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| {{Multiple issues|
| | Let me initial begin by introducing myself. My name is Boyd Butts even though it is not the title on my beginning certificate. The favorite hobby for my kids and me is to perform baseball but I haven't produced a dime with it. My day occupation is a meter reader. California is our beginning place.<br><br>Feel free to visit my webpage ... [http://chatbook.biz/blogs/post/922 std testing at home] |
| {{technical|date=August 2009}}
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| {{expert-subject|date=July 2009}}
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| {{unreferenced|date=July 2009}}
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| }}
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| '''Flipped SO(10)''' is a [[grand unified theory]] which is to standard [[SO(10) (physics)|'''SO'''(10)]] as [[flipped SU(5)|flipped '''SU'''(5)]] is to [[Georgi-Glashow|'''SU'''(5)]].
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| In conventional '''SO'''(10) models, the fermions lie in three spinorial 16 representations, one for each generation, which decomposes under ['''SU'''(5) × '''U'''(1)<sub>χ</sub>]/'''Z'''<sub>5</sub> as
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| :<math>16 \rightarrow 10_1 \oplus \bar{5}_{-3} \oplus 1_5</math>
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| This can either be the [[Georgi-Glashow]] '''SU'''(5) or flipped '''SU'''(5).
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| In flipped '''SO'''(10) models, however, the gauge group is not just '''SO'''(10) but '''SO'''(10)<sub>F</sub> × '''U'''(1)<sub>B</sub> or ['''SO'''(10)<sub>F</sub> × '''U'''(1)<sub>B</sub>]/'''Z'''<sub>4</sub>. The fermion fields are now three copies of
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| :<math>16_1\oplus 10_{-2} \oplus 1_4</math>
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| These contain the Standard Model fermions as well as additional vector fermions with GUT scale masses. If we suppose ['''SU'''(5) × '''U'''(1)<sub>χ</sub>]/'''Z'''<sub>5</sub> is a subgroup of '''SO'''(10)<sub>F</sub>, then we have the intermediate scale symmetry breaking ['''SO'''(10)<sub>F</sub> × '''U'''(1)<sub>B</sub>]/'''Z'''<sub>5</sub> → ['''SU'''(5) × '''U'''(1)<sub>χ</sub>]/'''Z'''<sub>5</sub> where
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| :<math>\chi=-{A\over 4}+{5B\over 4}</math>
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| In that case,
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| :<math>\begin{align}
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| 16_1&\rightarrow 10_1 \oplus \bar{5}_2 \oplus 1_0 \\
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| 10_{-2}&\rightarrow 5_{-2} \oplus \bar{5}_{-3} \\
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| 1_4 &\rightarrow 1_5
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| \end{align}</math>
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| note that the Standard Model fermion fields (including the [[right handed neutrino]]s) come from all three ['''SO'''(10)<sub>F</sub> × '''U'''(1)<sub>B</sub>]/'''Z'''<sub>5</sub> representations. In particular, they happen to be the 10<sub>1</sub> of 16<sub>1</sub>, the <math>\bar{5}_{-3}</math> of 10<sub>−2</sub> and the 1<sub>5</sub> of 1<sub>4</sub> (my apologies for mixing up '''SO'''(10) × '''U'''(1) notation with '''SU'''(5) × '''U'''(1) notation, but it would be really cumbersome if we have to spell out which group any given notation happens to refer to. It is left up to the reader to determine the group from the context. This is a standard practice in the GUT model building literature anyway).
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| The other remaining fermions are vectorlike. To see this, note that with a 16<sub>1H</sub> and a <math>\overline{16}_{-1H}</math> Higgs field, we can have [[VEV]]s which breaks the GUT group down to ['''SU'''(5) × '''U'''(1)<sub>χ</sub>]/'''Z'''<sub>4</sub>. The [[Yukawa coupling]] 16<sub>1H</sub> 16<sub>1</sub> 10<sub>−2</sub> will pair up the 5<sub>−2</sub> and <math>\bar{5}_2</math> fermions. And we can always introduce a sterile neutrino φ which is invariant under ['''SO'''(10) × '''U'''(1)<sub>B</sub>]/'''Z'''<sub>4</sub> and add the Yukawa coupling
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| :<math><\overline{16}_{-1H}>16_1 \phi</math> | |
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| OR we can add the nonrenormalizable term
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| :<math><\overline{16}_{-1H}><\overline{16}_{-1H}>16_1 16_1</math>
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| Either way, the 1<sub>0</sub> component of the fermion 16<sub>1</sub> gets taken care of so that it is no longer chiral.
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| It has been left unspecified so far whether ['''SU'''(5) × '''U'''(1)<sub>χ</sub>]/'''Z'''<sub>5</sub> is the Georgi-Glashow '''SU'''(5) or the flipped '''SU'''(5). This is because both alternatives lead to reasonable GUT models.
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| One reason for studying flipped '''SO'''(10) is because it can be derived from an '''E'''<sub>6</sub> GUT model.
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| ==References==
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| {{Reflist}}
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| [[Category:Particle physics]]
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Let me initial begin by introducing myself. My name is Boyd Butts even though it is not the title on my beginning certificate. The favorite hobby for my kids and me is to perform baseball but I haven't produced a dime with it. My day occupation is a meter reader. California is our beginning place.
Feel free to visit my webpage ... std testing at home