OZI Rule Research Articles

Φ PRODUCTION IN pp COLLISIONS

The data for near-threshold cross section for the reaction pp → ppɸ published by the DISTO and ANKE Collaboration are analyzed in order to evaluate the OZI ratio at low energies by taking into account corrections from the kinematics and the final-state interaction. Combining these new data with the few measurements available at higher energies the limit for the OZI rule violation is evaluated and the possible contribution from a five-quark baryonic resonance coupled to the ɸp system is estimated.

Light scalar mesons in QCD

I present a mini-review of the masses and couplings of the bare (unmixed) light scalar mesons : $\bar qq, (\overline{qq})(qq), (\bar qq)(\bar qq), gg$ from QCD spectral sum rules (QSSR) and low-energy theorems (LET) which we compare with recent lattice calculations when available. Some unbiased comments on the different scenarios are given. The possiblity for the $\sigma (0.6)$ to be mostly a gluonium/glueball with a huge violation of the OZI rule in its decay is discussed. This review complements and updates the ones presented earlier [1]. Despite some progresses, the internal structure of the light scalar mesons remain puzzling, and some further efforts are required. It will be more fun at LHC if the Higgs of the Standard Model is a $\sigma$-like resonance.

Further study of D+ s decays into π-π+π+

A Dalitz plot analysis of the OZI rule violating decay D+ s into π-π+π+ is presented using different partial wave approaches. Scalar and vector waves are described by K-matrices; their production is parameterized in a P-vector approach. Alternatively, Breit–Wigner amplitudes and Flatte parametrization are used. Special emphasis is devoted to scalar mesons. The f0(980) resonance provides the most significant contribution. Adding f0(1500) to the scalar wave leads to an acceptable fit while introduction of f0(1370) and/or f0(1710) does not lead to significant improvements. A scan of the scalar wave optimizes for M=1452 ± 22 MeV/c 2. When f0(1710) is added, the mass uncertainty increases, and the fit yields M=1470 ± 60 MeV/c 2 which is fully compatible with the nominal f0(1500) mass. The scalar wave seems to exhibit a phase motion of 270° units in the mass range from 1200 to 1650 MeV/c 2.

Low-energy ππ and πK scatterings revisited in three-flavour resummed chiral perturbation theory

Chiral symmetry breaking may exhibit significantly different patterns in two chiral limits: Nf=2 massless flavours (mu=md=0, ms physical) and Nf=3 massless flavours (mu=md=ms=0). Such a difference may arise due to vacuum fluctuations of ss̄ pairs related to the violation of the Zweig rule in the scalar sector, and it could yield numerical competition between contributions counted as leading and next-to-leading order in the chiral expansions of the observables. We recall and extend resummed chiral perturbation theory (ReχPT), a framework that we introduced previously to deal with such instabilities: it requires a more careful definition of the relevant observables and their one-loop chiral expansions. We analyse the amplitudes for low-energy ππ and πK scatterings within ReχPT, which we match in subthreshold regions with dispersive representations obtained from the solutions of the Roy and Roy–Steiner equations. Using a frequentist approach, we constrain the quark mass ratio as well as the quark condensate and the pseudoscalar decay constant in the Nf=3 chiral limit. The results mildly favour significant contributions of vacuum fluctuations suppressing the Nf=3 quark condensate compared to its Nf=2 counterpart.

Charmonium Hadronic Decays and the OZI Rule Violation Effects

We discuss the scalar meson mixing scenario and present an OZI rule violation mechanism for understanding the scalar productions in charmoium hadronic decays. We stress that the OZI violation could play a key role in disentangling the structure of the scalars: f0(1370), f0(1500) and f0(1710).

