Neutrino Electron Scattering

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN-PPE/93-65

15 April 1993

y x

GabyRadel and Rolf Beyer

DESY, Hamburg, Germany

CERN, Geneva, Switzerland.

(to appear in Mod. Phys. Lett. A)

Abstract

This article reviews exp erimental results obtained from studies of neutrino elec-

tron scattering and shows in particular the imp ortant input from these exp eri-

ments to the improved knowledge of weak neutral currents and the con rmation

of the Standard Mo del at tree level. Sp ecial emphasis is put on recent high pre-

cision e-exp eriments, whose results on electroweak parameters allow, in combi-

nation with precise results obtained at higher Q , a test of the Standard Mo del

at the level of higher order corrections.

Neutrino Electron Scattering

Gaby Radel and Rolf Beyer

Intro duction

The rst observation of a handful of e-scattering events by the Gargamelle bubble chamber [1]in

1973 was a turning p oint in elementary particle physics. The existence of weak neutral currents was

demonstrated. A phenomenon which could not b e explained by the long-standing Fermi-typ e theory

of weak interactions but was predicted by a combined electroweak theory, formulated by Glashow,

Weinb erg, and Salam [2]: the so-called 'Standard Mo del' of electroweak interactions. Since then

several exp eriments with the aim of studying the elastic scattering of neutrinos on electrons have b een

p erformed, all of which added further supp ort to the Standard Mo del.

The rst generation of e-exp eriments, p erformed in the 1970's, were exp eriments dedicated to

the con rmation of the Standard Mo del at tree level. Integral cross sections and rst values for the

electroweak mixing angle, sin ,were obtained. These early exp eriments were either p erformed at

accelerators in or b eams or at nuclear reactors, where e scattering was observed for the rst

time. However, all these exp eriments su ered from rather p o or statistics, due to the very low cross

section of e scattering. In 1980 the numb er of observed events by all exp eriments was in the order

of 100.

The situation changed in the 1980's with the second generation of exp eriments. They were counter

exp eriments with large target mass dedicated neutrino detectors utilizing high intensity neutrino

b eams. The statistics collected were an order of magnitude higher than for the previous generation,

thus making it p ossible to measure kinematical distributions and di erential cross sections. With

the last exp eriment in this series (CHARM I I [3]) electroweak parameters were measured to such

an accuracy that testing the Standard Mo del at higher orders b ecame p ossible. In addition limits

on quantities b eyond the Standard Mo del could b e derived. At last neutrino electron scattering

nowadays is used even as an exp erimental to ol to detect solar neutrinos [4], thus testing the Standard

Solar Mo del.

From a theoretical p oint of view the pro cess of e-scattering is comparatively simple. In the rst,

theoretical, section of this article we de ne the relevant quantities to describ e e-scattering in the

theoretical frame, of the Standard Mo del at tree level. Going to higher orders we make some remarks

on radiative corrections as well as physics b eyond the Standard Mo del.

On the other hand, exp erimentally e-scattering is a very dicult task due the smallness of its

42 2

cross section ( 10 cm ) and to the presence of abundant comp eting pro cesses which cannot b e

totally eliminated on an eventbyevent basis. Therefore sophisticated exp erimental metho ds have

b een invented, whose realization we describ e in the more detailed second section. For each metho d a

selected exp eriment is describ ed in detail and its results are presented.

Finally we combine the results of all e-exp eriments and compare them to the results of other

measurements and to the predictions of the Standard Mo del.

1 Some Theoretical Remarks

Neutrino-electron scattering is a purely leptonic pro cess where a neutrino scatters o an electron by

the exchange of a virtual vector b oson ( g. 1). The Q range covered at presentby neutrino electron

6 2

scattering exp eriments reaches from 10 at nuclear reactors to 10 at accelerators but is always

small compared to the mass of the Z . 1

@ @ @ @

@ @

() ()

@ @

@R @R

@ @

(e) (e)

@ @

@ @ @ @

@ @

e e e

@ @

@R @R

@ @

(a) (b) (c)

Figure 1: Feynman diagrams for the processes of neutral current (NC) e-scattering (a), and charged

current (CC) e-scattering via the exchange of a W -Boson (b,c).

Kinematics

The kinematics of elastic neutrino electron scattering is fully describ ed by a single variable; for instance

by , the angle of the outgoing electron with resp ect to the neutrino b eam. Let E and E be

e e

the energies of the incoming neutrino and outgoing electron resp ectively, m the electron mass, and

y = E =E b e the fractional energy loss of the neutrino in the lab oratory system. With the assumption

of m E and the small angle approximation for cos one nds

e e e

E =2m (1 y ); (1)

e e

and, as 0 y 1, the exp erimentally imp ortant constraint: E < 2m :

e e

This means the outgoing electron is scattered in extremely forward direction, which is used exp eri-

mentally to subtract, on a statistical basis, background events, whichhaveamuch broader distribution

in E . On the other hand this signature makes it imp ossible to measure directly the y -distribution

of e-reactions, as reachable resolutions are just in the same order of magnitude as the kinematical

b ound.

