Recent results on e+e− → Hadrons and CVC

__ __ EB

CEA

PROCEEDINGS SUPPLEMENTS Nuclear Physics B (hoc. Suppl.)

ELSEVIER

Recent Results

on e+e- -+ Hadrons

98 (2001) 281-288

www.elsevier.nVlocate/npe

and CVC

S.I. Eidelmana a Budker Institute of Nuclear Physics, Academician Lavrentyev 11, Russia

630090, Novosibirsk-90,

New results on e+e- + hadrons coming from two detectors at the e+e- collider VEPP-2M are presented. Conserved vector current (CVC) predictions for the branching ratios and mass spectra derived from e+e- data are in general consistent with the data on 7 decays although some problems with the normalization can exist. Possible applications of CVC to the calculation of the hadronic contribution to the muon anomalous magnetic moment ae discussed.

1. Introduction The hypothesis of the conserved vector current (CVC) and isospin symmetry relate to each other e+e- annihilation into isovector hadronic states and corresponding hadronic decays of the r lepton [l]. For the Cabibbo allowed vector part of the weak hadronic current the distribution over the mass of produced hadrons is given by G$wsze,SEW

dr &%=

327r2a2m3 c

x (4 - q2)2(m? + 2q2)vl(q2) where GF is the Fermi constant, & is the Cabibbo angle, SEW is a factor taking into account electroweak radiative corrections approximately equal to 1.02 [2] and vl(q2) is a spectral function:

q2g:+=,1(q2) s(d)

=

4lra2

*

The allowed quantum numbers hadronic final states are: JPG=~--+ >

7

+

2nau,,

for the relevant

WlrUT, Q7r?rzJ,,. . .

After integration the branching ratio of the decay into some hadronic state X is B(r-

+

x-u,> =

3SEwws2B,B(r-

+

e-DeuT)

2na2m* T

2

X

I

m,

dqzq2(m~

q2)2 (m:

+ 2q2) cez+=el_(q2).

4mZ,

0920-5632/01/$ - see t’ront matter 0 2001 Elsevier Science R.V PI1 SO920-5632(Ol)O1236-I

Using experimental data on e+e- + hadrons with I=1 one can confront the CVC predictions and r lepton data both for decay spectra and branching ratios. Such theoretical predictions for various decay modes of the r based on CVC have been given before by different authors, see [3] and references therein. Significant progress has been achieved in experimental studies of 7 lepton decays by CLEO as well as by four LEP detectors during last years. On the other hand, for more than five years two new detectors CMD-2 [4] and SND [5] have been studying low energy e+e- annihilation at the e+e- collider VEPP-2M at Novosibirsk. Their results make possible a new test of CVC by comparing the 7 and e+e- data at a different level of accuracy. It is also interesting to address the question whether our understanding of CVC is adequate to use the r decays in addition to e+edata improving thereby the accuracy of the calculations of aecd - the hadronic contribution to the anomalous magnetic moment of the muon as suggested by [6]. As in our previous works [7,8,3,9], to calculate the branching ratios we directly integrate the experimental cross sections avoiding as much as possible any additional theoretical input or some approximations of the data. In such an approach one hopes to get an unbiased result and deal with statistical and systematic uncertainties of separate experiments in a straightforward manner. To illustrate the recent experimental progress, we compare in Table 1 the size of event sam-

All rights reserved

S. I. Eidelmar~ / Nrrclear Phy.y.~icsB (Proc. SlippI.)

282

‘)cI (2001) 281-288

ples and systematic uncertainties for production of two and four pions in the most precise experiments of CLEO in the r [lO,ll] and of CMD-2 in the e+e- sector [12,13]. It can be seen that in contrast to the previous years, data samples in the e+e- case are larger than those for the r decay. Moreover, the resulting uncertainties for the cross sections and branching ratios dominated by systematic effects are of the same order in e+eand r sectors.

