Studies of light mesons at BELLE

Studies of light mesons in experiments with the Belle detector at the KEKB B-factory are described. Three types of hadron production processes are discussed: two-photon production, production via initial state radiation and hadronic tau lepton decays.


Introduction
Experiments with the Belle detector [1] at the asymmetricenergy e + e − KEKB collider [2] were performed from 1999 to 2010 in the centre-of-mass energy range within the Υ-meson family.In these experiments the KEKB collider achieved the world highest collider luminosity, 2.1 × 10 34 cm −2 s −1 .The total integrated luminosity collected by Belle is more than 1000 fb −1 .The primary goal of the Belle experiment was to discover CP violation (CPV) in B meson decays and to measure the parameters of CPV.This was achieved in 2001, when the time-dependent CP asymmetry was observed in the decay B 0 → J/ΨK 0 decay [3].However, besides of the main task, a lot of other important results were obtained.So a wide research area become possible because of the clean event environment and well-defined e + e − initial state as well as high luminosity and general-purpose detector.
In this report, studies of light mesons performed in the first three processes will be discussed.

Collider and detector
The KEKB asymmetric-energy collider operated with 8 GeV electron and 3.5 GeV positron beams (βγ=0.42 for the center-of-mass system).The Belle detector is a large-solid-angle forward/backward asymmetric detector that combines precise magnetic spectrometry, excellent calorimetry and sophisticated particle ID ability.The schematic view of Belle is presented in Fig. 1.
The detector contains a silicon vertex detector (SVD), a 50-layer central drift chamber (CDC), an array of 1188 aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter (ECL) comprised of 8736 CsI(Tl) crystals located inside a superconducting solenoid coil that provides a 1.5 T magnetic field.An iron flux return placed outside of the coil is instrumented to detect K 0 L mesons and to identify muons (KLM).The detector solenoid is oriented along the z axis, pointing in the direction opposite to that of the positron beam.The r-ϕ plane is transverse to this axis.

Two-photon collisions
High luminosity of the B-factory provides wide possibilities to study low mass C-even hadron states via twophoton production.In these studies properties of the light mesons as well as energy dependence of the production cross section are determined.The Feynman diagram corresponding to these processes is shown in Fig. 2.
The total cross section of the process e + e − → e + e − + γ * γ * → e + e − + hadrons is given by the formula: where dL/dW is an effective differential luminosity.
In the relatively low energy range, below 2-2.5 GeV, the cross section energy dependence is determined mostly  by the resonances, thus the properties of various light mesons can be carefully studied.At the higher energy the cross section energy dependence is smooth and comparison of the total cross section with the QCD prediction can be performed.Measurements of the light hadron pair production performed by the Belle collaboration are summarized in Table 1.
A recent study of the γγ → K S K S process with high statistics [9] gave precise results on the total cross section of this process presented in Fig. 3. Five resonance-like peaks are seen in the mass range below 3 GeV.These are, expectedly, f 2 (1270), f 2 (1525), f J (1710) and/or a J (1710), f J (2200) and/or a J (2200), f J (2500) and/or a J (2500).Due to high statistics and good momentum and angular resolution of the Belle, partial wave analysis could be performed that provided a separation of the contributions of resonances with the different spin-parity quantum numbers.Evaluated parameters of resonances are listed in Table 2.
Another important study is a determination of the π 0 transition form factor (TFF) from the process γγ * → π 0 , where γ * is a virtual photon with large 4-momentum square, Q 2 .This process is studied using events of twophoton π 0 production (e + e − → e + e − π 0 ), when one of the electrons is scattered at a large angle.The Feynman diagram of this process is shown in Fig. 4 The form factor  W (GeV) section dσ/dQ 2 [13].Results of this study are presented in Fig. 5 in comparison with results from other experiments: BaBar [14], CELLO [15] and CLEO [16].Form factor values obtained by Belle are in good agreement with QCD prediction and somewhat ( 2.3σ) lower than the BaBar results at Q 2 > 10 GeV 2 .In the low Q 2 range all experimental results are in good agreement.

