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

Altmannshofer, Wolfgang; Lewis, Nathan

doi:10.48550/arxiv.2112.03437

“…and β = (21.74 ± 0.84) • , S ψK S = sin(2β) = 0.688 ± 0.022, (HYBRID) (12) in perfect agreement with the experimental measurements in (10). This brief exercise is an overture to the new tensions emerging from the exclusive strategy.…”

Section: Strategysupporting

confidence: 87%

“…4 and In this context we should emphasize that the R(K) and R(K * ) anomalies being independent of |V cb | remain. On the other hand, as analysed in [12], lowering the value of |V cb | decreases the anomalies in B → Kµ + µ − , B → K * µ + µ − and B s → φµ + µ − decay branching ratios but to remove them completely values of |V cb | significantly lower than the exclusive ones are required.…”

Section: Discussionmentioning

confidence: 98%

The Exclusive Vision of Rare $K$ and $B$ Decays and of the Quark Mixing in the Standard Model

Buras,

Venturini

2022

Preprint

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The most common predictions for rare K and B decay branching ratios in the Standard Model in the literature are based on the CKM elements |V cb | and |V ub | resulting from global fits, that are in the ballpark of their inclusive and exclusive determinations, respectively. In the present paper we follow another route, which to our knowledge has not been explored for ∆M s,d and rare K and B decays by anybody to date. We assume, in contrast to the prevailing inclusive expectations for |V cb |, that the future true values of |V cb | and |V ub | will be both from exclusive determinations and set them equal to the most recent ones from FLAG. With the precisely known |V us | the resulting rare decay branching ratios, ε K , ∆M d , ∆M s and S ψK S depend then only on the angles β and γ in the unitarity triangle that moreover are correlated through the CKM unitarity. An unusual pattern of SM predictions results from this study with some existing tensions being dwarfed and new tensions being born. In particular using HPQCD B 0 s,d − B0 s,d hadronic matrix elements a 3.1σ tension in ∆M s independently of γ is found. For 60 • ≤ γ ≤ 75 • the tension in ∆M d between 4.0σ and 1.1σ is found and in the case of ε K between 5.2σ and 2.1σ. Moreover, the room for new physics indecays is significantly increased. We compare the results in this EXCLUSIVE scenario with the HYBRID one in which |V cb | in the former scenario is replaced by the most recent inclusive |V cb | and present the dependence of all observables considered by us in both scenarios as functions of γ. As a byproduct we compare the determination of |V cb | from ∆M s , ∆M d , ε K and S ψK S using B 0 s,d − B0 s,d hadronic matrix elements from LQCD with 2 + 1 + 1 flavours, 2 + 1 flavours and their average. Only for the 2 + 1 + 1 case values for β and γ exist for which the same value of |V cb | is found: |V cb | = 42.6(7) × 10 −3 , γ = 64.6(4.0) • and β = 22.2(7) • . This in turn implies a 2.7σ anomaly in B s → µ + µ − .

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“…Our present analysis extends the |V cb | − γ strategy, developed in [10,11], to rare K decays, not considered in [20], resurrecting some old ideas from the 1990s [14,22,23] and improving significantly on them. In this context it should be noted that in [22] the possibility of the determination of β from K + → π + ν ν and K L → π 0 ν ν, basically independently of |V cb | and γ , has been pointed out.…”

Section: Introductionmentioning

confidence: 68%

“…It should be remarked that the authors of [20] performed recently a determination of |V cb | and |V ub | from loop processes, rare decays and quark mixing, by assuming no NP contributions to these observables. To this end they used only well measured observables in the B system and ε K .…”

Section: Introductionmentioning

confidence: 99%

On the superiority of the $$|V_{cb}|-\gamma $$ plots over the unitarity triangle plots in the 2020s

