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Gravity Based Integral Charge Quark and Higgs Super Symmetry

U. V. S. Seshavatharam*, S. Lakshminarayana

Honorary faculty, I-SERVE, Alakapuri, Hyderabad-35, Telangana, India

Abstract: From gravity point of view, so far no model succeeded in understanding the link between strongly interacting massive fermions and strongly interacting massive bosons/mesons. One should not forget the fact that, strongly interacting massive fermions are only playing a major role in the formation of observable luminous and non-luminous massive celestial objects. By interconnecting the strong coupling constant and gravitational constant via the Schwarzschild interaction, in this paper, the authors reviewed the basics of strong nuclear interaction and also reviewed the previously published “integral charge Quark and Higgs super symmetry” results and proposed a very simple mechanism for understanding the observed unstable baryons. For the unstable hadronic particles and unstable electro weak particles- ‘classification scheme', ‘mass spectrum' and ‘charge spectrum' are the three vital factors and these three things can be understood with ‘integral charge super symmetry’. Here the authors would like to stress the fact that, the observed Mesonic mass spectrum, Baryonic mass spectrum and Higgs mass spectrum can be reproduced with ‘integral charge Quark and Higgs super symmetry’. Important point to be noted is that without considering the currently believed ‘color' charge concept, observed unstable baryons ‘mass' and ‘charge' spectrum can be understood. By any chance if any light quark boson having integral charge couples with any integral charge baryon, then a neutral baryon can be generated. This idea is very much similar to the ‘photon absorption’ by electron. In this context, the authors produced many clear cut evidences.

Keywords: schwarzschild interaction, avogadro number, electroweak interaction, strong interaction and super symmetry

Received March 26, 2015; Revised May 31, 2015; Accepted July 01, 2015

Citation: U. V. S. Seshavatharam, S. Lakshminarayana, Gravity Based Integral Charge Quark and Higgs Super Symmetry. Frontiers of Astronomy Astrophysics and Cosmology, 1 (2). 74-89. January 2015. doi:10.12691/faac-1-2-1

1. Introduction

Quantum chromo dynamics is successful in understanding sub nuclear physics, General theory of relativity is successful in understanding cosmology and celestial mechanics and Quantum mechanics is successful in understanding particle physics, thermodynamics and astrophysics. But so far no model is successful in understanding Super symmetry and final unification. Here it may be noted that, strongly interacting massive fermions are only playing a major role in the formation of observable massive stars and compact objects like neutron stars and black holes etc. If one is willing to consider any celestial object as a big elementary particle generator, then it is inevitable to study ‘Strong interaction’, ‘gravity’ and ‘Super symmetry’ in a unified manner. In this context - by considering the strength of Schwarzschild interaction as ‘unity’ and by considering Avogadro number as a suitable scaling factor, the authors made an attempt to fit and understand the basics of final unification and super symmetry.

2. Integral Charge Quark and Higgs Physics

Calculations based on fractional charge quarks and lattice gauge formalism have successfully reproduced the masses of many hadrons, including the proton. Here the key point to be noted is that, fractional charge quarks are well founded theoretically and ‘not yet all evidenced experimentally'. This negative result of modern collider experiments strongly cast doubt on the ‘natural existence' of “fractional charge bare quark fermions”. In the previously published papers [1,2,3,4] the authors proposed that there exist integral charge quark fermions, integral charge quark bosons, integral charge (massive) effective quark fermi-gluons and integral charge (massive) quark boso-gluons. Clearly speaking, for baryons, currently believed role of quark fermions is taken up by the ‘effective quark fermi-gluons’ and for mesons, currently believed role of quark fermions is taken up by massive ‘quark boso-gluons'. Note that in this paper, “integral charge (massive) effective quark fermi-gluons” have been eliminated and a simplified mechanism is proposed for understanding the observed baryonic mass and charge spectrum. Important point to be noted is that without considering the currently believed ‘color' charge concept, observed unstable baryons ‘mass' and ‘charge' spectrum can be understood. By any chance if any light quark boson having integral charge couples with any charged baryon, then a neutral baryon can be generated. This idea is very much similar to ‘photon absorption’ by electron. When a weakly interacting electron is able to absorb a boson, in strong interaction it is certainly possible. Moreover, if any unstable baryon couples with two or three unstable light quark bosons then the unstable baryon mass increases and charge also changes. In most of the cases baryon charge changes from e to neutral and neutral to e. In rare cases unstable baryon with 2e can also be generated. Note that, if any two oppositely charged quark boso-gluons couple together then a neutral quark boson or meson can be generated.

