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Effect of an RRRR dimension 5 operator on the proton decay in the minimal SU(5) SUGRA GUT model

Toru Goto, Takeshi Nihei

TL;DR

This work reevaluates proton decay in the minimal SU(5) SUGRA GUT by incorporating the Higgsino-dressed $RRRR$ dimension-5 operator. The authors show that the $RRRR$ contribution can dominate the $p \rightarrow K^+ \overline{\nu}_{\tau}$ channel, especially at large $\tan\beta$, and that adjusting relative phases alone cannot suppress both the $\nu_{\tau}$ and $\nu_{\mu}$ channels, leading to stronger bounds on the colored Higgs mass $M_C$ and sfermion masses $m_{\tilde f}$ from Super-Kamiokande. They perform a comprehensive numerical analysis including all dressing diagrams and flavor mixings, concluding that the minimal model is strongly constrained (and in some parameter regions excluded) when $\tan\beta$ is around 2.5, with $M_C$ needing to exceed about $6.5\times10^{16}$ GeV for $m_{\tilde f}<1$ TeV or $m_{\tilde f}>2.5$ TeV for $M_C<2.5\times10^{16}$ GeV. The results underscore the importance of $RRRR$ effects in evaluating GUT-scale proton decay and their impact on viability of SUSY GUTs with light superpartners.

Abstract

We reanalyze the proton decay in the minimal SU(5) SUGRA GUT model. Unlike previous analyses, we take into account a Higgsino dressing diagram of dimension 5 operator with right-handed matter fields ($RRRR$ operator). It is shown that this diagram gives a dominant contribution for $p\to K^+\barν_τ$ over that from $LLLL$ operator, and decay rate of this mode can be comparable with that of $p\to K^+\barν_μ$ which is dominated by the $LLLL$ contribution. It is found that we cannot reduce both the decay rate of $p\to K^+\barν_τ$ and that of $p\to K^+\barν_μ$ simultaneously by adjusting relative phases between Yukawa couplings at colored Higgs interactions. Constraints on the colored Higgs mass $M_C$ and a typical squark and slepton mass $m_{\tilde{f}}$ from Super-Kamiokande limit become considerably stronger due to the Higgsino dressing diagram of the $RRRR$ operator: $M_C > 6.5 \times 10^{16}\gev$ for $m_{\tilde{f}} < 1 \tev$, and $m_{\tilde{f}} > 2.5 \tev$ for $M_C < 2.5 \times 10^{16} \gev$.

Effect of an RRRR dimension 5 operator on the proton decay in the minimal SU(5) SUGRA GUT model

TL;DR

This work reevaluates proton decay in the minimal SU(5) SUGRA GUT by incorporating the Higgsino-dressed dimension-5 operator. The authors show that the contribution can dominate the channel, especially at large , and that adjusting relative phases alone cannot suppress both the and channels, leading to stronger bounds on the colored Higgs mass and sfermion masses from Super-Kamiokande. They perform a comprehensive numerical analysis including all dressing diagrams and flavor mixings, concluding that the minimal model is strongly constrained (and in some parameter regions excluded) when is around 2.5, with needing to exceed about GeV for TeV or TeV for GeV. The results underscore the importance of effects in evaluating GUT-scale proton decay and their impact on viability of SUSY GUTs with light superpartners.

Abstract

We reanalyze the proton decay in the minimal SU(5) SUGRA GUT model. Unlike previous analyses, we take into account a Higgsino dressing diagram of dimension 5 operator with right-handed matter fields ( operator). It is shown that this diagram gives a dominant contribution for over that from operator, and decay rate of this mode can be comparable with that of which is dominated by the contribution. It is found that we cannot reduce both the decay rate of and that of simultaneously by adjusting relative phases between Yukawa couplings at colored Higgs interactions. Constraints on the colored Higgs mass and a typical squark and slepton mass from Super-Kamiokande limit become considerably stronger due to the Higgsino dressing diagram of the operator: for , and for .

