Higher twist in fast π− production by antineutrinos

Nuclear l'hysicsB(Proc. Suppl.) 7B(1989) 189 199 North-llolland, Amsterdam

189

HIGHER TWIST IN FAST ~- PRODUCTION

BY ANTINEUTRINOS

Kevin VAKVELL School of Physics and Space Research, University P.O. Box 363, Birmingham, BI5 2TT, UK.

of Birmingham,

In the BEBC WA59 experiment, high z ~- production in antineutrinonucleon scattering is examined with a view to testing Berger's higher twist prediction. Evidence for a significant contribution to production of ~- with z > 0.5 is found.

I.

INTRODUCTION In 1980, Berger I published

I/Q 2 C~higher t w i s t "

a calculation

correction

for leading pion production

present

analysis

describes

production

referred

for a detailed

to clarify For

are already

a test of this prediction

published

treatment.

the main points

(anti)neutrino

section

calculated

in lepton-nucleon

of ~- by antineutrino

PN These results

an explicit

to the Quark Parton Model

section

semi-inclusive

which predicted

)

(QPM)

cross

scattering.

The

for the

scattering

from nucleons

(1)

lt+Tr-X

in reference

2, to which the reader

The following

discussion

is designed

of the analysis.

nucleon

scattering,

the pion production

by Berger from the diagrams

in Figure

z) 2

cross

i takes the form

d4a(PN ---* # + ; - X ) dxdydzdp~

,x

q(x__._J zp~ [ ( I - g ) 2 ( 1 -

4 (l~y)p~ ] + 9

d4a(uN ---+#-w+X) dx dg dz dp~

~

q(x) z) 2 4 (l~y)p~ ] z p~ [ ( 1 + 9

Q2 eure the normal Bjorken x, Bjorken y and current

four-momentum

squaured of deep inelastic

the laboratory

frame,

system carried

pion relative momentum

of the energy tremsferred

z is the fraction,

from the neutrino

by the pion, PT is the transverse

to the fragmenting

quark direction,

momentum

in

to the of the

and q(x) is the quark

distribution.

In each case, twist

scattering,

(2) (3)

Here x, y and

hadron

is

the first term in squaure brackets

(LT) contribution

higher twist

to the cross

(HT) contribution.

section,

and the second term is the

These equations,

0920 4632/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

is the QPM, or leading

applicable

at large z

K. Varvell/ Higher twist in fast 7r- productioH

190

and moderate

Q2,

are interesting

the z distributions variables

because

they break the independence

from y and Q2, predicting

which can be searched

correlations

between

of

these

for by experiment.

~÷

~-

w-

y

FIGURE

1

Diagrams used in calculating higher twist contribution to ~ N scattering.

After integrating

over p~, equations

d3a(PN ---+#+=-X) dxdydz

q(x) z [(1-Y)2(1-z)2

~

d3a(vg ---* p-=+X) dx dy dz Note that < K ~ relative neglected relative

q(x) [(l-z) z

> is not strictly

to the fragmenting

quark,

in the derivation importance

contribution,

2 and 3 may be cast in the form

2 +

(4)

4 (1 - y) - <1( 5>]

9

(5)

Q2

the same as the mean p~ of the pion since it also includes mass terms

of equations

2 and 3.

of the HT contribution

with Berger's

4 (1 - y) + 9 Q2 ]

prediction

It does measure

compared

requiring

the

to the LT

a non-zero

value for

. A natural distributions We might

way to test equations in different

regions

4 and 5 would be to plot the observed

z

of y and Q2 and look for differences.

expect the following:

i. For neutrino

scattering,

the z distribution

y (where the (i -- y) dependence 2. For antineutrino

scattering,

should be softer at high

kills the second term) the z distribution

than at low y.

should be harder at

high y (where the (I-- y)2 factor kills the QPM first term faster)

a t low y.

than

K. Varvell/ Higher twist in fast ~- production

191

3. Both effects should be enhanced as we go to lower Q2. The above was tested for neutrino nucleon scattering ~V > 2 G e V ,

i < Q2 < 80 G e V 2 by the Gargamelle

effect being observed for ~+ production softer z distribution

at low Q2 (I < Q2 < I0 GeV2).

in agreement

with equation 5.

observed at higher Q2 or in the (non-leading) fitting the y distribution

~- z distributions.

o f < ~'~ > o f 1.5 ± 0.4 G e V 2

a value

in the ~+ sample 4 or to simple phase space

The problem of proton misidentification

prediction

~- production with antineutrinos. for antineutrino

the neutrino

scattering

is avoided when

In addition,

the Berger

is now in the opposite

direction to

case, and cannot be faked by phase space effects,

remain in the same direction. ;- a preferable

These facts make antineutrino

correlation

which

production

of

reaction to study.

