P-wave Quarkonium Research Articles

Resummation and renormalization of kinematical effects in inclusive P-wave quarkonium production

We investigate the renormalization properties of the shape function formalism for inclusive production of P-wave heavy quarkonia, which arises from resumming a class of corrections coming from kinematical effects associated with the motion of the heavy quark and antiquark pair relative to the quarkonium. Such kinematical effects are encoded in the nonperturbative shape functions, which are normalized to the corresponding nonrelativistic QCD long-distance matrix elements. By using the known ultraviolet divergences in the matrix elements, we derive the large-momentum asymptotic behavior of the shape functions. This strongly constrains the form of the shape functions and significantly reduces the dependence on the nonperturbative model. Based on these results we show that the shape function formalism at loop level can be useful in taming the threshold logarithms at large transverse momentum, and at small transverse momentum the kinematical corrections reduce the sizes of χc and χb cross sections which may improve agreement with measurements.

BEEC2.0: An upgraded version for the production of heavy quarkonium at electron-positron collider

The event generator BEEC (Yang et al. (2013) [11]) was devoted to the simulation of heavy quarkonium production at an unpolarized electron-positron collider. We upgraded it here by adding the generation of quarkonium with polarized electron and positron beams. In addition, the production of color-singlet 2S-wave states were included. Several future electron-positron colliders with high luminosity have been under discussion in the past decade. Especially, their possibility of producing polarized beams is important for providing more insights into the underlying physics. This upgraded version offers a useful tool for the feasibility study on quarkonium from the experimental side. New version program summaryProgram title: BEEC version 2.0CPC Library link to program files:https://doi.org/10.17632/bvtwwm22tj.1Licensing provisions: GNU General Public License 3Programming language: FORTRAN 77/90Journal Reference of previous version: Comput. Phys. Commun. 184 (2013) 2848Does the new version supersede the previous version?: YesReasons for the new version: The proposed electron-positron colliders could possibly produce polarized beams, with which it would be helpful to provide more insights into the structure of the underlying physics in heavy quarkonium. Thus, it is essential to simulate the quarkonium production through polarized beams. In addition, the Bc(2S) state attracted more and more interests since its discovery, which makes it necessary to produce the 2S-wave excited states.Summary of revisions: Two polarized amplitudes of leptonic scattering are computed theoretically. The relevant codes of the formula are included in BEEC2.0. Meanwhile, new parameters for the 2S-excited states are also included.Nature of problem: Although PYTHIA can generate events for many processes, a dedicated event generator is also necessary. Especially, PYTHIA does not internally produce events with polarized beams. BEEC is implemented into PYTHIA as an external process for simulating heavy quarkonium events with high efficiency. Further hadronization and decay simulation can be done by using PYTHIA subroutine.Solution method: Two projection operators are used to calculate the polarized leptonic scattering amplitudes with the help of improved trace technology [1,2]. The code with option can generate events through unpolarized and polarized initial beams. In addition to the (QQ′¯)-quarkonium (Q,Q′=b,c) in color-singlet 1S-wave states, 1P-wave states, and the color-octet 1S-wave states in the last version, BEEC 2.0 also deal with the production of 2S-wave excited states within the framework of non-relativistic QCD [3].Additional comments including restrictions and unusual features: About the running time, it depends on which option one chooses to match PYTHIA when generating the heavy quarkonium events. Typically, for the production of the S-wave quarkonium states, if setting IDWTUP=1 (unweighted events), then it takes about 21 minutes on a 3.22 GHz Apple M1 Pro Processor machine to generate 105 events; if setting IDWTUP=3 (weighted events), it takes only ∼5 minutes to generate 105 events. While for the production of the P-wave quarkonium states, the time will be almost one hundred times longer than the case of the S-wave quarkonium.

Inclusive Hadroproduction of P-wave Heavy Quarkonia in pNRQCD

We compute NRQCD long-distance matrix elements that appear in the inclusive production cross sections of P-wave heavy quarkonia in the framework of potential NRQCD. The formalism developed in this work applies to strongly coupled charmonia and bottomonia. This makes possible the determination of color-octet NRQCD long-distance matrix elements without relying on measured cross section data, which has not been possible so far. We obtain results for inclusive production cross sections of χcJ and χbJ at the LHC, which are in good agreement with measurements.

