Scale Independent Workable Model of Final Unification

We show that, Schwarzschild radius of Planck mass plays a vital role in electroweak and strong interactions. With reference to the observed large proportionality ratio, ( ) 0.1153 , p e m m it seems appropriate to consider a large nuclear gravitational constant, 3 -1 -2 3.3295608 m kg sec . s G ≅ Qualitatively this idea is in agreement with “Strong gravity” concept proposed by Abdus Salam and C.Sivaram [Mod. Phys. Lett., A8(4), 321326. (1993)]. We would like to suggest that, by replacing the Newtonian gravitational constant with the proposed nuclear gravitational constant, predicted high energy levels of String theory can be brought down to the current hadronic scale. Based on this idea, we defined the nuclear Planck mass, 2 546.7 MeV/ npl s m c G c ≅ ≅  and proposed a quantized model mechanism for understanding the hadronic mass spectrum.


Introduction
A Grand Unified Theory (GUT) is a model in particle physics in which at high energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single force. Unifying gravity with the other three interactions would provide a theory of everything (TOE) [1][2][3][4]. In general, GUT is often seen as an intermediate step towards a TOE. The most desirable cases of any unified description [4] are: 1) To simplify the complicated issues of known physics. 2) To predict new effects, arising from a combination of the fields inherent in the unified description.
So far it has never been achieved. In this paper, we geared up the following things. 3.3295608 m kg sec , s G ≅ assumed to be associated with nuclear structure, we eliminated the higher powers of proton-electron mass ratio and proposed unified and simplified semi empirical relations. D). By replacing the Newtonian gravitational constant with the proposed nuclear gravitational constant, we defined the nuclear Planck mass, 2 546.7 MeV/ npl s m c G c ≅ ≅  and developed a quantized model mechanism for understanding the hadronic mass spectrum.

Strange Result Connected with Strong Coupling Constant
From relations (6) and (7) 12 2 From above relations, we would like to say that, magnitude of s α seems to be around 0.1153. The same conclusion can also be extracted from Particle data group's (PDG) review on Quantum chromodynamics [5]. See the following table-1.

To Eliminate the Higher Powers of Proton-electron Mass Ratio
It is true that, unless stringent requirements are met, in general, speculative alternatives to currently accepted theories cannot be accepted or published. Scientific papers having content that lie outside the mainstream of current research must justify by including a clear, detailed discussion of the motivation for the new speculation, with reasons for introducing any new concepts. If the new formulation results are in contradiction with the accepted theory, then there must both be a discussion of which experiments could be done to verify that the conventional theory needs improvement, and also an analysis showing the consistency of the new theory with the existing experiments.
Qualitatively, this assumption is not new and is having a long standing history [6][7][8][9][10][11][12][13][14]. For more information, readers are encouraged to see Abdus Salam's 'Strong gravity' concept [12]. In the early seventies Abdus Salam and his co-workers proposed the concept of strong gravity. In this context, in physics literature one can see valuable papers on 'strong gravity' proposed by C. J. Isham, Abdus Salam, C. Sivaram, J. Strathdee, K. P. Sinha, Y. Ne'eman and Dj. Sijacki. In Strong gravity, the successive self -interaction of a nonlinear spin-2 field was used to describe a non-abelian field of strong interactions. This idea was formulated in a two-tensor theory of strong and gravitational interactions, where the strong tensor fields are governed by Einstein-type field equations with a strong gravitational constant G f ≈ 10 38 times the Newtonian gravitational constant, G N . Within the framework of this proposal, tensor fields were identified to play a fundamental role in the strong-interaction physics of quantum chromodynamics (QCD). Modifying these concepts, O. F. Akinto and Farida Tahir recently posted their work in arXiv preprint [14]. They elaborately discussed on modified strong gravity concepts pertaining to QCD and general relativity. In 2013. Roberto Onofrio [15] proposed a very interesting concept: Weak interactions are peculiar manifestations of quantum gravity at the Fermi scale, and that the Fermi coupling constant is related to the Newtonian constant of gravitation. In his opinion, at atto-meter scale, Newtonian gravitational constant seems to reach a magnitude of 22 3 -1 -2 8.205 10 m kg sec . × With this assumption, 10 th and 12 th powers of ( ) p e m m can be eliminated. In our recent published papers [16][17][18][19][20][21][22][23] and conference proceedings [24][25][26][27][28], we proposed that, there exist two large pseudo gravitational constants associated with nuclear and electromagnetic interactions and presented many interesting applications starting from nuclear radii to neutron star radius. By eliminating the two pseudo gravitational constants, in this paper, we proposed the above relations (1) to (9). See the following simplified relations (11) to (24).

Application-4
Root mean square radius of proton, Application-5

Application-8
Neutron weak decay, is very close to Avogadro number.

