Photoproduc*on  and  Decay        of  Light  Meson  in  CLAS  

Moskov  Amaryan  

Old  Dominion  University  Norfolk,  Virginia,  USA  

On  behalf  of  the  CLAS  Collabora*on  

7th  Interna*onal  Workshop  on  Chiral  Dynamics                                              August  9,  2012,  JLAB  

Outline  

Pseudoscalar,  Vector,  Axial  Vector  Mesons  

1.  Dalitz  Decays  2.  Radia*ve  Decays  3.  Hadronic  Decays  

 π0   e+e-­‐γ  η   e+e-­‐γ   π+π-­‐γ   π+π-­‐π0  

 η’   e+e-­‐γ   π+π-­‐γ   π+π-­‐π0   π+π-­‐η  

ρ   π+π-­‐γ  

ω   e+e-­‐  π0   π+π-­‐γ   π+π-­‐π0  

ϕ   π+π-­‐π0   π+π-­‐η  

f1(1285)   π+π-­‐η  

Light  Mesons  in  CLAS  

3

pendix A. The vector meson propagators DV are

DV (Q2) = [Q2 −M2

V + i√

Q2Γtot,V (Q2)]−1. (5)

In this paper we consider only the data in the space-likeregion of photon virtuality, thus the modeling of the vec-tor resonance energy dependent widths Γtot,V (Q2) is notrelevant as the widths are equal to zero. We take the val-ues of the masses of all particles according to PDG [42].We require that the form factors Fγ∗γ∗P(t1, t2) given

in (2), (3) and (4) vanish when the photon virtuality t1goes to infinity for any value of t2:

limt1→−∞

Fγ∗γ∗P(t1, t2)∣

∣

∣

t2=const= 0. (6)

Notice, that in this case the conditions

limt→−∞

Fγ∗γ∗P (t, t) = 0, (7)

limt→−∞

Fγ∗γ∗P(t, 0) = 0 (8)

are automatically satisfied, which is considered as a cor-rect short-distance behavior of the form factors (see, forexample, discussion in [24]). The constraint (6) leads tothe following relations for the couplings:

√2hVi

fVi− σVi

f2Vi

= 0, i = 1, . . . , n , (9)

−Nc

4π2+ 8

√2

n∑

i=1

hVifVi

= 0 . (10)

Therefore, for an ansatz with n vector resonance octetsthe two-photon form factors Fγ∗γ∗P(t1, t2) are deter-mined by 2n parameters (i.e., the products of the cou-plings: fVi

hViand σVi

f2Vi, i = 1, . . . , n), from which n−1

are to be determined by experiment and the rest n+1 arefixed by (9) and (10). For the one octet ansatz there areno free parameters and in case of the two octets ansatzthere is one free parameter.One of the main objectives of this paper was to de-

velop a reliable model for the γ∗γ∗P (P = π0, η, η′) tran-sition form factors in the space-like region reflecting theexperimental data and theoretical constrains and in thesame time being as simple as possible. Even if we knowthat the SU(3) flavor symmetry is broken we start ourinvestigations using an SU(3)-symmetric model (apartfrom the masses of the mesons, which are fixed at theirPDG [42] values) and try to see how many resonanceoctets we have to include in order to describe the datawell. The existing data for the transition form factors inspace-like region [1, 2, 45, 46] come from single-tag exper-iments, where one of the invariants is very close to zero(the one associated with the “untagged” lepton), thus wehave information only about Fγ∗γ∗P (t, 0). It is commonto define the γ∗γP form factor FP (Q2, 0) ≡ Fγ∗γ∗P(t, 0)with Q2 ≡ −t (associated with the “tagged” lepton).From Eqs. (2), (3) and (4) we see that FP(Q2, 0) isdriven by n parameters (i.e., the products of the cou-plings: fVi

hVi, i = 1, . . . , n) and there is always only one

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Q2 |F

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BL 1

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BaBar 2009CELLO 91CLEO 98

2 octets1 octet

FIG. 2: Transition form factor γ∗γπ0 compared to the data.The Brodsky-Lepage [23] high-Q2 limit (BL) is shown as abold solid straight line at 2× fπ = 2×0.0924 GeV. The high-Q2 limit in our 1 octet ansatz and and 2 octets ansatz aremarked as (1) and (2), correspondingly.

constraint (10) for any n. Therefore, the number of pa-rameters in FP(Q2, 0) to be determined by experiment(“free parameters”) equals to n− 1 (similarly to the caseof the Fγ∗γ∗P(t1, t2)). In case of the one octet ansatzthere are no free parameters and in the two octets casethere is one free parameter.

