Study of the $B^0\to \rho(770)^0 K^*(892)^0$ decay with an amplitude analysis of $B^0\to (\pi^+\pi^-) (K^+\pi^-)$ decays

Information

LHCb-PAPER-2018-042
CERN-EP-2018-316
arXiv:1812.07008 [PDF]

(Submitted on 17 Dec 2018)
JHEP 05 (2019) 026
Inspire 1709949

Tools

Abstract

An amplitude analysis of ${B^0\to (\pi^+\pi^-) (K^+\pi^-)}$ decays is performed in the two-body invariant mass regions ${300 < m(\pi^+\pi^-)<1100}$ MeV/$c^2$, accounting for the $\rho^0$, $\omega$, $f_0(500)$, $f_0(980)$ and $f_0(1370)$ resonances, and ${750 < m(K^+\pi^-)<1200}$ MeV/$c^2$, which is dominated by the $K^{*}(892)^0$ meson. The analysis uses 3 fb$^{-1}$ of proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The $CP$ averages and asymmetries are measured for the magnitudes and phase differences of the contributing amplitudes. The $CP$-averaged longitudinal polarisation fractions of the vector-vector modes are found to be $\tilde{f}^0_{\rho K^{*}} = 0.164 \pm 0.015 \pm 0.022$ and $\tilde{f}^0_{\omega K^{*}} = 0.68 \pm 0.17 \pm 0.16$, and their $CP$ asymmetries, $\mathcal{A}^0_{\rho K^{*}} = -0.62 \pm 0.09 \pm 0.09$ and $\mathcal{A}^0_{\omega K^{*}} = -0.13 \pm 0.27 \pm 0.13$, where the first uncertainty is statistical and the second systematic.

Figures and captions

Leading Feynman diagrams in the $ B ^0 \rightarrow \rho ^0 K ^{*0} $ decay, from left to right: doubly Cabibbo-suppressed tree, gluonic-penguin and electroweak-penguin diagrams.	BRhoKs[..].pdf [8 KiB] HiDef png [204 KiB] Thumbnail [129 KiB] *.C file
	BRhoKst_GP.pdf [9 KiB] HiDef png [282 KiB] Thumbnail [171 KiB] *.C file
	BRhoKs[..].pdf [9 KiB] HiDef png [243 KiB] Thumbnail [152 KiB] *.C file
Fit to the invariant-mass distribution of selected (left) $ B ^0$ and (right) $\overline{ B }{} {}^0$ candidates after the subtraction of $ B ^0_ s \rightarrow K ^{0} \overline{ K }{} {}^{0} $ background decays. The four trigger and data-taking year categories are aggregated in the figures. The contributions due to the $ B ^0 \rightarrow (\pi ^+ \pi ^- )( K ^+ \pi ^- )$ signal, $\overline{ B }{} {}^0_ s \rightarrow (\pi ^+ \pi ^- )( K ^+ \pi ^- )$ background and combinatorial background are represented by the solid green, red and grey lines, respectively. Data are shown using black dots and the overall fit is represented by the solid blue line.	paper_mB.pdf [26 KiB] HiDef png [297 KiB] Thumbnail [246 KiB] *.C file
	paper_[..].pdf [26 KiB] HiDef png [294 KiB] Thumbnail [245 KiB] *.C file
Definition of the helicity angles in the $ B ^0 \rightarrow \rho ^0 K ^{*0} $ decay.	angles.pdf [26 KiB] HiDef png [136 KiB] Thumbnail [84 KiB] *.C file
Projections of the amplitude fit to the (left) $ B ^0$ and (right) $\overline{ B }{} {}^0$ data samples. The four trigger and data-taking year categories are aggregated in the figures. Data are shown by black points with uncertainties and the overall fit is represented by the solid blue line. The contributions of the partial waves sharing the same angular dependence are shown as ($VV$) solid green, ($VS$) dash-dotted violet, ($SV$) dashed dark magenta and ($SS$) dotted orange lines. Direct $ C P$ -violating effects are most visible in the projections of the $VV$ component over $\cos\theta_{K\pi}$ and $\cos\theta_{\pi\pi}$ and in the different oscillation frequency in $\phi$.	B_cosT[..].pdf [17 KiB] HiDef png [213 KiB] Thumbnail [198 KiB] *.C file
	Bbar_c[..].pdf [17 KiB] HiDef png [216 KiB] Thumbnail [198 KiB] *.C file
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	B_m1_MCvis.pdf [24 KiB] HiDef png [254 KiB] Thumbnail [221 KiB] *.C file
	Bbar_m[..].pdf [24 KiB] HiDef png [262 KiB] Thumbnail [229 KiB] *.C file
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Legend for the plots. The partial waves sharing the same angular dependence are represented as ($VV$) solid green, ($VS$) dash-dotted violet, ($SV$) dashed dark magenta and ($SS$) dotted orange lines. The overall fit is shown by a solid blue line.	paper_[..].pdf [13 KiB] HiDef png [220 KiB] Thumbnail [130 KiB] *.C file
Animated gif made out of all figures.	PAPER-2018-042.gif Thumbnail

