Present status of e+e− → hadrons

Nuclear Physics B (Proc. Suppl.) 76 (1999) 319-326

ELSEVIER

PROCEEDINGS SUPPLEMENTS

P r e s e n t S t a t u s of e + e - - + H a d r o n s S.I. Eidelman and V.N. Ivanchenko ~ * Budker Institute of Nuclear Physics, 630090, Novosibirsk, Academician Lavrentyev 11, Russia and Novosibirsk State University, 630090, Novosibirsk, Pirogova 2, Russia The current status of the low energy measurements of e + e - annihilation into hadrons in Novosibirsk is described. Results of the calculations of the r-lepton branching ratios based on the hypothesis of the conserved vector current (CVC) are presented. The consistency of CVC predictions for the branching ratios derived from e+e - data with the results from r-lepton decays is discussed together with possible future improvements.

1. I N T R O D U C T I O N The aim of this talk is to describe the current status of the low energy measurements of e+e annihilation into hadrons in Novosibirsk relevant to the tests of the hypothesis of the conserved vector current (CVC). It is well known that CVC and isospin s y m m e t r y relate to each other e+e - annihilation into isovector hadronic states and corresponding hadronic decays of the r-lepton [1]. For the Cabibbo allowed vector part of the weak hadronic current the distribution over the mass of produced hadrons is given by dF dq 2

G2FCOS2OcSEw 327r2c~2rnr a

× where angle, count vl(q~)

(-¢

-

(m2T + 2q 2) vl(q

GF is the Fermi constant, 0c is the C a b i b b o S E w = l . O 1 9 4 is a factor taking into acelectroweak radiative corrections [2] and is a spectral function: ~20.I=1 (,,2~

47to 2 The allowed q u a n t u m numbers for the relevant hadronic final states are: jPG = 1-+,

7" --+ 2n~rur, w~ur,

~yr~rur,...

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

-

q2)

3cos2a~

+

2q

2

Using experimental d a t a on e+e - --+ hadrons with I=1 one can confront the CVC predictions and 7.-lepton d a t a both for decay spectra and branching ratios. Such theoretical predictions for various decay modes of the 7- based on CVC have been given before by different authors [3-17]. Since the previous 4th Workshop on 7.-lepton physics in Estes Park in 1996 significant progress has been achieved in experimental studies of 7,lepton decays by CLEO and LEP detectors. In addition, new results started coming from two detectors CMD-2 and SND collecting d a t a at the e+e - collider VEPP-2M at Novosibirsk [18, 19]. This makes a new analysis of the situation with CVC quite timely. As in our previous works [9, 15, 17], to calculate the branching ratios using CVC we prefer the direct integration of the experimental cross sections to the integration of the fits to the d a t a or their parametrizations. As argued before, this approach allows to take into account in a model independent way both statistical and systematic uncertainties of separate experiments, the latter usually neglected in the second approach. In addition to the old experimental d a t a from Novosibirsk, Orsay and Frascati used in our previous calculations [15], we'll also include recent preliminary results from V E P P - 2 M at Novosibirsk

[20, 21]. Results of the calculations will be presented both in terms of Re and B ( r - --+ X - u ¢ ) using for the latter the value B(7.- -+ e - ~ e u r ) = (17.81 -4- 0.07)% [22].

e+e-

*The work is partially supported by RFBR (Grants No 96-15-96327) and STP "Integration" (Grant No 274).

0920-5632/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII S0920-5632(99)00485-5

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S.I. Eidelman, V.N. Ivanchenko/Nuclear Physics B (Proc. Suppl.) 76 (1999) 319-326

