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On a possibility of observing elastic photon-gluon scattering in ep collisions
Volume 112B, number 6
PHYSICS LETTERS
27 May 1982
ON A POSSIBILITY OF OBSERVING ELASTIC PHOTON-GLUON SCATTERING IN ep COLLISIONS C. CARIMALO, P. KESSLER, J. PARISI 1 and J. SILVA 2 Laboratoire de Physique Corpusculaire, Collkge de France, Paris, France Received 8 July 1981
It is shown that photon gluon scatteiing via the quark-box diagram, which may be considered a critical test of higherorder quantum chromodynamics, should become a predominant and measurable effect in an experiment designed to study the reaction ep ~ e + (high-pT)-~ + (high-PT) jet + X under certain kinematic conditions at a superhigh-energy electronproton storage ring such as HERA.
As was emphasized in a recent paper by Combridge [ 1 ], the experimental observation o f contributions of the quark-loop diagram of fig. 1, where the external vector particles would be either two photons plus two gluons, or one photon plus three gluons, would provide evidence for the applicability of higher-order perturbation theory to processes involving hadrons and, in particular, o f perturbative QCD to other than simple tree-diagram subprocesses. As emphasized in ref. [1 ], those contributions should be compared to competing diagrams as shown in fig. 2, i.e. 2 7 - 2 q (as a background to 2 7 - 2 g ) or 1 7 - 1 g - 2 q (as a background to l~'-3g). It is of course to be noticed that, as far as gluons or quarks are to appear in the final state, those competing diagrams might be eliminated if some obvious criteria were available, allowing one to distinguish between quark and gluon jets. However, this is not the case at present and remains problematic for the future. The author of ref. [1] then shows that for 1 7 - 3 g subprocesses the signal to background ratio appears very small (at most a few percent), mainly because of destructive interference between different flavor loops. On the other hand, the situation appears more promising for the 23,-2g graphs. 1 Visitor at the Institute for Theoretical Physics, Stony Brook, NY, USA. 2 Also at Laboratoire de Physique des Particules, Universit~ de Picardie, Amiens, France. 484
\
/1 Fig. 1. Vector-particle scattering through a quark loop. Five additional contributing diagrams are obtained by permutations.
/
Fig. 2. Diagrams for 23,-2q or l q , - l g - 2 q subprocesses.
0 0 3 1 - 9 1 6 3 / 8 2 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © 1982 North-Holland
Volume 112B, number 6
PHYSICS LETTERS
The following 2T-2g subprocesses and corresponding experiments are to be considered: (i) T7 -+ gg, to be observed in: ee -+ (ee)gg. (ii) gg ~ 77, to be observed in: NN -+ TTX. (iii) 7g ~ Tg, to be observed in: 7N -+ 7(g)X. Where in (i) either an outgoing electron may be observed or not, and in (iii) the gluon jet may be observed or not. Reaction (i) was studied in some detail in refs. [ 1 - 3 ] , and reaction (ii) in refs. [1,4]. This paper is devoted to investigating the possibility of observing subprocess (iii). As was shown in ref. [1] comparing reactions involving (a) 7g -+ Tg and (b) 7q -+ Yq scattering, (a) may be enhanced with respect to (b) by chosing a particular kinematic configuration combining two advantages: a small value of the scaling parameter x, favouring the gluon distribution with respect to the quark distribution within the nucleon; and a small value of the photon's scattering angle 0 (in the c.m. frame), disfavouring the reaction (b) since Compton scattering is backward peaked. However, a minimum value should be fixed for PT (typically, PT ~> 3 GeV), so that one may assume that above this value it is possible to properly distinguish between direct photons and indirect ones, the latter being mainly due to 7r° production and decay. Now it appears that, with presently available photon-beam energies (E --~ 2 0 0 300 GeV), keeping PT sufficiently large, x and 0 cannot both become small enough to make (a) predominate over (b). This can be seen by using the kinematic formula (specific to photoproduction, neglecting any masses): 2PT/X/)-= X/-xsin 0. If one wishes to get a more than 100% signal to background ratio, one should keep x ~ 0.1 in order to roughly gain one order of magnitude when comparing the gluon distribution function with that of the quark, and at the same time keep 0 smaller than, let us say, 30 ° in order tomake sure that one looses less than one order of magnitude when comparing (do/d~)~,g~,rg with (da/d(2)~q__,,tq (including color and charge factors, and noticing that q should mainly be identified with the u-quark; see our formulas farther below). Accounting for PT ~ 3 GeV/c, one then concludes that one should have V ~ > 40 GeV, i.e. Ee >~ 800 GeV; in other words, one would have to wait for a particle accelerator in the TeV range.