Tables and captions

Yields obtained in the extended simultaneous four-body invariant mass fit to the four categories and for the two final states. The quoted uncertainties are statistical only.	Table_1.pdf [77 KiB] HiDef png [80 KiB] Thumbnail [40 KiB] tex code
Contributions to the total amplitude and their angular and mass dependencies.	Table_2.pdf [87 KiB] HiDef png [134 KiB] Thumbnail [58 KiB] tex code
Numerical fit results for the $ C P$ averages and asymmetries in the (top) modulus and (bottom) phase differences of all the contributing amplitudes and among the $VV$ polarisation fractions. For the numbers in the table, the first and second uncertainties correspond to the statistical and total systematic, respectively. The total systematic uncertainty is obtained from the sum in quadrature of the individual sources detailed in Sect. ???, accounting for 100% correlation of the common systematic uncertainties for $ B ^0$ and $\overline{ B }{} {}^0$ .	Table_3.pdf [89 KiB] HiDef png [320 KiB] Thumbnail [153 KiB] tex code
Comparison of theoretical predictions for the $ B ^0 \rightarrow \rho (770)^0 K ^* (892)^0$ mode with the results obtained from this analysis. It should be noted that the theoretical predictions involving the $ C P$ averaged value of $\delta^\perp_{\rho K ^* }$ have been shifted by $\pi$ on account of the different phase conventions used in the theoretical and experimental works.	Table_4.pdf [89 KiB] HiDef png [106 KiB] Thumbnail [47 KiB] tex code
Table (I) of the systematic uncertainties. The abbreviations $S1, S2$ and $S3$ stand for $f_0(500), f_0(980)$ and $f_0(1370)$, respectively. Negligible values are represented by a dash ($-$).	Table_5.pdf [84 KiB] HiDef png [189 KiB] Thumbnail [67 KiB] tex code
Table (II) of the systematic uncertainties. The abbreviations $S1, S2$ and $S3$ stand for $f_0(500), f_0(980)$ and $f_0(1370)$, respectively. Negligible values are represented by a dash ($-$).	Table_6.pdf [84 KiB] HiDef png [202 KiB] Thumbnail [73 KiB] tex code
Central values of the mass-propagator parameters and their uncertainties, used to estimate the corresponding systematic uncertainties. The values of the parameters used to describe the $f_0(500)$ and $f_0(1370)$ resonances were taken from Ref. \cite{Aaij:2014emv} and the rest, from Ref. \cite{PDG2018}.	Table_7.pdf [92 KiB] HiDef png [227 KiB] Thumbnail [106 KiB] tex code

Supplementary Material [file]

Supplementary material full pdf	supple[..].pdf [321 KiB]
This ZIP file contains supplemetary material for the publication LHCb-PAPER-2018-042. The files are: Supplementary.* : An overview of the extra figures .pdf, .png, *.eps : The figures in various formats	Fig1_M[..].pdf [23 KiB] HiDef png [275 KiB] Thumbnail [254 KiB] *C file
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