- Email: [email protected]
Probing the gluon structure of the proton with HERA
Volume 225, number 1,2
PHYSICS LETTERS B
13 July 1989
P R O B I N G T H E G L U O N S T R U C T U R E OF T H E P H O T O N W I T H H E R A
R.S. F L E T C H E R , F. H A L Z E N Department qf Physics, Universityof I4%'consin.Madison, W153706, USA and R.W. R O B I N E T T Department of Physics and Astronomy, Pennsylvania State University, UniversityPark, PA 16802, USA Received 9 May 1989
We study the production of ~¢ mesons in ep collisions and argue that ~¢'s form the ideal experimental signature for directly identifying the "'anomalous" gluon structure of the photon. The observation is of relevance to studies of the nucleon structure functions using HERA and to high energy ~,-rayastronomy.
The production o f tV's in high energy ep collisions has been extensively studied as a m e c h a n i s m for probing the gluon structure of the proton [ 1 ] see fig. la. The ~s is produced in the subprocess yg-~cg which constitutes a direct probe of the gluon structure o f the proton. This analysis is adequate for presently available ep laboratory energies. F o r higher energy accelerators such as H E R A ~ ' s can also be p r o d u c e d via the hadronic c o m p o n e n t of the photon [ 2 ] as shown in fig. lb; previous analyses have ignored this possibility. We will refer to the diagrams of figs. l a and l b as " d i r e c t " and " a n o m a l o u s " production, respectively. " A n o m a l o u s " is a c o m m o n , but in a sense ina p p r o p r i a t e nomenclature as the g g ~ c e diagrams o f fig. l b are the d o m i n a n t source o f t~'s at very high energies. We will show this further on, but on the theoretical side there is no mystery. The direct diagram is O(c~c~ . The a n o m a l o u s d i a g r a m consists of two parts: (i) the production to O(c~c~ 2 In Q2) o f z states followed by the decay Z ~ ~7 and (ii) the production o f ~ ' s via g g ~ g to O(c~c~31n Q2). At high energy a large logarithm associated with the gluon structure function in the diagram o f fig. lb raises the a n o m a lous contributions ( i ) and (ii) to O(c~c~s) and O (c~c~), respectively, as In Q2 ~ cC ~. It is further enhanced because o f the abundance o f soft gluons in Q C D at long distance and high energy. 176
~t,X e-
a
P fg/P% ~,Z e- fg ~ b Fig. 1. (a) Direct production of charmonium in ep collisions. (b) Anomalous production of charmonium through gluon fusion in ep collisions.
0370-2693/89/$ 03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing D i v i s i o n )
Volume 225, number 1,2
PHYSICS LETTERS B
A detailed study of the anomalous structure of the photon is of interest for a variety of reasons. The gluon structure of the photon has not been identified experimentally. Its observation will provide further confirmation of the QCD structure of the photon [2 ]. Because our calculation will show that the direct and anomalous production compete at HERA energies, the complete structure of the perturbative calculation of t~ production will have to be taken into account in order to correctly extract the gluon structure function of the proton from data. Finally, the hadtonic structure of the photon is of considerable interest [ 3 ] to astrophysicists detecting very high energy y rays from space after they interact with the Earth's atmosphere. HERA can give us a first glimpse at the transition of the low energy "vector meson" to the high energy gluon structure of photons in the same way that p13 colliders revealed nucleons interacting predominantly via gluons rather than valence quarks. Several methods have been proposed for measuring the gluon structure of the photon. At very high energies, not just gt's but also heavy quarks, jets, and hadrons in general, will be predominantly [4] photoproduced via the anomalous component of the photon. We will show that tV's are an unusually effective and very clean signature. The bulk of the ~'s produced via the hadronic component of the photon are however hidden in small-angle proton debris as expected from inspection of fig. lb where the "gluoninside-the-photon" is characterized on average by very small x-values. We will identify cuts in t~ energy and rapidity which allow identification of the twocomponent structure of the ~ photoproduction cross section with planned detectors. Our proposal seems superior to others [4] using jets or b-quarks as a signature for the anomalous component of the photon. Our results are summarized in figs. 2, 3 and 4; we describe the calculations next. The sources of~¢ mesons in yp collisions are Tg-,~g,
(la)
gg~t~g,
(lb)
gg-* X, ( -"~T)g,
(lc)
gq-*)G ( -~vY)q,
(lc)
qQ~Xi ( -*~tY)g,
(ld)
13 July 1989
gg~zi ~ Y ,
(le)
yp-~b (--,W[)I~,
(l f)
where Zi represents any of the three • states. We obtain cross sections for ep collisions at HERA by applying the Weiszacker-Williams equivalent photon approximation. The ep cross sections are given by da,,p = j dzfv/,,(z)d%p(E 7 =zEo) ,
(2)
where
fv/~(z,E)_
a l+(1-z)
27r
2
z
In
Ee M2
.
