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arXiv:1012.1694v1 [hep-ex] 8 Dec 2010

International Journal of Modern Physics: Conference Series

c ? World Scientific Publishing Company

Measurement of B(J/ψ → ηcγ) at KEDR∗†

V.V. Anashin1V.M. Aulchenko1,2E.M. Baldin1,2A.K. Barladyan1A.Yu. Barnyakov1

M.Yu. Barnyakov1S.E. Baru1,2I.Yu. Basok1I.V. Bedny1O.L. Beloborodova1,2A.E. Blinov1

V.E. Blinov1,3A.V. Bobrov1V.S. Bobrovnikov1A.V. Bogomyagkov1,2A.E. Bondar1,2

A.R. Buzykaev1S.I. Eidelman1,2Yu.M. Glukhovchenko1V.V. Gulevich1D.V. Gusev1

S.E. Karnaev1G.V. Karpov1S.V. Karpov1T.A. Kharlamova1,2V.A. Kiselev1

S.A. Kononov1,2K.Yu. Kotov1E.A. Kravchenko1,2V.F. Kulikov1,2G.Ya. Kurkin1,3

E.A. Kuper1,2E.B. Levichev1,3D.A. Maksimov1V.M. Malyshev1;1)A.L. Maslennikov1

A.S. Medvedko1,2O.I. Meshkov1,2A.I. Milstein1S.I. Mishnev1I.I. Morozov1,2

N.Yu. Muchnoi1,2V.V. Neufeld1S.A. Nikitin1I.B. Nikolaev1,2I.N. Okunev1

A.P. Onuchin1,3S.B. Oreshkin1I.O. Orlov1,2A.A. Osipov1S.V. Peleganchuk1

S.G. Pivovarov1,3P.A. Piminov1V.V. Petrov1A.O. Poluektov1D.N. Shatilov1

G.E. Pospelov1V.G. Prisekin1A.A. Ruban1V.K. Sandyrev1G.A. Savinov1A.G. Shamov1

B.A. Shwartz1,2E.A. Simonov1S.V. Sinyatkin1Yu.I. Skovpen1,2A.N. Skrinsky1

V.V. Smaluk1,2A.V. Sokolov1A.M. Sukharev1E.V. Starostina1,2A.A. Talyshev1,2

V.A. Tayursky1V.I. Telnov1,2Yu.A. Tikhonov1,2K.Yu. Todyshev1,2G.M. Tumaikin1

Yu.V. Usov1A.I. Vorobiov1A.N. Yushkov1V.N. Zhilich1V.V.Zhulanov1,2A.N. Zhuravlev1,2

1 Budker Institute of Nuclear Physics, 11, Lavrentiev prospect, Novosibirsk, 630090, Russia

2 Novosibirsk State University, 2, Pirogova street, Novosibirsk, 630090, Russia

3 Novosibirsk State Technical University, 20, Karl Marx prospect, Novosibirsk, 630092, Russia

1) E-mail: V.M.Malyshev@inp.nsk.su

We present a study of the inclusive photon spectrum from 6.3 million J/ψ decays collected

with the KEDR detector at the VEPP-4M e+e−collider. We measure the branching

fraction of the radiative decay J/ψ → ηcγ, ηc width and mass. Taking into account an

asymmetric photon line shape we obtain: Mηc= (2978.1 ± 1.4 ± 2.0) MeV/c2, Γηc=

(43.5 ± 5.4 ± 15.8) MeV, B(J/ψ → ηcγ) = (2.59 ± 0.16 ± 0.31)%.

Keywords: charmonium; radiative decays

PACS numbers: 13.20.Gd, 13.40.Hq, 14.40.Pq

1. Introduction

J/ψ → ηcγ decay is a magnetic dipole radiative transition with photon energy ω

about 114 MeV, and a relatively large branching fraction of about 2%. This is a

transition between 1S states of charmonium and its rate can be easily calculated

in potential models. The transition does not change a spatial part of the wave

function and its matrix element in the leading approximation equals one. A simple

∗A talk presented at the CHARM2010 conference in Beijing, October 2010

†Partially supported by the Russian Foundation for Basic Research, grants 08-02-00258, 08-02-

00258, and RF Presidential Grant for Sc. Sch. NSh-5655.2008.2.

1

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2 V.V. Anashin et al.

calculation without relativistic corrections gives the result1B(J/ψ → ηcγ) = 3.05%.

It was expected that relativistic corrections are of order 20-30%, similarly to the

case of the electric dipole transitions in charmonium. Therefore, it was surprising

when in 1986 the Crystal Ball Collaboration measured this branching fraction in

the inclusive photon spectrum and obtained (1.27 ± 0.36)%2. There are a lot of

theoretical predictions for this decay rate3−8, based on QCD sum rules, lattice

QCD calculations and so on, but as a rule they give values approximately twice as

large as the Crystal Ball result.

This puzzle remained for more than twenty years. Only in 2009 the CLEO

Collaboration published9the result of a new measurement of this branching fraction

using analysis of 12 exclusive decay modes of ηc. The obtained value B(J/ψ →

ηcγ) = (1.98 ± 0.09 ± 0.30)% is closer to theory. Combining the Crystal Ball and

CLEO results, PDG10got B(J/ψ → ηcγ) = (1.7±0.4)% with a scale factor of 1.6.

In this work we report a result of the new independent measurement.

2. Photon spectrum

The photon spectrum in J/ψ → ηcγ decay can be written as1

dΓ(ω)

dω

=4

3αe2

c

m2

c

ω3|M|2BW(ω). (1)

Here M =< ηc|j0(ωr/2)|J/ψ > is the matrix element of the transition, j0(x) =

sin(x)/x, ecand mcare c-quark charge (in electron charge units) and mass while

BW(ω) is a Breit-Wigner function taking into account a nonzero ηc width. The

matrix element tends to unity when ω tends to zero and decreases slowly with the

photon energy increase.

CLEO found that the photon line shape of this transition is asymmetric, and a

Breit-Wigner function alone provides a poor fit to data. Its modification with ω3

improves the fit around the peak, but gives a diverging tail at higher photon energies.

To suppress this tail, CLEO used in their fit |M|2= exp(−ω2

explaining it by the overlap of the ground state wave functions. However, such a

form of the matrix element is valid for the wave functions of the harmonic oscillator

only. In all other potentials, |M|2dependence will be proportional to some negative

degree of ω when ω tends to infinity.

We tried to fit the CLEO data using another line shape: at photon energy ω

near the resonance the decay probability dΓ/dω is proportional to ω3BW(ω), but

at higher energies the factor ω3is replaced with ω. We found that the function

ω3ω2

0

ωω0+(ω−ω0)2BW(ω), where ω0 =

ω2

0

ωω0+(ω−ω0)2 is a smooth function near the resonance. Results of

fits with the CLEO function and our function are shown in Table 1. One can see

that results on the ηc mass, width, and decay rate are close, and the confidence

level of the fit with our function is also good. Therefore, we use the latter function

in the analysis of our data.

8β2) with β = 65 MeV,

dΓ/dω ∼

M2

J/ψ−M2

2M2

J/ψ

ηc

, is also suitable. Here the

correction factor

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Measurement of B(J/ψ → ηcγ) at KEDR3

Table 1.

NEXC

1S

Results of the fits to CLEO data using various decay probability functions.

is the number of signal photons in the fit.

dΓ/dωMηc, MeV/c2

Γηc, MeVNEXC

1S

χ2/ndf (C.L.)

∼ ω3exp(−ω2

ω3ω2

ωω0+(ω−ω0)2BW(ω)

8β2)BW(ω) 2982.4 ± 0.7 32.5 ± 1.8 6142 ± 430 38.0/38 (0.47)

∼

0

2981.8 ± 0.5 33.6 ± 1.9 6494 ± 36239.1/39 (0.47)

3. KEDR data

The experiment was performed at the KEDR detector11of the VEPP-4M

collider12.

The collider operates with a peak luminosity of about 1.5·1030cm−2s−1near the

J/ψ peak energy. Luminosity is measured with single Bremsstrahlung online and

with small-angle Bhabha scattering offline. Two methods of beam energy determi-

nation are used: resonant depolarization with accuracy of 8 ÷ 30 keV and IR-light

Compton backscattering with accuracy ∼ 100 keV13.

This analysis is based on a data sample of 1.52±0.08 pb−1collected at the J/ψ

peak. Three J/ψ scans were performed. Using a measured beam energy spread as

well as known10Γ(J/ψ → e+e−) and Γ(J/ψ → hadrons), we calculate the J/ψ

production cross section at the peak and get NJ/ψ= (6.3 ± 0.3) · 106.

Event selection was performed in two steps. At the first step, multihadron decays

of J/ψ were selected with the following cuts: total energy in the calorimeters is

greater than 0.8 GeV; at least four clusters with the energy greater than 30 MeV

in the calorimeters are detected; at least one central track in the drift chamber

is reconstructed; there are no muon tubes activated in the third layer of the muon

system. These cuts suppress background from the cosmic rays, beam-gas interactions

and Bhabha events. At the second step, photons in these events were identified.

A photon is a cluster in the liquid krypton calorimeter which is not associated

with the reconstructed tracks in the drift chamber and has no time-of-flight (ToF)

scintillation counters activated in front of it. According to the simulation, the photon

detection efficiency with the above mentioned cuts is about 28% and is almost

constant in the investigated range of the photon energies.

4. Data analysis

The inclusive photon spectrum and a fit to our data is shown in Fig. 1 . The spectrum

was fit with a sum of the signal having a shape dΓ/dω ∼

convolved with the calorimeter response function (logarithmic normal distribution14

with σE = 7.4 MeV at 110 MeV and a=-0.33), and background. The background

shape was taken in the form ln(dN/dω) = a · exp(−ω/b) + p2(ω) + c · MIP(ω),

where the first term describes ”fake” photons appearing due to nuclear interactions

of hadrons in the calorimeter and usually having energies less than 60 MeV, the

second term is the second-order polynomial describing photons arising mainly from

ω3ω2

0

ωω0+(ω−ω0)2BW(ω),

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4 V.V. Anashin et al.

, MeV

ω

50 100 150 200 250 300 350 400

Events/4 MeV

20

40

60

80

100

120

140

160

180

200

220

3

10

×

Photon spectrum

, MeV

ω

50100 150 200 250300350

Events/4 MeV

-1000

0

1000

2000

3000

Photon spectrum, background subtracted

Fig. 1.Fit of the inclusive photon spectrum.

π0decays, and MIP(ω) is the spectrum of charged particles (a charged particle can

be also misidentified as a photon). The Breit-Wigner function of the form BW(ω) ∼

s/((s − M2

J/ψ− 2ωMJ/ψ, was used in the fit.

We also tried to fit our data using other line shapes. We used BW(ω) alone,

ω3BW(ω), the CLEO function, and our function. Again, as first noted by CLEO,

we found that the BW(ω) function alone gives a shifted value of ηcmass compared

to other functions: M(ηc) = 2974.3±1.4 MeV/c2. The function ω3BW(ω) leads to

a large tail at higher photon energies, giving for the branching fraction B(J/ψ →

ηcγ) = (7.3 ± 0.5)% (here the decay probability function was integrated up to

MJ/ψ/2). The last two functions give close fit results. Since the CLEO function has

an exponential factor, the result for the branching fraction with this function can

be considered as a lower limit. The difference between the results obtained with

the two last functions is used to estimate a systematic error appearing due to the

unknown line shape.

ηc)2+ sΓ2

ηc), where s = M2

5. Systematic errors

Systematic errors of our measurements are listed in Table 2.

The uncertainty of the ηcwidth leads to an error, which we evaluated varying the

ηcwidth in the fit by 2.2 MeV (the current PDG error). A systematic error related

to the background subtraction was estimated by using in the fit a polynomial of the

third order instead of the second-order one, varying ranges of the fit, and applying or

not the ToF veto in photon selection. The error in the number of J/ψ produced was

evaluated using the known uncertainty of the luminosity measurement. Since the

cluster multiplicity is different in the simulation and experimental photon spectrum

in J/ψ decays, the error due to the photon detection efficiency was estimated by

changing by 25% weights of events with small (n < 4) and large (n > 3) track

multiplicities, and taking different MC generators for the ηcdecays. The calibration

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Measurement of B(J/ψ → ηcγ) at KEDR5

Table 2.Systematic errors.

Systematic errorMηc, MeV/c2

Γηc, MeV

B(J/ψ) → γηc),%

Line shape

ηc width

Background subtraction

Number of J/ψ produced

Photon efficiency

Photon energy scale

0.7

0.4

0.8

2.30.15

0.15

0.17

0.13

0.08

15.6

1.7

Total2.015.8 0.31

of the photon energy scale was performed using π0→ 2γ decays and ψ′→ γχcJ→

γJ/ψ transitions.

6. Results and conclusions

A new direct measurement of J/ψ → ηcγ decay was performed. We measured

the ηc mass, width, and branching fraction of J/ψ → ηcγ decay. The values of

the branching fraction and ηc mass are sensitive to the line shape of the photon

spectrum and it should be taken into account during analysis. Our results on the

ηcmass and width are:

Mηc= 2978.1± 1.4 ± 2.0 MeV/c2,

Γηc= 43.5 ± 5.4 ± 15.8 MeV.

Before our experiment these parameters were measured in J/ψ and B meson

decays, as well as in γγ and p¯ p collisions. Measurements of Crystal Ball, MARK3,

BES, and KEDR were performed using the radiative J/ψ decays, therefore, a mass

shift should be taken into account. Crystal Ball and KEDR made such a correction,

but MARK3 and BES did not. Therefore we believe that MARK3 and BES results

on the ηcmass should be corrected by approximately 4 MeV towards higher values.

Our result on the branching fraction of J/ψ → ηcγ decay is

B(J/ψ → ηcγ) = (2.59 ± 0.16 ± 0.31)%.

It is consistent with that of CLEO, is higher than the old Crystal Ball value and

close to theoretical predictions.

The authors are grateful to N. Brambilla and A. Vairo for useful discussions.

References

1. E.E. Eichten et al., Rev.Mod.Phys. 80, 1161 (2008).

2. J.Gaiser et al., Phys. Rev. D 34, 711 (1986).

3. M. Shifman, Z. Physik C 4, 345 (1980).

4. A.Yu Khodjamirian, Sov. J. Nucl. Phys. 39, 614 (1984).

5. V.A. Beilin, A.V. Radyushkin, Sov. J. Nucl. Phys. 45, 342 (1987).

6. N. Brambilla, Yu Jia, A. Vairo, Phys. Rev. D 73, 054005 (2006).

Page 6

6V.V. Anashin et al.

7. J.J. Dudek et al., Phys. Rev. D 73, 074507 (2006).

8. N. Brambilla et al., arXiv:1010.5827.

9. R.E. Mitchell et al., Phys. Rev. Lett. 102, 011801 (2009).

10. K. Nakamura et al., J. Phys. G 37, 075021 (2010).

11. V.V. Anashin et al., Nucl. Instr. and Meth. A 478, 420 (2002).

12. V. Anashin et al., Stockholm 1998, EPAC 98*, 400 (1998), Prepared for 6th European

Particle Accelerator Conference(EPAC 98), Stockholm, Sweden, 22-26 Jun 1998.

13. V.E. Blinov et al., Nucl. Instr. and Meth. A 598, 23 (2009).

14. V.M. Aulchenko et al., Nucl. Instr. and Meth. A 379, 475 (1996).