Update of the e+e− → π+π− cross section measured by the spherical neutral detector in the energy region 400 < √s < 1000 MeV

Abstract

The corrected cross section of the e
+
e
− → π+π− process measured in the spherical neutral detector experiment at the VEPP-2M e
+
e
− collider is presented. The update is necessary due to a flaw in the e
+
e
− → π+π− and e
+
e
− → μ+μ− Monte Carlo event generators used previously in data analysis.

Full text

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arXiv:hep-ex/0605013v1 5 May 2006
Update of the e+e−→ π+π−cross section measured by SND
detector in the energy region 400 <√s < 1000 MeV.
M.N.Achasov,∗K.I.Beloborodov, A.V.Berdyugin, A.G.Bogdanchikov,
A.V.Bozhenok, A.D.Bukin, D.A.Bukin, T.V.Dimova, V.P.Druzhinin, V.B.Golubev,
A.A.Korol, S.V.Koshuba, E.V.Pakhtusova, S.I.Serednyakov, Yu.M.Shatunov,
V.A.Sidorov, Z.K.Silagadze, A.N.Skrinsky, Yu.A.Tikhonov, and A.V.Vasiljev
Budker Institute of Nuclear Physics,
Siberian Branch of the Russian Academy of Sciences
11 Lavrentyev,Novosibirsk,630090, Russia
Novosibirsk State University,
630090, Novosibirsk, Russia
The corrected cross section of the e+e−→ π+π−process measured in the SND
experiment at the VEPP-2M e+e−collider is presented. The update is necessary due
to a flaw in the e+e−→ π+π−and e+e−→ µ+µ−Monte Carlo events generators
used previously in data analysis.
PACS numbers: 13.66Bc, 13.66Jn, 13.25Jx, 12.40Vv
The spherical neutral detector SND [1] operated from 1995 to 2000 at VEPP-2M e+e−
collider [2]. One of the recent SND results was the measurement of the e+e−→ π+π−
process cross section in the energy region√s < 1000 MeV [3]. The systematic error of
the cross section determination was estimated to be 1.3 %. Studies of the e+e−→ π+π−
reaction allow us to determine the ρ and ω meson parameters and provide information on
the G-parity violation mechanism in the ω → π+π−decay.
In the last time the comprehension of the high precision results of the muon anomalous
magnetic moment measurement [4, 5] attracted heightened attention to the e+e−→ π+π−
cross section.
The comparison of the e+e−→ π+π−process cross section with the spectral function in
the τ±→ π±π0ντdecay [6, 7, 8] is used to test the conservation of the vector current (CVC).
∗Electronic address: achasov@inp.nsk.su

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Theoretical calculations of the e+e−→ e+e−,π+π−,µ+µ−reactions cross sections play
important role in the e+e−→ π+π−process measurements. They are necessary for lumi-
nosity measurements (e+e−→ e+e−events), for the e+e−→ µ+µ−background subtraction,
for the radiative corrections and e+e−→ π+π−detection efficiency determination. The
e+e−→ π+π−,µ+µ−cross sections were calculated according to the formulae of Ref. [9, 10],
which take into account the photons radiation by the initial and final state particles and
have accuracy of about 0.2%.
Recently it was found that the e+e−→ π+π−and µ+µ−Monte Carlo events generators
used in the SND data analysis were not quite correct and understated the e+e−→ π+π−
and e+e−→ µ+µ−cross sections by about 2.5% and 1.5% respectively.
In this paper, in order to correct the error, the measured cross section σ0is multiplied
by correction factors:
σ = σ0· δπ· δµ, (1)
where δπand δµare corrections due to mistakes in the e+e−→ π+π−and e+e−→ µ+µ−
cross sections calculations respectively. The δπand δµcoefficients were determined using the
MCGPJ e+e−→ µ+µ−, π+π−events generator [11], which is based on the same approach
[9, 10]. The applied corrections have not altered the systematic error value of the e+e−→
π+π−cross section measurement, which is 1.3 % for the energy region√s ≥ 420 MeV and
3.2 % for√s < 420 MeV.
The energy dependence of the δπand δµis shown in Fig.1. The error in the e+e−→ µ+µ−
cross section calculation is significant only in the energy region√s < 500 MeV. The corrected
values of the e+e−→ π+π−cross section σππ(s), of the form factor
|Fπ(s)|2=
3s
πα2β3σππ(s), β =
?
1 − 4m2
π/s(2)
and of the bare cross section (the cross section without vacuum polarization contribution
but with the final state radiation taken into account) are listed in Table I. The cross section
decreased by two systematic errors in average. The results presented in Table I supersede
the results quoted in the original work [3] Table 1.
The comparison of the obtained cross section with CMD-2 [12] and KLOE [13] measure-
ments is shown in Figs.2,3. The CMD-2 result exceeds the SND data by 1.4±1.5% in average.
Here the error includes both systematic and statistical uncertainties. The uncorrected SND

