  Penguin contributions, being not negligible in general, can hide the
information on the CKM angle alpha coming from the measurement of the
time-dependent B0(t) -> pi+pi- CP-asymmetry. Nevertheless, we show that this
information can be summarized in a set of simple equations, expressing alpha as
a multi-valued function of a single theoretically unknown parameter, which
conveniently can be chosen as a well-defined ratio of penguin to tree
amplitudes. Using these exact analytic expressions, free of any assumption
besides the Standard Model, and some reasonable hypotheses to constrain the
modulus of the penguin amplitude, we derive several new upper bounds on the
penguin-induced shift |2alpha-2alpha_eff|, generalizing the recent result of
Grossman and Quinn. These bounds depend on the averaged branching ratios of
some decays (pi0pi0, K0K0bar, K+-pi-+) particularly sensitive to the penguin.
On the other hand, with further and less conservative approximations, we show
that the knowledge of the B+- -> Kpi+- branching ratio alone gives sufficient
information to extract the free parameter without the need of other
measurements, and without knowing |V_td| or |V_ub|. More generally, knowing the
modulus of the penguin amplitude with an accuracy of ~30% might result in an
extraction of alpha competitive with the experimentally more difficult isospin
analysis. We also show that our framework allows to recover most of the
previous approaches in a transparent and simple way, and in some cases to
improve them. In addition we discuss in detail the problem of the various kinds
of discrete ambiguities.