27 May 1982
Looking out for future machinesto design this type of experiment, one should remark that it might be more promising to consider, instead of real-photon beams, the quasi-real photon flux available in an electron-proton storage ring of very high energy. In this context, the HERA project [5] (E e ~-- 30 GeV, Ep 800 GeV) should be quite appropriate, since there the upper limit of the equivalent-photon flux would be as high as 50 TeV in the proton's rest frame. On the other hand, the dissymmetry between the electron and the proton should be an important advantage in such an experiment, since it should allow the interesting photon emission angles in the laboratory frame, with respect to the electron-beam direction, to be large enough for experimental detection. Some preconditions must, however, be assumed: (i) Photon detectors should be available in the forward hemisphere with respect to the electron beam, down to a minimal emission angle of, let us say, 10° (This would be useful, as well, for other experiments, designed to study the range of very small x values.) (ii) For the sake of kinetic reconstitution of the subprocess, it should be possible to observe the jet produced together with the photon (with opposite and approxi mately equal PT) and to measure the angle of the j e t axis down to a minimal value, of let us say, 10° with respect to the proton beam. (rio In order to avoid a large background from electron bremsstrahlung and at the same time to keep the photons quasi real, it should be possible to restrict the electrons' scattering angle to very small values; this might be done by anti-tagging, i.e. by vetoing all electrons scattered at angles larger than the minimal tagging angle, which should be of the order of 10 mrad according to the project. (It may be noticed that the PLUTO Collaboration presently uses such an anti-tagging at PETRA). The corresponding kinematic scheme is shown in fig. 3. Imposing the constraint 0 < 30 ° using the kinematic relation (valid when any masses are neglected)
x
[
~
Oe,
Fig. 3. Kinetic schemefor ep ~ eq, + (high-pT)jet + X. 485
Volume 112B, number 6
PHYSICS LETTERS
Ca)
(b)
27May 1982 dz d(cos 0) dx
4PT
dPT d(cos 0) d(cos 0)
s sin20 sin 2 0
fife(Z) = (2a/rrz) {(1 - z + ½z 2) X In {(Ee/me)[(1 - z)/z]O max + 1} - ~-(1 - z)}, do~g~vg/d(cos O) = (50~rala2/81 S) g(O), where
q( c ) / ~
(d)
¢
z = (PT/2Ee)(CO.t 0/2 + tan 0[2), x = (PT/2Ep) (tan 0]2 + cot 0]2),
d = 4ZXEeE p = zxs,
(e) Fig. 4. Diagrams for various contributions to ep ~ e3' + (highPT) jet + X. (a) ep ~ e~,gX: (b) ep ~ e3'q (or ~) X (involving 3'q or q,CtCompton scattering as a subprocess); (c) ep ~ ep e.yq (or q) X (involving 3'e Compton scattering as a subprocess); (d) ep ~ e-~q~X (an additional diagram, where q and are exchanged, is implicitly included); (e) ep ~ eTqq (or q) X. tan20/2 = tan 0/2 tan 0 / 2 , a lower limit of 10 ° for both 0, 0results in an upper limit of--~ 75 ° for either of them. In addition to the main diagram of fig. 4a, various background processes, shown in figs. 4 b - 4 e , are to be considered. Figs. 4b, 4c, respectively, involve 7q a