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cross section exceeds the CMD-2 one by the same value. In the KLOE experiment at the
DAΦNE φ-factory the form factor |Fπ(s)|2was measured using “radiative return” method
with the systematic error of 0.9 % [13]. In Ref.[13] the bare form factor values are listed.
So in order to compare the KLOE result with the SND one, the form factor was appro-
priately dressed by us. The results of this comparison are shown in Fig.3. The difference
between SND and KLOE data is energy dependent. The point that jumped out is situated
in the region of the sharp rise of the cross section due to the ρ−ω interference. The KLOE
measurement is in conflict with the SND result as well as with the CMD-2 one.
The cross section was fitted as described in the original work [3]. The fit results together
with their deviation from the previous outcomes [3] (in units of measurement errors) are
listed in Table II. These values supersede the results of the previous work [3]. All parameters
except σ(ρ → π+π−), B(ρ → e+e−)×B(ρ → π+π−) and Γ(ρ → e+e−) changed by less than
0.5 error values, while σ(ρ → π+π−), B(ρ → e+e−) × B(ρ → π+π−) and Γ(ρ → e+e−) – by
less than two errors. The discussion of the parameters and conclusions made in the original
work [3] are still valid.
The comparison of the e+e−→ π+π−cross section obtained under the CVC hypothesis
from the τ-lepton spectral function from the τ−→ π−π0ντ decay [7, 8] with the isovector
part of the cross section measured by SND is shown in Fig.4, 5. In order to compare
with the τ spectral function, the radiative correction SEW= 1.0198 ± 0.0006 [7, 8, 14] was
applied. The e+e−→ π+π−cross section was undressed from the vacuum polarization, the
contribution from the ω → π+π−decay was excluded and correction for the π±and π0mass
difference was applied. As a result one can see the picture well known from Ref.[8, 15]. It is
interesting that the difference between e+e−and τ data is approximately equal to the value
of the accepted vacuum polarization contribution to the e+e−annihilation. The comparison
of τ data with dressed e+e−→ π+π−cross section is shown in Fig.6, 7.
The authors are grateful to G.V. Fedotovich, F.V. Ignatov, G.N. Shestakov, A.L.
Sibidanov for useful discussions. The work is supported in part by grants Sci.School-
905.2006.2, RFBR 04-02-16181-a, 04-02-16184-a, 05-02-16250-a, 06-02-16192-a.