Paper Structure

This paper contains 15 sections, 18 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Dimension 5 operators in the minimal SU(5) SUGRA GUT
  3. $RRRR$ contribution to the proton decay
  4. Numerical results
  5. Conclusions
  6. Formulas for the calculation of the nucleon decay
  7. MSSM part
  8. Superpotential
  9. Soft SUSY breaking terms
  10. Mass matrices
  11. Interaction Lagrangian in mass basis
  12. Formulas specific to the nucleon decay
  13. Dimension five operators
  14. Effective interactions
  15. Nucleon partial decay widths

Figures (5)

  • Figure 1: Higgsino dressing diagram which gives a dominant contribution to the $p\rightarrow K^+ \overline{\nu}_\tau$ mode. The circle represents the $RRRR$ dimension 5 operator. We also have a similar diagram for $(u_R s_R)(d_L \nu_{\tau L})$.
  • Figure 2: Decay rates $\Gamma(p\rightarrow K^+ \overline{\nu}_i)$ ($i$$=$$e$, $\mu$ and $\tau$) as functions of the phase $\phi_{23}$ for $\tan \beta$$=2.5$. The other phase $\phi_{13}$ is fixed at $210^\circ$. The CKM phase is taken as $\delta_{13}=90^\circ$. We fix the soft SUSY breaking parameters as $m_0$$=$$1 \,{\rm TeV}$, $M_{gX}$$=$$125 \,{\rm GeV}$ and $A_X$$=0$. The sign of the supersymmetric Higgsino mass $\mu$ is taken to be positive. The colored Higgs mass $M_C$ and the heavy gauge boson mass $M_V$ are assumed as $M_C$$=$$M_V$$=$$2 \times 10^{16} \,{\rm GeV}$. The horizontal lower line corresponds to the Super-Kamiokande limit $\tau(p\rightarrow K^+ \overline{\nu})$$>$$5.5 \times 10^{32}$ years, and the horizontal upper line corresponds to the Kamiokande limit $\tau(p\rightarrow K^+ \overline{\nu})$$>$$1.0 \times 10^{32}$ years.
  • Figure 3: Contour plot for the partial lifetime $\tau(p\rightarrow K^+ \overline{\nu})$ in the $\phi_{13}$-$\phi_{23}$ plane. The contributions of three modes $K^+ \overline{\nu}_e$, $K^+ \overline{\nu}_\mu$ and $K^+ \overline{\nu}_\tau$ are included. We use the same parameters as that in Fig. \ref{['fig:phi23']}. The maximum value of the contour is less than $0.5 \times 10^{32}$ years.
  • Figure 4: Lower bound on the colored Higgs mass $M_C$ as a function of the left-handed scalar up-quark mass $m_{\tilde{u}_L}$. The soft breaking parameters $m_0$, $M_{gX}$ and $A_X$ are scanned within the range of $0<m_0<3 \,{\rm TeV}$, $0<M_{gX}<1 \,{\rm TeV}$ and $-5<A_X<5$, and $\tan \beta$ is fixed at 2.5. Both signs of $\mu$ are considered. The whole parameter region of the two phases $\phi_{13}$ and $\phi_{23}$ is examined. The solid curve represents the bound derived from the Super-Kamiokande limit $\tau(p\rightarrow K^+ \overline{\nu})$$>$$5.5 \times 10^{32}$ years, and the dashed curve represents the corresponding result without the $RRRR$ effect. Left-hand side of the vertical dotted line is excluded by other experimental constraints. The dash-dotted curve represents the bound derived from the Kamiokande limit on the neutron partial lifetime $\tau (n\rightarrow K^0 \overline{\nu})$$>$$0.86 \times 10^{32}$ years.
  • Figure 5: The lower bound on the colored Higgs mass $M_C$ obtained from the Super-Kamiokande limit as a function of $\tan \beta$. The phase matrix $P$ is fixed by $\phi_{13}$$=210^\circ$ and $\phi_{23}$$=150^\circ$. The region below the solid curve is excluded if the left-handed scalar up-quark mass $m_{\tilde{u}_L}$ is less than $1 \,{\rm TeV}$. The lower bound reduces to the dashed curve if we allow $m_{\tilde{u}_L}$ up to $3 \,{\rm TeV}$. The result in the case where we ignore the $RRRR$ effect is shown by the dotted curve for $m_{\tilde{u}_L}$$<$$1 \,{\rm TeV}$.