Cross sections

The mo del indep endent e ective neutral currentinteraction Lagrangian can b e written as [5]:

L =2 2G ( )(g e e + g e e )+ h:c: (2)

F L L L L L R R R

In the limit of small Q , propagator e ects can b e neglected. L; R denote the chirality of the fermion.

The same can b e expressed in terms of the axialvector and vector couplings of the neutral vector b oson

e e

to the electron. The relation b etween the chiral couplings and g and g is given by

V A

2g = g + g and 2g = g g (3)

L V A R V A

From the e ective Lagrangian the di erential cross section | often called y -distribution | is

readily calculable:

; 2

d 2G m m y

e e

F 2 2 2

= E g + g (1 y ) g g : (4)

L R

L;R R;L

dy E

The (1 y ) -term originates from angular momentum conservation, and suppresses backward scattering

(y = 1) of (anti)neutrinos o (left-)right-handed electrons. For high neutrino energies (E m ) the

term linear in y is negligible. 2 g 1 A a ν− µe σ/Eν b

νµe 10 νee ν− ee -1 − νµe νµe ν− ee -2

ν 1 ee ×10-42 cm 2 GeV -1

-3 -3 -2 -1 0 1 0 0.2 0.4 0.6 0.8 1 2 g sin Θ

V W

Figure 2: Dependence of neutrino-electron cross section on electroweak parameters. a): contours in

the g g plane. The contours correspond to four ideal measurements with sin = 0.23. b): Cross

V A W

section as a function of sin . Note the logarithmic scale.

To obtain the cross section of -scattering, where the charged currentinteraction contributes to

the scattering amplitude, one has simply to substitute g by g +1:

L L

The Standard Mo del relates the coupling constants and the electroweak mixing angle sin and

the relative coupling strength of the neutral current (NC) with resp ect to the charged current (CC):

2 2

g = sin and g = (sin 1=2): (5)

R W L W

The resulting cross section dep endence on sin is shown in g. 2b. Obviously the neutral current

coupling constants cannot b e determined from a single measurement. Even a measurementof ( e)

and ( e) leaves a fourfold ambiguity for the coupling constants. A measurement of electron-neutrino

electron scattering cross sections only partly resolves the problem. A twofold ambiguity remains. This

problem can b e solved using measurements fo the forward-backward asymmetry in e e -collisions.

2 2

These exp eriments yield g g [6].

V A

Radiative corrections

When considered in the context of the electroweak p erturbation theory, the expression for the cross

sections (4) is only true in rst order of the coupling constant, i.e. in Born approximation (tree level).

Exp eriments have, however, achieved an accuracy that makes it necessary to consider also contributions

of higher order in the p erturbation series (radiative corrections). Including corrections prop ortional

to G in the matrix elements, the di erential cross section of neutrino-electron scattering (one-lo op

cross section) can b e written as [7]:

ew QE D

d d d

e e

= + : (6)

d y d y d y

The second term corresp onds to pure QED corrections, while the rst term is obtained from the

tree-level result by replacing:

2 2

2 e 2

G ! G (Q ) and sin ! (Q )sin :

F F e W W 3

e 2 2

(Q ) and (Q ) are correction functions which dep end on the unknown parameters of the Standard

Mo del, like the mass of the top quark m , and on the renormalization scheme applied. Neutrino-

electron scattering exp eriments extract results on sin from the tree-level formula, yielding so-called

e ectivevalues (sin ). To p erform comparisons with results of other exp eriments one has to correct

b oth results according to the same renormalizationscheme. Therefore the choice of the renormalization

MS scheme [8], scheme, and thus the de nition of sin b ecomes imp ortant. One p ossibility is the

2 2

2 2 2 2

where sin is de ned as the ratio of the coupling constants sin = e (Q )=g (Q ).

W W

A consequence of the QED term in (6) is that the y -distribution is changed according to the

exp erimental metho d of its measurement. If the energy carried by external bremsstrahlung photons is

not distinguished form the energy of the scattered electron, such as in the case of calorimetric detectors,

the correction amounts to a few p ercent only [9]. In bubble chamb er exp eriments however, where cuts

are applied on additional vertex activity, QED e ects might result in larger corrections. It is therefore

essential that exp erimental results are corrected for all p ossible higher order electromagnetic e ects.

Beyond the Standard Mo del

Inside the Standard Mo del a magnetic moment of the neutrino is forbidden. However, its p ossible

existence has b een discussed my many authors [10, 11]. A e-scattering pro cess via a magnetic moment

would change the helicity of the neutrino and contribute a non-coherent part to the cross section [10]:

d 1 y

2 2

= : (7)

B ohr

d y y

Limits on the magnetic moment can b e derived by comparing cross section measurements of e-

scattering to measurements were no neutrinos are involved. Due to the rise of (7) for low neutrino

energies (the expression is not divergent due to a lower kinematic b ound of the electron energy), the

exp erimental limits are the b etter the lower the low-energy cut-o relative to the neutrino energy is.

The integral cross section rises only logarithmically with the neutrino energy, so that p ossible magnetic

moment e ects are to b e detected more easily at low energy neutrino sources.

A non-zero charge radius of the neutrino, on the other hand, do es not change the spin of the

neutrino and an additional term to the cross section would b e added coherently. As a matter of fact,

higher order vertex corrections, inside the Standard Mo del, do intro duce a charge radius in the order

2 34 2

of hr i O(10 cm ) [12].