n d 3"e Compton scattering as a subprocess. In figs. 4d and 4e, where the subprocesses involved are, respectively, qg -+ 3'q (or ?qg ~ 7?t) and q?:l-+ 7g, we suppose an additional undetected beam-pipe jet to be emitted in the electron-beam direction; we shall assume that the maximal angle of the jet axis with respect to the beam axis, allowing such a jet to escape detection, would be 5 ° . For computing those diagrams, we use the following formulas (taking all particles massless wherever permitted): (a): d3o(a) = Dfy/e(Z ) d~g+3"g fg/p(X), dPT d (cos 0) d(cos 0) d(cos 0) where D is a kinematic factor, and where fv/e(Z) and fg/p(X) are, respectively, the distribution functions of the photon within the electron and of the gluon within th e proton. One has
486
cos 0 = 1 - tan 0/2 tan 0/2 1 + tan 0/2 tan 0/2 ' and g(0) is an analytically rather complicated function, steadily decreasing from~-~ 100 at 0 = 2 ° to 4 = 1 at 0 = 90 °; its detailed expression and curve is shown in ref. [2]. Finally we use the numerical values E e = 30 GeV, Ep = 800 GeV, 0emax = 10 mrad. (b): d 3 Orb) dPT d(cos 0) d(cos 0)
=Dr'tie(Z)
~
do~,q~yq [fq/p(X) + fCt/p(X)]
q=u,d,s d(cos 0)
,
where fq/p(X) (fq/p(X)) is the quark (antiquark) distribution function within the proton, and one has: d_Ovq-*vq = Oro~2/g)e4 [(cos20/2) -1 + cos20/2] , d(cos 0) everything else being defined as in (a). (c): d 3 °(c) dPTd(Cos 0) d(cos 0) f d3oeq-~eqv(0e ~ 0 °) = D q=u,d,s ~ ( a g d~cos ~ d(cos ~-e) d(c°s 0e))
X [fq/p(X) + fgl/p(X)] , where
Volume 112B, number 6
f
PHYSICS LETTERS
27 May 1982 dD /d(cose)
d3aeq-+eqT(Oe --~ 0°) d(cos Oe)
(pb)
10(
= a3eq2(0max)2(1 --Z + ½Z2)
1(
X [(zE2 cot40/2)/dp 2] [(cos20/2) -1
+ cos20/2] .
(d): d3O(d) 0.1
dPT d(cos 0) d(cos 0)
=D ~-J (fqje(Z)
doqg-->Tq~f,
u,d,s,
(X)
g/P
i
'
10
z+#
fqH(p)
=
given by (defining: p = z/y):
(a/e~r)e~
X {[p2 + (1 -- p ) 2 ] l n [ ( ¢ 2 a x + ~2)/~21 + 2 p ( 1 -- P)~//max/(~max 2 2 + ~2)}, defining ~ = p/(y - z) and calling ~max the maximal angle for the jet axis(with respect to the beam axis) of an undetected beam-pipe jet emitted in the electron direction. We here take ~max = 5° ; and, for simplicity, m u = m d = m s = 0.3 GeV (while the neglect of the charm-quark contribution is justified by the high value o f mc) , and: _~
2
50
60
70 80
functions were chosen according to the model o f Feynman and Field [6], whereas for the gluon we chose: fq/p(X) = (3/x)(1 - x ) 5 ; for the strong-coupling constant %, we chose the value: a s = 0.3. At the same time we checked that, using a scaleviolating model [7] and a running coupling constant as, the results obtained were essentially similar.
d6/dPT(pb/G~:) 10
do
40
Fig. 5. Contributions of the various diagrams of fig. 4 to do/ d(cos0) for the reaction: ep~ e3, + (high-PT) jet + X, computed (with the kinematic restrictions mentioned) according to the model described in the text. a, b, c, d e: contributions of (a), (b), (c), (d), (e). B: total background, i.e. sum of (b), (c), (d), (e). T: signal plus background, i.e. sum of (a), (b), (c), (d), (e).
fq/e(z) = f f'r/e(Y) dy y-lfqH(Z/y), mq/Ee, and fq/7
30
e(deg.)
