Study of CP violation in B−→K−π+π− and

Abstract

In this work, we study the localized CP violation in B − → K − π + π − and B − → K − σ(600) decays by employing the quasi two-body QCD factorization approach. Both the resonance and the nonresonance contributions are studied for the B − → K − π + π − decay. The resonance contributions include those not only from [ππ] channels including σ(600), ρ 0 (770) and ω(782) but also from [Kπ] channels including K * (892), K * 0 (1430), K * (1410), K * (1680) and K * 2 (1430). By fitting the experimental data A CP (K − π + π − ) = 0.678 ± 0.078 ± 0.0323 ± 0.007 for m 2 K − π + < 15 GeV 2 and 0.08 < m 2 π + π − < 0.66 GeV 2 , we get the end-point divergence parameters in our model, φ S ∈ [4.75, 5.95] and ρ S ∈ [4.2, 8]. Using these results for ρ S and φ S , we predict that the CP asymmetry parameter A CP ∈ [−0.094, −0.034] and the branching fraction B ∈ [1.82, 20.0] × 10 −5 for the B − → K − σ(600) decay. In addition, we also analyse contributions to the localized CP asymmetry A CP (B − → K − π + π − ) from [ππ], [Kπ] channel resonances and nonresonance individually, which are found to beComparing these results, we can see that the localized CP asymmetry in the B − → K − π + π − decay is mainly induced by the [ππ] channel resonances while contributions from the [Kπ] channel resonances and nonresonance are both very small. Nonleptonic decays of hadrons containing a heavy quark play an important role in testing the Standard Model (SM) picture of the Charge-Parity (CP ) violation mechanism in flavor physics, improving our understanding of nonperturbative and perturbative QCD and exploring new physics beyond the SM. CP violation is related to the weak complex phase in the Cabibbo-Kobayashi-Maskawa (CKM) matrix, whichdescribes the mixing of different generations of quarks [1,2]. Besides the weak phase, a large strong phase is also needed for a large CP asymmetry. Generally, this strong phase is provided by QCD loop corrections and some phenomenological models.Three-body decays of heavy mesons are more complicated than the two-body case as they receive resonant and nonresonant contributions and involve three-body matrix elements. The direct nonresonant three-body decay of mesons generally receives two separate contributions: one from the point like weak transition and the other from the pole diagrams that involve three-point or four-point strong vertices.The nonresonant background in charmless three-body B decays due to the transition B → M 1 M 2 M 3 has been studied extensively based on Heavy Meson Chiral Perturbation Theory (HMChPT) [3][4][5]. However, the predicted decay rates are, in general, unexpectedly large and not recovered in the soft meson region.

Quasi-two-body decays $$B \rightarrow D K^*(892) \rightarrow D K \pi $$ in the perturbative QCD approach

“…In Ref. [38], the calculation of the localized C P violation in B − → K − π + π − decays has been done with the K π channels including K * (892), K * 0 (1430), K * (1410), K * (1680) and K * 2 (1430). Using a simple model on the basis of the factorization approach, the branching ratios and direct C P violation for the charmless three-body hadronic decays B (s) → K K π and B (s) → K ππ have been calculated in Refs.…”

Four-body decays B(s) → (Kπ)S/P(Kπ)S/P in the perturbative QCD approach

“…fully applied to numerous hadronic three-body B meson decays in the perturbative QCD (PQCD) [50][51][52][53][54][55][56][57][58][59][60][61][62][63] and QCD factorization (QCDF) approaches [64][65][66][67][68][69][70][71][72].…”

Resonant contributions to three-body $$B\rightarrow KKK$$ decays in perturbative QCD approach

“…Some decays such as B 0 → K S K S K S mediated by the flavour-changing neutral-current b → s transition provide a sensitive probe of the effect of new physics beyond SM. Motivated by the experimental results, many theoretical studies of various three-body non-leptonic B decays have been performed in different frameworks, such as approaches based on the symmetry principles [33][34][35][36][37], the QCD factorization (QCDF) [38][39][40][41][42][43][44][45][46], the perturbative QCD approach (PQCD) , and other theoretical methods [72][73][74][75][76].…”