Fourth generation quark masses and KM phenomenology from a fritzsch mass matrix

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From the patterns of the quark mass matrices observed in two and three generations of quarks, a plausible form of the quark mass matrix with phases (of multiples of ½ π) is proposed for four generations of quarks. This allows the determination of the entire 4 × 4 KM matrix as a function of just two unknowns ( m b′ and m t′ ), and the allowed mass ranges of the 4th generation quarks (which we call b′ and t′) are obtained from the present constraints on the KM matrix in the first 3-generation sector. The possibility of a light 4th generation quark ( m b′ < 45 GeV) is shown, while the most likely bounds on the masses are m b′ ⩾ 32 GeV, m t′ ⩾ 82 GeV for the “bag” factor | B K | > 0.1. It is pointed out that UA1's t-quark data may also contain the b′-quark with m b′ ⩽ 50 GeV, and in this case, m t′ is shown to be bounded from above, m t′ ⩽ 190 GeV. Some low-energy phenomenology such as B 0 − B̄ 0 mixing and CP violation, in which the effects of the 4th generation quarks may be observable, are also considered. The main result is that the mixing parameter R odd for B 0 d − B̄ 0 d is 5–6 times larger than in the 3-generation case and may be observable ( R odd ∼ 10%) if the uncertainties in the parameters used are taken into account. The CP -violating parameter l ± is shown to be too small to be observed (O(10 −4 −10 −6 )) for both B 0 d and B s 0 , while the mixing parameter R odd for B s 0 − B̄ s 0 is shown to be definitely observable ( R odd > 50%) regardless of the 4th generation quark masses.