An anomoulus charge radius has the e ect of mo difying the vector part of the interaction and

manifests itself in a change of the e ective sin [13]:

1 2

g ! + 2 (sin + ) with = hr i : (8)

V W anom

2 3G

Limits for the charge radius can b e obtained comparing sin obtained from neutrino scattering to

sin from other pro cesses.

Neutrino-electron scattering cross sections are sensitive to the existence of additional Z-bosons.It

is, however, not p ossible to de ne a universal mass-limitvalid for all mo dels which predict additional

Z -b osons, since the coupling and the mass dep ends on the details of the sp eci c mo del. A wayto

gauge limits on additional Z -b osons is describ ed in [14]. With the de nition, g = g g and

A A

e 0

g = g g , one can write for a coupling g :

V V

2 2

0 0

10 5 g g

2 2 2 2

m g and m = m g ; (9) m =

0 0

A V

Z Z Z Z

g 3 g 3

i.e. the e ective coupling constants are changed. 4

2 Exp erimental metho ds and results

As already p ointed out, elastic neutrino-electron scattering manifests exp erimentally as a single for-

ward scattered electron. This signature and the small cross section set the b oundary conditions for

exp erimental metho ds and devices.

Firstly,anintense neutrino b eam and a large target mass are required to overcome small event

rates. Secondly, go o d electron identi cation and reconstruction is essential. Esp ecially an angular

resolution in the same order of magnitude as the small scattering angles should b e aimed at. Thirdly,

the detector should have a large discrimination p ower against hadron and photon induced backgrounds.

In the following we brie y describ e some selected exp eriments whichhave contributed in a sp eci c

way to our knowledge of neutrino-electron scattering. A more complete description can b e found in

[15]. Emphasis is put on exp erimental metho ds whichhaveevolved with time and increasing number

of detected neutrino-electron scattering events.

Muon-neutrino electron scattering

The study of muon-neutrino elec- as only p ossible when tron scattering w 4 υ Beam υ Beam

intensivemuon-neutrino b eams could

b e provided. At high energy accelera-

3 eak tors the source of neutrinos are w 10

ys of kaons and pions pro duced deca µ

υµ y protons in an external target. The

b 2 10

GeV harge se-

mesons are fo cussed and c υµ y magnetic lenses (horns) [16] lected b 1 10 υµ

Events/

b efore entering a decay region where

υe

y mainly into muons part of them deca 0 υ

10 e

and muon-neutrinos. The surviving

υe

hadrons and muons are stopp ed in mas-

-1 υ

e shieldings. Changing the p olar-

siv 10 e

ity of the magnetic lenses leads to ei-

0 40 80 120 0 40 80 120

ther neutrino or antineutrino b eams.

E (GeV)

wever, muon-neutrino b eams are not

Ho υ

pure. Due to de ciencies in the meson

Figure 3: Neutrino energy spectra and beam composition

charge selection and due to K decays

of the CERN 450 GeV SPS wide band neutrino beam. The

contaminations of muon-antineutrinos

scales are in arbitrary units.

(5-15%) and electron-(anti)-neutrinos

( 1%) are present. The CERN SPS wide band neutrino b eam (WBB) has a mean energy of 25 GeV

( g. 3). The neutrino uxes can b e measured by either neutrino induced events for which the cross

section is precisely known, or by a measurement of the correlated muon ux in the shielding of the

neutrino b eam [17].

The Gargamelle exp eriment

The rst detection of a neutrino-electron-scattering eventwas achieved in the Gargamelle exp eri-

ment [18]. This big bubble chamber was exp osed to b oth the CERN PS neutrino b eam (hE i 2 GeV)

and the SPS WBB. The bubble chamb er allowed a go o d particle identi cation and due to a magnetic

eld a charge determination. Together with a go o d angular resolution a p owerful background reduction

was achieved.

In bubble chamb ers the main backgrounds are caused by converted -rays from interactions outside

the chamb er or from bremsstrahlung bymuons, quasi-elastic reactions of electron-neutrinos, and

neutral pion pro duction. 5

In total three (including the historical rst NC event) e- and ten e-events could b e detected.

This allowed a rst determination of the two cross sections, listed in tab. 3. Given the large errors

the result was well in agreement with the prediction of the, at that time, young combined electroweak

theory.

To increase statistics a new approachwas needed. The task was to increase the target mass while

keeping the ability to detect and reconstruct electrons.

The CHARM exp eriment

In 1977 the CHARM collab oration had assembled a

e( 100 tons) counter exp eriment, initially in-

massiv 3

tended to study semi-leptonic neutrino interactions at σ(νµe)

−−−−−−−−−−−−

w band b eam (NBB) [19]. The detector,

the CERN narro −

σ(νµe)

however, was well suited to study also neutrino-electron

2 R

scattering. Toachieve higher rates it was also exp osed

to the wide-band neutrino b eam (WBB). It consisted

of a target-calorimeter followed byamuon-sp ectrometer.

