cern.ch

First measurement of the $CP$-violating phase $\phi_s^{d\overline{d}}$ in $B_s^0\to(K^+\pi^-)(K^-\pi^+)$ decays

[to restricted-access page]

Abstract

A flavour-tagged decay-time-dependent amplitude analysis of $B_s^0\to(K^+\pi^-)(K^-\pi^+)$ decays is presented in the $K^{\pm}\pi^{\mp}$ mass range from 750 to 1600 MeV$/c^2$. The analysis uses $pp$ collision data collected with the LHCb detector at centre-of-mass energies of $7$ and $8$ TeV, corresponding to an integrated luminosity of $3.0$ fb$^{-1}$. Several quasi-two-body decay modes are considered, corresponding to $K^{\pm}\pi^{\mp}$ combinations with spin 0, 1 and 2, which are dominated by the $K_0^*(800)^0$ and $K_0^*(1430)^0$, the $K^*(892)^0$ and the $K_2^*(1430)^0$ resonances, respectively. The longitudinal polarisation fraction for the $B_s^0\to K^*(892)^0\overline{K}^*(892)^0$ decay is measured as $f_L=0.208 \pm 0.032 \pm 0.046$, where the first uncertainty is statistical and the second is systematic. The first measurement of the mixing-induced $CP$-violating phase, $\phi_s^{d\overline{d}}$, in $b\to d\overline{d}s$ transitions is performed, yielding a value of $\phi_s^{d\overline{d}}=-0.10$ $\pm$ $0.13$ (stat) $\pm$ $0.14$ (syst) rad.

Figures and captions

Leading-order SM Feynman diagram of the $ { B ^0_ s \rightarrow K ^{*0} \overline{ K }{} {}^{*0} }$ decay.

Fig1.pdf [9 KiB]
HiDef png [251 KiB]
Thumbnail [41 KiB]
*.C file
Fig1.pdf

Graphical definition of the angles in the helicity basis. Taking the example of a $ B ^0_ s \rightarrow Q_1 Q_2$ decay (this analysis uses $ B ^0_ s \rightarrow SS$, $ B ^0_ s \rightarrow SV$, $ B ^0_ s \rightarrow VS$, $ B ^0_ s \rightarrow VV$, $ B ^0_ s \rightarrow ST$, $ B ^0_ s \rightarrow TS$, $ B ^0_ s \rightarrow VT$, $ B ^0_ s \rightarrow TV$ and $ B ^0_ s \rightarrow TT$), with each final-state quasi-two-body meson decaying to pseudoscalars ($Q_1 \rightarrow K^+\pi^-$ and $Q_2 \rightarrow K^-\pi^+$), $\theta_1$ ($\theta_2$) is defined as the angle between the directions of motion of $K^+$ ($K^-$) in the $Q_1$ ($Q_2$) rest frame and $Q_1$ ($Q_2$) in the $ B ^0_ s $ rest frame, and $\varphi$ as the angle between the plane defined by $K^+\pi^-$ and the plane defined by $K^-\pi^+$ in the $ B ^0_ s $ rest frame.

Fig2.pdf [27 KiB]
HiDef png [181 KiB]
Thumbnail [35 KiB]
*.C file
Fig2.pdf

Four-body invariant mass distribution on a (left) linear and (right) logarithmic scale superimposed with the mass fit model.

Fig3a.pdf [30 KiB]
HiDef png [555 KiB]
Thumbnail [109 KiB]
*.C file
Fig3a.pdf
Fig3b.pdf [28 KiB]
HiDef png [444 KiB]
Thumbnail [89 KiB] *.C file
Fig3b.pdf

Distribution of the two $(K\pi)$ pair invariant masses, with the signal weights applied, after all of the selection requirements.

Fig4.pdf [34 KiB]
HiDef png [410 KiB]
Thumbnail [94 KiB]
*.C file
Fig4.pdf

Kinematic acceptance and decay-time distributions evaluated with simulated vector-vector $ { B ^0_ s \rightarrow K ^{*0} \overline{ K }{} {}^{*0} }$ and pure phase-space $ { B ^0_ s \rightarrow ( K ^+ \pi ^- )( K ^- \pi ^+ )}$ candidates scaled by the mean acceptance. In the bottom right plot the decay-time acceptance obtained from the simulated sample is shown as the black points and the parametric form of the acceptance obtained with cubic splines is shown as the red curve. In the other three plots the black points show the acceptance distribution for the masses and angles. The two $\cos\theta$ variables and the two $m(K\pi)$ masses have been averaged for the purpose of illustration. In the fit, the kinematic acceptance enters via the normalisation weights.

Fig5a.pdf [16 KiB]
HiDef png [142 KiB]
Thumbnail [34 KiB]
*.C file
Fig5a.pdf
Fig5b.pdf [15 KiB]
HiDef png [105 KiB]
Thumbnail [25 KiB] *.C file
Fig5b.pdf
Fig5c.pdf [15 KiB]
HiDef png [110 KiB]
Thumbnail [29 KiB] *.C file
Fig5c.pdf
Fig5d.pdf [16 KiB]
HiDef png [262 KiB]
Thumbnail [64 KiB] *.C file
Fig5d.pdf

Per-event decay-time resolution, $\sigma_t$, versus the estimated per-event decay-time uncertainty, $\delta_t$, obtained from simulated samples containing both vector-vector resonant $ { B ^0_ s \rightarrow K ^{*0} \overline{ K }{} {}^{*0} }$ and phase-space $ { B ^0_ s \rightarrow K ^+ \pi ^- K ^- \pi ^+ }$ events.