where fq/e(Z) represents the quark distribution within an electron, obtained by convolution as follows: 1
with p =
20
,
,
,
~
i
i
l
~
i
l
3
~
5
6
7
8
9
10 11 12~3
-
q~ ~_g - (nasa/e)e q [(sin20/2) -1 + s i n 2 0 ] ,
d(cos 0)
(e): d3O(e)
0.I
dPTd(Cos 0) d(cos O) 23 = "~D q=u,d,s (fq/e(Z)
daq~?g
\
d(cos 0)
[fq/p(X) +fCt/p(X)]l/
wllere doq~_~g _
om , 0
(rrasa/~)e2(cot2~/2 + tan20/2)
•
d(cos 0) For numerical computations, based on the above formulas for processes (a)-(e), the quark distribution
PT(6eV/c) Fig. 6. Contributions of the various diagrams of fig. 4 to de/
dpT for the reaction: ep -+ e~t + (high-pT) jet + X, computed (with the kinematic restrictions mentioned) according to the model described in the text. Curves are labeled as in fig. 5. 487
Volume 112B, number 6
PHYSICS LETTERS
Integrating over cos 0 and PT (taking into account I O the constraints 0 < 30 °, 0 h 0 , PT > 3 GeV in addition to the limits z < 1, x < 1, one gets the various contributions to do/d(cos 0) shown in fig. 5. On the other hand, integrating over cos 0 and cos 6 (accounting for: 0 < 3 0 ° , 0 > 10 ° , 0 > 10°;Z < 1 , x < 1), one gets the various contributions to do/dPT shown in fig. 6. It can be seen that the contribution of diagram (a) dominates over all backgrounds taken together. One concludes that the strong enhancement o f the counting rate in the restricted kinematic range should be a clear signature for the contribution of the quark-loop diagram: As for the absolute cross section; it appears rather small; nevertheless such a measurement should be feasible with an acceptable counting rate, assuming the luminosity of the ep colliding beam machine to be of the order o f 1031-1032 cm - 2 s -1.
488
27 May 1982
One o f us (J.S.) wishes to thank the Division des Recherches et Etudes Techniques for its financial support.
References [1] [2] [3] [4]
B.L. Combridge, Nucl. Phys. B174 (1980) 243. F.N. Cahn and J.F. Gunion, Phys. Rev. D20 (1979) 2253. K. Kajantie and R. Raitio, Phys. Lett. 87B (1979) 133. C. Carimalo, M. Crozon, P. Kessler and J. Parisi, Phys. Lett. 98B (1981) 105. [5] Study on the proton-electron storage ring project HERA, ECFA ieport 80/42 (1980). [6] R.D. Field and R.P. Feynman, Phys. Rev. D15 (1977) 2590. [7] R. Baler, J. Engels and B. Peterson, Z. Phys. C2 (1972) 265.
PHYSICS LETTERS
27 May 1982
ON A POSSIBILITY OF OBSERVING ELASTIC PHOTON-GLUON SCATTERING IN ep COLLISIONS C. CARIMALO, P. KESSLER, J. PARISI 1 and J. SILVA 2 Laboratoire de Physique Corpusculaire, Collkge de France, Paris, France Received 8 July 1981
It is shown that photon gluon scatteiing via the quark-box diagram, which may be considered a critical test of higherorder quantum chromodynamics, should become a predominant and measurable effect in an experiment designed to study the reaction ep ~ e + (high-pT)-~ + (high-PT) jet + X under certain kinematic conditions at a superhigh-energy electronproton storage ring such as HERA.
As was emphasized in a recent paper by Combridge [ 1 ], the experimental observation o f contributions of the quark-loop diagram of fig. 1, where the external vector particles would be either two photons plus two gluons, or one photon plus three gluons, would provide evidence for the applicability of higher-order perturbation theory to processes involving hadrons and, in particular, o f perturbative QCD to other than simple tree-diagram subprocesses. As emphasized in ref. [1 ], those contributions should be compared to competing diagrams as shown in fig. 2, i.e. 2 7 - 2 q (as a background to 2 7 - 2 g ) or 1 7 - 1 g - 2 q (as a background to l~'-3g). It is of course to be noticed that, as far as gluons or quarks are to appear in the final state, those competing diagrams might be eliminated if some obvious criteria were available, allowing one to distinguish between quark and gluon jets. However, this is not the case at present and remains problematic for the future. The author of ref. [1] then shows that for 1 7 - 3 g subprocesses the signal to background ratio appears very small (at most a few percent), mainly because of destructive interference between different flavor loops. On the other hand, the situation appears more promising for the 23,-2g graphs. 1 Visitor at the Institute for Theoretical Physics, Stony Brook, NY, USA. 2 Also at Laboratoire de Physique des Particules, Universit~ de Picardie, Amiens, France. 484
\
/1 Fig. 1. Vector-particle scattering through a quark loop. Five additional contributing diagrams are obtained by permutations.