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[1] M.N. Achasov et al., Nucl. Instr. and Meth. A 449, 125 (2000)
[2] A.N. Skrinsky, in Proc. of Workshop on physics and detectors for DAΦNE, Frascati, Italy,
April 4-7, 1995, p.3
[3] M.N. Achasov et al., Zh. Eksp. Teor. Fiz. B 128, 1201 (2005)
[4] H.N. Brown et al., Phys. Rev. Lett. 86, 2227 (2001)
[5] G.W. Bennet et al., Phys. Rev. Lett. 92, 161802 (2004)
[6] K. Ackerstaff et al., Eur. Phys. J. C 7, 571, (1999)
[7] S. Anderson et al., Phys. Rev. D 61, 112002, (2000)
[8] S. Shael et al., Phys. Rept. 421, 191 (2005)
[9] A.B. Arbuzov et al., JHEP 10, 001 (1997)
[10] A.B. Arbuzov et al., JHEP 10, 006 (1997)
[11] A.B. Arbuzov et al., Report of Budker INP N 2004-70, Novosibirsk (2004)
hep-ph/0504233
Computer code was got from http://cmd.inp.nsk.su/~sibid/radnsk.tar.bz2
[12] R.R. Akhmetshin et al, Phys. Lett. B527, 161, (2002);
R.R. Akhmetshin et al, Phys. Lett. B578, 285, (2004)
[13] A. Aloisio et al., Phys. Lett. B606, 12, (2005)
[14] E. Braaten, S. Narison and A. Pich, Nucl. Phys. B 373, 581 (1992)
[15] M. Davier et al., Eur. Phys. J. C 27, 497 (2003)
M. Davier et al., Eur. Phys. J. C 31, 503 (2003)

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TABLE I: The results of the e+e−→ π+π−cross section measurements. σππand |Fπ|2are the
cross section and the form factor of the e+e−→ π+π−process, σpol
cross section without vacuum polarization but with the final state radiation. Only uncorrelated
errors are shown. The correlated systematic error σsysis 1.3 % for√s ≥ 420 MeV and 3.2 % for
√s < 420 MeV.
√s (MeV)σππ(nb)
ππ is the e+e−→ π+π−undressed
|Fπ|2
σpol
ππ(nb)
970.0 76.68± 1.79
91.33± 1.96
101.52± 1.93
115.14± 1.57
147.78± 5.15
246.38± 2.80 10.30±0.12 237.93± 2.70
450.70± 4.19 17.46±0.16 433.39± 4.03
622.54± 5.54 23.19±0.21 597.24± 5.31
715.94± 6.21 26.15±0.23 685.26± 5.94
822.66± 7.05 29.46±0.25 785.42± 6.73
859.35± 7.19 30.41±0.25 815.84± 6.83
855.55±16.98 30.04±0.60 806.96±16.02
874.23± 7.42 30.45±0.26 820.44± 6.96
887.68± 8.81 30.86±0.31 835.25± 8.29
940.42±19.12 32.62±0.66 890.94±18.11
1022.45±10.99 35.40±0.38 979.52±10.53
1106.69±26.44 38.24±0.91 1073.85±25.66
1161.62±10.84 40.06±0.37 1138.88±10.63
1233.58±10.17 42.45±0.35 1220.00±10.06
1314.33± 9.78 45.05±0.34 1309.00± 9.74
1331.59± 9.87 45.28±0.34 1326.86± 9.83
1302.16± 9.67 43.92±0.33 1296.23± 9.63
1304.40± 9.80 43.47±0.33 1297.32± 9.75
1308.40±10.08 43.26±0.33 1301.28±10.03
1291.96±22.80 41.86±0.74 1288.31±22.74
1060.14± 7.11 32.31±0.22 1064.32± 7.14
3.78±0.09
4.41±0.09
4.83±0.09
5.38±0.07
6.66±0.23
75.06± 1.75
89.22± 1.91
99.07± 1.88
112.25± 1.53
143.57± 5.00
958.0
950.0
940.0
920.0
880.0
840.0
820.0
810.0
800.0
794.0
790.0
786.0
785.0
784.0
783.0
782.0
781.0
780.0
778.0
774.0
770.0
764.0
760.0
750.0
720.0

