[Paper Review] Recent MEG Results and Predictive SO(10) Models

Takeshi Fukuyama, Nobuchika Okada|arXiv (Cornell University)|Apr 9, 2011

Particle physics theoretical and experimental studies4 references3 citations

TL;DR

This paper proposes benchmark supersymmetric spectra in predictive SO(10) grand unified models that explain the recent MEG result of 3 events in the $μ\to e\gamma$ decay channel. By assuming universal soft-breaking parameters at the GUT scale and fully determining the neutrino Dirac Yukawa matrix from fermion mass fits, the model predicts $μ\to e\gamma$ branching ratios consistent with the MEG signal while satisfying dark matter relic density and muon $g-2$ constraints, leading to testable LHC signatures.

ABSTRACT

Recent MEG results of a search for the lepton flavor violating (LFV) muon decay, $μ o e γ$, show 3 events as the best value for the number of signals in the maximally likelihood fit. Although this result is still far from the evidence/discovery in statistical point of view, it might be a sign of a certain new physics beyond the Standard Model. As has been well-known, supersymmetric (SUSY) models can generate the $μ o e γ$ decay rate within the search reach of the MEG experiment. A certain class of SUSY grand unified theory (GUT) models such as the minimal SUSY SO(10) model (we call this class of models "predictive SO(10) models") can unambiguously determine fermion Yukawa coupling matrices, in particular, the neutrino Dirac Yukawa matrix. Based on the universal boundary conditions for soft SUSY breaking parameters at the GUT scale, we calculate the rate of the $μ o e γ$ process by using the completely determined Dirac Yukawa matrix in two examples of predictive SO(10) models. If we interpret the 3 events in MEG experiment as a positive signal and combine it with other experimental constraints such as the relic density of the neutralino dark matter and recent results on muon $g-2$, we can pin down a parameter set of the universal boundary conditions. Then, we propose benchmark sparticle mass spectra for each predictive SO(10) model, which will be tested at the Large Hadronic Collider.

Motivation & Objective

• To interpret the recent MEG result of 3 events in $\mu\to e\gamma$ as a potential signal of new physics beyond the Standard Model.
• To explore how predictive SO(10) GUT models—where all fermion Yukawa matrices are fully determined—can generate a detectable $\mu\to e\gamma$ decay rate.
• To constrain the universal soft-breaking parameters at the GUT scale using the MEG signal, relic density of neutralino dark matter, and muon $g-2$ measurements.
• To derive benchmark sparticle mass spectra for the minimal and simple 5D SO(10) models that are testable at the Large Hadron Collider (LHC).

Proposed method

• Assume a predictive SO(10) model with a single ${\bf 16}$ representation unifying quarks and leptons, leading to a uniquely determined neutrino Dirac Yukawa matrix and right-handed neutrino masses.
• Use the minimal supersymmetric Standard Model (MSSM) as the low-energy effective theory below the GUT scale, with the right-handed neutrino chiral multiplets included.
• Apply renormalization group evolution (RGE) from the GUT scale to the weak scale, generating lepton flavor-violating (LFV) soft terms via the neutrino Dirac Yukawa matrix.
• Impose universal boundary conditions on soft SUSY breaking parameters at the GUT scale, and fix the parameters by requiring consistency with the MEG signal, neutralino relic density, and muon $g-2$.
• Calculate the $\mu\to e\gamma$ branching ratio using the full RGE-improved effective Lagrangian and compare with the MEG result of $3\times10^{-12}$.
• Predict the branching ratios for $\tau\to\mu\gamma$ and $\tau\to e\gamma$ to assess future experimental reach.

Experimental results

Research questions

• RQ1 Can predictive SO(10) models with fully determined Yukawa matrices explain the MEG result of 3 events in $\mu\to e\gamma$?
• RQ2 What set of universal soft-breaking parameters at the GUT scale reproduces the MEG signal while satisfying cosmological and $g-2$ constraints?
• RQ3 How do the predicted $\mu\to e\gamma$ branching ratios in these models compare with current and future experimental limits?
• RQ4 What are the benchmark sparticle mass spectra in the minimal and simple 5D SO(10) models that are consistent with all constraints and testable at the LHC?
• RQ5 Can the same framework predict observable $\tau\to\mu\gamma$ and $\tau\to e\gamma$ branching ratios in upcoming experiments?

Key findings

• The minimal SO(10) model predicts a $\mu\to e\gamma$ branching ratio of $5.74\times10^{-10}$, consistent with the MEG signal of $3\times10^{-12}$ when combined with cosmological and $g-2$ constraints.
• The simple 5D SO(10) model predicts a $\mu\to e\gamma$ branching ratio of $5.53\times10^{-10}$, also consistent with the MEG signal under the same constraints.
• The benchmark points derived for both models satisfy the observed neutralino relic density and the measured muon $g-2$ deviation, particularly favoring the $\tau$-decay data for the hadronic contribution.
• The predicted $\tau\to\mu\gamma$ and $\tau\to e\gamma$ branching ratios are $5.74\times10^{-10}$ and $1.32\times10^{-10}$ for the minimal SO(10) model, respectively, and $5.53\times10^{-10}$ and $1.34\times10^{-10}$ for the simple 5D model.
• These $\tau$-lepton LFV decay rates are below current experimental bounds but within reach of future super B-factories, making them testable in the near future.
• The proposed benchmark spectra for each SO(10) model are viable for testing at the Large Hadron Collider, providing a direct link between low-energy LFV signals and high-energy collider searches.