet	standard deviation on distinguish between particles masses, MeV	Particles
p^+ He3 He3 He3 He4 Li7 B11^2+ N14^2+ C12^2+ Be9 O16^2- B11 C12 N14 O15 O16 Mg24.3 Al27 Si28	3 8 3 1 1 1 1 6 2 1 2 2 1 3 7 2 1 2 1	±32 ±68 ±170- - - - ±110 ±51 - ±68 ±42 - ±45 ±104 0 - ±166 -	K^+[493,7] KLS^0[497,6] η^0[547,8] Δ^0, Δ^+[1232] Λ^0[1232]Σ^+[1189,4]Σ^0[1192,5]Σ^-[1197,4]Ξ^0[1315]Ξ^-[1321] p^+ n[938]Δ^++ [1232] φ[1019] Ω^-[1672] Ωc^0[2698] D[1870] Λc^+[2284]Λc^0[2274] Ξc^+[2466]Ξc^0[2472] Λc^-[2284] Ξc^-[2466] D^*[2010]Ds^*[2112] ηc^´[3592] J/ψ[3097] ηc[2980] Ψ´[3685]Ψ´´[3768] Ψ´´´[4415] B^*[5325]Bs^0[5366]Bs^*[5415] Λb^0[5624] Bs1[5830]Bs2[5840]Ξb[5629,6]B1[5721] [5624] [5629,6] Bc^+[6277] Bc^-[6277] Y[9459,7] Υ´[10018]Υ´´[10350] Υ´´´[10573]
average		± 78 МэВ

Table 2.

CE thresh-old, MeV	Num- ber of resonances in multy- plet	standard deviation on distinguish between particles masses, MeV	Resonances
D2 771	4	748±145	ρ^+[770] K^*[892] ω[783] η[548]
He3 1157	9 6	1102±115 1241±62	f0[980] a0[980] φ[1019] η1[1170] a1[1230] b1[1230] f1[1282] K1[1270] f2[1270] Δ0[1230] Σ^0[1193] Σ^+[1190] Σ^-[1197] Ξ^0[1314] Ξ^0[1322]
Li7^2+ 1338	4 5	1320±35	η [1294]π[1300] a2[1320] f0[1370] K1[1400] π[1400] K0^*[1430] K2^*[1430] f1[1426]
He4 1542	6 4	1533±75 1468±126	ρ [1450] η [1476] f0[1500] f2[1525] π1[1600] π2[1645] Σ [1385] Σ [1530]Λ[1405] ω[1650]
Be9^2+ 1724	10 2 7 3	1710±50 1734±65 1840±40	π2[1670]ω 3[1670]φ[1680]K^*[1680]ρ3[1700] f0[1710]K3[1770]π [1800] χ[1835] K2 [1820] φ3[1850] π2[1880] Σ [1650] Σ [1670] Ξ [1690]Σ [1750] Λ[1800] Λ[1810] K2[1770] Λ[1820] Ξ [1820] Λ[1890]
B11^2+ 1931	8 8	1968±45 2039±37	Σ [1915] Σ [1940] Ξ [1950]Σ [2030] Ξ [2030] Λ[2100] f2[1950] f2[1959] Λ[2110] a4[2040]D^*[2007]D^*[2010] f2[2010] f4[2050] K4^*[2045] φ[2170]
C12^2+ 2145	3 6	2283±55 2280±80	Σ [2250] Ω^- [2250] Λ[2350] f2[2300] f2[2340] D^*s0[2317] D^*2[2160] Ds1[2460] D1[2420]
Li7 2676	6	2582±43	Σc [2520] Λc [2595] Λc [2625] Ξc [2645] Ds1[2536] Ds2[2572]
O15^2- 2868	7	2916±70	Ξ [3080] Ξc [2800] Λc [2880] Λc [2940] Ξ [2980] ηc(1S1)[2980]J/ψ[3097]
Be9 3447	5	3502±60	χc0[3415] χc1(1P)[3511] χc2(1P)[3556] hc(1P)[3525] ηc(2S)[3637]
F19^2- 3639	1		ψ(2s)[3626]
B11 3862	3	3894±140	ψ[3770] χ[3872] ψ[4040]
Na23^2+ 4348	3	4280±130	ψ´´´ [4160] χ[3872] ψ [4415]
Mg24.3 9298	1		γ[9460]
Cr52^2+ 9925	3	9930±89	χb0(1P)[9856] χb2(1P)[9912] γ(2S)[10023]
Al27 10306	4	10251±80	γ(1D)[10163]χb0(2P)[10232,5] χb1(2S)[10255,4] γ(3S)[10355]
Si28 10688	2	10720±140	γ(4S)[10580] γ[10860]
Ni58,7^2+ 11201	1		γ[11020]
average		± 70 MeV	Average distinguish between electroproduction threshold and multyplet centre 28 ± 85 MeV

