Measuring $|V_{td}|$ at the LHC

We propose a direct measurement of the Cabibbo-Kobayashi-Maskawa element $V_{td}$ at the LHC. Making use of the imbalance between $d$ and $\overline{d}$ quark content in the proton, we show that a nonzero $V_{td}$ induces a charge asymmetry in the $tW$ associated production. The main backgrounds to this process—$t\overline{t}$ production, and $tW$-associated production mediated by $V_{tb}$—give charge-symmetric contributions at leading order in QCD. Therefore, using specific kinematic features of the signal, we construct a charge asymmetry in the dilepton final state which—due also to a reduction of systematic uncertainties in the asymmetry—is potentially sensitive to $V_{td}$ suppressed effects. In particular, using signal and background simulations up to the detector level, we show that this new observable could already improve the current direct upper bound on $|V_{td}|$ with existing LHC data. We also project that $|V_{td}|$ values down to $\sim 10$ times the standard model prediction could be probed at the high-luminosity LHC.

Figure 1

Feynman diagrams contributing to $pp\to tW$ production proportional to $V_{td}$ at LO in QCD.

Figure 2

Examples of Feynman diagrams contributing to further $V_{td}$-sensitive processes at the LHC.

Figure 3

Distributions of $p_T$ and $\eta$ of the final particles at the parton level for the LO signal (red solid line) and the main backgrounds NLO $t\overline{t}$ (blue dashed line) and LO $tW(b)$ (green dotted line). Each sample contains the corresponding process and its charge conjugate, since on an event-by-event basis one cannot distinguish which lepton comes from the $t$ decay and which from the associatively produced $W$ decay.

Figure 4

Density plot of normalized event distributions of the signal (left) and the main background $t\overline{t}$ (center) in the $\mathrm{\Delta }|\eta (\ell )|/\mathrm{\Sigma }|\eta (\ell )|$ versus $\mathrm{\Delta }{p}_T(\ell )/\mathrm{\Sigma }{p}_T(\ell )$ plane. In the right panel we show the difference between the two distributions, which demonstrates that (compared to the almost symmetric background) signal events are predominantly in the third quadrant of the plot, whereas they are missing in the first quadrant. This correlation between the plotted variables points out that an asymmetry between these quadrants would be useful to enhance signal over background.

Figure 5

Expected value of the asymmetry $A(\eta ,p_T)$ (solid red) as function of the NP parameter $r=|V_{td}/V_{td}^{\mathrm{SM}}|$. The shaded area represents statistical (darker)+assumed systematic (lighter) uncertainties ($\pm 1\sigma$) with the event selection indicated in the text at the prospective LHC luminosity of $L=3000{\mathrm{fb}}^{-1}$. The blue line represents the SM value of the asymmetry, which is mainly due to NLO QCD effects in $t\overline{t}$. Also shown (in dashed red) is an estimation of the asymmetry assuming a reduction of the dominant $t\overline{t}$ background by half (see the text for details).

Figure 6

Contour lines for the $2\sigma$, $3\sigma$, and $5\sigma$ measurement of $|V_{td}|$ parametrized as a function of $r=|V_{td}/V_{td}^{\mathrm{SM}}|$ and the LHC luminosity. Dashed lines correspond to the estimation of the same analysis assuming a further reduction of the $t\overline{t}$ background by half (see text for details).