P-wave quarkonium wavefunctions at the origin in the overline{mathrm{MS}} scheme

We compute P-wave quarkonium wavefunctions at the origin in the overline{mathrm{MS}} scheme based on nonrelativistic effective field theories. We include nonperturbative effects from the long-distance behaviors of the potential, while the short-distance behaviors are determined from perturbative QCD. We obtain overline{mathrm{MS}} -renormalized P-wave quarkonium wavefunctions at the origin that have the correct scale dependences that are expected from factorization formalisms, so that the dependences on the scheme and scale cancel in physical quantities. This greatly reduces the theoretical uncertainties associated with scheme and scale dependences in predictions of decay and production rates. Based on the calculation of the P-wave wavefunctions at the origin in this work, we make first-principles predictions of electromagnetic decay rates and exclusive electromagnetic production rates of P-wave charmonia and bottomonia, and compare them with measurements.

Next-to-next-to-leading-order radiative corrections to e+e\u2212\u2192 \u03c7cJ + \u03b3 at B factory

Within the nonrelativistic QCD (NRQCD) factorization framework, we have computed the mathcal{O}left({alpha}_s^2right) corrections to the exclusive production of P-wave spin-triplet charmonia χcJ (J = 0, 1, 2) accompanied with a hard photon at B factory. For the first time, we have explicitly verified the validity of NRQCD factorization for exclusive P-wave quarkonium production to two-loop order. Unlike the χcJ electromagnetic decays, the mathcal{O}left({alpha}_s^2right) corrections are found to be smaller than the mathcal{O} (αs) corrections in all three channels e+e− → χc0,1,2 + γ. In particular, the mathcal{O}left({alpha}_s^2right) corrections appear moderate for χc1 + γ case, and marginal for χc0 + γ. Moreover, the predictions in next-to-next-to-leading order (NNLO) accuracy for the production rates of χc0,1 + γ are insensitive to the renormalization and factorization scales. All these features may indicate that perturbative expansion in these two channels exhibits a decent convergence behavior. By contrast, both the mathcal{O} (αs) and mathcal{O}left({alpha}_s^2right) corrections to the χc2 + γ production rate are sizable, which reduce the Born order cross section by one order of magnitude after including the NNLO perturbative corrections. Taking the values of the long-distance NRQCD matrix elements from nonrelativistic potential model, our prediction to χc1 + γ production rate is consistent with the recent Belle measurement. The NNLO predictions to the χc0,2 + γ production rates are much smaller than that for χc1 + γ, which seems to naturally explain why the e+e− → χc0,2 + γ channels have escaped experimental detection to date.

Two-photon decay of P-wave positronium: a tutorial

A detailed exposition of two-photon decays of P-wave positronium is given to fill an existing gap in the pedagogical literature. Annihilation decay rates of P-wave positronium are negligible compared to the rates of radiative electric dipole transitions to the lower energy S-states. This circumstance makes such decays experimentally inaccessible. However, the situation is different for quarkonium and the experimental and theoretical research of two-photon and two-gluon decays of P-wave quarkonia is a still a flourishing field.

Quarkonium radiative decays from the hadronic Paschen-Back effect

We study the radiative (E1 and M1) decays of P-wave quarkonia in a strong magnetic field based on the Lagrangian of potential nonrelativistic QCD. To investigate their properties, we implement a polarized wave function basis justified in the Paschen-Back limit. In a magnetic field stronger than the spin-orbit coupling, the wave functions of the P-wave quarkonia are drastically deformed by the Hadronic Paschen-Back effect. Such deformation leads to the anisotropy of the direction of decays from the P-wave quarkonia. The analytic formulas for the radiative decay widths in the nonrelativistic limit are shown, and the qualitative decay properties are discussed.

