['1 SI-\,'II--R

I September 1994

Physics Letters B 335 (1994) 246-252

PHYSICS LETTERS B

Precision measurement of electroweak parameters from the scattering of muon-neutrinos on electrons

CHARM II Collaboration

P. Vilain a.l, G. Wilquet a'l , R. Beyer b, W. Flegel b, H. Grote h, T. Mouthuy b,2, H. Overas b, J. Panman b, A. Rozanov b'3 K. Winter b, G. Zacek b, V. Zacek h, F.W. Biisser c, C Foos c,

C5 "" " " L. Gerland c, T. Layda c'4, F. Niebergall c, G. R~del '-, P. St;,ihelln c, T. Voss c, D. Favart d, G. Gr6goire d, E. Knoops d,7, V. Lema~tre d, p. Gorbunov e, E. Grigoriev e, V. Khovansky e,

A. Maslennikov e, W. Lippich f, A. Nathaniel f, A. Staude f, J. Vogt f, A.G. Cocco g, A. Ereditato g, G. Fiorillog, E Marchetti-Stasi g, V. Palladino g, P. Stroling, A. Capone h,

D. De Pedis h, U. Dore h, A. Frenkel-Rambaldi h, P.E Loverre h, D. Macina h, G. Piredda h, R. Santacesaria h, E. Di Capua i, S. Ricciardi i, B. Saitta i, B. Akkus j,8, E. Arik j'8, M. Serin-ZeyrekJ, R. Sever -i, P. TolunJ, K. Hiller k, R. Nahnhauer k, H.E. Roloff k

a Inter-University Institute for High Energies (ULB-VUB), Brussels. Belgium b CERN, Geneva, Switzerland

c II. Institutfiir Experimentalphysik, Universitiit, Hamburg, Germany 6 d Universitd Catholique de Lzmvain, Iz~uvain-la-Neuve. Belgium

e Institute for Theoretical and Experimental Physics, Moscow, Russian Federation f Sektion Physik der Universitiit Mfinchen, Miinchen, Germany 6

g Universit~ and lstituto Nazionale di Fisica Nucleare (INFN), Naples, Italy h Universitd 'La Sapienza' and lstituto Nazionale di Fisica Nucleare (INFN), Rome, Italy i Universitt'l di Ferrara and lstituto Nationale di Fisica Nucleare (INFN), Ferrara, Italy

J High Energy Physics Research Centre. YEFAM, Ankara. 7krkey k DESY - lnstitut fiir Hochenergiephysik. Zeuthen, Germany

Received 26 May 1994 Editor: K. Winter

A b s t r a c t

We report final results on electroweak parameters from muon-neutrino electron scattering observed in the C H A R M II detector from 1987 till 1991. In total 2677 + 82 and 2752 ± 88 neutrino-electron scattering events have been detected in the v and ~-beam, respectively. From the ratio o f differential cross sections we obtain for the electroweak mixing angle sin 2 ®,,, = 0.2324 4- 0.0083. From the absolute neutrino-electron scattering event rate we determined the effective vector and axial-vector neutral current coupling constants to be g~," = - 0 . 0 3 5 4- 0.017 and g~" = - 0 . 5 0 3 -~ 0.017.

I National Foundation for Scientific Research, Belgium 2 Now at Centre de Physique des Particules de Marseille, Facult6

0370-2693/94/$07.00 (~) 1994 Elsevier Science B.V. All rights reserved SSDI 0 3 7 0 - 2 6 9 3 ( 9 4 ) 0 0 7 3 6 - Q

CHARM II Collaboration /Physics Letters B 335 (1994).X6-252 247

1. Introduction

The study of muon-neutrino and muon-antineutrino scattering on electrons has provided results which are crucial for the understanding of the neutral current weak interaction. The observation of one event in 1973 [ I] was a corner stone in the discovery of this new in- teraction. The first quantitative study by the CHARM Collaboration based on 200 events [ 21 led to a deter- mination of the axial vector coupling g$ of the elec- tron to the Z. A value close to -i was found lend- ing strong support to a local internal symmetry under which the leptons transform as doublets. The CHARM II experiment aimed at an increase of statistics by an order of magnitude to investigate higher order contri- butions, so-called radiative corrections. We are report- ing in this letter the final data sample collected in the years 1987 to 1991.

