Recent results at the -meson region from the CMD-3 detector at the VEPP-2000 collider

This report is devoted to the recent results of the study of the processes , , , at the -meson region with the CMD-3 detector at the VEPP-2000 collider. From the combined analysis of and final states the -meson parameters were measured, and the obtained ratio of and couplings was found to be compatible with the isospin symmetry. From the analyzes of the and final states the branching ratios and were determined.


Introduction
A high precision measurement of the inclusive cross section is required for a calculation of the hadronic contribution to the muon anomalous magnetic moment in the frame of the Standard Model.To confirm or deny the observed difference between the calculated [1] and measured [2] values more precise measurements of the exclusive channels of are necessary.On the other hand, the study of the exclusive final states can provide useful information about the precision of the isospin symmetry, particle parameters, branching ratios and coupling constants.

VEPP-2000 collider and CMD-3 detector
The VEPP-2000 collider [3] at the Budker Institute of Nuclear Physics (Novosibirsk, Russia) covers the center-of-mass energy ( ) range from 0.32 to 2.0 GeV and employs a novel technique of round beams to reach luminosity up to at 2.0 GeV.The Cryogenic Magnetic Detector (CMD-3), described in [4], is installed in one of the two beams interaction regions.The detector tracking system consists of the cylindrical drift chamber (DC) and double-layer cylindrical multiwire proportional Z-chamber, installed inside a thin superconducting solenoid with 1.0-1.3T magnetic field.Both subsystems are also used to provide the trigger signals.DC contains 1218 hexagonal cells in 18 layers and allows one to measure charged particle momentum with 1.5-4.5% accuracy in the 40-1000 MeV/c range, and the polar and azimuthal angles with 20 mrad and 3.5-8.0mrad accuracy, respectively.Amplitude information from the DC wires is used to measure the ionization losses of charged particles.The barrel electromagnetic calorimeters based on liquid xenon (LXe) (5.4 X 0 ) and CsI crystals (8.1 X 0 ) are placed outside the solenoid [5].The total amount of material in front of the barrel calorimeter is 0.13 X 0 that includes the solenoid as well as the radiation shield and vacuum vessel walls.BGO crystals of 13.4 X 0 thicknesses are used in the endcap calorimeter.The magnetic flux return yoke is surrounded by scintillation counters which are used to tag cosmic events.
The energy range MeV was scanned in 2013 year, and 9.8 pb -1 of integral luminosity in 22 energy points was collected.The integral luminosity at each point was determined using the events of the processes and with about 1% accuracy [6].The beam energy was monitored by using the Back-Scattering-Laser-Light system [7].The main goals of the VEPP-2000 complex are: to achieve 1% systematic error of the cross section measurement for the major exclusive channels; to study other exclusive processes, especially those which were not measured before and were taken into account in the calculation of via the isotopic relations; to measure the parameters of "excited" vector mesons like , , , etc.; to test the conservation of vector current; to study the nucleon electromagnetic form factors; to study some of the diphoton processes (e.g. ).It should be noted that the study of -meson energy range is not a priority of CMD-3, but is very important for studying of photon, pion and kaon detection efficiencies and for studying the energy depositions in the calorimeters (necessary for proper separation).On the other hand, CMD-3 can provide interesting results on some problems, where the systematic uncertainty is decisive.

Study of the processes at
To select the charged kaons, we demand the event to have 2 tracks in the DC, passing from the beams interaction region and satisfying the collinearity conditions || | | rad and | |< 0.3 rad.Then the almost background-free sample of signal events with charged kaons are extracted using losses (see Fig. 3).The signal identification for the final state is based on the detection of two pions from the decay.The longitudinal distance and the transverse coordinate of the vertex should be less than 10 and 6 cm correspondingly.Pions from decay are required to have polar angles 1 rad .Then, the vs. particle momenta distribution is used to select the signal events (see Fig. 4).The signal/background separation is performed by the fitting of the distribution of invariant mass of two pions (see Fig. 5).The major background process was found to be .The measured cross sections together with their approximation are shown in Figs.6-7 respectively.Systematic uncertainty is estimated to be 3% in charged channel and 1.8% in neutral channel.The final results for are published in [8].The cross sections were approximated according to the Vector Dominance Model: where is the denominator of the propagator, are the functions describing contributions of and resonances, constant describes the contribution of higher resonances.The sign «+» before the in formula (1) corresponds to channel, «-» -to channel.Further, the couplings and are equal