The WA25 D2 collaboration G studied both equations 4 and 5.

observed

By

It has been suggested that such an effect could be due to

proton misidentification

considering

No effect was

at high z (> 0.5) with a form

d a / d g ~ co.nst. + 4 / 9 ( 1 - g) < K ~ > / Q 2 ,

effects 5 .

A

was obtained at high y (y > 0.5) than at low y

(y < 0.5), qualitatively

was obtained.

in the range x > 0.15,

collaboration 3, with an

Whilst the

seen by the Gargamelle group in the neutrino to ~+ case was

(with cuts z > 0.15, 1 < Q2 < I0 GeV2),

softening of the z distribution by antineutrinos,

similar

at high y was observed for ~- production

in conflict with prediction

cut was applied the y dependence

qualitatively

vanished,

2) above.

When a ~r > 3 G e V

leading to the conclusion

that

the effect was due to trivial phase space effects.

2.

METHOD OF ANALYSIS The present analysis uses 15603 antineutrino

filled with a 75 mole percent neon-hydrogen and ~V > 3 G e V attempts

were applied,

to improve

interactions

mixture.

from BEBC

Cuts of Q2 > 1 G e V 2

reducing the sample to 8100 events.

It

on the analyses just described in the following ways:

i. Use of an antineutrino misidentification

beam avoids problems with proton

and the ambiguity of the prediction

with phase

space effects. 2. With a neon target high statistics resolution

in z due to a higher detection

secondary particles.

efficiency for neutral

The effect on resolution

loss, the major systematic chambers,

are obtained and improved

in neutrino

is treated in detail.

of neutral energy

interactions

in bubble

192

K. ~'hrvell/ Higher twist in fast ~- production

3.

It modifies the Berger predictions to include sea quark terms thus avoiding an x cut.

4. It employs a maximum likelihood fit to determine the parameters specifying the predicted HT term, avoiding problems in binning of data and retaining maximum information on correlation between variables. Let us discuss these points in more detail. the formalism,

If sea quarks are included in

equation 2 becomes

p1~ ~( l[-~z()x )2+ q ( x ) ( 1

d4a(vN--~#+u-X)dxdydzdp~

1 ! (l~_2g)[~(x) ] _ _ + q(x) (c) _y)21 + 9p~-4

with the first term again the LT contribution and the second term the lIT contribution.

(Note that the neutrino to ~+ cross section is simply

obtained by interchanging q(x) and ~(x)).

We define a variable

R(x,y,Q 2)

as follows

R(x,y, Q2) ~ 4 (1Q2y)

q(x)(1 - y)2 + ~(x)

There is nothing mysterious about R kinematic variable,

(7)

q(x) +~(x)

9

- it is simply a convenient

change of

in which is embodied the ratio of the x, y, Q2

dependent terms in the predicted HT and LT cross sections.

The

generalization of equation 4 is now

d3a(~N --~ p+~-X) dx dy dz

(1 - z) 2 z

+ × [



R ( x , y , Q 2)

Z ~(~.) + q(~)(1 - y)~ ]

] (s)

The ratio of the HT to LT cross sections for z > z0 is therefore

SliT(X, y, R, z > Zo) O'LT(X , y.~ R.~ z > Zo)

= < IC~- >

f l° 1/zdz fzio (1

-

-

z)2/zdz

R ( x , y , Q 2)

(9)

0ne can think of < K ~ > as a measure of the overall size of the effect,

and

R(x,y,Q 2) as

predicting bow the size of the effect should vary as x, y

and Q2 are varied.

For this analysis we choose z0 ----0.5.

To determine < IC~ >,

one method would be to integrate equation 8 over

x, y and a chosen range in z from z0 to I in bins of R straight line ~ ( R ) = intercept ratio. result < K ~ > =

A +

BR, < K~

> being proportional to the slope to

This approach was used by Ammosov et al. 7 to obtain a (0.18 q-0.06) G e V 2.

sample in our data for ~V > 3 G e V Table i.

and to fit a

The same method, when applied to the ~-

and ~ V > 4 C e V

gives the results in

The results are given for three different methods of correcting

events for neutral energy loss, and for no correction.