2. E X P E R I M E N T S

AT VEPP-2M

VEPP-2M is the only world e+e - collider running today in the tow energy range from the threshold of hadron production up to 1.4 GeV in center-of-mass [23]. Since the beginning of its operation in 1974 it has been permanently upgraded and during last four seasons has been showing good stability allowing to simultaneously provide high luminosity up to 5 x 1030 cm -2 s -1 to CMD2 and SND detectors. CMD-2 described in detail elsewhere [24] is a general purpose detector consisting of a drift chamber (DC) with about 250 # space resolution transverse to the beam and proportional Zchamber used for trigger, both inside a thin (0.4 X0) superconducting solenoid with a field of 1 T. The barrel calorimeter placed outside of the solenoid consists of 892 CsI crystals of 6 x 6 x 1 5 cm 3 size (8.1 X0). Its energy resolution for photons is about 9 % in the energy range from 50 to 600 MeV. The endcap calorimeter consists of 680 BGO crystals of 2.5x2.5×15 cm 3 size (13.5 X0) and its energy resolution for photons is 6 % at 500 MeV. The muon system is composed ot two layers of streamer tubes separated by the 15 cm thick iron magnet yoke. Its spatial resolution is about 2.5 cm. The trigger signal is generated either by the trackfinder based on the DC and Z-chamber hits or by the neutral trigger taking into account the number of clusters detected in the calorimeter as well as the total energy deposition. The main goal of the experiment is to measure with high accuracy parameters of the low lying vector mesons (p, w and ¢) as well the exclusive cross sections of e+e - annihilation into hadrons. Such measurements will enable to improve the accuracy of the calculations of the hadronic vacuum polarization contribution to (g-2)u and OIQED (M 2) [25]. With this aim the whole energy range of VEPP-2M was scanned with a 10 MeV step. Special fine step energy scans were also performed in the vicinity of the w- and e-mesons. SND is a nonmagnetic detector [26] which main part is a three layer electromagnetic calorimeter, consisting of 1630 NaI(T1) crystals [27]. The granularity of the calorimeter is 9 o x 9 ° , the length is 13.5 X0. The energy resolution of the calorime-

ter for photons can be described as a ' E / E = 4 . 2 % / ' v / E ( G e V ) [28], the angular resolution is about 1.5 °. The total weight of NaI(T1) is 3.6 t, the solid angle coverage is about 90 % of 47r steradian. Charged particle tracks are measured by two cylindrical drift chambers covering 95 % of 47r. The angular accuracy of charged track measurements (~r) is about 0.40 and 2.00 in azimuth and polar directions respectively. A m o m e n t u m of a charged particle is determined using a kinematical fit. Particle identification is based on the information about the longitudinal and transverse profile of the energy deposition of a particle in the calorimeter. From outside SND is covered by the muon system consisting of streamer tubes and plastic scintillation counters. The main physical goal of SND is to study p,w, C-meson decays as well as to measure cross sections of hadron production [21]. The ambitious task of measuring the cross section with high accuracy requires first of all special attention to possible systematic effects. Table 1 demonstrates current understanding of the sources of the systematic uncertainty for the reaction e+e - --4 rr+Tr- for the CMD-2 experiment where the goal is to reach 6C%y~ of less than 1%.

Table 1 Sources of 6o'8y8 for e+e - -+ lr+TrFiducial volume and acceptance Event separation Trigger and reconstruction efficiency Correction for ~r losses Energy calibration Radiative corrections Total

at CMD-2 0.3 % 0.5-1.0 % <0.3% 0.2% <0.7% 1% 1.2-1.4 %

We hope that in future the total systematic uncertainty in this channel can reach the level of 0.7 %, most of the expected progress due to better calculation and Monte Carlo generation of radiative corrections.

S.I. Eidelman, V.N. lvanchenko /Nuclear Physics B (Proc. Suppl.) 76 (1999) 319-326

3. C V C CALCULATION BRANCHING RATIOS

OF

THE

3.1. D e c a y s i n t o 2 p i o n s For this channel we are using data obtained before by OLYA (400-1400 MeV) [29], CMD (360820 MeV) [29], DM1 (483-1096 MeV) [30] and DM2 (1400-M~) [31] as well as recent high precision data by CMD-2 (630-980 MeV) [20]. Energy dependence of the pion form factor coming from the latter experiment is shown in Fig.1 together with the points of CMD and OLYA. The agreement with the previous measurements is quite good and the systematic uncertainty of this value is 1.2 % only. The current 2rr data sample accumulated by CMD-2 contains more that two million events compared to about 100,000 events ot> served in total by (?LEO and LEP detectors.

[]

45 ~

321

energy range close to the peak of the p-meson (630-830 MeV).

Table 2 Re near the p-meson peak Group I Re CMD 10.908 4- 0.029 -4- 0.018 OLYA 10.898 4- 0.010 4- 0.045 CMD-2 0.892 4- 0.007" 4- 0.013 DM1 0.796 4- 0.029 4- 0.018

The value based on the DM1 results is much lower than those of other groups. In our opinion, their systematic uncertainty is underestimated and for filrther calculations we'll enlarge it by hand from 2.2 % to 5 %. After averaging results from different groups and correcting for the I=0 contribution to the cross section clue to the p interference, we obtain:

OLVA + CMD

R~ = 1.:377+ 0.018, CMD-2

40

95 data)

(94

and for the branching ratio 35 ~ i

(24.52

+

0.33)%

CVC,

(25.32

+

0.15)%

RPP-98.

