Puzzles in B physics

I discuss some puzzles observed in exclusive B-meson decays, concentrating on the large difference between the direct CP asymmetries in the B ⁰ → π⁻ K ⁼ and B ^± → π⁰ K ^± modes, the large B ⁰ → π⁰π⁰ branching ratio, and the large deviation of the mixing-induced CP asymmetries in the b → sqq penguins from those in the b → ccs trees.     

Di-pion emission in heavy quarkonia decays

The dipion spectrum for the ϒ(nS) → ϒ(n′S) transition with n < 4 has the form dw/dq ∼ (phase space) |η − x|², with x = q ² − 4m _π² / (ΔM)² − 4m _π² < q ² ≡ M _ππ², and ΔM = M(nS) − M(n′S). The parameter η is calculated and the spectrum is shown to reproduce the experimental data for all three types of decays: 3 → 1, 2 → 1, and 3 → 2 with η ≈ 0.5, 0, and −3, respectively. The text was submitted by the author in English.     

Beauty-conserving strangeness-changing rare semileptonic decays ofB s meson

The beauty-conserving strangeness-changing decays ofB _s meson are examined. In the charm sector, charm-conserving strangeness changing (Δc = 0, Δs ≠ 0) decays are Cabibbo suppressed and are governed by the CKM elementV _us which is much smaller than the CKM diagonal elementV _cs, so may be of little interest. On the other hand, in theb-sector, beauty-conserving strangeness changing (Δb = 0, Δs ≠ 0) decays are CKM allowed as the CKM matrix elementV _us governing such decays is much larger thanV _bc orV _bu which govern respectively theb →c orb →u transitions. The phase space available, however, is too small for the decays considered here. The numerical estimates for the decay widths of two such modes ofB _s meson are presented.     

Bs,d→ππ,πK,KK: status and prospects

Several years ago, it was pointed out that the U-spin-related decays B_d→π⁺π^-, B_s→K⁺K^- and B_d→π^∓K^±, B_s→π^±K^∓ offer interesting strategies for the extraction of the angle γ of the unitarity triangle. Using the first results from the Tevatron on the B_s decays and the B-factory data on B_u,d modes, we compare the determinations of γ from both strategies, study the sensitivity on U-spin-breaking effects, discuss the resolution of discrete ambiguities, predict observables that were not yet measured but will be accessible at LHCb, explore the extraction of the width difference ΔΓ_s from untagged B_s→K⁺K^- rates, and address the impact of new physics. The data for the B_d→π⁺π^-, B_s→K⁺K^- system favour the BaBar measurement of direct CP violation in B_d→π⁺π^-, which will be used in the numerical analysis and result in a fortunate situation, yielding γ=(66.6^+4.3+4.0 _-5.0-3.0)^°, where the latter errors correspond to a generous estimate of U-spin-breaking effects. On the other hand, the B_d→π^∓K^±, B_s→π^±K^∓ analysis leaves us with 26°≤γ≤70°, and points to a value of the B_s→π^±K^∓ branching ratio that is larger than the current Tevatron result. An important further step will be the measurement of mixing-induced CP violation in B_s→K⁺K^-, which will also allow us to extract the B⁰ _s–B̄⁰ _s mixing phase unambiguously with the help of B_s→J/ψφ at the LHC. Finally, the measurement of direct CP violation in B_s→K⁺K^- will make the full exploitation of the physics potential of the B_s,d→ππ,πK,KK modes possible.     

