The branching fraction of $$ {B}_s^0\to {K}^0{\overline{K}}^0 $$: three puzzles
Abstract: The branching fraction of the $$ {B}_s\to {K}^0{\overline{K}}^0 $$ B s → K 0 K ¯ 0 decay has been recently measured by the LHCb and Belle experiments. We study the consistency of t… Show more
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Cited by 6 publications
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We build a set of new observables using closely related non-leptonic penguin-mediated Bd and Bs decays: $$ {\overline{B}}_{d,s}\to {K}^{\ast 0}{\overline{K}}^{\ast 0},{\overline{B}}_{d,s}\to {K}^0{\overline{K}}^0,{\overline{B}}_{d,s}\to {K}^0{\overline{K}}^{\ast 0} $$ B ¯ d , s → K ∗ 0 K ¯ ∗ 0 , B ¯ d , s → K 0 K ¯ 0 , B ¯ d , s → K 0 K ¯ ∗ 0 and $$ {\overline{B}}_{d,s}\to {\overline{K}}^0{K}^{\ast 0} $$ B ¯ d , s → K ¯ 0 K ∗ 0 together with their CP conjugate partners. These optimised observables are designed to reduce hadronic uncertainties, mainly coming from form factors and power-suppressed contributions, and thus maximize their sensitivity to New Physics (NP). The deviations observed with respect to the Standard Model (SM) in the ratios of branching ratios of $$ {\overline{B}}_{d,s}\to {K}^{\ast 0}{\overline{K}}^{\ast 0}\left(2.6\sigma \right) $$ B ¯ d , s → K ∗ 0 K ¯ ∗ 0 2.6 σ and $$ {\overline{B}}_{d,s}\to {K}^0{\overline{K}}^0\left(2.4\sigma \right) $$ B ¯ d , s → K 0 K ¯ 0 2.4 σ can be explained by simple NP scenarios involving the Wilson coefficients $$ \mathcal{C} $$ C 4 and $$ \mathcal{C} $$ C 6 associated with QCD penguin operators and the coefficient $$ \mathcal{C} $$ C 8g of the chromomagnetic operator. The optimised observables for $$ {\overline{B}}_{d,s}\to {K}^0{\overline{K}}^{\ast 0} $$ B ¯ d , s → K 0 K ¯ ∗ 0 and $$ {\overline{B}}_{d,s}\to {\overline{K}}^0{K}^{\ast 0} $$ B ¯ d , s → K ¯ 0 K ∗ 0 show distinctive patterns of deviations with respect to their SM predictions under these NP scenarios. The pattern of deviations of individual branching ratios, though affected by significant hadronic uncertainties, suggests that NP is needed both in b → d and b → s transitions. We provide the regions for the Wilson coefficients consistent with both optimised observables and individual branching ratios. The NP scenarios considered to explain the deviations of $$ {\overline{B}}_{d,s}\to {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ B ¯ d , s → K ∗ 0 K ¯ ∗ 0 and $$ {\overline{B}}_{d,s}\to {K}^0{\overline{K}}^0 $$ B ¯ d , s → K 0 K ¯ 0 can yield deviations up to an order of magnitude among the observables that we introduced for $$ {\overline{B}}_{d,s}\to {K}^0{\overline{K}}^{\ast 0} $$ B ¯ d , s → K 0 K ¯ ∗ 0 and $$ {\overline{B}}_{d,s}\to {\overline{K}}^0{K}^{\ast 0} $$ B ¯ d , s → K ¯ 0 K ∗ 0 . Probing these new observables experimentally by improving the measurements of individual branching ratios of penguin-mediated decays would confirm the consistency of the deviations already observed and provide a highly valuable hint of NP in the non-leptonic sector.
