General CP Violation in Minimal Left-Right Symmetric Model and Constraints on the Right-Handed Scale (0712.4218v1)

Abstract: In minimal left-right symmetric theories, the requirement of parity invariance allows only one complex phase in the Higgs potential and one in the Yukawa couplings, leading to a two-phase theory with both spontaneous and explicit CP violations. We present a systematic way to solve the right-handed quark mixing matrix analytically in this model and find that the leading order solution has the same hierarchical structure as the left-handed CKM matrix with one more CP-violating phase coming from the complex Higgs vev. Armed with this explicit right-handed mixing matrix, we explore its implications for flavor changing and conserving processes in detail, low-energy CP-violating observables in particular. We report an improved lower bound on the $W_R$ mass of 2.5 TeV from $\Delta M_K$ and $\Delta M_{B}$, and a somewhat higher bound (4 TeV) from kaon decay parameters $\epsilon$, $\epsilon'$, and neutron electric dipole moment. The new bound on the flavor-changing neutral Higgs mass is 25 TeV.

• The paper presents an analytical approach solving the right-handed quark mixing matrix to reveal novel CP violation effects.
• It derives improved lower bounds of 2.5 TeV for the right-handed gauge boson and 25 TeV for flavor-changing neutral Higgs masses using updated lattice QCD data.
• The results refine CP violation understanding in kaon and B-meson systems while highlighting significant implications for neutron EDM constraints.

Analysis of CP Violation in the Minimal Left-Right Symmetric Model

The paper presents a comprehensive analysis of charge-parity (CP) violation in the Minimal Left-Right Symmetric Model (MLRSM) and explores its implications for determining constraints on right-handed gauge boson mass ($M_{W_R}$) and flavor-changing neutral Higgs (FCNH) mass ($M_{H}$). The authors address both spontaneous and explicit sources of CP violation, employing an analytical approach to solve the right-handed quark mixing matrix, which reveals novel insights about CP-violating phenomena.

Analytical Framework and Right-Handed Quark Mixing

In this work, the authors focus on the right-handed quark mixing matrix in a generic MLRSM context, highlighting explicit formulas and demonstrating how the new CP violation phases can alter known CKM phenomenology. They utilize a hierarchical structure of quark masses and mixing angles, ensuring their approach remains robust across orders of magnitude in small mixing probabilities and mass ratios. Unique to this analysis is dealing with two CP-violating sources: the conventional Dirac phase from the CKM matrix and a spontaneous CP phase arising from Higgs sector dynamics.

Key Results and Constraints

1. Constraints on $M_{W_R}$:
   • An improved lower bound of 2.5 TeV for the right-handed gauge boson mass is derived from kaon mass mixing measurements. The authors revisit these constraints utilizing updates in lattice QCD parameters, providing an enhanced understanding of low-energy phenomenology in MLRSM.
2. FCNH Contributions:
   • Employing the flavor-changing neutral Higgs mechanism, the authors set a significant lower bound of 25 TeV for the neutral Higgs masses. This is a pivotal improvement over earlier formulations given new constraints derived from modern lattice evaluations.
3. CP Violation in Kaon and B-Meson Systems:
   • Indirect CP violation parameter $\epsilon$ and direct CP violation parameter $\epsilon'$ are extensively analyzed. This leads to refined constraints on $M_{W_R}$ and an estimation of the spontaneous CP phase. A key highlight is the potential cancellation within different CP-violating contributions, rooting from a combined interplay of explicit and spontaneous CP violations.
4. Neutron Electric Dipole Moment (EDM):
   • The neutron EDM bounds offer an indirect yet stringent constraint on $M_{W_R}$, underscoring the necessity of both spontaneous and explicit CP-breaking effects in formulating realistic MLRSM predictions.

Theoretical Implications and Potential Extensions

The nuances of spontaneous and explicit CP-breaking phenomena gleaned from this analysis push theoretical considerations forward, hinting at the need for extended Higgs sectors or more fine-tuned parameter spaces to achieve plausible phenomenological alignment with experimental benchmarks.

The paper also reveals an interplay between various CP-violating observables, suggesting a direction for future investigations. For example, the analytical solution for CP phases offers a clearer window into examining potential B-meson decays or assessing future collider experiments' sensitivity to right-handed gauge interactions.

Conclusion

This paper delivers a critical step in confining the parametric uncertainties inherent in the MLRSM, employing state-of-the-art lattice data and innovative analytical techniques. The evaluation of general CP violations within left-right symmetry models bridges the gap between historical phenomenological challenges and the forefront of high-energy physics. Future research endeavors are expected to leverage these insights, guiding more precise experimental tests and theoretical explorations of non-standard CP-violation mechanisms.