CMS-BPH-15-002

CMS-BPH-15-002 ; CERN-EP-2017-331
Measurement of the $ \Lambda_{\mathrm{b}} $ polarization and angular parameters in $ \Lambda_{\mathrm{b}} \to \mathrm{J}/\psi \Lambda $ decays from pp collisions at $\sqrt{s}= $ 7 and 8 TeV
CMS Collaboration
13 February 2018
Phys. Rev. D 97 (2018) 072010
Abstract: An analysis of the decay $ \Lambda_{\mathrm{b}} \to \mathrm{J}/\psi ( \to \mu^{+} \mu^{-}) \Lambda (\to \mathrm{p} \pi^{-}) $ is performed to measure the $ \Lambda_{\mathrm{b}} $ polarization and three angular parameters in data from pp collisions at $\sqrt{s} = $ 7 and 8 TeV, collected by the CMS experiment at the LHC. The $ \Lambda_{\mathrm{b}} $ polarization is measured to be 0.00 $\pm$ 0.06 (stat) $\pm$ 0.06 (syst) and the parity-violating asymmetry parameter is determined to be 0.14 $\pm$ 0.14 (stat) $\pm$ 0.10 (syst). The measurements are compared to various theoretical predictions, including those from perturbative quantum chromodynamics.
Links: e-print arXiv:1802.04867 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Definition of the angles used to describe the ${{\Lambda_{\mathrm{b}}}} \to { \mathrm{J} / \psi } { \Lambda }$ decay into the ${{{\mu ^+}} {{\mu ^-}}} {{\mathrm {p}} {\pi ^-}}$ final state as explained in the text.
png pdf	Figure 2: The efficiencies as a function of (a) $\cos {\theta _{ \Lambda }} $, (b) $\cos {\theta _{{\mathrm {p}}}} $, and (c) $\cos {\theta _{{{\mu}}}} $ obtained from simulated $ {{\Lambda_{\mathrm{b}}}} \to { \mathrm{J} / \psi } { \Lambda } $ decays at $\sqrt {s}= $ 8 TeV. The vertical bars on the points are the statistical uncertainties in the simulated data, and the lines show the projections of a 3D fit to the distributions using Chebyshev polynomials. The scales of the vertical axes are arbitrary.
png pdf	Figure 2-a: The efficiency as a function of $\cos {\theta _{ \Lambda }} $ obtained from simulated $ {{\Lambda_{\mathrm{b}}}} \to { \mathrm{J} / \psi } { \Lambda } $ decays at $\sqrt {s}= $ 8 TeV. The vertical bars on the points are the statistical uncertainties in the simulated data, and the lines show the projections of a 3D fit to the distributions using Chebyshev polynomials. The scale of the vertical axis is arbitrary.
png pdf	Figure 2-b: The efficiency as a function of $\cos {\theta _{{\mathrm {p}}}} $ obtained from simulated $ {{\Lambda_{\mathrm{b}}}} \to { \mathrm{J} / \psi } { \Lambda } $ decays at $\sqrt {s}= $ 8 TeV. The vertical bars on the points are the statistical uncertainties in the simulated data, and the lines show the projections of a 3D fit to the distributions using Chebyshev polynomials. The scale of the vertical axis is arbitrary.
png pdf	Figure 2-c: The efficiency as a function of $\cos {\theta _{{{\mu}}}} $ obtained from simulated $ {{\Lambda_{\mathrm{b}}}} \to { \mathrm{J} / \psi } { \Lambda } $ decays at $\sqrt {s}= $ 8 TeV. The vertical bars on the points are the statistical uncertainties in the simulated data, and the lines show the projections of a 3D fit to the distributions using Chebyshev polynomials. The scale of the vertical axis is arbitrary.
png pdf	Figure 3: The background angular distributions of (a) $\cos {\theta _{ \Lambda }} $, (b) $\cos {\theta _{{\mathrm {p}}}} $, and (c) $\cos {\theta _{{{\mu}}}} $ are shown, as obtained from the sidebands in the $ { \mathrm{J} / \psi } { \Lambda }$ invariant mass distribution at $\sqrt {s}= $ 8 TeV. The vertical bars on the points represent the statistical uncertainties, and the solid lines are the results of the fits to data as described in the text.
png pdf	Figure 3-a: The background angular distribution of $\cos {\theta _{ \Lambda }} $ is shown, as obtained from the sidebands in the $ { \mathrm{J} / \psi } { \Lambda }$ invariant mass distribution at $\sqrt {s}= $ 8 TeV. The vertical bars on the points represent the statistical uncertainties, and the solid lines are the results of the fits to data as described in the text.
png pdf	Figure 3-b: The background angular distribution of $\cos {\theta _{{\mathrm {p}}}} $ is shown, as obtained from the sidebands in the $ { \mathrm{J} / \psi } { \Lambda }$ invariant mass distribution at $\sqrt {s}= $ 8 TeV. The vertical bars on the points represent the statistical uncertainties, and the solid lines are the results of the fits to data as described in the text.
