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We present measurements of the cross sections for the two main productionmodes of single top quarks in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV inthe Run II data collected with the D0 detector at the Fermilab TevatronCollider, corresponding to an integrated luminosity of 9.7 fb$^{-1}$. Thes-channel cross section is measured to be $\sigma(p\bar{p} \to tb+X) =1.10^{+0.33}_{-0.31}$ pb with no assumptions on the value of the t-channelcross section. Similarly, the t-channel cross section is measured to be$\sigma(p\bar{p} \to tqb+X) = 3.07^{+0.54}_{-0.49}$ pb. We also measure the$s+t$ combined cross section as $\sigma(p\bar{p} \to tb+X, tqb+X) =4.11^{+0.60}_{-0.55}$ pb and set a lower limit on the CKM matrix element$|V_{tb}| > 0.92$ at $95\%$ C.L., assuming $m_t=172.5$ GeV. The probability tomeasure a cross section for the s channel at the observed value or higher inthe absence of signal is $1.0\times 10^{-4}$, corresponding to a significanceof 3.7 standard deviations.

Evidence for s-channel single top quark production in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV