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Hattori, Chuichiro; Matsunaga, Mamoru; Matsuoka, Takeo

doi:10.1103/physrevd.83.015009

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…This result gives no practical significance to the SM physics, except for predictions about exotic matter fields, which have already been given in Ref. [2]. However, the reasoning given here will serve the study of beyond-SM gauge groups and matter contents.…”

mentioning

confidence: 59%

Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic toSU(3)c×SU(
Hashimoto
¹
,
Matsunaga
²
,
Yamamoto
³

2013
Phys. Rev. D
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mentioning

confidence: 59%

Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic toSU(3)c×SU(
Hashimoto
¹
,
Matsunaga
²
,
Yamamoto
³

2013
Phys. Rev. D
Self Cite
1
0
1
0
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“…the latter of which is shown to be isomorphic to G ′ SM in Ref. [2]. They are, in fact, isomorphic to each other.…”

mentioning

confidence: 85%

Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic to SU(3)_c X SU(2)_L X U(1)_Y

Hashimoto,

Matsunaga,

Yamamoto

2013

Preprint

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In the Standard Model the hypercharges of quarks and leptons are not determined by the gauge group itself. In a recent paper [C. Hattori et al. Phys. Rev. D 83, 015009 (2011)] it is shown that, if the direct product gauge group G SM is slightly modified to the semidirect product group G ′ SM , hypercharges are restricted to quantized values as n/6 mod Z (n = 0, 1, 3, 4). In this brief paper, we examine all of the compact Lie groups locally isomorphic to G SM , and show that G ′ SM (or its isomorphisms) is the unique possibility that yields the correct hypercharge quantization.

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“…The extra factor group 2 resolves some shortcomings of the model, and it can be viewed as a D3 − D7 brane system in type IIB supergravity. The semi-direct product group (SU(3) C × SU(2) L ) ⋊ U(1) Y and anomaly cancellation were used by [15] to put constraints on matter field hypercharge. As evidenced by the literature, it is possible to construct interesting models with extra U(1) factors.…”

Section: Introductionmentioning

confidence: 99%

The Three Faces of $U(3)$

LaChapelle¹

2022

Preprint

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SU(3) × U (1) as a gauge symmetry is known to be phenomenologically problematic unless the U (1) factor lives in a "dark" or "hidden" sector. By contrast, U (3) is a semi-direct product group that is characterized by non-trivial homomorphisms mapping U (1) into the automorphism group of SU (3). Since the semi-direct product includes mutual coupling among all gauge field mass-energy, U (3) at least has a chance of being phenomenologically sensible as a gauge symmetry outside of any dark or hidden sector. For U (3), there are three different non-trivial homomorphisms that induce three separate defining representations. In a toy model of U (3) Yang-Mills (endowed with a suitable inner product) coupled to massive fermions, this renders three distinct covariant derivatives acting on a single matter field. By employing a mod 3 permutation of the vector space carrying the defining representation induced by a "large" gauge transformation, the three covariant derivatives and one matter field can alternatively be expressed as a single covariant derivative acting on three distinct species of matter fields possessing the same U (3) quantum numbers but different renormalized masses. One can interpret this as three generations of matter fields.

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Semidirect product gauge group[SU(3)c×SU(2)L

Cited by 5 publications

References 11 publications

Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic toSU(3)c×SU(
Hashimoto
¹
,
Matsunaga
²
,
Yamamoto
³

2013
Phys. Rev. D
Self Cite
1
0
1
0
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Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic toSU(3)c×SU(
Hashimoto
¹
,
Matsunaga
²
,
Yamamoto
³

2013
Phys. Rev. D
Self Cite
1
0
1
0
View full text Add to dashboard Cite

Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic to SU(3)_c X SU(2)_L X U(1)_Y

The Three Faces of $U(3)$

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Semidirect product gauge group[SU(3)c×SU(2)L

Cited by 5 publications

References 11 publications

Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic toSU(3)c×SU(Hashimoto1, Matsunaga2, Yamamoto3 2013Phys. Rev. DSelf Cite1010View full textAdd to dashboardCite

Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic toSU(3)c×SU(Hashimoto1, Matsunaga2, Yamamoto3 2013Phys. Rev. DSelf Cite1010View full textAdd to dashboardCite

Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic to SU(3)_c X SU(2)_L X U(1)_Y

The Three Faces of $U(3)$

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Product

Resources

About

Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic toSU(3)c×SU(
Hashimoto
¹
,
Matsunaga
²
,
Yamamoto
³

2013
Phys. Rev. D
Self Cite
1
0
1
0
View full text Add to dashboard Cite

Quantization of hypercharge in gauge groups locally isomorphic but globally nonisomorphic toSU(3)c×SU(
Hashimoto
¹
,
Matsunaga
²
,
Yamamoto
³

2013
Phys. Rev. D
Self Cite
1
0
1
0
View full text Add to dashboard Cite