charming penguins strike back

23 August 2001

Physics Letters B 515 (2001) 33–41www.elsevier.com/locate/npe

Charming penguins strike back

M. Ciuchinia, E. Francob, G. Martinellib, M. Pierinib, L. Silvestrinib

a Dipartimento di Fisica, Università di Roma Tre, and INFN, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Rome, Italyb Dipartimento di Fisica, Università “La Sapienza” and INFN, Sezione di Roma, Piazzale A. Moro, I-00185 Rome, Italy

Received 18 May 2001; accepted 5 June 2001Editor: G.F. Giudice

Abstract

By using the recent experimental measurements ofB → ππ andB → Kπ branching ratios, we find that factorization isunable to reproduce the observed BRs even taking into account the uncertainties of the input parameters. Charming and GIMpenguins allow to reconcile the theoretical predictions with the data. Because of these large effects, we conclude, however,that it is not possible, with the present theoretical and experimental accuracy, to determine the CP violation angleγ fromthese decays. Contrary to factorization, we predict large asymmetries for several of the particle–antiparticle BRs, in particularBR(B+ → K+π0), BR(Bd → K+π−) andBR(Bd → π+π−). This opens new perspectives for the study of CP violation inB systems. 2001 Elsevier Science B.V. All rights reserved.

1. Introduction

The theoretical understanding of non-leptonic twobodyB decays is a fundamental step for testing flavourphysics and CP violation in the Standard Model andfor detecting signals of new physics [1–5]. The in-creasing accuracy of the experimental measurementsat theB factories [6,7] calls for a significant improve-ment of the theoretical predictions. In this respect, im-portant progress has been recently achieved by sys-tematic studies of factorization made by two indepen-dent groups [8,9]. These studies, while confirming thephysical idea [10] that factorization holds for hadronscontaining heavy quarks,mQ � ΛQCD, give the ex-plicit formulae necessary to compute quantitativelythe relevant amplitudes at the leading order of theΛQCD/mQ expansion. They also examine some of thecontributions entering at higher order inΛQCD/mQ.

E-mail address:[email protected] (M. Ciuchini).

The question which naturally arises is whether in prac-tice the power-suppressed corrections, for which quan-titative estimates are missing to date, may be phenom-enologically important forB decays. This problemwas previously addressed in Refs. [11–13]. In partic-ular, the main conclusion of Ref. [11] was thatnon-perturbativepenguin contractions of the leading oper-ators of the effective weak Hamiltonian,Q1 andQ2,although formally ofO(ΛQCD/mQ), may be impor-tant in cases where the factorized amplitudes are ei-ther colour- or Cabibbo-suppressed. The most dra-matic effect of these non-factorizable penguin contrac-tions manifested itself in the very large enhancementof theB → Kπ branching ratios, as was also emerg-ing from the first measurements by the CLEO Col-laboration [14]. In this case, the effect was triggeredby Cabibbo-enhanced penguin contractions of the op-eratorsQc

1 andQc2, usually referred to ascharming

penguins. Since the original publications, about threeyears ago, several other decay channels have beenmeasured [15–17] and the precision of the measure-

0370-2693/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved.PII: S0370-2693(01)00700-6

34 M. Ciuchini et al. / Physics Letters B 515 (2001) 33–41

ments is constantly improving. With respect to pre-vious analyses, it is now possible to attempt a morequantitative study of charming penguin effects andof the corrections expected to the factorized predic-tions. We now present the main conclusions of our newanalysis.

1.1. Factorization with|Vub| andγ from otherdeterminations

Using the available experimental information on|Vub| and on the CP angleγ provided by the unitar-ity triangle analysis (UTA) [18], the branching ratiospredicted with the factorized amplitudes, including theO(αs) corrections computed according to Ref. [9],fail to reproduce the experimentalB → Kπ branch-ing ratios that are systematically larger than the the-oretical predictions. In addition,BR(Bd → π+π−),which depends on the semileptonic form factorfπ (0),is about a factor of 2 larger than its experimentalvalue.1 We note that the value ofBR(Bd → π+π−)within factorization is essentially fixed by the mea-suredBR(B+ → π+π0) rate. Thus, contrary to thestatement of Ref. [9], the predicted value ofBR(Bd →π+π−) is independent of the theoretical assumptionson the value offπ (0). This holds essentially true alsofor theB →Kπ BRs since the value of the “semilep-tonic” form factor at zero momentum transferfK(0)is correlated tofπ(0) by the approximateSU(3) sym-metry.

1.2. Factorization fittingγ

Even if one ignores the value ofγ from UTA,which is only justified if there are contributions to�F = 2 mixing due to physics beyond the StandardModel, there are serious difficulties in reproducing theexperimental results. In particular,BR(Bd → K0π0)

and BR(B+ → K0π+) are much smaller than theirexperimental values. Moreover, the value ofγ ex-tracted from a fit to the data,γ = (163± 12)◦, isin total disagreement with that from the UTA,γ =(54.8 ± 6.2)◦ [18]. In addition, in order to enhance

1 Unless explicitly stated the BRs always refer to the average ofparticles and antiparticles, e.g,BR(Bd → K0π0) ≡ 1

2 (BR(B 0d

→K 0π0)+ BR(B0

d →K0π0)).

theB → Kπ rates, the preferred values offK(0) =0.40±0.02 andfπ (0)= 0.34±0.01 are incompatiblewith the latest theoretical estimates,fπ (0) = 0.26±0.05±0.04,fK(0)/fπ(0)= 1.21±0.09+0.00

−0.09 [19] and

fπ(0) = 0.28± 0.05, fK(0)/fπ(0) = 1.28+0.18−0.10 [20],

whereas|Vub| must have a rather low value,|Vub| =(2.79± 0.19) × 10−3 instead of that extracted frominclusive [21] and exclusive [22] semileptonicB de-cays,|Vub| = (3.25± 0.29± 0.55) × 10−3. We con-clude that, even relaxing the constraint onγ , it is verydifficult to reconcile the predictions from factorizationwith the experimental and theoretical findings. For thisreason any attempt to extract, within factorization, thevalue ofγ from ratios of BRs, for which the discrepan-cies with the experiments can be accidentally hidden,is not very useful. We think that a preliminary step isto understand the missing dynamical effects.

1.3. Factorization and charming penguins

The inclusion of charming penguin effects, whichwill be explained in detail in Section 2, considerablyimproves the situation for theB → Kπ channels,with values of |Vub| and γ well compatible withother determinations. In contrast to theB → Kπ

case, charming penguins are not Cabibbo-enhancedin B → ππ decays and are thus expecteda priorito play a minor role. For this reason they shouldbe consistently neglected, together with all otherΛQCD/mb corrections. This would leave the problemof a too large predictedBR(Bd → π+π−) unsolved.A natural question is then whether the inclusion ofΛQCD/mb effects inBd → π+π− can improve theagreement of the predictions with the experimentaldata. In particular, besides the charming penguins,penguin contractions ofQu

1 andQu2 (GIM penguins

in the notation of Ref. [11]), which are Cabibbo-suppressed inB →Kπ , might play an important role.We show that, for numerical values of the charmingand GIM penguin amplitudes of the expected size,ΛQCD/mb ∼ 0.1–0.2, we can easily reproduce theexperimental data for bothB → Kπ andB → ππ

decays while respecting the constraints from the UTA.The sensitivity ofB → π+π− to Λ/mb effects castsserious doubts on the possibility of extracting sin 2α

from the coefficient of the sin�mBd t term obtainedfrom CP asymmetry measurements. On the other

M. Ciuchini et al. / Physics Letters B 515 (2001) 33–41 35

hand, we find that the value of the rate asymmetry,

A(Bd → π+π−)

(1)= BR(B 0d → π+π−)− BR(B0

d → π+π−)BR(B 0

d → π+π−)+ BR(B0d → π+π−)

,

could be unexpectedly large and call our experimentalcolleagues for separate measurements of theB andB BRs. In particular, we find|A(B± → K±π0)| =0.18 ± 0.06, |A(Bd → K±π∓)| = 0.17± 0.06. Wealso find|A(Bd → π+π−)| = 0.30–0.50. In the lattercase, as discussed in the following, the results aresubject to other effects on which we do not havecontrol. For this reason we do not quote an error. Wesimply signal that there is room for a large asymmetryalso inBd → π+π− decays.

2. Results

In this section we describe and discuss more indetail the different cases which have been consideredin our analysis.

The physical amplitudes forB →Kπ andB → ππ

are more conveniently written in terms of RG invari-ant parameters built using the Wick contractions of theeffective Hamiltonian [23]. In the heavy quark limit,following the approach of Ref. [9], it is possible tocompute these RG invariant parameters using factor-ization. The formalism has been developed so that itis possible to include also the perturbative correctionsto orderαs , i.e., at the next-to-leading order in per-turbation theory. We present results obtained with thisformalism with the addition of the non-perturbativeΛQCD/mb corrections to factorization described be-low in this section. An alternative framework is pro-vided by the approach of Ref. [8]. This method differsin the treatment of theO(αs ) terms; unlike the methodof Ref. [9], the calculations are only valid at the lead-ing logarithmic order and it is not clear how the inde-pendence of the final result from the renormalizationscale of the operators of the effective Hamiltonian isrecovered. Moreover, the Sudakov suppression of theendpoint region, advocated in [8], is still rather contro-versial from both the theoretical and phenomenologi-cal point of view. For these reasons we prefer to post-pone the analysis with the approach of Ref. [8] untilthe theoretical situation will become clearer.

In the leading amplitudes, we have taken into ac-count theSU(3) breaking terms by using the appro-priate decay constants,fK andfπ , and form factors,fK(0) andfπ(0). Strictly speaking, the form factorsshould be evaluated at the invariant mass of the emit-ted meson (fK(m2

π), fπ (m2K) or fπ (m2

π)). The dif-ference is however of higher order inΛQCD/mb andnot Cabibbo- or colour-enhanced and can safely beneglected (it is also numerically immaterial) [24]. Asfor ΛQCD/mb corrections, we have assumed insteadSU(3) symmetry and neglected Zweig-suppressedcontributions. In this approximation, bySU(3) sym-metry one can show that all the Cabibbo-enhancedΛQCD/mb corrections toB → Kπ decays can be re-absorbed in a single parameterP1. Several correctionsare contained inP1: this parameter includes not onlythe charming penguin contributions, but also annihila-tion and penguin contractions of penguin operators. Itdoes not include leading emission amplitudes of pen-guin operators (Q3–Q6) which have been explicitlyevaluated using factorization. Had we included theseterms, this contribution would exactly correspond tothe parameterP1 of Ref. [23]. The parameterP1 (P1)encodes automatically not only the effect of the anni-hilation diagrams considered in [25], but all the othercontributions ofO(ΛQCD/mb) with the same quan-tum numbers of the charming penguins. In this respectit is the most general parameterization of all the per-turbative and non-perturbative contributions of the op-eratorsQ5 andQ6 (Q3 andQ4), including the worry-ing higher-twist infrared divergent contribution to an-nihilation discussed in Ref. [26]. The parameterP1is of O(ΛQCD/mb) and has the same quantum num-bers and physical effects as the original charming pen-guins proposed in [11], although it has a more gen-eral meaning. In some of the previous analyses, seefor example [27], penguin contractions of the operatorQ6, computed by using perturbation theory and fac-torization, are enhanced by taking a low effective scalefor αs . This procedure produces a physical effect simi-lar to that coming from the non-perturbative charmingpenguins that we are using here, since they have thesame quantum numbers.

If one also includesB → ππ decays we haveseveral other parameters, for examplePGIM

1 andP3,in the formalism of Ref. [23]. A closer look toP3 shows that this term is due either to Zweig-suppressed annihilation diagrams (called CPA and


Table 1Input values used in the numerical analysis. The form factors are taken from Refs. [19,20], the CKM parameters from Ref. [18] and the BRscorrespond to our average of CLEO, BaBar and Belle results [15–17]. All the BRs are given in units of 10−6

fπ (0) 0.27± 0.08 fK(0)/fπ (0) 1.2± 0.1

ρ 0.224± 0.038 η 0.317± 0.040

BR(Bd →K0π0) 10.4± 2.6 BR(B+ →K+π0) 12.1± 1.7

BR(B+ →K0π+) 17.2± 2.6 BR(Bd →K+π−) 17.2± 1.6

BR(Bd → π+π−) 4.4± 0.9 BR(B+ → π+π0) 5.2± 1.7

DPA in Ref. [11]) or to annihilation diagrams whichare colour-suppressed with respect to those enteringP1. For this reason we have putP3 to zero.PGIM

1 willbe discussed later on.

We give now the explicit expression of theBd →K+π− amplitude as an illustrative example. In termsof the parameters defined in [23], this amplitude reads

A(Bd → K+π−)= −VusV

∗ub

(E1(s, u,u;Bd,K

+,π−)− PGIM

1 (s, u;Bd,K+,π−)

)(2)+ VtsV

∗tbP1(s, u;Bd,K

+,π−).Using the approach of [9], we have

E1(s, u,u;Bd,K+,π−)

= au1(Kπ)⟨Qu

1

⟩fact + au2(Kπ)

⟨Qu

2

⟩fact + E1,

P1(s, u;Bd,K+,π−) =

6∑i=3

aci (Kπ)〈Qi〉fact + P1,

PGIM1 (s, u;Bd,K

+,π−)

(3)=6∑

i=3

(aci (Kπ)− aui (Kπ)

)〈Qi 〉fact + PGIM1 ,

where〈Qi〉fact denotes the factorized matrix element,and the parametersai are defined in [9]. The tildedparameters representΛQCD/mb corrections; inB →Kπ channels the only Cabibbo-enhanced correctionis given byP1. This term has no arguments since wetake it in theSU(3) symmetry limit.

We use input parameters (likeρ, η, the form fac-tors) with errors, and extract output quantities (like theBRs, the asymmetries, but alsoγ , or the form factorswhen they are not used as inputs) with their uncertain-ties. Let us explain how we used the input errors and

extracted the output uncertainties. We proceed withthe usual likelihood method, by generating the inputquantities weighted by their probability density func-tion (p.d.f.). In the case of theoretical quantities this isassumed to be flat, whereas the experimental quanti-ties are extracted with Gaussian distributions. Proba-bility density functions, averages and standard devia-tions are then obtained by weighting the output quan-tities by the likelihood factor

(4)L= exp

{−1

2

∑i

(BRi − BRexpi )2

σ 2i

},

whereσi are the standard deviations of the experimen-tal BRs,BRexp

i , given in Table 1. In cases where the ex-perimental input has a systematic error dominated bytheoretical uncertainties, we should extract the latterwith a flat distribution [18]. We have instead combinedthe errors in quadrature and extracted all the experi-mental quantities with Gaussian distributions. Withinthe present accuracy, and taking into account the un-known non-perturbative parameters, this procedure isfully justified. We have also verified that by extract-ing the theoretical errors with a Gaussian distribution,we obtain very similar results. For more details onthe likelihood procedure, the reader is referred to [18],where all aspects are discussed at length.

2.1. Results with factorization

We start by considering the case in which we usefactorization and take the CKM parameters|Vub| andγ from other experimental determinations. We discussfirst BR(B+ → π+π0) since in this case, due toisospin symmetry, we do not have the complicationsdue to penguin contractions. Thus, at fixed|Vub|, the


Table 2Results for the BRs obtained with factorization without charming or GIM penguins. All the BRs are given in units of 10−6