(3)
The 7P cross sections are calculated using the standard parton model formulas. For the direct mechanism ( 1a) dad;"ect = j dxfg/p(x)dayg .vg(~=zxs) ,
(4)
and for each of the anomalous contributions ( l b ) (le)
da~, ..... = f da'~ f dx2fi/v(x,)fj/p(x2) X doij_)~ or ~.(S = ZXI X2S ) ,
(5)
where f/k is the parton distribution for parton i in particle k. We used the photon and hadron structure function of refs. [ 5,6 ], respectively, unless otherwise noted. We have chosen Q2 = m 2 as the evolution scale of the running coupling as well as the structure functions. The subprocess cross sections d% .~.x, given in ref. [ 7 ], depend on the value of the ~¢or )~wave function. We use the values given by ref. [8 ]. In the end the calculation is very similar to those performed for g, production in pp interactions [7,8]. We refer to ref. [ 8 ] for a discussion of the ambiguities in the calculation, especially the choice of Q2. The calculated Wyields for HERA energy are shown in figs. 2a, 2b as a function of the transverse momentum and rapidity of the W. Positive rapidities indicate the proton direction. For large pw-values the cross section is dominated by the production of b[~ pairs with one of the B mesons decaying into a W with a branching ratio of 0.01. For PT< 2 GeV the anomalous production dominates and the small-pv region will be therefore the further focus of our discussion. The diagrams fall into two categories with subprocess of the 2-+2 ( l a ) - ( l d ) and the 2-.1 (le) type. The 177
Volume 225, number 1,2
a
\
-
100
PHYSICS LETTERS B
\\
:gg~Pg XQ\
Q)
Anomalous' 'Direct'
"gg~x~g~\x ~ \ \ gg~x x \ \
r""m
>
-
_
10-1
\
igg~xlg- k
\
"x\
\
,.Q ,-,
10-2
,
xx.\
b
~
\ \
10-3
....
10-4
~. . . . . 4 PL [GeV]
0
:i ~
;2
. . . .
i
.~. 8
6
. . . .
i
. . . .
/
gg~lpg
i
'
0.100 - -
'Direct'
.
.
.
.
\
0.050
gg~x~g
q3 b
q3
///
0.010
_._
~ \
.~
\ \\
-
0.005
,,
0.001
.ll .
-g
.
.
.
.
.
.
.
.