/
Fig. 2. Diagrams for 23,-2q or l q , - l g - 2 q subprocesses.
0 0 3 1 - 9 1 6 3 / 8 2 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © 1982 North-Holland
Volume 112B, number 6
PHYSICS LETTERS
The following 2T-2g subprocesses and corresponding experiments are to be considered: (i) T7 -+ gg, to be observed in: ee -+ (ee)gg. (ii) gg ~ 77, to be observed in: NN -+ TTX. (iii) 7g ~ Tg, to be observed in: 7N -+ 7(g)X. Where in (i) either an outgoing electron may be observed or not, and in (iii) the gluon jet may be observed or not. Reaction (i) was studied in some detail in refs. [ 1 - 3 ] , and reaction (ii) in refs. [1,4]. This paper is devoted to investigating the possibility of observing subprocess (iii). As was shown in ref. [1] comparing reactions involving (a) 7g -+ Tg and (b) 7q -+ Yq scattering, (a) may be enhanced with respect to (b) by chosing a particular kinematic configuration combining two advantages: a small value of the scaling parameter x, favouring the gluon distribution with respect to the quark distribution within the nucleon; and a small value of the photon's scattering angle 0 (in the c.m. frame), disfavouring the reaction (b) since Compton scattering is backward peaked. However, a minimum value should be fixed for PT (typically, PT ~> 3 GeV), so that one may assume that above this value it is possible to properly distinguish between direct photons and indirect ones, the latter being mainly due to 7r° production and decay. Now it appears that, with presently available photon-beam energies (E --~ 2 0 0 300 GeV), keeping PT sufficiently large, x and 0 cannot both become small enough to make (a) predominate over (b). This can be seen by using the kinematic formula (specific to photoproduction, neglecting any masses): 2PT/X/)-= X/-xsin 0. If one wishes to get a more than 100% signal to background ratio, one should keep x ~ 0.1 in order to roughly gain one order of magnitude when comparing the gluon distribution function with that of the quark, and at the same time keep 0 smaller than, let us say, 30 ° in order tomake sure that one looses less than one order of magnitude when comparing (do/d~)~,g~,rg with (da/d(2)~q__,,tq (including color and charge factors, and noticing that q should mainly be identified with the u-quark; see our formulas farther below). Accounting for PT ~ 3 GeV/c, one then concludes that one should have V ~ > 40 GeV, i.e. Ee >~ 800 GeV; in other words, one would have to wait for a particle accelerator in the TeV range.
27 May 1982
Looking out for future machinesto design this type of experiment, one should remark that it might be more promising to consider, instead of real-photon beams, the quasi-real photon flux available in an electron-proton storage ring of very high energy. In this context, the HERA project [5] (E e ~-- 30 GeV, Ep 800 GeV) should be quite appropriate, since there the upper limit of the equivalent-photon flux would be as high as 50 TeV in the proton's rest frame. On the other hand, the dissymmetry between the electron and the proton should be an important advantage in such an experiment, since it should allow the interesting photon emission angles in the laboratory frame, with respect to the electron-beam direction, to be large enough for experimental detection. Some preconditions must, however, be assumed: (i) Photon detectors should be available in the forward hemisphere with respect to the electron beam, down to a minimal emission angle of, let us say, 10° (This would be useful, as well, for other experiments, designed to study the range of very small x values.) (ii) For the sake of kinetic reconstitution of the subprocess, it should