[Paper Review] The decay $B o K+ν+\barν$ at Belle II and a massless bino in R-parity-violating supersymmetry

Zeren Simon Wang, Herbert K. Dreiner+1 more|arXiv (Cornell University)|Sep 7, 2023

Particle physics theoretical and experimental studiesPhysics and Astronomy3 citations

TL;DR

This paper proposes that the Belle II observation of the rare $B^+ \to K^+ \nu\bar{\nu}$ decay at 3.6σ significance—exceeding the Standard Model prediction by 2.8σ—could be explained by R-parity-violating supersymmetry with a massless bino. The decay proceeds via a tree-level $B^+ \to K^+ \nu\tilde{\chi}_1^0$ process induced by non-zero $\lambda'_{i23}$ or $\lambda'_{i32}$ couplings, with large regions of parameter space accommodating the measurement within 2σ while evading current experimental bounds.

ABSTRACT

Recently, exttt{Belle II} announced evidence for the decay $B^+ o K^+ +ν+\barν$ at the $3.5\,σ$ significance, and measured the corresponding decay branching ratio to be $2.7\,σ$ above the Standard Model prediction. Here, we provide a theoretical explanation based on a massless bino in R-parity-violating (RPV) supersymmetry. With a single non-vanishing RPV coupling $λ'_{i23/i32}$, $λ'_{i13/i33}$, or $λ'_{i12/i22}$, where $i=1,2,3$, the decay $B^+ o K^+ +\overset{\scriptscriptstyle(-)}{ν_i}+ ildeχ^0_1$ can be induced, which would lead to the same signature as $B^+ o K^+ +ν+\barν$. Taking into account both theoretical and experimental uncertainties, we derive the regions of the parameter space spanned by the RPV couplings and sfermion masses that could accommodate the new measurement at various significance levels and obey the existing bounds simultaneously.

Motivation & Objective

• To explain the Belle II observation of $B^+ \to K^+ \nu\bar{\nu}$ at 3.6σ, which exceeds the Standard Model prediction by 2.8σ.
• To investigate whether a massless bino in R-parity-violating supersymmetry can account for the observed branching ratio enhancement.
• To identify viable parameter regions in the RPV coupling and sfermion mass space that simultaneously explain the Belle II measurement and satisfy current experimental constraints.

Proposed method

• Construct an R-parity-violating supersymmetric model with non-zero $\lambda'_{ijk}$ couplings to generate a tree-level $B^+ \to K^+ \nu\tilde{\chi}_1^0$ decay.
• Use effective field theory to integrate out heavy sfermions, deriving an effective four-fermion interaction for the $b \to s \nu\tilde{\chi}_1^0$ transition.
• Compute the decay width $\Gamma(B^+ \to K^+ \nu\tilde{\chi}_1^0)$ for $\lambda'_{i23}$, $\lambda'_{i32}$, $\lambda'_{i13}$, $\lambda'_{i33}$, $\lambda'_{i12}$, and $\lambda'_{i22}$ couplings.
• Include CKM matrix elements to account for flavor suppression in the $\lambda'_{i13}$, $\lambda'_{i33}$, $\lambda'_{i12}$, and $\lambda'_{i22}$ cases.
• Compare the predicted branching ratio to Belle II's measured value $(2.4 \pm 0.7) \times 10^{-5}$, assessing significance levels while incorporating theoretical and experimental uncertainties.
• Apply current experimental bounds on $\lambda'$ couplings to constrain viable parameter space.

Experimental results

Research questions

• RQ1 Can a massless bino in R-parity-violating supersymmetry explain the Belle II observation of $B^+ \to K^+ \nu\bar{\nu}$ at 3.6σ significance?
• RQ2 Which RPV couplings $\lambda'_{ijk}$ can generate a tree-level $B^+ \to K^+ \nu\tilde{\chi}_1^0$ decay that mimics the SM $B^+ \to K^+ \nu\bar{\nu}$ signature?
• RQ3 What regions of the $\lambda'$ coupling and sfermion mass parameter space can simultaneously explain the Belle II measurement within 2σ and satisfy current experimental bounds?
• RQ4 How do CKM suppression effects influence the viability of different $\lambda'$ couplings in explaining the observed branching ratio enhancement?
• RQ5 Can the $\lambda'_{i23}$ and $\lambda'_{i32}$ couplings provide a viable explanation for the Belle II result while remaining consistent with existing constraints?

Key findings

• The $\lambda'_{i23}$ and $\lambda'_{i32}$ couplings yield nearly identical results and can explain the Belle II measurement within 2σ significance for large regions of the parameter space.
• For $\lambda'_{i23}$ and $\lambda'_{i32}$, the $2\sigma$ region of the Belle II measurement is compatible with current experimental bounds on $\lambda'$ couplings, especially when sfermion masses are degenerate and sufficiently heavy.
• The $\lambda'_{i13}$ and $\lambda'_{i33}$ couplings are strongly CKM-suppressed due to small $V_{ts}$, limiting their contributions and requiring large $\lambda'$ values and small sfermion masses to explain the measurement, which are often excluded by current bounds.
• The $\lambda'_{i12}$ and $\lambda'_{i22}$ couplings are also CKM-suppressed, with $\lambda'_{i12}$ requiring $\lambda'$ values more than an order of magnitude larger than current bounds allow, and $\lambda'_{i22}$ only allowing a small region of parameter space compatible with both the measurement and bounds.
• For $\lambda'_{133}$, the current bound on the coupling is orders of magnitude stronger than the $2\sigma$ region, effectively excluding the entire viable parameter space.