BR γ UTA γ free BR γ UTA γ free

K0π0 5.9± 0.2 5.7± 0.4 K+π0 4.8± 0.2 9.1± 0.5

K0π+ 11.7± 0.5 11.6± 0.8 K+π− 9.8± 0.4 17.7± 1.0

π+π− 8.5± 0.3 5.1± 0.7 π+π0 4.2± 0.2 5.4± 0.6

π0π0 0.19± 0.01 0.59± 0.04

prediction for BR(B+ → π+π0) only depends onfπ (0) (trivial dependences as fromfπ will be omittedin this discussion). By using the theoretical estimateand uncertainty offπ (0) from [19], and taking intoaccount the uncertainties on|Vub|, we predict in thiscaseBR(B+ → π+π0) = (5.0 ± 1.5) × 10−6 in verygood agreement with the experimental average givenin Table 1. A complementary exercise is to use as input|Vub| and the experimental value ofBR(B+ → π+π0)

in order to extract the value offπ (0). In this case wefindfπ(0)= 0.28±0.06, in very good agreement withlattice and QCD sum rules estimates. This exerciseshows that we do not need to rely on theoreticalcalculations for the form factors. Indeed, also forfK(0) we only needfK(0)/fπ(0) which cannot differtoo much from one. Moreover, it is likely that a largepart of the uncertainties of the theoretical predictionscancel in this ratio.

Here and in all the other cases where|Vub| andγare taken from other experimental determinations, weuse as equivalent input parameters the values ofρ andη given in Table 1 from the UTA analysis of Ref. [18].These values correspond to

(5)γ = (54.8± 6.2)◦.

By using fπ (0) either from theory or from the fitto BR(B+ → π+π0) and assuming factorization, wethen predictBR(Bd → π+π−) as a function ofγ only.Besides, in order to analyze allB → Kπ decays, weonly needfK(0)/fπ(0) to which the previous consid-erations apply. Alternatively, we may take only|Vub|from the experiments and fit the value ofγ . In thefirst case, the results are given in Table 2 labeled as“γ UTA” and show a generalized disagreement be-tween predictions and experimental data. In the secondcase, the value ofγ is fitted and the results are labeled

as “γ free”. In this case the disagreement is reducedfor BR(B+ → K+π0) and BR(Bd → K+π−), andalso forBR(Bd → π+π−), but it remains sizable forBR(Bd → K0π0) andBR(B+ → K0π+). The patternBR(B+ → K0π+) : BR(Bd → K+π−) : BR(Bd →K0π0) : BR(B+ → K+π0) = 2 : 2 : 1 : 1, which issuggested by the data, and is well reproduced when thecontribution of the charming penguins is large, as dis-cussed in the following, is lost in this case. Moreover,the fitted value ofγ = (163± 12)◦ is in striking dis-agreement with the results of the UTA. Although onemay question on the quoted uncertainty of the UTA re-sult, it is clearly impossible to reconcile the two num-bers. Thus either there is new physics orΛQCD/mb

corrections are important. We now discuss the latterpossibility.

2.2. Factorization with charming and GIM penguins

We now discuss the effects of charming penguins,parameterized byP1. P1 is a complex amplitude thatwe fit on theB → Kπ BRs. In order to have areference scale for its size, we introduce a suitable“Bag” parameter,B1, by writing

(6)P1 = GF√2fπfπ (0)g1B1,

whereGF is the Fermi constant. We usefπ (0) forboth B → Kπ and B → ππ channels since, asmentioned before, for charming penguins we workin the SU(3) limit. g1 is a Clebsh–Gordan parameterdepending on the finalKπ (ππ ) channel. In the casewhere|Vub| andγ are taken from the UTA, by fittingtheB → Kπ channels andB+ → π+π0 only, we find

(7)∣∣B1

∣∣ = 0.14± 0.05.


Fig. 1. p.d.f. forφ, in the case where onlyP1 (left) and bothP1 andPGIM1 (right) are included.

Table 3BRs with charming or charming and GIM penguins. All the BRs are given in units of 10−6

BR Charming Charming Charming BR Charming Charming Charming

with π+π− + GIM with π+π− + GIM

K0π0 9.2± 1.1 8.7± 0.9 8.8± 1.0 K+π0 9.2± 0.8 9.3± 0.7 9.3± 0.7

K0π+ 18.3± 2.1 17.4± 1.8 17.6± 1.8 K+π− 18.2± 1.4 18.6± 1.4 18.4± 1.3

π+π− 9.1± 2.5 5.1± 1.8 4.7± 0.8 π+π0 4.8± 1.4 2.7± 0.5 3.5± 0.9

π0π0 0.37± 0.05 0.36± 0.05 0.69± 0.30

Note that the size of the charming penguin effectsis of the expected magnitude. As for the phaseφ =Arg(B1), it is very instructive to consider its distri-bution, which is displayed in Fig. 1: the preferredvalue of φ has a sign ambiguity since we are fit-ting the average of theB0

d and B 0d BRs (or of the

B+ and B− BRs). The ambiguity can be resolvedby measuring separately particle and anti-particleBRs.

By using the distribution on the left of Fig. 1,we compute the mean value of|φ| with the result|φ| = (75 ± 44)◦ and leave the sign undetermined.This is a reasonable procedure, given the approximatesymmetry of the distribution and the large uncertainty.In view of the discussion of the particle–antiparticleasymmetry which we present at the end of thispaper, we note here that the value ofφ could berather large. In Table 3 we give the correspondingpredicted values and uncertainties for the relevantbranching ratios (label “Charming”). We observe aremarkable improvement for theKπ channels and

a large shift in the value ofBR(Bd → π0π0), 2 inspite of the fact that in the latter case penguin effectsare not Cabibbo-enhanced (theπ0π0 amplitude is,however, colour-suppressed). The predicted value forBR(Bd → π+π−) remains however much larger thanthe experimental one.

If one fits theB → Kπ channels,B+ → π+π0

andBd → π+π− simultaneously, one finds a betteragreement forBR(Bd → π+π−) but a rather smallvalue forBR(B+ → π+π0) (column “Charming withπ+π−” of Table 3). This happens at the price ofreducing the fitted value of the form factor,fπ (0) ∼0.22, which is pushed down byBR(Bd → π+π−).In fact, the latter has an experimental error muchsmaller thanBR(B+ → π+π0), and therefore governsthe fit. However, we do not think that this is thecorrect procedure: theoretically,BR(B+ → π+π0) ison much more solid grounds thanBR(Bd → π+π−),since it is not affected by penguins or annihilations,and thus is much more suitable to constrainfπ (0).

2 This effect was already noticed in [11].


Fig. 2. p.d.f. for the largest CP asymmetries, in the case where onlyP1 (left) and bothP1 andPGIM1 (right) are included. From top to bottom,

we giveA(B+ →K+π0), A(Bd →K+π−) andA(Bd → π+π−).

In order to reduce the predictedBR(Bd → π+π−)without affectingBR(B+ → π+π0), one may includeother effects of the same order of the charming pen-guins, as for example the GIM penguins introduced inRef. [11]. In this case we fit all the BRs given in Ta-ble 1. With GIM and charming penguins included, wefind

∣∣B1∣∣ = 0.16± 0.03, |φ| = (56± 32)◦,∣∣BGIM

1

∣∣ = 0.23± 0.11,

(8)∣∣φGIM

∣∣ = (135± 37)◦,

where the notation is self-explaining. We have giventhe absolute value ofφ since, as in the previous case,the sign ambiguity persists when we include GIMpenguins. The distribution is also shown in Fig. 1.The results for the BRs can be found in Table 3with the label “Charming+ GIM”. They show thatthe extra GIM parameter improves the agreementfor the measuredB → ππ BRs. We do not claim,however, to be able to predictBR(Bd → π+π−):our results instead show that accurate predictions forBd → ππ decays can only be obtained by controllingquantitatively theO(ΛQCD/mb) corrections, whichis presently beyond the theoretical reach. Estimates


Table 4Absolute values of the rate CP asymmetries forB →Kπ andB → ππ decays. The columns labeled by “Charming” and “Charming+ GIM”correspond respectively to the cases in which onlyP1 and bothP1 andPGIM

1 are introduced. The asymmetry inB → π+π0 vanishes exactly

|A| Charming Charming+ GIM |A| Charming Charming+ GIM

K0π0 0.02± 0.01 0.05± 0.03 K+π0 0.23± 0.10 0.18± 0.06

K0π+ 0.00± 0.00 0.03± 0.03 K+π− 0.21± 0.10 0.17± 0.06

π+π− 0.36± 0.16 0.52± 0.18 π0π0 0.40± 0.19 0.58± 0.29

for charming penguin effects can also be obtained byusing some phenomenological model, as for exampledone in Ref. [12]. We observe that the sensitivityof the BRs to the value ofγ is lost, with thepresent experimental accuracy, once penguin effectsare introduced. Indeed, when one tries to fitB1 (BGIM

1 )andγ simultaneously, one finds that the value ofγ isessentially undetermined. From the above discussion itclearly emerges that one of the important step for theimprovement of this kind of analyses is a more precisemeasurement ofBR(B+ → π+π0).

2.3. Particle–antiparticle asymmetries for thebranching ratios

The large absolute values ofφ, and the sizable ef-fects that penguins have on the BRs, stimulated us toconsider whether we could find observable particle–antiparticle asymmetries as the one defined in Eq. (1).We find large effects inBR(B+ → K+π0), BR(Bd →K+π−) and BR(Bd → π+π−), as shown in Fig. 2.As discussed before, forBR(Bd → π+π−) our pre-dictions suffer from very large uncertainties due tocontributions which cannot be fixed theoretically. Forthis reason, the values of the asymmetry reported inTable 4 are only an indication that a large asymme-try could be observed also in this channel. The signambiguity of φ is reflected in the asymmetryA ∼sinγ sinφ. This ambiguity can be solved only by anexperimental measurement or, but this is extremelyremote, by a theoretical calculation of the relevantamplitudes. For each channel, we give the absolutevalue of the asymmetry in Table 4. Note that withinfactorization all asymmetries would be unobservablysmall, since the strong phase is a perturbative effectof O(αs ) [9]. The possibility of observing large asym-

metries in these decays opens new perspectives. Thesepoints will be the subject of a future study.

3. Conclusion

We have analyzed the predictions of factorizationfor B → ππ andB → Kπ decays. We note that thenormalization of all the other BRs is essentially fixedby the value ofBR(B+ → π+π0) and SU(3) sym-metry. Even taking into account the uncertainties ofthe input parameters, we find that factorization is un-able to reproduce the observed BRs. The introduc-tion of charming and GIM penguins [11] allows toreconcile the theoretical predictions with the data. Italso shows however that it is not possible, with thepresent theoretical and experimental accuracy, to de-termine the CP violation angleγ . Contrary to factor-ization, we predict large asymmetries for several ofthe particle–antiparticle BRs, in particularBR(B+ →K+π0), BR(Bd → K+π−) and BR(Bd → π+π−).This opens new perspectives for the study of CP vi-olation inB systems.

Acknowledgements

We thank G. Buchalla and C. Sachrajda for usefuldiscussions on our work. M.C. thanks the TH divisionat CERN where part of this work has been done. L.S.thanks Hsiang-nan Li for very informative discussionsand J. Matias for pointing out a misprint.

References

[1] M. Ciuchini, E. Franco, G. Martinelli, A. Masiero, L. Sil-vestrini, Phys. Rev. Lett. 79 (1997) 978, hep-ph/9704274.


[2] R. Barbieri, A. Strumia, Nucl. Phys. B 508 (1997) 3, hep-ph/9704402.

[3] R. Fleischer, T. Mannel, hep-ph/9706261.[4] A.F. Falk, A.L. Kagan, Y. Nir, A.A. Petrov, Phys. Rev. D 57

(1998) 4290, hep-ph/9712225.[5] S. Baek, P. Ko, Phys. Rev. Lett. 83 (1999) 488, hep-

ph/9812229.[6] The Babar Physics Book, P.F. Harrison and H.R. Quinn (Eds.),

SLAC report SLAC-R-504, October 1998.[7] F. Takasaki, in: J.A. Jaros, M.E. Peskin (Eds.), Proc. of the 19th

Int. Symp. on Photon and Lepton Interactions at High EnergyLP99, Int. J. Mod. Phys. A 15S1 (2000) 12, hep-ex/9912004.

[8] H.-n. Li, H.L. Yu, Phys. Rev. Lett. 74 (1995) 4388;H.-n. Li, H.L. Yu, Phys. Rev. D 53 (1996) 2480;C.H. Chang, H.-n. Li, Phys. Rev. D 55 (1997) 5577;T.W. Yeh, H.-n. Li, Phys. Rev. D 56 (1997) 1615;H.Y. Cheng, H.-n. Li, K.C. Yang, Phys. Rev. D 60 (1999)094005;For a recent review see: H.-n. Li, hep-ph/0103305.

[9] M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, Phys.Rev. Lett. 83 (1999) 1914;M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, Nucl.Phys. B 591 (2000) 313;M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, hep-ph/0007256.

[10] J.D. Bjorken, Nucl. Phys. B Proc. Suppl. 11 (1989) 325;M.J. Dugan, B. Grinstein, Phys. Lett. B 255 (1991) 583;H.D. Politzer, M.B. Wise, Phys. Lett. B 257 (1991) 399.

[11] M. Ciuchini, E. Franco, G. Martinelli, L. Silvestrini, Nucl.Phys. B 501 (1997) 271, hep-ph/9703353;M. Ciuchini, R. Contino, E. Franco, G. Martinelli, L. Sil-vestrini, Nucl. Phys. B 512 (1998) 3, hep-ph/9708222.

[12] P. Colangelo, G. Nardulli, N. Paver, Riazuddin, Z. Phys. C 45(1990) 575;C. Isola, M. Ladisa, G. Nardulli, T.N. Pham, P. Santorelli, hep-ph/0101118.

[13] A.J. Buras, R. Fleischer, Phys. Lett. B 341 (1995) 379, hep-ph/9409244.

[14] R. Godang et al., CLEO Collaboration, Phys. Rev. Lett. 80(1998) 3456, hep-ex/9711010.

[15] D. Cronin-Hennessy et al., CLEO Collaboration, hep-ex/0001010;D.M. Asner et al., CLEO Collaboration, hep-ex/0103040.

[16] G. Cavoto, BaBar Collaboration, Talk given at the XXXVIRencontres de Moriond QCD.

[17] B. Casey, Belle Collaboration, Talk given at the XXXVIRencontres de Moriond QCD.

[18] M. Ciuchini et al., hep-ph/0012308.[19] A. Abada, D. Becirevic, P. Boucaud, J.P. Leroy, V. Lubicz, F.

Mescia, hep-lat/0011065;See also: L. Del Debbio, J.M. Flynn, L. Lellouch, J. Nieves,UKQCD Collaboration, Phys. Lett. B 416 (1998) 392, hep-lat/9708008.

[20] A. Khodjamirian, R. Ruckl, S. Weinzierl, C.W. Winhart, O.Yakovlev, Phys. Rev. D 62 (2000) 114002, hep-ph/0001297;For an earlier determination of the form factors see also: P.Ball, JHEP 9809 (1998) 005, hep-ph/9802394.

[21] LEP Working group onVub , http://battagl.home.cern.ch/battagl/vub/vub.html.

[22] B.H. Behrens et al., CLEO Collaboration, Phys. Rev. D 61(2000) 052001.

[23] A.J. Buras, L. Silvestrini, Nucl. Phys. B 569 (2000) 3, hep-ph/9812392.

[24] W.N. Cottingham, H. Mehrban, I.B. Whittingham, hep-ph/0102012.

[25] Y. Keum, H. Li, A.I. Sanda, hep-ph/0004004;Y.Y. Keum, H. Li, A.I. Sanda, Phys. Rev. D 63 (2001) 054008,hep-ph/0004173.

[26] M. Beneke, hep-ph/0009328.[27] A. Ali, C. Greub, Phys. Rev. D 57 (1998) 2996, hep-

ph/9707251;A. Ali, G. Kramer, C. Lu, Phys. Rev. D 58 (1998) 094009,hep-ph/9804363;A. Ali, G. Kramer, C. Lu, Phys. Rev. D 59 (1999) 014005,hep-ph/9805403.

charming penguins strike back

Documents