3. False Failure of Super Symmetry

Super symmetry differs notably from currently known symmetries in that its corresponding conserved charge (via Noether’s theorem) is a fermion called a super charge and carrying spin-1/2, as opposed to a scalar (spin-0) or vector (spin-1). A super symmetry may also be interpreted as new fermionic (anticommuting) dimensions of spacetime, super partners of the usual bosonic spacetime coordinates, and in this formulation the theory is said to live in super space. Currently there is only indirect evidence for the existence of super symmetry, primarily in the form of evidence for gauge coupling unification. A central motivation for super symmetry close to the TeV energy scale is the resolution of the hierarchy problem of the Standard Model [5,6,7]. Without the extra super symmetric particles, the Higgs boson mass is subject to quantum corrections which are so large as to naturally drive it close to the Planck mass barring its fine tuning to an extraordinarily tiny value. In the super symmetric theory, on the other hand, these quantum corrections are cancelled by those from the corresponding super partners above the super symmetry breaking scale, which becomes the new characteristic natural scale for the Higgs mass.

Other attractive features of TeV-scale super symmetry are the fact that it often provides a candidate dark matter particle at a mass scale consistent with thermal relic abundance calculations, provides a natural mechanism for electroweak symmetry breaking and allows for the precise high-energy unification of the weak, the strong and electromagnetic interactions. Therefore, scenarios where super symmetric partners appear with masses not much greater than 1 TeV are considered as the most well-motivated by theorists. These scenarios would imply that experimental traces of the super partners should begin to emerge in high-energy collisions at the LHC relatively soon. The Large Hadron Collider at CERN is currently producing the world’s highest energy collisions and offers the best chance at discovering super particles for the foreseeable future.

In a conventional and currently believed modern approach, as of February 2015, no meaningful signs of the super partners have been observed in LHC. The (false) failure of the Large Hadron Collider to find evidence for super symmetry has led some physicists to suggest that the theory should be abandoned or modified. The authors are also thinking in the same direction. Clearly speaking, if one is willing to modify the current concepts of SUSY, certainly one can recognize and appreciate the great success of LHC. If one is willing to consider the ‘charged electro weak W boson’ as the SUSY partner of Top quark or if one is willing to consider the neutral electroweak Z boson as the SUSY partner of pair of Higgs fermions or if one is willing to consider ‘neutral pion’ as a SUSY candidate of pair of strange quark fermions or if one is willing to consider the charged pion as the SUSY partner of Proton and Muon or if one is willing to consider the observed light mesons as the ‘excited SUSY levels of proton’, it is certainly possible to say that, LHC has succeeded in confirming the basics of SUSY. The authors would like to stress the fact that, “confirmation of SYSY” depends on how we perceive, how we analyze and how we interpret the data produced by LHC and problem is not with LHC. In this very critical condition, with reference to the published paper [1] entitled “Super symmetry in strong and weak interactions” , the authors extended the scope of electroweak interaction and SUSY to atomic level and successfully developed a simple relation for understanding the total energy of electron [4] in Hydrogen atom.

4. To Fit the Strong Interaction Physical Parameters

From gravity point of view, so far no model succeeded in understanding the link between strongly interacting massive fermions and strongly interacting massive bosons/mesons. One should not forget the fact that, strongly interacting massive fermions are only playing a major role in the formation of observable luminous and non-luminous massive celestial objects. In this section the authors made an attempt to explore the meaning of “strength of atomic interactions” with reference to Black holes [8,9] and quantitatively developed heuristic relations in between the gravitational constant, strong coupling constant and weak coupling constants.

1) If it is true that and are fundamental physical constants, then can be considered as a fundamental compound constant related to a characteristic limiting force.

2) Black holes are the ultimate state of matter’s geometric structure.

3) Magnitude of the operating force at the black hole surface is the order of .

4) Gravitational interaction taking place at black holes can be called as ‘Schwarzschild interaction’.

5) Strength of ‘Schwarzschild interaction’ can be assumed to be unity.

6) Strength of any other interaction can be defined as the ratio of operating force magnitude and the classical or astrophysical force magnitude.

