Flipped SU(5) GUT phenomenology: proton decay and $$\mathbf {g_\mu - 2}$$
John Ellis, Jason L. Evans, Natsumi Nagata, Dimitri V. Nanopoulos, Keith A. Olive
Abstract
Abstract We consider proton decay and $$g_\mu - 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>g</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> in flipped SU(5) GUT models. We first study scenarios in which the soft supersymmetry-breaking parameters are constrained to be universal at some high scale $$M_{in}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mrow> <mml:mi>in</mml:mi> </mml:mrow> </mml:msub> </mml:math> above the standard GUT scale where the QCD and electroweak SU(2) couplings unify. In this case the proton lifetime is typically $$ > rsim 10^{36}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≳</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>36</mml:mn> </mml:msup> </mml:mrow> </mml:math> years, too long to be detected in the foreseeable future, and the supersymmetric contribution to $$g_\mu - 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>g</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> is too small to contribute significantly to resolving the discrepancy between the experimental measurement and data-driven calculations within the Standard Model. However, we identify a region of the constrained flipped SU(5) parameter space with large couplings between the 10- and 5-dimensional GUT Higgs representations where $$p \rightarrow e^+ \pi ^0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>π</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:mrow> </mml:math> decay may be detectable in the Hyper-Kamiokande experiment now under construction, though the contribution to $$g_\mu -2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>g</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> is still small. A substantial contribution to $$g_\mu - 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>g</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> is possible, however, if the universality constraints on the soft supersymmetry-breaking masses are relaxed. We find a ‘quadrifecta’ region where observable proton decay co-exists with a (partial) supersymmetric resolution of the $$g_\mu - 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>g</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> discrepancy and acceptable values of $$m_h$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>h</mml:mi> </mml:msub> </mml:math> and the relic LSP density.