png pdf	Figure 3-c: The background angular distribution of $\cos {\theta _{{{\mu}}}} $ is shown, as obtained from the sidebands in the $ { \mathrm{J} / \psi } { \Lambda }$ invariant mass distribution at $\sqrt {s}= $ 8 TeV. The vertical bars on the points represent the statistical uncertainties, and the solid lines are the results of the fits to data as described in the text.
png pdf	Figure 4: Distributions in (a) $ {m_{{ \mathrm{J} / \psi } { \Lambda }}} $, (b) $\cos {\theta _{{\mathrm {p}}}} $, (c) $\cos {\theta _{ \Lambda }} $, and (d) $\cos {\theta _{{{\mu}}}} $ for ${\Lambda_{\mathrm{b}}}$ candidates in the combined $\sqrt {s}= $ 7 and 8 TeV data. The vertical bars on the points are the statistical uncertainties in the data, the solid line shows the result of the fit, and the dashed and dotted lines represent, respectively, the signal and background contributions from the fit.
png pdf	Figure 4-a: Distribution in $ {m_{{ \mathrm{J} / \psi } { \Lambda }}} $ for ${\Lambda_{\mathrm{b}}}$ candidates in the combined $\sqrt {s}= $ 7 and 8 TeV data. The vertical bars on the points are the statistical uncertainties in the data, the solid line shows the result of the fit, and the dashed and dotted lines represent, respectively, the signal and background contributions from the fit.
png pdf	Figure 4-b: Distribution in $\cos {\theta _{{\mathrm {p}}}} $ candidates in the combined $\sqrt {s}= $ 7 and 8 TeV data. The vertical bars on the points are the statistical uncertainties in the data, the solid line shows the result of the fit, and the dashed and dotted lines represent, respectively, the signal and background contributions from the fit.
png pdf	Figure 4-c: Distribution in $\cos {\theta _{ \Lambda }} $ for ${\Lambda_{\mathrm{b}}}$ candidates in the combined $\sqrt {s}= $ 7 and 8 TeV data. The vertical bars on the points are the statistical uncertainties in the data, the solid line shows the result of the fit, and the dashed and dotted lines represent, respectively, the signal and background contributions from the fit.
png pdf	Figure 4-d: Distribution in $\cos {\theta _{{{\mu}}}} $ for ${\Lambda_{\mathrm{b}}}$ candidates in the combined $\sqrt {s}= $ 7 and 8 TeV data. The vertical bars on the points are the statistical uncertainties in the data, the solid line shows the result of the fit, and the dashed and dotted lines represent, respectively, the signal and background contributions from the fit.
png pdf	Figure 5: Distributions in (a) $ {m_{{ \mathrm{J} / \psi } {{\overline { \Lambda }}}}} $, (b) $\cos {\theta _{{\mathrm {p}}}} $, (c) $\cos {\theta _{ \Lambda }} $, and (d) $\cos {\theta _{{{\mu}}}} $ for ${{{\overline { \Lambda }}_{\mathrm {b}}}}$ candidates in the combined $\sqrt {s}= $ 7 and 8 TeV data. The vertical bars on the points are the statistical uncertainties in the data, the solid line shows the result of the fit, and the dashed and dotted lines represent, respectively, the signal and background contributions from the fit.
png pdf	Figure 5-a: Distribution in $ {m_{{ \mathrm{J} / \psi } {{\overline { \Lambda }}}}} $ for ${{{\overline { \Lambda }}_{\mathrm {b}}}}$ candidates in the combined $\sqrt {s}= $ 7 and 8 TeV data. The vertical bars on the points are the statistical uncertainties in the data, the solid line shows the result of the fit, and the dashed and dotted lines represent, respectively, the signal and background contributions from the fit.
png pdf	Figure 5-b: Distribution in $\cos {\theta _{{\mathrm {p}}}} $ for ${{{\overline { \Lambda }}_{\mathrm {b}}}}$ candidates in the combined $\sqrt {s}= $ 7 and 8 TeV data. The vertical bars on the points are the statistical uncertainties in the data, the solid line shows the result of the fit, and the dashed and dotted lines represent, respectively, the signal and background contributions from the fit.
png pdf	Figure 5-c: Distribution in $\cos {\theta _{{\mathrm {p}}}} $ for ${{{\overline { \Lambda }}_{\mathrm {b}}}}$ candidates in the combined $\sqrt {s}= $ 7 and 8 TeV data. The vertical bars on the points are the statistical uncertainties in the data, the solid line shows the result of the fit, and the dashed and dotted lines represent, respectively, the signal and background contributions from the fit.
png pdf	Figure 5-d: Distribution in $\cos {\theta _{{{\mu}}}} $ for ${{{\overline { \Lambda }}_{\mathrm {b}}}}$ candidates in the combined $\sqrt {s}= $ 7 and 8 TeV data. The vertical bars on the points are the statistical uncertainties in the data, the solid line shows the result of the fit, and the dashed and dotted lines represent, respectively, the signal and background contributions from the fit.