The calorimeter, built from 78 marble plates interspaced

1 Rmeasured

with scintillation and prop ortional counters, combined

calorimetry and tracking, and allowed a go o d discrim-

ination b etween electromagnetic and hadronic showers.

t background to neutrino-electron scatter- The dominan 0 0 0.2 0.4 0.6 0.8 1

0 sin2 Θ

t and di ractive -

ing in this energy domain is coheren w

pro duction, resulting in an electromagnetic shower hardly

Figure 4: Ratio of cross sections as a

distinguishable from a shower induced by an electron.

function of sin .

Quasi-elastic scattering of electron-neutrinos on nucleons

contribute to a smaller extend to the background. The

background is characterized byamuch broader distribution in the scattering angle than neutrino-

electron scattering (eqn. 1) which is made use of when subtracting the background statistically.

In two data taking p erio ds (1979-81, 83) in total 83 16 e- and (116 21) e-events were

found [20] leading to measurements of the absolute cross sections for b oth neutrino and antineutrino

electron scattering, (tab. 3). Statistical and systematical errors contribute equally to the total un-

certainty. The largest systematic error sources were the neutrino ux normalization and acceptance

corrections.

To extract the electroweak mixing angle from their data the CHARM collab oration had invented

a new metho d using the cross section ratio:

1+ + ( e)

= with =14sin (10) R =

( e) 1 +

2 2

which has a large sensitivitytosin in the region of interest (sin =1=8R, g. 4). Sytematic

W W

errors cancel largely in this ratio and no absolute knowledge of the neutrino uxes and selection

eciencies is required. In practice the sensitivityof R to sin is weakened ( g. 4) due to admixtures

of di erenttyp es of neutrinos in the b eam and exp eriment dep endent kinematical cuts. Compared to

earlier determinations of sin from single cross section measurements this technique resulted in a

largely reduced error on sin , (tab. 3).

The exp eriment E734 at BNL

The exp eriment E734 was p erformed at the Bro okhaven National Lab oratory (BNL). The neutrino

source was the fo cused wide band neutrino (antineutrino) b eam at the AGS (Alternating Gradient

Synchroton), with a mean neutrino energy of 1.3 GeV. 6

The detector design aimed at go o d particle identi cation, high angular resolution and a large total

mass (170 tons) [21]. The main part of the detector was formed by a target calorimeter followed

by a gamma catcher and a muon sp ectrometer. The calorimeter consisted of 112 planes of liquid

scintillator, and two planes of prop ortional drift tub es. The mo dule thickness of only 0.22 X provided

a precise dE =dx measurement and made it p ossible to separate b etween electrons and photons and

to reduce the -induced background. An excellent angular resolutions for electrons of ( )=

pr oj

((13 1) E =GeV mrad) could b e achieved.

Data were taken in three running p erio ds from 1981 to 1986. After background subtraction a total

of N (e) = 160 17 4 and N (e)= 9713 5 were found in the data sample [22]. To

stat sy st stat sy st

obtain results on absolute cross sections and on the cross section ratio these numb ers are corrected

for wrong-typ e neutrino contaminations using the currentworld average for sin . W

80 80

υ υ υµe υµe µe µe 60 60

40 40 Events Events

20 20

0 0.01 0.02 0.03 0 0.01 0.02 0.03

θ2 (rad 2 ) θ2 (rad 2 )

Figure 5: Experimental data and the result of the best t for the BNL E734 experiment. Data are

plotted against as ful l circles and the t results are displayed as a line. The y -independent term is

light-shaded (upper part); the (1 y ) -term is dark-shaded (lower part).

As the angular resolution of this exp erimentwas excellent a rst attempt to explore the information

contained in the di erential cross sections was made. For that the signal was decomp osed into two

y -dep endent comp onents, corresp onding to the left-handed and right-handed terms in the expression

for the di erential cross sections (eqn. 4). The contributions from the wrong helicity comp onents

and the electron-neutrinos in the b eam were neglected. The data are shown in g. 5. Values of the

electroweak couplings g and g were obtained by tting the following function to the distributions

V A

of the data:

y G m

i e

2 2

hE i (g g ) A f +(g g ) A +N b : (11) n =

V A 1 i V A 2 b i i

2 3

The index i runs over the bins. The distributions f and y corresp ond to the y -indep endent and

i i

(1 y ) -dep endent term, resp ectively,weighted by acceptance functions A , and N b is the absolute

k b i

numb er of background events.

This metho d shows a slightly b etter sensitivity to electroweak parameters and provides results

with sup erior accuracy than those from the absolute cross sections.

The CHARM I I exp eriment

In 1987 the CHARM I I exp eriment at the CERN-SPS WBB started to take data, with the aim of

increasing the numb er of observed e events by an order of magnitude compared to previous

exp eriments and thus p erforming a high precision measurement of sin . The original idea again, as

in CHARM, was to use the ratio of absolute cross sections for e- and e-scattering. Later also other

metho ds were develop ed. In particular the most precise value of sin was achieved by combining

the information of measured distributions of kinematical variables with the pure ratio metho d to a

measurement of the ratio of di erential cross sections. The last p erio d of data taking for CHARM I I

ended in August 1991.