I
, J
4
Fig_ 2. (a) PT distributions of xC's produced in ep collisions (\/s= 315 GeV) via the various production mechanisms of eq. ( 1), calculated using the parton distributions of refs. [5,6] and assuming Q2=M~. The curve for b--*~¢ is reproduced from Kunszt [ 1]. (b) Rapidity distributions ofxc's in ep collisions tbr PT> 1 GeV. Calculations as in (a). former are divergent for pT-+0 and are shown in fig. 2a for Pr > 1 GeV. Diagrams o f the form g g ~ x , produce a Z with pv~--0 and therefore the ~ from X--'~7 decay is p r o d u c e d with very small transverse momentum. One cannot o f course assume that all Z'S have PT = 0; the results in fig. 2 are based on a universal m T = (rn~," + P T2 ) 1 / 2 scaling o f particle production [9]
da/ dp;r = a exp ( - braT) 178
(6)
13 July 1989
with b ~ 6 GeV. The normalization a is fixed by the 0.24 nb total rate calculated from the parton model for gg-~x. The rapidity distribution o f the ~ for the various production mechanisms is shown in fig. 2b. To what extent does the inclusion of the anomalous production interfere with the straightforward d e t e r m i n a t i o n o f the gluon structure function o f the nucleon based on an analysis assuming direct production only? As can be seen in fig. 2 there is, unfortunately, no PT regime where direct ~ production d o m i n a t e s and the previously proposed analyses can be applied. F o r a cut PT > 5 GeV a n o m a l o u s ~ ' s are p r o d u c e d roughly at the 25% level o f direct ~'s; see fig. I a. The former compete closely with ~ ' s from b decay and the two sources of ~ ' s have to be separated. F o r smaller values of PT, say PT> 1 GeV, the b--,~ events become negligible but a n o m a l o u s production makes a significant contribution to k~ production. The leading-order production g g - ~ x ~ , has a cross section of about 0.1 nb and contributes for PT < 2.5 GeV, although this conclusion depends on the treatment o f the Pr distribution o f X's based on eq. (6). We now turn to the question of directly observing the a n o m a l o u s gluon c o m p o n e n t o f the photon. At first sight it should be easy as the cross sections are large: 0.1 nb for reaction eq. ( l e ) and 0.47 nb for eqs. ( l b ) - ( l d ) with p v > 1 GeV. This corresponds to 3 × 104 dilepton events per year. As there is no PT range where the anomalous contribution clearly d o m i n a t e s we have to i m p l e m e n t some cuts to enhance it over direct production. The key is that the gluons in the photon are on average very soft and therefore (i) the ~¢ carries a small fraction z = E v / E ~ of the photon energy and (ii) the ~ will be boosted in rapidity in the direction o f the proton. We investigate both possibilities. Case ( i ) is illustrated in fig. 3. For z~<0.1 ~ production is d o m i n a t e d by the anomalous diagrams of fig. l b in ~,p collisions o f x / s = 2 2 9 GeV. Unfortunately after transforming YP to ep using the W e i s z a c k e r - W i l l i a m s distribution o f eq. (3) the effectiveness of a cut in z is greatly reduced. The cut in z=Ev/E~ now selects "soft photons from the electron" as well as "soft gluons in the photon". One has to prepare a photon b e a m by tagging the recoil electron. This however results into a beam of virtual photons, typically Qe > 5 GeV 2, which is outside the do-
Volume 225, number 1,2 10 2
....
PHYSICS LETTERS B
i ....
i ....
q. . . .
13 July 1989
100
J ....
a us'
101
'Direct'
~
--'Anomalous' . . . . Direct'
"
~
10-1
/
/
\
_
/ /
!
\
N
b
100
b
//
'D
10-2
10-3
10-1 0
0.1
0.2
0.3
0.4
0.5
,
i
-2
0.6
0
2
Z 10 0
Fig. 3. z( =E~,/E~ in proton rest frame) distributions of~'s produced in yp interactions at v~=229 OeV via direct and anomalous production mechanisms. main of applicability of the formalism used to perform our calculation. Possibility (ii) is illustrated in figs. 4a and 4b. Clearly we have identified a region in rapidity y > 2 where anomalous production is the d o m i n a n t source o f ~ ' s . No cut is in fact necessary. G i v e n the expected statistics one will be able to separate the two production mechanisms as they have very different shapes. At this point it is however i m p o r t a n t to r e m e m b e r that this shape depends on the shape of not only the proton's, but especially the photon's gluon structure function. We repeated the calculation for two sets [ 5,10 ] of photon structure functions; see figs. 4a and 4b. Also shown are the same rapidity distributions after requiring that the leptons from the ~ decay are detected by the proposed experiments which detect particles separated by 3 ° or more from the beams. Another possible mechanism for studying the gluon structure of the photon at HERA is ~y production. In fig. 1b we can replace the final state gluon with a photon. This replacement is not allowed in the direct process because of color conservation. In s u m m a r y we believe that the gluon structure of high energy photons can be demonstrated and studied at HERA. We believe ~'s are an ideal experimental signature especially in the kinematic range Pv < 5 GeV. The event rates are very high. Z production followed by the decay Z - ~ ] , is an i m p o r t a n t source of
4
Y .
