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.     

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 use of quantum-correlated D<Superscript>0</Superscript> decays for φ<Subscript>3</Subscript> measurement

We report the results of the Monte Carlo study of the method to determine the CKM angle φ₃ using Dalitz plot analysis of D⁰ produced in B^±→DK^± decay. Our main goal is to find the optimal strategy for a model-independent φ₃ extraction. We find that the analysis using decays of CP-tagged D mesons only cannot provide a completely model-independent measurement in the case of a limited data sample. The procedure involving binned analysis of B^±→DK^± and ψ(3770)→(K⁰ _Sπ⁺π^-)_D(K⁰ _Sπ⁺π^-)_D decays is proposed which, in contrast, allows not only to reach the φ₃ precision comparable to an unbinned model-dependent fit, but also provides an unbiased measurement with currently available data. PACS 11.30.Er; 12.15.Hh     

Charm changing weak decays 1/2+ → 3/2+ + 0−/γ in SU(4) and SU(8) w

Weak decay modes (1/2⁺ → 3/2⁺ + 0⁻/γ) of charmed baryons are studied. Relations among the various decay amplitudes are derived in isospin, SU(3), SU(4) and SU(8) _w symmetries. Sextet dominance in SU(3) forbidsB(3) →D(10) +P(3*) decays. 20″ dominance in SU(4) specifies all the decays in terms of Θ⁻ decays. Weak decays of Θ* ₃ ⁺⁺ and Θ⁻ are also discussed. SU(8) _w symmetry predictsα , which is consistent with the experimental value.     

K→3π final state interactions at NLO in CHPT and Cabibbo’s proposal to measure a<Subscript>0</Subscript>-a<Subscript>2</Subscript>

We present the analytical results for the K→3π final state interaction phases at next-to-leading order (NLO) in CHPT. We also study the recent proposal of Cabibbo to measure the ππ scattering lengths combination a₀-a₂ from the cusp effect in the π⁰π⁰ energy spectrum at threshold for K⁺→π⁰π⁰π⁺ and K_L→π⁰π⁰π⁰, and we give the relevant formulas to describe it at NLO. We estimate the theoretical uncertainty of the a₀-a₂ determination at NLO in our approach and obtain the result that it is not smaller than 5% if added quadratically and 7% if added linearly, for K⁺→π⁰π⁰π⁺. One gets similar theoretical uncertainties if the neutral K_L→π⁰π⁰π⁰ decay data below threshold are used instead. For this decay, there are very large theoretical uncertainties above threshold due to cancellations, and data above threshold cannot be used to get the scattering lengths. We do not include isospin corrections apart from two-pion phase space factors which are physical. We compare our results for the cusp effect with those due to Cabibbo and Isidori. PACS 13.25.Es; 12.39.Fe; 13.75.Lb     

New physics hints in B decays and collider outlook

There are currently two hints for new physics involving CP violation in b → s transitions: ΔS ≡ S _f − S _J ^ϕK ≠ 0, and difference in direct CP asymmetry ΔA _Kπ ≡ A _K+π ⁰ − A _K+π ⁻ ≠ 0. We explore the two scenarios with a large and unique new CP phase in b ↔ s transitions. Motivated by ΔS ≠ 0, we update on the right-handed strange-beauty squark sb _1R at TeV scale. Motivated by ΔA _Kπ ≠ 0, we explore sequential fourth generation t′ and b′ quarks. Both scenarios can survive constraints such as SM level b → sγ, sll and B _s mixing, and predict sizable CP violation in B _s mixing. The fourth generation picture predicts sizable K _L → π ⁰ vv. Direct search for sb _R, b′ and t′ at hadronic colliders, such as Tevatron Run II and LHC, can complement further CP violation studies at these machines, as well as at the future Super B factory.     

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.     

The cusp effect in <Emphasis Type="Italic">η</Emphasis>′→<Emphasis Type="Italic">η</Emphasis><Emphasis Type="Italic">π</Emphasis><Emphasis Type="Italic">π</Emphasis> decays

Strong final-state interactions create a pronounced cusp in η′→η π ⁰ π ⁰ decays. We adapt and generalize the non-relativistic effective field theory framework developed for the extraction of π π scattering lengths from K→3π decays to this case. The cusp effect is predicted to have an effect of more than 8% on the decay spectrum below the π ⁺ π ⁻ threshold.     

