# High statistics study of the resonance in production

###### Abstract

We report on a high statistics measurement of the cross section of the process in the invariant mass range with 85.9 fb of data collected at GeV and 10.52 GeV with the Belle detector. A clear signal for the resonance is observed. From a fit to the mass spectrum, the mass, and two-photon decay widths of the resonance are found to be

###### pacs:

13.66.Bc, 14.40.GxThe Belle Collaboration

The nature of low mass (below 1 GeV/) scalar mesons has been a puzzle for decades with little progress made on its understanding bib:scalar . Among the low mass scalar mesons, the existence of the and mesons is experimentally well established. One of the key ingredients in understanding their nature is measurement of the two-photon production cross sections and in particular the two-photon widths extracted from them. According to a relativistic quark model calculation, assuming the meson to be a non-strange state, its two-photon width should be in the range 1.3 keV to 1.8 keV bib:relquark . However, a much smaller width is expected for an exotic state (0.2 - 0.6 keV for a molecule state) bib:barnes , or for an state (0.3 - 0.5 keV) bib:oller .

A factory is one of the best laboratories for a detailed investigation of low mass scalar mesons through two-photon production, where overwhelming statistics can be obtained. Two-photon production of mesons has advantages over meson production in hadronic processes; the production rate can be reliably calculated from QED with as the only unknown parameter. In addition, a meson can be produced alone without additional hadronic debris, and the quantum numbers of the final state are restricted to states of charge conjugation with forbidden (Landau-Yang’s theorem bib:Yang ).

In the past, using of data, Mark II observed a shoulder in the mass region, which was tentatively identified as the resonance bib:mark2 . The reaction was analyzed using of data taken with the Crystal Ball detector bib:crysball . They found a hint of formation with a significance of 2.2 standard deviations. Measurements of were also performed with the JADE detector using data bib:JADE . They observed a small shoulder at around , which was interpreted as the production of the . CELLO studied the reaction using a data sample of 86 pb and concluded that an signal at the level reported in Refs. bib:mark2 ; bib:crysball ; bib:JADE cannot be excluded with their errors bib:CELLO .

Using data from Mark II, Crystal Ball, and CELLO, Boglione and Pennington (BP) performed an amplitude analysis of and cross sections bib:Amplitude . They found two distinct classes of solutions where one solution has a peak (“peak solution”) and the other has a wiggle (“dip solution”) in the mass region. The two solutions give quite different results for the two-photon width of the and the size of the -wave component. Thus, it is important to distinguish them experimentally.

In this paper, we report on a high statistics study of the meson in the reaction based on data taken with the Belle detector at the KEKB asymmetric-energy collider bib:kekb . The data sample corresponds to a total integrated luminosity of 85.9 fb, accumulated on the resonance and 60 MeV below the resonance (8.6 fb of the total). Since the difference in the cross sections between the two energies is only about 0.3%, we combine both samples. We observe the two-photon process in the “zero-tag” mode, where neither the final-state electron nor positron is detected, and the system has small transverse momentum.

A comprehensive description of the Belle detector is given in Ref. bib:belle . Charged track coordinates near the collision point are measured by a silicon vertex detector (SVD) that surrounds a 2 cm radius beryllium beam pipe. Track trajectory coordinates are reconstructed in a central drift chamber (CDC), and momentum measurements are made together with the SVD. An array of 1188 silica-aerogel Cherenkov counters (ACC) provides separation between kaons and pions for momenta above 1.2 GeV/. The time-of-flight counter (TOF) system consists of a barrel-like arrangement of 128 plastic scintillation counters and is effective for separation for tracks with momenta below 1.2 GeV/. Low energy kaons and protons are also identified by specific ionization () measurements in the CDC. Photon detection and energy measurements of photons and electrons are provided by an electromagnetic calorimeter (ECL) consisting of an array of 8736 CsI(Tl) crystals all pointing toward the interaction point. These detector components are located in a uniform magnetic field of 1.5 T provided by a superconducting solenoid coil. An iron flux-return located outside the solenoid coil is instrumented to detect mesons and to identify muons (KLM).