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Table I: (Continued)
√s (MeV)σππ(nb)|Fπ|2
σpol
ππ(nb)
690.0 764.53± 8.31 21.92±0.24 769.56± 8.36
543.75± 6.24 14.66±0.17 546.05± 6.27
398.61± 8.73 10.11±0.22 399.49± 8.75
296.06±10.92 7.08±0.26 296.17±10.92
261.49±14.78 6.01±0.34 261.11±14.76
230.91±12.69 5.12±0.28 230.54±12.67
221.00±17.83 4.81±0.39 220.33±17.78
215.61±13.79 4.62±0.30 214.99±13.75
202.32±23.04 4.26±0.49 201.77±22.98
179.55±10.42 3.72±0.22 179.10±10.39
175.37±16.81 3.58±0.34 174.62±16.74
176.32±10.93 3.55±0.22 175.60±10.89
165.60± 9.72 3.26±0.19 165.01± 9.69
143.61±13.28 2.81±0.26 143.14±13.24
140.47±14.24 2.71±0.28 139.82±14.17
114.75±15.51 2.22±0.30 114.26±15.44
109.25±12.54 2.11±0.24 108.83±12.49
125.06±18.92 2.46±0.37 124.70±18.87
116.37±21.78 2.39±0.45 116.17±21.74
660.0
630.0
600.0
580.0
560.0
550.0
540.0
530.0
520.0
510.0
500.0
480.0
470.0
450.0
440.0
430.0
410.0
390.0

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TABLE II: The ρ and ω mesons parameters measured in this work. In the third column the
parameters deviations from the original work results [3] in units of measurement errors are listed.
Parameters Values Deviations
mρ, MeV774.6±0.4±0.5
146.1±0.8±1.5
1193±7±16
0.5
Γρ, MeV0.2
σ(ρ → π+π−), nb
B(ρ → e+e−) × B(ρ → π+π−) (4.876 ± 0.023 ± 0.064) × 10−5
Γ(ρ → e+e−), keV
σ(ω → π+π−), nb
B(ω → e+e−) × B(ω → π+π−) (1.225 ± 0.058 ± 0.041) × 10−6
φρω, degrees
1.6
1.6
7.12 ± 0.02 ± 0.11
29.3±1.4±1.0
1.7
0.3
0.3
113.7±1.3±2.00.1
√s
--, MeV
δ
(2)
(1)
(3)
0.92
0.94
0.96
0.98
1
400 600800 1000
FIG. 1: Corrections δ = δπ·δµto the e+e−→ π+π−cross section [3], which take into account the
mistakes of the e+e−→ π+π−(1) and e+e−→ µ+µ−(2) cross sections calculations and the total
correction δ (3).

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√s
--, MeV
σexp / σfit
0.8
0.9
1
1.1
1.2
600 700800900
FIG. 2: The ratio σexp/σfitof the e+e−→ π+π−cross section measured by CMD-2 [12] to the
SND fit curve. The shaded area shows the joint systematic error.
√s
--, MeV
σexp / σfit
0.9
0.95
1
1.05
1.1
600700 800900
FIG. 3: The ratio σexp/σfitof the e+e−→ π+π−cross section measured by KLOE [13] to the SND
fit curve. The shaded area shows the joint systematic error.

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√s
--, MeV
στ / σfit
0.8
0.9
1
1.1
1.2
400600 8001000
FIG. 4: The ratio of the στ/σfitof the e+e−→ π+π−cross section calculated from the τ−→
π−π0ντdecay spectral function measured by CLEOII [7] to the isovector part of the e+e−→ π+π−
cross section corrected in this work. The shaded area shows the joint systematic error.
√s
--, MeV
στ / σfit
0.8
0.9
1
1.1
1.2
4006008001000
FIG. 5: The ratio of the στ/σfitof the e+e−→ π+π−cross section calculated from the τ−→
π−π0ντdecay spectral function measured by ALEPH [8] to the isovector part of the e+e−→ π+π−

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√s
--, MeV
στ / σfit
0.8
0.9
1
1.1
1.2
400 6008001000
FIG. 6: The ratio of the στ/σfitof the e+e−→ π+π−cross section calculated from the τ−→
π−π0ντdecay spectral function measured by CLEOII [7] to the isovector part of the e+e−→ π+π−
cross section corrected in this work when the vacuum polarization contribution is not extracted
from the SND data. The shaded area shows the joint systematic error.
√s
--, MeV
στ / σfit
0.8
0.9
1
1.1
1.2
400 600 8001000
FIG. 7: The ratio of the στ/σfitof the e+e−→ π+π−cross section calculated from the τ−→
π−π0ντdecays spectral function measured by ALEPH [8] to the isovector part of the e+e−→ π+π−