Here we will restrict ourselves to mesons (q-qbar) states. Meson classification based on SU(3) x SU(3) has been quite successful. The pseudoscalars J(P)=0(-), vector mesons 1(-) and tensor mesons 2(+) have all been found. There were initially a number of open questions concerning the degree of degeneracy observed in the various multiplets:

1. The pseudoscalars are very light.

2. There is a mass splitting within the same multiplets (pion vs Kaon and phi vs omega for example).

3. The scalar mesons (our subject here) J(P)=0(+) are heavy resonances (between 1-2 GeV) i.e. much heavier than their pseudoscalar cousins.

4. The eta' pseudoscalar meson was too heavy (U(1) problem, not to be discussed here).

Point 2 has an obvious answer: the quarks have some bare mass and especially the s quark has a mass of about 150MeV ie quite large as compared to u and d quarks (5 MeV).

Points 1,3 it is now understood that a few micsec after the big-bang the vacuum of QCD went through a transition that "spontaneously" broke SU(3) x SU(3) down to SU(3). Although this is not a spont. symm. breaking in the strict sense (the quarks have masses) it is a good approximation since the u,d,s quarks are quite lighter than 1 GeV (the scale of the chiral symmetry breaking CSB). Such transitions produce zero mass pseudoscalars (light in our case where the quarks have mass). The scalar counterparts of pion nonet are expected to be as heavy as the vector mesons, something also consistent with the experiment.

In this study we focus on the scalar mesons. There are two reasons in our interest in the scalar mesons:

	The classification of the isospin 0 members of the scalar meson nonet is not understood.
	QCD predicts non q-qbar bound states made entirely of gluons which have the same quantum numbers with the scalar mesons 0(+). These states can mix with the isospin 0 members of the scalar meson nonet.

A natural place to look for scalar mesons is Ks Ks final state. The KK system couples to J=even Parity=+ states, so one hopes to be able to probe scalar and tensor mesons by reconstructing KK invariant mass. Higher J states are expected to be too heavy to be observed.

In what follows we give a brief review of the current status of the KK final state including recent experimental results and I report on our analysis at ZEUS.

The well understood vector and tensor meson nonets are listed below. One can see that the singlet member mixes with the nonet I=0 state in an "ideal" fashion leading to one ssbar state and a uubar+ddbar state. This is the case with the omega(782 MeV) and phi(1020 MeV) for the vectors, and f2(1270) and f2'(1525) for the tensors. The approximate 250 MeV splitting is mainly coming from the strange quark mass.

Glueballs are expected to be produced in a gluon rich environment like J/psi radiative decays and p-pbar diffractive scattering. While they are expected to be absent in gamma-gamma collisions like those at CERN and KEK. In this respect photon- photon to Ks Ks final state are very interesting because they should couple very little to glueball candidates.

The published Ksh Ksh final state from L3 at CERN is shown below. The f2(1525) is seen and a state at 1700MeV which has both 0 and 2 spin components. No state was seen at 2.2GeV mass region. These result suggest that the f0(1710) is probably a member of the scalar nonet, most likely the singlet member.

Similar results are observed by the BELLE collaboration: in particular a broad state is seen at 1750MeV which is mostly of 0 spin. From these data is not obvious if there is more than just one state in the 1750 region.

 We use DIS events selected from 121.6 pb-1 of data collected from 1996 to 2000.

1996	1997	1998	1999-1	1999-2	2000
p/e+	p/e+	p/e-	p/e-	p/e+	p/e+
10.8 pb-1	27.8 pb-1	4.6 pb-1	12.1 pb-1	19.7 pb-1	46.6 pb-1

 First we select only events which pass by a set of DIS triggers carefully chosen according to the year/period of data taking. This is important once the trigger definitions may change from period to period. A common trigger defined as DST 9 (electron finder) is required for all the years and further triggers/period are defined here:

Run Period	TLT inclusive	RCAL boxcut	Portion of Lumi for this period	Run Range	Chosen Trigger for analysis
1996	DIS01	12x6	0.15	21186<=run<21631 22449<=run<22462 22662<=run<22954 25190<=run<25337	DIS01, HPP20
1996	DIS03	14x14	0.12	21634<=run<21853 21871<=run<22448	DIS03, HPP20
1996-97	DIS03	R>25cm	0.73	22466<=run<22660 25344<=run<27889	HPP20 (12x10)
1998-99e	DIS03	R>25cm	0.68	30405<=run<31557	HPP20 (12x10)
1998-99e	DIS01	12x6	0.32	31557<=run<32214	DIS01, HPP20 (12x10), HPP24
1998-99e	SPP15	12x6	0.68 b	32215<=run<33000	SPP15, HPP20, HPP24
1999p-2000p	DIS03	R>35cm	0.17	33125<=run<33821 33905<=run<34048	HPP24 (12x10)
1999p-2000p	SPP15	13x9	0.06	33821<=run<33902 34051<=run<34165	SPP15, HPP24 (12x10)
1999p-2000p	SPP15	18x18	0.12	34166<=run<35179	HPP24 (12x10)
1999p-2000p	SPP15	R>30cm	0.65	35179<=run<37715	HPP24 (12x10)

 Some standard offline DIS and CTD-like cuts are applied in order to clean further the sample that has passed by the triggers and contain the events within the CTD acceptance region. These so called pre-cuts are listed bellow:

Electron_Energy (double angle) > 8.5 GeV	good efficiency in electron identification.
38 < E-Pz < 60 GeV	cuts php and beam-gas backg events. Helps in removing bad reconstructed vertices.
RCAl box cut of 14 x 14 cm	electromagnetic shower is fully contained in RCAL and avoids board effects.
y_ele < 0.95	good efficiency in electron identification.
|zvtx| < 50 cm	eliminates beam-gas and cosmic events.
y_jb > 0.04	good percentage of events with tracks in CTD.

Here we show the control plots for the DIS variables Q2, EmPz, Elec_ene, y_ele, y_jb, zvtx, yvtx, xvtx

We apply the following corrections (DATA only)

• RCALCORR-like : Corrects RCAL and BCAL energy scale. (phantom routine rcalcorr.fpp v6.3)
• CALCORR-like: Corrects BCAL and FCAL non-electron cells.
• Electron energy : Corrects for dead material. (xzero3 map)  
  

 After the pre-cuts, we reconstruct the secondary vertex using the CTD ADAMO tables VCVTXSEC and VCPARSEC. If the table VCVTXSEC is empty, the VCEAZE routine is called. We use CTD-only tracks with CTDCORR routine applied.

 Here you find control plots after secondary vertex identification for the variables Px, Py, Pz and Pt of the K0 candidate and its 2 pions (called first and second pion) decay product. Only pre-cuts are applied:

---

Single Ks Invariant mass for different years:

 Here we show the pi+pi- invariant mass for events from inclusive DIS data.

Tracking Quality Cuts and Ks Selection

• NDoF of the pions from the first Ks candidate
• NDoF of the pions from the second Ks candidate
• Upper most layer for the pions from the first Ks candidate
• Upper most layer for the pions from the first Ks candidate
• Number of tracks
• dxy of the Ks candidates
• dyz of the Ks candidates
• Collinearity of the Ks candidates

In the following plots we examine:

-All events with at least 2Ks that pass 1,2 and 3 steps in the "Analysis Scheme" described on the top of the page.

-We remove events for which 3 tracks (charged) were assigned to the same vertex. These events create fake double Ks events.

The following plot shows the cossine of the KsKs angle distribution for data and MC. There is a clear excess for cosKK > 0.8 with respect to MC. The normalization was done for cosKK<0.8. The std Pythia does not contain any scalar or tensor resonances. This means that MC only has uncorrelated KsKs pairs. (One might have to worry here perhaps about Bose Einstein type effects but the observed effect seems large).

In the following plots we show that the distribution of the Ks agrees with MC and also there is nothing unusual with the decay lengths of the 2 Ks. One could expect reconstruction problems with the abs(dlen1-dlen2)< few mm, but as the plot shows the distribution is as expected.

We will return to the discussion about the threshold region and the cosKsKs cut later.

A further requirement on the mass of the reconstructed Ks to be inside a 2*sigma region around the fitted mass peak. The figure bellow illustrated the mass of the Ks after all cuts.