7) If one is willing to represent the magnitude of the operating force as a fraction of i.e , where , then

[picture] | (1)

If is very small, becomes very large. In this way, can be called as the strength of interaction. Clearly speaking, strength of any interaction is times less than the ‘Schwarzschild interaction’ and effective becomes .

8) Avogadro number is an absolute number [10-16] q and it is having no units like ‘per mole’. Atomic interaction strength is times less than the Schwarzschild interaction and hence atomic gravitational constant can be expressed as:

[picture] | (2)

Here, is the unified atomic mass unit, is the molar mass unit expressed as ‘one gram’ and hence it is possible to think that, constitutes number of atoms which in turn constitutes number of protons.

9) Since 2009, the authors are working on this concept and proposed many coincidences. This proposal is well received by reviewers of many online physics journals. Finally by considering the Schwarzschild interaction, the authors succeeded in exploring the beauty of its back ground physics and many foreground applications. For further details readers are requested to see the published papers and references therein [14,15,16].

10) can be considered as the unified elementary interaction strength. It is having many applications in nuclear physics and atomic physics. one can see different forms of

11) Strong coupling constant can be expressed as:

[picture] | (3)

This can be compared with the experimental value . This is the most precise result obtained at a hadron - hadron collider [17]. This is one of the many foreground applications of the proposed atomic gravitational constant.

12) Down and Up quark mass ratio can be expressed as:

[picture] | (4)

This proposed ratio of up and down quark mass ratio can be compared with the current estimates [17] of 0.46(5).

13) Ratio of Up quark and electron rest mass can be expressed as [1]:

[picture] | (5)

14) Proton’s rest mass can be expressed as:

[picture] | (6)

15) Nucleon mass difference can be expressed as:

[picture] | (7)

16) Proton’s characteristic radius can be expressed as:

[picture] | (8)

17) Proton’s rms radius can be expressed as [19]:

[picture] | (9)

18) Nuclear charge radius can be expressed as [20]:

[picture] | (10)

19) Proton number based nuclear stable mass number can be expressed as [15,16]:

[picture] | (11)

20) Nuclear binding energy at the stable mass number can be expressed as [15,16,21,22,23,24]:

[picture] | (12)

21) Approximately nuclear binding energy above and below the stable mass number can be expressed as:

[picture] | (13)

It needs further study and theoretical back up.

22) At the stable mass number, proton’s kinetic energy can be expressed as [23,24]:

[picture] | (14)

Clearly speaking, protons kinetic energy is equal to the nuclear binding energy [23,24].

23) At the stable mass number, neutrons’ kinetic energy can be expressed as follows [23,24].

[picture] | (15)

24) At the stable mass number, nucleons’ kinetic energy can be expressed as:

[picture] | (16)

This can be compared with the Fermi gas model of nucleons total kinetic energy [23,24,25] expression,

25) The characteristic atomic force can be represented by and the famous Fermi’s weak coupling constant can be expressed as [18]:

[picture] | (17)

where

can be considered as the characteristic length associated with weak interaction range and can be considered as the characteristic volume associated with weak interaction.

26) Ground state potential energy of electron in hydrogen atom can be expressed as [16]:

[picture] | (18)

5. Basic Concepts of Modified and Revised Integral Charge Quark and Higgs Super Symmetry

1. If and are the rest masses of fermion and boson,

[picture] | (19)

This idea can be applied to protons, quarks, Higgs particles and charged leptons. Based on the observed mesonic mass spectrum, magnitude of the proposed fermion-boson mass rario can be fixed in many ways. Its value seems to lie in bewteen and and for practical purpose in this paper the authors consider a value of In a semi empirical approach it can be fitted in the following way and it needs theoretical back up.

[picture] | (20)

where .

2. There exist nature friendly ‘integral charge quark fermions’ and ‘integral charge quark bosons’. If and are the rest masses of quark fermion and quark boson respectively,

27) There exists integral charge Higgs fermion [1-3] and mass ratio of Higgs fermion and electron can be expressed as:

[picture] | (21)

3. There exists integral charge Higgs boson of rest energy close to

[picture] | (22)

Coincidence-1: With this integral charge Higgs boson, neutral Z boson rest energy can be obtained in the following form.

[picture] | (23)

It can be compared with the observed mass of the neutral electroweak boson of rest energy 91187 MeV [18].