Signal candidates are primarily triggered by a two-track trigger that requires two CDC tracks with associated TOF hits and ECL clusters with an opening angle greater than 135 degrees. Exclusive events are selected by requiring two oppositely charged tracks coming from the interaction region; each track is required to satisfy cm and cm, where () is the () component of the closest approach to the nominal collision point. The axis of the detector is defined to be opposite to the direction of the positron beam and is the transverse distance from the axis. The difference of the ’s of the two tracks must satisfy the requirement . The event must contain one and only one positively charged track that satisfies and , where and are the transverse component of momentum and the angle with respect to the -axis. The scalar sum of track momenta in each event is required to be smaller than , and the sum of the ECL energies of the event must be less than . Events should not include an extra track with . The cosine of the opening angle of the tracks must be greater than to reject cosmic-ray events. The sum of the transverse momentum vectors of the two tracks should satisfy ; this requirement separates exclusive two-track events from quasi-real two-photon collisions.

Electrons and positrons are distinguished from hadrons using the ratio , where is the energy measured in the ECL, and is the momentum from the CDC. Kaon (proton) candidates are identified using normalized kaon (proton) and pion likelihood functions obtained from the particle identification system ( () and , respectively) with the criterion (), which gives a typical identification efficiency of 90% with a pion misidentification probability of 3%. All charged tracks that are not identified as electrons, kaons or protons are treated as pions. We require both tracks to be pions.

In this measurement, the KLM detector cannot be used for muon identification, since it is insensitive in the region of interest where the transverse momenta of tracks are below . Therefore, we have developed a method for statistically separating and events using ECL information; muons deposit energy corresponding to the ionization loss for minimum ionizing particles, while pions give wider energy distributions since they interact hadronically in the ECL, which corresponds to approximately one interaction length of material. Probability density functions (PDFs) for the distributions of energy deposits from () pairs () are obtained with GEANT-3 bib:geant Monte Carlo (MC) simulation. Here represents the -th bin of in 20 MeV and 0.1 steps, where is the invariant mass of the (or ) pair in each event (the pion mass is assumed in the calculation), and is the polar angle of the produced meson (or lepton) in the center-of-mass system of two initial photons. Note that the effect of muons from pion decays is taken into account by the pion PDFs using this method. We obtain , the fraction of in the -th bin through the equation:

where is the distribution of data and is the total number of events in that bin. The values of ratios obtained must be corrected since the MC cannot simulate hadronic interactions accurately enough. By introducing mis-ID probabilities, and , the value for each bin (the bin number is omitted) can be written as:

where () is the number of true () pair events in that bin. We assume that and are independent of . Applying the separation method described above to a sample of data events positively identified as muons by the KLM, we find that is statistically consistent with zero. The values of in each bin are determined such that the ratio of the data and MC for pairs, which is one ideally, gives a straight line in the spectrum. The values of vary between 0.08 to 0.13 in bins. Because they are determined for each bin of , the bin-by-bin variation of systematic errors is rather large in the angular distribution.

The total cross section for with is evaluated using the following equation:

Here is the number of events in a bin, is the two-photon luminosity function bib:lum_func and is the integrated luminosity. The size of the bin is chosen to be ; a typical mass resolution for a system is 2 MeV according to a MC study. The detection (trigger) efficiencies, () are estimated with a MC simulation. Events of the process are generated using TREPS bib:treps . The detection efficiency is extracted from MC simulation and the trigger efficiency is estimated with the trigger simulator. Since the trigger simulator does not simulate triggers well, particularly in the low energy region, the efficiency values have to be corrected. We calculate the correction factors by comparing events in data and MC that are triggered by the two-track trigger. The resulting factors steeply rise from 0.5 at to 0.8 at and then increase gradually for higher . The muon-background subtraction and all the correction factors are applied using smooth functions obtained by parameterizing the results of bin-by-bin analyses.