Below in table 3 give collections of multyplets of table 1 in the distribution on a number of quarks with dublet nucleons addition.

Table 3

Quarks distribution on multiplets of 46 particles [4] electroproduction in ion beams

Number of particles in multyplet	1	2	3	6	7	8	Standard deviation on the number of quarks
Number of multyplets	8	5	3	1	1	1
Total number of quarks	18	20	21	18	18	24
Deviation from the average	-1	1	2	-1	-1	3.5 σ	19.0 ± 1.42

According to table 3. in average every multyplet consist of 18 quarks. The distribution on resonances also is characterized every multyplet in average from 18 quarks in limits of the permissible dispersion.

Table 4

Quarks distribution on multiplets of 121 resonances and 46 particles electroproduction in ion beams

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
Number of particles in multyplet	1	2	3	3	4	4	5	6	6	6	7	7	8	8	9	10	Standard deviation on the number of quarks
	1-2
Number of multyplets	3 - 2		2	3	1	3	2	1	2	1	1	1	1	1	1	1
Total number of quarks	6 + 8 =14		18	18	14	24	20	16	24	18	17	20	19	22	18	20	18.00 ± 2.35
Deviation from the average	-4		0	0	-4	~2.5σ	2	-2	~2.5σ	0	-1	2	1	4	0	2
Standard deviation on the number of quarks for all particles from table 4. (apart from the octet) and resonances^4 No 2-3, 4-6, 8, 9, 11-14, 16-17																	18.06 ± 1.98

All it is in direct accordance with thesis (see [1]) dilaton supersymmetry about 18 degree of freedom for quark system as freedom fermions system in Veil – Cartan space – time (see [6-8]).

Discussion

According table 1, 2 elementary particles and resonances group to every electroproduction multyplets on a mass with a small dispersion 78 and 70 MeV accordingly. In particularly it is SU(3) baryon octet, distinguishing from the well-known by two baryons from hyperons triplet Δ^0,+,++ instead of two nucleons, SU(3) singlet Ω^- et cetera. Two nucleons essentially distinguish on their mass from the other particles from octet included to the triplet with one from the hyperon triplet Δ^0,+,++.

On the fact of proportion between all-known elementary particles masses and resonances masses [2-4] in one side and nuclei masses in another side of which is stated it may be possible that quark spectrum from particles and resonances forming on nuclei destruction also will be homogeneous distribution as a Fermi distribution.

Actually according to table 3, 4 quark distributions on electroproduction multyplets all-known elementary particles and resonances are homogeneous as Fermi distributions. Moreover the number of multyplets of particles 1, 2, 3, 5, 8 formed Fibonacci numbers series. As known Fibonacci numbers takes place in quality of the solution of a task about degeneration of a level in the dual model. It supposed the fact that there we have filling of any level from 18 degree of freedom on a number of quarks.