30--

25

Note that the CVC value is 2.2 0. lower than the world average. We'll discuss this deviation later.

2O

15

10

0 ~ 600

~ 650

~

£ 700

•

L 750

~

• 800

~

I 850

,

1

•

900

• 950

Center-of-mass energy, MeV

Figure 1. New Data on Pion Form Factor

Our calculation shows that below 1000 MeV the points of DM1 are systematically lower than those of OLYA, CMD and CMD-2 which are consistent. This is illustrated by Table 2 showing the contributions of different groups to Re in the

3.2. D e c a y s i n t o 4 p i o n s There are two possible channels in c+e - annihilation (2rr+27r - , rr+~r-2rr °) as well as two decay modes of the v-lepton (rr-3~r°uT, 2rr-Tr+uT). From the isotopic symmetry the branching ratios of these decay modes are related to the following combinations of the e + e - cross sections (denoted by cq and 0.2 respectively): 0" 1

~

0.5

" 0"2rr+2r r-

0" 2

~

0.5

' 0.2~'r+2~'-

, "~-

0.~'+rr-2rr °"

In addition to the data samples used in the previous calculation, we can now use new data published by SND [21]. Figures 2 and 3 show their results (black squares) together with the old points for the reactions e+e - --+ 2rr+2rr - and e+e - --+ lr~-rr-2rr ° respectively. Only statistical

322

S.I. Eidelman, V.N. Ivanchenko ~Nuclear Physics B (Proc. Suppl.) 76 (1999) 319-326

errors are shown while the systematic uncertainty of the new SND d a t a is at the m o m e n t conservatively estimated by the authors to be 15 %.

~ 5° E 6

45

40

,/ill t

55

50

25

20

i!

'i 15

0 ,¢¢JJ ,o'o;' ',,'o;' '~2'o;' '~'oo' '14o' ~'oo '1~;0 ' '.oo ' ',~'oo e'e- -~ ~ ' . ' ~ ' ~ "

2E. MeV

Figure 2. Cross Section of the Reaction e+e - --+ 2~r+27r -

For the first reaction new SND d a t a are consistent with the previous measurements in this energy range while for the second one they are obviously much lower than the previous results from ND [32] and consistent with the OLYA measurements [33]. This result is also confirmed by the preliminary analysis of the CMD-2 data. One can assume t h a t the systematic error in the ND measurement was underestimated. The consistence of the new d a t a on the ~r+zr-2~r° channel seems to solve the old discrepancy between the measurements of ND and OLYA. Since integration of the ND d a t a gives a value which is formally within two standard deviations from those of OLYA and SND, we will use it for averaging. This results in a higher value of the branching ratio for the

Figure 3. Cross ~ection of the Reaction e+e - --+ 7r+ 7r- 27r°

2~r-Tr+~r ° m o d e and correspondingly in a bigger uncertainty due to a large scale factor. The resulting values of R~ are: R~ = ( 6.17 + 0.25) • 10 -~, zr-3~r ° , R~ = (22.80± 1.40)-10 -2, 2~r-Tr+Tr° . The branching ratio to 7r-3zr ° is (1.10

:h

0.04)%

CVC,

(1.11

:h

0.14)%

RPP-98,

while for the m o d e 27r-Tr+lr ° it is (4.06

+

0.25)%

CVC,

(4.22

+

0.10)%

RPP-98.

Finally, we can use the new d a t a from SND for the channel e+e - -~ w~r° (see Fig. 4) which in the energy range below 1.4 GeV are consistent

S.L Eidelman, V.N.Ivanchenko/Nuclear Physics B (Proc. Suppl.) 76 (1999) 319-326 with the previous m e a s u r e m e n t of ND [34], and obtain R~ = (9.93 + 0.70). 10 -2 , and for the corresponding branching ratio (1.77

4-

0.12) %

CVC,

(1.93

4-

0.06)%

RPP-98.