B. The one octet ansatz for the form factors

Let us consider first the one octet ansatz. In this case

fV1hV1 =3

32π2√2, (11)

and the model gives a prediction for the form factorsFP(Q2, 0) without any possibility for adjustment. Thepredictions of this model are compared with experimen-tal data in Figs. 2-4 (dotted line). To quantify the qual-ity of the agreement of the model predictions we havecalculated the χ2 values for each data set. For the piontransition form factor the model agrees with CELLO [45]and CLEO [46] and disagrees with the BaBar data [1], ascan be seen from Table I, which shows the χ2 values perexperiment. For the η and η′ transition form factor themodel is in a perfect agreement with CELLO, howeverfor CLEO and BaBar the χ2 is not good. In total, for theone octet ansatz we obtain χ2 ≈ 358 for 116 experimentalpoints.Even though the overall agreement of this simple model

with the data is not bad, there is a way to improve it, aswill be discussed below.

e+e-­‐  èπ0  Space-­‐Like  Form  Factor  

F(Q2)~1+aπQ2  

aπ  =  0.0309±0.0008±0.0009  (CLEO)   Q2>0.5GeV2  

Time-­‐Like  Form  Factor   π0èe+e-­‐γ  

1

I. INTRODUCTION

Low energy Quantum Chromodynamics (QCD) is responsible for the binding of hadrons and for the mass of thevisible universe. A unique way to explore low energy QCD is by measuring the decays of light mesons, specificallythe π0, η and η� pseudoscalar mesons. In particular, the η and η� mesons present important information on thelow energy dynamics of QCD: the mechanism of spontaneous chiral symmetry breaking and the UA(1) anomaly.The importance of this topic is shown by the number of experiments performed at an impressive array of facilitiesincluding KLOE, CLEO, BES, MAMI, Bonn, COSY, BABAR, BELLE, and CERN. We have recently shown thatCLAS photoproduction data has superior statistics in many channels, exceeding that of published results by a factorof up to ten.

Close to the zero-energy limit of the spontaneous breaking of chiral symmetry, chiral perturbation theory (ChPT)and, more generally, effective field theories, incorporate the symmetries of QCD while avoiding the tremendouscalculational difficulties of the full theory in the non-perturbative regime. Comparisons of ChPT predictions withhigh statistics data on the branching ratios and decay distributions of light mesons will provide insight into thenon-perturbative regime of strong interactions and provide important information for a firmer foundation of hadronicphysics rooted in the standard model.

II. PSEUDOSCALAR MESONS

Below we outline a physics program to explore light meson decays measured in the CLAS g11 and g12 hydrogenphotoproduction experiments. Preliminary analyses of these data show that CLAS data can have a major impact onstudies of light meson decays measured in other facilities and is independent of the production vertex. Experimentaldata are presented with emphasis on the photoproduction reactions

γ + p → p+

π0

ηη�

(1)

collected in the following decay modes:

• Dalitz decays: π0, η, or η� → e+e−γ

• Radiative decays: η or η� → π+π−γ

• Hadronic decays: η or η� → π+π−π0 and η� → π+π−η

In order to fully exploit this rich vein of data and to cast more light on low energy QCD, dedicated efforts andsufficient manpower is needed to complete the analyses and publish these results.

1. Dalitz decays

The branching ratios for radiative decay of pseudoscalar mesons π0 and η have been measured and are recorded bythe PDG [1], however there is only an upper limit quoted for η� → e+e−γ.

In this proposal we briefly present our preliminary distribution of the e+e−γ invariant mass from CLAS photo-production data. This is a H(γ, pe+e−γ)X four-fold coincidence event sample with an upper bound on the missingenergy.

Peaks of π0, η and η� are shown separately, with fitted positions corresponding to their PDG values. In addition,there is a clear signal in the ρ-ω region, and a small peak at the φ-mass. With a branching ratio of (1.174± 0.035)%, the three body decay π0 → e+e−γ is the second most important decay channel of the neutral pion and is deeplyconnected to the main decay mode π0 → γγ (Br = 98.823± 0.034%) with anomalous π0 − γ − γ vertex. Significantinterest to the Dalitz decay of π0 lies in the fact that it provides information on the semi off-shell π0−γ−γ∗ transitionform factor Fπ0γγ∗(q2) in the time-like region, and more specifically on its slope parameter aπ. The determinationsof aπ obtained from the differential decay rate of Dalitz decay

aπ = −0.11± 0.03± 0.08 [2]

aπ = +0.026± 0.024± 0.0048 [3]

aπ = +0.025± 0.014± 0.026 [4]

11

[1] K. Nakamura et al. (Particle Data Group), J. Phys. G37, 075021 (2010).[2] H. Fonvieille, N. Bensayah, J. Berthot, P. Bertin, M. Crouau, et al., Phys.Lett. B233, 65 (1989).[3] F. Farzanpay, P. Gumplinger, A. Stetz, J. Poutissou, I. Blevis, et al., Phys.Lett. B278, 413 (1992).[4] R. Meijer Drees et al. (SINDRUM-I Collaboration), Phys.Rev. D45, 1439 (1992).[5] H. Behrend et al. (CELLO Collaboration), Z.Phys. C49, 401 (1991).[6] J. Gronberg et al. (CLEO Collaboration), Phys.Rev. D57, 33 (1998), hep-ex/9707031.[7] B. Aubert et al. (BABAR Collaboration), Phys.Rev. D80, 052002 (2009), 0905.4778.[8] H. N. Brown et al. ((Muon g-2 Collaboration)), Phys. Rev. Lett. 86, 2227 (2001).[9] H. Czyz, S. Ivashyn, A. Korchin, and O. Shekhovtsova (2012), 1202.1171.