The total cross section obtained is shown in Fig. 1 together with the results of some past experiments; an expanded view of the region is shown in Fig. 2(a). A clear peak corresponding to the meson is visible, and thus the peak solution of the BP analysis is selected. Systematic errors for the total cross section are summarized in Table 1. They are dominated by the uncertainty of the separation and that of the trigger efficiency. Systematic errors arising from the separation are estimated by changing the value in the allowable range in each angular bin. Since events are well identified for , the allowable range is determined in this region. These well identified events are also used in estimating systematic errors of the trigger efficiency. Comparing data and MC for events in the region and extrapolating linearly downward, the systematic errors are found to be 4% at and 10% at . The total systematic error is obtained by summing the systematic errors in quadrature and is also shown in Fig. 1.

Parameter | Syst. error (%) |
---|---|

Tracking efficiency | 2.4 |

Trigger efficiency | 4 – 10 |

-separation | 0 – 1 |

-separation | 5 – 7 |

Luminosity function | 5 |

Integrated luminosity | 1.4 |

Total | 11.1 – 12.3 |

Our results are in good agreement with past experiments except for the mass peak region, where they are about 10 to 15% larger, but still within the systematic errors.

A fit to the total cross section is performed to obtain the parameters of the meson. We have to take into account the effect of the channel that opens within the mass region. The fitting function for the scalar resonance is parameterized as follows:

(1) |

where the factor 4.8 includes the fiducial angular acceptance , is the velocity of the particles with mass in the two-body final states, is the amplitude of the meson, which interferes with the helicity-0-background amplitude with relative phase , and is the total background cross section. The amplitude can be written as

(2) |

where is related to the partial width of the meson via . The factor is given as follows bib:denom :

where for or ,

(3) |

The factor is real in the region and becomes imaginary for . The mass difference between and is included by using .

In the fit, we assume to be constant and the relative phase to be a slowly varying function of ; this is motivated by the nearly energy-independent behavior of the scalar Born amplitude bib:morgan . We fix taking the latest value from the BES measurement bib:bes . The background function is evaluated by fitting the cross section with a 4-th order polynomial in outside of the region and . The value of for the fit is 0.88 for 46 degrees of freedom (). A fit to the resonance is then performed with Eq. (1) in the region , where the parameters of are fixed; the free parameters are , , (evaluated at the mass), and .

The result of the fit is shown in Figs. 2(a) and 2(b). In Fig. 2(b), one can see a significant interference effect, which is visible as a deviation from a Breit-Wigner-like shape in Fig. 2(a). In the same figure, the cross section is also plotted, which is obtained by evaluating the first term in Eq. (1), substituting instead of and in Eq. (2) instead of . Note that the cross section is zero below the threshold even though the amplitude is non zero.

The value of of the fit is 1.04 for 15 . The helicity-0-background component that interferes with the meson () is found to be nb. The value of is approximately , which is consistent with the general phase shift study bib:Amplitude .

The parameters of the meson are found to be

The two-photon width given by the PDG bib:PDG is , and the value found by BP is eV. Our results are consistent with them within errors as well as with the prediction of the four-quark model of 270 eV bib:achasov .

The dominant systematic errors come from fitting. The value of is quite sensitive to changes in parameters of the background cross section (fitted outside of the resonance). Systematic errors are evaluated by changing each background parameter by , taking their correlations into account; the error is strongly correlated with that of (i.e. ). The error in the normalization of the total cross section has little effect on the value of the mass, however it is a significant contribution to the error in and . The errors in are also taken into account in the systematic errors. Individual systematic errors are summed in quadrature to obtain the total uncertainty.

In summary, we have made a high statistics measurement of the cross section in the invariant mass region in fine bins of (5 MeV) and (0.05) with the Belle detector at the KEKB accelerator. We have observed a significant signal corresponding to the resonance. Our data clearly select the peak solution of the Boglione-Pennington amplitude analysis bib:Amplitude . The total cross section is fitted to obtain the parameters of the meson. Its two-photon width is found to be eV, consistent with past experiments.