• Armenteros variable for the Ks candidates
• Decay Length of the Ks candidates
• Reconstructed mass of the Ks candidates

• NDoF of the pions from the first Ks candidate
• NDoF of the pions from the second Ks candidate
• Upper most layer for the pions from the first Ks candidate
• Upper most layer for the pions from the first Ks candidate
• Number of tracks
• dxy of the Ks candidates
• dyz of the Ks candidates
• Collinearity of the Ks candidates
• Armenteros variable for the Ks candidates
• Decay Length of the Ks candidates
• Reconstructed mass of the Ks candidates

Final KsKs Invariant Mass :

The latest KsKs Invariant Mass plot is shown below. A 14 parameter fit is performed from 1.2 to 2.8 GeV. This fit includes 4 Breit-Wigner distributions (12 parameters) and the following background function:

bgnd=par(13)*X**(par(14))*exp(-sqrt(x)*par(15))

It should be noted that the background goes through the dips between the peaks while the full fit lines go higher due to the folding of the signals.

(click on the figure for a .ps file):

The same plot after applying the costheta(KsKs)<0.92 is shown below using 15 MeV binning:

In the figure the two parts of the KsKs spectrum for costheta(KsKs)<0.92 and costheta(KsKs)>0.92 (green) is shown, in order to demonstrate the presence of the f(980) attraction at the KK threshold (see link at the end of page, compare also with MC below). 

The final ksks mass spectrum is shown bellow:

In the figure above the statistical significance of the 3 heavier states is shown. The standard way to calculate this is to use an estimate of the background (in our case it is obtained by a fit a*exp(-x*b) which we call fit1) and calculate the probability that the signal above the background is a statistical poisson fluctuation.

Comparison with second analysis:

The comparison between the two analyses is shown below. M. Barbi's results are the one with the errorbars and are in good agreement with the first analysis. The small difference may be because of small difference in the cuts or Ks selection algorithms.

MC simulation

PYTHIA/ARIADNE MC without resonances:

This is the standard ZEUS DIS MC. If one runs djangoh for example by default the tensor and scalar meson resonances are not included.

Simulation kinematic variable choice:

Q2>4GeV^2. MC ARIADNE including resonances:

We have ran the MC events through our full reconstruction and analysis software and made the same cuts as for the data for the particular years. The number of events in the Mkk plot is 4.2k i.e. only twice the data statistics. We observe no resonant structure in the MC.

PYTHIA/ARIADNE MC including resonances 2:

Full fit (DATA):

Normalized MC + Full fit (DATA):

The reason of the disagreement in the background normalization is due to the bad description of the Ks Pt by the MC. At higher Pt MC undershoots the Ks Pt from the data. The figures bellow illustrate the comparison between DATA and MC for Pt of the pions from the 2 Ks, Pt of each of the Ks from the pair, and Pt of the resonance state candidate
KsKs.

PYTHIA/ARIADNE MC including resonances 2:

MC ARIADNE without resonances:

We have ran the MC events through our full reconstruction and analysis software and made the same cuts as for the data for the particular years. These MC files include scalar and tensor meson resonances (please look at the various files generated) with various filters used. It is possible to select DIS events containing at least 2Ks from any resonance. This means that 1Ks might be from f(1270) and one from f2(1525). It is also possible to "switch off" tensors and keep only scalars. One can also turn off one or more decay channels so that the simulation is enriched in a particular signal.

The current MC statistics is still not as high as we would like but we will be submiting more files according to requests for specific studies.

In Pythia the prominent resonances that decay to KsKs are f2(1270) and f2(1525) while there is some f0(1GeV) and f2(1710).

Presented Plot:

We made an attempt to put the normalized to the data background (yellow histogram) MC without resonance plot (see plot above), together with the various "known" resonances from MC. We have normalized the MC to the data resonance signal after the fit. This normalization is still not final.

In the figure above we clearly see a reproduction of the real data. It is important to consider the particle widths in the MC. It seems that the f2(1275) might be wider in the MC.

The KsKs threshold region ( f(980), Bose Einstein, or Systematic? )

Bose Einstein KsKs effect at threshold?

The MC generator level plot below shows that the effect of BE KsKs correlation is very small to be seen. So this possibility has been excluded.

f0(980), f2(1270), f2(1525), f(1710) Mass resolutions

Laze event display example of a "collinear" KsKs event:

More KsKs Zeus Event Displayed Events (Laze)