We determined the differential cross sections of muon-neutrino and muon-antineutrino scattering on electrons. Within the framework of the electroweak theory ‘t Hooft [ 31 has derived the expression for the cross section,

G;s drr; dv -q,r(gv~gA)2+(gv~RA)2(1-Y)21

where s = 2m,E,, y = Ee/Ey = (1 - cosO*)/2 and @* is the c.m. scattering angle, gv and gA are the vec- tor and axial vector electron-Z couplings. The neutrino beams contain muon-neutrinos and a small contamina- tion of electron-neutrinos. For electron-neutrinos there is an additional term, (2 i- gv + gA)2. It is accounting for the interference of neutral and charged current con- tributions. About 10% of the neutrino-electron scatter- ing events were induced by electron-neutrinos. From the simultaneous measurement of dcr/dy for ype and cpe and for y,e and ij,e scattering we derived g,J and gv with a two-fold sign ambiguity. Results from ex-

de Luminy, Marseille, France s On leave of absence from ITEP, Moscow, Russian Federation 4 Now at University of California at Santa Cruz, USA 5 Now at DESY, Hamburg, Germany 6 Supported by the German Bundersministerium fur Forschung und Technologie (BMFT), under contract numbers 05-5HH22P and 05.5MU12P ’ Inter-University Institute for Nuclear Science, Belgium * Bogazici University, Istanbul, Turkey

periments on e+e-+e+e- annihilation have also a two-fold sign ambiguity. Taken together they select a single solution.

We have already published results on the shapes of the differential cross sections [4]. They are sensitive to the handedness of the electrons on which the neu- trinos scatter. While the charged current weak inter- action distinguishes left- from right-handed particles, violating parity maximally, we showed that the Z cou- ples to both left- and right-handed electrons, although with different strength as predicted by the theory. We also gave the first experimental evidence for flavour universality of neutrino couplings with the Z, a crucial input for the determination of the number of light neu- trino families from the properties of the Z pole [ 51. Limits on Z’ states and on electromagnetic properties of muon-neutrinos will be published in forthcoming papers.

The detector was conceived to study neutrino- electron scattering [ 61. It consists of a massive target calorimeter (692 t) followed by a muon spectrometer. The calorimeter has low density and is instrumented with streamer tubes equiped with digital and analog readout to measure both the energy and the direction of particles produced. This detector was exposed to the horn focused wide band neutrino beam at CERN. Neutrinos were produced by a 450 GeV proton beam accelerated in the Super Proton Synchrotron (SPS) for 2.5 . 1019 protons on target. Approximately IO8 neutrino interactions occurred in the detector. Data were collected from 1987- 199 1. Results based on par- tial samples have already been published previously [7-91.

The signature of neutrino-electron scattering is a single, forward scattered electron producing an elec- tromagnetic shower in the calorimeter. Low Z mate- rial (glass) was chosen for the target calorimeter to ensure good angular resolution for electron showers [ lo]. Candidate events with electron energies between 3 and 24 GeV were selected.

Electron and pion induced showers were discrimi- nated by their characteristic different width. The vari- able EC@:, the product of electron energy and the square of the scattering angle, is kinematically con- strained to values smaller than 1 MeV. This fact is used to separate neutrino electron scattering from the background of semileptonic events which has a broad distribution.