As the ~" cut is

K. Varvell / Higher twist in fast

production

~r-

t!)3

TABLE 1 from straight line fits to R distributions. Energy correction Method Heilmann Francois Myatt No

raised, effect.

SV > 3 G e V Fitted < I(~ > 0,I0 4- 0.06 0,28 4- 0.08 0.20 4- 0.06

correction

SV > 4 G e V

Fitted < /(~ > 0.12 4- 0.07 0.32 q- 0.11 0.32 i 0.i0

0.12 i 0.04

the signal persists,

0.16 ± 0.07

suggesting that it is not a trivial kinematic

Also note that the fitted value of < /£"~ >

is dependent

on the

method of correction for neutral energy loss, indicating that in each case the experimental

resolution

in the kinematic variables must be carefully

considered. za(z,R]

If-z) 2 distrlbutAon~ Fixed R ~

~ D'2>.~b"R dlstrLbut[on V////X

i . t .... p t ~k\\\\~

V////////}~ z " t .... p t

0

FIGUKE 2 The predicted cross section as a function of

R and ( l - - z ) 2. We apply the maximum likelihood method to this problem, utilize fully the correlations Motivation

for this approach

between variables

can be generated

the cross section in equation 8.

where A

is a constant.

relationship

in order to

in determining


>.

if we consider the form of

Integrated over x and y, we see that

If we look at a three dimensional plot of this

(Figure 2) we see that for fixed R,

the (i -- z)2 distribution

K. Varvell/ Higher twist in fast r- production

194

is linear with slope A and an intercept (i -- z)2

A


the R >.

distribution

Thus in fitting

is carried

in the slope,

on < I ( ~ >

is carried

distribution utilize

an R

whilst

10.

functions.

distribution,

and for fixed

A(1 - z)2 and slope

the information

for a (I -- z) 2 distribution,

in the intercept.

separately,

R,

is linear with intercept

integrated

the full information

equation

of A < I C ~ >

However,

fitting

the information either

over the other variable,

on z -- R

correlations

To proceed we construct

inherent

two independent

on < I ( ~ >

does not in

probability

density

The first,

z)l,>,o

(11)

describes

the shape of the ~- high z distribution

retaining

correlations.

some additional

the unpredicted for details). probability

f~o a(R, z) dz f~ a(R, z) dz

-

(12)

by relating the high z cross

information

low z cross section,

which we parametrize

section

density functions

~

in a log likelihood

{ln®~ + I n e R } +

z>zoJr-

(see reference

distributions

2

~

function

conditions, according A

having as input, to BergerJs

evts

for z > z0, x, y and Q2

prediction,

with a smooth

I0

N -O

v

A z

I

v

10

-I

10

-2

I

O.

I

I

O.4-

I

O.8 Z

FIGURE

z distributions

(13)

In(1 -- OR)

z
energy loss was treated using a Monte Carlo simulating

experimental

to

Using all events within our cuts we combine these

L = Neutral

of R,

The second,

OR(R) gives

as a function

3

for the fastest

~-.

the

195

K. Varvell / Higher twist in fast 7r- production

2.

1.75

~ ~

1.5 1.25

~

1.

U

F

0.75 0.5 0.25 O.

O.

0.4 0.8 1.2 INPUT < K.r'> (GeV/c) 2

FIGURE 4 Unsmearing curves for < K ~ > . Correction methods: H - Heilmann, F - Francois,

Hyatt, continuation

M -

U - No correction.

to low z which fitted our measured ¢ distributions,

in Figure 3 (solid curve).

In this and subsequent figures,

as shown

distributions

are shown for events corrected with one of the four correction methods used 8 (which is representative). found in reference neutral

2.

Distributions

The events so generated were then corrected for

energy loss in the same way as the data and < K ~

using the likelihood curve relating

function.

((true ~' ~ I ~ >

Figure 4, and graphically correction methods,

> was fitted

By varying the input < A ~ > to ((fitted ~' < K ~

was constructed for each energy correction.

3.

for all methods may be

illustrate,

>

a resolution

(following

smearing)

These curves are given in

through the differences

between

the necessity to unsmear in analyses of this type.