3.3. O t h e r d e c a y m o d e s The analysis of various channels of e+e - annihilation into h a d r o n s is in progress at b o t h C M D - 2 and SND and one can soon expect new results on m o s t of the other final states relevant to r - l e p t o n decays in addition to those discussed above: r/rr+rr - , I£[£ ( K + K -, K ~ K ° ) ,

I(h'rc

(I4.+K-~r °,

K ° K ° r r °,

I4_+K°rr~:),

67r (37r+37r - , 2rr+27r-27r °, n-+rr-4rr°).

i 20

15

i

i; ',o~oo' ','oo ' 12'o~' :~oo ' ',,'o; ' '~'oo' ',6'oU',7'oo' ,8oo e.e- -9. w ~ ©

2E. MeV

Figure 4. Cross Section of the Reaction e+e - -+ o37r 0

Recent observation by C L E O of the decay

323

m o d e r - -+ q(37r)-uT [35] provided strong evidence for a significant G = - 1 c o m p o n e n t in r - -~ (6~r)-uT decays. T h e suppression of the G = +1 c o m p o n e n t was further confirmed by their m e a s u r e m e n t of the branching ratio of the decay m o d e r - --+ ~ ' - 27r°v~ [36]. It is clear t h a t for a meaningful comparison with C V C one m u s t be sure t h a t the 6~" state observed in e+e - has really G = +1. To this end one should first subtract any r / c o m p o n e n t in the 61r final state and only after t h a t calculate the C V C prediction from the remaining part of the cross section. Unfortunately, such information is not yet available. T h e discussed p h e n o m e n o n can p r o b a b l y account for a slightly higher CVC prediction for the (67c-) m o d e c o m p a r e d to experiment obtained by us in [17]. Results of our calculations of the r - l e p t o n branching ratios are s u m m a r i z e d in Table 3 together with the current world average values from [22]. For completeness we also include there our previously obtained C V C estimates [17] for the channels in which no new d a t a appeared in e+e annihilation. One can see t h a t C V C predictions do not contradict to the experimental observations within experimental errors, but are usually lower (except for the 67r channel). T h e total predicted branching ratio of the v-lepton decay into hadronic states with I = l is (30.05 + 0.42) %, i.e. (0.96 4- 0.48) % or 2c~ lower t h a n the experimentally observed one, mostly due to the mentioned above difference in the 27r channel.

Table 3 Branching Ratios of r - --+ X - uT, % Hadronic World Average CVC Predictions State X 1998 a - - :rt"° 25.32 4- 0.15 24.52 4- 0.33 rr-3rr ° 1.11 4- 0.14 1.10 4- 0.04 2 7 r - Tr+ rr° 4.22 4- 0.10 4.06 4- 0.25 ~T/'-1.77 4- 0.12 1.93 4- 0.06 6a'0.028 4- 0.009 _> (0.125 4- 0.019) 31r-2rr+ rr° 0.014 4- 0.006 > (0.025 4- 0.004) 27r- 7r+3rr° 0.014 4- 0.006 > (0.025 4- 0.004) r / T r - 7r ° 0.130 4- 0.020 0.174 4- 0.024 K-K o 0.159 4- 0.024 0.113 4- 0.031 ¢1r< (0.012 - 0.020) < 0.03 Total 31.01 4- 0.23 30.05 4- 0.42

S.I. Eidelman, P,N, Ivanchenko/NuclearPhysics B (Proc. Suppl.) 76 (1999) 319-326

324 4. D I S C U S S I O N

Because of the different binning in the experiments on the r decay and e+e - annihilation it's not easy to directly compare the points and understand the reason of the possible problems in the 27r channel. Instead, we'll compare the area under the points by introducing the function rn 2

f(m2) = L

cr~,~(q2)dq2

and calculating (f

- f

o- I ) l f I j I .

Our calculation shows that for A L E P H d a t a [37] the area is about 5% higher than that in e+e - . A similar effect is found for C L E O d a t a [38] where in addition the observed p - - m e s o n seems to be broader than the p°-meson from e+e - experiments. Moreover, while fitting their d a t a with free normalization C L E O obtains IF~ (0)12 = 1.22 -4- 0.03. This is in obvious contrast with the claim of both groups that their d a t a are consistent with those of e+e - annihilation. How serious is the observed 2or difference between the experiment and CVC prediction? It m a y be that isospin s y m m e t r y breaking effects are underestimated (see e.g. [39]), there exist additional radiative corrections a n d / o r systematic uncertainties, or we are dealing with statistical fluctuations and results will move with time. Whatever the reason of the current difference in the 2~r channel is, it definitely deserves further analysis. If we assume that everything is OK with CVC and current discrepances are due to some unaccounted experimental uncertainties, then one should conservatively take into account the effect above by enlarging the uncertainty of any calculation based on the hypothesis of CVC validity. The magnitude of such additional uncertainty depends on the specific calculation. Consider, for example, the calculation of the hadronic contribution to (g-2)u. The impressive improvement of the accuracy was recently achieved in Ref. [40] where the authors used d a t a samples of A L E P H on the r-lepton decays into 2~" and 4~r in addition to e+e - d a t a samples. In this way they decreased the error from 15.3 if only e+e - d a t a are