We build a set of new observables using closely related non-leptonic penguin-mediated Bd and Bs decays: $$ {\overline{B}}_{d,s}\to {K}^{\ast 0}{\overline{K}}^{\ast 0},{\overline{B}}_{d,s}\to {K}^0{\overline{K}}^0,{\overline{B}}_{d,s}\to {K}^0{\overline{K}}^{\ast 0} $$ B ¯ d , s → K ∗ 0 K ¯ ∗ 0 , B ¯ d , s → K 0 K ¯ 0 , B ¯ d , s → K 0 K ¯ ∗ 0 and $$ {\overline{B}}_{d,s}\to {\overline{K}}^0{K}^{\ast 0} $$ B ¯ d , s → K ¯ 0 K ∗ 0 together with their CP conjugate partners. These optimised observables are designed to reduce hadronic uncertainties, mainly coming from form factors and power-suppressed contributions, and thus maximize their sensitivity to New Physics (NP). The deviations observed with respect to the Standard Model (SM) in the ratios of branching ratios of $$ {\overline{B}}_{d,s}\to {K}^{\ast 0}{\overline{K}}^{\ast 0}\left(2.6\sigma \right) $$ B ¯ d , s → K ∗ 0 K ¯ ∗ 0 2.6 σ and $$ {\overline{B}}_{d,s}\to {K}^0{\overline{K}}^0\left(2.4\sigma \right) $$ B ¯ d , s → K 0 K ¯ 0 2.4 σ can be explained by simple NP scenarios involving the Wilson coefficients $$ \mathcal{C} $$ C 4 and $$ \mathcal{C} $$ C 6 associated with QCD penguin operators and the coefficient $$ \mathcal{C} $$ C 8g of the chromomagnetic operator. The optimised observables for $$ {\overline{B}}_{d,s}\to {K}^0{\overline{K}}^{\ast 0} $$ B ¯ d , s → K 0 K ¯ ∗ 0 and $$ {\overline{B}}_{d,s}\to {\overline{K}}^0{K}^{\ast 0} $$ B ¯ d , s → K ¯ 0 K ∗ 0 show distinctive patterns of deviations with respect to their SM predictions under these NP scenarios. The pattern of deviations of individual branching ratios, though affected by significant hadronic uncertainties, suggests that NP is needed both in b → d and b → s transitions. We provide the regions for the Wilson coefficients consistent with both optimised observables and individual branching ratios. The NP scenarios considered to explain the deviations of $$ {\overline{B}}_{d,s}\to {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ B ¯ d , s → K ∗ 0 K ¯ ∗ 0 and $$ {\overline{B}}_{d,s}\to {K}^0{\overline{K}}^0 $$ B ¯ d , s → K 0 K ¯ 0 can yield deviations up to an order of magnitude among the observables that we introduced for $$ {\overline{B}}_{d,s}\to {K}^0{\overline{K}}^{\ast 0} $$ B ¯ d , s → K 0 K ¯ ∗ 0 and $$ {\overline{B}}_{d,s}\to {\overline{K}}^0{K}^{\ast 0} $$ B ¯ d , s → K ¯ 0 K ∗ 0 . Probing these new observables experimentally by improving the measurements of individual branching ratios of penguin-mediated decays would confirm the consistency of the deviations already observed and provide a highly valuable hint of NP in the non-leptonic sector.
A new puzzle in non-leptonic B decays
We propose a set of new optimized observables using penguin mediated B𝑑 and B𝑠 decays: B𝑑,𝑠 → 𝐾 * 0 K * 0 , B𝑑,𝑠 → 𝐾 0 K0 , B𝑑,𝑠 → 𝐾 0 K * 0 and B𝑑,𝑠 → K0 𝐾 * 0 together with their CP conjugate partners. These observables are substantially cleaner than the corresponding branching ratios, which are plagued by large end point divergences. We find that the dominant contribution to the uncertainties of these observables stem from the corresponding form factors. The Standard Model estimates for these observables corresponding to the 𝐾 * 0 K * 0 and 𝐾 0 K0 final states are in tension with their respective experimental numbers at the ∼ 2.5𝜎 level. The pattern of deviations w.r.t these observables as well as the individual branching ratios suggest that a possible explanation might be new physics both in 𝑏 → 𝑠 and 𝑏 → 𝑑 transitions. We find that, taken one at a time, only the Wilson coefficients 𝐶 𝑁 𝑃 4𝑑,𝑠 and 𝐶 𝑁 𝑃 8𝑔𝑑,𝑠 can potentially satisfy all the current experimental data on the branching ratios as well as the optimized observables. Furthermore, such observables involving mixed (pseudoscalar-vector) states like 𝐾 * 0 K0 etc show distinctive patterns sensitive to these different new physics explanations.
$$ \overline{B}\to \overline{D}D $$ decays and the extraction of fd/fu at hadron colliders
We perform a detailed model-independent phenomenological analysis of $$ \overline{B}\to \overline{D}D $$ B ¯ → D ¯ D decays. Employing an SU(3)F analysis including symmetry-breaking contributions together with a conservative power counting for various suppression effects, we obtain updated Standard Model predictions for all branching fractions and CP asymmetries from a fit to the available experimental data, testable at Belle II and the LHC experiments. These results include all relevant suppressed contributions, thereby providing upper limits on subleading Standard Model (SM) effects like “penguin pollution”, enabling searches for physics beyond the SM. Importantly, allowing in the same fit for the production fractions of charged and neutral B mesons to be different, we find fd/fu = 0.86 ± 0.05, which is 2.5σ away from unity, which, if confirmed, would have important phenomenological consequences.
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