AXIAL VECTOR CURRENT MATRIX ELEMENTS AND QCD SUM RULES

The matrix element of the isoscalar axial vector current, [Formula: see text], between nucleon states is computed using the external field QCD sum rule method. The external field induced correlator, [Formula: see text], is calculated from the spectrum of the isoscalar axial vector meson states. Since it is difficult to ascertain, from QCD sum rule for hyperons, the accuracy of validity of flavor SU(3) symmetry in hyperon decays when strange quark mass is taken into account, we rely on the empirical validity of Cabbibo theory to determine the matrix element [Formula: see text] between nucleon states. Combining with our calculation of [Formula: see text] and the well-known nucleon β-decay constant allows us to determine [Formula: see text] occurring in the Bjorken sum rule. The result is in reasonable agreement with experiment. We also discuss the role of the anomaly in maintaining flavor symmetry and validity of OZI rule.

Aspects of φ-meson production in proton-proton collisions

We analyze near-threshold cross section data for the reaction pp->pp phi published by the DISTO collaboration and recent, still preliminary results presented by the ANKE Collaboration. We formulate a procedure to evaluate the OZI ratio at low energies by taking into account corrections from the kinematics and the final-state interaction. Combining the new data with the few measurements available at higher energies we give a limit for the OZI rule violation and estimate the possible contribution from a five-quark baryonic resonance coupled to the phi-p system.

SCALAR GLUEBALL PRODUCTION IN J/ψ HADRONIC DECAYS

The recent data for J/ψ hadronic decays from BES raise "puzzles" about the scalar meson properties, which are different from the naive OZI rule expectation. In this work, we study the implications of a glueball-[Formula: see text] mixing scheme in the scalar meson productions in J/ψ hadronic decays. We show that the significant OZI violations in [Formula: see text] (i = 1, 2, 3 correspond to f0(1710), f0(1500) and f0(1370), respectively) are consistent with the requirement of strong glueball-[Formula: see text] mixings within the scalar meson wavefunctions.

CHIRAL EFFECTIVE ACTION OF QCD: PRECISION TESTS, QUESTIONS AND ELECTROWEAK EXTENSIONS

This talk first discusses some aspects of the chiral expansion with three light flavours related to the (non) applicability of the OZI rule. Next, the extension of ChPT to an effective theory of the full standard model is considered. Some applications of a systematic description of the coupling constants by sum rules (e.g. to the determination of quark masses and Kl3decays) are presented.

Holographic decays of large-spin mesons

We study the decay process of large-spin mesons in the context of the gauge/string duality, using generic properties of confining backgrounds and systems with flavour branes. In the string picture, meson decay corresponds to the quantum-mechanical process in which a string rotating on the IR "wall" fluctuates, touches a flavour brane and splits into two smaller strings. This process automatically encodes flavour conservation as well as the Zweig rule. We show that the decay width computed in the string picture is in remarkable agreement with the decay width obtained using the phenomenological Lund model.

Analysis of new charmless strange B decay data leaves high [formula omitted] and [formula omitted] still unexplained

The question of whether the anomalously large B→Kη′ and B→Kη′X (inclusive) branching ratios are consistent with the standard model or a sign of new physics is still open and in the experimental court. The nature of the extra hadron X in B→Kη′X is completely unknown. Directions for investigation and analysis of inclusive data are suggested as well as for comparable inclusive data on B→KηX.New data confirming the prediction BR(K±ρ0)=BR(K±ω) support flavor-topology B→VP sum rules based on the OZI rule and emphasize the sharp contrast with the failure of the analogous B→PP sum rule due to the anomalously large BR(B→Kη′). Confirmation of OZI validity in B-decay analyses for VP final states suggests improving data on the analogous neutral decay difference BR(B0→K0ρ0)−BR(B0→K0ω) which measures tree-penguin interference and possible direct CP violation.A successful approximate isospin sum rule is rearranged and reinterpreted to pinpoint tree-penguin interference in B→Kπ and B→Kρ transitions. The magnitude of the interference is shown to still be at the statistical noise level with present data.