.
f
.
.
.
~
.
.
.
.
~
iii /
10 --1 .~
.
. . . .
,-
"-. ",
/ /
,~
1//
\ \
I
b q~
.
'Anomalous' . . . . Direct'
b
\
10 -2
i
10-3
,
I -2
0
2
4
Y Fig. 4. (a) ~ rapidity distributions at HERA. The lower curve shows the effect of requiring that the leptons from ~ decay be separated from the beam axis by > 3 °. For comparison with previous figuresthe curves have not been multipliedby the ~g-,p+p.branching fraction. (b) Same as (a) except that the photon structure functions ofref. [ 10] were used. anomalous ~'s. Therefore the associated y can provide an additional experimental signature. At higher energies, e.g. an ep collider exploiting LEP and LHC, the problem u n d e r consideration becomes trivial. Anomalous interactions simply d o m i n a t e photoproduction as can be seen from fig. 5. That is also why the problem is relevant to high energy y-ray ast r o n o m y [ 3 ]. The hadrons produced by y rays are a crucial experimental signature for tagging photons in modern cosmic ray telescopes. 179
Volume 225, number 1,2
i01
,
r
I
. . . .
PHYSICS LETTERS B
-T
. . . .
I
. . . .
!
. . . .
I
--'AIloma].ol3.s'
i0 0
~m
b
¢/"~i10
port was provided by NSF grant Phy-8620118 and US Department of Education Award no. P200A80214. We thank D. Reeder, W. Smith, and Manuel Drees for helpful conversations. One of us, R.R., would like to thank the Phenomenology Institute at the University of Wisconsin-Madison for its hospitality.
References
1
10-2 -2.5
0
2.5
5
7.5
Y Fig. 5. ~ rapidity distributions at LHC×LEP, 8 TeV protons on 100 GeV electrons, for the direct process ( l a ) 2-1 anomalous processes ( l e ) , and 2-2 anomalous processes ( l b ) - ( l d ) .
While this work was in progress we received a publication [ 11 ] by Kunszt and Stirling which contains some of the results of fig. 2a. This research was supported in part by the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation, and in part by the US Department of Energy under contract DE-AC02-76ER00881. Further sup-
180
13 July 1989
[ l ] A.D. Martin, C.K. Ng and W.J. Stirling, Phys. Lett. B 191 (1987) 200; S.M. Tkalzy, W.J. Stirling and D.H. Saxon, preprint RAL88-041 ; Z. Kunszt, Phys. Lett. B 207 (1988) 103; Z. He and R. Huang, Phys. Rev. D 38 (1988) 3387. [2] E. Witten, Nucl. Phys. B 120 (1977) 189. [3] M. Drees and F. Halzen, Phys. Rev. Lett. 61 (1988) 275; M. Drees, F. Halzen and K. Hikasa, Phys. Rev. D 39 (1989) 1310. [4] M. Drees and R.M. Godbole, Phys. Rev. D 39 (1989) 169; Phys. Rev. Left. 61 (1988) 682. [ 5 ] M. Drees and K. Grassie, Z. Phys. C 28 ( 1985 ) 451. [6] D.W. Duke and J.F. Owens, Phys. Rev. D 30 (1984) 49. [7] R. Gastmans, W. Troost and T.T. Wu, Phys. Lett. B 184 (1987) 257: R. Baier and R. Rtickl, Z. Phys. C 19 ( 1983 ) 251. [8] E.W.N. Glover, F. Halzen and A.D. Martin, Phys. Len. B 185 (1987) 441. [9] H. Satz, Phys. Rev. D 17 (1978) 914. [ 10] D.W. Duke and J.F. Owens, Phys. Rev. D 22 (1980) 2280. [ 11 ] Z. Kunszt and W.J. Stirling, Phys. Lett. B 217 (1989) 53.