[10] H. Berghauser, V. Metag, A. Starostin, P. Aguar-Bartolome, L. Akasoy, et al., Phys.Lett. B701, 562 (2011).[11] R. Arnaldi et al. (NA60 Collaboration), Phys.Lett. B677, 260 (2009), 0902.2547.[12] F. Stollenwerk, C. Hanhart, A. Kupsc, U.-G. Meissner, and A. Wirzba, Phys.Lett. B707, 184 (2012), 1108.2419.[13] P. Adlarson et al. (WASA-at-COSY Collaboration), Phys.Lett. B707, 243 (2012), 1107.5277.[14] M. Gormley, E. Hyman, W.-Y. Lee, T. Nash, J. Peoples, et al., Phys.Rev. D2, 501 (1970).[15] A. Abele et al. (Crystal Barrel Collaboration), Phys.Lett. B402, 195 (1997).[16] D. J. Gross, S. Treiman, and F. Wilczek, Phys.Rev. D19, 2188 (1979).[17] M. Ablikim et al. (The BESIII), Phys. Rev. D83, 012003 (2011), 1012.1117.[18] N. N. Achasov and A. A. Kozhevnikov, Int. J. Mod. Phys. A7, 4825 (1992).[19] E. Abouzaid et al. (KTeV Collaboration), Phys.Rev. D75, 012004 (2007), hep-ex/0610072.[20] A. E. Dorokhov and M. A. Ivanov, Phys.Rev. D75, 114007 (2007), 0704.3498.[21] A. Dorokhov, M. Ivanov, and S. Kovalenko, Phys.Lett. B677, 145 (2009), 0903.4249.[22] L. Landsberg, Phys.Rept. 128, 301 (1985).[23] C. Terschlusen and S. Leupold, Phys.Lett. B691, 191 (2010), 1003.1030.[24] R. Dzhelyadin, S. Golovkin, A. Konstantinov, V. Konstantinov, V. Kubarovsky, et al., Phys.Lett. B102, 296 (1981).[25] R. Barate et al. (ALEPH Collaboration), Phys.Lett. B472, 189 (2000), report-no: CERN-EP/99-153, hep-ex/9911022.[26] L. Faddeev, A. J. Niemi, and U. Wiedner, Phys.Rev. D70, 114033 (2004), hep-ph/0308240.

[2]  

[3]  

[4]  

Slope  is  measured  with  very  large  errors:  

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in Fig. 3. Thus, for the KLOE-2 case the possible effectof the photon virtualities which can influence the accu-racy of eq. (4) is negligible. Our simulation shows thatthe uncertainty in the measurement of Γ (π0 → γγ) dueto the form factor parametrization in the generator isexpected to be less than 0.1 %.

Entries 1000000

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trie

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2Photon q

No HET selection

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Fig. 3 Distribution of the photon virtuality in γ∗γ∗ → π0.The lepton double tagging (HET-HET) selects the events (reddiamonds) with small virtuality of the photons.

4 Feasibility of the γ∗γπ

0 transition form

factor measurement

By requiring one lepton inside the KLOE detector (20◦ <θ < 160◦, corresponding to 0.01 < |q21 | < 0.1GeV2) andthe other lepton in the HET detector (corresponding to|q22 | ! 10−4GeV2 for most of the events) one can mea-sure the differential cross section (dσ/dQ2)data, whereQ2 ≡ −q21 . Using eq. (5), the form factor |F (Q2)| canbe extracted from this cross section.

The simulation has been performed using a low-est meson dominance ansatz with two vector multiplets(LMD+V) for the form factor Fπ0γ∗γ∗ , which is avail-able in EKHARA. The LMD+V ansatz is based onlarge-NC QCD matched to short-distance constraintsfrom the operator-product expansion (OPE), see theRef. [39]. In the following we use the definition of theLMD+V parameters h5 = h5 + h3m2

π and h7 = h7 +h6m2

π + h4m4π. Figure 4 shows the expected experi-

mental uncertainty (statistical) on F (Q2) achievable atKLOE-2 with an integrated luminosity of 5 fb−1. In thismeasurement the detection efficiency is different and isestimated to be about 20%. From our simulation weconclude that a statistical uncertainty of less than 6%for every bin is feasible.

