Predictive Non-Minimal SU(5) GUT

Abstract

Breaking of $SU(5)$ down to the Standard Model gauge group can be implemented by any non-trivial self-conjugate scalar representation with a suitable vacuum expectation value. The Georgi-Glashow model accomplishes this breaking with a 24-dimensional representation. That choice, although the most economical one, fails to unify the gauge coupling constants. Moreover, subsequent breaking of the Standard Model down to $SU(3) \times U(1)_\mathrm{em}$ with a $5$-dimensional representation fails to simultaneously provide viable masses for the down-type quarks and the charged leptons. We show that the substitution of the $24$-dimensional representation with a $75$-dimensional representation fixes the gauge coupling unification issue outrightly. We furthermore pin down, by computing the full mass spectrum of the multiplets in $75$-dimensional representation, the range of the unification scale $m_{\rm GUT}$ to be $10^{15}\,\text{GeV} \lesssim m_{\rm GUT} \lesssim 10^{16}\,\text{GeV}$. This unification window is partially excluded by Super-Kamiokande data and will be experimentally accessible at Hyper-Kamiokande. The second issue with the Georgi-Glashow model can be addressed, for example, with vectorlike fermions. The $24$-dimensional scenario admits three different types of vectorlike fermions that can properly account for the mismatch between the down-type quark and the charged lepton masses. The $75$-dimensional scenario, on the other hand, offers enhanced predictivity by allowing only a unique vectorlike addition of $10_F + \overline{10}_F$ that restores realistic charged fermion masses and modestly pushes the upper limit on the unification scale to $m_{\rm GUT} \lesssim 3\times10^{16}\,\text{GeV}$. The proposed framework with $75$-dimensional scalar representation can thus serve as a phenomenologically viable alternative to the standard Georgi-Glashow symmetry breaking paradigm.