be possible to observe the jet produced together with the photon (with opposite and approxi mately equal PT) and to measure the angle of the j e t axis down to a minimal value, of let us say, 10° with respect to the proton beam. (rio In order to avoid a large background from electron bremsstrahlung and at the same time to keep the photons quasi real, it should be possible to restrict the electrons' scattering angle to very small values; this might be done by anti-tagging, i.e. by vetoing all electrons scattered at angles larger than the minimal tagging angle, which should be of the order of 10 mrad according to the project. (It may be noticed that the PLUTO Collaboration presently uses such an anti-tagging at PETRA). The corresponding kinematic scheme is shown in fig. 3. Imposing the constraint 0 < 30 ° using the kinematic relation (valid when any masses are neglected)
x
[
~
Oe,
Fig. 3. Kinetic schemefor ep ~ eq, + (high-pT)jet + X. 485
Volume 112B, number 6
PHYSICS LETTERS
Ca)
(b)
27May 1982 dz d(cos 0) dx
4PT
dPT d(cos 0) d(cos 0)
s sin20 sin 2 0
fife(Z) = (2a/rrz) {(1 - z + ½z 2) X In {(Ee/me)[(1 - z)/z]O max + 1} - ~-(1 - z)}, do~g~vg/d(cos O) = (50~rala2/81 S) g(O), where
q( c ) / ~
(d)
¢
z = (PT/2Ee)(CO.t 0/2 + tan 0[2), x = (PT/2Ep) (tan 0]2 + cot 0]2),
d = 4ZXEeE p = zxs,
(e) Fig. 4. Diagrams for various contributions to ep ~ e3' + (highPT) jet + X. (a) ep ~ e~,gX: (b) ep ~ e3'q (or ~) X (involving 3'q or q,CtCompton scattering as a subprocess); (c) ep ~ ep e.yq (or q) X (involving 3'e Compton scattering as a subprocess); (d) ep ~ e-~q~X (an additional diagram, where q and are exchanged, is implicitly included); (e) ep ~ eTqq (or q) X. tan20/2 = tan 0/2 tan 0 / 2 , a lower limit of 10 ° for both 0, 0results in an upper limit of--~ 75 ° for either of them. In addition to the main diagram of fig. 4a, various background processes, shown in figs. 4 b - 4 e , are to be considered. Figs. 4b, 4c, respectively, involve 7q a n d 3"e Compton scattering as a subprocess. In figs. 4d and 4e, where the subprocesses involved are, respectively, qg -+ 3'q (or ?qg ~ 7?t) and q?:l-+ 7g, we suppose an additional undetected beam-pipe jet to be emitted in the electron-beam direction; we shall assume that the maximal angle of the jet axis with respect to the beam axis, allowing such a jet to escape detection, would be 5 ° . For computing those diagrams, we use the following formulas (taking all particles massless wherever permitted): (a): d3o(a) = Dfy/e(Z ) d~g+3"g fg/p(X), dPT d (cos 0) d(cos 0) d(cos 0) where D is a kinematic factor, and where fv/e(Z) and fg/p(X) are, respectively, the distribution functions of the photon within the electron and of the gluon within th e proton. One has
486
cos 0 = 1 - tan 0/2 tan 0/2 1 + tan 0/2 tan 0/2 ' and g(0) is an analytically rather complicated function, steadily decreasing from~-~ 100 at 0 = 2 ° to 4 = 1 at 0 = 90 °; its detailed expression and curve is shown in ref. [2]. Finally we use the numerical values E e = 30 GeV, Ep = 800 GeV, 0emax = 10 mrad. (b): d 3 Orb) dPT d(cos 0) d(cos 0)
=Dr'tie(Z)
~
do~,q~yq [fq/p(X) + fCt/p(X)]
q=u,d,s d(cos 0)
,
where fq/p(X) (fq/p(X)) is the quark (antiquark) distribution function within the proton, and one has: d_Ovq-*vq = Oro~2/g)e4 [(cos20/2) -1 + cos20/2] , d(cos 0) everything else being defined as in (a). (c): d 3 °(c) dPTd(Cos 0) d(cos 0) f d3oeq-~eqv(0e ~ 0 °) = D q=u,d,s ~ ( a g d~cos ~ d(cos ~-e) d(c°s 0e))
X [fq/p(X) + fgl/p(X)] , where
Volume 112B, number 6
f
PHYSICS LETTERS
27 May 1982 dD /d(cose)
d3aeq-+eqT(Oe --~ 0°) d(cos Oe)
(pb)
10(
= a3eq2(0max)2(1 --Z + ½Z2)
1(
X [(zE2 cot40/2)/dp 2] [(cos20/2) -1
+ cos20/2] .
