Aspden - An Empirical Approach to Meson Energy Correlation (1986)

8/7/2019 Aspden - An Empirical Approach to Meson Energy Correlation (1986)

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HADRONIC JOURNAL VOLUME 9, NUMBER 4 31 JULY 1986

An empirical approach to meson energy correlationH. Aspden

Department of Electrical Engineering, The University, Southampton, S095NH, England(Received 15 July 1986)

An alternative empirical approach, differing from the quark model, is presentedfor analyzing particle constitution. It relies upon an energy correlation based upon theThomson charge-mass formula and primary energy quanta, notably those of the proton (938MeV), the related dimuon (211 MeV), and two graviton-re1ated quanta, denoted g(2587MeV) and g*(3259 MeV), respectively.

When confronted with a vast amount of numer-ical data pertaining to certain physical parame-ters, the search for a correlation has often to pro-ceed empirically, with only limited intuitive physi-cal justification. Eventually, a viable theory mayemerge. The analysis of the line spectra of atoms inadvance of the Bohr theory is one example. Particlephysics now provides the scope for such an em-pirical study.Here, there has been an interesting analysis byMacffregor;' who has shown the possible relevanceof the fine-structure constant as a logarithmic scal-ing factor relating particle lifetimes and masses.MacGregor has written extensively on the quarksand subquarks, as constituents of fundamental par-ticles, and in the paper just referenced he identifieslifetime clusters in his empirical system with thedecays arising from the annihilation or transforma-tion of unpaired substates, including, for example,

Q o ::= 70 MeV and Q3::= 210 MeV.The annihilation of the subquark Q3(210) is seen, inparticular, as relevant to the A, ~ , :::, and nhyperon decays..Following MacGregor's example, we here ex-amine the scope for a fruitful empirical enquiry intothe energy constitution of a set of fundamentalparticles, taking all the mesons listed in a section ofthe Data Card Listings of the Particle Data Group. 2These are the nine mesons listed in Table I below.They appear on pages S-160 to S-164 of Ref. 2.It will be shown how the energies of each of thesemesons can be constituted by a plausible particlereaction process, involving essentially two primaryenergy quanta Q(211) and g(2587) and their de-rivative forms P(938) and g*(3259). The numbersin brackets denote energy in MeV. The analysiswhich follows considers energy components and

makes no reference to particle properties, such ascharge or spin. The object is merely to show anatural correlation by which the scalar energyparameter characterizing a particle can be de-termined in charge reaction processes. Such proc-esses may be influenced by the quasistabilizing effectbetween particles not directly involved in a trans-formation of states, a subject discussed in an earlierpaper by Aspden.! The new results reported in thispaper are intended to show that the earlier-reportedcorrelations [as between the unitary dimuon Q(211)and the proton P(938), for example, and as be-tween the graviton g(2587) and the psi particles1/1(3095)and 1/1(3683)]are not fortuitous and iso-lated examples having restricted relevance.We will rely upon the basic correlation of en-ergies E 1 and E 2, nucleated on charges e, confinedto spheres of radii a and b, respectively, accordingto the Thomson formulas

(1 )when the charges are held in contact at their chargesurfaces, by virtue of their opposite polarity. Thetotal energy E of the neutral aggregation is then E 1plus E 2 offset by e2j(a + b). From (1) this gives

3E1E2 (2 )and for E 1 constant and E 2 variable, E has aminimum E mi n when E 2 is ( i f - 1)E1 and EDlin isthen (V 6 - 1)E1To simplify presentation, our notation will bethat (E 1: E 2) signifies the neutral aggregation ofenergy E and (E 1: E 2)* signifies the same dualcharge unit of energy E m in , for which E 1 > E 2. Inthis latter case, if either E 1 or E 2 is specified, the

9 153 1986Hadronic Press, Nonantum, MA 02195, U.S.A.