B-decay CP-asymmetries in SUSY with a U(2)3 flavour symmetry

We study CP asymmetries in rare B decays within supersymmetry with a U(2)³ flavour symmetry, motivated by the SUSY flavour and CP problems, the hierarchies in the Yukawa couplings and the absence so far of any direct evidence for SUSY. Even in the absence of flavour-blind phases, we find potentially sizable CP violating contributions to b→s decay amplitudes. The effects in the mixing-induced CP asymmetries in B→ϕK _S and B→η′K _S , angular CP asymmetries in B→K ^∗ μ ⁺ μ ⁻ and the direct CP asymmetry in B→X _s γ can be in the region to be probed by LHCb and next generation B factories. At the same time, these effects in B decays are compatible with CP violating contributions to meson mixing, including a non-standard B _s mixing phase hinted by current tensions in the CKM fit mostly between S_yKS, e_KS_{\psi K_{S}}, \epsilon_{K} and DM_Bs/DM_Bd\Delta M_{B_{s}}/\Delta M_{B_{d}}.     

On puzzles and non-puzzles in B→ππ,πK decays

Recently, we have seen interesting progress in the exploration of CP violation in B⁰ _d→π⁺π^-: the measurements of mixing-induced CP violation by the BaBar and Belle collaborations are now in good agreement with each other, whereas the picture of direct CP violation is still unclear. Using the branching ratio and direct CP asymmetry of B⁰ _d→π^-K⁺, this situation can be clarified. We predict , which favours the BaBar result, and we extract γ=(70.0^+3.8 _-4.3)^°, which agrees with the unitarity triangle fits. Extending our analysis to other B→πK modes and B⁰ _s→K⁺K^- with the help of the SU(3) flavour symmetry and plausible dynamical assumptions, we find that all observables with colour-suppressed electroweak penguin contributions are measured to be in excellent agreement with the standard model. As far as the ratios R_c,n of the charged and neutral B→πK branching ratios are concerned, which are sizeably affected by electroweak penguin contributions, our standard-model predictions have almost unchanged central values but significantly reduced errors. Since the new data have moved quite a bit towards these results, the “B→πK puzzle” for the CP conserving quantities has been significantly reduced. However, the mixing-induced CP violation of B⁰ _d→π⁰K_S does look puzzling; if confirmed by future measurements, this effect could be accommodated through a modified electroweak penguin sector with a large CP violating new-physics phase. Finally, we point out that the established difference between the direct CP asymmetries of B^±→π⁰K^± and B_d→π^∓K^± appears to be generated by hadronic and not by new physics.     

Phenomenological applications of<Emphasis Type="Italic">k</Emphasis><Subscript>T</Subscript>factorization

We discuss applications of the perturbative QCD approach in the exclusive non-leptonic two-bodyB-meson decays. We briefly review its ingredients and some important theoretical issues on the factorization approach. PQCD results are compatible with present experimental data for charmless B-meson decays. We predict the possibility of large direct CP asymmetry in B⁰ → π⁺π⁻ (23 +7%) and B⁰ →K ⁺π⁻ (− 17 ± 5%). We also investigate the branching ratios, CP asymmetry and isospin symmetry breaking in radiativeB →(K*/ρ)γ decays.     

Precocious signs of new physics: Are we eight now?

Although the CKM-paradigm seems to work to an accuracy of about 15–20%, we emphasize that there are by now several indications that suggest the need for a beyond the Standard Model CP-odd phase. The value of sin 2β measured via the goldplated (tree) mode, B → ψK _s is smaller than the value deduced by using improved lattice matrix elements. The value of sin 2β measured via ‘penguin-dominated’ (loop) decays tends to be even smaller still. There is also a rather large difference between the direct CP asymmetries in → K ⁻ π ⁺ and B ⁻ → K ⁻ π ⁰ that is rather difficult to understand. More recently, CDF and D0 are finding about a 2σ signal in CP asymmetry in the corresponding gold-plated mode B _s → ψϕ. If true, this would be consistent with the indications of new CP-phase in penguin b → s transitions seen at B-factories. After describing these possible signs of trouble for the SM-CKM paradigm, we give a brief discussion of some of the BSM scenarios that could be the underlying cause of these deviations. In particular, we find that the data are quite suggestive of a fourth family with m′ _t in the range of 400–600 GeV as perhaps the simplest BSM candidate which ‘naturally’ explains the data.      

