The gluon content of the pion from high-pt photon production

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Volume 233, number 3,4 PHYSICS LETTERS B 28 December 1989

THE G L U O N C O N T E N T OF THE PION FROM H I G H - p t D I R E C T P H O T O N P R O D U C T I O N P. A U R E N C H E

Fermi National Accelerator Laboratory, Batavia, 1L 60439, USA and LAPP, B.P. 110, F-74941 Annecy-le- Vieux Cedex, France R. BALER

Fakultdt J~r Physik, Universitdt Bielefeld, D-4800 Bielefeld 1, FRG M. F O N T A N N A Z

LPTHE, B&timent 211, Universitb de Paris XI, F-91405 Orsay Cedex, France M.N. KIENZLE-FOCACCI

DPNC, Universitb de Genbve, CH-1211 Geneva 4, Switzerland

and

M. WERLEN

IPN, Universitb de Lausanne, BSP Dorigny, CH-1015 Lausanne, Switzerland Received 19 September 1989

A fit to the large p, direct photon cross-sections for the reactions n-+p--,yX, using complete beyond leading logarithm QCD expressions, allows the determination of the content of gluons and valence quarks inside the pion and defines the shape of the gluon structure function for x > 0.2. The QCD scale parameter AM is in good agreement with the most precise deep inelastic scattering determinations.

Direct photon production by n + and n - beams incident on protons is well described [ 1 ] by Q C D cal- culations complete up to O ( c ~ ) [2]. Up to now, the comparison between theory and experimental data was done using the values of the QCD scale parameter A and the structure functions determined by other experiments. In particular the set 1 (A=0.200 GeV) of the leading order parametrization of Duke and Owens for nucleons [3] and pions [4] was found to give satisfactory agreement within the systematic errors of the experiment. However, while the valence quark distribution is well determined by deep inelastic scattering (DIS) for the proton and by Drell-Yan experiments ( D - Y ) for the pion, the gluon structure functions are rather indirectly fixed by DIS and J / ~ production. There is also a correlation between the

values of parameters which enter the theoretical pre- dictions, for example between the structure functions and the value of A. In direct photon production, the pp--,yX and n+p--,yX cross sections are dominated by qg scattering, thus directly sensitive to the gluon distributions while the difference of cross sections

~ r ( n - p ) - a ( n + p ) is dominated by q(t annihilation, thus providing a sensitive determination of A. The pp--,yX data of the WA70 experiment [ 1 ] were al- ready used [5], together with the DIS data of the BCDMS Collaboration [6], to determine beyond leading logarithms the value of A and the gluon structure function of the proton. In this paper we analyze in a similar way the n - p and n+p WA70 data [ 1 ], integrated with respect to the variable XF

( I XFI < 0.45 ), to determine the gluon structure func-

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Volume 233, number 3,4 PHYSICS LETTERS B 28 December 1989 tion o f the p i o n a n d its relative weight to the valence

d i s t r i b u t i o n . T h e d a t a o f the N A 2 4 e x p e r i m e n t [ 7 ] , well c o m p a t i b l e with W A 7 0 results, are also sepa- rately fitted.

The cross sections are c a l c u l a t e d [ 2 ] b e y o n d leading order, up to O (o~ z or), in the MS f a c t o r i z a t i o n a n d r e n o r m a l i z a t i o n schemes a n d four flavors are used t h r o u g h o u t the calculation. The P r i n c i p l e o f M i n i - mal Sensitivity [8] ~ d e t e r m i n e s the o p t i m u m values o f the f a c t o r i z a t i o n scale M ( w h i c h a p p e a r s in the d i s t r i b u t i o n f u n c t i o n s ) a n d o f the r e n o r m a l i z a t i o n scale/t ( w h i c h is the a r g u m e n t o f the strong coupling c o n s t a n t ) . These o p t i m u m values are taken to rep- resent the stability d o m a i n o f the cross-sections, i.e.

the d o m a i n where the cross-sections are not influ- enced by r a t h e r large changes o f the ( u n p h y s i c a l ) scales M a n d #. The structure functions necessary to describe the e x p e r i m e n t a l cross sections are the dis- t r i b u t i o n s o f the valence quarks, the gluon a n d the sea inside the p i o n a n d the p r o t o n . T h e y are p a r a - m e t r i z e d at Qo 2 = 2 G e V 2 and e v o l v e d to different Q2 with the second o r d e r A l t a r e l l i - P a r i s i e q u a t i o n s using the u p d a t e d code f r o m ref. [ 10]. T h e p i o n structure functions are p a r a m e t r i z e d at Qo 2 = 2 G e V 2 by the forms

x V ( x ) = N v ( ~ , f l ) x ~ ( 1 - x ) p,

f l = 0 . 8 5 ,

xS(x) = 2x[a(x) +d(x) +g(x)

