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| CMS-TOP-17-012 ; CERN-EP-2020-047 | ||
| Measurement of CKM matrix elements in single top quark $t$-channel production in proton-proton collisions at $\sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 25 April 2020 | ||
| Phys. Lett. B 808 (2020) 135609 | ||
| Abstract: The first direct, model-independent measurement is presented of the modulus of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|{{V_{\mathrm{t}\mathrm{b}}}}|$, $|{V_{\mathrm{t}\mathrm{d}}}|$, and $|{V_{\mathrm{t}\mathrm{s}}}|$, in final states enriched in single top quark $t$-channel events. The analysis uses proton-proton collision data from the LHC, collected during 2016 by the CMS experiment, at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Processes directly sensitive to these matrix elements are considered at both the production and decay vertices of the top quark. In the standard model hypothesis of CKM unitarity, a lower limit of $|{V_{\mathrm{t}\mathrm{b}}}| > $ 0.970 is measured at the 95% confidence level. Several theories beyond the standard model are considered, and by releasing all constraints among the involved parameters, the values $|{V_{\mathrm{t}\mathrm{b}}}| = $ 0.988 $\pm$ 0.024, and $|{V_{\mathrm{t}\mathrm{d}}}|^2 +|{V_{\mathrm{t}\mathrm{s}}}|^2 = $ 0.06 $\pm$ 0.06, where the uncertainties include both statistical and systematic components, are measured. | ||
| Links: e-print arXiv:2004.12181 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Leading-order Feynman diagrams for single top quark production via the $t$ channel featuring: (a) a tWb vertex in production and decay, (b) a tWb vertex in production and a tWq in decay, with q being an s or d quark, (c) a tWq vertex in production and a tWb in decay, and (d) a process initiated by a d quark and enhanced due to contributions from these valence quarks. The $\ell $ refers to e or $\mu$ leptons. |
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Figure 1-a:
Leading-order Feynman diagram for single top quark production via the $t$ channel featuring: a tWb vertex in production and decay. The $\ell $ refers to e or $\mu$ leptons. |
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Figure 1-b:
Leading-order Feynman diagram for single top quark production via the $t$ channel featuring: a tWb vertex in production and a tWq in decay, with q being an s or d quark. The $\ell $ refers to e or $\mu$ leptons. |
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Figure 1-c:
Leading-order Feynman diagram for single top quark production via the $t$ channel featuring: a tWq vertex in production and a tWb in decay. The $\ell $ refers to e or $\mu$ leptons. |
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Figure 1-d:
Leading-order Feynman diagram for single top quark production via the $t$ channel featuring: a process initiated by a d quark and enhanced due to contributions from these valence quarks. The $\ell $ refers to e or $\mu$ leptons. |
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Figure 2:
The ${{m_{\mathrm {T}}} ^{\mathrm{W}}}$ distribution from data (points) and simulation (shaded histograms) in the 2j1t (left) and 3j1t (right) categories for the muon (upper) and electron (lower) channels. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panels show the ratio of the data to the MC prediction. |
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Figure 2-a:
The ${{m_{\mathrm {T}}} ^{\mathrm{W}}}$ distribution from data (points) and simulation (shaded histograms) in the 2j1t category for the muon channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
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Figure 2-b:
The ${{m_{\mathrm {T}}} ^{\mathrm{W}}}$ distribution from data (points) and simulation (shaded histograms) in the 3j1t category for the muon channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
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Figure 2-c:
The ${{m_{\mathrm {T}}} ^{\mathrm{W}}}$ distribution from data (points) and simulation (shaded histograms) in the 2j1t category for the electron channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
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Figure 2-d:
The ${{m_{\mathrm {T}}} ^{\mathrm{W}}}$ distribution from data (points) and simulation (shaded histograms) in the 3j1t category for the electron channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
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Figure 3:
Distributions of the two most discriminating variables from data (points) and simulation (shaded histograms) in the 2j1t category: the ${{| \eta |}}$ of the non-b-tagged jet ${\eta _{\text {j}'}}$ (left) and the invariant mass of lepton and b jet momenta system (right), shown for the muon (upper) and electron (lower) channels, respectively. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panels show the ratio of the data to the MC prediction. |
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Figure 3-a:
Distribution of the ${{| \eta |}}$ of the non-b-tagged jet ${\eta _{\text {j}'}}$, from data (points) and simulation (shaded histograms) in the 2j1t category, shown for the muon channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
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Figure 3-b:
Distribution of the invariant mass of lepton and b jet momenta system, from data (points) and simulation (shaded histograms) in the 2j1t category, shown for the muon channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
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Figure 3-c:
Distribution of the ${{| \eta |}}$ of the non-b-tagged jet ${\eta _{\text {j}'}}$, from data (points) and simulation (shaded histograms) in the 2j1t category, shown for the electron channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
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Figure 3-d:
Distribution of the invariant mass of lepton and b jet momenta system, from data (points) and simulation (shaded histograms) in the 2j1t category, shown for the electron channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
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Figure 4:
Distributions of the two most discriminating variables from data (points) and simulation (shaded histograms) in the 3j1t category: the ${{p_{\mathrm {T}}} ^\text {miss}}$ in the transverse plane (left) and the value of the MVA b tagger discriminator when applied to the extra jet (right) are shown for the muon (upper) and electron (lower) channels, respectively. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panels show the ratio of the data to the MC prediction. |
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Figure 4-a:
Distribution of |
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Figure 4-b:
Distribution of the value of the MVA b tagger discriminator when applied to the extra jet, from data (points) and simulation (shaded histograms) in the 3j1t category, shown for the muon channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
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Figure 4-c:
Distribution of the ${{p_{\mathrm {T}}} ^\text {miss}}$ in the transverse plane, from data (points) and simulation (shaded histograms) in the 3j1t category, shown for the electron channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
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Figure 4-d:
Distribution of the value of the MVA b tagger discriminator when applied to the extra jet, from data (points) and simulation (shaded histograms) in the 3j1t category, shown for the electron channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
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Figure 5:
Distributions of the two most discriminating variables from data (points) and simulation (shaded histograms) in the 3j2t category: the ${{| \eta |}}$ of the non-b-tagged jet ${\eta _{\text {j}'}}$ (left) and the invariant mass of lepton and non-b-tagged jet system (right) are shown for the muon (upper) and electron (lower) channels, respectively. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panels show the ratio of the data to the MC prediction. |
png pdf |
Figure 5-a:
Distribution of the ${{| \eta |}}$ of the non-b-tagged jet ${\eta _{\text {j}'}}$, from data (points) and simulation (shaded histograms) in the 3j2t category, shown for the muon channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
png pdf |
Figure 5-b:
Distribution of the invariant mass of lepton and non-b-tagged jet system, from data (points) and simulation (shaded histograms) in the 3j2t category, shown for the muon channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
png pdf |
Figure 5-c:
Distribution of the ${{| \eta |}}$ of the non-b-tagged jet ${\eta _{\text {j}'}}$, from data (points) and simulation (shaded histograms) in the 3j2t category, shown for the electron channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
png pdf |
Figure 5-d:
Distribution of the invariant mass of lepton and non-b-tagged jet system, from data (points) and simulation (shaded histograms) in the 3j2t category, shown for the electron channel. The vertical lines on the points and the hatched bands show the experimental and MC statistical uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the MC prediction. |
png pdf |
Figure 6:
Distribution of the multivariate discriminators, comparing data to simulation normalised after the fit procedure, for the muon channel on the left and for the electron channel on the right, for 2j1t (upper), 3j1t (middle), and 3j2t (lower). The vertical lines on the points and the hatched bands show the experimental and fit uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panels show the ratio of the data to the fit. |
png pdf |
Figure 6-a:
Distribution of the multivariate discriminator, comparing data to simulation normalised after the fit procedure, for the muon channel, for 2j1t. The vertical lines on the points and the hatched bands show the experimental and fit uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the fit. |
png pdf |
Figure 6-b:
Distribution of the multivariate discriminator, comparing data to simulation normalised after the fit procedure, for the electron channel, for 2j1t.The vertical lines on the points and the hatched bands show the experimental and fit uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the fit. |
png pdf |
Figure 6-c:
Distribution of the multivariate discriminator, comparing data to simulation normalised after the fit procedure, for the muon channel, for 3j1t. The vertical lines on the points and the hatched bands show the experimental and fit uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the fit. |
png pdf |
Figure 6-d:
Distribution of the multivariate discriminator, comparing data to simulation normalised after the fit procedure, for the electron channel, for 3j1t. The vertical lines on the points and the hatched bands show the experimental and fit uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the fit. |
png pdf |
Figure 6-e:
Distribution of the multivariate discriminator, comparing data to simulation normalised after the fit procedure, for the muon channel, for 3j2t. The vertical lines on the points and the hatched bands show the experimental and fit uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the fit. |
png pdf |
Figure 6-f:
Distribution of the multivariate discriminator, comparing data to simulation normalised after the fit procedure, for the electron channel, for 3j2t. The vertical lines on the points and the hatched bands show the experimental and fit uncertainties, respectively. The expected distribution from the $ {ST_{\mathrm{q},\mathrm{b}}}+ {ST_{\mathrm{b},\mathrm{q}}}$ processes (multiplied by a factor of 1000) is shown by the solid blue line. The lower panel shows the ratio of the data to the fit. |
| Tables | |
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Table 1:
Values of the third-row elements of the CKM matrix inferred from low-energy measurements, taken from Ref. [12], with the respective values of the top quark decay branching fractions. The q in ${{| V_{\mathrm{t} \mathrm{q}} |}}$ and $ {\mathcal {B}(\mathrm{t} \to \mathrm{W} \mathrm{q})}$ in the first column refers to b, s, and d quarks, according to the quark label shown in the header row. |
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Table 2:
For each of the production and decay vertices, the cross section times branching fraction for the corresponding signal process from simulation. The uncertainties shown include those from the factorisation and renormalisation scales, the PDFs, and any experimental uncertainties, where appropriate. |
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Table 3:
For each category, the corresponding signal process, the cross section times branching fraction expression, and the specific Feynman diagram from Fig. 1 are shown. |
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Table 4:
The sources and relative values in percent of the systematic uncertainty in the measurement of the ${ST_{\mathrm{b},\mathrm{b}}}$ cross section. The uncertainties are broken up into profiled and nonprofiled sources. |
| Summary |
|
A measurement of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|{V_{\mathrm{t}\mathrm{b}}}| $, $|{V_{\mathrm{t}\mathrm{d}}}| $, and $|{V_{\mathrm{t}\mathrm{s}}}|$ has been performed in an event sample enriched in $t$-channel single top quark events, featuring one muon or electron and jets in the final state. The data are from proton-proton collisions at $\sqrt{s} = $ 13 TeV, acquired at the LHC by the CMS experiment and correspond to an integrated luminosity of 35.9 fb$^{-1}$. The contributions from single top quark processes featuring all three matrix elements in the production vertex have been considered as separate signal processes, as well as contributions from decays of single top quarks involving all three quark families. The yields of the signal processes have been extracted through a simultaneous fit to data in different selected event categories, and the values of the CKM matrix elements have been inferred from the signal strengths, which are the ratios of the measured top quark $t$-channel cross sections times branching ratios to the expected values. The signal strengths obtained from the fit are $\mu_{\mathrm{b}} = $ 0.99 $\pm$ 0.12, where the uncertainty includes both the statistical and systematic components, and $\mu_{\mathrm{s}\mathrm{d}} < $ 87 at 95% confidence level (CL ). Under the standard model assumption of CKM unitarity, the values are found to be $ |{{V_{\mathrm{t}\mathrm{b}}}}| > $ 0.970 and $ |{V_{\mathrm{t}\mathrm{d}}}|^2 +|{V_{\mathrm{t}\mathrm{s}}}|^2 < $ 0.057 both at 95% CL. Fits were also performed under two different beyond-the-standard-model scenarios. In the first, we assume the presence of additional quark families that are heavier than the top quark. The unitarity constraint for the three CKM matrix elements no longer holds, but the top quark decays through the same channels as in the standard model. We assume the partial width of each top quark decay only varies because of a modified CKM matrix element. The fit gives: $|{V_{\mathrm{t}\mathrm{d}}}|^2 +|{V_{\mathrm{t}\mathrm{s}}}|^2 = $ 0.06 $\pm$ 0.06 where the uncertainties include both the statistical and systematic components. In the second scenario, the top quark width is left unconstrained under the assumption that the contributions to the total width from the mixing of the three families are negligible. The corresponding measured values are: $|{V_{\mathrm{t}\mathrm{d}}}|^2 +|{V_{\mathrm{t}\mathrm{s}}}|^2 = $ 0.06 $\pm$ 0.06 $\Gamma_{\mathrm{t}}^{\text{obs}}/\Gamma_{\mathrm{t}} = $ 0.99 $\pm$ 0.42 where again, both the statistical and systematic uncertainties are included. All results are consistent with each other, and show no deviation with respect to extrapolations of low-energy measurements. These results are the first direct, model-independent measurements of the CKM matrix elements for the third-generation quarks, and provide the best determination of these fundamental SM parameters via single top quark measurements. |
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