THE VALUE DF ~ K ~ >

In Table 2 the fitted values of < K ~

> are given for the four

correction methods along with the unsmeared values statistical). demonstrates

The consistency

of the results following unsmearing

both the reliability

taking smearing into account.

(errors are

of the unsmearing and the necessity

Taking the mean of the four results

using the spread of the values as a measure of the systematic quote a value of

< K~ >= 0.65 +0.24 (siaL) ± 0.09(syst.) -0.16

of

and

error,

we

K. %'%rvell/ Higher twist in fast 7r- prod t~ctiozl

196

Using this value, that 5 1 ± 8 ~

0.16,

the mean value of R of

of ~- with z > 0.5 are attributable

Fitted

TABLE 2 and unsmeared v a l u e s

Energy correction method Fitted +0.O6 0.23 -0.05 +0.16 0.66 -0.12 +0.16 0.45 -0.09 +0.17 0.97 -0.13 32/3

Francois Myatt No correction

x2/NDF The value of < I(~ > obtained the cutoff in z.

4.

Consistent

to higher twist effects.

>.

of < / ( ~
Heilmann

when

and equation 9, we estimate

GeV z

>

Unsmeared +0.34 0.82 -0.22 +O.22 0.69 -0.16 +0.29 0.64 -0.15 +0.11 0.46 -0.09 2.9/3

is not sensitive to the exact value of

results

(with larger errors)

were obtained

the analysis was repeated with z0 = 0.7. THE x, y, Q2 DEPENDENCE

The significant hard component

non-zero

to the ~-

value for < K ~

z distribution

> points to the presence of a

in addition to the (I -- z)2/z

leading twist dependence.

It does not test explicitly

dependence

0ne could envisage a different

of the effect.

R(I~y, Q2) giving an equally significant result. definition

of R

was generalised

the x, y, Q2 definition

To test this,

of

the

as follows

4 1 q(x)(1--yf-~+~(x)(1--y) q(x)(1 - y)2 + ~ ( x )

°

(14)

R ( x ' Y ' Q 2 ) ~ 9 Q 2b with the additional dependences analysis

parameters

(a = b = 1 is

a and b a l l o w i n g

the Berger prediction).

was repeated with the additional

correction methods,

for

different

y a n d Q2

The maximum l i k e l i h o o d

parameters

for the four

and the values of a and b compared

in each case with

those obtained by fitting to events generated by I. the LT + HT Monte Carlo with the Berger form and the fitted < I(~ > value. 2. a LT Monte Carlo with a hard z component giving the same z distribution

as the above but with no z, y or Q2 dependence.

K. Varvcll/ }figher twist in fast ~ - productioi~

The observation

from this comparison was that the fitted values of the

Q2 power ~ clearly indicated better agreement (LT + HT Monte Carlo) Carlo).

197

with a I / Q 2 dependent

than with a Q2 independent

This can be seen from Table 3.

specifying the y dependence,

form

form (LT + hard z Monte

In the case of parameter

a,

both Monte Carlos gave good agreement

with

the fitted values.

TABLE 3

Q=

Fitted values of Correction method

Data

Myatt

+0.44 1.22 -0.37 +0.12 0.52 -0.11 +0.19 0.58 - 0 . 1 4

No c o r r e c t i o n

1.02

Heilmann Francois

We therefore -

-

LT + HT Monte Carlo +0.ii 0.93 -0.i0 +0.05 0.47 -0.05 +0.05 0.54 --0.05

+0.23 -0.22

0.91

+0.04 -0.04

power b.

LT (hard z) Monte Carlo +0.09 0.12 -0.09 +0.04 0.12 -0.04 +0.03 0.08 - 0 . 0 4 0.38

Lund no gluons +0.09 0.27 -0.09 +0.07 0.25 -0.07 +0.07 0.25 - 0 . 0 7

+0.09 -0.09

0.22

Lund max.

gluons +0.19 0.35 -0.19 +0.08 0.30 -0.08 +0.09 0.36 - 0 . 0 9

+0.04 -0.04

0.22

+0.05 -0.05

conclude:

the data support

a I/Q 2 dependence

as predicted by Berger.

the data cannot resolve the y dependence.

The situation here is

similar to that observed by the EMC collaboration 9 .

5.

COMPARISON

WITH THE LUND MODEL

Since the Lund model and kinematics, effects

in leading twist QCD, can predict a Q2 evolution for fragmentation

functions,

the present data was compared with the Lund Monte Carlo,

incorporating

the specific

other Monte Carlos used. features

as well as gluon bremsstrahlung

of our data

experimental

(c.f.

