Recent results from CMD-3

Regular data taking with the CMD-3 at the electron-positron collider VEPP-2000 is under way since 2010. The collected data sample corresponds to about 200 inverse picobarns of integrated luminosity per detector in the energy range from 0.32 up to 2 GeV, with a goal to collect about 1 f b−1 during next five years. Some of the recent results from the CMD-3 detector are discussed.


Introduction
The electron-positron collider VEPP-2000 [1] has been operating at Budker Institute of Nuclear Physics since 2010. The collider is designed to provide luminosity up to 10 32 cm −2 s −1 at the maximum center-of-mass energy √ s = 2 GeV. At present two detectors, CMD-3 [2,3] and SND [4], are installed in the interaction regions of the collider. In 2010 both experiments started data taking. The current collected integrated luminosity is about 200 pb −1 per detector. The physics program [5] includes high-precision measurements of the e + e − → hadrons cross sections in the wide energy range up to 2 GeV, with rich intermediate dynamics involved, studies of known and searches for new vector mesons, studies of nn and pp production cross sections near threshold and searches for exotic hadrons. It requires a detector with high efficiency for multiparticle events and good energy and angular resolutions for charged particles as well as for photons.
CMD-3 (Cryogenic Magnetic Detector) is a general-purpose detector, see Fig. 1. Coordinates, angles and momenta of charged particles are measured by the cylindrical drift chamber with a hexagonal cell for uniform reconstruction of tracks, which is placed inside of the superconducting solenoid providing 1.3 T magnetic field.
The calorimetry is performed with the endcap BGO calorimeter and the barrel calorimeter. The barrel calorimeter placed outside of the superconducting solenoid consists of two systems: the inner ionisation Liquid Xenon calorimeter and the the CsI scintillation calorimeter. The total thickness of the barrel calorimeter is about 13.5X 0 . The LXe calorimeter has seven layers with strip readout which give information about a shower profile and are also able to measure coordinates of photons with about millimeter precision.
During 2013-2016 the VEPP-2000 collider and the detectors have been upgraded. Starting from 2017 the accelerator complex is running with a new injection facility, which helps to solve a problem of deficit of positrons. Also the "Beamshaking" technique was introduced in 2018, which suppresses beam instabilities by introducing controllable additional kicking of a beam. As a result of such improvements, a luminosity was increased by ∼ 5 times at middle and high energies, but is still lower than the design value by a factor of two at top energies. The 4 × 10 31 cm −2 s −1 luminosity was reached by the VEPP-2000 collider. The already collected integrated luminosity is 200 pb −1 per detector, with about 135 pb −1 above the φ energy and 65 pb −1 from a scan below the φ (Fig. 2).
The dominant contribution to production of hadrons in the energy range √ s < 1 GeV comes from the e + e − → π + π − mode. This channel gives the main contribution to the hadronic term and overall theoretical precision of the anomalous magnetic moment of the muon g − 2.
It is the most challenging channel because of a high-precision requirement, necessitating a systematic precision of 0.2% to fulfill requirements of new g-2 experiments and physics at future electron-positron colliders. The CMD-3 has plans to further reduce a systematic uncertainty achieved by CMD-2. Two energy scan below 1 GeV for the π + π − measurement was performed at VEPP-2000 in 2013 and 2018. The collected data sample corresponds to about 63 pb −1 of integrated luminosity with 18 pb −1 during the first scan and 45 pb −1 during the second one. It is already higher than in any other experiments like previous CMD-2, the BaBar [6] and the KLOE [7,8] experiments (Fig. 3).  . Preliminary results on F 2 π from CMD-3. Open crosses -separation done using the calorimeter information, filled squares -using particle momentum. Some additional corrections, common to two methods, are not applied The crucial pieces of analysis to reach the claimed goal include stable e/µ/π separation, precise fiducial volume determination, theoretical precision of radiative corrections, etc. An important point is that many systematic studies rely on high collected statistics.
The π + π − process has a simple event signature with two back-to-back charged particles. They can be selected by using the following criteria: two collinear well reconstructed charged tracks are detected, these tracks are close to the interaction point, both tracks are inside a good region of the drift chamber. The selected data sample includes events with e + e − , µ + µ − , π + π − pairs and cosmic muons, and it practically doesn't contain any other physical background at energies √ s < 1 GeV. These final states can be separated using either the information about energy deposition in the calorimeter or that about particle momenta in the drift chamber. At low energies the momentum resolution of the drift chamber is sufficient to separate different types of particles. The pion momentum is well aside from the electron one up to energies √ s 0.9 GeV, while the µ + µ − events are separated from others up to √ s 0.66 GeV. At higher energies the peak of an electron shower in the calorimeter is far away from the peak of minimal ionization particles. Separation using energy deposition works better at higher energies and becomes less robust at lower energies.