Table 1 Comparison Mode 2lr 4x

of data samples for efe- and T e+e7 Nev, 10’ Asysr% Nev, 10’ AByB,% 2000 0.6-1.5 104 1.4 57 7 24 5

Results of the calculations will be presented in terms of B(T+ X-v,). To calculate it, we’ll take the leptonic branching ratio B(r+ e-De+) = (17.83 f O.OS)% [14]. 2. Experiments

at VEPP-2M

Since 1974 VEPP-BM, the e+e- collider in the Budker Institute of Nuclear Physics in Novosibirsk [15], has been running in the energy range from the threshold of hadron production to 1400 MeV. Its luminosity reaching 3 ~10~~ cm-2s-1 at the 4 meson energy was reliably delivered to two detectors (CMD-2 and SND) which by the end of the June 2000 run collected about 30 pb-r of data each. CMD-2 shown in Fig. 1 and described in detail elsewhere [16] is a general purpose detector. Inside a superconducting solenoid with a field of 1 T there are a drift chamber, a proportional Zchamber and an endcap BGO calorimeter. Outside there is a barrel CsI calorimeter and muon streamer tube chambers. The main goal of CMD2 is to perform a high precision measurement of the exclusive cross sections of various hadronic channels and determine parameters of the low lying vector mesons.

Figure 1. CMD-2 detector: 1 - beam pipe; 2 drift chamber; 3 - Z-chamber; 4 - superconducting solenoid; 5 - compensating magnet; 6 - endcap BGO calrometer; 7 - barrel CsI(T1) calorimeter; 8 - muon range system; 9 - yoke; 10 - quadrupole lenses.

SND shown in Fig. 2 and described in detail elsewhere [17] is a nonmagnetic detector with drift chambers for tracking and a three layer electromagnetic NaI calorimeter. Outside it there are a muon chamber of streamer tubes and plastic scintillators. The main goal of SND is to study p, w and $ decays as well as the main hadronic channels. One should mention some special features of both experiments making high precision measurements feasible: large data samples due to the high integrated luminosity and large solid angle of detection multiple scans of the same energy ranges to avoid possible systematic effects; the step was 10 MeV for the continuum region and l-2 MeV near the w and I#Jpeaks good space and energy resolution in combination with the low average multiplicity lead to small background redundancy - the unstable particles are independently detected via different decay modes (w + 7r+rr-xo, ~‘7, q + 27,7r+7r-7ro, 37rs, n+n-$

S.I. Eidelmnn/Nuclrur

Physics B (Proc.

SuppI.)

9X (2001)

2x3

283-288

i

ri

L

Figure 2. SND detector: 1 - beam pipe; 2 drift chambers; 3 - scintillation counters; 4 - light guides; 5 - PMT’s; 6 - NaI(T1) crystals; 7 - vacuum phototriodes; 8 - iron absorber; 9 - streamer tubes; 10 - 1 cm iron plates; 11 - scintillation counters; 12 and 13 - elements of the collider magnetic system

l

detection efficiencies and calorimeter response are studied by using “pure” experimental data samples rather than Monte Carlo events; more than 20 million I$ me son decays can be used for that purpose.

New results are available on most of the hadronic channels. We’ll briefly mention only those which are relevant to the CVC studies. In Fig. 3 we show results for the pion form factor coming from CMD-2. This plot combines several measurements: results in the energy range 610-960 MeV are final and have a systematic uncertainty of 0.6% [18], results below 600 MeV (a systematic error of about 1%) as well as from 600 to 1400 MeV (1.5% systematics) are still preliminary [12]. In the whole energy range new results are consistent with the previous measurements and have a much better systematic error. There are new results from CMD-2 on both possible channels (2~+27r-, ?r+n-2n0) in e+eannihilation above 1 GeV [13] as well as on the

1250 2Eb, MeV

Figure

3. New data on the pion form factor

channel 2n+2nbelow 1 GeV [19]. The corresponding cross sections are shown in Fig. 4 and Fig. 5 together with the results of the previous measurements at VEPP-2M, DC1 and ADONE (for the references see [13]). It is worth noting that CMD-2 results on both channels are consistent with the previous measurements within the uncertainties and are more precise. The striking exception is the channel n+7r-2n0 in which the cross sections measured by the ND group [20] are significantly higher than those from CMD-2 as well as from other groups. In our opinion, systematic errors in this measurement were underestimated and these results should not be taken into account while integrating. CMD-2 has also performed the detailed analysis of the intermediate mechanisms in the production of four pions [13]. The conclusion was that the aF(1260)7? state dominates the 27r+2n- channel while two different states U# and aF(1260)7rF are important in the n+7r-2n0 channel. The contribution of other possible states is small.