Coincidence-2: The obtained top quark boson rest energy is 80438 MeV and is very close to the observed boson of rest energy 80385 MeV [18]. Really this is a great coincidence and support for the proposed new idea of ‘‘fermion-boson” unification scheme. This strongly supports super symmetry with small modifications. It is noticed that Higg's charged boson and top quark boson couple together to form a new ‘neutral’ boson of rest energy 126.0 GeV.

[picture] | (24)

Table 1. Fitting of quark fermion and quark boson smasses

Coincidence-3: Neutral pion seems to be the combination of strange qurark boson pair and can be expressed as:

[picture] | (25)

Here represent strange quark fermion and strange quark boson rest masses respectively.

Coincidence-4: Charged pion can be considered as the geometric mean of ‘super symmetric boson of proton’ and ‘super symmetric boson of muon’ and can be expressed as follows.

[picture] | (26)

4. There exist integral charge massive quark gluons. Here, gluon means massive bosons having integral charge. These gluons play a vital role in understanding and generating the observed mesons rest mass.

5. The quark gluon rest energy is equal to

[picture] | (27)

6. ‘Integral charge light quark bosons’ in one or two numbers couple with the ground or excited unstable baryons and generate doublets and triplets. This is similar to ‘absorption of photons’ by electron.

6. Proposed Integral Charge Quark Fermions, Bosons and Gluons

In the previous published paper [1], the authors suggested that up, strange and bottom quarks are in geometric series. Similarly down, charm and top quarks are in another geometric series. Please see Table 1 for the proposed quark ‘fermion’ masses, ‘boson’ masses and ‘gluon’ masses.

Note that, baryon and meson charge-mass spectrum can be generated from these mass units. Quark fermions, quark bosons, quark gluons and their connecting relations can be expressed in the following way. Note that all these relations got publihsed in the reference [1] and here in this paper the key operating numbers are reviewed in a unfied approach and needs firther research at fundamenatl level. It can be suggested that, ratio of electron rest mass and up quark fermion mass is close to the magnitude of strong coupling constant.

The proposed USB geometric ratio is

[picture] | (28)

If the DCT series is the second generation series, its geometric ratio is

[picture] | and(29)

[picture] | (30)

Quark boson mass can be defined by the following relation.

[picture] | (31)

Quark gluon mass can be defined by the following relation.

[picture] | (32)

Predicted short lived strongly interacting neutral quark boson rest energies are: 3.9 MeV, 8.4 MeV, 1160 MeV, 4674 MeV and 160878 MeV.

7. To Fit and Predict the Baryonic Mass Spectrum

The authhors proposed a complicated mechanism in the previously proposed paper. By eliminating the previously proposed concept of “quark fermi gluons”, in this paper the authgors proposed a very simple and straight forward mechanism for understanding, fitting and predicting the the observed baryonic mass and charge spectrum. Basic concepts can be expressed as follows.

1) Nucleus can be considered as a sea of protons, integral charge quark bosons and integral charge quark gluons.

2) Under high energy collision, like absorption of photons by electron, proton combines with any one quark boson and generates a neutral ground state baryon. This type of baryon can be called as Mono boson baryon.

3) Under high energy collision, proton combines with quark boson pair and generates a charged ground state baryon. This type of baryon can be called as Bi boson baryon.

4) Primary excited levels follow

Presently understood Regge trajectory of some of the Baryons and Mesons can be fitted in this way. If one is willing to express the rest mass of any quark fermion or boson with , then with reference to the basic concept of vector atom model, excited levels of any quark fermion or quark boson can be

where is a factor.

5) Like absorption of photons by electron, excited levels again couple with up or down quark bosons and generate neutral or charged observable baryons and thus doublets and triplets can be understood.

6) Secondary energy levels follow Based on primary energy levels and by any reason quark boson or fermion under goes a cubic root, then energy levels seems to follow

8. Ground and Excited Mono Boson Neutral Baryons

Step-1: Proton combines with one quark boson and generates a neutral ground state baryon.

[picture] | (33)

Step-2: Primary energy levels of neutral ground state baryon can be understood as follows.

[picture] | (34)

Step-3: Secondary energy levels of neutral excited state baryon can be understood as follows.

[picture] | (35)

See the following Table 2 to Table 9.

1. Observed Lamda baryon can be classified and fitted with first primary energy level of Proton+Up boson in Table 2.

2. Primary energy levels of (Proton+Up boson) and (Proton+Down boson) can be compared with the currently believed nucleon excited levels.