Chiral extrapolations on the lattice with strange sea quarks

The (light but not-so-light) strange quark may play a special role in the low-energy dynamics of QCD. Strange sea-quark pairs may induce significant differences in the pattern of chiral symmetry breaking in the chiral limits of two and three massless flavours, in relation with the violation of the Zweig rule in the scalar sector. This effect could affect chiral extrapolations of unquenched lattice simulations with three dynamical flavours, and it could be detected through the quark-mass dependence of hadron observables [S. Descotes-Genon, hep-ph/0410233].

Okubo-Zweig-Iizuka rule violation in photoproduction

We investigate OZI rule violation in $\ensuremath{\omega}$ and $\ensuremath{\phi}$-meson photoproduction off nucleons. Data on the total cross sections indicate a large $\ensuremath{\phi}/\ensuremath{\omega}$ ratio of about 0.8 at the maximal available photon energy that is in good agreement with expectations from QCD. On the other hand, data at large four-momentum transfer exhibit a ratio of about 0.07, showing that the perturbative QCD regime is not approached at $|t|>2\text{ }\text{ }{\mathrm{GeV}}^{2}$ and photon energies ${E}_{\ensuremath{\gamma}}<4\text{ }\text{ }\mathrm{GeV}$. The anomanously large $\ensuremath{\phi}/\ensuremath{\omega}$ ratio at low energies, that is close to the reaction threshold, remains to be explained within nonperturbative QCD.

UNITARY CHIRAL DYNAMICS IN J/Ψ DECAYS INTO VPP AND THE ROLE OF THE SCALAR MESONS

We make a theoretical study of the J/Ψ decays into ωππ, ϕππ, [Formula: see text] and [Formula: see text] using the techniques of the chiral unitary approach stressing the important role of the scalar resonances dynamically generated through the final state interaction of the two pseudoscalar mesons. We also discuss the importance of new mechanisms with intermediate exchange of vector and axial-vector mesons and the role played by the OZI rule in the J/Ψϕππ vertex, quantifying its effects. The results nicely reproduce the experimental data for the invariant mass distributions in all the channels considered.

The role of strange sea quarks in chiral extrapolations on the lattice

Since the strange quark has a light mass of order Lambda_QCD, fluctuations of sea s-s bar pairs may play a special role in the low-energy dynamics of QCD by inducing significantly different patterns of chiral symmetry breaking in the chiral limits N_f=2 (m_u=m_d=0, m_s physical) and N_f=3 (m_u=m_d=m_s=0). This effect of vacuum fluctuations of s-s bar pairs is related to the violation of the Zweig rule in the scalar sector, described through the two O(p^4) low-energy constants L_4 and L_6 of the three-flavour strong chiral lagrangian. In the case of significant vacuum fluctuations, three-flavour chiral expansions might exhibit a numerical competition between leading- and next-to-leading-order terms according to the chiral counting, and chiral extrapolations should be handled with a special care. We investigate the impact of the fluctuations of s-s bar pairs on chiral extrapolations in the case of lattice simulations with three dynamical flavours in the isospin limit. Information on the size of the vacuum fluctuations can be obtained from the dependence of the masses and decay constants of pions and kaons on the light quark masses. Even in the case of large fluctuations, corrections due to the finite size of spatial dimensions can be kept under control for large enough boxes (L around 2.5 fm).

Evidence for a fourth state related to the threeJPC=2++,π−p→ϕϕnstates explainable by2++glueball production