PHYSICS LETTERS B
13 July 1989
P R O B I N G T H E G L U O N S T R U C T U R E OF T H E P H O T O N W I T H H E R A
R.S. F L E T C H E R , F. H A L Z E N Department qf Physics, Universityof I4%'consin.Madison, W153706, USA and R.W. R O B I N E T T Department of Physics and Astronomy, Pennsylvania State University, UniversityPark, PA 16802, USA Received 9 May 1989
We study the production of ~¢ mesons in ep collisions and argue that ~¢'s form the ideal experimental signature for directly identifying the "'anomalous" gluon structure of the photon. The observation is of relevance to studies of the nucleon structure functions using HERA and to high energy ~,-rayastronomy.
The production o f tV's in high energy ep collisions has been extensively studied as a m e c h a n i s m for probing the gluon structure of the proton [ 1 ] see fig. la. The ~s is produced in the subprocess yg-~cg which constitutes a direct probe of the gluon structure o f the proton. This analysis is adequate for presently available ep laboratory energies. F o r higher energy accelerators such as H E R A ~ ' s can also be p r o d u c e d via the hadronic c o m p o n e n t of the photon [ 2 ] as shown in fig. lb; previous analyses have ignored this possibility. We will refer to the diagrams of figs. l a and l b as " d i r e c t " and " a n o m a l o u s " production, respectively. " A n o m a l o u s " is a c o m m o n , but in a sense ina p p r o p r i a t e nomenclature as the g g ~ c e diagrams o f fig. l b are the d o m i n a n t source o f t~'s at very high energies. We will show this further on, but on the theoretical side there is no mystery. The direct diagram is O(c~c~ . The a n o m a l o u s d i a g r a m consists of two parts: (i) the production to O(c~c~ 2 In Q2) o f z states followed by the decay Z ~ ~7 and (ii) the production o f ~ ' s via g g ~ g to O(c~c~31n Q2). At high energy a large logarithm associated with the gluon structure function in the diagram o f fig. lb raises the a n o m a lous contributions ( i ) and (ii) to O(c~c~s) and O (c~c~), respectively, as In Q2 ~ cC ~. It is further enhanced because o f the abundance o f soft gluons in Q C D at long distance and high energy. 176
~t,X e-
a
P fg/P% ~,Z e- fg ~ b Fig. 1. (a) Direct production of charmonium in ep collisions. (b) Anomalous production of charmonium through gluon fusion in ep collisions.
0370-2693/89/$ 03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing D i v i s i o n )
Volume 225, number 1,2
PHYSICS LETTERS B
A detailed study of the anomalous structure of the photon is of interest for a variety of reasons. The gluon structure of the photon has not been identified experimentally. Its observation will provide further confirmation of the QCD structure of the photon [2 ]. Because our calculation will show that the direct and anomalous production compete at HERA energies, the complete structure of the perturbative calculation of t~ production will have to be taken into account in order to correctly extract the gluon structure function of the proton from data. Finally, the hadtonic structure of the photon is of considerable interest [ 3 ] to astrophysicists detecting very high energy y rays from space after they interact with the Earth's atmosphere. HERA can give us a first glimpse at the transition of the low energy "vector meson" to the high energy gluon structure of photons in the same way that p13 colliders revealed nucleons interacting predominantly via gluons rather than valence quarks. Several methods have been proposed for measuring the gluon structure of the photon. At very high energies, not just gt's but also heavy quarks, jets, and hadrons in general, will be predominantly [4] photoproduced via the anomalous component of the photon. We will show that tV's are an unusually effective and very clean signature. The bulk of the ~'s produced via the hadronic component of the photon are however hidden in small-angle proton debris as expected from inspection of fig. lb where the "gluoninside-the-photon" is characterized on average by very small x-values. We will identify cuts in t~ energy and rapidity which allow identification of the twocomponent structure of the ~ photoproduction cross section with planned detectors. Our proposal seems superior to others [4] using jets or b-quarks as a signature for the anomalous component of the photon. Our results are summarized in figs. 2, 3 and 4; we describe the calculations next. The sources of~¢ mesons in yp collisions are Tg-,~g,
(la)
gg~t~g,
(lb)
gg-* X, ( -"~T)g,
(lc)
gq-*)G ( -~vY)q,
(lc)
qQ~Xi ( -*~tY)g,
(ld)
13 July 1989
gg~zi ~ Y ,
(le)
yp-~b (--,W[)I~,
(l f)
where Zi represents any of the three • states. We obtain cross sections for ep collisions at HERA by applying the Weiszacker-Williams equivalent photon approximation. The ep cross sections are given by da,,p = j dzfv/,,(z)d%p(E 7 =zEo) ,
(2)
where
fv/~(z,E)_
a l+(1-z)
27r
2
z
In
Ee M2
.