Having measured the form factor, one can evaluatealso the slope parameter a of the form factor at the

origin1

a ≡ m2π

1

Fπ0γ∗γ∗(0, 0)

dFπ0γ∗γ∗(q2, 0)

d q2

∣

∣

∣

∣

q2=0

. (7)

Though for time-like photon virtualities (q2 > 0), theslope can be measured directly in the rare decay π0 →e+e−γ, the current experimental uncertainty is verybig [40,41]. The PDG average value of the slope pa-rameter is quite precise, a = 0.032 ± 0.004 [8], and itis dominated by the CELLO result [14]. In the latter,a simple vector-meson dominance (VMD) form factorparametrization was fitted to the data [14] and thenthe slope was calculated according to eq. (7). Thus theCELLO procedure for the slope calculation suffers frommodel dependence not accounted for in the error esti-mation. The validity of such a procedure has never beenverified, because there were no data at Q2 < 0.5 GeV2.Therefore, filling of this gap in Q2 by the KLOE-2 ex-periment can provide a valuable test of the form factorparametrizations.

2 [GeV]2Q-210 -110 1 10

)|2|F

(Q

0

0.05

0.1

0.15

0.2

0.25

0! " #*#

Fig. 4 Simulation of KLOE-2 measurement of F (Q2) (redtriangles) with statistical errors for 5 fb−1. Dashed line isthe F (Q2) form factor according to LMD+V model [39],solid line is F (0) given by Wess-Zumino-Witten term, eq. (8).CELLO [14] (black crosses) and CLEO [15] (blue stars) dataat high Q2 are also shown for illustration.

When the normalization of the form factor is fixedto the decay width π0 → γγ or to some effective piondecay constant Fπ, the VMD and (on-shell) LMD+Vmodels have only one free parameter2. For VMD thisparameter is the vector-meson mass MV (sometimes

1 We would like to stress that the q2 range of KLOE-2 mea-surement is not small enough to use the linear approxima-tion Fπ0γ∗γ∗(q2, 0) = Fπ0γ∗γ∗(0, 0)(1 + q2 a/m2

π) becausethe higher order terms are not negligible.2In the Brodsky-Lepage ansatz [42,43,44] the parameter Fπ

fixes the normalization and the asymptotic behavior at thesame time. Comparison with data from CELLO and CLEOshows that the asymptotic behavior is off by about 20%, oncethe normalization is fixed from π0 → γγ.

KLOE-­‐2  Proposal   CLAS  g12  Data  

CLAS  provides  unprecedented  sta3s3cs  for  precision    measurement  of  the  TFF  slope!  

Also  Important  for  LbyL  radia*ve  correc*ons  to  g-­‐2  

Transi*on  Form  Factor  

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6. Results

]2 [GeV/c-l+lM0 0.1 0.2 0.3 0.4 0.5

2 | !|F

1

10WASACB/TAPS MAMI-CNA60Fit to all points

Fig. 6.10: Experimental spectrum of the squared transition form factor,|Fη|2, as a function of the Ml+l−. The green, solid line is the fit to allexperimental points. The black, solid line is the QED model assumptionof a point-like meson.

one of the CODATA compilation of physical constants, < r2P >1/2= (0.8768±0.0069) fm [73]. The CODATA values of the radius of the proton are deter-mined via the Lamb shift in electronic [73] hydrogen and via unpolarized [74]and polarized [75] electron scattering. The discrepancy between the CODATAand the value extracted using the Lamb shift method in muonic [72] hydro-gen is under a world-wide discussion with a tendency to see the cause of theproblem in a not sufficiently exact QED calculations [76].

6.3 Charge Radius of the η Meson 79

Time-­‐Like  Form  Factor  of  η  

World  Data   CLAS  g12  Data  preliminary  

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Accepted Correct Spectrum

PREL

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First  measurement  of  Dalitz  Decay  of  eta’  from  CLAS    

Radia*ve  Decay     η,η’èπ+π-γ  

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Chapter 3

Anomalous decays

In the following Chapter we will discuss the decays of the neutral pseudoscalar mesonsP ∈ {π0, η, η′} that are induced by the chiral anomaly. We differentiate between the oneswhich are governed by the triangle anomaly and the ones resulting from the box anomaly,because the structure of the pertinent form factors will be quite similar in the respectivecases.

P

γ(!)

γ(!)

Figure 3.1: triangle anomaly

P

π+

π−

γ(∗)

Figure 3.2: box anomaly

The leading decays induced by the triangle anomaly are discussed next. We add herethe qualifier ’leading’ in order to discriminate these decays from those which involve sub-leading sequential decays as, e.g., Bremsstrahlung corrections etc. The discussed decays are

P → γγ,

P → l+l−γ,

P → l+l−l+l−,

P → l+l−,

where l+l− are lepton-antilepton pairs. Obviously only electrons and muons are involved,

19

Why  is  radia*ve  decay  interes*ng?  

It  gives  an  access  to  the  box  anomaly  term  of  Wess-­‐Zumino-­‐Wiqen  Lagrangian  !  

triangle   box  

0 0.05 0.1 0.15 0.2E! [GeV]

012345678

d"/d

E ! [a

rb. u

nits]

0 0.1 0.2 0.3 0.4E! [GeV]

0

5

10

15

20

d"/d

E ! [a

rb. u

nits]

Fig. 2. Experimental data and error weighted fits for η (left, data are from Ref. [17](filled squares) and Ref. [18] (open circles)) and η′ (right, data are from Ref. [20])to π+π−γ according to Eqs. (1) and (2) with sππ = mη(′)(mη(′) − 2Eγ).

uncertainty of the α′ value should include both statistical and systematic un-certainties.

