Testing the SM with penguin- dominated B-decays Amarjit Soni HET,BNL

Outline How good a null test is this? How well does the penguin-dominate? Possible dynamical enhancement of u-quark ? Why (LD)FSI has become a significant concern? How can we tackle this complication? How well can we exploit correlation between ΔS f (=S f – S ψK ) and C f ? Can we make stronger statement about the sign of ΔS f ? Are there (theoretically) problematic modes? Averaging issue Summary and Conclusions.

Questions for the Super-B Workshop

Brief Recapitulation: Basic Idea Dominant decay amp.has 0 weak phase [just as in B->ψK S ] up to O(λ 2 )

Brief remarks on the old study(with London, PLB’97) Originally motivated by the thenCLEO discovery of Huge inclusive (see Browder..) as well as exclusive (see J. Smith…) Brs. into η ’ Suggest with Atwood(PLB97;PRL97) use of η ’ X s(d) for search of NP via DIRCP as in SM expect very small With London suggest use of MICP in [η ’, η,π 0,ρ 0,ω,φ….]K S to test CKM-paradigm via sin2φ 1 (β) Present simple (naïve) estimates of T/P …for All cases T/P <0.04 Due to obvious limitations of method suggest conservative Bound ΔS f <0.10 for the SM For DIRCP see also Hou&Tseng, PRL’98

J. WA ~ 2.7σ

Averaging issue:Are we making a mountain outa anthill? I am rather sceptical and concerned about averaging over many small deviations, leading to ~3.7 σ ….On the other hand, London&A.S, hep-ph/

Null Test(s) In light of B-factory results (existing exptal info+lattice+phenomenology)-> deviations from CKM-paradigm due BSM-CP-odd phase(s) are likely to be small-> should develop Null Tests Since CP is not an exact symmetry of SM->No EXACT NULL TESTS-> Need “Approximate Null Tests” (ANTs). In b->s transitions, penguin-dominated B-decays are a powerful ANT W(“worthiness”)=C(“cleanliness”) X S(“sensitivity”)=4.5* X 5* ANT: In large class of modes such as (π 0,ρ,ω,η ’,φ,f 0,K 0 K 0 …)K 0, (penguin/Total) ~ 1 -> ΔS f ~0 Summary of early (London + AS, PLB’97) study…. ΔS f < 0.1 in the SM (for modes discussed therein) Summary of Recent Reaxmination (Cheng,Chua+AS,hepph/ ….), ΔS f > 0.1 most likely due BSM-CP-odd phase (for many modes)

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A possible complications: large FSI phases in 2-body B decays The original papers predicting ΔS f =S f - S ψK ~0 used naïve factorization ideas; in particular FSI were completely ignored. A remarkable discovery of the past year is that direct CP in charmless 2-body modes is very large-> (LD)FS phases in B-decays need not be small SINCE THESE ARE INHERENTLY Non-perturbative model dependence becomes unavoidable

HYC-CKM05

All rescattering diagrams contribute to penguin topology, dominated by charm intermediate states fit to rates  r D = r D*  0.67  predict direct CPV B   Should reduce model dependence Significantly for CPV

HYC-CKM05

Cheng,Chua,A.S. Hep-ph/ Note in SD, ΔS switches sign bet. ω,ρ for us no change 2. LD rescattering effects on S & C are highly correlated and similarly C’s of isospin partners are correlated -> many testable predictions,e.g LARGE (13%)DIR CP for ω K S & HUGE for ρ K S (~ -46%)

BR SD (10 -6 ) BR with FSI (10 -6 ) BR Expt (10 -6 ) DCPV SD DCPV with FSI DCPV Expt BB   0.03 B0B0   0.02 B0B0   0.04 B0B0   0.14 Only LD uncertainties due to form-factor cutoff are shown here. Total errors=SD+LD, for example, FSI yields correct sign and magnitude for A(  +K-) P/T| SD =0.12 exp(-i177  ), P/T SD+LD =(0.14  0.01)exp[i(147  8)  ] _ _ _ _

Note the very large (~ -40%) DCP in ρ0 K - & ρ0 K 0

More remarks & ρ 0 K S May be a good way Based on our study it seems difficult to accommodate ΔS>0.10 within the SM at least for K S [ή,φ]

Summary (1 of 2) 1) Penguin dominated B-decays (b->s) are very useful “ANTs” of SM; for many modes ΔS>0.10 difficult to accommodate in SM. 2) The η’ K S is esp. clean…due dominance of Penguin (huge Br), which was in fact the original motivation for suggesting the η’ ; Model calculations show ΔS(η’ K S )~0.01. Since expt. Error for η’ K S is smallest (0.11), prospects for precision for this mode seem promising. 3) S-C correlation provides a very useful check On the models -> improved expt. measurements should lead to improvements in the models -> other modes may also become useful. 4) Noteable predictions of our model: large dir.CP in [ π,ρ] K -, [ρ,ω]K S 5) The sign of ΔS in our (and several other) model(s) tends to be positive with small central value (compared to largish ) errors; thus conclusive statements regarding the sign are difficult to make (Exptal. sign of ΔS tends to be negative!)

Sign of ΔS in the SM Mode pQCD(SM ) QCDF(MB) QCDF+FSI(CCS) η’K S.01(.01,-.01).00(.00,-.04) φK S..020(.004,-.008).02(.01,-.01).03(.01,-.04) πK S.009(.001,-.003).07(.05,-.04).04(.02,-.03)

Summary (2):Bottomline Most of the effect currently is driven by the largish ΔS for η’ K S. If New Physics is responsible for this then NP MUST show up in numerous (b ->s) channels e.g. η’ K -, φ[K 0,K - …] (*), affecting mixing, dir and triple-corr CP…AND B S physics. Also, in all liklihood, radiative, leptonic (b->s) should also be effected making Expts. With higher luminosities extremely rich and exciting!