] = N s ( 1 - x ) % 6 = 7 . 5 , ( x S ( x ) ) = 0 . 1 4 ,

xG(x)=Ng(1-x)%

respectively for the valence, total sea a n d gluon dis- t r i b u t i o n s , a s s u m i n g the s a m e d i s t r i b u t i o n for valence q u a r k a n d a n t i q u a r k a n d SU ( 3 ) s y m m e t r y for the sea. The relative c o n t r i b u t i o n o f the three c o m - p o n e n t s is c o n s t r a i n e d by the m o m e n t u m s u m rule

f dx[2xV(x) +xS(x) +xG(x) ] = 1.

The p a r a m e t e r fl a n d the sea c o n t r i b u t i o n are t a k e n as external i n p u t s f r o m D - Y analyses which deter- m i n e the structure functions at ( Q 2 ) = 3 0 G e V 2 a n d the value o f these p a r a m e t e r s are therefore e x t r a p o - lated to Q~ = 2 G e V 2. A n u m b e r o f D - Y e x p e r i m e n t s [ 1 1 - 1 4 ] with 7t- b e a m s i n c i d e n t on h e a v y targets

#~ For details on the use of the optimization approach in real photon processes see ref. [9].

have s t u d i e d the valence q u a r k d i s t r i b u t i o n . How- ever, fits to the d a t a are sensitive to the assumed value o f A, to the n o r m a l i z a t i o n K-factor a n d to the nu- cleon valence p a r a m e t e r s , which m a y be taken f r o m v a r i o u s D I S e x p e r i m e n t s . A consistent analysis o f all the d a t a is missing. The difficulty to have a u n i q u e value for

xV(x)

is illustrated in fig. 1. O n l y the pa- r a m e t e r fl has therefore been fixed to a value consistent with D - Y e x p e r i m e n t s inside their q u o t e d errors, while the valence c o n t r i b u t i o n 2

( x V ( x ) ) = 2o~/

( 1 + f l + a ) is a free p a r a m e t e r in the fit. T h e sea dis- t r i b u t i o n was d e t e r m i n e d only by N A 3 [ 11 ] a n d it has been fixed to its value. F o r the p r o t o n we use the set o f structure functions d e t e r m i n e d by the c o m - b i n e d analysis o f B C D M S a n d W A 7 0 d a t a [ 5 ].

First we have p e r f o r m e d a least squares fit between the theoretical p r e d i c t i o n s a n d the 13 d a t a p o i n t s o f the W A 7 0 e x p e r i m e n t ( p t > 4.25 G e V / c ) using only statistical errors, with A (in the expression for ors),

2 ( x V ( x ) )

a n d q as free p a r a m e t e r s . In the structure function evolution, for b o t h p i o n a n d proton, A is fixed to 0.231 GeV, the value o b t a i n e d by the c o m - b i n e d B C D M S a n d W A 7 0 analysis [ 5 ] . T h e results o f the fit are listed in table 1; the d a t a are well repro-

0 5

0.4 0 2 = 5 0 O e V 2

0 1 O W E N S ~ " ~

- w A 7 o

0 ~ , , , I , I L , I , , I , , , , vl

0 0.2 0.4 0.6 0.8

X

Fig. 1. A compilation of the valence structure function of the pion from Drell-Yan data [ 11-14] and from the Owens [4] set 1 parametrization for Q2=30 GeV 2. The NA3 and E537 results (not shown ) are compatible with the fit from NA 10. Superimposed as a continuous line is the result of the fit to direct photon data from WA70.

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Volume 233, number 3,4 Table 1

Best fit to direct photon data.

PHYSICS LETTERS B 28 December 1989

Collaboration A (GeV) q 2<xV(x)> z2/dof

scales defined by Principle of Minimal Sensitivity

WA70 0.229 _+ 0.043 1.86 _+ 0.42 0.415 _+ 0.042 9.8/10

WA70 0.231 fixed 1.94 + 0.20 0.413 _+ 0.020 9.9/11

systematic error + 0.39 + 0.052

-0.17 -0.030

NA24 0.231 fixed 1.82 _+ 0.37 0.338 _+ 0.046 8.6/7

scales defined by M= ,u =pJ 2

WA70 0.231 fixed 1.48_+0.21 0.475+0.021 17/11

scales defined by M= I1 =Pt

WA70 0.688 + 0.114 2.03 + 0.46 0.396 + 0.036 9.7/10

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 ⁱ

0

:'~', Q L 2 2

~'~, ~, Q = 50 aeV

',, 'i:.

