aa r X i v : . [ phy s i c s . g e n - ph ] J un HIGGS BOSON MASS IN THE MINIMAL UNIFIED SUBQUARKMODEL
Hidezumi Terazawa ∗ Center of Asia and Oceania for Science(CAOS),3-11-26 Maesawa, Higashi-kurume, Tokyo 203-0032, JapanandMidlands Academy of Business & Technology(MABT),Mansion House, 41 Guildhall Lane, Leicester LE1 5FR, United Kingdom
Abstract
In the minimal unified subquark model of all fundamental particles and forces, the mass ofthe Higgs boson in the standard model of electroweak interactions( m H ) is predicted to be about2 √ m W / m W is the mass of the charged weak boson) so that m H = 131 GeV for m W =80 . GeV , to which the experimental values of 125 − GeV recently found by the ATLAS and CMSColaborations at the LHC are very close.What most of us can expect to find in high energy experiments at the Large Hadron Collider is theHiggs boson( H ), which is the only fundamental particle that has not yet been found in the standardmodel of electroweak interactions[1]. In the unified composite model of all fundamental particles andforces[2], the mass of the Higgs boson has been predicted in the following three ways:In general, in composite models of the Nambu-Jona-Lasinio type[3], the Higgs boson appears asa composite state of fermion- antifermion pairs with the mass twice as much as the fermion mass.The unified subquark model of the Nambu-Jona-Lasinio type [4] has predicted the following two sumrules: m W = [3( m w + m w ) / / and m H = 2[( m w + m w ) / ( m w + m w )] / , where m w and m w are the masses of the weak-iso-doublet spinor subquarks called “wakems” standingfor weak and electromagnetic( w i for i = 1 ,
2) while m W and m H are the masses of the charged weakboson( W ) and physical Higgs scalar in the standard model, respectively. By combining these sumrules, the following relation has been obtained if m w = m w : m w : m W : m H = 1 : √ . From this relation, the wakem and Higgs boson masses have been predicted as m w = m W / √ . GeV ∗ E-mail address: [email protected] m H = 2 m W / √ . GeV for m W = 80 . GeV [5]. On the other hand,if m w /m w = 0 or m w /mw = 0, the other relation canbe obtained: m w : m W : m H = 1 : p / . From this relation, the non-vanishing wakem and Higgs boson masses can be predicted as m w = m W / p / . GeV and m H = 2 m W / p / GeV for m W = 80 . GeV [5]. More generally, from the two sum rules, the Higgs boson mass can be boundedas 92 . GeV = 2 m W / √ ≤ m H ≤ √ m W / GeV.
In the unified quark-lepton model of the Nambu-Jona-Lasinio type[4], the following two sum rulesfor m W and m H have been predicted: m W = (3 < m q,l > ) / and m H = 2( X m q,l / X m q,l ) / , where m q,l ’s are the quark and lepton masses and <> denotes the average value for all the quarksand leptons. If there exist only three generations of quarks and leptons, these sum rules completelydetermine the top quark and Higgs boson masses[6] as m t ∼ = (2 √ / m W = 131 GeV and m H ∼ = 2 m t ∼ = (4 √ / m W = 263 GeV.
Furthermore, triplicity of hadrons, quarks, and subquarks[7] tells us that these sum rules can befurther extended to the approximate sum rules of m W ∼ = (3 < m B,l > ) / and m H ∼ = 2( X m B,l / X m B,l ) / , where m B,l s are the “canonical baryon” and lepton masses and <> denotes the average value for allthe canonical baryons and leptons. The “canonical baryon” means either one of p, n and other ground-state baryons of spin 1/2 and weak-isospin 1/2 consisting of a quark heavier than the u and d quarksand a scalar and isoscalar diquark made of u and d quarks. If there exist only three generations ofquarks and leptons, these sum rules completely determine the masses of the canonical topped baryon, T , and the Higgs scalar as m T ∼ = 2 m W = 161 GeV and m H ∼ = 2 m T ∼ = 4 m W = 322 GeV.
Therefore, if the Higgs boson is found with the mass between 92.8GeV and 131GeV, it looks likea composite state of subquark-antisubquark pairs. If it is found heavier with m H around 263GeV oreven 322GeV, it can be taken as a bound state of tt (“topponium”) or T T (“topped-baryonium”),respectively. If it is found with the mass lying between these typical masses, it may be taken as amixture of subquark-antisubquark pairs and quark-antiquark pairs, etc. .2ery recently, the ATLAS and CMS Collaboration experiments at the CERN Large Hadron Col-lider have almost excluded the two ranges for the Higgs boson mass: the one lower than 114GeV andthe other between 141GeV and 476GeV[8,9], which disagrees with both the prediction in the unifiedquark-lepton model of the Nambu-Jona-Lasinio type[4] and that in the unified baryon-lepton model ofthe Nambu-Jona-Lasinio type[7]. Instead, the prediction in the unified subquark model[4](92 . GeV ≤ m H ≤ GeV ) shows a right ballpark on which the mass of the Higgs boson in the standard modelshould land. Moreover, the fact that the experimental values of m H = 125 − GeV recently foundby the ATLAS and CMS Collaborations are very close to the predicted one of m H = 2 √ m W / GeV seems to strongly suggest that either m w /m w or m w /m w vanishes. It seems to indicatethat the Higgs boson is a composite of the isodoublet spinor subquark-antisubquark pairs well de-scribed by the minimal unified subquark model with either one of subquark masses vanishing. Let ushope that the future LHC experiments will tell us whether the minimal unified subquark model is aviable model of all fundamental particles and forces! Acknowledgements
The author thanks Professor Yuichi Chikashige for very useful helps in correcting errors in theoriginal manuscripts.
References [1] S.L.Glashow, Nucl.Phys. , 579(1961); A.Salam, in Elementary Particle Physics , edited byN.Svartholm (Almqvist and Wiksell, Stockholm, 1968), p.368; S.Weinberg, Phys.Rev.Lett. ,1264(1967).[2] For a classical review, see H.Terazawa, in Proc. 22nd International Conf. on High EnergyPhysics , Leipzig, 1984, edited by A.Meyer and E.Wieczorek(Akademie der Wissenschaften derDDR, Zeuthen, 1984), Vol.I, p.63. For more recent reviews, see H.Terazawa, in
Proc. Interna-tional Conf. “New Trends in High-Energy Physics” , Alushta, Crimea, 2003, edited byP.N.Bogolyubov, L.L.Jenkovszky, and V.V.Magas(Bogolyubov Institute for Theoretical Physics,Kiev, 2003), Ukrainian J.Phys. , 1292(2003); in Proc. XXII-d International Conf. onNew Trends in High-Energy Physics , Alushta(Crimea), 2011, edited by P.N.Bogolyubovand L.L.Jenkovszky(Bogolyubov Institute for Theoretical Physics, Kiev, 2011), p.352.[3] Y.Nambu and G.Jona-Lasinio, Phys.Rev. , 345(1961).[4] H.Terazawa, Y.Chikashige, and K.Akama, Phys.Rev.D , 480(1977); H.Terazawa, ibid. ,184(1980).[5] K.Nakamura et al. (Particle Data Group), J.Phys.G , 075021(2010).[6] H.Terazawa, Phys.Rev.D , 2921(1980); , 3541(E)(1990).[7] H.Terazawa, Mod. Phys. Lett. A , 1031(1990).[8] ATLAS Collaboration, Eur.Phys.J.C , 1728(2011), arXiv:1106.2748; arXiv:1109.3357;arXiv:1109.4747; Phys.Lett.B705