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

Abstract

We reemphasize the strong dependence of the branching ratios B(K + → π + ν ν) and B(K L → π 0 ν ν) on |V cb | that is stronger than in rare B decays, in particular for K L → π 0 ν ν. 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 forWe use as basic CKM parameters V us , |V cb | and the angles β and γ in the unitarity triangle (UT) with the latter two determined through the measurements of tree-level B decays. This avoids the use of the problematic |V ub |. A ratio involving B(K + → π + ν ν) and B(B s → µ + 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 + → K + ν ν) and B(B s → µ + 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 , ∆M d and ∆M s finding tensions between these three determinations of |V cb | within the SM. We point out that from ∆M s and S ψK S alone one finds |V cb | = 41.7(6) × 10 −3 and |V ub | = 3.64(12) × 10 −3 . We stress the importance of a precise measurement of γ.

Loopy Determinations of $V_{ub}$ and $V_{cb}$

“…We first focus on the meson oscillation observables, K , ∆M d , ∆M s , and sin(2β) as discussed in sections III A and III B. In Figure 2 we show the individual 1σ and 2σ constraints also agree very well with the ones recently found in [26].…”

“…For the CKM angle γ, we use the HFLAV average γ = (66.1 +3.4 −3.6 ) • [38], which is dominated by the precise LHCb results from [67] (see also the very recent update [68]). The importance of precise determinations of γ has recently been emphasized also in [26,69]. By profiling over γ we arrive at best fit contours in the |V cb | -|V ub | plane.…”

“…Combining (25) with (26) We use the experimental world average of the branching ratios that has been determined in [56], based on the most recent experimental results on B s → µ + µ − and B 0 → µ + µ − from the LHCb, ATLAS, and CMS collaborations [57-60]…”

“…Improving the theoretical description of inclusive and exclusive b → c ν and b → u ν decays is thus of high priority (see [10][11][12][13][14][15][16][17][18][19][20][21][22][23] for recent progress). Alternatively, one can focus on combinations of loop observables that are independent of V cb and/or V ub as emphasized for example in [24][25][26].…”

Exclusive determinations of $\vert V_{cb} \vert$ and $R(D^{*})$ through unitarity

“…[7] and more recently in Ref. [8]. The DM method allows also to predict the ratio R(D * ) from theory, obtaining R(D * ) = 0.269 ± 0.008, which is compatible with the experimental world average R(D * ) = 0.295±0.011±0.008 [9] at the ∼ 1.6σ level.…”