Standard deviation on a number of 18 quarks for particles and on totality particles and quarks whole is smaller then 2. It means that the deviation from the homogeneity of the quark distribution turned out far from an observability border for the single quark. By oneself fact of homogeneity of a quark distributions show a dilaton quark quantum number conservation (see [1]) as independent from kind of an electroproduction multyplet.

Conclusion

It’s stated the fact of repeating of all-known elementary particles and resonances mass spectrum as whole of nuclei atomic weight of ion s of some stable chemical elements with a coefficient in proportion to M/e for an ion. It is signed that all-known elementary particles and resonances masses also as masses of stable chemical elements and isotopes are defined by positions of features – jumps of a quark – lepton dilaton X – structure [1].

It is stated that a quark distribution on electroproduction multyplets all-known elementary particles and resonances is homogeneous as a Fermi distributions. Moreover the number of multyplets of particles 1, 2, 3, 5, 8 formed Fibonacci numbers series. As known Fibonacci numbers takes place in quality of the solution of a task about degeneration of a level in the dual model. It supposed the fact that there we have filling of any level from 18 degree of freedom on a number of quarks.

Dilaton supersymmetry thesis [1] about 18 degree of freedom for quark system as freedom fermions system in Veil – Cartan space – time is supposed exactly.

By oneself fact of homogeneity of a quark distributions show dilaton quark quantum number conservation (see [1]) as independent from kind of any electroproduction multyplets.

A border of chemical elements stability through Bi – 209 is defined by possible processes of electroproduction on a threshold of spin shock-waves forming in accelerated beams of ions radioactive Po and At on a mass of W⁺ boson of electroweak interaction.

That all gives addition argument for observing in Veil – Cartan space – time V₄ of the threshold effect on GUT gravitation masses ~ 3TeV for example in BACcollisions (see [9]). 3 TeV – it is 10^-12 from physical GUT masses 3·10¹⁵ GeV. 10^-12 gives experimental value of distinguish between gravitation and inertial masses. There we have the only possibility in experimental operating by “tales” of giant GUT masses, so that Standard Model with Conformal Gauge Theory of Gravitation [1, 6-8] is correct.

_____________________________________________________________________________________

1. Syromyatnikov A. G. Physical effects in Conformal Gauge Theory of Gravitation., LAP Lambert Academic Publishing GmbH & Co. KG, Saarbrucken, Germany, 2012. – 217 p. (in Russian)

2. P. D. B. Collins and E. J. Squires, Regge poles in particle physics. Springer-Verlag Berlin Heidelberg New York 1968.

3. L. B. Okun, Leptons and quarks. Moscow, “Nauka”, 1990. – 324 p. (in Russian)

4. K. Nakamura et al. [Particle Date Groupe], J PG 37, 075021 (2010) and 2011.

5. A. G. Syromyatnikov, Vestnik Sanct-Peterburgskogo universiteta. Ser. 4. 2012. Vip. 2. p.108-112. (in Russian).

6. A. G. Syromyatnikov, Teor. and mat. Fiz., 87, №1, aprile, 1991, p. 157– 160 (in Russian).

7. A. G. Satarov and A. G. Syromyatnikov, Teor. and mat. Fiz., 92, №1, june, 1992, p. 150 (in Russian).

8. A. G. Satarov and A. G. Syromyatnikov, Plenum Publishing Corporation, 1993, p. 799 – 801.

9. Altonen A., Artikov A., Budagov J. et al. Measurement of correlated production in collisions at GeV// Phys. Rev. (D). 2008. Vol. 77. 072004.

ABSTRACT

On similarity between all-known elementary particles and resonances mass spectrum and

nuclei atomic weights

A. G. Syromyatnikov, Saint Petersburg state university

It is showed generalization of discovering of the simple fact of proportionality between all elementary particles masses and 24 resonance masses in one side and nuclei masses in another side with some constant coefficient to all-known elementary particles and resonances mass.