√ √
The results of the approximation procedure in comparison with the PDG values (see [9]) are shown in Table 1.The contributions from the and were fixed from quark model and SU(3) symmetry of u-, d-and s-quarks.But if we introduce in the fit the additional floating parameter , describing the relative deviation of the and from their SU(3)-predicted values, we obtain a compatible with unity result .It is seen, that systematic errors dominate the uncertainty, and we still are working on the improvements.(preliminary results), measured with the CMD-3 detector, together with its approximation.
The combined analysis of processes provides a possibility to check the precision of the isospin invariance of the u-and d-quarks, which predicts the value of unity to the factor where and are the momenta of charged and neutral kaons in ̅ decays at , and is the Sommerfeld-Gamov-Sakharov factor, which takes into account the Coulomb interaction of charged kaons in the final state ( is the fine structure constant, is the velocity of charged kaons over the speed of light).The previous measurements gave , , (see [9]) and one can suspect a significant deviation of from unity.Our measurement gives , and thus we do not see statistically significant deviation of from unity.

Study of the processes at 4.1 Study of the process
To select the final state events, we perform the 5C kinematic fit with all the combinations of 4 photons and 2 DC-tracks with opposite curvatures in the event, demanding the energy and momentum conservation, as well as the invariant mass of one pair of photons to be fixed at mass.Having selected the combination with the smallest , we apply the cut <30 to suppress the background (see Fig. 8).For the signal/background separation the approximation of the invariant mass of the second pair of photons (the invariant mass of which was not fixed at in the kinematic fit) is used (see Fig. 9).The signal and background shapes were taken from simulation with additional smearing.MeV is due to events of process.

Study of the process at
The process was studied in decay mode in the range from 1.0 to 1.03 GeV on the base of 5.5 of integrated luminosity.To select the signal, we consider the events, having at least 3 photons with the polar angles in the range from 0.42 to rad.Then the kinematic cuts, as shown in Fig. 16, are applied.After that the major background processes are and .We perform the kinematic fit, requiring the energy and momentum conservation and considering the common vertex of three photons as a floating parameter.After kinematic fit we arrange 3 photons according to their energies: .(see vs. distribution in Fig, 17).As it follows from the kinematics, in the -meson energy region the monochromatic photon in reaction has, in the majority of cases, the medium energy .
Signal/background separation is performed using the approximation of the distribution in the experiment (see Fig. 18).The preliminary results for the cross section measurement at are shown in Fig. 19.The systematic uncertainties are now being studied, and the major uncertainty is the difference between the photon detection efficiency in the Monte Carlo and experiment.

Conclusion
The recent results of the study of the processes , , , at the -meson region with the CMD-3 detector at the VEPP-2000 collider were described.From the combined analysis of and final states the -meson parameters were measured, and the obtained ratio of and couplings was found to be compatible with the isospin symmetry.From the analyzes of the and

Fig. 3 .
Fig. 3.The ionization losses vs momentum for positive tracks for data at GeV. Line shows selection of signal koans.

Fig. 4 .Fig. 5 .
Fig. 4. The ionisation losses in DC vs momentum for positively charged pions for data at energy GeV.The line shows selections of pions from the decay.

Fig. 9 .
Fig. 9.The approximation of the invariant mass of the second pair of photons atGeV.

Fig. 10 .
Fig. 10.Cross section of process, measured with the CMD-3 detector, together with its approximation.

Fig. 11 .
Fig. 11.The distribution of the () versus the invariant mass of two oppositely charged pions in the experiment (data from all are used).The events in the frame (mainly ) are rejected.

Fig. 12 .Fig. 13 .
Fig. 12.The distribution of the energy disbalance for the events with four tracks at MeV.

Fig. 14 .
Fig. 14.The polar angle distributions of charged pions in the experiment (circle markers) and simulation (red open histogram) for 4-track (a) and 3-track (b) events, respectively (data from allare used).For 3-track events also the distributions of the polar angle of missed pion in the experiment (square markers) and simulation (dashed line) are shown.

Fig. 15 .
Fig. 15.Cross section of the process, measured with the CMD-3 detector, together with its approximation.

Fig. 16 .
Fig. 16.The total energy vs. total momentum of all the combinations of three photons in the event (data from all are used).Combination inside the frame is accepted.

Fig. 17
Fig. 17.The vs. distribution for the photons after kinematic fit (data from all are used).
Fig. 17.The vs. distribution for the photons after kinematic fit (data from all are used).

Fig. 18 .
Fig. 18.Signal/background separation by the approximation of the distribution in the experiment ( GeV).

Fig. 19 .
Fig. 19.The preliminary results for the cross section measurement in themeson region with the CMD-3 detector.

Table 1 .
The results of the approximation of the cross sections of processes measured with the CMD-3 detector in comparison with PDG values.
keV Fig. 6.Cross section of process, Fig. 7. Cross section of process