The CHARM-I I detector [23] consisted of a ne-grained, massive target calorimeter followed by

amuon sp ectrometer. The target calorimeter was comp osed of 420 equal units with a total target

mass of 600 tons. Each unit consisted of a 5 cm (0.5 radiation length) thick glass plate followed by

a plane of streamer tub es, whichwere read out directly on the wire in a digital mo de as well as in

an analog mo de through pick up strips glued to the back of the tub es. The high granularity of active

elements and the low Z of the target material ensure a go o d angular resolution and together with the

ne sampling a reliable distinction of electromagnetic and hadronic showers. The energy resolution

E=GeV + 0:05. The angular resolution was equivalent for electrons was found to b e E=E =0:23=

to 17 mrad= E=GeV in the energy range of the analysis [24].

pro j

The ratio of the neutrino and antineutrino uxes was obtained by ve di erent metho ds, four of

whichwere measurements of event-rates of pro cesses with a known cross section ratio for neutrinos

and antineutrinos. The ratio of the muon uxes in the shielding downstream of the decay region

yielded a fth, indep endent determination. After combining the ve consistent results a precision on

the ux ratio of 2.2% was reached. The absolute normalization of the neutrino ux was obtained

from inclusive neutrino-nucleon scattering used as a monitor reaction. The total uncertaintyonthe

absolute ux measurementwas found to b e ab out 5%.

To explain the idea of the analysis we start with the cross section for e-scattering in a general

form:

2G m d

F 2 2 2

= E A g with g = g ; g = g ;g=(g +1) : (12)

i i 1 2 3 L

L R

d y

i=1

The expressions A are given in tab. 1 for the four pro cesses involved. The interference of neutral and

charged currents in electron-neutrino electron scattering is accounted for in the third term in eqn. 12.

Table 1: Terms of the di erential cross section for di erent processes.

Pro cess e ! e e ! e e ! e e ! e

e e e e

A 1 (1 y ) 0 0

2 2

A (1 y ) 1 (1 y ) 1

A 0 0 1 (1 y )

The measured event rates are given by:

3 4

X X

e e BG

dn =dy = f g + b f (13)

i i

i=1 i=1

where the di erential distributions f contain all information ab out the target density, energy sp ectra

and wrong comp onent contamination of the b eam, the cross section expressions A , and the exp eri-

mental resolutions and acceptances. All these quantities are either known by calculation or measured.

is a normalization factor related to the neutrino ux. The f stand for the di erent background

distributions that are due to semileptonic pro cesses with dominantly electromagnetic nal states. In

order of decreasing imp ortance these are: coherent or di ractive -pro duction, quasielastic scattering 8

of electron-neutrinos on nuclei and inclusive N -scattering. The b denote the relative abundance of

these pro cesses.

Figure 6: Experimental data and the result of the best t in the E projection: data are shown as

circles and the t results are displayed as a dashed line.

weak parameters are obtained from a

Electro 1

ultaneous t of mo delled di erential distribu- sim g

e A

tions f to the data collected in the - and -

b eam. Since the energy of the neutrino is un-

wn y cannot b e measured directly but instead

kno 0.5

the f are double di erential distributions in the

variables E and E . They discriminate b e-

e e e

2 −

tween signal and background in the variable E ,

e ν e − µ

0 νµ+νµ

and determine the background comp osition b e-

cause of their di erent energy (E ) distributions.

The di erent analyses describ ed in the follow- tial distributions,

ing, all based on these di eren -0.5 νµ

mainly di er in the treatment of the factors .

Making use of the absolute ux determina-

tion, i.e. xing and , allows to determine the

2 -1

two coupling constants g and g (or sin and

A W V -1 -0.5 0 0.5 1

) simultaneously. The sensitivity of this analy-

sis to g and g is illustrated in g. 7, where the

V A

Figure 7: 90% con dence level contours in the

allowed regions in the g g plane are shown,

V A

g g plane, as obtained by CHARM II. Only

V A

as obtained from the t.

statistical errors areconsidered.

Due to the electron-neutrino abundance in the

b eam the exp ected fourfold ambiguity is reduced

to a twofold one. The CHARM I I result, shown in g. 6 [3], is based on ab out 2200 e-events recorded

in eachchannel. The systematic error is dominated by uncertainties of the background determination,

of the neutrino ux measurement and the event selection eciency.

The most precise determination of sin results from a similiar t but uses only the knowledge of

the relative neutrino ux. This metho d is equivalent to the use of the ratio of cross sections, explained

ab ove, with the extension that now di erential cross sections are used. Also here the systematic error 9

is dominated by the background determination. An improved result from the full CHARM I I data

sample (87{91) is exp ected to b e published so on.

Table 2: Summary of results of the CHARM II experiment.

Measurement Metho d Result

g ;g g (e)=0:025 0:014 0:014

V A V stat: sy st:

g (e)=0:503 0:007 0:016

A stat: sy st:

(; )

d y

2 2

sin ; sin =0:237 0:007 0:007

e e e stat: sy st:

=1:006 0:014 0:033

e stat: sy st:

2 2

d d

sin ( )= () sin =0:237 0:007 0:007

e e stat: sy st:

d y d y

2 2

d n d n

sin ( ); () sin =0:212 0:027 0:006

e e stat: sy st:

d y d y

d n d n

2 2 2 2

g =g ( ); () g =g =0:60 0:19 0:09

stat: sy st:

R L R L

d y d y

The large statistics accumulated made it p ossible for the rst time to use the information of

the shap es of kinematical distributions [25] only. sin is obtained by another t in the variables

2 ;

(E ;E ), leaving b oth parameters free, hence assuming no knowledge on the neutrino ux.

e e e

dσ /dy[a.u.] dσ /dy[a.u.]