(3)
The 7P cross sections are calculated using the standard parton model formulas. For the direct mechanism ( 1a) dad;"ect = j dxfg/p(x)dayg .vg(~=zxs) ,
(4)
and for each of the anomalous contributions ( l b ) (le)
da~, ..... = f da'~ f dx2fi/v(x,)fj/p(x2) X doij_)~ or ~.(S = ZXI X2S ) ,
(5)
where f/k is the parton distribution for parton i in particle k. We used the photon and hadron structure function of refs. [ 5,6 ], respectively, unless otherwise noted. We have chosen Q2 = m 2 as the evolution scale of the running coupling as well as the structure functions. The subprocess cross sections d% .~.x, given in ref. [ 7 ], depend on the value of the ~¢or )~wave function. We use the values given by ref. [8 ]. In the end the calculation is very similar to those performed for g, production in pp interactions [7,8]. We refer to ref. [ 8 ] for a discussion of the ambiguities in the calculation, especially the choice of Q2. The calculated Wyields for HERA energy are shown in figs. 2a, 2b as a function of the transverse momentum and rapidity of the W. Positive rapidities indicate the proton direction. For large pw-values the cross section is dominated by the production of b[~ pairs with one of the B mesons decaying into a W with a branching ratio of 0.01. For PT< 2 GeV the anomalous production dominates and the small-pv region will be therefore the further focus of our discussion. The diagrams fall into two categories with subprocess of the 2-+2 ( l a ) - ( l d ) and the 2-.1 (le) type. The 177
Volume 225, number 1,2
a
\
-
100
PHYSICS LETTERS B
\\
:gg~Pg XQ\
Q)
Anomalous' 'Direct'
"gg~x~g~\x ~ \ \ gg~x x \ \
r""m
>
-
_
10-1
\
igg~xlg- k
\
"x\
\
,.Q ,-,
10-2
,
xx.\
b
~
\ \
10-3
....
10-4
~. . . . . 4 PL [GeV]
0
:i ~
;2
. . . .
i
.~. 8
6
. . . .
i
. . . .
/
gg~lpg
i
'
0.100 - -
'Direct'
.
.
.
.
\
0.050
gg~x~g
q3 b
q3
///
0.010
_._
~ \
.~
\ \\
-
0.005
,,
0.001
.ll .
-g
.
.
.
.
.
.
.
.