• \ .\ ~.

... :,t,, ",.

.?\ "~.

0 2 0.4 0.6 0.8

X

Fig. 2. The pion structure functions obtained with direct photon data for Q2= 30 GeV 2. The continuous line is the central value of the fit, the dashed line indicates the statistical errors and the dotted one the systematic errors of the WA70 experiment. The sea distribution is taken from NA3 [ 11 ].

d u c e d by the t h e o r y with a value o f A c o m p l e t e l y consistent with the one d e t e r m i n e d by the previous analysis [5 ]. T h e r e are strong correlations b e t w e e n the three p a r a m e t e r s , the c o r r e l a t i o n coefficient between A a n d r/is 0.89, b e t w e e n A a n d 2 < x V ( x ) > is - 0 . 8 8 , between 2 < x V ( x ) > a n d t/is - 0 . 6 2 . Since in the pre-

vious analysis [ 5 ] the precision o f the A p a r a m e t e r is m a i n l y due to the high statistics D I S data, this pa- r a m e t e r is finally fixed to its value o f 0.231 GeV, to i m p r o v e the accuracy o f the p i o n structure function p a r a m e t e r s . The results o f this fit are also listed in table 1, the central value o f the p i o n p a r a m e t e r s is unaffected by the c o n s t r a i n t on A, b u t the errors are c o n s i d e r a b l y reduced. The c o r r e l a t i o n coefficient between 2 < x V ( x ) > a n d r / i s 0.77. The systematic errors due to e x p e r i m e n t a l u n c e r t a i n t i e s are e s t i m a t e d by r e p e a t i n g the s a m e fit with statistical a n d systematic errors a d d e d in q u a d r a t u r e . The s a m e fit to the N A 2 4 d a t a (9 p o i n t s with Pt a b o v e 3.5 G e V / c [7] ) gives consistent results (table 1 ).

The shapes o f the p i o n structure functions thus ob- t a i n e d are d r a w n in fig. 2 for Q 2 = 30 G e V 2 together with the statistical a n d systematic u n c e r t a i n t y due to the WA70 data. The valence structure function is c o m p a r e d to D - Y d e t e r m i n a t i o n s in fig. 1 ( c o n t i n u - ous l i n e ) . The present results are s i m i l a r to m o s t o f the D - Y d e t e r m i n a t i o n s a n d to the Owens p a r a m e - trization, b u t ~ 20% lower t h a n the recent d e t e r m i - n a t i o n by the e x p e r i m e n t E615. A n o n - p e r t u r b a t i v e Q C D lattice calculation [15] finds a value o f 0.49 + 0.08 for the first m o m e n t o f the valence quarks in the p i o n at Q 2 = 4 9 GeV2; our p a r a m e t r i z a t i o n g i v e s 0 . 3 3 8 + 0 . 0 1 7 (stat.) [ + 0 . 0 4 3 , - 0 . 0 2 4 (syst.) ] when evolved to this Q2. Previously the gluon structure function o f the pion was m a i n l y d e t e r m i n e d from J / ~ a n d "f p r o d u c t i o n [ 16,17] on h e a v y nuclei, as- s u m i n g that these resonances are p r o d u c e d in r t - N

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Volume 233, n u m b e r 3,4 PHYSICS LETTERS B 28 December 1989

reactions via gluon-gluon fusion using a leading order QCD formalism. In fig. 3 the direct photon result is compared with determinations from J / ~ [ 16,4 ] at Q2 = 10 GeV2; the gluon distribution of the present analysis is below the previous determinations. For the

"I' production, the NA10 experiment [ 17] finds the same value of t/and keeps the same average value of

G(x)

as for J/t~ production; this result is rather difficult to understand if the gluon structure function is evolved to a Q2 corresponding to the "F mass. We re- call however that our analysis of the gluon distribution uses a next-to-leading logarithms formalism whereas the previous determinations, from heavy resonance production [4,16,17 ], were based on a leading logarithm approach and one should therefore be very cautious before drawing conclusions form the comparison.

We have repeated the fit to the WA70 data with a fixed choice of factorization and renormalization scales. Imposing

M=#=pt/2

the quality of the fit worsens (table 1), but the parameters r/ and

2(xV(x))

change only by two and three standard deviations respectively. This choice of scales gives therefore a fair representation for the stability region of the theoretical cross-sections in the kinematical

0.8

0.6

x

x 0.4

02

- - - NA3 ] "\'",

_ . _ OWENS ~ , ""L\

WA70 " ~ . . , .

