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Penguin contributions, being not negligible in general, can hide theinformation on the CKM angle alpha coming from the measurement of thetime-dependent B0(t) -> pi+pi- CP-asymmetry. Nevertheless, we show that thisinformation can be summarized in a set of simple equations, expressing alpha asa multi-valued function of a single theoretically unknown parameter, whichconveniently can be chosen as a well-defined ratio of penguin to treeamplitudes. Using these exact analytic expressions, free of any assumptionbesides the Standard Model, and some reasonable hypotheses to constrain themodulus of the penguin amplitude, we derive several new upper bounds on thepenguin-induced shift |2alpha-2alpha_eff|, generalizing the recent result ofGrossman and Quinn. These bounds depend on the averaged branching ratios ofsome decays (pi0pi0, K0K0bar, K+-pi-+) particularly sensitive to the penguin.On the other hand, with further and less conservative approximations, we showthat the knowledge of the B+- -> Kpi+- branching ratio alone gives sufficientinformation to extract the free parameter without the need of othermeasurements, and without knowing |V_td| or |V_ub|. More generally, knowing themodulus of the penguin amplitude with an accuracy of ~30% might result in anextraction of alpha competitive with the experimentally more difficult isospinanalysis. We also show that our framework allows to recover most of theprevious approaches in a transparent and simple way, and in some cases toimprove them. In addition we discuss in detail the problem of the various kindsof discrete ambiguities.Comment: LaTeX2e, 44 pages, 9 figures (from 18 postscript files) included with  epsf. Minor changes, references updated. New CLEO results from ICHEP'98 are  taken into account. To appear in Phys. Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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Taming the penguin contributions in theBd0(t)→π+