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154other energy parameter is determined by themathematical relationship just derived.We will otherwise rely only on one principlediscussed in previous papers. 3,4 This is that there isa mutual equilibrium between charges having thesame energy, whether these are part of a complexdefined by Eq. (2) or whether an energy in Eq. (2) isinfluenced by the near presence of a charge externalto the complex but in the near vicinity.The dimuon Q(211) is taken as a basic prevalentquantum throughout space. It may arise becauseEq. (2) tells us that E = E 1 when E 2 is the energyof a virtual muon and space is deemed to be wellpopulated with pairs of virtual muons. The dimuonQ(211) features in MacGregor's empirical study asQ3(210) . Aspden and Eagles! have discussed itsrole in a theory for the proton/electron mass ratio,because it forms a complex (P : Q )* with the pro-ton. Note that P is then ( I f - 1)-1(211) MeV, or938 MeV. The P (938) energy quantum and (P : Q )*are clearly very basic units in particle energy build-ing.The author next appeals to analysis of experi-mental particle data by LoSecco in 1975.6 At thattime dimuon events in high-energy neutrino scatter-ing had just been discovered. LoSecco dem-onstrated that these could be caused by the three-body decay of a particle of mass energy in theregion of 2.5 GeV. This was in good accord with theauthor's own theoretical prediction dating from 1966that a particle of mass 2.587 GeV decayed byshedding pairs of muons to leave energy accountingfor the creation of members of the hyperon family."The author's incentive was to obtain empirical sup-port for a theory of gravitation giving the constantof gravitation G as

(3 )

where g is the graviton mass in terms of electronmass and e /rn , is the charge/mass ratio of theelectron. This makes g(2587) a likely primary en-ergy quantum, and a derivative form resulting fromenergy priming which converts a graviton pair intotwo heavy graviton pairs was indicated empirically.Note that if space occupied by the charges is con-served in such a transition, the heavy graviton g*will have an energy related to the graviton g, thus:(4 )

From this we find that g* is 3.259 GeV.

. . 'H.ASPDEN 9

Our task is now to confine attention to the fourprimary quanta Q (211), P (938), g(2587), andg*(3259) in showing how other particle energies areconstituted.As discussed in Refs. 3 and 4, the correlationlinking with the first-discovered psi particles is

1/;(3095) = (g*: E 2)* ' 1/;(3683) = (g*: g),(5 )

because 3095 is (.f6 - t) (3259), and 3683 is E in(2 ) when E 1 is 3259 and E 2 is 2587.Reference 4 extended the theory to show that anumber of decay products of 1/;(3683) could beexplained using Eq. (2) and involving Q(211) andits derivatives.Note that we are concerned with large energyquantities in comparison with the electron andpositron energy quanta, and though we do notmake distinction between neutral- and charged-particle energies, it is implicit that an electron orpositron could be involved to assure charge primingor neutralization.When the discovery of the upsilon particle ofmass energy 6.1 GeV was announced in 1976,8 theauthor noted that (g* : g* : g*) is 6110 MeV. Thishitherto unpublished correlation applies to a tripleparticle group. The dual group of Eq. (2) may beseen to have an energy 1.25 times that of eachenergy constituent, if they are equal. A correspond-ing calculation for three identical components givesan energy of 1.875 times each constituent energyquantum. 6110 MeV is 1.875 times the energy ofg*(3259).With the above introduction we can now tabulatein Table I the nine mesons under review and thecorrelated energy formulation. It is believed thatparticle correlations 1, 2, 4, 8, and 9 are self-explanatory from the prior discussion.Correlation 3 is an evaluation of the energythreshold at which energy shared by a proton Pand a unitary dimuon Q will, with their rest massenergies, allow them to create a graviton pair. Con-versely, a graviton pair could mutually annihilate tocreate P and Q and shed an energy quantum,accounting for the creation of the psi particle repre-sented.Correlation 5 says that two 1/;(3683) energy reso-nance states interact at the same energy level tocause their energy constituents to adopt equal en-ergies X, but that the whole system degenerates bypair annihilation to leave one X intact and put allthe rest of the energy into one residual psi particle.


