[Paper Review] Searching for New Physics in Rare $K$ and $B$ Decays without $|V_{cb}|$ and $|V_{ub}|$ Uncertainties

Andrzej J. Buras, Elena Venturini|arXiv (Cornell University)|Sep 22, 2021

Particle physics theoretical and experimental studies5 citations

TL;DR

This paper proposes a method to search for new physics in rare kaon and B decays by constructing $|V_{cb}|$-independent ratios of branching ratios, eliminating uncertainties from the problematic $|V_{cb}|$ determination. It demonstrates that ratios involving $\mathcal{B}(K^+\to\pi^+\nu\bar{\nu})$ and $\overline{\mathcal{B}}(B_s\to\mu^+\mu^-)$ are sensitive to the CKM angle $\gamma$ and exhibit a $1.8\sigma$ tension with the SM, while providing the most precise SM predictions for rare kaon decays: $\mathcal{B}(K^+\to\pi^+\nu\bar{\nu})_{\text{SM}} = (8.60\pm 0.42)\times 10^{-11}$ and $\mathcal{B}(K_L\to\pi^0\nu\bar{\nu})_{\text{SM}} = (2.94\pm 0.15)\times 10^{-11}$, with only $\beta$-dependent uncertainty.

ABSTRACT

We reemphasize the strong dependence of the branching ratios $B(K^+ oπ^+ν\barν)$ and $B(K_L oπ^0ν\barν)$ on $|V_{cb}|$ that is stronger than in rare $B$ decays, in particular for $K_L oπ^0ν\barν$. Thereby the persistent tension between inclusive and exclusive determinations of $|V_{cb}|$ weakens the power of these theoretically clean decays in the search for new physics (NP). We demonstrate how this uncertainty can be practically removed by considering within the SM suitable ratios of the two branching ratios between each other and with other observables like the branching ratios for $K_S oμ^+μ^-$, $B_{s,d} oμ^+μ^-$ and $B o K(K^*)ν\barν$. We use as basic CKM parameters $V_{us}$, $|V_{cb}|$ and the angles $β$ and $γ$ in the unitarity triangle (UT). This avoids the use of the problematic $|V_{ub}|$. A ratio involving $B(K^+ oπ^+ν\barν)$ and $B(B_s oμ^+μ^-)$ while being $|V_{cb}|$-independent exhibits sizable dependence on the angle $γ$. It should be of interest for several experimental groups in the coming years. We point out that the $|V_{cb}|$-independent ratio of $B(B^+ o K^+ν\barν)$ and $B(B_s oμ^+μ^-)$ from Belle II and LHCb signals a $1.8σ$ tension with its SM value. As a complementary test of the Standard Model, we propose to extract $|V_{cb}|$ from different observables as a function of $β$ and $γ$. We illustrate this with $ε_K$, $ΔM_d$ and $ΔM_s$ finding tensions between these three determinations of $|V_{cb}|$ within the SM. From $ΔM_s$ and $S_{ψK_S}$ alone we find $|V_{cb}|=41.8(6) imes 10^{-3}$ and $|V_{ub}|=3.65(12) imes 10^{-3}$. We stress the importance of a precise measurement of $γ$. We obtain most precise SM predictions for considered branching ratios of rare K and B decays to date.

Motivation & Objective

• To address the persistent tension in $|V_{cb}|$ determinations (inclusive vs. exclusive) that undermines the theoretical cleanliness of rare $K$ and $B$ decays in new physics searches.
• To eliminate $|V_{cb}|$ uncertainty by constructing ratios of branching ratios involving $K^+\to\pi^+\nu\bar{\nu}$, $K_L\to\pi^0\nu\bar{\nu}$, $K_S\to\mu^+\mu^-$, $B_{s,d}\to\mu^+\mu^-$, and $B\to K^{(*)}\nu\bar{\nu}$.
• To provide $|V_{cb}|$-independent SM predictions for rare kaon decays using $\beta$, $\gamma$, and $V_{us}$, with only CKM uncertainty from $\beta$, which is precisely known.
• To test the consistency of the SM by comparing $|V_{cb}|$ extracted from $\varepsilon_K$, $\Delta M_d$, and $\Delta M_s$, revealing tensions within the SM.