1.5 1.5

1 1

0.5 0.5 − νµ νµ

0 0 0 0.5 1 0 0.5 1

y y

Figure 8: Di erential cross sections for e-scattering (left), and e-scattering (right) in arbitrary

units. Only statistical errors are shown. The dashed line corresponds to the prediction of the Standard

Model for a value of the electroweak mixing angle of sin = 0.212.

An indep endent analysis, which is again using only shap es of kinematical distributions is the regu-

larized unfolding [26] of the y -distributions for e and e-scattering from the measured distributions

of the variables (E ;E ). The unfolded cross sections are shown in g. 8. A t of the Standard

e e

2 2

Mo del prediction for the di erential cross sections determines the ratio of coupling constants (g =g )

R L

(tab. 2) [25]. The main contribution to the systematic error is the uncertainty on the absolute energy

scale. The result con rms the existence of a coupling of right-handed electrons to the Z by three

standard deviations and by this non-maximal parity violation in neutral currentinteractions. 10

Electron-neutrino electron scattering

Compared to the muon-neutrino sector the numb er of exp erimental results in electron-neutrino electron

scattering is still rather p o or. This has two reasons, rstly, pure electron-neutrino b eams are more

dicult to pro duce than muon-neutrino b eams, and secondly - and -b eams are muchlower in

e e

energy, so that large event rates are dicult to achieve.

Electron-antineutrino electron scattering was rst observed in the Savannah River Reactor exp er-

iment [27]. The ssion reactor pro duced a high ux of . The data were analysed in two energy

regions and gave results consistent with the Standard Mo del (tab. 3).

The exp eriment E225 at LAMPF

A dedicated exp eriment to search for e-scattering was p erformed at the Los Alamos Meson Physics

Facility (LAMPF) [28]. It aimed at a measurement of the NC{CC interference term in e-scattering.

An elegantway of pro ducing a -enriched neutrino b eam was p erformed at LAMPF. Starting with

an 800 MeV proton b eam, pions are pro duced, stopp ed, and decay at rest pro ducing an isotropic ux

of mono chromatic muon-neutrinos (30 MeV). In the subsequentmuon decay a continious sp ectrum of

and ( g. 10) is pro duced. The sp ectra can easily b e calculated, however, the determination of

the absolute neutrino ux requires some dedicated calibration exp eriments.

The detector consisted of a 15 ton central active target, segmented into 40 scintillator planes

interspaced bymulti-plane ash chamb er mo dules. The scintillators were used to measure the energy

loss, while the ash chamb ers determined p osition and direction of the particles. The main background

sources are cosmic rays, neutron capture, and C reactions. e

200

υ π+ µ++ υµ υµ µ 150 + e +υe+υµ

100

υe

Events/0.02 50 Neutrino spectra

0 10 20 30 40 50 -50 0.6 0.7 0.8 0.9 1.0 Neutrino energy (MeV)

cos (θeυ)

Figure 9: Angular distribution of the measured e- Figure 10: Energy spectrum of the LAMPF

signal in E225. The solid line is the result of the best neutrino beam produced by pion and muon

t, N (e) = 295 35 events. The dashed line is the decay at rest.

background contribution due to e and e.

The e-signal was extracted from the data by a t to the distributions of the recoil energy E and

angle cos ( g. 9). After subtracting the contributions from e and e-scattering, using measured

cross sections, 236 35 e-events were found from which a total cross section measurementwas

derived [29].

The result was interpreted in terms of the NC{CC interference. The cross section for electron- 11

neutrino electron scattering can b e written as:

( e)= E [ 2 CC

e 0

2 2

+ 2(g +1=3g ) NC

L R

+ I ] NC CC

where I denotes the interference term. After subtraction of the pure NC and CC contributions

destructiveinterference was found:

I = 1:07 0:17 0:11 (14)

stat sy st

in very go o d agreement with the Standard Mo del prediction of:

2 2

I =4g =2 + 4 sin = 1:07 with sin =0:233: (15)

L W W

Pro tting from the low neutrino energy a limit on a magnetic moment of the neutrino derived from

neutrino electron scattering could b e presented [30]:

< 0:61 10 (90%C:L:) (16)

B ohr

This is, at present, the b est limit from either reactor or accelerator exp eriments. It has to comp ete

with limits derived from astrophysical arguments. Those are more stringentby ab out three orders of

magnitudes, but on the other hand relying on many more theoretical assumptions.

Discussion

In tab. 3 results from all neutrino-electron scattering exp eriments are summarized. A few comments

are necessary. All quoted cross section results are mo del-dep endent. This has the following reasons.

The rawevent rates have to b e corrected for the limited kinematical acceptance of the exp eriment

and for the admixture of events originating from other neutrino typ es. For these corrections a mo del

has to b e assumed. This is normally the Standard Mo del, however with di erentvalues for sin .