248 CHARM II Collaboration / Physics Letters B 335 (I 994)246-252

>

c- Q) >

UJ

3000

2500

2000

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1000

500

f ' I E

i l ' l ' l ' I v - beam

. . . . . tit

I I v e -- ) v e

vA --~ vn0A vN ~ vn0N

, ~ l YeN ~ eN

3500

3000

2500

2000

1500

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500

0 0 . 0 2 0 . 0 4 0 . 0 6 0

E0 2 ( GeV )

i I i l i I i I i I i I

~- beam

%,

. . . . . fit

I I v e - ~ v e

vA ~ v~OA vN ~ v~0N

YeN -~ eN t

I : -o,_~ 2 : ? . . ~

i: . . . . :: ~ .-

0.02 0.04 0.06

Ee 2 ( GeV )

Fig. I. Experimental data and the result of the best fit; data are shown as circles and the fit results are displayed as a dashed line. Only • . 2 the projections in EeOe of the 2-dim. distributions are shown. The different background components are added on top of each other. The

bin size varies with the experimental resolution.

2 . A n a l y s i s

We lol lowed the analysis method which was de- scribed in detail in a previous publication [9] , con- cerning event selection, neutrino llux measurement and the simultaneous fit of the modelled distributions of events as a function of the invariant Ee(-) 2 (see Fig. 1 ) and of Ee • The experimental data and the result of the tit is shown in Fig. I ; the bin size has been chosen according to the experimental resolution.

2677 + 82 events in the u beam and

2752 + 88 events in the ~ beam

are attributed to neutrino-electron scattering. We have made an experimental verification of the

model l ing of the background processes. The back- ground consists of single 7"r ° production by neutral current neutrino interaction (Tr °) and of quasi-elastic scattering of electron neutrinos on nucleons (qe) . A small background of inclusive production of electro- magnetic showers is not shown in Fig. 1 but was taken into account in the fit. A shower induced by a photon yields an even number of charged particles while elec- tron induced showers yield odd numbers. The char- acteristic difference between electron and photon in-

duced showers is best observed in an early stage of shower development [ 11 ]. The analysis of one sample was therefore restricted to those events starting in glass plates directly followed by a scintillator plane. We ensured that detected particles should have traversed the full thickness (3 cm) of a scintillation counter by requiring that the reconstructed impact point of the shower is at least 1 cm away from the edges of the counter and at least 5 cm away from its ends. The scin- tillation counters covered every fifth module of the tar- get calorimeter. Each counter was composed of twenty 15 cm wide and 3 cm thick elements. The geometrical acceptance of this selection compared to the standard fiducial volume is 14.7%. In the event selection one and only one of the counter element was allowed to be hit by a shower starting in the glass plate preceding it. The efficiency for this selection is different lbr 7"r ° production ('tr °) and quasi-elastic p~ scattering (qe) ; the values are given as Esci, in Table I. The scintil lator pulse heights were corrected for light attenuation and for the signal amplilication of the individual counter.

The most probable energy loss of a single electron traversing one scintillation counter is 5 MeV. We se- lected events associated with a single electron by re- quiring an energy loss of less than 8 MeV. The effi- ciency calculated by Monte Carlo methods for detect-

CHARM II Collaboration /Physics Letters B 335 (I 994)246-252 249

Table 1 Efficiency of scintillator event selection

Events e.sci, ,

• r ~ (82.5 ± 2.8)% qe (76.7 ± 1.6)%

Table 2 Efficiency of E < 8 MeV selection, events and background ratios

u beam ~ beam

Another use of the energy loss information in the scintillation counters was to define for each candi- date event the probabil i ty to be due to a single elec- tron. Classifying the events according to their electron probabili ty we obtained a sample enriched in neutrino- electron scattering events. The signal to background ratio of this sample is improved by a factor of about 3.5 (see Fig. 2).

aqe 0.561 + 0.022 0.582 :J: 0.027 N at~-~rr° a 0.103 + 0.009 0.102 ± 0.009

3886 4996 N data 609 855 N r;° 3430 ± 102 4276 ± 121 N qe 456 ± 87 720 ± 106 RI?~z 0.14 ± 0.03 0.18 q'- 0.03 R m 0.141 -~- 0.006 0.199 ± 0.006 hg

ing the processes is given as e8 in Table 2, separately for the neutrino and the antineutrino beam.