I
, J
4
Fig_ 2. (a) PT distributions of xC's produced in ep collisions (\/s= 315 GeV) via the various production mechanisms of eq. ( 1), calculated using the parton distributions of refs. [5,6] and assuming Q2=M~. The curve for b--*~¢ is reproduced from Kunszt [ 1]. (b) Rapidity distributions ofxc's in ep collisions tbr PT> 1 GeV. Calculations as in (a). former are divergent for pT-+0 and are shown in fig. 2a for Pr > 1 GeV. Diagrams o f the form g g ~ x , produce a Z with pv~--0 and therefore the ~ from X--'~7 decay is p r o d u c e d with very small transverse momentum. One cannot o f course assume that all Z'S have PT = 0; the results in fig. 2 are based on a universal m T = (rn~," + P T2 ) 1 / 2 scaling o f particle production [9]
da/ dp;r = a exp ( - braT) 178
(6)
13 July 1989
with b ~ 6 GeV. The normalization a is fixed by the 0.24 nb total rate calculated from the parton model for gg-~x. The rapidity distribution o f the ~ for the various production mechanisms is shown in fig. 2b. To what extent does the inclusion of the anomalous production interfere with the straightforward d e t e r m i n a t i o n o f the gluon structure function o f the nucleon based on an analysis assuming direct production only? As can be seen in fig. 2 there is, unfortunately, no PT regime where direct ~ production d o m i n a t e s and the previously proposed analyses can be applied. F o r a cut PT > 5 GeV a n o m a l o u s ~ ' s are p r o d u c e d roughly at the 25% level o f direct ~'s; see fig. I a. The former compete closely with ~ ' s from b decay and the two sources of ~ ' s have to be separated. F o r smaller values of PT, say PT> 1 GeV, the b--,~ events become negligible but a n o m a l o u s production makes a significant contribution to k~ production. The leading-order production g g - ~ x ~ , has a cross section of about 0.1 nb and contributes for PT < 2.5 GeV, although this conclusion depends on the treatment o f the Pr distribution o f X's based on eq. (6). We now turn to the question of directly observing the a n o m a l o u s gluon c o m p o n e n t o f the photon. At first sight it should be easy as the cross sections are large: 0.1 nb for reaction eq. ( l e ) and 0.47 nb for eqs. ( l b ) - ( l d ) with p v > 1 GeV. This corresponds to 3 × 104 dilepton events per year. As there is no PT range where the anomalous contribution clearly d o m i n a t e s we have to i m p l e m e n t some cuts to enhance it over direct production. The key is that the gluons in the photon are on average very soft and therefore (i) the ~¢ carries a small fraction z = E v / E ~ of the photon energy and (ii) the ~ will be boosted in rapidity in the direction o f the proton. We investigate both possibilities. Case ( i ) is illustrated in fig. 3. For z~<0.1 ~ production is d o m i n a t e d by the anomalous diagrams of fig. l b in ~,p collisions o f x / s = 2 2 9 GeV. Unfortunately after transforming YP to ep using the W e i s z a c k e r - W i l l i a m s distribution o f eq. (3) the effectiveness of a cut in z is greatly reduced. The cut in z=Ev/E~ now selects "soft photons from the electron" as well as "soft gluons in the photon". One has to prepare a photon b e a m by tagging the recoil electron. This however results into a beam of virtual photons, typically Qe > 5 GeV 2, which is outside the do-
Volume 225, number 1,2 10 2
....
PHYSICS LETTERS B
i ....
i ....
q. . . .
13 July 1989
100
J ....
a us'
101
'Direct'
~
--'Anomalous' . . . . Direct'
"
~
10-1
/
/
\
_
/ /
!
\
N
b
100
b
//
'D
10-2
10-3
10-1 0
0.1
0.2
0.3
0.4
0.5
,
i
-2
0.6
0
2
Z 10 0
Fig. 3. z( =E~,/E~ in proton rest frame) distributions of~'s produced in yp interactions at v~=229 OeV via direct and anomalous production mechanisms. main of applicability of the formalism used to perform our calculation. Possibility (ii) is illustrated in figs. 4a and 4b. Clearly we have identified a region in rapidity y > 2 where anomalous production is the d o m i n a n t source o f ~ ' s . No cut is in fact necessary. G i v e n the expected statistics one will be able to separate the two production mechanisms as they have very different shapes. At this point it is however i m p o r t a n t to r e m e m b e r that this shape depends on the shape of not only the proton's, but especially the photon's gluon structure function. We repeated the calculation for two sets [ 5,10 ] of photon structure functions; see figs. 4a and 4b. Also shown are the same rapidity distributions after requiring that the leptons from the ~ decay are detected by the proposed experiments which detect particles separated by 3 ° or more from the beams. Another possible mechanism for studying the gluon structure of the photon at HERA is ~y production. In fig. 1b we can replace the final state gluon with a photon. This replacement is not allowed in the direct process because of color conservation. In s u m m a r y we believe that the gluon structure of high energy photons can be demonstrated and studied at HERA. We believe ~'s are an ideal experimental signature especially in the kinematic range Pv < 5 GeV. The event rates are very high. Z production followed by the decay Z - ~ ] , is an i m p o r t a n t source of
4
Y .
