[Paper Review] Measurement of the Inclusive and Fiducial Cross-Section of Single Top-Quark $t$-Channel Events in $pp$ Collisions at $\sqrt{s}$ = 8 TeV

Phillipp Tepel|arXiv (Cornell University)|Nov 27, 2014

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper presents the first measurement of the fiducial cross-section for $t$-channel single top-quark production in $pp$ collisions at $\sqrt{s} = 8$ TeV using 20.3 fb$^{-1}$ of data. A neural network discriminant was used to separate signal from background, yielding a fiducial cross-section of $3.37 \pm 0.05~(\text{stat.}) \pm 0.47~(\text{syst.}) \pm 0.09~(\text{lumi.})$ pb, consistent with Standard Model predictions and enabling a determination of $|V_{tb}| = 0.97^{+0.09}_{-0.10}$ at 95% confidence level.

ABSTRACT

This article presents the measurement of a $t$-channel single top-quark production fiducial cross-section in the lepton+jets channel with 20.3 fb$^{-1}$ of 8 TeV data using a neural-network discriminant. A fiducial cross-section quoted within the detector acceptance of $σ_{ m fid} = 3.37 \pm 0.05 \, (\mathrm{stat.}) \pm 0.47 \, (\mathrm{syst.}) \pm 0.09 \, (\mathrm{lumi.})~ ext{pb}$ is obtained. The total inclusive $t$-channel cross-section is calculated using the acceptance predicted by various Monte Carlo generators. If the acceptance from the a MC@NLO + Herwig event generator is used, a value of $σ_t = 82.6 \pm 1.2 \, (\mathrm{stat.}) \pm 11.4 \, (\mathrm{syst.}) \pm 3.1 \, (\mathrm{PDF}) \pm 2.3 \, (\mathrm{lumi.})~ ext{pb}$ is obtained, consistent with the Standard Model prediction. Using the ratio of the measured inclusive cross-section to the predicted cross-section and assuming that the top-quark-related CKM matrix elements obey the relation $|V_{tb}|\gg |V_{ts}|, |V_{td}|$, the coupling strength at the $W$-$t$-$b$ vertex is determined to be $|V_{tb}|=0.97^{+0.09}_{-0.10}$. Assuming that $|V_{tb}|\leq 1$ a lower limit of $|V_{tb}|>0.78$ is obtained at the 95% confidence level.

Motivation & Objective

• To measure the fiducial cross-section for $t$-channel single top-quark production in $pp$ collisions at $\sqrt{s} = 8$ TeV.
• To reduce model dependence by focusing on a fiducial phase space defined by detector acceptance and kinematic cuts.
• To extract the $W$-top-bottom coupling strength $|V_{tb}|$ using the measured cross-section and theoretical predictions.
• To validate the consistency of the measurement with the Standard Model through comparison to NLO+NNLL calculations.

Proposed method

• Events were selected with one isolated lepton ($p_T > 25$ GeV, $|\eta| < 2.5$), exactly two jets ($p_T > 30$ GeV, $|\eta| < 4.5$, with $p_T > 35$ GeV in $2.75 < |\eta| < 3.5$), one $b$-tagged jet, and $E_T^{\text{miss}} > 30$ GeV.
• A neural network trained on 14 kinematic observables was used to enhance signal-background separation, with inputs validated for agreement between data and simulation.
• Background contributions were estimated using theoretical predictions for all processes except multijet, which was extracted via a binned maximum-likelihood fit to the $E_T^{\text{miss}}$ distribution.
• The multijet background was modeled using the jet-lepton method in the electron channel and the anti-muon method in the muon channel, both based on data-driven techniques.
• The fiducial cross-section was calculated using the ratio $R_f = \epsilon_{\text{corr,sel}} / \epsilon_{\text{corr,fid}}$, with $\hat{\nu}$ obtained from the fit to the neural network output.
• The inclusive cross-section was extrapolated from the fiducial cross-section using acceptance values from Monte Carlo generators such as a MC@NLO + Herwig, with uncertainties propagated via pseudo-experiments.

Experimental results

Research questions

• RQ1 What is the fiducial cross-section for $t$-channel single top-quark production in $pp$ collisions at $\sqrt{s} = 8$ TeV?
• RQ2 How does the measured fiducial cross-section compare to theoretical predictions from NLO and matched LO generators?
• RQ3 What is the measured value of the $W$-top-bottom CKM matrix element $|V_{tb}|$ based on the cross-section measurement?
• RQ4 What is the 95% confidence level lower limit on $|V_{tb}|$ assuming $|V_{tb}| \leq 1$?
• RQ5 How do systematic uncertainties—especially jet energy scale and generator modeling—affect the precision of the cross-section measurement?

Key findings

• The fiducial cross-section for $t$-channel single top-quark production was measured as $\sigma_{\text{fid}} = 3.37 \pm 0.05~(\text{stat.}) \pm 0.47~(\text{syst.}) \pm 0.09~(\text{lumi.})$ pb.
• The total inclusive $t$-channel cross-section, extrapolated using the a MC@NLO + Herwig generator, is $\sigma_t = 82.6 \pm 1.2~(\text{stat.}) \pm 11.4~(\text{syst.}) \pm 3.1~(\text{PDF}) \pm 2.3~(\text{lumi.})$ pb.
• The measured fiducial cross-section is in excellent agreement with NLO+NNLL theoretical predictions, with a difference of only 1.7% when using POWHEG and a MC@NLO generators.
• The coupling strength at the $W$-top-bottom vertex is determined to be $|V_{tb}| = 0.97^{+0.09}_{-0.10}$, consistent with the unitarity of the CKM matrix.
• A 95% confidence level lower limit of $|V_{tb}| > 0.78$ is established under the assumption $|V_{tb}| \leq 1$.
• The dominant systematic uncertainties arise from jet energy scale $\eta$-intercalibration and $t$-channel generator modeling, contributing significantly to the total uncertainty of $\pm 14\%$.