The background composit ion for the region 5 < EO 2 < 72 MeV can be described by two equations; one equation holds for the candidate sample,

N data = N ~0 Nqe + , ( 2 )

the other applies for selected events with less than 8 MeV energy loss in a scintillation counter element,

Ndata rr ° 1;- ° = e s N + ¢~egqe . (3)

Soh, ing these two equations for N ~'° and N qe wc ob- tained the values given in Table 2. The errors are due to the uncertainty of the efficiencies and the event statistics. The result can be expressed in the form of background ratios for the reference region. In order to obtain the background ratio in the candidate sam- ple, Rhg, one has to correct for the different selection efficiency of 1;" ° and quasi-elastic v,, events (Table i )

Nqe rr n escin ( 4 )

qt" • Rbg = N ~ ; ~Sscin

The corrected ratios for the neutrino and antineutrino beam are given in Table 2, together with the ratios ~,f,t "'bg obtained from the fit of the modelled distributions in Fig. 1. The two background ratios are in agreement and confirm the modell ing of the background distributions.

3. Results

Turning now to the determination of gA and gv we used the samples with and without energy loss infor- mation, to reduce the statistical error. Moreover, the absolute normalisation of neutrino fluxes and the pres- ence of uee and Pee events detected in the same ex- periment was used to reduce the well known four-fold ambiguity of gA and gv to two solutions.

We calculated the ratio of v,, and Pe fluxes with re- spect to the dominant vu and ~u fluxes using Monte Carlo methods and measurements of pion and kaon production [ 12 ]. The agreement of the ratio of quasi- elastic Ve scattering and single ¢r ° production deter- mined from the energy loss in a scintillation hodoscope counter and from the fit o f the modelled distributions in Fig. ! is lending support to this flux evaluation.

The 67% confidence domains ofgA and gv thus de- termined from the absolute differential cross sections o f rue , P#e and v,.e, P~e scattering are shown in Fig. 3. They are intersecting each other in two regions of gv and ga. Also shown in Fig. 3 are two cones of values determined by the experiments on the torward- backward asymmetry in e ~ e - --, e+e - annihilat ions at LEP [ 13]. These two solutions are selected out of eight possible cones by the results on e ÷ e - annihil- iations to lepton pairs off the Z pole at PETRA and PEP [ 15]. For clarity we do not display the results on the Z decay width to e + e - , l 'e, which define a ring of possible ga and gv values. Contributions to the sys- tematic errors are given in Table 3. One of the cones is intersecting one of the two solutions of neutrino elec- tron scattering from the C H A R M II experiment; this single solution is in agreement with g~ = -½ :

250 CHARM 11 Collaboration / Physics Letters B 335 (I 994)246-252

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0.02 0.04 0.06 0

E02 (GeV) 0.02 0.04 0.06

E02 (GeV)

Fig. 2. Experimental data and the result of the best fit for the sample of events with energy loss information weighted with the electron probability. The signal to background ratio is improved by a factor 3.5 with respect to the total sample shown in Fig. 1. The bin size varies with the experimental resolution.

1.0 gA

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-0.6 v e r v e

-0.8

-1.0 -1.0-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0

gv

Fig. 3. 90% confidence level contours in the gv-gA plane, as obtained from the fit to the data from the v-beam, the P-beam and to other beams. Only statistical errors are considered. Re- sults from experiments on the forward-backward asymmetry for e+e - ~ e+e - at LEP 1131 are shown as well. Together they select a single solution in agreement with ~,~ = -½ .