used [25] to 9.4 when a combined set of e+e and r d a t a is used (errors are given in units of 10-1°). However, this calculation assumes the validity of CVC. Using the conservative approach mentioned above, one should also present an additional model uncertainty which reflects a current accuracy of this assumption. Even if it is 1% only, the additional model error of the (g-2)u is about 7x 10 -1° making the accuracy improvement marginal. Note that if we try to improve the accuracy of this calculation using only e+e d a t a and additionally include recent results from V E P P - 2 M reported in this talk, then the uncertainty of (g-2)~, will go down from 15.3×10 - l ° to approximately 12× 10 -1°. It is clear that the improvement will be much higher if we assume the absolute validity of CVC and additionally use the r d a t a samples. Let us emphasize once again the importance of complete understanding of the real accuracy with which CVC holds. W h a t accuracy of CVC predictions can be expected in future? In 1999, when two groups at V E P P - 2 M complete analysis, one can expect a systematic uncertainty of 0.7% for the rr+Tr- and 2.0% or even better for 47r channels. After that the accuracy of CVC predictions will be comparable to that of r-decay measurements and will be limited by the accuracy of the d a t a in the energy range above 1.4 GeV. None of the existing colliders (VEPP-2M and VEPP-4M in Novosibirsk, D A e N E in Frascati, B E P C in Beijing) is able to study the energy range between 1.4 GeV and My. Further improvement can be reached at a new machine where the accuracy of 2% will be achieved for all multihadronic channels in the whole energy range. A project of the new e+e collider for the energy range between ¢ and J/¢ and a luminosity of 1032 cm -2 s -1 is now under discussion in Novosibirsk. Table 4 illustrates how the accuracy of e+e - based calculations should improve by the end of 1999. If we hypothetically assume that the central value is unchanged and the accuracy of the e+e experiments is improved as planned today, then in a year from now the difference between the CVC predictions and the experimental value will reach a level of more than 3~r. In our opinion, a new joint analysis of both r and e+e - d a t a is

S.1. Eidelman, V.N. Ivanchenko /Nuclear Physics B (Proc. Suppl.) 76 (1999) 319-326

Table 4 Branching Ratios of r - --+ X - ur, % CVC Hadronic World Average State X 1998 Today 7T--~ ° 25.32 4- 0.15 24.52 4- 0.33 7r-3n° 1.11 4- 0.14 1.10 -4- 0.04 2r.- 7r+lr° 4.22 4- 0. i0 4.06 4- 0.25 Others 0.36 4- 0.04 0.37 4- 0.04 Total 31.01 4- 0.23 30.05 4- 0.42

CVC in 1999 24.52 -4- 0.18 1.10 -4- 0.03 4.06 4- 0.09 0.37 4- 0.03 30.05 4- 0.21

Special thanks are due to M.Davier, S.Dolinsky, A.Hgcker, P.Krokovny, J.H.Kiihn, L.Kurdadze, I.Logashenko, V.Shary, J.Urheim, A.Vainshtein and A.Weinstein for numerous useful discussions. REFERENCES

1

2 absolutely necessary to understand the existing problems and move filrther.

3

5. C O N C L U S I O N S

4

* Two detectors at Novosibirsk are providing a lot of new data on all hadronic channels from 2m~ up to 1.4 GeV. Data samples in e+e - annihilation are typically higher than for r decays. The expected systematic uncertainty is 0.7% for rr+rr - and 2.0% or better for other hadronic channels.

5 6 7 8

, CVC predictions for the branching ratios based on e+e - data including the preliminary results from Novosibirsk are systematically lower than observed in 7- decays (the total branching of r into hadrons with I = l is 2q higher than the CVC prediction).

10 11

* There are hints at a possible discrepancy between e+e - and r in the 2rr channel: the spectral function from ALEPH is higher (by about 5%) than that in e+e - while the p--meson width from CLEO is higher than that of the p°-meson in e+e - experiments.

14 15

* Joint efforts of v and e+e - groups are necessary to test CVC. • Further progress requires new measurements of e+e - -+ hadrons above 1.4 GeV.

9

12 13

16 17 18

19 20

The authors are grateful to the Workshop organizers and particularly to A.Pich and A.Ruiz for an opportunity to attend the Workshop and present this talk. We are indebted to the whole staff of VEPP-2M, CMD-2 and SND whose excellent performance provided a basis of this work.

325

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