0 2= I 0 0 e V 2

0.2 0 4 0 6 0 8

x

Fig. 3. Gluon structure function o f the pion at Q 2 = 10 GeV 2 from the WA70 experiment (continuous line) compared to the parametrization o f Owens [4] set 1 (dash-dotted l i n e ) a n d to the fit o f J/t~ data o f N A 3 [ 16] (dashed line).

range explored by the data under investigation. In contrast a conventional choice of scales M = / t = p t , does not allow to reproduce the data with the A parameter fixed to 0.231 GeV. In this case it is necessary to leave A free to reach a higher value: A =0.688 GeV (table 1 ). A similar pattern has also been obtained in fitting the p p ~ T X reaction [ 5 ]. Despite the unreasonable value

of A,

the other parameters change by less than one standard deviation.

The sensitivity of this fit to a variation of the parameters fixed by other analysis is difficult to quan- tify since all parameters are highly correlated. An in- dication of the sensitivity is given in table 2 where the variation of q and

2(xV(x) )

is obtained by re- peating the fit to the WA70 data for the two extreme values each fixed parameter can assume. The parameter fl of the pion valence structure function, varied between the different estimates of the D - Y experiments, gives a small effect. When the sea parameters are varied inside the uncertainties given by NA3, the shape of the gluon distribution appears rather sensitive to the sea normalization, while no effect is ob- servable on the average valence distribution. To es- timate the errors induced by the proton structure functions determination we take the proton gluon shape parameter t/o and the QCD parameter A to the limit of their systematic errors and we find that the effect on the pion structure functions is of the same order as the experimental systematic errors (table 2 ).

In conclusion the analysis of high Pt direct photon data produced by 280 G e V / c n + and n - incident on hydrogen, in the framework of a Q C D calculation complete up to the order ot~ a with the choice of scales defined by the Principle of Minimal Sensitivity, gives a scale parameter of QCD A, in the MS scheme, consistent with the most precise deep inelastic scattering

Table 2

Sensitivity to variations o f the fixed parameters.

Parameter Variation 8q ~(2<xV(x) > )

/3=0.85 +0.15 -T-0.04 +0.005

~ = 7 . 5 + 2 . 2 - 0 . 0 3 - 2 . 2 + 0 . 0 7 ( x S ( x ) ) = O . 14 +0.05 -T-0.25

t/p=4.0 + 0 . 8 - 0 . 2 3 +0.001

- 0 . 6 + 0 . 2 7 - 0 . 0 0 1 A=0.231 + 0 . 0 5 + 0 . 3 7 - 0 . 0 4 1 - 0 . 0 5 - 0 . 3 4 + 0 . 0 5 4

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Volume 233, number 3,4 PHYSICS LETTERS B 28 December 1989

d e t e r m i n a t i o n s [ 5 ]. T h e a v e r a g e m o m e n t u m o f t h e p i o n v a l e n c e at Q 2 = 2 G e V 2 is f o u n d to be

2(xV(x))

= 0 . 4 1 3 + 0.020 ( s t a t . ) [ + 0 . 0 5 2 , - 0.030 ( s y s t . ) ], c o m p a t i b l e w i t h m o s t o f D r e l l - Y a n e x p e r i m e n t s [ 1 1 -

13], b u t l o w e r t h a n e x p e c t e d by t h e r e c e n t E 6 1 5 analysis [ 1 4 ] . T h e g l u o n s t r u c t u r e f u n c t i o n o f t h e p i o n at Q2 = 2 G e V 2 is f o u n d to be

xG(x)

= 1.3( 1 - x ) %

q = 1.94_+ 0 . 2 0 ( s t a t . ) [ + 0 . 3 9 , - 0 . 1 7 ( s y s t . ) ] . I f t h e c h o i c e o f f a c t o r i z a t i o n a n d r e n o r m a l i z a t i o n scales is left o p e n , t h e t h e o r y p r e d i c t i o n s m a y v a r y c o n s i d e r a b l y : h i g h v a l u e s o f # 2 a n d M 2 m u s t be c o m - p e n s a t e d by a large v a l u e o f A (A = 0.688 G e V for t h e c o n v e n t i o n a l c h o i c e M = / t = p t ) , b u t t h e s t r u c t u r e f u n c t i o n s p a r a m e t e r s r e m a i n inside t h e statistical a n d s y s t e m a t i c e r r o r s o f t h e e x p e r i m e n t s .

We a r e grateful to K. F r e u d e n r e i c h f o r h e l p f u l dis- c u s s i o n s o n t h e D r e l l - Y a n e x p e r i m e n t s a n d to t h e w h o l e W A 7 0 C o l l a b o r a t i o n for e n c o u r a g e m e n t .

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