This creates no problem as long as the corrections, which can b e as large as 10{20%, are much smaller

than the exp erimental error. However, for precision measurements it is preferable to measure directly

g and g rather than the cross sections. This is almost mo del-indep endent since any admixture of V

V A

and A terms is allowed, and, even more imp ortant, all neutrino sp ecies can b e treated in the same way,

hence no correction has to b e applied. This pro cedure was applied by the CHARM I I exp eriment, but

the fact that it is not used by all exp eriments makes a combination o results dicult.

Nevertheless an attempt was made to combine all results listed in tab. 3, taking into account

p ossible correlations b etween the single results. A - t was p erformed with the neutral current

coupling constants g and g as free parameter. The result is:

V A

g (e)=0:034 0:016 and g (e)=0:504 0:014 (17)

V total A total

with a correlation co ecient of 0.05. The quality of the t is go o d ( =7:7=14).

()

The result is shown in g. 11 together with results of individual exp eriments sep erately for -

()

and -exp eriments. Obviously the precision of the combined results is dominated by the CHARM I I

result.

Using relation (3) and (5) the result can b e expressed in terms of the electroweak mixing angle

and the relative coupling strength of the neutral and charged current:

sin =0:233 0:008 and =1:007 0:028 : (18)

e total e total

The correlation factor is 0.09. 12

The high precision on electroweak parameters achieved now in neutrino-electron scattering exp er-

iments makes it interesting to compare these results to high precision results obtained in exp eriments

studying di erent pro cesses.

+ 0

At LEP, for instance, the annihilation pro cess e e ! l l via Z exchange is studied, whose

diagram is related by crossing symmetry to the one of e-scattering. However, the two measurements

2 2

refer to di erent Q scales. Di erences of the two couplings at the two scales (Q =0:01 GeV and

2 2

Q = m ) are exp ected to arise from the running of the ne structure constant and the e ect of the

neutrino charge radius. By chance these di erent contributions numerically cancel almost completely,

resulting in a di erence of g (e) g (LE P )= 0:002, while the individual contributions to radiative

V V

corrections are larger by an order of magnitude [9]. Both contributions dep end on the masses of the

top quark and of the Higgs b oson. For the calculation the masses had b een xed to m = 150 GeV

top

and m = 100 GeV . Thus it is p ossible to compare e-results directly to those obtained from a

measurement of the partial width (assuming lepton universality) at the Z resonance and the

forward-backward asymmetry A at LEP.

Fig. 12 shows this comparison. Remarkable is that results from neutrino-electron scattering have

e 2

reached comparable precision in g and the excellent agreement of measurements over a Q -range of

Table 3: Compilation of total cross section and sin measurements for al l neutrino-electron scat-

tering experiments. Limits are given at the 90% C.L.

Exp eriment ( e)=E ( e)=E sin

45 2

(10 cm MeV )

+2:1

Gargamelle (PS) [18] < 1:4 1:0 0:1

0:9

Aachen-Padova (PS) [31] 1:1 0:6 2:2 1:0 0:35 0:08

+1:2 +0:11

Gargamelle (SPS) [18] 2:4 < 2:7 0:12

0:9 0:07

+0:07

VMWOF (FNAL) [32] 1:4 0:3 0:4 0:25 0:8

0:05

+0:06

BNL-COL (AGS) [33] 1:67 0:44 0:20

0:05

15-feet BC (FNAL) [34] < 2:1 < 0:37

BEBC-TST (SPS) [35] < 3:4 < 0:45

CHARM (SPS) [20] 2:2 0:4 0:4 1:6 0:3 0:3 0:211 0:035 0:011

BNL E734 (AGS) [22] 1:8 0:2 0:25 1:17 0:16 0:13 0:195 0:018 0:013

CHARM-I I (SPS) [3] 1:53 0:04 0:12 1:39 0:04 0:10 0:237 0:007 0:007

( e)=E ( e)

e e

42 2 46 2

(10 cm GeV ) (10 cm )

Savannah River [27,36] 7:62:2 0:25 0:05

(Reactor) 1:86 0:48

Kurchatov (Reactor) [37] 6:8 4:5 0:29 0:10

LAMPF E225 (LAMPF) [29] 10:0 1:5 0:9 0:249 0:063

The result on the cross section was derived from the published result on the coupling constants.

Preliminary result.

Region in visible energy: [1:5::3:0] MeV

Region in visible energy: [3:0::4:5] MeV 13 90% C.L. 90% C.L. 1 gA g A -0.3

ν 0.5 LAMPF (E225) ee -0.4 BNL (E734)

Savannah River allν e 0 − -0.5 ν ee CHARM II

allν e -0.6 -0.5

CHARM -0.7

-1 -1 -0.5 0 0.5 1 -0.3 -0.2 -0.1 0 0.1 0.2 g V

Figure 11: Left: Comparison of results from e and escattering and the result of the t to al l e-

e e (e)

data in the g -g plane. Right: Comparison of the most recent e-scattering experiments and the t

V A

to al l data. From the solutions of the e and e data the ones with g 0:5 or g 0:5 are

V A

selectedby e and e experiments. The solution g 0:5 is excludedby e e data.

e e V

gA -0.48 ALEPH L3 DELPHI

-0.49 OPAL

12: Comparison of results

CHARM II Figure

from neutrino-electron scattering and

+ 0

-0.5 +

e e ! l l annihilation at the Z

pole in the g g plane. The

V A

osses show di erent experimental

-0.51 cr

data points [6 , 3].

