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# Georgi-Glashow model

In particle physics, the Georgi-Glashow model is a particular grand unification theory (GUT) proposed by Howard Georgi and Sheldon Glashow in 1974. In this model the standard model gauge groups SU(3)×SU(2)×U(1) are combined into a single simple gauge group -- SU(5). The unified group SU(5) is then thought to be spontaneously broken to the standard model subgroup at some high energy scale called the grand unification scale.

Since the Georgi-Glashow model combines leptons and quarks into single irreducible representations there exist interactions which do not conserve baryon number. This yields a mechanism for proton decay, and the rate of proton decay can be predicted from the dynamics of the model. However, proton decay has not yet been observed experimentally, and the resulting lower limit on the lifetime of the proton contradicts the predictions of this model. However, the elegance of the model has led particle physicists to use it as the foundation for more complex models which yield longer proton lifetimes.

This model suffers from the doublet-triplet splitting problem.

## Breaking SU(5)

SU(5) breaking occurs when a scalar field, analogous to the Higgs field, and transforming in the adjoint of SU(5) acquires a vacuum expectation value proportional to the hypercharge generator

$Y=\operatorname{diag}\left(1/2, 1/2, -1/3, -1/3, -1/3\right)$

When this occurs SU(5) is spontaneously broken to the subgroup of SU(5) commuting with the group generated by Y. This unbroken subgroup is just the standard model group: [SU(3)×SU(2)×U(1)]/Z6.

Under the unbroken subgroup the adjoint 24 transforms as

$24\rightarrow (8,1)_0\oplus (1,3)_0\oplus (1,1)_0\oplus (3,2)_{\frac{5}{6}}\oplus (\bar{3},2)_{-\frac{5}{6}}$

giving the gauge bosons of the standard model. See restricted representation.

The standard model quarks and leptons fit neatly into representations of SU(5). Specifically, the left-handed fermions combine into 3 generations of $\mathbf{\bar{5}}\oplus\mathbf{10}\oplus\mathbf{1}$. Under the unbroken subgroup these transform as

$\bar{5}\rightarrow (\bar{3},1)_{\frac{1}{3}}\oplus (1,2)_{-\frac{1}{2}}$
$10\rightarrow (3,2)_{\frac{1}{6}}\oplus (\bar{3},1)_{-\frac{2}{3}}\oplus (1,1)_1$
$1\rightarrow (1,1)_0$

giving precisely the left-handed fermionic content of the standard model. Note that fermions transforming as a 1 under SU(5) are now thought to be necessary because of the evidence for neutrino oscillations. Actually though, it is possible for there to be only left handed neutrinos without any right handed neutrinos if we could somehow introduce a tiny Majorana coupling for the left handed neutrinos.

Since the homotopy group

$\pi_2\left(\frac{SU(5)}{[SU(3)\times SU(2)\times U(1)]/\mathbb{Z}_6}\right)=\mathbb{Z}$

this model predicts magnetic monopoles.

## Matter parity

To prevent unwanted couplings in the supersymmetric version of the model, we assign a Z2 matter parity to the chiral superfields with the matter fields having odd parity and the Higgs having even parity. This is unnecessary in the nonsupersymmetric version, but then, we can't protect the electroweak Higgs from quadratic radiative mass corrections. See hierarchy problem.

## References

• Howard Georgi and Sheldon Glashow, Unity of All Elementary-Particle Forces, Physical Review Letters, 32 (1974) 438.
03-10-2013 05:06:04
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