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Motivation for the Higher Luminosity $B$ Factory

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Since the end of the last century, two asymmetric-energy %$e^+e^-$% %$B$% factories, the KEKB collider for the Belle experiment at KEK and the PEPII collider for the BaBar experiment at SLAC, have been achieving a tremendous success that lead to the confirmation of the Standard Model (SM) in the quark flavor sector. In the summer of 2001, the presence of %$CP$% violation in the %$B$% meson system was established by the Belle collaboration and simultaneously by the BaBar collaboration through the measurement of the time dependent asymmetry in the decay process %$B^0(\bar{B}^0)\rightarrow J/\psi K^0_S$% . This measurement was the main target of the present %$B$% factories, and it was achieved as originally planned. The experimental data indicated that the Kobayashi-Maskawa mechanism, which is now a part of the SM of elementary particles, is indeed the dominant source of the observed %$CP$% violation in Nature. Following the experimental confirmation, M. Kobayashi and T. Maskawa were awarded the 2008 Nobel Prize for physics.

The present paper aims to provide the motivation, experimental methods and at least part of the scientific output that could be expected with an upgraded %$B$% factory, based on the succesfull KEKB collider and Belle detector, and planned to start operation in few years.

The Belle experiment proved its ability to measure a number of decay modes of the %$B$% meson and to extract Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and other interesting observables: the precision of the measurement of the angle %$\phi_1$% of the unitarity triangle through the %$B^0\rightarrow J/\psi K^0_S$% time-dependent asymmetry has improved to better than 5% direct %$CP$% violation was observed in %$B^0\rightarrow \pi^+ \pi^-$% and %$K^+ \pi^+$% decays; the angle %$\phi_2$% has been measured with %$B\rightarrow \pi\pi$%, %$\rho\pi$% and %$\rho\rho$% systems using isospin symmetries; the angle %$\phi_3$% has also been measured through the processes %$B\rightarrow D^{()}K^{()}$% and the evidence of direct %$CP$% violation in %$B\rightarrow DK$% decays was obtained; the magnitudes of the CKM matrix elements have been measured much more precisely than before; rare %$B$% decays such as %$B\rightarrow K^{(*)}\ell\ell$% , %$\rho\gamma$% and %$\tau\nu$% have been observed for the first time; the first evidence of %$D^0-\bar{D}^0$% mixing surfaced ; the quantum entaglement of neutral %$B$% meson pairs was directly confirmed . Through these precise measurements and new observations we have succeeded to overconstrain the quark flavor sector of the SM. The latter proves to be self-consistent within the current accuracy of the experimental results.

In spite of the tremendous success mentioned above, several fundamental questions remain in the flavor sector of quarks and leptons. First of all, the SM includes too many parameters - the masses and mixing parameters of the quarks and leptons - all of which are apriori unknown and should be determined experimentally. This is due to the fact that there is no principle to govern the Yukawa terms in the SM Lagrangian. Any Yukawa coupling between two fermions, irrespective of the generation they belong to, is allowed, as far as it is gauge-invariant and renormalizable. In spite of this fact, the measured CKM matrix elements show a clear pattern as shown in