-0.52

-0.08 -0.04 0 0.04

six orders of magnitude.

As was demonstrated rst by the CHARM exp eriment [20] the combination of e e and e-results

selects g = 1=2; con rming the prediction from the doublet structure of fermions in the Standard

Mo del.

The coupling constants g and g , measured in e-scattering are in fact a pro duct of the neutrino

V A

coupling to the Z and the electron coupling to the Z [38]. The same parameters measured in the

+ + e

pro cess e e ! e e are sensitive to the e Z coupling, g , only. The measurement of the invisible

width of the Z at LEP determines the coupling to a mixture of all three neutrino sp ecies. When we 14

e e

use the notation g and g for the coupling measured in e-scattering, one nds

V A

e e

g =2g g (19)

V;A V;A

where g is the Z coupling, predicted by the weak isospin structure of the Standard Mo del to b e

g = g = g =1=2: (20)

V A

If no assumption of lepton universality is made, the combination of LEP-data and the CHARM-I I

data gives:

j2g j =1:006 0:036: (21)

Hence e-data provide a unique measurement of the muon-neutrino coupling, while the LEP-result

from the invisible width yields [6, 38]:

j2g j =1:006 0:006; (22)

for the mixture of the three contributing neutrinos. The fact that b oth numb ers agree among each

other con rms lepton universality in the neutrino sector for neutral-currentinteractions. The values

also con rm the prediction based on the weak isospin structure of the Standard Mo del.

Since the mass of the Z is measured precisely at LEP [6] sin is a derived quantity in the

Standard Mo del. To compare the now rather precise results of neutrino-electron scattering with the

predictions of the Standard Mo del one has to apply higher order corrections (section 1). Using the

MS renormalization scheme [8] one can correct the combined result (18) of sin and . The net

correction for sin is negligible and for it is 0:005, with a theoretical uncertaintyof 0:002 and

0:004, resp ectively, induced by assuming a reasonable range of masses (m = [80::180] GeV and

top

m = [50::1000] GeV). Applying these corrections to the combined result (18) one obtains:

sin (e) = 0:233 0:008 0:002 (23)

exp: theor:

(e) = 1:002 0:029 0:004 : (24)

exp: theor:

This result can b e compared to the exp ectation from the Standard Mo del using as input parameters

, G , and the mass of the Z as measured at LEP [6]:

sin ( ; G ;m ) = 0:233 0:002 (25)

F Z theor:

( ; G ;m ) = 1:001 0:004 : (26)

F Z theor:

The agreement is excellent. Due to the relatively large error on the exp erimental results it is not p ossi-

ble to derive comp etetive limits on the top quark mass from this comparison alone. In a global t to all

neutral current data, however, results from neutrino-electron scattering contribute signi cantly [39].

Also limits on contributions from terms b eyond the Standard Mo del description can b e b e derived.

From a comparison of results on the neutral current coupling constants from neutrino-electron scat-

tering (17) and LEP we obtain a limit for the mass of an additional Z -b oson with the assumption of

equal coupling compared to the standard Z :

m > 462 GeV (90% C.L.) (27)

This limit is comp etitive to the b est published value, obtained in pp collisions by the CDF collab ora-

tion [40]: m > 412 GeV (95% C:L:):

A limit on the anomalous charge radius of the neutrino is obtained comparing results for the

electroweak mixing angle from neutrino-electron scattering given in (18) with LEP measurements of

pro cesses Z ! l l, where l; l are charged leptons [6]:

2 32 2

jhr i j < 0:40 10 cm (90% C.L.) (28)

anom 15

The future of dedicated neutrino-electron scattering exp eriments probing the Standard Mo del is

uncertain. A promising prop osal has b een presented at LAMPF, aiming for a 1% measurementof

sin [42]. The approval is still p ending.

As the pro cess seems to b e understo o d very well neutrino-electron scattering may b e used to

explore elds where more understanding is needed, e.g. the solar neutrino problem, or the intrinsic

prop erties of neutrinos.

Conclusion

During twentyyears since the discovery of neutral currentinteractions, neutrino-electron scattering

has contributed in a ma jor way to our understanding of the Standard Mo del. All p ossible e-reactions

have b een observed and studied and recent exp eriments have collected many thousands of e events.

Exp erimental results obtained from these exp eriments are in very go o d agreement with predictions

of the Standard Mo del and the very precise results from LEP exp eriments. The weak-isospin structure

of the Standard Mo del has b een veri ed in the neutral-current sector, lepton-universality for neutrinos

has b een demonstrated in the neutral-current sector, the ability of the Standard Mo del to describ e

precision results using higher order corrections has b een shown, and once again no deviation from the

Standard Mo del has b een found.

Acknowledgements

Many fruitful discussions with our colleagues in the CHARM I I collab oration are kindly acknowledged.

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