XI.

Eidelmnn/Nucleur~

Physics

B (Proc.

Suppl.)

98 (2001)

281-288

20

10

Figure 4. Cross section of the process e+ex+n-27ro

+

New e+e- data on the channel W~FO are available below 1400 MeV from CMD-2 (in the channel w + ~+B-?TO [13] and w + nay [21]) and from SND (in the channel w + x07 [22]). Three measurements are consistent within the errors and their results are shown in Fig. 6. Finally, we show in Fig. 7 recent results from CMD-2 on the qn+n- final state obtained via the decay modes q + 27, &n-x0 [23]. 3. Comparison

to T lepton decays

We’ll now discuss how recent e+e- results are compared to those from the r decays. In the 27r channel the spectral function of CLEO [lo] (see also A.Weinstein’s talk in these Proceedings) is consistent with this from ALEPH [24] and in general well reproduces the picture observed in e+eannihilation: the ~(‘770) meson peak followed by the ~(1450) and possibly ~(1700) (for obvious reasons there is no p - w interference in the r decay). The CLEO spectral function is slightly, by (3.2 zt 1.4)%, higher than that in e+e- indicat-

Figure 5. Cross section of the process e+e2lr+2n-

+

ing some normalization problems. The deviation can probably decrease after CMD-2 completes its analysis since a new, more precise procedure of the radiative corrections tends to make the e+espectral function a bit higher in the energy range to the left of the p meson peak. We can also compare results in the w7r channel. From Fig. 6 which in addition to e+e- points shows recent results from CLEO [ll] recalculated to the e+e- case, it is clear that in the VEPP-PM energy range (below 1400 MeV) results from the T sector are compatible with ese- whereas above 1400 MeV the T spectral function is systematically higher than that from DM2 measurements

P51* The CMD-2 analysis of intermediate mechanisms in the 4n production is consistent with the conclusions of CLEO. The model used by CMD-2 to describe their results has been successfully applied [26] to describe various two pion and three pion distributions for both CLEO and ALEPH. However, there is an obvious ,problem with the normalization since the T- + 27r-n+nOv, spec-

71. Eidelnmn/Nuclear

Physics

E, GeV

Figure 6. Cross section of the process e+e-

B (Proc.

Suppl.)

98 (2001)

1400

-+

W7F

tral function is higher than that from e+e- in the whole energy range (Fig. 8), the difference reaching 20%. We summarize the comparison in Table 2 showing the expected branching ratios for various r decays which were obtained by assuming that CVC is correct and averaging recent results from VEPP-2M with those from the previous measure ments. From Table 2 it can be seen that with the exdecay mode ception of the r- + 2n-n+1r’u, CVC predictions do not contradict the world average results [14]. Although CVC predictions are slightly lower than r measurements, the difference is not statistically significant in most of the cases. Better understanding of the CVC validity can be expected after very high data sample experiments at B-factories in the 7 sector as well as the future improvement of the accuracy after two groups at VEPP-2M complete their analysis. Moreover, experiments at the upgraded VEPP-2M machine VEPP-2000 which will be able to cover the whole energy range from threshold of hadron produc-