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"9 AN EMPIRICAL APPROACH TO MESON ENERGY ... 155

TABLE ICorr. EnergyNo. Particle Energy Correlation (MeV)1 ~(3683) ~ = (g* : g ) 3,6832 ~(3770) (~: Q ) = (g* : g) 3,7723 ~(4030) 2 g = ~ + P + Q 4,0254 ~(4160) (~: P )* 4,1735 ~(4415) 2(g * : g ) = 2 (X : X ) = ~ + X 4,4196 y(9460) 4g = (P : Q )* + e + p + Y 9,4567 y(I0020) y = g * + g + ~(4160) 10,0208 y(I0400) y = P + y(9460) 10,3949 K(892) K = (P : Q )* 891

Correlation 6 is similar to 3. Itindicates that if anelectron e and a positron p are caused to collidewith equal energies and the collision involves en-ergy transfer to the basic (P: Q)* system, the lattersystem can be split and the four particles involvedcould all convert into gravitons. The onward decayof these gravitons might appear as four jets in thereaction products.Correlation 7 is a process in which the ~(4I60)particle engages with the isolated components ofa split ~(3683) particle. Note the precision ofthe correlation in that ,.(10020) is (1 + 21 /3)g +( I f - I)-Ip, where g. is 2587 MeV and P is 938MeV.It is hoped that the theoretical energy quanta

shown in the last column of Table I will, by theirvery close correlation with the nominal energies ofthe meson states listed, assure the reader that wehave here the basis for a new kind of particletheory.Unfortunately, however, the argument concernsonly the possible energy levels at which particles arecreated and completely ignores the experimentallywell-defined pattern of internal quantum numberswhich the related particles possess. Nor is the ques-tion of spin properties and magnetic moment ad-dressed. Nevertheless, by showing how discreteenergy levels can become available for particle for-mation, we have some partial answer to the overallproblem.To reinforce this argument, the author" has re-cently shown how the Thomson charge formula canbe used to deduce, quite rigorously, the mass andmagnetic moment of the neutron and deuteron inrelation to the proton, as well as the neutron life-time. The theory gives values in precise accordwith measurement, even at the part per millionlevel of measurement precision. Furthermore,in a separate paper'? the same energy analysis

has been used to derive all the energy levels of theintermediate particles in the electron-proton energyspectrum.To show the further power of the theory, themethod used will now be extended to derive theenergies of a baryon group below the energy levelsof Table I. This involves consideration of chargepair annihilation within triple clusters of tau and

muon leptons.Equation (4) assumed that charges could trans-

form their states in reactions which conserved thespace they occupied. This idea is crucial to thetheory under discussion. It resembles, in some re-spects, a theory discussed by Johnson'! concerning aquark confinement process (the bag model) in whichordinary space is pushed aside in order to inflatebubbles enclosing the quarks. TrellI2,13 has ex-tended these ideas in terms of a volume-preservingtransformation of a spherical ground state, fromwhich he deduces baryon mass relationships, in-4eluding the correlation 1 :{3 for the proton: deltamass ratio.Earlier, Aspderr' showed that the mutual interac-tion of charged particles assures a quasistability,owing to the volume conservation process, and thatpair annihilation within a three-particle cluster in-

3volves an energy adjustment in the ratio 13 : 1, justas Eq. (4) implies a relationship for the transition3from four to two particles in the ratio {i:1.Chargevolume conservation has also been explored in rela-tion to the creation of the W and ZO bosons.l"Note that in these transitions, now to be discussed,the charges are not in close association in the senseof the aggregations considered in Table I.They areclose enough to exhibit a charge-paired relation-ship, but not close enough, even in their clusters, tohave interactions effectively changing their collec-tive mass property.