Four separate experiments [A. Etkin et al., Phys. Rev. Lett. 41, 784 (1978).][A. Etkin et al., Phys. Rev. Lett. 49, 1620 (1982).][A. Etkin et al., Phys. Lett. B 165, 217 (1985).][A. Etkin et al., Phys. Lett. B 201, 568 (1988).] observing the OZI forbidden disconnected reaction ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\phi}n$ with increasing statistics were consistent. These experiments, very selectively, completely broke down the OZI suppression by three $\ensuremath{\phi}\ensuremath{\phi}$ resonances with ${I}^{G}{J}^{PC}={0}^{+}{2}^{++}$ in the observed mass region 2.038 GeV to 2.600 GeV. The only viable proposed explanation has been that the ${I}^{G}{J}^{PC}={0}^{+}{2}^{++}$ glueball expected in this mass region caused the hard glue in the disconnection to resonate and very selectively break down the OZI suppression for its quantum numbers only. Recently a $pp$ central production spin analysis found that the ${f}_{2}(1950)$ had a dominant decay mode ${f}_{2}(1270)\ensuremath{\pi}\ensuremath{\pi}$ [D. Barberis et al., Phys. Lett. B 471, 440 (2000).]). We consider if it is related to the $\ensuremath{\phi}\ensuremath{\phi}$ resonances, and find that it likely is.

Unitary chiral dynamics in [formula omitted] decays and the role of scalar mesons

We make a theoretical study of the J / Ψ decays into ω π π , ϕ π π , ω K K ¯ and ϕ K K ¯ using the techniques of the chiral unitary approach stressing the important role of the scalar resonances dynamically generated through the final state interaction of the two pseudoscalar mesons. We also discuss the importance of new mechanisms with intermediate exchange of vector and axial-vector mesons and the role played by the OZI rule in the J / Ψ ϕ π π vertex, quantifying its effects. The results nicely reproduce the experimental data for the invariant mass distributions in all the channels considered.

KScattering in Three Flavour ChPT

We present the scattering lengths for the $\pi K$ processes in the three flavour Chiral Perturbation Theory (ChPT) framework at next-to-next-to-leading order (NNLO). The calculation has been performed analytically but we only include analytical results for the dependence on the low-energy constants (LECs) at NNLO due to the size of the expressions. These results, together with resonance estimates of the NNLO LECs are used to obtain constraints on the Zweig rule suppressed LECs at NLO, $L_4^r$ and $L_6^r$. Contrary to expectations from NLO order calculations we find them to be compatible with zero. We do a preliminary study of combining the results from $\pi\pi$ scattering, $\pi K$ scattering and the scalar form-factors and find only a marginal compatibility with all experimental/dispersive input data.

Resumming QCD vacuum fluctuations in three-flavor Chiral Perturbation Theory

Due to its light mass of order Lambda_QCD, the strange quark can play a special role in Chiral Symmetry Breaking (ChSB): differences in the pattern of ChSB in the limits N_f=2 (m_u,m_d->0, m_s physical) and N_f=3 (m_u,m_d,m_s->0) may arise due to vacuum fluctuations of s-bar s pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p^4) low-energy constants L_4 and L_6. In case of large fluctuations, we show that the customary treatment of SU(3)xSU(3) chiral expansions generate instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming nonperturbatively vacuum fluctuations of s-bar s pairs, in order to extract information about ChSB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavour analysis of the low-energy pi-pi scattering and show that the recent experimental data imply a lower bound on the quark mass ratio 2m_s/(m_u+m_d) > 14 at 95 % confidence level. We outline how additional information may be incorporated to further constrain the pattern of ChSB in the N_f=3 chiral limit.

Strong two-body decays of light mesons

In this paper, we present results on strong two-body decay widths of light $q\bar q$ mesons calculated in a covariant quark model. The model is based on the Bethe-Salpeter equation in its instantaneous approximation and has already been used for computing the complete meson mass spectrum and many electroweak decay observables. Our approach relies on the use of a phenomenological confinement potential with an appropriate spinorial Dirac structure and 't Hooft's instanton--induced interaction as a residual force for pseudoscalar and scalar mesons. The transition matrix element for the decay of one initial meson into two final mesons is evaluated in lowest order by considering conventional decays via quark loops as well as Zweig rule violating instanton--induced decays generated by the six--quark vertex of 't Hooft's interaction; the latter mechanism only contributes if all mesons in the decay have zero total angular momentum. We show that the interference of both decay mechanisms plays an important role in the description of the partial widths of scalar and pseudoscalar mesons.