285

281-288

1600

1800

2000

J

2400 2200 E c.m ’ *ev

Figure 7. Cross section of the process e+er]n+lr-

+

tion up to 1800-2000 MeV, will make possible a CVC test by one detector. In addition, serious theoretical input is needed to clarify how important the isospin breaking effects are. In contrast to the original analysis of such effects in [6], a recent result from [27] may indicate some more significant effects of m, # rnd (see also [28]). Another place worth theoretical efforts is the calculation of the electroweak radiative corrections. If SEW appears to be slightly higher than its currently accepted value of 1.02, most of the problems with the normalization mentioned above will disappear. 4. Application of CVC to a, It is interesting to study whether recent improvements both in r and e+e- sectors can influence the accuracy with which we know atad the hadronic contribution to the muon anomalous magnetic moment up. It is well known that the current uncertainty of the theoretical value of a, is dominated by the

286

Table 2 Branching ratio B(F

+ X-v,),

%

Hadronic State X

cvc,

7r-7rO

24.94 & 0.2:

25.31 f 0.18 0.37 f 0.29

1.02 f 0.05

1.08 f 0.10

0.06 f 0.11

17r--n+lr0 3.55 f 0.20

4.19 zt 0.23

0.64 & 0.30

WT-

1.73 f 0.06

1.92 f 0.07

0.19 f 0.09

7pr-7rO

0.13 f 0.02

0.17 f 0.02

0.04 f 0.03

Others

0.37 f 0.11

0.24 f 0.02 -0.13 f 0.11

n-37?

Total

2000

World Average

WA - CVC

30.01 f 0.33 10.99 f- 0.31 0.98 f 0.45

contribution of strong interactions. In its turn, the latter can be expressed by dispersion relations in terms of the integral of the total cross section of e+e- + hadrons with the kernel emphasizing the role of very low energies. As a result, the largest contribution to aiad comes from the energy range from threshold of hadron production to 2 GeV. Careful analysis of all available e+e- data performed in [29] gave a conservative estimate of the uncertainty of apd of 15 - lo-lo, mostly due to the insufficient accuracy with which the cross section of the process e+e- + &rr- is known. In [6] it was suggested to increase the accuracy of the apd calculation by using data on the decay modes r- + n-no+, (4n)-Y, in addition to those from e+e-. The idea is to apply CVC to convert the hadronic mass spectrum from the r decays to the cross section of e+e- and benefit from the high accuracy of the r data by averaging the calculated contribution from the I- data sample with that from e+e-. The first attempt

of this kind showed an impressive improvement of the accuracy from 15 to 9 in units of lo-lo. The improvement can be even higher so that the uncertainty becomes as low as 6.10-10 if one relies not on the data only, but additionally uses some theoretical assumptions like the validity of perturbative QCD and QCD sum rules [30]. Here, however, we confine ourselves to the calculations based on the experimental data only. Table 3 shows results of the estimate of a: based on e’e- data only (the first line uses the data sample from [29] whereas the second one additionally uses recent data from CMD-2 [12,18]), a corresponding value extracted through CVC from ALEPH [6] and CLEO [lo] and finally the average of the most recent e+e- and r lepton contributions.

It is clear that the significant improvement of

287

Table 3 Calculations of a;* fIF, lo-lo

Data

Source

e+e-

EJ, 1995 ADH, 1997

495.9 f 12.5

e+e-

This work, 2000

498.8 f 5.0

7

ALEPH, 1997

502.2 f 6.9

7

CLEO, 1999

513.1 f 5.8

e+e- + 7

ALEPH, 1997

500.8 f 6.0

e+e- + 7

CLEO, 1999

510.0 f 5.3

e+e- + r

This work, 2000

504.3 f 3.3

the accuracy is due to both higher accuracy of the e+e- data and application of the r data through cvc. 5. Conclusions l

l

l

Two detectors at Novosibirsk are studying various hadronic channels at fi < 1400 MeV with large data samples and small systematic uncertainty CVC predicts the shape of spectral functions and production mechanisms qualitatively well

world average of (30.99 & 0.31)% 3. More theoretical input is necessary to calculate radiative corrections and effects of isospin breaking Joint efforts of T and e+e- groups are needed to test CVC and improve the accuracy of aiad VEPP-2000 (the upgraded VEPP-2M collider in Novosibirsk) will cover the energy range from threshold to 1800-2000 MeV, able to test CVC in the whole energy range (2m, - m,) in one experiment

There are normalization problems: 1. r spectral functions are slightly higher than in e+e-

regularly

2. The total predicted Br(r- + X;=,z+) is (30.01 f 0.33)% compared to the

The author is grateful to the Workshop organizers MRoney, R.Sobie and B.Welsh for an opportunity to present this talk and for the excellent organization of the Workshop. Special thanks are due to A.E.Bondar, M.Davier, K.K.Gan,

28X

XI.