Covariant tensor formalism for partial-wave analyses of ψ decays into γB¯, γγV and ψ(2s)↦γχ<Subscript>c0,1,2</Subscript> with χ<Subscript>c0,1,2</Subscript>↦K¯πand 2π<Superscript>+</Superscript>2π<Superscript>-</Superscript>

With accumulation of high statistics data at BES and CLEO-c, many new interesting channels can get enough statistics for partial-wave analysis (PWA). Among them, ψ↦γpˉ,γΛˉ,γΣˉ,γΞˉ channels provide a good place for studying baryon-antibaryon interactions; the double radiative decays ψ↦γγV with V ≡ ρ,ω,φ have a potential to provide information on the flavor content of any meson resonances (R) with positive charge parity (C = +) and mass above 1 GeV through ψ↦γR↦γγV; ψ(2s)↦γχ_c0,1,2 with χ_c0,1,2↦Kˉπ⁺π^- and 2π⁺2π^- decays are good processes to study χ_cJ charmonium decays. Using the covariant tensor formalism, here we provide theoretical PWA formulae for these channels.     

Final-state polarization in <Emphasis Type="Italic">B</Emphasis><Stack><Subscript><Emphasis Type="Italic">s</Emphasis></Subscript><Superscript>0</Superscript></Stack> decays

Certain B _s ⁰→V ₁ V ₂ decays (V _i is a vector meson) can be related by flavor SU(3) symmetry to corresponding B _d ⁰→V ₃ V ₄ decays. In this paper, we show that the final-state polarization can be predicted in the B _s ⁰ decay, assuming polarization measurements of the B _d ⁰ decay. This can be done within the scenario of penguin annihilation (PA), which has been suggested as an explanation of the unexpectedly large transverse polarization in B→φ K ^*. PA is used to estimate the breaking of flavor SU(3) symmetry in pairs of decays. Two of these for which PA makes a reasonably precise prediction of the size of SU(3) breaking are (B _s ⁰→φ φ,B _d ⁰→φ K ^0*) and ( ). The polarization measurement in the B _d ⁰ decay can be used to predict the transverse polarization in the B _s ⁰ decay and will allow for testing of PA as well as the other assumptions in the analysis.     

Analysis of two recent tests of T-invariance

Inequality of the rates for K ⁰ → π⁺ e ⁻ υ₋ and K ⁰ → π⁻ e ⁺ ν transitions, reported by CPLEAR, and an asymmetry in the distribution of the dihedral angle between the π⁺π⁻ and e ⁺ e ⁻ planes in K _L → π⁺π⁻ e ⁺ e ⁻ decays, found by KTeV, have been announced as demonstrations of T-noninvariance. These results are critically interpreted and compared as proofs of the failure of reciprocity.     

Width effects of theZ resonance and CP-violating asymmetry ine + e − annihilation

CP-violating rate asymmetry can be generated in a process only if its amplitude possesses an absorptive part. It is pointed out that such an absorptive part can be provided ine ⁺ e ⁻ annihilation by the presence of aZ(Z′) resonance of non-zero width. The CP asymmetry in the process , wherel _i are charged leptons, is discussed in several models. In a specific two-Z model, large and observable CP asymmetry ine ⁺ e ⁻ →τ ⁺ e ⁻ (τ ⁻ e ⁺) is shown to be possible at LEP/SLC energies.     

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.      

Electromagnetic corrections in <Emphasis Type="Italic">η</Emphasis>→3<Emphasis Type="Italic">π</Emphasis> decays

We re-evaluate the electromagnetic corrections to η→3π decays at next-to-leading order in the chiral expansion, arguing that effects of order e ²(m _u −m _d ) disregarded so far are not negligible compared to other contributions of order e ² times a light-quark mass. Despite the appearance of the Coulomb pole in η→π ⁺ π ⁻ π ⁰ and cusps in η→3π ⁰, the overall corrections remain small.     

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).     

On CP-odd effects in KL → 2π and K± → π±π±π± decays generated by direct CP violation

The amplitudes of the K ^± → 3π and K→ 2π decays are expressed in terms of different combinations of one and the same set of CP-conserving and CP-odd parameters. Extracting the magnitudes of these parameters from the data on K → 2π decays, we estimate an expected CP-odd difference between the values of the slope parameters g ⁺ and g ⁻ of the energy distributions of “odd” pions in K ⁺ → π⁺π⁺π⁻ and K ⁻ → π⁻π⁻π⁺ decays. From Yadernaya Fizika, Vol. 68, No. 1, 2005, pp. 89–94. Original English Text Copyright ? 2005 by Shabalin. This article was submitted by the author in English.     

Excitation of the Roper resonance in single- and double-pion production in nucleon-nucleon collisions⋆

In most investigations the Roper resonance is sensed only very indirectly via complex partial-wave analyses. We find indications for its excitation in the invariant nπ⁺ mass spectrum of the pp → npπ⁺ reaction at M ≈ 1360 MeV with a width of ≈ 150 MeV . The values fit very favorably to the most recent phase shift results as well as to the observations at BES. In the near-threshold two-pion production pp → ppπ⁰π⁰ , where the Roper excitation and its subsequent decays via the routes N ^* → Δπ → Nππ and N ^* → Nσ are the only dominant processes, we find its direct decay into the Nσ channel to be the by far dominating decay process --in favor of a monopole excitation of the Roper resonance.     

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.