cern.ch

Differential branching fraction and angular moments analysis of the decay $B^0 \to K^+ \pi^- \mu^+ \mu^-$ in the $K^*_{0,2}(1430)^0$ region

[to restricted-access page]

Abstract

Measurements of the differential branching fraction and angular moments of the decay $B^0 \to K^+ \pi^- \mu^+ \mu^-$ in the $K^+\pi^-$ invariant mass range $1330<m(K^+ \pi^-)<1530 MeV/c^2$ are presented. Proton-proton collision data are used, corresponding to an integrated luminosity of 3 $fb^{-1}$ collected by the LHCb experiment. Differential branching fraction measurements are reported in five bins of the invariant mass squared of the dimuon system, $q^2$, between 0.1 and 8.0 $GeV^2/c^4$. For the first time, an angular analysis sensitive to the S-, P- and D-wave contributions of this rare decay is performed. The set of 40 normalised angular moments describing the decay is presented for the $q^2$ range 1.1--6.0 $GeV^2/c^4$.

Figures and captions

Background-subtracted $ m( K ^+ \pi ^- )$ distribution for $ B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^- $ decays in the range $1.1< q^2 <6.0 {\mathrm{\,GeV^2\!/}c^4} $. The region $1330< m( K ^+ \pi ^- ) <1530 {\mathrm{\,MeV\!/}c^2} $ is indicated by the blue, hatched area.

Fig1.pdf [17 KiB]
HiDef png [186 KiB]
Thumbnail [54 KiB]
*.C file
Fig1.pdf

Angle conventions for (a) $\overline{ B }{} {}^0 \rightarrow K ^- \pi ^+ \mu ^- \mu ^+ $ and (b) $ B ^0 \rightarrow K ^+ \pi ^- \mu ^+ \mu ^- $, as described in Ref. [12]. The leptonic and hadronic frames are back-to-back with a common $\hat{y}$ axis. For the dihedral angle $\phi$ between the leptonic and hadronic decay planes, there is an additional sign flip $\phi\rightarrow -\phi$ compared to previous LHCb analyses [1,2,3,4].

Fig2a.pdf [19 KiB]
HiDef png [243 KiB]
Thumbnail [60 KiB]
*.C file
Fig2a.pdf
Fig2b.pdf [19 KiB]
HiDef png [244 KiB]
Thumbnail [60 KiB] *.C file
Fig2b.pdf

Relative efficiency in $\cos{\theta_\ell}$ , $\cos{\theta_K}$ and $\phi'$ in the region $1.1< q^2 <6.0 {\mathrm{\,GeV^2\!/}c^4} $ and $1330< m( K ^+ \pi ^- ) <1530 {\mathrm{\,MeV\!/}c^2} $ as determined from a moment analysis of simulated $ B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^- $ decays, shown as a histogram. The efficiency function is shown by the blue, dashed line.

Fig3a.pdf [13 KiB]
HiDef png [102 KiB]
Thumbnail [34 KiB]
*.C file
Fig3a.pdf
Fig3b.pdf [13 KiB]
HiDef png [106 KiB]
Thumbnail [35 KiB] *.C file
Fig3b.pdf
Fig3c.pdf [14 KiB]
HiDef png [93 KiB]
Thumbnail [31 KiB] *.C file
Fig3c.pdf

Invariant mass $ m( K ^+ \pi ^- \mu ^+ \mu ^- )$ for (left) the control decay $ B ^0 \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^{*0} $ and (right) the signal decay $ B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^- $ in the bin $1.1 < q^2 < 6.0 {\mathrm{\,GeV^2\!/}c^4} $. The solid black line represents the total fitted function. The individual components of the signal (blue, shaded area) and combinatorial background (red, hatched area) are also shown.

Fig4a.pdf [20 KiB]
HiDef png [146 KiB]
Thumbnail [47 KiB]
*.C file
Fig4a.pdf
Fig4b.pdf [21 KiB]
HiDef png [299 KiB]
Thumbnail [83 KiB] *.C file
Fig4b.pdf

Differential branching fraction of $ B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^- $ in bins of $ q^2$ for the range $1330< m( K ^+ \pi ^- ) <1530 {\mathrm{\,MeV\!/}c^2} $. The error bars indicate the sums in quadrature of the statistical and systematic uncertainties.

Fig5.pdf [14 KiB]
HiDef png [57 KiB]
Thumbnail [14 KiB]
*.C file
Fig5.pdf

Measurement of the normalised moments, $\overline{\Gamma}_{i}$, of the decay $ B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^- $ in the range $1.1< q^2 <6.0 {\mathrm{\,GeV^2\!/}c^4} $ and $1330< m( K ^+ \pi ^- ) <1530 {\mathrm{\,MeV\!/}c^2} $. The error bars indicate the sums in quadrature of the statistical and systematic uncertainties.