.
f
.
.
.
~
.
.
.
.
~
iii /
10 --1 .~
.
. . . .
,-
"-. ",
/ /
,~
1//
\ \
I
b q~
.
'Anomalous' . . . . Direct'
b
\
10 -2
i
10-3
,
I -2
0
2
4
Y Fig. 4. (a) ~ rapidity distributions at HERA. The lower curve shows the effect of requiring that the leptons from ~ decay be separated from the beam axis by > 3 °. For comparison with previous figuresthe curves have not been multipliedby the ~g-,p+p.branching fraction. (b) Same as (a) except that the photon structure functions ofref. [ 10] were used. anomalous ~'s. Therefore the associated y can provide an additional experimental signature. At higher energies, e.g. an ep collider exploiting LEP and LHC, the problem u n d e r consideration becomes trivial. Anomalous interactions simply d o m i n a t e photoproduction as can be seen from fig. 5. That is also why the problem is relevant to high energy y-ray ast r o n o m y [ 3 ]. The hadrons produced by y rays are a crucial experimental signature for tagging photons in modern cosmic ray telescopes. 179
Volume 225, number 1,2
i01
,
r
I
. . . .
PHYSICS LETTERS B
-T
. . . .
I
. . . .
!
. . . .
I
--'AIloma].ol3.s'
i0 0
~m
b
¢/"~i10
port was provided by NSF grant Phy-8620118 and US Department of Education Award no. P200A80214. We thank D. Reeder, W. Smith, and Manuel Drees for helpful conversations. One of us, R.R., would like to thank the Phenomenology Institute at the University of Wisconsin-Madison for its hospitality.
References
1
10-2 -2.5
0
2.5
5
7.5
Y Fig. 5. ~ rapidity distributions at LHC×LEP, 8 TeV protons on 100 GeV electrons, for the direct process ( l a ) 2-1 anomalous processes ( l e ) , and 2-2 anomalous processes ( l b ) - ( l d ) .
While this work was in progress we received a publication [ 11 ] by Kunszt and Stirling which contains some of the results of fig. 2a. This research was supported in part by the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation, and in part by the US Department of Energy under contract DE-AC02-76ER00881. Further sup-
180
13 July 1989
[ l ] A.D. Martin, C.K. Ng and W.J. Stirling, Phys. Lett. B 191 (1987) 200; S.M. Tkalzy, W.J. Stirling and D.H. Saxon, preprint RAL88-041 ; Z. Kunszt, Phys. Lett. B 207 (1988) 103; Z. He and R. Huang, Phys. Rev. D 38 (1988) 3387. [2] E. Witten, Nucl. Phys. B 120 (1977) 189. [3] M. Drees and F. Halzen, Phys. Rev. Lett. 61 (1988) 275; M. Drees, F. Halzen and K. Hikasa, Phys. Rev. D 39 (1989) 1310. [4] M. Drees and R.M. Godbole, Phys. Rev. D 39 (1989) 169; Phys. Rev. Left. 61 (1988) 682. [ 5 ] M. Drees and K. Grassie, Z. Phys. C 28 ( 1985 ) 451. [6] D.W. Duke and J.F. Owens, Phys. Rev. D 30 (1984) 49. [7] R. Gastmans, W. Troost and T.T. Wu, Phys. Lett. B 184 (1987) 257: R. Baier and R. Rtickl, Z. Phys. C 19 ( 1983 ) 251. [8] E.W.N. Glover, F. Halzen and A.D. Martin, Phys. Len. B 185 (1987) 441. [9] H. Satz, Phys. Rev. D 17 (1978) 914. [ 10] D.W. Duke and J.F. Owens, Phys. Rev. D 22 (1980) 2280. [ 11 ] Z. Kunszt and W.J. Stirling, Phys. Lett. B 217 (1989) 53.