From identical S- and P-wave p_mathrm{T} spectra to maximally distinct polarizations: probing NRQCD with chi states

A global analysis of ATLAS and CMS measurements reveals that, at mid-rapidity, the directly-produced chi _{c1}, chi _{c2} and J/psi mesons have differential cross sections of seemingly identical shapes, when presented as a function of the mass-rescaled transverse momentum, p_mathrm{T}/M. This identity of kinematic behaviours among S- and P-wave quarkonia is certainly not a natural expectation of non-relativistic QCD (NRQCD), where each quarkonium state is supposed to reflect a specific family of elementary production processes, of significantly different p_mathrm{T}-differential cross sections. Remarkably, accurate kinematic cancellations among the various NRQCD terms (colour singlets and octets) of its factorization expansion can lead to a surprisingly good description of the data. This peculiar tuning of the NRQCD mixtures leads to a clear prediction regarding the chi _{c1} and chi _{c2} polarizations, the only observables not yet measured: they should be almost maximally different from one another, and from the J/psi polarization, a striking exception in the global panorama of quarkonium production. Measurements of the difference between the chi _{c1}, chi _{c2} and J/psi polarizations, complementing the observed identity of momentum dependences, represent a decisive probe of NRQCD.

High statistics study of in-medium S- and P-wave quarkonium states in lattice Non-relativistic QCD

Many measurements of quarkonium suppression at the LHC, e.g. the nuclear modification factor RAA of J/Ψ, are well described by a multitude of different models. Thus pinpointing the underlying physics aspects is difficult and guidance based on first principles is needed. Here we present the current status of our ongoing high precision study of in-medium spectral properties of both bottomonium and charmonium based on NRQCD on the lattice. This effective field theory allows us to capture the physics of quarkonium without modeling assumptions in a thermal QCD medium. In our study a first principles and realistic description of the QCD medium is provided by state-of-the-art lattices of the HotQCD collaboration at almost physical pion mass. Our updated results corroborate a picture of sequential modification of states with respect to their vacuum binding energy. Using a novel low-gain variant of the Bayesian BR method for reconstructing spectral functions we find that remnant features of the Upsilon may survive up to T ∼ 400MeV, while the χb signal disappears around T ∼ 270MeV. The cc‾ analysis hints at melting of χc below T ∼ 190MeV while some J/Ψ remnant feature might survive up to T ∼ 245MeV. An improved understanding of the numerical artifacts in the Bayesian approach and the availability of increased statistics have made possible a first quantitative study of the in-medium ground state masses, which tend to lower values as T increases, consistent with lattice potential based studies.

In-medium P-wave quarkonium from the complex lattice QCD potential

We extend our lattice QCD potential based study arXiv:1509.07366 (JHEP 1512 (2015) 101) of the in-medium properties of heavy quark bound states to P-wave bottomonium and charmonium. Similar to the behavior found in the S-wave channel their spectra show a characteristic broadening, as well as mass shifts to lower energy with increasing temperature. In contrast to the S-wave states, finite angular momentum leads to the survival of spectral peaks even at temperatures, where the continuum threshold reaches below the bound state remnant mass. We elaborate on the ensuing challenges in defining quarkonium dissolution, present estimates of melting temperatures for the spin averaged $\chi_b$ and $\chi_c$ states and contrast the findings to recent direct lattice NRQCD studies of P-wave quarkonium. As an application to heavy-ion collisions we estimate the contribution of feed down to S-wave quarkonium through the P-wave states after freezeout.

Production of ϒJ/ψ pairs at the LHC

The inclusive production of ϒJ/ψ pairs in proton–proton interaction is studied under conditions of the LHCb experiment. In the leading order of perturbation theory, the production of a pair of color-singlet vector quarkonia is forbidden in this reaction, so that channels such as double parton scattering and χbχc pair production followed by radiative decays of P-wave quarkonia are considered in detail in the present study along with the contribution of color-octet states and next-to-leading-order (NLO) corrections. For all these channels, we obtain theoretical predictions for total cross sections in the case of measurements with the LHCb detector and for distributions of various kinematical variables. According to the results obtained in the present study, a dominant contribution to the reaction cross section comes from double parton interaction.

Study of P-wave quarkonium states with the LHCb detector

The production of P-wave quarkonium states, χb, was studied in the LHCb experiment at the Large Hadron Collider (LHC, CERN) in proton–proton collisions at the c.m. energies of 7 and 8 TeV. The results obtained on the basis of a measurement of the relative cross sections for χb-meson production, the first ever observation of the decay process χb(3P) → ϒ(3S)γ, and a precise measurement of the mass of the χb1(3P) state are presented in this article.

