Download - Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
1/23
Nucleon, lambda, sigma, delta, xi, omega
Ari LehtoAugust 2010
- ,
- ,
,
,
,
- , , , , , , , 0 1/3 2/3 3/3 4/3 N
1/4
2/4
3/4
All 60 BaryonsM
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
2/23
Period doubling is a common property of nonlineardynamical systems. It has been suggested earlier [1 and
references therein] that period doubling may take place in
processes involving 1/rtype potential.
In this presentation we clarify the period doubling model
and apply the model to the Baryons.
It is shown that the Baryon rest energies accumulate in
lattice points determined by period doubling.
2Presentation at Physics Foundations Society Seminar, August 17, 2010
1. Ari Lehto, On the Planck Scale and Properties of Matter, Nonlinear Dynamics
Volume 55, Number 3, 279-298, February, 2009
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
3/23
In the period doubling model the rest energy of a particleis described by mass-energy (3-degrees of freedom) andelectromagnetic energy (4-degrees of freedom).
Both are subject to period doubling (due to nonlinearity)
The rest energyENMof a particle can be expressed by
whereN(=integer/3) andM(=integer/4) represent
halvings in the mass-energy and electromagnetic energyrespectively. Erefis reference energy (Eref>ENM in thiscase).
3
ref
MN
NM EE 22
Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
4/23
Examples: Proton (938.3 MeV) is taken as reference.
EOmega- =2N2M EProton=2
0.833 Eproton=20.33320.5Eproton
N=1/3 and M=2/4
ELambda =20.25EProton=2
0 20.25Eproton
N=0/3 and M=1/4
4Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
5/23
Nrepresents doublings in the mass-energy (3 degrees of freedom)andMin the electromagnetic
energy (4 degrees of freedom) of a particle.
Theoretical values forNare 0, 1/3, 2/3, 3/3, 4/3 etc. and values forMare 0, 1/4, 2/4, 3/4, 4/4 etc.
(negative values are allowed).
Presentation at Physics Foundations Society Seminar, August 17, 2010 5
Concentration in theoretical
lattice points of 60 Baryons.
Protons rest energy is used as
the reference energyEref.
0 1/3 2/3 3/3 4/3 N
1/4
2/4
3/4
All 60 BaryonsM
ref
MN
NM EE 22
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
6/23
If the mass-energy and EM-energy are assumed to beindependent parts of the rest energy of a particle, then
(1)
where 3Nis the total number of doublings (or halvings)
of the 3-d mass-energy and 4Mthe (independent) total
number of doublings (or halvings) of the 4-d
electromagnetic (EM) energy.
6
ref
MN
ref
MN
NM EEE
222
Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
7/23
ENMis the rest energy of the particle (e.g. Omega minus)andErefthe rest energy of the reference particle (Proton in
this case).
One can calculate the value ofN+Monly.