We are indebted to T. Barnes who provided us with a more complete list of theoretical references to calculations of the two-photon widths of scalar mesons, and to M. Pennington for various enlightening discussions and useful suggestions. We thank the KEKB group for excellent operation of the accelerator, the KEK cryogenics group for efficient solenoid operations, and the KEK computer group and the NII for valuable computing and Super-SINET network support. We acknowledge support from MEXT and JSPS (Japan); ARC and DEST (Australia); NSFC and KIP of CAS (China); DST (India); MOEHRD, KOSEF and KRF (Korea); KBN (Poland); MIST (Russia); ARRS (Slovenia); SNSF (Switzerland); NSC and MOE (Taiwan); and DOE (USA).

## References

- (1) For a review, see C. Amsler and N. A. Trnqvist, Phys. Rep. 389, 61 (2004).
- (2) C. R. Mnz, Nucl. Phys. A 609, 364 (1996).
- (3) see, e.g. T. Barnes, IXth International Workshop on Photon-Photon Collisions, March 1992, Ed. D. O. Caldwell and H. P. Paar, World Scientific, p263.
- (4) J. A. Oller and E. Oset, Hadron 97 Conf., AIP Conf. Proc. 432, 413 (1998); R. Delbourgo et al., Phys. Lett. B 446, 332 (1999).
- (5) L. D. Landau, Sov. Phys. Dokl. 60, 207 (1948); C. N. Yang, Phys. Rev. 77, 242 (1950).
- (6) J. Boyer et al. (Mark II Collab.), Phys. Rev. D42, 1350 (1990).
- (7) H. Marsiske et al. (Crystal Ball Collab.), Phys. Rev. D 41, 3324 (1990).
- (8) T.Oest et al. (JADE Collab.), Z. Phys. C - Particles and Fields 47, 343 (1990).
- (9) H. -J. Behrend et al. (CELLO Collab.), Z. Phys. C - Particles and Fields 56, 381 (1992).
- (10) M. Boglione and M. R. Pennington, Eur. Phys. J. C 9, 11(1999); referred to as BP.
- (11) S. Kurokawa and E. Kikutani, Nucl. Instrum. and. Meth. A 499, 1 (2003), and other papers included in this volume.
- (12) A. Abashian et al. (Belle Collab.), Nucl. Instrum. and Meth. A 479, 117 (2002).
- (13) R. Brun et al., CERN DD/EE/84-1 (1987).
- (14) V. M. Budnev et al., Phys. Rep. 15, 181 (1975).
- (15) S. Uehara, KEK Report 96-11 (1996).
- (16) S. M. Flatt, Phys. Lett. 63B, 224 (1976); N. N. Achasov and G. N. Shestakov, Phys. Rev. D 72, 013006 (2005).
- (17) D. Morgan and M. R. Pennington, Z. Phys. C - Particles and Fields 37, 431 (1988).
- (18) M. Ablikim et al. (BES Collab.), Phys. Lett. B 607, 243 (2005). This value of the ratio of the coupling constants is within errors compatible with the results from the radiative decays obtained by R. R. Akhmetshin et al. (CMD-2 Collab.), Phys. Lett. B 462, 380 (1999); M. N. Achasov et al. (SND Collab.), Phys. Lett. B 479, 53 (2000); A. Aloisio et al. (KLOE Collab.), Phys. Lett. B 537, 21 (2002) and F. Ambrosino et al. (KLOE Collab.), Phys. Lett. B 634, 148 (2006).
- (19) W.-M. Yao et al. (PDG), J. Phys. G 33, 1 (2006).
- (20) N. N. Achasov, S. A. Devyanin and G. N. Shestakov, Phys. Lett. B 108, 134 (1982); Z. Phys. C 16, 55 (1982).