Enhanced direct <Emphasis Type="Italic">CP</Emphasis> violation and branching ratios in bottom hadron decays

In the framework of factorization we study direct CP violation in the decays of bottom hadrons containing a strange quark or a charm quark, H _b →f ρ ⁰(ω)→f π ⁺ π ⁻ (H _b is the bottom hadron and f is the product hadron) including the effect of ρ–ω mixing. We find that the CP violating asymmetry can be enhanced greatly via the ρ–ω mixing mechanism when the invariant mass of the π ⁺ π ⁻ pair is in the vicinity of the ω resonance. For the processes associated with b→d transitions, e.g. , , B _c ⁻→D ⁻ π ⁺ π ⁻, B _c ⁻→D ^*− π ⁺ π ⁻, Ξ _b ⁰→Λ π ⁺ π ⁻, and Ω _b ⁻→Ξ ⁻ π ⁺ π ⁻, the maximum CP violating asymmetries can reach about −84%, while for the processes associated with b→s transitions, e.g. , , B _c ⁻→D _s ⁻ π ⁺ π ⁻, B _c ⁻→D _s ^*− π ⁺ π ⁻, Ξ _b ⁻→Ξ ⁻ π ⁺ π ⁻, and Ω _b ⁻→Ω ⁻ π ⁺ π ⁻, the CP violating asymmetries can be enhanced to about 95%. Furthermore, taking ρ–ω mixing into account we calculate the b-hadron decay branching ratios. We also discuss the possibility to observe the predicted CP violating asymmetries at the LHC.     

Strong isospin violation andη−π mixing in |ΔS|=1 weak transition

We consider the effects ofη−π mixing on the violation of the |ΔI|=1/2 rule in |ΔS|=1 weak transitions. The processes considered are theK→2π,K→3π, Λ, Ξ and Λ hyperon decays.     

Strong decays B<Subscript>s0</Subscript>→B<Subscript>s</Subscript>π and B<Subscript>s1</Subscript>→B<Superscript>*</Superscript><Subscript>s</Subscript>π with light-cone QCD sum rules

In this article, we calculate the strong coupling constants g_Bs0Bsη and g_Bs1B*sη with the light-cone QCD sum rules. Then we take into account the small η–π⁰ transition matrix according to Dashen’s theorem, and we obtain the small decay widths for the isospin violation processes B_s0→B_sη→B_sπ⁰ and B_s1→B_s ^*η→B_s ^*π⁰. We can search the strange-bottomed (0⁺,1⁺) mesons B_s0 and B_s1 in the invariant B_sπ⁰ and B^* _sπ⁰ mass distributions, respectively. PACS  12.38.Lg; 13.25.Hw; 14.40.Nd     

The exclusive reaction of pion quasi-elastic knockout from nucleon <Emphasis Type="Italic">p(e,e′ π)B</Emphasis> to various states of the final baryon-spectator <Emphasis Type="Italic">B</Emphasis> and the quark models for the pion cloud of nucleon

The pion momentum distributions (MDs) in four channels of virtual decay p→B+π, B = N, Δ, N _1/2-(1535), N _1/2+(1440) are calculated in two models, the microscopic model of ³ P ₀ scalar q−q fluctuation with the pion as a composite q−q-system and the chiral semi-microscopic model of πq interaction with the pion as a structureless Goldstone boson. The results of the above models are similar for the baryon states B = N, Δ, N _1/2-(1535) but are rather different for the Roper resonance N _1/2+(1440) which corresponds to excitation of two oscillator quanta in the nucleon. The experimental investigation of pion MDs by means of the reaction of quasi-elastic knockout of pion by an electron of a few GeV energy p(e, e′ π)B may be very suitable for Jefferson Laboratory, Virginia (JLab).     