Application-9
Weak coupling angle and up-down quark mass ratio, where ,

Application-13
From relations (10) and (12), Newtonian gravitational constant, 12 All these relations clearly indicate and establish the role of the proposed large nuclear gravitational constant. It may be noted that. 1) Relation (11) is a very simple relation pertaining to strong coupling constant. 2) Relation (12) indicates the massive origin of proton and needs special attention. (13) is a direct consequence of relation (11). 4) Relation (14) is a best fit for the recommended value of the root mean square radius of proton. 5) Relation (15) is a best fit in electroweak sector. 6) Relations (16) and (17) clearly indicate the simplified versions of nuclear stability and binding energy. 7) Relation (18) seems to be a good clue in understanding the weak decay of neutron. 8) Relations (19) and (20) seem to be a nice fit for understanding weak coupling angle, up and down quark masses and magnetic dipole moments of nucleons. 9) Relations (21) and (22)  Based on these points, we would like to stress that, 1) In the development of science and engineering, 'data fitting' and 'workability' are the two essential tools by using which physical models can be generated and validated in a progressive manner.

3) Relation
2) The problem is with 'our understanding and our perception' by using which the current 'scientific standards' and 'procedures' can be reviewed for a better understanding of nature. 3) With reference to String theory models and Quantum gravity models, proposed nuclear gravitational constant and presented results can be given some consideration in developing a 'workable model' of 'scale independent final unification'. 4) Considering the wide applicable range of the proposed assumption, we are confident to say that, with further research and analysis, 'hidden and left over physics' can easily be explored.

To Synchronize Our Model with String Theory and Electroweak Theory
The basic idea of String theory is very simple, very interesting and highly intuitive. Hence most of the science community strongly believes in String theory and its super child 'M-theory'. Unfortunately, there are no concrete new predictions of string theories on low energy scales and high energy scale predictions are beyond the reach of current technology. In addition, with string theory, so far, no one could estimate/implement the Newtonian gravitational 202 Scale Independent Workable Model of Final Unification constant in nuclear interactions. Many critics of string theory have expressed concerns about the large number of possible solutions and possible universes described by string theory. To sustain the ideology of String theory, to keep its mathematical beauty intact and to make it as a practical model of the nucleus, we would like to emphasize the following two points. 1) String theory was originally introduced for understanding the basic hadronic mass spectrum. 2) By replacing the Newtonian gravitational constant with the proposed strong interaction gravitational constant, original energy levels of String theory can be brought down to the current LHC scale. Electroweak theory is very important for modern cosmology, particularly on how the universe evolved. This is because shortly after the Big Bang, the temperature was approximately above 10 15 K. Electromagnetic force and weak force were merged into a combined electroweak force. Very interesting feature is that, in our model, we proposed useful relations for fitting and understanding the Fermi's electroweak coupling constant, weak coupling angle and neutron's weak decay. Proceeding further, we proposed a very interesting relation for understanding the proton magnetic moment. Extending this relation, we made another bold attempt to fit and understand our earth's magnetic dipole moment.

To Understand the Hadronic Mass Spectrum
In 2010, we published our paper on super symmetry with title "Supersymmetry in strong and weak interactions". Interested readers may refer [29][30][31][32][33][34]. The basic concepts were: 1) Fermion -boson mass ratio is very close 2.26. In this section, we propose a model mechanism for understanding the hadronic mass spectrum having a neutral charge. Basic idea is that, 1  First generation neutral baryons can be classified with relation (25). See the following table-2. Sub levels can be approximated with further study and analysis. In some cases, either a neutral pion or a charged pion also combines with estimated neutral baryon and generates a neutral/charged baryon. The same idea can be applied to second and third generation neutral baryons.
Second generation neutral baryons can be estimated with, See the following table-3.
See the following table-5. Currently believed and newly reported charmed and charmed strange mesons [35,36] See the following table-6.
where factor 2.26 is an ad hoc factor assumed to be connected with fermion-boson mass ratio pertaining to Super symmetry. It needs in depth analysis at fundamental level. See the following table-9.  Whether, relations (31) and (32) are applicable for all the first generation baryons or applicable only for the ground state of the first generation baryon, is to be decided with further study.

Conclusions
Subject of final unification is having a long history. So far, no model succeeded in implementing the Newtonian gravitational constant or Planck scale in nuclear and electroweak interactions. Even though, the basic idea of String theory is very simple, very interesting and highly intuitive, there are no concrete new predictions on low energy scales and high energy scale predictions are beyond the reach of current technology. It is an indication of 'incompleteness' in String theory paradigm. In this paper, with reference to Planck scale, we presented a variety of relations pertaining to nuclear and electroweak coupling Universal Journal of Physics and Application 10(6): 198-206, 2016 205 constants. It is clear from the above discussion that we could satisfactorily fit the nuclear data through empirical relations. This sincere attempt is to be ascertained by the scientific community. We would like to appeal that, with respect to currently believed String theory and Quantum gravity models -proposed assumption, proposed semi empirical relations, proposed procedure for understanding the hadronic mass spectrum, can be given some consideration in developing a 'workable model' of TOE.