A full energy deposition in combined LXe and CsI calorimeters is used at the moment. Further methods are under development to exploit full power of the layered barrel calorimeter. Additional information from independent measurements of energy deposition in seven strip layers of the LXe and in the CsI calorimeter gives better discrimination power between different particles due to different interaction process involved (electromagnetic shower, ionization process, nuclear interaction).  The preliminary result on the pion formfactor measured by the CMD-3 is shown in Fig. 4 comparing two approaches using either momentum information or energy deposition. The additional corrections, common to two methods (e.g., the trigger efficiency), are not applied. These two methods overlap in the wide energy range and provide a cross-check of each other, allowing to reach in future a systematic error of event separation at the level of 0.2%.
The contribution to systematic precision from e/µ/π separation at the peak of the ρ resonance is estimated now as 0.2% when using momentum information and up to 1.% in case of energy deposition, where in the second case work is still in progress and this number represents a current level of studies. Comparison of both methods is an important step before publishing first results.
The current estimated systematic uncertainty is about 0.65% at the ρ-peak and up to 0.9% at lowest points.
The comparison of results from two seasons of 2013 and 2018 is shown in Fig. 6 (from the analysis based on momentum information). Good agreement is seen at the level of 0.1%, while the condition of the DCH was very different, like a different level of correlated noise, one HV layer was off in 2013 and so on, which affect very stronlgy applied corrections.
One of the tests in this analysis is a measurement of the e + e − → µ + µ − cross section at low energy, where separation was performed using momentum information. Preliminary results of this test are consistent with the QED prediction with an overall precision of 0.25% as shown in Fig. 5.
For some sources of systematics there is a clear way of how to bring it down. e/µ/π separation should be greatly improved with exploiting full power of the combined barrel calorimeter. The 0.3% systematic contribution coming from the pion specific losses like nuclear interactions and decays in flight will be improved with better understanding of the drift chamber (which includes a detailed description of per cell inefficiencies, noise level, etc) and possible dedicated study based on the 3π-channel.
Another important source of systematics is a theoretical precision of radiative corrections [9], which contribution is estimated as 0.45% in case of event separation based on momentum information and is mainly coming from the theoretical prediction of momentum spectra from differential cross sections. Additional studies like crosschecks of different calculation approaches and further proof from comparison with experimental data are necessary in this field. As seen from effects of two-photon contributions to momentum spectra, it becomes very desirable to have an exact NNLO e + e − → e + e − (γγ) generator to reach precision 0.1%. Hopefully, growing up activity in such calculations for future high-precision experiments like MuOnE [10] and FCC-ee [11] will also help our experiment.
The largest contribution to R(s) at the φ meson comes from two kaon production channels. The recent CMD-3 result for the e + e − → K S K L cross section [12] is shown in Fig. 7. This is the most precise measurement of this cross section with reached 1.8% systematic uncertainty. The data is very well consistent with previous experiments, and the obtained parameters of the φ meson are in good agreement with the PDG data.  Results on the e + e − → K + K − channel were recently published by the CMD-3 [14] experiment below 1.06 GeV as shown in Fig. 8. This cross section was measured in the φmeson energy range with 2% systematic accuracy. As shown in Figs. 9 and 10, the obtained results have comparable accuracy, but they are not consistent, in general, with the previous data. In particular, an inconsistency between the old CMD-2 [15] result and more recent BaBar data [16] was confirmed. The new CMD-3 measurements of e + e − → K + K − and e + e − → K S K L mentioned above demonstrate good agreement with isospin symmetry: the ratio of the coupling constants with the Coulomb factor taken into account is g φK + K − /g φK S K L / Z(m 2 φ ) = 0.990 ± 0.017. The lower CMD-2 e + e − → K + K − cross section is explained by overestimation of the value of the trigger efficiency for slow kaons in the previous experiment and a reanalysis of CMD-2 data is expected.  Figure 9. Comparison of the CMD-3 measurement of e + e − → K + K − to previous CMD-2 [15] and SND [13] measurements. The width of the band shows the systematic uncertainties in the CMD-3 study.  Figure 10. Comparison of the CMD-3 measurement of e + e − → K + K − to the BaBar measurement [16] using the ISR approach. The width of the band shows the systematic uncertainties in the CMD-3 study. Figure 11. The e + e − → 3(π + π − )π 0 cross section measured with the CMD-3 detector at VEPP-2000 (dots). The contributions from the e + e − → 2(π + π − )η and e + e − → 2(π + π − )ω reactions are shown by triangles and open circles, respectively.

Unaccounted modes
The total e + e − → hadron cross section below 2 GeV is calculated as a sum of exclusive cross sections for all possible hadronic modes. Some unmeasured channels are calculated using rough isospin relations, which can be very approximate. To fulfill a precise R(s) measurement program, it is very important to take into account all possible channels and to do measurements of unaccounted modes or accounted by indirect isospin relations. Some of them were recently studied by the CMD-3 group.
The process e + e − → π + π − π 0 η was studied using the π + π − 4γ final state [17]. This channel can go through several intermediate states. At least four mechanisms of this reaction: ωη, φη, a 0 (980)ρ and structureless π + π − π 0 η were observed. About 50% of the total cross section in the region below 1.8 GeV is due to the ωη, φη contributions. Above 1.8 GeV the dominant mechanism of the reaction is a 0 (980)ρ. The only known before ωη and φη contributions were taken into account in the total hadron cross section, while not accounted parts give about 3-5% of the total R(s) in this energy range.