We also studied other data sets for η and η′. Concerning the former decay,Gormley et al. [18] provides α = (1.7±0.4) GeV−2 while Layter et al. [19] givesα = (−1.0± 0.1) GeV−2. The acceptance correction of these old experimentswas derived from the specified dΓ/dEγ distributions, respectively, under theassumption that the pertinent matrix element is the simplest gauge invariantone (corresponding here to P (sππ) and FV (sππ) equal to one). The Layteret al. result seems to be inconsistent both with WASA [17] and Gormley etal. [18]. However, from the information provided in those old experimentalpapers it is impossible to evaluate systematic uncertainties. In case of the η′,we obtain α′ = (3± 1) GeV−2 from the data of the GAMS-200 collaboration[21], which is larger, but within error bars consistent with the value listedabove. Hence, in the following, we use the values given in Eq. (8).

Instead of looking at the data themselves it is illustrative to extract from datadirectly the polynomials P (sππ). These are shown for both radiative η and η′

decay in the left and right panel of Fig. 3, respectively. Here one clearly seesthat the residual sππ dependence for both transition amplitudes — once thepion form factor and the phase space are divided out — has a linear behavior toa very good approximation. The statement is further corroborated by the factthat any additional quadratic term to the linear polynomial with coefficientsas specified in Eq. (8) is compatible with zero: β = (0.07 ± 0.65) GeV−4 andβ ′ = (0.10 ± 0.38) GeV−4. This appears reassuring, although it came as asurprise that even for the η′ a first-order polynomial is sufficient. The originof this might be in the current quality of the data which is best in the regionof large values of Eγ which corresponds to moderate values of sππ — this isthe region where the chiral expansion is expected to converge (once resonanceeffects are taken out). This can also be seen in Fig. 3, right panel: clearlythe fit is dominated by values of sππ ≤ 0.6GeV2 (this corresponds to pion

6

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ηèπ+π-γ   η’èπ+π-γ  

Theory:  E.Stollenwerk  et  al.  PL  B707,  184,  2012  

CLAS  Hadronic  decays:  g11  Data  

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(

About  17M  ω’s  

6

branching ratio is known to 15% precision, only an upper bound for the ω is quoted in the PDG [1]. This channelmay also yield new results, in particular a measurement of ω → π+π−γ branching ratio.

3. Hadronic decays

In this section we present experimental data for the reaction

γ + p → pπ+π−�

π0

η. (5)

The π0 or η is identified via missing mass of the H(γ, pπ+π−)X reaction.In Fig. 9 (left panel) a distribution of missing mass of the proton in the γ + p → pπ+π−π0 reaction is presented

showing clear peaks for the η and ω mesons with ∼2M and ∼20M events in the peaks, respectively. Our Dalitz plotdistribution for the decay η → π+π−π0 is seen in Fig. 10

There are also hints of η� and φ mesons. To see the η� and φ signals, in Fig. 9 (right panel) we plot a zoom of thesame distribution in the mass range above the ω meson. We clearly observe one of the rare decays η� → π+π−π0

(Br = 3.6± 0.1× 10−3) and the OZI violating decay φ → π+π−π0 (Br=15.3%). This is the first observation of thesedecays in photoproduction. According to Gross, Treiman, and Wilczek [16], the decay width ratio:

Γ(η� → π0π+π−)

Γ(η� → ηπ+π−)∝

�md −mu

ms

�2(6)

is sensitive to the quark mass difference md−mu, where md. mu, and ms are masses of u, d and s quarks respectively.

FIG. 9: Left panel: distribution of missing mass of the proton in the reaction γ + p → pπ+π−π0. Right panel: the same for

the range of invariant mass above ω meson production. Experimental data are from CLAS g11 experiment.

In Fig. 11 (left panel) we present the distribution of missing mass of the proton in the reaction γ + p → pπ+π−η,where η is reconstructed in the missing mass of the pπ+π− system, i.e. γ(1H, pπ+π−)X. As one can see there is aclear peak of η� with ∼300K events, which is almost an order of magnitude higher than the recent BES [17] data. InFig. 12 we show our Dalitz plot distribution for the decay η� → π+π−η.

The internal dynamics of the decay η → π+π−π0 and η� → π+π−η can be described by two degrees of freedomsince all particles involved have spin zero. The Dalitz plot distribution for the decay η → π+π−π0 is described by thefollowing two variables:

X =

√3

Q(Tπ+ − Tπ−), Y =

3Tπ0

Q− 1, (7)

ω → π+π−π0

Not  corrected  for  acceptance  

CLAS  

6

branching ratio is known to 15% precision, only an upper bound for the ω is quoted in the PDG [1]. This channelmay also yield new results, in particular a measurement of ω → π+π−γ branching ratio.

