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

Abstract

The results of an amplitude analysis of the charmless three-body decay B þ → π þ π þ π − , in which CP-violation effects are taken into account, are reported. The analysis is based on a data sample corresponding to an integrated luminosity of 3 fb −1 of pp collisions recorded with the LHCb detector. The most challenging aspect of the analysis is the description of the behavior of the π þ π − S-wave contribution, which is achieved by using three complementary approaches based on the isobar model, the K-matrix formalism, and a quasi-model-independent procedure. Additional resonant contributions for all three methods are described using a common isobar model, and include the ρð770Þ 0 , ωð782Þ and ρð1450Þ 0 resonances in the π þ π − P-wave, the f 2 ð1270Þ resonance in the π þ π − D-wave, and the ρ 3 ð1690Þ 0 resonance in the π þ π − F-wave. Significant CP-violation effects are observed in both Sand D-waves, as well as in the interference between the Sand P-waves. The results from all three approaches agree and provide new insight into the dynamics and the origin of CP-violation effects in B þ → π þ π þ π − decays.

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

“…A detailed inspection of the behavior of the S wave, given in Ref. [29], shows that this CP asymmetry remains approximately constant up to the inelastic threshold 2m K , where it appears to change sign; this is seen in all three approaches to the S wave description. Estimates of the significance of this CP -violation effect give values in excess of ten Gaussian standard deviations (σ) in all the S-wave models.…”

“…The results are based on a data sample corresponding to 3 fb −1 of pp collisions at center-of-mass energies of 7 and 8 TeV, collected with the LHCb detector. A more detailed description of the analysis is given in a companion paper [29]. The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, described in detail in Refs.…”

Amplitude Analysis of B±→π±K+K− Decays

“…fixed to their known values [27]. The corresponding B AE → ρð1450Þ 0 π AE fit fraction is approximately 30%, a rather large contribution not expected for the K þ K − pair as the dominant decay mode is ππ and the ρð1450Þ 0 contribution in B AE → π AE π þ π − is observed to be much lower [40,41]. A future analysis with the addition of the run 2 data recorded with the LHCb detector should be able to better pinpoint this effect.…”

Direct CP violation in beauty and charm hadron decays

“…One is a quasi-model-independent approach, where the S-wave amplitude is binned throughout the two-body invariant mass range to fit for its amplitude and phase in each bin, as in Refs. [99][100][101][102]. Another one is the K-matrix approach [103], which imposes two-body unitarity by using external data from scattering experiments, as in Refs.…”