Towards new frontiers in the exploration of charmless non-leptonic B decays

Abstract

Non-leptonic B decays into charmless final states offer an important laboratory to study CP violation and the dynamics of strong interactions. Particularly interesting are B 0 s → K − K + and B 0 d → π − π + decays, which are related by the U -spin symmetry of strong interactions, and allow for the extraction of CP-violating phases and tests of the Standard Model. The theoretical precision is limited by U -spin-breaking corrections and innovative methods are needed in view of the impressive future experimental precision expected in the era of Belle II and the LHCb upgrade. We have recently proposed a novel method to determine the B 0decays are a new ingredient and the theoretical situation is very favourable. We discuss this strategy in detail, with a focus on penguin contributions as well as exchange and penguin-annihilation topologies which can be probed by a variety of non-leptonic B decays into charmless final states. We show that a theoretical precision as high as O(0.5 • ) for φ s can be attained in the future, thereby offering unprecedented prospects for the search for new sources of CP violation. 7 Prospects of the new strategy 42 8 Conclusions 462 Decay amplitudes and CP asymmetries TopologiesThe non-leptonic decay B 0 d → π − π + , characterized by ab →ūud transition, is governed by the decay topologies depicted in figure 1. The decay amplitude is dominated by contributions from the tree (T ) and penguin (P ) topologies, but also receives contributions from exchange (E) and penguin-annihilation (P A) topologies. In the SM, we have [4]2.1) which is only sensitive to non-factorizable U -spin-breaking corrections because the factorizable contributions cancel in these ratios of amplitudes. Contrary, the U -spin relation C = C (2.10) is affected by both factorizable and non-factorizable U -spin-breaking effects. JHEP03(2017)055 Current [21, 32] Upgrade [3]A dir CP (B d → π − π + ) −0.31 ± 0.05 −0.31 ± 0.008A mix CP (B d → π − π + ) 0.66 ± 0.06 0.66 ± 0.008A dir CP (B s → K − K + ) 0.14 ± 0.11 0.087 ± 0.008A mix CP (B s → K − K + ) −0.30 ± 0.13 −0.19 ± 0.008 1 To be conservative, we consider only the largest uncertainty for K in eq. (2.28).

U -spin sum rules for CP asymmetries of three-body charmed baryon decays

“…For implications for meson decays see, e.g., Refs. [67,[72][73][74]. In order to include these corrections within perturbation theory we perform the tensor products with the unperturbed Hamiltonian.…”

Measurement of CP asymmetries in two-body B(s)0 -meson decays to charged p

“…1 It has been shown that a combined analysis of the branching fractions and CP asymmetries in two-body B-meson decays, accounting for U-spin breaking effects, allows stringent constraints on the CKM angle γ and on the CP-violating phase −2β s to be set [10,11]. More recently, it has been proposed to combine the CP asymmetries of the B 0 → π þ π − and B 0 s → K þ K − decays with information provided by the semileptonic decays B 0 → π − l þ ν and B 0 s → K − l þ ν, in order to achieve a substantial reduction of the theoretical uncertainty on the determination of −2β s [12,13]. The CP asymmetry in the B 0 → π þ π − decay is also a relevant input to the determination of the CKM angle α, when combined with other measurements from the isospin-related decays B 0 → π 0 π 0 and B þ → π þ π 0 [14][15][16].…”

Towards new frontiers with B → πK decays

“…(7). Employing SU (3) methods, even the tiny angle between the B + → π + K 0 and B − → π −K 0 amplitudes arising from O(λ 2 ) corrections can be taken into account [21,22], as done in our numerical analysis.…”

“…In the corresponding φ 00 curves, we take color-suppressed EW penguin contributions through R and A π − K + CP into account, and show both the theoretical (wide bands) and experimental (small bands) uncertainties. The former correspond to non-factorizable SU (3)-breaking effects of 20%, although we expect a much sharper picture of SU (3)breaking effects by the time these measurements will be available through data-driven methods and progress in theory [21,22]. Since Belle II did not give uncertainties for S π 0 KS CP , we assume a resolution as for ∆A π 0 K 0 CP [33].…”