Near-Brane Su(6)-Origin Higgs in Scherk–schwarz Breaking of Five-Dimensional Su(6) Gut

Abstract

The symmetry breaking of 5-dimensional SU(6) GUT is realized by Scherk-Schwarz mechanisms through trivial and pseudo non-trivial orbifold S 1 /Z 2 breakings to produce dimensional deconstruction 5D SU(6)→4D SU(6). The latter also induces near-brane weakly-coupled SU(6) Baby Higgs to further break the symmetry into SU(3) C ⊗SU(3) H ⊗U(1) C . The model successfully provides a scenario of the origin of (Little) Higgs from GUT scale, produces the (intermediate and light) Higgs boson with the most preferred range and establishes coupling unification and compactification scale correctly.October 18, 2018 1:15 WSPC/INSTRUCTION FILE Near-brane˙SU6˙IJMP 2 October 18, 2018 1:15 WSPC/INSTRUCTION FILE Near-brane˙SU6˙IJMP 3Higgses produce SM-like Higgses and become the topic of discussion in this paper. The second symmetry breaking of 4D SU(6)→ 4D SU(3)⊗SU(3)⊗U(1) is performed by SU (6) Little-like Higgs through orbifold-based field re-definition and the broken shift symmetry induced by the properties of VEV in lower-near-brane [15,16]. The VEV s are obtained from two Scherk-Schwarz parameters [4][5][6][7].One can immediately predict the birth of SU(3) Little Higgses from the SU(6)origin Little Higgses. This derivation is indeed workable and quite successful.The paper is organized as follows, first special conditions of Scherk-Schwarz breaking, the trivial and pseudo non-trivial orbifold S 1 /Z 2 breaking [15,22,24] are revealed in the next Section, then 5D model of SU(6) with 2 branes and the bulk [32,33] where gauge bosons and scalar bosons live in near-brane area (y ∼ 0) which will provide SU(6)-origin Little Higgs, and SU(6) Baby Higgs which is basically weakly-coupled. The two have been well reconciled within the model as well as SU(6) GUT and Baby Higgs.The pseudo non-trivial symmetry breaking to SU(3)⊗SU(3)⊗U(1) is explained in the next section. Subsequently it is shown that the emerging gauge bosons from broken 5-dimensional SU(6) could be considered as scalar boson [6,7,20] which provides the Coleman Weinberg potential for radiative symmetry breaking of 4D SU(6). Before summarizing the results, a brief discussion on the order estimations of relevant physical observables within the model is given.

On the unification of Higgs-Nambu Goldstone boson in the formation of near-brane exotic scalar via Scherk-Shwarz breaking in 5-dimensional SU(6) symmetry

“…Following recent development on extra dimension physics [22,27,32,36,43], the Scherk-Schwarz breaking [3,19,20,22,27] and Orbifold breaking [12,22,23,25,26,27] have opened the way for producing Higgs through the extra-dimensional compactification effect which induces the Higgs itself, and known as the gauge-Higgs boson unification [11,12,21,22,27]. Recently a grand gauge-Higgs unification based on 5D SU(6) compactified on an orbifold S 1 /Z 2 with fermions in two 6-plets and one 20-plet shows successful breaking with no proton decay at tree level but a little low compactification scale and heavy Higgs [8].…”

“…Recently a grand gauge-Higgs unification based on 5D SU(6) compactified on an orbifold S 1 /Z 2 with fermions in two 6-plets and one 20-plet shows successful breaking with no proton decay at tree level but a little low compactification scale and heavy Higgs [8]. Other work such as Hosotani mechanism with non-zero VEV being developed by extra-dimensional parameters results in instant gauge symmetry breaking after dimensional deconstruction [25,27,47] and some other works in extra dimension and non-Higgs mechanism have been developed [3,4,13,14,15,21,22,24,26,27,35,40,41,48] including the pioneer one [32,34].…”

“…Corresponding to 5D SU(6) local gauge symmetry, based on AdS/CFT correspondence, SU (6) global symmetry also exists [3,8], and breaks after shift symmetry breaking takes place, and produces massive PNB. It means that the scalars come from the fifth components of 5D gauge bosons [8,11,12,25,27] and/or directly from the bulk [13,26,27].…”

“…In the paper [3], special conditions of Scherk-Schwarz mechanism are utilized to resolve the problem of breaking the SU(6) GUT. The trivial and the non-trivial breaking pattern are simultaneously realized by compactification of orbifold S 1 /Z 2 in 5-dimensional (5D) SU (6), not like the trivial the (pseudo) non-trivial condition generates the scalar bosons.…”

“…The trivial and the non-trivial breaking pattern are simultaneously realized by compactification of orbifold S 1 /Z 2 in 5-dimensional (5D) SU (6), not like the trivial the (pseudo) non-trivial condition generates the scalar bosons. The condition facilitates for the periodic 5D scalar [3,11,12,13,26] with extra-dimensional local and global symmetry for small extra dimension in the so-called near-brane area [3,8,35]. Here, in the near-brane area, the first (trivial) symmetry breaking of 5D SU(6)→ 4D SU(6) is triggered by ScherkSchwarz mechanism and followed by trivial and pseudo non-trivial Orbifold breaking [3,23,26] to produce SU(6)-origin would-be Little (Baby) Higgs scalar as the origin of SU(6) will-be-SimplestLittleHiggs and SU(6) Baby Higgs scalars successively [3].…”