7
)2ln(
)/ln( refNM EEMN
Presentation at Physics Foundations Society Seminar, August 17, 2010
(2)
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
8/23
Omega-:
Lambda:
Omega: (N;M)=(1/3;2/4)
Lambda: (N;M)=(0;1/4)
8
MeVMeVMeV 9382293821673 5.0333.0833.0
833.0)2ln(
)938/1673ln( MeVMeVMN
25.0)2ln(
)938/1116ln( MeVMeVMN
MeVMeVMeV 9382293821116 25.0025.0
Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
9/239
Source: http://pdg.lbl.gov (14.8.2010)
Baryon E (MeV)
Proton 938,28
Neutron 939,58
N(1440) 1440
N(1520) 1520
N(1535) 1535
N(1650) 1650
N(1675) 1675N(1680) 1680
N(1700) 1700
N(1710) 1710
N(1720) 1720
N(2190) 2190
N(2220) 2220
N(2250) 2250
N(2600) 2600
Baryon E (MeV)
Lambda 1116
Lambda (1405) 1406
Lambda (1520) 1520
Lambda (1600) 1600
Lambda (1670) 1670
Lambda (1690) 1690
Lambda (1800) 1800Lambda (1810) 1810
Lambda (1820) 1820
Lambda (1830) 1830
Lambda (1890) 1890
Lambda (2100) 2100
Lambda (2110) 2110
Lambda (2350) 2350
Baryon E (MeV)
Sigma + 1189,37
Sigma 0 1192,64
Sigma - 1197,45
Sigma (1385) 1382,8
Sigma (1660) 1660
Sigma (1670) 1670
Sigma (1750) 1750Sigma (1775) 1775
Sigma (1915) 1915
Sigma (1940) 1940
Sigma (2030) 2030
Sigma (2250) 2250
Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
10/2310
Baryon E (MeV)
Delta 1232
Delta (1600) 1600
Delta (1620) 1630
Delta (1700) 1700
Delta (1905) 1890
Delta (1910) 1910
Delta (1920) 1920Delta (1930) 1960
Delta (1950) 1930
Delta (2420) 2420
Baryon E (MeV)
Ksi 0 1314,9
Ksi - 1321,7
Ksi (1530) 1531,8
Ksi (1690) 1690
Ksi (1820) 1823
Ksi (1950) 1950
Ksi (2030) 2025
Omega - 1672,5
Omega (2250) 2252
Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
11/23
Eq. (2) yields the following values forN+M, ifProtonsrest energy is taken as reference:
11Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
12/23
12Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
13/23
13
It is assumed here that the period doubling process in the EM-energy formation is
accurate (i.e. M=0, 1/4, 2/4, 3/4 ). The corresponding value forNhas been
calculated from the experimentalN+M-value, andNcontains the experimental
uncertainties and the possibility that the model is bad. (N,M) pairs are plotted in
the figure.
If the doubling process takes place on the mass-energy, too, then the calculated
N-values should concentrate in N=0, 1/3, 2/3, 3/3 This seems to be so.(the figure does not change much if the doubling process is assumed accurate in the mass-energy side).
Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
14/23
14
TheN-values concentrate inN=0, 1/3, 2/3, 3/3 , showing that the Lambda
mass-energies result from the period doubling process.
Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
15/23
15Presentation at Physics Foundations Society Seminar, August 17, 2010
TheN-values concentrate inN=0, 1/3, 2/3, 3/3 , showing that the Sigma
mass-energies also result from the period doubling process.
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
16/23
16Presentation at Physics Foundations Society Seminar, August 17, 2010
TheN-values concentrate inN=0,
1/3, 2/3, 3/3 , showing that the
Xi and Omega minus mass-energies
also result from the period doublingprocess.
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
17/23
17
The figure shows that the doubling process does not work well with two of the
Deltas (1232 MeV and 2420 MeV).
Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
18/23
18
The figure shows that all Deltas fit to the period tripling process (which
always accompanies period doubling).
Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
19/23
19
Baryons concentrate in (N,M)-lattice points, which are characteristic to
period doubling in three (N) and four degrees (M) of freedom (mass-
energy and EM-energy).
Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
20/23
Planck scale reference
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
21/23
If the Planck energyEo is used as the reference energy,then the rest-energy of a particle is:
The particle is now characterized by notation:
(i,j,k;l,m,n,p)
Example: Proton (65,65,65;0,0,0,0)Lambda (65,65,65;0,0,0,1)
21
o
pnmlkji
lmnpijk EE43
; 22
Presentation at Physics Foundations Society Seminar, August 17, 2010
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
22/23
Previous results of the period doubling model (concerningelementary particles):
Electrons rest energy (from the Planck energy)
Electrons magnetic moment
Elementary electric charge (from the Planck charge)
Fine structure constant (geometric factor)
Protons rest energy and magnetic moment
Neutrons rest energy and magnetic moment
Presentation at Physics Foundations Society Seminar, August 17, 2010 22
-
8/3/2019 Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega
23/23
Presentation at Physics Foundations Society Seminar August 17 2010 23