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

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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


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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


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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


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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



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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


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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



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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


(2)


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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



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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



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



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Eq. (2) yields the following values forN+M, ifProtonsrest energy is taken as reference:



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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).



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14

TheN-values concentrate inN=0, 1/3, 2/3, 3/3 , showing that the Lambda

mass-energies result from the period doubling process.



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TheN-values concentrate inN=0, 1/3, 2/3, 3/3 , showing that the Sigma

mass-energies also result from the period doubling process.


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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.


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17

The figure shows that the doubling process does not work well with two of the

Deltas (1232 MeV and 2420 MeV).



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18

The figure shows that all Deltas fit to the period tripling process (which

always accompanies period doubling).



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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).



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Planck scale reference


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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



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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


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Presentation at Physics Foundations Society Seminar August 17 2010 23

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Ari Lehto- On the Baryon System in View of Period Doubling: Nucleon, lambda, sigma, delta, xi, omega