(d): d3O(d) 0.1
dPT d(cos 0) d(cos 0)
=D ~-J (fqje(Z)
doqg-->Tq~f,
u,d,s,
(X)
g/P
i
'
10
z+#
fqH(p)
=
given by (defining: p = z/y):
(a/e~r)e~
X {[p2 + (1 -- p ) 2 ] l n [ ( ¢ 2 a x + ~2)/~21 + 2 p ( 1 -- P)~//max/(~max 2 2 + ~2)}, defining ~ = p/(y - z) and calling ~max the maximal angle for the jet axis(with respect to the beam axis) of an undetected beam-pipe jet emitted in the electron direction. We here take ~max = 5° ; and, for simplicity, m u = m d = m s = 0.3 GeV (while the neglect of the charm-quark contribution is justified by the high value o f mc) , and: _~
2
50
60
70 80
functions were chosen according to the model o f Feynman and Field [6], whereas for the gluon we chose: fq/p(X) = (3/x)(1 - x ) 5 ; for the strong-coupling constant %, we chose the value: a s = 0.3. At the same time we checked that, using a scaleviolating model [7] and a running coupling constant as, the results obtained were essentially similar.
d6/dPT(pb/G~:) 10
do
40
Fig. 5. Contributions of the various diagrams of fig. 4 to do/ d(cos0) for the reaction: ep~ e3, + (high-PT) jet + X, computed (with the kinematic restrictions mentioned) according to the model described in the text. a, b, c, d e: contributions of (a), (b), (c), (d), (e). B: total background, i.e. sum of (b), (c), (d), (e). T: signal plus background, i.e. sum of (a), (b), (c), (d), (e).
fq/e(z) = f f'r/e(Y) dy y-lfqH(Z/y), mq/Ee, and fq/7
30
e(deg.)
where fq/e(Z) represents the quark distribution within an electron, obtained by convolution as follows: 1
with p =
20
,
,
,
~
i
i
l
~
i
l
3
~
5
6
7
8
9
10 11 12~3
-
q~ ~_g - (nasa/e)e q [(sin20/2) -1 + s i n 2 0 ] ,
d(cos 0)
(e): d3O(e)
0.I
dPTd(Cos 0) d(cos O) 23 = "~D q=u,d,s (fq/e(Z)
daq~?g
\
d(cos 0)
[fq/p(X) +fCt/p(X)]l/
wllere doq~_~g _
om , 0
(rrasa/~)e2(cot2~/2 + tan20/2)
•
d(cos 0) For numerical computations, based on the above formulas for processes (a)-(e), the quark distribution
PT(6eV/c) Fig. 6. Contributions of the various diagrams of fig. 4 to de/
dpT for the reaction: ep -+ e~t + (high-pT) jet + X, computed (with the kinematic restrictions mentioned) according to the model described in the text. Curves are labeled as in fig. 5. 487
Volume 112B, number 6
PHYSICS LETTERS
Integrating over cos 0 and PT (taking into account I O the constraints 0 < 30 °, 0 h 0 , PT > 3 GeV in addition to the limits z < 1, x < 1, one gets the various contributions to do/d(cos 0) shown in fig. 5. On the other hand, integrating over cos 0 and cos 6 (accounting for: 0 < 3 0 ° , 0 > 10 ° , 0 > 10°;Z < 1 , x < 1), one gets the various contributions to do/dPT shown in fig. 6. It can be seen that the contribution of diagram (a) dominates over all backgrounds taken together. One concludes that the strong enhancement o f the counting rate in the restricted kinematic range should be a clear signature for the contribution of the quark-loop diagram: As for the absolute cross section; it appears rather small; nevertheless such a measurement should be feasible with an acceptable counting rate, assuming the luminosity of the ep colliding beam machine to be of the order o f 1031-1032 cm - 2 s -1.
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27 May 1982
One o f us (J.S.) wishes to thank the Division des Recherches et Etudes Techniques for its financial support.
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B.L. Combridge, Nucl. Phys. B174 (1980) 243. F.N. Cahn and J.F. Gunion, Phys. Rev. D20 (1979) 2253. K. Kajantie and R. Raitio, Phys. Lett. 87B (1979) 133. C. Carimalo, M. Crozon, P. Kessler and J. Parisi, Phys. Lett. 98B (1981) 105. [5] Study on the proton-electron storage ring project HERA, ECFA ieport 80/42 (1980). [6] R.D. Field and R.P. Feynman, Phys. Rev. D15 (1977) 2590. [7] R. Baler, J. Engels and B. Peterson, Z. Phys. C2 (1972) 265.