The Newtonian Gravitational Constant in Fermi Theory with Weak Radiative Corrections
[1]
Nikola Perkovic, Institute of Physics and Mathematics, Faculty of Science, University of Novi Sad, Novi Sad, Serbia.
The Newtonian gravitational constant G is still not known to high levels of accuracy after approximately two hundred years of experimental work. This presents a problem since G is one of the most fundamental constants in physics. We will attempt to advance the study of G by establishing a new method that relates it to the Fermi coupling constant. This will be done via a formulaic representation of G depending only on muonic and tauonic parameters, respectively. The first formula relates G with the muon Compton wavelength, mass and mean lifetime as well as the running value of the fine structure constant on the muonic scale. The second formula uses parameters of tau leptons. Using the mean lifetime of muons we rewrite the formula and establish the aforementioned relation between G and the Fermi coupling constant after which we proceed to account for the weak corrections on the muon mean lifetime. The results obtain by the two formulas for muons and tau leptons, respectively, are 98.11% and 99.9% in agreement with the value of G provided by NIST. It is concluded that there is a possibility for the “running” of G thus requiring the calculation of an effective value.
Newtonian Gravitational Constant, Fermi Coupling Constant, Fine Structure Constant, Fermi Theory
[1]
S. M. Berman and A. Sirlin, Some considerations on the radiative corrections to muon and neutron decay, Ann. Phys. 20 (1962) 20-43.
[2]
M. Tanabashi et al. (Particle Data Group) Phys. Rev. D 98, 030001 (2018).
[3]
R. Hofstadter, Nuclear and Nucleon Scattering of High-Energy Electrons, Ann. Revs. Nuclear Sci. 7 (1957) 231-316.
[4]
T. van Ritbergen, R. G. Stuart, Nucl. Phys. B564 (2000) 343-390.
[5]
A. Sirlin, Current algebra formulation of radiative corrections in gauge theories and the universality of the weak interactions, Rev. Mod. Phys. 50, 3 (1978) 573-905.
[6]
A. Sirlin, Radiative corrections in the SU (2)L X U(1)Y theory: A simple renormalization frameworkPhys. Rev. 224, 4, D 22 (1980) 971.
[7]
N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10 (1963) 531.
[8]
M. Kobayashi and T. Maskawa, CP-Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652–657.
[9]
E. Braaten, S. Narison and A. Pich, QCD analysis of the tau hadronic width, Nucl. Phys. B 373 (1992) 581-612.
[10]
A. Sirlin, Radiative Corrections in the standard model, Nucl. Phys. B 196 (1982) 331-341.
[11]
E. S. Narison, V-A hadronic tau decays: a QCD laboratory, Nucl. Phys. B 96, 1-3 (2001) 364-374.
[12]
A. L. Kataev and V. V. Starshenko, Estimates of the higher-order QCD corrections to R (s), Rτ and deep-inelasstic scattering sum rules, Mod. Phys. Lett. A 10 (1995) 235-250.
[13]
M. Neubert, The Physics of Hadrons, Nucl. Phys. B 463 (1996) 511-546.
[14]
A. Pich, QCD description of hadronic tau decays, Nucl. Phys. B 218, 1 (2011) 89-97.
[15]
A. A. Pivovarov, Running electromagnetic-coupling constant: Low-energy normalization and the value at Mz, Phys. Atom. Nuclei 65, 7 (2002) 1319-1340.
[16]
M. Agostini, et al. Test of Electric Charge Conservation with Borexino, Phys. Rev. Lett. 115, 23, 231802 (2015).
[17]
R. Onofrio, Proton radius puzzle and quantum gravity at the Fermi scale, EPL 104, 2, 20002 (2013).
[18]
R. Onofrio, On weak interactions as short-distance manifestations of gravity, Mod. Phys. Lett. A28, 1350022 (2013).
[19]
F. W. Hehl and B. K. Datta, Nonlinear Spinor Equation and Asymmetric Connection in General RelativityJ. Math. Phys. 12, 7, 1334 (1971).
[20]
N. A. Batakis, The gravitoweak connection, Phys. Lett. B 148, (1984) 51-54.
[21]
N. A. Batakis, Extra Gauge Field Structure Uncovered in the {Kaluza-Klein} Framework, Class. Quant. Grav. 3 (1986) 99-105.
[22]
Yu. M. Loskutov, Graviweak interactions and their role in gravitational dynamics and electrodynamic, JETP 80, 150 (1995) 283-298.
[23]
S. Alexander, A. Marcian`o, and L. Smolin, Gravitational origin of the weak interaction's chirality, Phys. Rev. D 89, 6, 065017 (2014).
[24]
G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, Precision measurement of the Newtonian gravitational constant using cold atoms, Nature 510, 7506, (2014) 518-521.
[25]
J. B. Fixler, G. T. Foster, J. M. Mc Guirk and M. A. Kasevich, Atom interferometer measurement of the newtonian constant of gravity, Science 315, 5808 (2007) 74-77.
[26]
Qing Li et al, Measurements of the gravitational constant using two independent methods, Nature 560 (2018) 582–588.
[27]
S. Capozziello, et al, Running coupling in electroweak interactions of leptons from f (R)-gravity with torsion, Eur. Phys. J. C 72, 1908 (2012).
[28]
X. Calmet, S. D. H. Hsu, and D. Reeb, Quantum gravity at a TeV and the renormalization of Newton's constant, Phys. Rev. D 77, 125015 (2008).
[29]
J. Valle, Neutrino physics overview, Jour. of Phys., Conference Series 53, 1, (2006) 473–505.
[30]
Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870–880.