Figure 3, dashed curve).

likelihood

(dotted curves).

(b) for 0.7 < z < I.

analysis

However,

to give quantitative

the parameter b measures last two columns

of the ~- fragmentation

the general

Indeed,

Curves

in Figure 5

function at high

reproduced by both the LT + HT Monte Carlo

and by the Lund Monte Carlo 0.5 < z < 0.7 and

in the same way as the

The Lund Monte Carlo reproduces

we see that the Q2 dependence is qualitatively

conditions

(solid curves)

(a) are for

using the full maximum

infozTnation,

the power of I/Q 2 present

and remembering

in the HT term,

that

the

in Table 3 indicate that the Lund Monte Carlo cannot

reproduce the Q2 dependence of the data,

either when no gluon emission is

198

K. Varvell/Higher twist in fast 7r- productiofl

I a

c~

F--_T_,X_T.,_C_~_~ (o) 10

-1

- ~~10

-2

J

t

*

~ (b)

J t~,lJ

,

J

*

,*lJl

10

10 2

Q2 (GeV 2)

Q2 dependence allowed,

6.

FIGUKE 5 of fragmentation

function.

or for maximal gluon emission.

THE p~ DEPENDENCE If we consider equation 6 we can see that the presence of the higher

twist term would predict

I/p~

while HT goes as

a hardening of the p~ distribution

i/p~).

This means that

R(z,y,Q 2) should

I. as p~ increases,

the mean value of

2. as p~ increases,

the mean value of (I - z) 2 should fall

Thus < ( l - - z ) 2 / R >

should fall as a function of p~.

plotted in Figure 6 as a function of p ~ lepton plane,

The results

would be predicted,

This quantity

(the component

are more suggestive

because of kinematical

(solid curve).

behave as predicted

is

of p~ out of the

of a rise than a fall,

and QCD effects,

- if the Berger predicted form is present,

probably too low to reasonably

does not

it is

In fact the p~ range of our data is

expect to distinguish

Similar observations

as

by the Lund

We conclude that the p~ distribution

masked in our data by other effects.

behaviour.

increase.

a better measured quantity than p~, which is more sensitive

to smearing).

Monte Carlo

(LT goes as

on the ~

I/p~

or

I/p~

dependence were obtained by the

EMC collaboration 9 .

7.

CONCLUSIONS Evidence is seen for a non-scaling,

high z ~- production

in antineutrino

non-factorising interactions.

contribution

to

When this effect is

analysed within the framework of the specific predictions

of Berger I , we

K. Varvell / tligher twist in fast ~- production

A

4.

a

3.5

>" x"

3.

[!ff)

2.5 .~

2. 1.5

v

1. 0.5

O.

I

[

I

I

0.5

O.

I

I

I.

I

I .5

2.

PTo

(o~v ~)

FIGURE 6

< (1-zl2/R(x,y,Q

21 > vs p ~ .

find the following: I. The data is consistent contribution

with a Q2 independent

and a Q2 dependent

2. The Q2 dependence

hard z distribution.

of the hard component

form as predicted.

soft z leading twist

is consistent

with a I / Q 2

It is not reproduced by kinematical

leading twist QCD effects as implemented

effects or It

in the Lund Monte Carlo.

would therefore appear to be a higher twist effect. 3. The y dependence

of the effect cannot be resolved by our data.

4. The PT dependence

of the effect is not as predicted.

REFERENCES

1) E

L. Berger,

Phys.

2) P

J. Fitch et al., Z. Phys.

3) M

Hagenauer

4) P

Renton,

5) P

Mazzanti,

89B (1980) 241.

6) D

Allasia et al., Phys.

C - Particles

et al., Phys. Left.

W.S.C.

7) V V. Ammosov

Lett.

Williams,

R. Odorico,

IOOB

and Fields 31 (1986)

(1981)

185.

Ann. Rev. Nucl. Part.

V. Roberto, Lett.

et al., JETP Lett.

Phys.

Left.

124B (1983) 39 (1984)

51.

Sci. 31 (1981) 98B

193.

(1981) 360.

543. 537.

CERN/ECFA/72-4 Vol. II (1972) i17.

8) G

Myatt,

9) J

3. Aubert et al., Z. Phys. C - Particles

and Fields 30 (1986)

23.