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156A collective particle transformation is of specialinterest, where a three-particle cluster (e.g. twopositive and one negative charges of like mass)involves pair annihilation with energy transferelsewhere, followed by local adjustments withnumerous other such clusters to conserve both en-

ergy and charge volume. The energy/volume ratiois then one-third that of the original particle form.From the Thomson formula (1) this implies that thecharge radius (inversely proportional to energy) has4decreased by the factor V 3 . Such a process canoccur in reverse as energy is forced into a particlesystem. There is an analogous process where pairannihilation occurs in the presence of other similarpairs, which then share the additional space. The4factor involved is if. This process, like the previ-ous one, appears reversible. Indeed, the examples to

be given relate only to the reverse process, becauseone of the particles is the proton and we have onlyevidence of synthesis of more massive particle forms.These appear as the first two examples in TableII. The remainder of the data in the table show howthe simple transformation of a three-particle clusterto or from a single particle at constant volumebuilds the several hyperons listed. The delta hy-peron .!l(l235) forms the tau 1 ' ( 1782 ) , and this haslepton characteristics .and can combine with theQ(211) quantum, the energy of two virtual muons,to form a state from which there is decay to thehyperon forms listed. As with the data in Table I,the dimuon unit seems to be a dominant feature.It is submitted that these quite simple connectedmass relationships are significant, especially whenconsidered alongside the data in Table I and thedata given in Ref. 10. However, before concluding,there is one further surprise from this analysis. The2.587-GeV graviton, which is basic to Eq. (3) andthe particle synthesis in Table I, can actually bededuced by extrapolation from Table II.

TABLE IIEnergyHyperon Process (MeV)

AO(1115) 4V2(P) 11164~(1235) V3(P) 1235

3~*(1385) ('I' + Q)/(V3) 1381:::*(1530) 3('I' + 2Q)/(V3) 1528

30-(1675) ('I' + 3Q)/(V3) 16743'1'(1782) V3(~) 1781

H.ASPDEN 9The dominant role which this hidden particlestate g(2587) asserts means that it is either a leptonor quasistable, because its presence is needed tosustain gravitational action. The action appears toinvolve a triple particle cluster in which three gparticles degenerate to the form g+, '7'-,1 '- or

g", 1 '+ , 1 '+ , so that pair annihilation cannot readilyoccur, and the residual three particle cluster istherefore a quasistable system. As with the processalready discussed, this will have the energy/volumeratio one-third that of the original g-particle. Theaction is a collective action involving adjustment bypair creation and annihilation between clusters un-til this equilibrium state is achieved. This gravi-tation theme provides a clear role for the tau lep-ton.The energy-volume compatibility requirementthen tells us thatg + 2'7' g (6 )3(1 /g )3 '

where the symbols denote energies. Note again thatthe radius of the particle is inversely related to theenergy by the Thomson formula, so that (1 /g)3, forexample, is a measure of the volume occupied bythe g particle. Rearranged, (6) becomes

( g)3 '7 '-:; - 3-; - 1 = 0, (7 )which has a solution g = 1 .4526271 ' . Now, had wetaken the combination of energy l' + 4Q, which isthe next stage for building energy quanta from atau lepton and four muon pairs, we would havearrived at the energy 1781 + 4(211) = 2625 MeV.This could decay into a 1820-MeV particle by theprocess described, involving reduction by the factorV 3 . However, instead, it seems that, because wehave exceeded the value needed to create the gparticle, pairs of such particles are likely to becreated in the chaotic energy processes involved.Then decay should proceed via Eq. (7) as the tauleptons are reconstituted.The point, however, is that the solution g =1 . 4526271 ' tells us that the g particle has a mass-energy of 2587 MeV, which is exactly that expectedfrom the empirical data leading us to Table I.Indeed, because we have calculated the tau mass-energy as 37/12 times that of the proton (P) via thedata in Table II, we can determine the mass of theg particle with the same precision as the mass of