3. Hadronic decays

In this section we present experimental data for the reaction

γ + p → pπ+π−�

π0

η. (5)

The π0 or η is identified via missing mass of the H(γ, pπ+π−)X reaction.In Fig. 9 (left panel) a distribution of missing mass of the proton in the γ + p → pπ+π−π0 reaction is presented

showing clear peaks for the η and ω mesons with ∼2M and ∼20M events in the peaks, respectively. Our Dalitz plotdistribution for the decay η → π+π−π0 is seen in Fig. 10

There are also hints of η� and φ mesons. To see the η� and φ signals, in Fig. 9 (right panel) we plot a zoom of thesame distribution in the mass range above the ω meson. We clearly observe one of the rare decays η� → π+π−π0

(Br = 3.6± 0.1× 10−3) and the OZI violating decay φ → π+π−π0 (Br=15.3%). This is the first observation of thesedecays in photoproduction. According to Gross, Treiman, and Wilczek [16], the decay width ratio:

Γ(η� → π0π+π−)

Γ(η� → ηπ+π−)∝

�md −mu

ms

�2(6)

is sensitive to the quark mass difference md−mu, where md. mu, and ms are masses of u, d and s quarks respectively.

FIG. 9: Left panel: distribution of missing mass of the proton in the reaction γ + p → pπ+π−π0. Right panel: the same for

the range of invariant mass above ω meson production. Experimental data are from CLAS g11 experiment.

In Fig. 11 (left panel) we present the distribution of missing mass of the proton in the reaction γ + p → pπ+π−η,where η is reconstructed in the missing mass of the pπ+π− system, i.e. γ(1H, pπ+π−)X. As one can see there is aclear peak of η� with ∼300K events, which is almost an order of magnitude higher than the recent BES [17] data. InFig. 12 we show our Dalitz plot distribution for the decay η� → π+π−η.

The internal dynamics of the decay η → π+π−π0 and η� → π+π−η can be described by two degrees of freedomsince all particles involved have spin zero. The Dalitz plot distribution for the decay η → π+π−π0 is described by thefollowing two variables:

X =

√3

Q(Tπ+ − Tπ−), Y =

3Tπ0

Q− 1, (7)

η → π+π−π0

~2M  events  

CLAS  

M2 = A(1 + aY + bY 2 + cX + dX2)

(Decay  Matrix  element  expansion)    

X-1 -0.5 0 0.5 10

2000

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η → π+π−π0Dalitz  plot  projec*ons  

g11  Data  

(p) [GeV]XM0.8 1 1.2 1.4 1.6 1.80

10000

20000

30000

40000

50000

Yield: 287145Background: 90218

= 3.2BS

! 3.0 ±Range:

Mean:0.958 GeV:0.005 GeV!'"

(1285)1f

#

"-$+$%p&

!"#$%&'%()*+&,$-.-/*01&23415)*6-5/-$7-&*89:8;)*8<==)*>?-@,A4)*B-&$%('*

(p) [GeV]XM0.8 1 1.2 1.4 1.60

10000

20000

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!-"+"p#p$

(p) [GeV]XM1 1.01 1.02 1.03 1.04 1.05

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!!!!!!!!!"#$%&'()!!*'+,%-./!!012%)!+3!4!!516+.!7!!

589:;<9!"1*!=!8!;:;;>!"1*!!

$0"!?@A:!,'B'(!C&D9:E@9;#>!!!

CD*

E*

F=G=8;HI*

φ → π+π−ηFG1+&)!A&1H'2-+.I!C&J!!!!!!!!!!!!!!!!!!!!!!!!!!!K!!LM@9;#N!! #A4%31J)*K">"!"+4'3"*#)*L1@"M)*.1"*8<G=NN8)*O;8HI*

G-­‐Parity  viola*on  

Φèππη  η’èππη  

CLAS  g11  Data  (7  *mes  more  η’  than  in  BESIII)  3  *mes  more  on  tape  

Hadronic  decay  

η’èππη  Dalitz  plot  

X-1.5 -1 -0.5 0 0.5 1 1.50

500

1000

1500

2000

2500

Y-1.5 -1 -0.5 0 0.5 1 1.50

2004006008001000120014001600180020002200

!"#$%&'%()*+&,$-.-/*01&23415)*6-5/-$7-&*89:8;)*8<==)*>?-@,A4)*B-&$%('*

C&1$*D==*&?(**1(@'*

#EE,(D*D=8**F,@@*&-E?A-**3/%/"-&&"*7'*G%A/1&*1G*/F1*

η’èππη  Dalitz  plot  projec*ons  

arXiV:1012.1117  

CLAS  Preliminary  uncorrected  

Dalitz  decay   ωèe+e-­‐π0  

) [GeV]-e+(Pe2XM

-0.02 0 0.02 0.04 0.06

Num

ber o

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Background: 1314

= 3.7BS

! 2.0 ±Range:

0.0003 GeV±Mean:0.7833

0.0003 GeV±:0.0156 !

)"-e+(e#

)0$-e+(e%

CLAS  g12  Data  

Transi*on  Form  Factor       ωèe+e-­‐π0  

The pole parameter of the electromagnetic transi-tion form factor of the Dalitz decay η → µ+µ−γ

is measured to be Λ−2η =1.95±0.17(stat.)±0.05(syst.)GeV−2. It perfectly agrees with the previous mea-surement of the Lepton-G experiment Λ−2η =1.90±0.40GeV−2 as well as with predictions from VMD, Λ−2η =1.8

0 0.1 0.2 0.3 0.4 0.5 0.6

1

10

base

Entries 0Mean x 0Mean y 0

RMS x 0RMS y 0

base

Entries 0Mean x 0Mean y 0

RMS x 0RMS y 0

-20.4 GeV±=1.90!-2"Lepton G:

-20.04GeV±0.17±=1.95!-2"NA60 :

-2=1.8 GeV!-2"VMD :

2 | !|F

M (GeV)

#-µ+µ$!

Figure 4: Experimental data on the η-meson electromagnetic transi-tion form factor (red triangles), compared to the previous measure-ment by the Lepton-G experiment (open circles) and to the expecta-tion from VMD (blue dashed line). The solid red and black dashed-dotted lines are results of fitting the experimental data with the poledependence Eq. (1). The normalization is such that |Fη(M = 0)|=1.

GeV−2 [2]. The characteristic mass Λ is equal toΛη=0.716±0.031(stat.)±0.009(syst.) GeV, as comparedto the value from Lepton-G of Λη=0.724±0.076 GeVor to the VMD value of Λη=0.745 GeV. Our result im-proves the Lepton-G error by a factor of 2.3, equivalentto a factor of 5 larger statistics. The error improvementto be expected from the difference in sample sizes (9 000vs. 600) would have been larger (a factor of 3.8), butthis is only found if the ω Dalitz decay is frozen in thefit [18].The pole parameter of the electromagnetic transi-

tion form factor of the Dalitz decay ω → µ+µ−π0

is measured to be Λ−2ω = 2.24±0.06(stat.)±0.02(syst.)GeV−2. Within errors, it agrees with the Lepton-G value of Λ−2ω =2.36±0.21 GeV−2. Both experimen-

tal results differ from the expectation of VMD ofΛ−2ω =1.68 GeV−2 [2]. The anomaly is therefore fullyconfirmed. The characteristic mass Λ is found to beΛω=0.668±0.009(stat.)±0.003(syst.) GeV, as comparedto the value from Lepton-G ofΛω=0.65±0.03GeV or tothe VMD value of Λω=Mρ=0.770 GeV. The confirma-

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1

10

210

310base

Entries 0Mean x 0Mean y 0

RMS x 0RMS y 0

base

Entries 0Mean x 0Mean y 0

RMS x 0RMS y 02 | %|F

M (GeV)

0&-µ+µ$%

-20.21 GeV±=2.36%-2"Lepton G:

-20.02 GeV±0.06±=2.24%-2"NA60 :

-2=1.68 GeV%-2"VMD :

Figure 5: Experimental data on the ω-meson electromagnetic transi-tion form factor (red triangles), compared to the previous measure-ment by the Lepton-G experiment (open circles) and to the expecta-tion from VMD (blue dashed line). The solid red and black dashed-dotted lines are results of fitting the experimental data with the poledependence Eq. (1). The normalization is such that |Fω(M = 0)|=1.

tion of the anomaly receives particular weight throughthe fact that the statistical errors are improved by a fac-tor of nearly 4, equivalent to a statistics larger by a factorof >10. Referred to Λ−2, the previous measurement dif-fered by three standard deviations (3σ) from the VMDexpectation, while our newmeasurement differs by 10σ.The error improvement to be expected from the differ-ence in sample sizes (3 000 vs. 60) would have beenstill larger (by a factor of 7), but this is only found if theη Dalitz decay is frozen in the fit [18].The branching ratio of the ω Dalitz decay BR(ω →µ+µ−π0) is found to be larger by a factor of1.79±0.26(stat.)±0.15(syst.) than that of the PDG [16],i.e. Lepton-G [6], corresponding to a new absolutevalue of (1.72±0.25(stat.)±0.14(syst.))·10−4. Taking ac-

7

) [GeV]-e+M(e0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Num

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f Eve

nts

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210

3100!-e+e"#

World  data   CLAS  g12  Data  

Summary  We  expect  to  release  at  least  the  following  results:  

10

suspect it might be a glueball? First of all, one of the states is supernumerous and cannot be accommodated by the

traditional quark model. Second of all, all the processes, which are believed to be gluon-rich, like antiproton-proton

annihilations, radiative charmonium decays or central production processes have a significant production cross section

for the f0(1500). γγ collisions, in contrast, are supposed to act as an anti-glueball filter since photons do not couple

to uncharged gluons. The ALEPH collaboration has searched, in γγ collisions, for an f0(1500) decay into ππ and

found no evidence for it there [25]. This points to the importance not only to look at the decay pattern, but also

compare different production processes.