Eidelnmn/Nuclear

Physics

E. GeV

Figure 8. Spectral function for the decay mode r- + 27r-n+7r0

H.Kiihn, P.P.Krokovny, V.N.Ivanchenko, I.B.Logashenko, P.Lichard, L.M.Kurdadze, A.I.Milstein, LNarsky, N.I.Root, V.P.Savinov, S.I.Serednyakov, A.I.Vainshtein, A.Weinstein for numerous useful discussions. REFERENCES 1. Y.S.Tsai, Phys. Rev. D4 (1971) 2821. H.B.Thacker and J.J.Sakurai, Phys. Lett. B36 (1971) 103. 2. W.J.Marciano and A.Sirlin, Phys. Rev. Lett. 61 (1988) 1815. Nucl. 3. S.1.Eidehna.n and V.N.Ivanchenko, Phys. B (Proc. Suppl.) 55C (1997) 181. 4. R.R.Akhmetshin et al., Preprint BudkerINP 95-62, Novosibirsk, 1995. 5. M.N.Achasov et al., Preprint BudkerINP 9865, Novosibirsk, 1998. 6. R.Alemany, M.Davier and A.H&ker, Eur. Phys. J. C2 (1998) 123. 7. S.I.Eidelman and V.N.Ivanchenko, Phys. Lett. B257 (1991) 437.

B (Plac.

Suppl.)

98 (2001)

281-288

Nucl. 8. S.I.Eidelman and V.N.Ivanchenko, Phys. B (Proc. Suppl.) 40 (1995) 131. Nucl. 9. S.I.Eidelman and V.N.Ivanchenko, Phys. B (Proc. Suppl.) 76 (1999) 319. 10. SAnderson et al., Phys. Rev. D61 (2000) 112002. 11. K.W.Edwards et al., Phys. Rev. D61 (2000) 072003. 12. A.E.Bondar, Talk at the Int. Conf. on High Energy Physics, Osaka, 2000. 13. R.R.Akhmetshin et al., Phys. Lett. B466 (1999) 392. 14. D.E.Groom et ai., Eur. Phys. J. Cl5 (2000) 1. 15. V.V.Anashin et al., Preprint INP 84-114, Novosibirsk, 1984. 16. E.V.Anashkin et aI., ICFA Instrumentation Bulletin 5 (1988) 18. 17. M.N.Achasov et al., Preprint BudkerINP 9647, Novosibirsk, 1996. 18. R.R.Akhmetshin et al., Preprint BudkerINP 99-10, Novosibirsk, 1999. et al., Phys. Lett. B475 19. R.R.Akhmetshin (2000) 190. 20. S.I.Dolinsky et al., Phys. Rep. 202 (1991) 99. 21. P.P.Krokovny, Master’s Thesis, Novosibirsk State University, 2000. 22. M.N.Achasov et 23. 24. 25. 26. 27. 28. 29. 30.

et al., Phys. Lett. B489 (2000) 125. R.Barate et al., Z. Phys. C76 (1997) 15. D.Bisello et al., Preprint LAL-91-64, Orsay, 1991. A.E.Bondar et al., Phys. Lett. B466 (1999) 403. H.Czyi and J.Kiihn, hep-ph/0008262,2000. K.Maltman, Phys. Rev. D58 (1998) 014008. S.Eidelman and F.Jegerlehner, Z. Phys. C67 (1995) 585. M.Davier and A.Hocker, Phys. Lett. B435 (1998) 427.