Conventional versus single-ladder-splitting contributions to double parton scattering production of two quarkonia, two Higgs bosons, andcc¯cc¯

The double parton distributions (dPDF), both conventional (i.e. double ladder) and those corresponding to $1\ensuremath{\rightarrow}2$ ladder splitting, are calculated and compared for different two-parton combinations. The conventional and splitting dPDFs have very similar shape in ${x}_{1}$ and ${x}_{2}$. We make a first quantitative evaluation of the single-ladder-splitting contribution to double parton scattering (DPS) production of two S- or P-wave quarkonia, two Higgs bosons and $c\overline{c}c\overline{c}$. The ratio of the single-ladder-splitting to conventional (i.e. double ladder against double ladder) contributions is discussed as a function of center-of-mass energy, mass of the produced system and other kinematical variables. Using a simple model for the dependence of the conventional two-parton distribution on transverse parton separation (Gaussian and independent of ${x}_{i}$ and scales), we find that the single-ladder-splitting (or 2v1) contribution is as big as the conventional (or 2v2) contribution discussed in recent years in the literature. In many experimental studies of DPS, one extracts the quantity $1/{\ensuremath{\sigma}}_{\mathrm{eff}}={\ensuremath{\sigma}}^{\mathrm{DPS}}/({\ensuremath{\sigma}}^{\mathrm{SPS},1}{\ensuremath{\sigma}}^{\mathrm{SPS},2}$), with ${\ensuremath{\sigma}}^{\mathrm{SPS},1}$ and ${\ensuremath{\sigma}}^{\mathrm{SPS},2}$ being the single scattering cross sections for the two subprocesses in the DPS process. Many past phenomenological studies of DPS have only considered the conventional contribution and have obtained values a factor of $\ensuremath{\sim}2$ too small for $1/{\ensuremath{\sigma}}_{\mathrm{eff}}$. Our analysis shows that it is important also to consider the ladder-splitting mechanism, and that this might resolve the discrepancy (this was also pointed out in a recent study by Blok et al.). The differential distributions in rapidity and transverse momenta calculated for conventional and single-ladder-splitting DPS processes are however very similar which causes their experimental separation to be rather difficult, if not impossible. The direct consequence of the existence of the two components (conventional and splitting) is the energy and process dependence of the empirical parameter ${\ensuremath{\sigma}}_{\mathrm{eff}}$. This is illustrated in our paper for the considered processes.

Breakdown of QCD factorization for P-wave quarkonium production at low transverse momentum

Quarkonium production at low transverse momentum in hadron collisions can be used to extract Transverse-Momentum-Dependent (TMD) gluon distribution functions, if TMD factorization holds there. We show that TMD factorization for the case of P-wave quarkonium with JPC=0++,2++ holds at one-loop level, but is violated beyond one-loop level. TMD factorization for other P-wave quarkonium is also violated already at one-loop level.

The leading twist light-cone distribution amplitudes for the S-wave and P-wave quarkonia and their applications in single quarkonium exclusive productions

In this paper, we calculate twist-2 light-cone distribution amplitudes (LCDAs) of the S-wave and P-wave quarkonia (namely $^1S_0$ state $\eta_{Q}$, $^3S_1$ state $J/\psi(\Upsilon)$, $^1P_1$ state $h_{Q}$ and $^3P_J$ states $\chi_{QJ}$ with $J=0,1,2$ and $Q=c,b$) to the next-leading order of the strong coupling $\alpha_s$ and leading order of the velocity expansion $v$ in the non-relativistic QCD (NRQCD). We apply these LCDAs to some single quarkonium exclusive productions at large center-of-mass energy, such as $\gamma^*\to \eta_Q\gamma, \chi_{QJ}\gamma~(J=0,1,2)$, $Z\to \eta_Q\gamma, \chi_{QJ}\gamma~(J=0,1,2), J/\psi (\Upsilon)\gamma, h_Q\gamma$ and $h\to J/\psi \gamma$, by adopting the collinear factorization. The asymptotic behaviors of those processes obtained in NRQCD factorization are reproduced.