Fig6.pdf [15 KiB]
HiDef png [205 KiB]
Thumbnail [47 KiB]
*.C file
Fig6.pdf

One-dimensional projections of the decay-time-dependent, flavour-tagged fit to (black points) the sPlot weighted data for (top row) the two $(K\pi)$ invariant masses, (middle row) the two $(K\pi)$ decay plane angles, (bottom left) the angle between the two $(K,\pi)$ decay planes and (bottom right) the decay-time. The solid gray line represents the total fit model along with the $ C\!P$ -averaged components for each contributing decay.

Fig7a.pdf [16 KiB]
HiDef png [370 KiB]
Thumbnail [83 KiB]
*.C file
Fig7a.pdf
Fig7b.pdf [16 KiB]
HiDef png [316 KiB]
Thumbnail [72 KiB] *.C file
Fig7b.pdf
Fig7c.pdf [15 KiB]
HiDef png [263 KiB]
Thumbnail [70 KiB] *.C file
Fig7c.pdf
Fig7d.pdf [15 KiB]
HiDef png [264 KiB]
Thumbnail [70 KiB] *.C file
Fig7d.pdf
Fig7e.pdf [15 KiB]
HiDef png [244 KiB]
Thumbnail [62 KiB] *.C file
Fig7e.pdf
Fig7f.pdf [15 KiB]
HiDef png [212 KiB]
Thumbnail [59 KiB] *.C file
Fig7f.pdf

Line-shapes of the (left) modulus and (right) phase of the scalar $K\pi$ mass-dependent amplitude. The nominal model is shown with a solid blue line and the model-independent parameterisation, used in systematic studies, is shown with a dashed red line.

Fig8a.pdf [26 KiB]
HiDef png [269 KiB]
Thumbnail [61 KiB]
*.C file
Fig8a.pdf
Fig8b.pdf [26 KiB]
HiDef png [233 KiB]
Thumbnail [54 KiB] *.C file
Fig8b.pdf

Animated gif made out of all figures.

PAPER-2017-048.gif
Thumbnail
thumbnail_PAPER-2017-048.gif

Tables and captions

Quasi-two-body decay channels and corresponding polarisation amplitudes contributing to the $ { B ^0_ s \rightarrow ( K ^+ \pi ^- )( K ^- \pi ^+ )}$ final state in the $K\pi$ mass window from 750 to 1600 $ {\mathrm{\,MeV\!/}c^2}$ . The different contributions are identified by the spin $j_1$ ($j_2$) of the $K^+\pi^-$ ($K^-\pi^+$) pair and the helicity $h$. In cases where more than one amplitude contributes, the polarisations are defined as being longitudinal, parallel, or perpendicular, which are then denoted by $0$, $\parallel$ and $\perp$ respectively, following the definitions given in Ref. \cite{PDG2016}. The subscripts 1 and 2 in the parallel and perpendicular helicities of the tensor-tensor component denote different spin states leading to a parallel or a perpendicular configuration, as discussed in Appendix ???.

Table_0.pdf [54 KiB]
HiDef png [73 KiB]
Thumbnail [11 KiB]
tex code
Table_0.pdf

Yields of the signal decay and the various background components considered in the four-body invariant mass fit. The uncertainties are statistical only. The signal region is defined as $\pm 60$ $ {\mathrm{\,MeV\!/}c^2}$ from the known $ B ^0_ s $ meson mass \cite{PDG2016}.

Table_1.pdf [54 KiB]
HiDef png [98 KiB]
Thumbnail [17 KiB]
tex code
Table_1.pdf

The flavour-tagging performance of the SS and OS tagging algorithms, as well as the combination of both, for the signal data sample used in the analysis. The quoted uncertainty includes both statistical and systematic contributions.

Table_2.pdf [37 KiB]
HiDef png [43 KiB]
Thumbnail [9 KiB]
tex code
Table_2.pdf

Results of the decay-time-dependent amplitude fit to data. The first uncertainty is statistical and the second uncertainty is systematic.

Table_3.pdf [63 KiB]
HiDef png [232 KiB]
Thumbnail [42 KiB]
tex code
Table_3.pdf

Functions containing the angular dependence of the amplitudes, as introduced in Eq. (???). For a discussion on some of the angular terms see Ref. \cite{Bhattacharya:2013sga}.

Table_4.pdf [63 KiB]
HiDef png [197 KiB]
Thumbnail [35 KiB]
tex code
Table_4.pdf

Parameters used in the nominal model for the scalar $K\pi$ mass-dependent amplitude. The correlations among them are found to be small, the largest ones been of the order of $50\%$.

Table_5.pdf [34 KiB]
HiDef png [68 KiB]
Thumbnail [13 KiB]
tex code
Table_5.pdf

Coefficients used in the model-independent parameterisation of the scalar $K\pi$ mass-dependent amplitude.

Table_6.pdf [36 KiB]
HiDef png [51 KiB]
Thumbnail [10 KiB]
tex code
Table_6.pdf

Supplementary Material [file]

Supplementary material full pdf

supple[..].pdf [141 KiB]
supplementary.pdf

This ZIP file contains supplementary material for the publication LHCb-PAPER-2017-048. The files are: supplementary.pdf : A description of the extra material, consisting on correlation matrices. *.pdf, *.eps, *.C : The correlation matrices in various formats.

Fig1-S.pdf [52 KiB]
HiDef png [2 MiB]
Thumbnail [270 KiB]
*C file
Fig1-S.pdf
Fig2-S.pdf [52 KiB]
HiDef png [2 MiB]
Thumbnail [272 KiB]
*C file
Fig2-S.pdf

Created on 11 December 2018.Citation count from INSPIRE on 11 December 2018.