Buras

¹

2022

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The unitarity triangle (UT) plots played already for three decades an important role in the tests of the Standard Model (SM) and the determination of the CKM parameters. As of 2022, among the four CKM parameters, $$|V_{us}|$$ | V us | and $$\beta $$ β are already measured with respectable precision, while this is not the case of $$|V_{cb}|$$ | V cb | and $$\gamma $$ γ . In the case of $$|V_{cb}|$$ | V cb | the main obstacle are the significant tensions between its inclusive and exclusive determinations from tree-level decays and it could still take some years before a unique value of this parameter will be known. The present uncertainty in $$\gamma $$ γ of $$4^\circ $$ 4 ∘ from tree-level decays will be reduced to $$1^\circ $$ 1 ∘ by the LHCb and Belle II collaborations in the coming years. Unfortunately in the common UT plots $$|V_{cb}|$$ | V cb | is not seen and the experimental improvements in the determination of $$\gamma $$ γ from tree-level decays at the level of a few degrees are difficult to appreciate. In view of these deficiencies of the UT plots with respect to $$|V_{cb}|$$ | V cb | and $$\gamma $$ γ and the central role these two CKM parameters will play in this decade, the recently proposed plots of $$|V_{cb}|$$ | V cb | versus $$\gamma $$ γ extracted from various processes appear to be superior to the UT plots in the flavour phenomenology of the 2020s. We illustrate this idea with $$\Delta F=2$$ Δ F = 2 observables $$\Delta M_s$$ Δ M s , $$\Delta M_d$$ Δ M d , $$\varepsilon _K$$ ε K and with rare decays $$B_s\rightarrow \mu ^+\mu ^-$$ B s → μ + μ - , $$B_d\rightarrow \mu ^+\mu ^-$$ B d → μ + μ - , $$K^+\rightarrow \pi ^+\nu \bar{\nu }$$ K + → π + ν ν ¯ and $$K_L\rightarrow \pi ^0\nu \bar{\nu }$$ K L → π 0 ν ν ¯ . In particular the power of $$\varepsilon _K$$ ε K , $$\mathcal {B}(K^+\rightarrow \pi ^+\nu \bar{\nu })$$ B ( K + → π + ν ν ¯ ) and $$\mathcal {B}(K_L\rightarrow \pi ^0\nu \bar{\nu })$$ B ( K L → π 0 ν ν ¯ ) in the determination of $$|V_{cb}|$$ | V cb | , due to their strong dependence on $$|V_{cb}|$$ | V cb | , is transparently exhibited in this manner. Combined with future reduced errors on $$\gamma $$ γ and $$|V_{cb}|$$ | V cb | from tree-level decays such plots can better exhibit possible inconsistencies between various determinations of these two parameters, caused by new physics, than it is possible with the UT plots. This can already be illustrated on the example of the recently found $$2.7\sigma $$ 2.7 σ anomaly in $$B_s\rightarrow \mu ^+\mu ^-$$ B s → μ + μ - .

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“…In this sense they offer complementary tests of the SM. It should be remarked that the authors of [20] performed recently a determination of |V cb | and |V ub | from loop processes, rare decays and quark mixing, by assuming no NP contributions to these observables. To this end they used only well measured observables in the B system and ε K .…”

Section: Introductionmentioning

confidence: 99%

On the Superiority of the $|V_{cb}|-γ$ Plots over the Unitarity Triangle Plots in the 2020s

Buras

2022

Preprint

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The Unitarity Triangle (UT) plots played already for three decades an important role in the tests of the Standard Model (SM) and the determination of the CKM parameters. As of 2022, among the four CKM parameters, |V us | and β are already measured with respectable precision, while this is not the case of |V cb | and γ. In the case of |V cb | the main obstacle are the significant tensions between its inclusive and exclusive determinations from tree-level decays and it could still take some years before a unique value of this parameter will be known. The present uncertainty in γ of 4 • from tree-level decays will be reduced to 1 • by the LHCb and Belle II collaborations in the coming years. Unfortunately in the common UT plots |V cb | is not seen and the experimental improvements in the determination of γ from tree-level decays at the level of a few degrees are difficult to appreciate. In view of these deficiencies of the UT plots with respect to |V cb | and γ and the central role these two CKM parameters will play in this decade, the recently proposed plots of |V cb | versus γ extracted from various processes appear to be superior to the UT plots in the flavour phenomenology of the 2020s. We illustrate this idea with ∆F = 2 observables ∆M s , ∆M d , ε K and with rare decaysIn particular the power of ε K , B(K + → π + ν ν) and B(K L → π 0 ν ν) in the determination of |V cb |, due to their strong dependence on |V cb |, is transparently exhibited in this manner. Combined with future reduced errors on γ and |V cb | from tree-level decays such plots can better exhibit possible inconsistencies between various determinations of these two parameters, caused by new physics, than it is possible with the UT plots. This can already be illustrated on the example of the recently found 2.7σ anomaly in B s → µ + µ − .

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

Cited by 7 publications

References 60 publications

The Exclusive Vision of Rare $K$ and $B$ Decays and of the Quark Mixing in the Standard Model

The Exclusive Vision of Rare $K$ and $B$ Decays and of the Quark Mixing in the Standard Model

On the superiority of the $$|V_{cb}|-\gamma $$ plots over the unitarity triangle plots in the 2020s

On the Superiority of the $|V_{cb}|-γ$ Plots over the Unitarity Triangle Plots in the 2020s

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