Quarkonium production and polarization in pp collisions with the CMS detector

Studies of the production of heavy quarkonium states are very important to improve our understanding of QCD and hadron formation, given that the heavy quark masses allow the application of theoretical tools less sensitive to nonperturbative effects. Thanks to a dedicated dimuon trigger strategy, combined with the record-level energy and luminosity provided by the LHC, the CMS experiment could collect large samples of pp collisions at 7 and 8 TeV, including quarkonium states decaying in the dimuon channel. This allowed the CMS collaboration to perform a series of systematic measurements in quarkonium production physics, including double-differential cross sections and polar- izations, as a function of rapidity and pT , for five S-wave quarkonia: J/ψ, ψ(2S), Y(1S), Y(2S), and Y(3S). Some of these measurements extend well above pT � 100 GeV, prob- ing regions of very high pT /mass, where the theory calculations are supposed to be the most reliable. Thanks to its high-granularity silicon tracker, CMS can reconstruct low- energy photons through their conversions to e + e − pairs, thereby accessing the radiative decays of the P-wave quarkonium states, with an extremely good mass resolution, so that the J=1 and J=2 1P states can be resolved. This allows CMS to determine cross-section ratios and feed-down decay fractions involving the χ states, in both the charmonium and bottomonium families. This talk presents some of the most recent CMS quarkonium production results, in pp collisions, in particular the production of Y(1S,2S,3S), the cross-section ratio of charmo- nium and bottomonium P-wave states and the polarization of S-wave c¯ c and b¯ b states.

BEEC: An event generator for simulating the [formula omitted] meson production at an [formula omitted] collider

The Bc meson is a doubly heavy quark–antiquark bound state and carries flavors explicitly, which provides a fruitful laboratory for testing potential models and understanding the weak decay mechanisms for heavy flavors. In view of the prospects in Bc physics at the hadronic colliders such as Tevatron and LHC, Bc physics is attracting more and more attention. It has been shown that a high luminosity e+e− collider running around the Z0-peak is also helpful for studying the properties of Bc meson and has its own advantages. For this purpose, we write down an event generator for simulating Bc meson production through e+e− annihilation according to relevant publications. We name it BEEC, in which the color-singlet S-wave and P-wave (cb̄)-quarkonium states together with the color-octet S-wave (cb̄)-quarkonium states can be generated. BEEC can also be adopted to generate the similar charmonium and bottomonium states via the semi-exclusive channels e++e−→|(QQ̄)[n]〉+Q+Q̄ with Q=b and c respectively. To increase the simulation efficiency, we simplify the amplitude as compact as possible by using the improved trace technology. BEEC is a Fortran program written in a PYTHIA-compatible format and is written in a modular structure, one may apply it to various situations or experimental environments conveniently by using the GNU C compiler make. A method to improve the efficiency of generating unweighted events within PYTHIA environment is proposed. Moreover, BEEC will generate a standard Les Houches Event data file that contains useful information of the meson and its accompanying partons, which can be conveniently imported into PYTHIA to do further hadronization and decay simulation. Program summaryProgram title: BEECCatalogue identifier: AEQC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEQC_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 114868No. of bytes in distributed program, including test data, etc.: 963939Distribution format: tar.gzProgramming language: FORTRAN 77/90.Computer: Any computer with Fortran compiler, the program is tested with GNU Fortran compiler and Intel Fortran compiler.Operating system: UNIX, Linux and Windows.RAM: About 2.0 MB.Classification: 11.2.Nature of problem:Production of charmonium, (cb̄)-quarkonium and bottomonium via e+e− annihilation channel around the Z0 peak.Solution method:The production of heavy (QQ̄′)-quarkonium (Q,Q′=b,c) via e+e− annihilation are estimated by using the improved trace technology. The (QQ̄′)-quarkonium in color-singlet 1S-wave state, 1P-wave state, and the color-octet 1S-wave states have been studied within the framework of non-relativistic QCD. The code with option can generate weighted and unweighted events conveniently, in particular, the unweighted events are generated by using an improved hit-and-miss approach so as to improve the generating efficiency.Restrictions:The generator is aimed at the production of double heavy quarkonium through e+e− annihilation at the Z0 peak. The considered processes are those that are associated with two heavy quark jets, which could provide sizable quarkonium events around the Z0 peak.Running time:It depends on which option one chooses to match PYTHIA when generating the heavy quarkonium events. Typically, for the production of the S-wave quarkonium states, if setting IDPP=2 (unweighted events), then it takes about 2 h on a 2.9 GHz AMD Athlon (tm) II×4 635 Processor machine to generate 105 events; if setting IDPP=3 (weighted events), it takes only ∼16 min to generate 105 events. For the production of the P-wave quarkonium states, the time will be almost one hundred times longer than the case of the S-wave quarkonium.