Proposed method

• The authors use a parametrization of the unitarity triangle with $V_{us}$, $|V_{cb}|$, and angles $\beta$ and $\gamma$, avoiding the problematic $|V_{ub}|$.
• They construct $|V_{cb}|$-independent ratios, such as $\mathcal{B}(K^+\to\pi^+\nu\bar{\nu}) / \overline{\mathcal{B}}(B_s\to\mu^+\mu^-)$, which depend on $\gamma$ and are sensitive to new physics.
• They derive $|V_{cb}|$ from $\varepsilon_K$, $\Delta M_d$, and $\Delta M_s$ as functions of $\beta$ and $\gamma$, revealing internal tensions in the SM.
• They compute the SM branching ratios for $K^+\to\pi^+\nu\bar{\nu}$ and $K_L\to\pi^0\nu\bar{\nu}$ using only $\beta$-dependent uncertainty, achieving the most precise predictions to date.
• They use NLO QCD and electroweak corrections in the calculation of Wilson coefficients, with updated values for $m_t(m_t)$ and $\eta_{\text{eff}}$, ensuring high accuracy.
• They validate the method by showing that the $|V_{cb}|$-independent ratio $\mathcal{B}(B^+\to K^+\nu\bar{\nu}) / \overline{\mathcal{B}}(B_s\to\mu^+\mu^-)$ exhibits a $1.8\sigma$ tension with the SM.

Experimental results

Research questions

• RQ1 Can $|V_{cb}|$-dependent uncertainties in rare $K$ and $B$ decays be eliminated to improve new physics sensitivity?
• RQ2 What $|V_{cb}|$-independent ratios of branching ratios are most sensitive to the CKM angle $\gamma$?
• RQ3 Does the observed $1.8\sigma$ tension in the $B^+\to K^+\nu\bar{\nu}$ to $B_s\to\mu^+\mu^-$ ratio indicate new physics?
• RQ4 Are the $|V_{cb}|$ values extracted from $\varepsilon_K$, $\Delta M_d$, and $\Delta M_s$ consistent within the SM?
• RQ5 What is the most precise $|V_{cb}|$-independent prediction for $\mathcal{B}(K^+\to\pi^+\nu\bar{\nu})$ and $\mathcal{B}(K_L\to\pi^0\nu\bar{\nu})$?

Key findings

• The $|V_{cb}|$-independent ratio $\mathcal{B}(K^+\to\pi^+\nu\bar{\nu}) / \overline{\mathcal{B}}(B_s\to\mu^+\mu^-)$ exhibits a $1.8\sigma$ tension with the SM prediction, suggesting a potential signal of new physics.
• The most precise $|V_{cb}|$-independent SM prediction for $\mathcal{B}(K^+\to\pi^+\nu\bar{\nu})$ is $(8.60\pm 0.42)\times 10^{-11}$, with uncertainty only from $\beta$, which is precisely known.
• The most precise $|V_{cb}|$-independent SM prediction for $\mathcal{B}(K_L\to\pi^0\nu\bar{\nu})$ is $(2.94\pm 0.15)\times 10^{-11}$, with uncertainty only from $\beta$.
• The $|V_{cb}|$ values extracted from $\varepsilon_K$, $\Delta M_d$, and $\Delta M_s$ show internal tensions within the SM, indicating possible inconsistencies.
• Using $\Delta M_s$ and $S_{\psi K_S}$, the authors extract $|V_{cb}|=41.8(6)\times 10^{-3}$ and $|V_{ub}|=3.65(12)\times 10^{-3}$, independent of $|V_{cb}|$ and $\gamma$, under the assumption of no new physics in $\varepsilon_K$ and $S_{\psi K_S}$.