Exploring CP violation and penguin effects through B0d→D+D- and B0s→D+sD-s

The decay B⁰ _d→D⁺D^- offers an interesting probe of CP violation, but it requires control of penguin effects, which can be done through B⁰ _s→D⁺ _sD^- _s by means of the U-spin flavour symmetry of strong interactions. Recently, the Belle collaboration reported indications of large CP violation in the B⁰ _d decay, which were, however, not confirmed by BaBar, and first signals of the B⁰ _s channel were observed at the Tevatron. In view of these developments and the quickly approaching start of the LHC, we explore the allowed region in observable space for CP violation in B⁰ _d→D⁺D^-, perform theoretical estimates of the relevant hadronic penguin parameters and observables, and we address questions both about the most promising strategies for the extraction of CP-violating phases and about the interplay with other measurements of CP violation and the search for new physics. As far as the latter aspect is concerned, we point out that the B⁰ _q→D_q ⁺D^- _q system provides a setting for the determination of the B⁰ _q–B̄⁰ _q mixing phases (q∈{d,s}) that is complementary to the conventional B⁰ _d→J/ψK_S and B⁰ _s→J/ψφ modes with respect to possible new-physics effects in the electroweak penguin sector.     

Power corrections in e+e?→π+π?,K+K? and B→Kπ,ππ

CLEO-c measurements of the timelike form factors F _π , F _K at ?s=3.671\sqrt{s}=3.671 GeV provide a direct probe of power corrections (PC’s) at energies near m _B . PC’s in F _π,K and B→Kπ,ππ are separated into perturbative and soft parts. In F _π,K the latter are ≥O(10) larger. A PC fit to the B→Kπ,ππ data also yields a ≥O(10) soft-to-perturbative hierarchy for the QCD penguin PC’s. Hence, both can be attributed to dominance of the soft-overlap between energetic (approximately) back-to-back collinear partons, and consistency of the B→Kπ,ππ fit with the Standard Model appears to be naturally realized. The CP asymmetries S_{Ks p⁰}S_{K_{s} \pi^{0}}, C_{Ks p⁰}C_{K_{s} \pi^{0}} are well determined, providing a clean test for new physics.     

Lattice matrix elements and CP violation in<Emphasis Type="Italic">B</Emphasis> and<Emphasis Type="Italic">K</Emphasis> physics: Status and outlook

Status of lattice calculations of hadron matrix elements along with CP violation inB and inK systems is reviewed. Lattice has provided useful input which, in conjunction with experimental data, leads to the conclusion that CP-odd phase in the CKM matrix plays the dominant role in the observed asymmetry inB → ψK _s. It is now quite likely that any beyond the SM, CP-odd, phase will cause only small deviations in B-physics. Search for the effects of the new phase(s) will consequently require very large data samples as well as very precise theoretical predictions. Clean determination ofall the angles of the unitarity triangle therefore becomes essential. In this regardB → KD⁰ processes play a unique role. RegardingK-decays, remarkable progress made by theory with regard to maintenance of chiral symmetry on the lattice is briefly discussed. First application already provide quantitative information onB _K and the ΔI = 1/2 rule. In the lattice calculation, the enhancement in Re A₀ appears to arise solely from tree operators, esp. Q₂; penguin contribution toRe A₀ appears to be very small. However, improved calculations are necessary for ε’/ε as the contributions of QCD penguins and electroweak penguins largely seem to cancel. There are good reasons, though, to believe that these cancellations will not survive improvements that are now underway. Importance of determining the unitarity triangle purely fromK-decays is also emphasized.     

Penguins with charm and quark–hadron duality

The integrated branching fraction of the process B→X _s l ⁺ l ⁻ is dominated by resonance background from narrow charmonium states, such as B→X _s ψ→X _s l ⁺ l ⁻, which exceeds the non-resonant charm-loop contribution by two orders of magnitude. The origin of this fact is discussed in view of the general expectation of quark–hadron duality. The situation in B→X _s l ⁺ l ⁻ is contrasted with charm-penguin amplitudes in two-body hadronic B decays of the type B→π π, for which it is demonstrated that resonance effects and the potentially non-perturbative threshold region do not invalidate the standard picture of QCD factorization. This holds irrespective of whether the charm quark is treated as a light or a heavy quark.     