Transverse momentum dependent factorization for quarkonium production at low transverse momentum

Quarkonium production in hadron collisions at low transverse momentum ${q}_{\ensuremath{\perp}}\ensuremath{\ll}M$ with $M$ as the quarkonium mass can be used for probing transverse momentum dependent (TMD) gluon distributions. For this purpose, one needs to establish the TMD factorization for the process. We examine the factorization at the one-loop level for the production of ${\ensuremath{\eta}}_{c}$ or ${\ensuremath{\eta}}_{b}$. The perturbative coefficient in the factorization is determined at one-loop accuracy. Comparing the factorization derived at tree level and that beyond the tree level, a soft factor is, in general, needed to completely cancel soft divergences. We have also discussed possible complications of TMD factorization of p-wave quarkonium production.

HELAC-Onia: An automatic matrix element generator for heavy quarkonium physics

By the virtues of the Dyson–Schwinger equations, we upgrade the published code HELAC to be capable to calculate the heavy quarkonium helicity amplitudes in the framework of NRQCD factorization, which we dub HELAC-Onia. We rewrote the original HELAC to make the new program be able to calculate helicity amplitudes of multi P-wave quarkonium states production at hadron colliders and electron–positron colliders by including new P-wave off-shell currents. Therefore, besides the high efficiencies in computation of multi-leg processes within the Standard Model, HELAC-Onia is also sufficiently numerical stable in dealing with P-wave quarkonia (e.g. hc,b,χc,b) and P-wave color-octet intermediate states. To the best of our knowledge, it is a first general-purpose automatic quarkonium matrix elements generator based on recursion relations on the market. Program summaryProgram title: HELAC-Onia.Catalogue identifier: AEPR_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEPR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 114595No. of bytes in distributed program, including test data, etc.: 1555550Distribution format: tar.gzProgramming language: Fortran 90.Computer: Any.Operating system: Windows, Unix.Classification: 4.4, 11.1, 11.2, 11.5.Nature of problem:An important way to explore the law of the nature is to investigate the heavy quarkonium physics at B factories and hadron colliders. However, its production mechanism is still unclear, though NRQCD can explain its decay mechanism in a sufficiently satisfactory manner. The substantial K-factor in heavy quarkonium production processes also implies that the associated production of quarkonium and a relatively large number of particles may play a crucial role in unveiling its production mechanism.Solution method:A labor-saving and efficient way is to make the tedious amplitudes calculation automatic. Based on a recursive algorithm derived from the Dyson–Schwinger equations, the goal of automatic calculation of heavy quarkonium helicity amplitudes in NRQCD has been achieved. Inheriting from the virtues of the recursion relations with the lower computational cost compared to the traditional Feynman-diagram based method, the multi-leg processes (with or without multi-quarkonia up to P-wave states) at colliders are also accessible.Running time:It depends on the process that is to be calculated. However, typically, for all of the tested processes, they take from several minutes to tens of minutes.

P-wave quarkonium decays to meson pairs

The processes of p-wave Quarkonium exclusive decays to two mesons are investigated, in which the final state vector mesons with various polarizations are considered separately. In the calculation, the initial heavy quarkonia are treated in the framework of non-relativistic quantum chromodynamics, whereas for light mesons, the light cone distribution amplitudes up to twist-3 are employed. It turns out that the higher twist contribution is significant and provides a possible explanation for the observation of the hadron helicity selection rule violated processes χ c1 → φφ, ωω by the BESIII collaboration in recently. We also evaluate the χ b1 → J/ψJ/ψ process and find that its branching ratio is big enough to be measured at the B-factories.