Three loop calculations and inclusive $V_{cb}$

Bordone, Marzia; Capdevila, Bernat; Gambino, Paolo

doi:10.48550/arxiv.2107.00604

Cited by 16 publications

(40 citation statements)

References 33 publications

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“…Using our theoretical bands of the FFs we have determined |V cb | from the experimental data and computed R(D * ) from theory. Our final result for |V cb | is |V cb | = (41.3 ± 1.7) • 10 −3 , which is compatible with the latest inclusive determination |V cb | incl = (42.16 ± 0.50) • 10 −3 [6] at the 1σ level. Moreover, we have obtained the pure theoretical value R(D * ) = 0.269±0.008, which is compatible with the experimental world average at the ∼ 1.6σ level.…”

Section: Discussionsupporting

confidence: 89%

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

Martinelli¹,

Simula²,

Vittorio³

2021

Preprint

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In this letter we apply the Dispersive Matrix (DM) method of Refs. [1,2] to the lattice computations of the Form Factors (FFs) entering the semileptonic B → D * ν decays, produced recently by the FNAL/MILC Collaborations [3] at small, but non-vanishing values of the recoil variable w. Thanks to the DM method we obtain the FFs in the whole kinematical range accessible to the semileptonic decays in a completely model-independent and non-perturbative way, implementing exactly both unitarity and kinematical constraints. Using our theoretical bands of the FFs we extract |V cb | from the experimental data and compute R(D * ) from theory. Our final result for |V cb | reads |V cb | = (41.3 ± 1.7) • 10 −3 , which is compatible with the most recent inclusive estimate at the 1σ level. Moreover, we obtain the pure theoretical value R(D * ) = 0.269 ± 0.008, which is compatible with the experimental world average at the ∼ 1.6σ level. THE UNITARITY BANDS OF THE FORM FACTORSWe apply the DM method to the final lattice computations of the FFs pro-

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Section: Discussionsupporting

confidence: 89%

“…Our result is |V cb | = (41.3 ± 1.7) • 10 −3 , which is compatible with the most recent inclusive determination |V cb | incl = (42.16±0.50)• 10 −3 [6]. This implies that the exclusive and the inclusive determinations of |V cb | are now compatible at the 1σ level.…”

Section: Introductionsupporting

confidence: 90%

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

Martinelli¹,

Simula²,

Vittorio³

2021

Preprint

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“…For the branching ratios for K + → π + ν ν and K L → π 0 ν ν decays, the formulae with the exact dependence on the CKM parameters are given in [2]. However, for the search of the |V cb |-independent relations it is useful to use the improved Wolfenstein parametrization and in particular the formulae in (9). Then the exact formulae for the branching ratios in questions are approximated by expressions that are particularly useful for our analysis and are shown in the following.…”

Section: Rare Kaon Decaysmentioning

confidence: 99%

“…In particular the value of |V cb | corresponding to (3), |V cb | = (40.5 ± 0.8) • 10 −3 , is in the ballpark of exclusive determinations of |V cb |, as for example from B → D ν [8]. Had the authors of [7] used the inclusive determination of |V cb |, that is the value |V cb | B→Xc = (42.16 ± 0.50) • 10 −3 [9], they would find significantly higher branching ratio as seen in Fig. 2, where the values of branching ratios for K + → π + ν ν and K L → π 0 ν ν have been plotted as functions of |V cb | for different values of γ and β.…”

Section: Introductionmentioning

confidence: 99%

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

Buras¹,

Venturini²

2021

Preprint

137

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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.

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“…Unfortunately the persistent tensions between inclusive and exclusive determinations of |V cb | and |V ub | (see e.g. [2][3][4][5][6]) weaken this power significantly. As recently reemphasized by us [7] this is in particular the case of the branching ratios for K-meson decays and the parameter ε K that exhibit stronger |V cb | dependences than rare B decay branching ratios and the ∆M s,d mass differences.…”

Section: Introductionmentioning

confidence: 99%

Standard Model Predictions for Rare $K$ and $B$ Decays without $|V_{cb}|$ and $|V_{ub}|$ Uncertainties

Buras¹,

Venturini²

2022

Preprint

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The persistent tensions between inclusive and exclusive determinations of |V cb | and |V ub | weaken the power of theoretically clean rare K and B 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 various branching ratios. This includes the branching ratios for∆M s and the mixing induced CP-asymmetry S ψK S , all measured already very precisely, play an important role in this analysis. The highlights of our analysis are 16 |V cb | and |V ub | independent ratios that often are independent of the CKM parameters or depend only on the angles β and γ in the Unitarity Triangle with β already precisely known and γ to be measured precisely in the coming years by the LHCb and Belle II colaborations. Once γ is measured precisely these 16 ratios taken together are expected to be a powerful tool in the search for new physics. Assuming no NP in |ε K | and S ψK S we determine independently of |V cb |: B(K + → π + ν ν) SM = (8.60 ± 0.42) × 10 −11 and B(K L → π 0 ν ν) SM = (2.94 ± 0.15) × 10 −11 . This are the most precise determinations to date. Assuming no NP in ∆M s,d allows to obtain analogous results for all B decay branching ratios considered in our paper without any CKM uncertainties.

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Three loop calculations and inclusive $V_{cb}$

Cited by 16 publications

References 33 publications

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

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

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

Standard Model Predictions for Rare $K$ and $B$ Decays without $|V_{cb}|$ and $|V_{ub}|$ Uncertainties

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