An experimental glueball candidate for the pseudoscalar glueball with JPC= 0

−+is the η(1405). Despite the fact

that the pseudoscalar glueball is predicted by lattice calculations to have a mass of 2.2 GeV/c2, the η(1405) fulfills

many criteria of a glueball. It appears clearly in gluon-rich processes, it has quantities like the stickiness and the

gluiness, which have been introduced to quantify the affinity of a meson to gluons. Also the state is supernumerous in

the presence of the η(1295) and η(1475). With this analysis proposal we would like to answer the following questions:

• is the η(1405) produced in photoproduction with a significant cross section in comparison to other mesons or

processes, which is not expected for glueballs?

• does the η(1295) exist in the photoproduction process?

• do we see evidence for both, the η(1405) and η(1475)?

If the η(1405) in the proposed analysis indeed shows glueball properties, it might be the mass degenerate partner

of the f0(1500) with a particular structure, as pointed out in an earlier paper [26].

V. SUMMARY

In conclusion from our preliminary analyses one can see that the CLAS data on photoproduction and decay of

light mesons can contribute significantly to essential topics of low energy QCD. The data already on tape at JLab in

some of these channels will take another decade to accomplish at other facilities. As we tried to underline above, we

anticipate at least the following physics results to be released within the scope of presented proposal:

1. Transition form factor of π0in the time-like region from Dalitz decay e+e−γ with unprecedented accuracy

2. Transition form factor of η in the time-like region from Dalitz decay e+e−γ with unprecedented accuracy

3. Branching ratio η� → e+e−γ for the first time

4. Measurement of Eγ distribution in radiative decay η → π+π−γ with highest statistical accuracy achieved so far

5. Measurement of Eγ distribution in radiative decay η� → π+π−γ with highest statistical accuracy achieved so

far

6. Transition form factor of ω in time-like region from Dalitz decay ω → e+e−π0with the highest statistical

accuracy up to date

7. Dalitz plot analysis of hadronic decay η → π+π−π0with statistical precision comparable to that obtained at

other facilities

8. Dalitz plot analysis of hadronic decay η� → π+π−η with almost an order of magnitude improvement in statistics

compared to the best measurement achieved at BES

9. First observation of G-parity violating decay φ → π+π−η

10. Search of heavy η’s with partial wave analysis in photoproduction reaction γ + p → pπ+π−η

Photoproduction and Decayof Light Mesons in CLAS

CLAS Analysis Proposal

M.J. Amaryan (spokesperson),1, ∗

Ya. Azimov,2M. Battaglieri,

3W.J. Briscoe,

4V. Crede,

5

R. De Vita,3C. Djalali,

6M. Dugger,

7G. Gavalian,

1L. Guo,

8, 9H. Haberzettl,

4C.E. Hyde,

1

D.G. Ireland,10

F. Klein,11

A. Kubarovsky,12, 13

V. Kubarovsky,9M.C. Kunkel,

1K. Nakayama,

14

C. Nepali (spokesperson),1E. Pasyuk,

9M.V. Polyakov,

15, 2B.G. Ritchie,

7J. Ritman,

16, 17, 18C. Salgado,

19

S. Schadmand (spokesperson),16, 17

I. Strakovsky,4D. Weygand,

9U. Wiedner,

18and A. Wirzba

16, 17, 20

1Old Dominion University, Norfolk, Virginia 235292Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188300, Russia

3INFN, Sezione di Genova, 16146 Genova, Italy4The George Washington University, Washington, DC 20052

5Florida State University, Tallahassee, Florida 323066University of South Carolina, Columbia, South Carolina 29208

7Arizona State University, Tempe, Arizona 85287-15048Florida International University, Miami, Florida 33199

9Thomas Jefferson National Accelerator Facility, Newport News, Virginia 2360610University of Glasgow, Glasgow G12 8QQ, United Kingdom

11Catholic University of America, Washington, DC 2006412Rensselaer Polytechnic Institute, Troy, New York 12180-359013Skobeltsyn Nuclear Physics Institute, 119899 Moscow, Russia

14Department of Physics and Astronomy, University of Georgia, Athens, GA 30602, USA15Institut fur Theoretische Physik II, Ruhr–Universitat Bochum, D–44780 Bochum, Germany

16Institut fur Kernphysik, Forschungszentrum, Juelich, Germany17Julich Center for Hadron Physics, Forschungszentrum Julich, 52425 Juich, Germany18Institut fur Experimentalphysik I, Ruhr Universitat Bochum, 44780 Bochum, Germany

19Norfolk State University, Norfolk, VA 23504, USA20Institute for Advanced Simulation, Forschungszentrum Julich, 52425 Julich, Germany

∗Electronic address: mamaryan@odu.edu; Contact person.

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