3. Observed Sigma and Xi baryons can be classified and fitted with secondary energy levels of 1118.1 MeV and 1120.8 MeV respectively.

4. Some times, excited levels couple with up or down bososns and generate integral charge baryons.

5. Observed neutral bottom baryons can be supposed to be the secondary energy levels of Proton and one Bottom boson . See Table 7, Table 8,Table 9.

6. Obseved and believed top quark seems to be the top quark baryon at I=20 with energy level 172084.6 MeV. Predicted other top quark baryon masses can be seen in Table 2, column-9.

Table 2. Ground and Primary energy levels of Mono boson neutral baryons

Table 3. Neutral and secondary energy levels of (Proton+Up boson) = 1118.1 MeV

Table 4. Neutral and secondary energy levels of (Proton+Up boson) = 1120.8 MeV

Table 5. Neutral and secondary energy levels of (Proton+Up boson) = 1195.9 MeV

Table 6. Neutral and secondary energy levels of (Proton+ Charm boson) = 1805.4 MeV

Table 7. Neutral and secondary energy levels of (Proton+ Bottom boson) = 3894.9 MeV

Table 8. Neutral and secondary energy levels of (Proton+ Bottom boson) = 4310.4 MeV

Table 9. Neutral and secondary energy levels of (Proton+ Bottom boson) = 5125.9 MeV

9. Ground and Excited Bi Boson Charged Baryons

Step-1: Proton couples with quark boson pair and generates a charged ground state baryon.

[picture] | (36)

Step-2: Primary energy levels of charged ground state baryon can be understood as follows.

[picture] | (37)

Step-3: Secondary energy levels of charged ground state baryon can be understood as follows.

[picture] | (38)

See the following Table 10.

Table 10. Ground and Primary energy levels of Bi boson charged baryons

1) Observed Omega and Charmed baryons can be classified and fitted with Primary energy levels of Proton and 2 Strange bosons. See Table 10 column-6. Clearly speaking, Omega baryons can be observed at I=2 and I=20 with rest energies 1680 MeV and 2269 MeV respectively and most of the believed Charmed baryons can be observed atI=6, I=7, I/2=21,I/2=28,I/2=36,I/2=45, I/2=55, and other baryons like 2455 MeV, 2575 MeV, can be classified with Primary energy levels of (Proton and 2 Up bosons) or (Proton and 2 Strange bosons) and can be seen in columns 3 and 4.

2) Observed neutral bottom baryons can be supposed to be the secondary energy levels of Proton and two charm baryons. See the following Table 13 columns at I=72 and 90 with enrgy levels 5739 MeV and 6111 MeV.

10. Ground and Excited Charged and Neutral Light Mesons

In the previously published paper [1], the authors proposed a simple procedure for fitting and predicting the light neutral and charged mesons.

Step-1: Super symmetric boson of Proton is the mother of observed light mesons and can be called as the “Sproton”.

[picture] | (39)

Step-2: Primary energy levels of Sproton can be understood as follows.

[picture] | (40)

See the following Table 11. These charged states join with up or down bosons and generate neutral light mesons.

Step-3: Ground and excited levels of Sproton couple with up or down bosons and generate neutral light mesons.

See Table 12 for neutral light mesons generated by considering Down boson of rest energy 4.18 MeV. One can see all the observed light mesons and this is a straight forward evidence for the proposed integral charge quark super symmetry and straight forward confirmation for the existence of susy partener of strongly interacting Proton.

Table 11. Charged and primary energy levels of Sproton =415.165 MeV

Table 12. Neutral and primary energy levels of Sproton =415.165 MeV joined with Down boson

11. Ground and Excited Neutral Heavy Quark Gluons

In the previously published paper, the authors proposed the following same procedure in understanding, fitting and predicting the heavy neutral and charged quark mesons.

Step-1: Oppositely charged quark gluons generate neutral and ground state heavy gluons.

[picture] | (41)

where, represent any two integral charge quark gluons.

Step-2: Primary energy levels of neutral quark gluons can be understood as follows.

[picture] | (42)

See the following Table 13 to Table 25.