Fig6a.pdf [15 KiB]
HiDef png [66 KiB]
Thumbnail [18 KiB]
*.C file
Fig6a.pdf
Fig6b.pdf [15 KiB]
HiDef png [72 KiB]
Thumbnail [18 KiB] *.C file
Fig6b.pdf

The distributions of each of the decay angles within the signal region. The acceptance-corrected data is represented by the points with error bars. The estimated signal distribution is shown by the blue, shaded histogram. The projected background from the upper mass sideband is shown by the red, hatched histogram, which is stacked onto the signal histogram.

Fig7a.pdf [15 KiB]
HiDef png [330 KiB]
Thumbnail [93 KiB]
*.C file
Fig7a.pdf
Fig7b.pdf [15 KiB]
HiDef png [383 KiB]
Thumbnail [104 KiB] *.C file
Fig7b.pdf
Fig7c.pdf [15 KiB]
HiDef png [385 KiB]
Thumbnail [101 KiB] *.C file
Fig7c.pdf

Invariant mass $ m( K ^+ \pi ^- \mu ^+ \mu ^- )$ distributions of the signal decay $ B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^- $ in each of the $ q^2$ bins used for the differential branching fraction measurement. The solid black line represents the total fitted function. The individual components of the signal (blue, shaded area) and combinatorial background (red, hatched area) are also shown.

Fig8a.pdf [20 KiB]
HiDef png [240 KiB]
Thumbnail [67 KiB]
*.C file
Fig8a.pdf
Fig8b.pdf [20 KiB]
HiDef png [270 KiB]
Thumbnail [77 KiB] *.C file
Fig8b.pdf
Fig8c.pdf [20 KiB]
HiDef png [275 KiB]
Thumbnail [79 KiB] *.C file
Fig8c.pdf
Fig8d.pdf [20 KiB]
HiDef png [305 KiB]
Thumbnail [86 KiB] *.C file
Fig8d.pdf
Fig8e.pdf [20 KiB]
HiDef png [343 KiB]
Thumbnail [94 KiB] *.C file
Fig8e.pdf
Fig8f.pdf [21 KiB]
HiDef png [299 KiB]
Thumbnail [83 KiB] *.C file
Fig8f.pdf

Animated gif made out of all figures.

PAPER-2016-025.gif
Thumbnail
thumbnail_PAPER-2016-025.gif

Tables and captions

Expected resonant contributions above the $ K ^{*}(892)^{0}$ mass range. For each, the spin-parity, $J^P$, and branching fraction to $ K \pi $, $\mathcal{B}(K\pi)$, are given (taken from Ref. [10]).

Table_1.pdf [54 KiB]
HiDef png [67 KiB]
Thumbnail [10 KiB]
tex code
Table_1.pdf

Differential branching fraction of $ B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^- $ in bins of $ q^2$ for the range $1330< m( K ^+ \pi ^- ) <1530 {\mathrm{\,MeV\!/}c^2} $. The first uncertainty is statistical, the second systematic and the third due to the uncertainty on the $ B ^0 \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^{*}(892)^{0}$ and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \!\rightarrow \mu ^+\mu ^- $ branching fractions.

Table_2.pdf [42 KiB]
HiDef png [105 KiB]
Thumbnail [17 KiB]
tex code
Table_2.pdf

Measurement of the normalised moments, $\overline{\Gamma}_{i}$, of the decay $ B ^0 \!\rightarrow K ^+ \pi ^- \mu ^+\mu ^- $ in the range $1.1< q^2 <6.0 {\mathrm{\,GeV^2\!/}c^4} $ and $1330< m( K ^+ \pi ^- ) <1530 {\mathrm{\,MeV\!/}c^2} $. The first uncertainty is statistical and the second systematic.

Table_3.pdf [44 KiB]
HiDef png [191 KiB]
Thumbnail [36 KiB]
tex code
Table_3.pdf

Summary of the main sources of systematic uncertainty for the differential branching fraction and the angular moments analysis. Typical ranges are quoted for the different $ q^2$ bins used in the differential branching fraction measurement, and for the moments measured in the angular analysis. The systematic uncertainties are significantly smaller than the statistical ones.

Table_4.pdf [56 KiB]
HiDef png [50 KiB]
Thumbnail [7 KiB]
tex code
Table_4.pdf

The transversity-basis moments of the 41 orthonormal angular functions $f_i(\Omega)$ in Eq. 1 [12]. The amplitudes correspond to the $\overline{ B }{} {}^0 $ decay.

Table_5.pdf [77 KiB]
HiDef png [293 KiB]
Thumbnail [47 KiB]
tex code
Table_5.pdf

Supplementary Material [file]

Supplementary material full pdf

supple[..].pdf [108 KiB]
supplementary.pdf

Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.