Letter of Intent for KEK Super B Factory Part I: Physics

By measuring the branching ratios of the three decay modes and the time dependent asymmetry
of π + π − , one can determine the absolute values |A0| and |A2| and their relative phase difference
arg(A0A ∗ 2 ), through a simple geometric reconstruction. Then, the angle φ2 can be determined
up to a four-fold ambiguity.
Another solution is to consider the isospin relations among B → ρπ decays [20]. There are
three possible decay chains B 0 → {ρ + π − , ρ 0 π 0 , ρ − π + } → π + π − π 0 . Together with their CP -
conjugate amplitudes, there exist six different amplitudes, each of which has contributions from
both tree and penguin diagrams. By combining the time-dependent asymmetry of this process
in the Dalitz plot one may extract the pure tree amplitude, and thus the angle φ2.
If there is non-negligible contribution from the electroweak penguin diagram, the isospin relations
are violated, since up and down quarks have different charges [21]. However, such a contribution
is suppressed compared to the gluon penguin by a factor α [weak(m 2 t /m 2 Z )]/αs ln(m 2 t /m 2 c)] ∼
0.1 [22]. At Super-KEKB, the actual size of the electroweak penguin amplitude can be estimated
from the analysis of Kπ decays [22–26].
The prospects of measuring the angle φ2 at Super-KEKB using these methods are discussed
in Section 4.7.
2.5 Theoretical Methods
In order to extract fundamental parameters, such as the quark masses and CKM matrix elements,
from B decay experiments, one needs model independent calculations of the decay amplitudes.
However, since B meson decays accompany complicated QCD interactions, which are highly
non-perturbative in general, the theoretical calculation of physical amplitudes is a non-trivial
task.
2.5.1 Heavy Quark Symmetry
One useful theoretical method with which one can avoid the hadronic uncertainty is to use
symmetries. Using isospin or SU(3) flavor symmetries, different decay amplitudes can be related
to each other. This approach is widely used in B decay analyses, e.g. the isospin analysis of ππ
decays to extract sin 2φ2 discussed in Section 2.4.2.
Another symmetry which is especially important in B physics is the heavy quark symmetry
[27, 28]. In the limit of an infinitely heavy quark mass, the heavy quark behaves as a static
color source and the QCD interaction cannot distinguish different flavors, i.e. charm or bottom.
Consequently the decay amplitudes (or form factors) of b and c hadrons are related to each
other (heavy quark flavor symmetry). Moreover, since the spin-dependent interaction decouples
in the infinitely heavy quark mass limit, some form factors become redundant (heavy quark spin
symmetry). The most famous example is the heavy-to-heavy semi-leptonic decay B → D (∗) ℓνℓ
form factors. In general there are 6 independent form factors for these exclusive decay modes,
but in the heavy quark limit they reduce to one: the Isgur-Wise function, and its normalization
in the zero-recoil limit is determined.
A more general formalism has also been developed in the language of effective field theory,
i.e. Heavy Quark Effective Theory (HQET) [29–31]. It provides a systematic expansion in terms
of ΛQCD/mQ.
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