Localized direct CP violation in $$B^\pm \rightarrow \rho ^0 (\omega )\pi ^\pm \rightarrow \pi ^+ \pi ^-\pi ^\pm $$ B ± → ρ 0 ( ω ) π ± → π + π - π ±

Abstract

We study the localized direct CP violation in the hadronic decays B ± → ρ 0 (ω)π ± → π + π − π ± , including the effect caused by an interesting mechanism involving the charge symmetry violating mixing between ρ 0 and ω. We calculate the localized integrated direct CP violation when the low invariant mass ofFor the five models of form factors investigated, we find that the localized integrated direct CP violation varies from −0.0752 to −0.0290 in the ranges of parameters in our model when 0.750 < m(π + π − ) low < 0.800 GeV. This result, especially the sign, agrees with the experimental data and is independent of the form factor models. The new experimental data shows that the signs of the localized integrated CP asymmetries in the regions 0.470 < m(π + π − ) low < 0.770 and 0.770 < m(π + π − ) low < 0.920 GeV are positive and negative, respectively. We find that ρ-ω mixing makes the localized integrated CP asymmetry move toward the negative direction, and therefore contributes to the sign change in those two regions. This behavior is also independent of the form factor models. We also calculate the localized integrated direct CP violating asymmetries in the regions 0.470 < m(π + π − ) low < 0.770, 0.770 < m(π + π − ) low < 0.920 and the whole region 0.470 < m(π + π − ) low < 0.920 GeV and find that they agree with the experimental data in some models of the form factors.

Observation of Several Sources of CP Violation in B+→π+π+π−<

“…2(b)] and is well described by the models. Contrary to some theoretical predictions [25][26][27], there is no evident CP -violation effect associated with ρ-ω mixing. However, a clear CP asymmetry is seen at values of mðπ þ π − Þ below the ρð770Þ 0 resonance, where only the S-wave amplitude contributes significantly [ Fig.…”

“…Many phenomenological studies [14][15][16][17][18][19][20] have provided possible interpretations of the asymmetries. Particular attention has been devoted to whether large CP -violation effects could arise from the interference between the broad low-mass spin-0 contributions and the spin-1 ρð770Þ 0 resonance [21][22][23][24], from mixing between the ρð770Þ 0 and ωð782Þ resonances [25][26][27], or from ππ ↔ KK rescattering [21,23,24,28]. Further experimental studies are needed to clarify which of these sources are connected to the observed CP asymmetries.…”

Amplitude analysis of the B+→π+π+π− decay

“…Other approaches [96][97][98][99] give predictions for this quantity which appear to now be ruled out. There is also no evident CP-violation effect associated with ρ-ω mixing, contrary to some theoretical predictions [27][28][29].…”

“…Phenomenological studies [21][22][23][24][25][26] have focused on investigating the localized CP asymmetries seen in the model-independent analysis of B þ → π þ π þ π − decays [12], with some works indicating the potential importance of the ρ-ω mixing effect between the ρð770Þ 0 and ωð782Þ resonances [27][28][29], and the interference between the ρð770Þ 0 resonance and the broad S-wave contribution [30][31][32][33]. Furthermore, the relative pattern of CP asymmetries between B þ → h þ h þ h − decays, where h is a kaon or pion, could be indicative of CP violation induced by ππ ↔ KK rescattering [30,32,34,35].…”

Contributions of $$ {K}_0^{\ast } $$(1430) and $$ {K}_0^{\ast } $$(1950) in the three-body decays B → Kπh

“…The charmless three-body hadronic B meson decay processes provide us a field to appraise different dynamical models of strong interaction, to investigate hadronic final-state interactions and analyze hadron spectroscopy, to determine the fundamental quark mixing parameters and understand CP asymmetries. In order to extract the significative information from experimental results and present the effective and accurate predictions for the three-body B decays, some methods have been adopted in abundant works, such as the U -spin, isospin and flavor SU(3) symmetries in [1][2][3][4][5][6][7][8][9][10], the QCD factorization (QCDF) in [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and the perturbative QCD (PQCD) approach in [26][27][28]. The three-body decays B → Kπh, with h is the pion or kaon, have been studied by Belle [29][30][31][32][33][34][35], BaBar [36][37][38][39][40][41][42][43] and LHCb [44]<...>…”