Flavor Changing Neutral Currents involving Heavy Quarks with Four Generations

We study various FCNC involving heavy quarks in the Standard Model (SM) with a sequential fourth generation. After imposing $B\to X_s\gamma$, $B\to X_sl^+l^-$ and $Z\to b\bar{b}$ constraints, we find ${\cal B}(Z\to s\bar{b}+\bar{s}b)$ can be enhanced by an order of magnitude to $10^{-7}$, while $t\to cZ, cH$ decays can reach $10^{-6}$, which are orders of magnitude higher than in SM. However,these rates are still not observable for the near future.With the era of LHC approaching, we focus on FCNC decays involving fourth generation $b^\prime$ and $t^\prime$ quarks. We calculate the rates for loop induced FCNC decays $b^\prime\to bZ, bH, bg, b\gamma$, as well as t^\prime\to tZ,\tH, tg, t\gamma. If $|V_{cb'}|$ is of order $|V_{cb}| \simeq 0.04$, tree level $b^\prime\to cW$ decay would dominate, posing a challenge since $b$-tagging is less effective. For $|V_{cb'}| \ll |V_{cb}|$, $b'\to tW$ would tend to dominate, while $b'\to t^\prime W^*$ could also open for heavier $b'$, leading to thepossibility of quadruple-$W$ signals via $b'\bar b'\to b\bar b W^+W^-W^+W^-$. The FCNC $b'\to bZ, bH$ decays could still dominate if $m_{b'}$ is just above 200 GeV. For the case of $t'$, ingeneral $t^\prime\to bW$ would be dominant, hence it behaves like a heavy top. For both $b'$ and $t'$, except for the intriguing light $b'$ case, FCNC decays are in the $10^{-4} -10^{-2}$ range, and are quite detectable at the LHC.For a possible future ILC, we find the associated production of FCNC $e^+e^-\to b\bar s$, $t\bar c$ are below sensitivity, while $e^+e^-\to b^\prime\bar b$ and$t^\prime\bar t$ can be better probed.Tevatron Run-II can still probe the lighter $b'$ or $t'$ scenario. LHC would either discover the fourth generation and measure the FCNC rates, or rule out the fourth generation conclusively.Comment: 31 pages, 15 eps figures, version to appear in JHE