π* ←π electronic transition in hydroxy-benzonitriles. I. Orthohydroxybenzonitrile

The longest wavelengthπ* ←π electronic band system of ortho-hydroxybenzonitrile vapour through the absorption technique has been reported for the first time. Assuming a planar molecular geometry in both the electronic states, the molecule is classified into aC _s point group, and the present spectrum is attributed to¹ A′ ←¹ A′ type corresponding to electric dipole forbidden transition¹ B _2u ←¹ A _1g (260 nm band system) of benzene. The most intense band at 33914 cm⁻¹ has been assigned as the 0, 0 band, and the other vibronic bands have been interpreted in terms of the excited state and a few ground state fundamentals.     

Hadronic weak decays of heavy mesons and nonfactorization

The parametersχ _1,2, which measure nonfactorizable soft gluon contributions to hadronic weak decays of mesons, are updated by extracting them from the data ofD, B→PP, VP decays (P: pseudoscalar meson,V: vector meson). It is found thatχ ₂ ranges from −0.36 to −0.60 in the decays fromD→Kπ toD ⁺→φπ ⁺,D→K*π, while it is of order 10% with a positive sign inB→ψK, Dπ, D*π, Dρ decays. Therefore, the effective parametera ₂ is process dependent in charm decay, whereas it stays fairly stable inB decay. This is in accordance with the picture that nonfactorizable soft gluon effects become stronger when the relative momentum of the decay particles becomes smaller. As forD, B→VV decays, the presence of nonfactorizable terms in general prevents a possible definition of effectivea ₁ anda ₂. This is reinforced by the observation of a large longitudinal polarization fraction inB→ψK* decay, implying nonfactorizable effects contributing differently toS-, P- andD-wave amplitudes. We found thatA ₁ ^nf /A ₁>0>A ₂ ^nf /A ₂,V ^nf/V (nf standing for nonfactorization) forB→ψK* decay and 0>A ₁ ^nf /A ₁>A ₂ ^nf /A ₂,V ^nf/V forD→K*ρ decay. A measurement of longitudinally and transversely polarized decay rates Γ _L and Γ _T in color-suppressed decay modesB ⁰→D*⁰ ρ ⁰,D*⁰ ω andD ⁺→φρ ⁺ is urged.     

Rescattering and electroweak penguin effects in strategies to constrain and determine the CKM angle γ from B → πK decays

A general parametrization of the B ⁺ → π ⁺ K ⁰ and B _d ⁰ → π ⁻ K ⁺ decay amplitudes is presented. It relies only on the isospin symmetry of strong interactions and the phase structure of the Standard Model and involves no approximations. In particular, this parametrization takes into account both rescattering and electroweak penguin effects, which limit the theoretical accuracy of bounds on γ arising from the combined B ^+- → π ^+- K, B _d → π ^∓ K ^± branching ratios. Generalized bounds making also use of the CP asymmetry in the latter decay are derived, and their sensitivity to possible rescattering and electroweak penguin effects is investigated. It is pointed out that experimental data on B ^± → K ^± K allow us to include rescattering processes in these bounds completely, and an improved theoretical treatment of electroweak penguins is presented. It is argued that rescattering effects may enhance the combined B ^± → K ^± K branching ratio by a factor of O(10) to the 10⁻⁵ level, and that they may be responsible for the small present central value of the ratio of the combined B _d → π ^∓ K ^± and B ^± → π ^± K branching ratios, which has recently been reported by the CLEO collaboration and, if confirmed, would exclude values of γ within a large region around 90°.