Tables
png pdf	Table 1: Functions used in Eq. (3) to describe the angular distribution in the decay ${{\Lambda_{\mathrm{b}}}} \to { \mathrm{J} / \psi } { \Lambda }$, with ${{ \mathrm{J} / \psi } \to {{{\mu ^+}} {{\mu ^-}}}}$ and $ { \Lambda }\to {{\mathrm {p}} {\pi ^-}} $.
png pdf	Table 2: Correlation matrix for the fitted parameters.
png pdf	Table 3: The sources and values of the systematic uncertainties in each parameter and the total uncertainty. Each value in the table should be multiplied by $10^{-2}$ to obtain the corresponding systematic uncertainty.

Summary

Based on an angular analysis of about 6000 $ \Lambda_{\mathrm{b}} \to \mathrm{J}/\psi ( \to \mu^{+} \mu^{-}) \Lambda (\to \mathrm{p} \pi^{-}) $ events collected by the CMS experiment at $\sqrt{s}= $ 7 and 8 TeV, a measurement of the $ \Lambda_{\mathrm{b}} $ polarization $P$, the parity-violating asymmetry parameter in the $ \Lambda_{\mathrm{b}} $ decay $\alpha_1$, the $ \Lambda $ longitudinal polarization $\alpha_2$, and the parameter $\gamma_0$ has been performed. The obtained values are

$ P = \ 0.00 \pm 0.06\ \mathrm{(stat)}\ \pm0.06\ \mathrm{(syst)}$,
$ \alpha_1 = \, \ 0.14 \pm 0.14\ \mathrm{(stat)}\ \pm 0.10\ \mathrm{(syst)}$,
$ \alpha_2 = -1.11 \pm 0.04\ \mathrm{(stat)}\ \pm 0.05\ \mathrm{(syst)}$,
$ \gamma_0 = -0.27 \pm 0.08\ \mathrm{(stat)}\ \pm 0.11\ \mathrm{(syst)}$,

corresponding to the squares of the helicity amplitudes

$ | T_{++} |^2 = \ \ 0.05 \pm 0.04\ \mathrm{(stat)}\ \pm 0.04\ \mathrm{(syst)} $,
$ | T_{+0} |^2 = -0.10 \pm 0.04\ \mathrm{(stat)}\ \pm 0.04\ \mathrm{(syst)} $,
$ | T_{-0} |^2 = \ \ 0.51 \pm 0.03\ \mathrm{(stat)}\ \pm 0.04\ \mathrm{(syst)} $,
$ | T_{--} |^2 = \ \ 0.52 \pm 0.04\ \mathrm{(stat)}\ \pm 0.04\ \mathrm{(syst)}$.

The measured $ \Lambda_{\mathrm{b}} $ polarization value given above is consistent with the LHCb measurement [11] and theoretical predictions of 0.10 [5] and 0.20 [6]. The many theoretical predictions for $\alpha_1$ include $-0.2$ to $-0.1$ from quark model techniques [9,27-30], $-0.17$ to $-0.14$ from perturbative quantum chromodynamics calculations [10], and 0.78 from heavy-quark effective theory [4,6]. The measured value is inconsistent at the level of almost 4 standard deviations with the heavy-quark effective theory prediction, but is consistent at about the 2 standard deviation level with the other predictions. The presented measurement of $\alpha_1$ is also consistent with the measurements 0.05 $\pm$ 0.17 (stat) $\pm$ 0.07 (syst) and 0.05 $\pm$ 0.16 (stat) $\pm$ 0.06 (syst) by LHCb [11] and ATLAS [12], respectively, and with no parity violation at the level of one standard deviation. The measurement of $\alpha_{2}$, compatible with $-1$, indicates that the positive-helicity states of the $ \Lambda $ coming from the $ \Lambda_{\mathrm{b}} $ decay are suppressed.

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