Table 13. Neutral and primary energy levels of Up-UP gluons

Table 14. Neutral and primary energy levels of Down-Dopwn gluons

Table 15. Neutral and primary energy levels of Up and Down gluons

Table 16. Neutral and primary energy levels of Strange and Up gluons

Table 17. Neutral and primary energy levels of Strange and Down gluons

Table 18. Neutral and primary energy levels of Strange and Strange gluons

Table 19. Neutral and primary energy levels of Charm and Up gluons

Table 20. Neutral and primary energy levels of Charm and Down gluons

Table 21. Neutral and primary energy levels of Charm and Strange gluons

Table 22. Neutral and primary energy levels of Charm and Charm gluons

Table 23. Neutral and primary energy levels of Bottom and Strange gluons

Table 24. Neutral and primary energy levels of Bottom and Bottom gluons

Table 25. Neutral and primary energy levels of Top and Top gluons

In this way many neutral gluons can be predicted and observed mesons can be fitted. This fitting procedure is very simple and suggets a revision in the current ‘Quark classification scheme’ connected with mesons.

12. Charged Charm - Strange Excited Mesons

It is noticed that, average of charmed and strange gluon mass is (2474+1207)/2=1840.5 MeV and is very close to the first charged Charm-Strange meson. Primary energy levels of charged 1840.5 MeV gluons can be understood as follows.

[picture] | (43)

See the following Table 26. With this 1840.5 MeV, the historical excited levels of charmed strange mesons 1968 MeV, 2112 MeV, 2317 MeV, 2460 MeV, 2532 MeV, 2572 MeV, 2632 MeV, 2700 MeV, 2860 MeVand 3044 MeV can be fitted. This data strongly support the current classification scheme of charmed strange mesons including 1968 MeV.

Table 26. Charged and primary energy levels of Sprotonic gluon

13. Ground and Excited Charged Gluons of Sproton

Charged “Sproton” transforms to gluonic form and generates the currently belived charmed strange mesons in the following way. Gluonic form of Sproton follows the same concept of quark gluon and its relation can be expressed as follows.

[picture] | (44)

Primary energy levels of charged heavy Sprotonic gluons can be understood as follows.

[picture] | (45)

See the following Table 27. The historical excited levels of charmed strange mesons 2317 MeV, 2460 MeV, 2572 MeV, 2632 MeV, 2700 MeV, 2860 MeVand 3044 MeV can be seen approximately.

Table 27. Charged and primary energy levels of Sprotonic gluon

14. Discussuion

For the present situation, it may not be possible to classify the hierarchy of the currently believed fundamental physical constants. But the authors are sure to say that, with the proposed relations it is certainly possible to correlate the physical constants of various branches of physics at fundamental level. In a semi empirical approach, the authors well connected the strong coupling constant and gravitational constant and clearly defined the quark mass generation formulae and relations. Even though all the relations are semi empirical, quark mass generation procedure has been interlinked with the strong coupling constant at fundamental level. Formulae for primary and secondary energy levels are very simple and are very easy to understand. By selecting suitable selection rules, number of baryonic and mesonic energy levels can be fine tuned and thus both, data fitting and data prediction can be made simple and straight forward. From the relations and data, one can easily understand the simpified scheme of “integral charge super symmetry” related to strong interaction and weak interaction. ‘Higgs fermion’ and ‘Higgs boson’ concepts can be recommended for in-depth discussion at fundamental level. With further research and analysis, both Standard model and SUSY can be studied in a unfied manner and the link between weakly interacting fermions and weakly interacting gravitons can be understood.

15. Conclusions

From all the above concepts, relations and data, it can be suggested that,

1. With reference to the well known Schwarzschild interaction, existence of can be confirmed with great confidence.

2. Fermion and boson mass ratio can be considered as 2.26 and can be recommended for implementation in current SUSY physics.

3. With reference to the well known observed elementary particle data starting from charged leptons to the (believed) top quark, integral charge Quark and Higgs super symmetry concepts can be recommended for further research and analysis.

4. can be considered as a fundamental form of unified elementary interaction strength. By nature, if one is willing to consider strong coupling constant as the utmost fundamental physical constant, then quantitatively it is possible to show that,

5. From particle physics point of view, both and can be considered as characteristic weakly interacting ‘dark matter’ mass units.

Acknowledgements

The first author is indebted to professor K. V. Krishna Murthy, Chairman, Institute of Scientific Research on Vedas (I-SERVE), Hyderabad, India and Shri K. V. R. S. Murthy, former scientist IICT (CSIR) Govt. of India, Director, Research and Development, I-SERVE, for their valuable guidance and great support in developing this subject.

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