Hadronic tau decays
Hadronic decays of τ-lepton provide very clean conditions for a study of the low mass hadronic states and measurements of the light meson characteristics.The τ decay amplitude in such processes can be factorized into a purely leptonic part including τ and ν τ and a hadronic spectral function.In this report we describe several relevant studies.
where BW i -are corresponding resonance amplitudes and α, β, γ -are complex constants, provided parameters of these resonances (listed in Table 3) with high precision.
A study of the τ − → K S π − ν τ decay at Belle [20] produced not only a precise value of the branching fraction but also an accurate K S π − invariant mass spectrum.The main contribution to this spectral function comes from the K * − (892).However, to describe this spectrum the K * − (892) resonance is not enough and additional contributions at lower (expectedly K * 0 (800)) and higher masses (K * 0 (1430) or/and K * (1410)) are needed.From the fit of the spectrum the precise values of the mass and width of Table 3. Results of fitting the M 2 ππ 0 distribution for τ → ππ 0 ν decay to the model with the ρ(770), ρ (1450), and ρ (1700) resonances.The first error is statistical while the second one is systematic.The systematic errors include the uncertainty on the backgrounds, unfolding as well as the uncertainty of the photon energy scale.The last row gives the significance of the ρ (1700) signal.

Parameter
Fit result (all free) M ρ , MeV/c 2 774.9 ± 0. The first error is statistical, the second one is systematic and the third -is an uncertainty related to the fit model.These values differ considerably from the parameters obtained in hadroproduction and close to the corresponding values for the neutral K * (892) mesons [21].
Recently the results of the measurements of branching fractions of τ-lepton decays with one or more K 0 S were published by the Belle collaboration [22].In addition to the precise determination of seven branching fractions, the final hadronic state in the τ − → π − K S K S π 0 ν τ decay was analyzed.It was found that main contributions to the final hadronic state in this decay are f 1 (1285)π − , f 1 (1420)π − and K * − K S π 0 .This is confirmed by the invariant mass spectra presented in Fig. 7.

Low energy hadronic physics with ISR
In the last years a lot of new data were obtained at the B-and φ-factories, by the BaBar, Belle and KLOE detectors, using initial state radiation (ISR) processes [23].The idea of this approach is illustrated by the diagram shown in Fig. 8.
After emission of a hard photon an e + e − pair can acquire any center-of-mass energy below the energy of the EPJ Web of Conferences 01028-p.4experiment.That means that one can study the processes of e + e − annihilation in the entire range from the threshold to the experiment energy.Studies of Belle in this field are mostly related to the charm sector.However, interesting results were also obtained for the processes e + e − → φπ + π − and e + e − → φ f 0 (980) in the energy range from 1.5 to 3 GeV with the total integrated luminosity of 673 fb −1 [24].Measured cross sections are shown in Fig. 9. Systematic uncertainties are 8.6% and 6.9% for the φπ + π − and φ f 0 (980) cross sections, respectively.Parameters of the φ(1680) and Y(2175) were measured to be:

Super KEKB and Belle II
At present a new advanced collider, SuperKEKB, with a project luminosity of 8 × 10 35 cm −2 s −1 is under construction at KEK.The new SuperKEKB collider is placed in the KEKB tunnel utilizing many elements of the previous B-factory.The KEKB cells are kept in the High Energy Ring (HER).Dipole magnets in the Low Energy Ring (LER) will be replaced, while other main magnets in the LER arcs are reused.The LER beam pipe will be completely replaced by a new one with ante-chambers.The injector for KEKB is upgraded as well.A special damping ring is constructed to produce high intensive positron beams with low emittance.
The basic idea of the new collider is the so called "Nano-Beam" scheme, first proposed in [25].Main parameters of the new collider are listed in The Belle II detector will have much better parameters than Belle.All subsystems of this detector are replaced or seriously modified.A tracking system will include new silicon pixel and strip vertex detectors.A new particle identification system based on the time-ofpropagation counters in the barrel and aerogel Cherenkov counters in the endcaps will provide powerful kaon/pion separation.An electromagnetic calorimeter will keep the same CsI(Tl) crystals but all the electronics will be replaced by a new, modern one.The Belle II detector intended for experiments at extremely high luminosity, 8×10 35 cm −2 s −1 , should work in hard background and radiation environment.The beam-related backgrounds at Su-perKEKB are expected to be 10-20 times higher than those at the previous collider.Main sources of the beam induced background are the electron and positron Touschek scattering, radiative Bhabha scattering and two-photon processes.The detailed description of the Belle II project can be found in the Technical Design Report [26].
A search for New Physics (NP), i.e. phenomena which are not described by the SM, becomes the most important task for the Belle II experiment.Evidence of the NP will be searched for not only in B mesons decays, but also in the charm sector and τ lepton decays.Other studies, like precise measurements of the hadronic cross sections and properties of the light mesons in the γγ and e + e − (γ IS R ) processes, are importants issues of the Belle II program.A high integrated luminosity expected at Belle II will provide widest possibilities for these studies.For example, at the integrated luminosity of 10 ab −1 the equivalent integrated luminosity obtained with the ISR approach will exceed the amounts available at VEPP-2000 and BEPC-II colliders in the energy ranges 1-2 GeV and 2-3 GeV, respectively.
Commissioning of the SuperKEKB/Belle II is scheduled in three phases.During the phase 1, in 2015, without Belle II and focussing quadrupoles, the machine tuning and vacuum scrubbing as well as damping ring commissioning will be made.At the phase 2, in 2016, the Belle II detector will be installed without PXD.The physics runs with the full detector are expected to start in 2017.

Conclusion
Huge data array collected by the B-factories yielded many important results on CP violation, hadron structure and tau lepton physics.However, many new questions arose and the broad field of research will be opened by the superB-factory.It is clear that the superB-factory with the Belle II detector will produce new important information in various fields of particle physics.This information will be complementary to that obtained in the experiments at LHC.At present, the superKEKB/Belle II project is under construction and we can hope for new exciting results in the next decade.

Figure 2 .
Figure 2. Two-photon production in the leading order.

Table 2 .
Parameters of resonances obtained by partial wave analysis of the K S K S final state.The first error is statistical while the second one is systematic.Resonance Mass (MeV/c 2 ) Width (MeV) Γ γγ × B(K K) (eV)

Figure 4 .
Figure 4. Single-tag π 0 production in two-photon process with a large-Q 2 and a small-Q 2 photon

Figure 3 .
Figure 3. Cross section of γγ → K S K S process measured by Belle [9] at | cos ϑ * < 0.8|.ϑ * is the K S scattering angle in the K S K S center-of-mass frame.The solid curve indicates systematic uncertainties.

Figure 7 .
Figure 7. Hadronic invariant mass spectra in τ − → π − K S K S π 0 ν τ decay, (a) -π 0 K S K S invariant mass, (b) -π − K S invariant mass.Points with error bars are experimental data, hatched histograms show background contributions, the solid line corresponds to the best fit, dashed and dotted lines present the contributions of different intermefiate states.

Figure 8 .
Figure 8. Diagram of the processes with initial state radiation.

Figure 9 .
Figure 9. Fit to: (a) e + e − → φπ + π − cross section with two incoherent Breit-Wigner (BW) functions, one for the φ(1680) and the other for the Y(2175) and (b) e + e − → φ f 0 (980) cross section with a single BW function that interferes with a non-resonant component.The curves show the projections from the best fit and the contribution from each component.In (b), the dashed curves are for the destructive interference solution and the dot-dashed curves for the constructive interference solution

Table 1 .
Measurements of the light hadron pair production in the Belle experiment.Final state Invariant mass range, GeV Angular range, | cos ϑ * | Integrated luminosity, fb −1 reference

Table 4 .
Table 4 in comparison with those achieved by KEKB.At present most of the collider elements are produced and installed in the tunnel.Comparison of the main parameters of SuperKEKB and previous KEKB colliders