Table 3 Breakdown of error sources

Error source 8gv &ga Ssin 2 O

statistics 0.012 0.006 0.0058

v-beam composition 0.005 0.002 0.0026 v-flux 0.006 0.009 0.0030 ~Lbackground 0.005 0.007 0.0025 yeN-background 0.001 0.002 0.0008 incl. vN-background 0.002 0.002 0.0007 detector resolution 0.006 0.005 0.0028 fit range 0.004 0.004 0.0019 selection efficiency 0.001 0.009 0.0007

.~, systematics 0.012 0.016 0.0059

total 0.017 0.017 0.0083

g ~ = - 0 . 0 3 5 :~ 0.012(stat) + 0 .012(sys t ) ,

g~A e = --0.503 • 0 .006(stat) + 0 .016(sys t ) .

This had been demonstrated already in 1984 by com- bining results from the C H A R M experiment [ 2] , from ~,ee scattering at a nuclear reactor [ 14] and from ex- periments on e+e - ---, /x+/x - events at PETRA and PEP [ 15]. It should be remembered that g~e and ~v e

CHARM 11 Collaboration / Physics Letters B 335 (1994) 246-252 251

gA

-0.48

-0.50

-052

-008

_+___ --+

I ' ' '

O ALEPH

I-1 L3

A DELPHI

<) OPAL

• CHARM tl

L , , J i ~ l A i i J A a i

-0.04 0 0.04

gv Fig. 4. Comparison of results from neutrino-electron scattering (this experiment) and measurements of the forward-backward asymmetry and of F e for e - e - ~ e + e - annihilations at the Z ° pole 1131 in the gv-gA plane.

are the product of gA " g"a and g v "g~" 1 5]. As a con- /J/x l 'u I

vention, the sign and the value of gA = gv = + ~ is assumed.

The neutral current coupl ings g,~ and g~ derived from neutr ino electron scattering and from e"-e- --, e ' ~'- annih i la t ion studies at LEP [ 13] surpris ingly agree, within the errors, as shown in Fig. 4, despite the large difference of energy scales, Q2 ~ 0 .01GeV ~ ( for ~'~e) and Q2 ,-~ 104GeV 2 (for e ~e- ). The agreement seems to occur because of the near cancellat ion of two large higher order terms arising from "y - Z mixing and from the neutr ino charge radius. The magni tude of the first term depends on the top quark mass and the cancel la t ion is therefore indeed surpris ing [ 16].

Cons t ra in ing only the relative neutr ino to ant ineu- trino flux in the fit o f the data we determined from the ratio of p~,e and P~,e differential cross sections the value of the electrowcak mixing angle. From the com- bined samplc we obtained

sin ~ O,,e = 0.2324 :t: 0 .0058(s ta t ) ~ 0.O059(syst) .

This value is in very good agreement with the results obtaincd at LEP [ 13 I.

In conclus ion, this high precision experiment on neutr ino electron scattering has provided clear exper- imental support for local internal gauge symmetry as

the principle under ly ing the unif icat ion of the weak and electromagnetic interactions, for flavour univer- sality of neu t r ino-Z coupl ing, and for a cancel lat ion of radiative corrections involving a part icular range of values of the top quark mass.

A c k n o w l e d g e m e n t s

We gratefully acknowledge the help ot" our many technical collaborators who have contr ibuted to the realisation and the operat ion of the detector. We are grateful for the grants from the Inter-Univers i ty Institute /'or Nuclear Sciences ( B e l g i u m ) , C E R N (Geneva, Switzer land) , the Bundesmin i s t e r ium fur Forschung und Technologie ( F R G ) , the Inst i tute of Theoretical and Experimental Physics (Moscow, Russian Federat ion) , the Istituto Nazionale di Fisica Nucleare ( I ta ly) , and the Turkish Scientific and Tech- nical Research Counci l ( T U B I T A K ) ; which made the experiment possible. We should like to thank the CERN SPS operat ing crew and the neutr ino beam staff l.or their competent assistance ensur ing the ex- cellent performance of their facilities.

R e f e r e n c e s

[1 12

13 14

lSl

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[101

II11

[121 [131

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