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9 AN EMPIRICAL APPROACH TO MESON ENERGY ... 157the proton. The proton/electron mass ratio is1836.1524, and when this is multiplied by 37/12 andby 1.452627, we obtain 5062.716. This is the valueof g for use in Eq. (3), and it may be verified asgiving G as 6.67 x 10-11 N m2 kg - Z , in accord withits measured value.Precise evaluation of G from this theory requiresan adjustment to Eq. (3) to allow for the fact thatthe analysis is based on a point charge assumption.For the record, this correction is the term e in-cluded in the tabulated data in Table I of a paperby Eagles.'! The correction to Eq. (3) is the factor1 + e, where e is calculable as 1.98 X 10-4 Thus,

the rigorous calculation of G based on the particletheory presented in this work gives a value of6.6705 X 10-11 N m2 kg-2.Such analysis convinces the author that the2.587-GeV particle is a major constituent of theparticle spectrum that has somehow eluded us. It isseemingly hidden in the space metric, where it playsits role with the tau lepton in regulating gravitation.The one direct indication which the author has seenarises from the likely possibility that the decay ofthe tau and the decay of the g particle may beassociated. The tau lepton has a lifetime of theorder of 4.6 x 10-13 s and falls in a class of par-ticles discussed by Prentice'" as "in the 10 -13 Srange." One such reported decay time was 10.69 X10-13 s for the "longest lived entry ... giving a fitted

mass of 2583 26 MeV /c? .... " This might bedirect evidence of the g(2587) particle.In conclusion, the author notes that the theoryfrom which Eq. (3) was formulated was developedessentially in order to account for the nature of thephoton and gave a calculated value of the fine-structure constant in close accord with the observedvalue. See the review, making comparison with othertheories, by Eagles15 and Petley.'? The derivation ofthe constant of gravitation emerged directly inqualitative terms because it was a characteristic ofthe space metric set in balance with the motion ofmatter in the oscillations at the Compton electronfrequency that were basic to the energy-angular-momentum relationships leading to the photon for-mulation. The problem was that quantitative formu-lation of G depended upon the knowledge of the gparticle which provided this balance. Its energystate could be calculated in terms of G, and effortswere made to explain how it might be created withits energy at 2587 MeV. However, it is only now, inthis paper, that this energy quantity has emergednaturally from analysis of hyperon energy states.The progress reported in this paper should thereforeallow a definitive theory of quantum gravitation tobe formulated, which has the attraction of allowingG to be theoretically determined by a process re-lated to the theoretical determination of the fine-structure constant.

1M. H. MacGregor, Lett. Nuovo Cimento 31,341 (1981).2Particle Data Group, Rev. Mod. Phys. 52 (2), Part II,S-160 (1980).3H. Aspden, Spec. Sci. Tech. 1,59 (1978).4H. Aspden, Lett. Nuovo Cimento 26, 257 (1979).5H. Aspden and D. M. Eagles, Nuovo Cimento 30A, 235(1979).6J. M. LoSecco, Phys. Rev. Lett. 36, 336 (1976).7H. Aspden, The Theory of Gravitation (Sabberton,Southampton, England, 1966), p. 81.8Editorial, New Scientist 69, 335 (1976).9H. Aspden, "The theoretical nature of the neutron and

the deuteron," Hadronic J., to be published.IOH. Aspden, "Meson production based on the Thomsonenergy correlation," Hadronic J., to be published.

11K. A. Johnson, Sci. Am. 241, 100 (July 1979).12E. Trell, Acta Phys. Austriaca, 55, 97 (1983).BE. Trell, Spec. Sci. Tech. 7, 269 (1984).14H. Aspden, Lett. Nuovo Cimento 40, 53 (1984).15D. M. Eagles, Int. J. Theor. Phys. 15,265 (1976).16J. D. Prentice, Phys. Rep. 83, 102 (1982).17B.W. Petley, The Fundamental Physical Constants andthe Frontier of Measurement (Adam Hilger, Bristol 1985),p.161.

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Aspden - An Empirical Approach to Meson Energy Correlation (1986)