- Email: [email protected]
On the possible observation of real Pomerons
14 July 1994 PHYSICS LETTERS B Physics Letters B 332 (1994) 136-140
ELSEVIER
On the possible observation of real Pomerons Peter E. Schlein 2 Umverstty of Cahforma, Los Angeles, CA 90024, USA 1 Recewed 23 April 1994 Editor: R. Gatto
Abstract Recent experimental (UA8) and phenomenological developments in Pomeron-exchange processes (diffraction) indicate that the Pomeron behaves hke a quasi-real state(s) within the proton. Observed cross sections in proton-proton collisions are a product of a Pomeron flux factor in the proton and a Pomeron-proton cross section. We compare this situation with the wellknown One-Pion-Exchange (OPE) processes, where a virtual (exchanged) pion becomes a real pion in the laboratory. In that case, observed cross sections can also be expressed as a product of a flux factor for a pion within the proton and a pion-proton cross section. In analogy with OPE, we suggest that it may be possible to produce real Pomerons in the laboratory. We suggest a number of reactions which may be used experimentally for this purpose, and discuss selection procedures and strategies.
S o m e o f the m o s t interesting and remarkable phen o m e n a in strong interaction physics occur in reactions w h i c h have b e a m - l i k e particles in the final states. O n e such reaction is:
a) Xp
p{~ p, + p ~
p f -q- X -q- charge c o n j u g a t e
(1)
w h e r e the final state " r e c o i l " proton, p f , with b e a m m o m e n t u m fraction xp > 0.9, contains the valence quarks f r o m the incident b e a m proton. Thus, the incident ~ interacts with the residual soft ( 1 - Xp) c o m p o n e n t o f the incident proton and yields the system X, w h i c h has squared invariant mass s I = s(1 - Xp) (see Fig. 1). S i n c e the 1960's [ 1], the (1 - X p ) " o b j e c t " w h i c h mediates these so-called inelastic diffraction reactions (as well as elastic scattering) has been identified as the P o m e r o n R e g g e trajectory.
1 Supported by U.S National Science Foundauon Grant PHY9303454. 2 E-mall address: [email protected] CH
',
I-Xp
b)
s
P
p
P
Fig. l. (a) The mmal state momentum vectors in the overall center-of-mass of Reaction (1) The p interacts with the soft ( l - xp ) component of the inittal state proton. The observed final state (spectator) proton has Xp > 0 9; (b) the t-channel exchange diagram version of the reaction. The ( 1 -- Xp) component of the initial state proton is labeled as the Pomeron and s ~ = s(1 - Xp).
0370-2693/94/$07 00 (~) 1994 Elsevier Science B V. All rights reserved SSDI 0370-2693 ( 94 ) 00659-U
P.E. Schlein / Physws Letters B 332 (1994) 136-140
When the momentum transfer to the proton is small, the observed (inclusive) momentum distribution is approximately described by [1] do-~d(1 - X p ) ,,, 1/( 1 -Xp). Although the most likely value of ( 1 - x p ) is near zero, at high energies the X-system which resuits from the Pomeron-p collision (for (1 - xp) < 0.1 ) can have quite large invariant mass, v/s7. Although early attempts were made [ 1,2] to extract values for the Pomeron-proton cross section from data on Reaction ( 1), only in the last decade have details of the Pomeron-proton interaction begun to emerge from experiments. It now seems that the Pomeron behaves like a quasi-real object(s) in the proton. Surprising "beam jets" are seen in the Pomeronproton rest frame in Reaction (1), both in exclusive final states [3] and inclusively [4]. These have been interpreted as evidence for Pomeron single-quark interactions, whose existence had been argued earlier by Donnachie and Landshoff [5]. Ingelman & Schlein [6] suggested that, if the Pomeron had partonic structure and s t were large enough, hard-scattering phenomena might be observable in Reaction ( 1). To calculate predictions for jet production, they took factorization literally in Reaction ( 1 ) and assumed that the observed cross section would be a product of two independent probabilities. One is the probability to find a Pomeron in a given state, the effective structure function of the Pomeron in the proton. The second is the cross section for Pomeron-proton hard scattering, whose QCD calculation requires the additional assumption that the Pomeron is a quasi-real object inside the proton with some internal structure. The hard scattering takes place between a parton in the Pomeron and a patton in the p, with a cross section trep. Using the notation of Donnachie & Landshoff [7] with ~ = 1 - Xp, the observed cross section may be written as: d2o -
d(dt = Fp/p( t, ~) O'pp,
(2)
where Fp/p (t, ~:) is the structure function (or flux factor) of the Pomeron, P, in the proton, t is the momentum transfer to the exchanged Pomeron and ~: is its momentum fraction of the beam. The subsequent observation [8,9] by experiment UA8 of jets in Reaction (1) with normal QCD properties, and with approximately the expected cross sec-
137
tion, established a partonic structure of the Pomeron and lent credibility to the quasi-real nature of the Pomeron inside a proton. The Pomeron's structure seems hard [9], like (1 - x) l, with evidence for an additional 8-function-like component. Whether the Pomeron is dominated by quarks or gluons is not yet known, although future Pomeron studies in e - p collisions at HERA [ 10,11 ] and comparison of diffractive production of bb pairs [ 12-14] and W ± or Z ° [7,15] should shed light on this question. Our best empirical knowledge of the flux factor of the Pomeron in the proton is that given by Donnachie & Landshoff [ 5 ] from their extensive studies of elastic and diffractive data: 9fl 2 ~l--2a(t)
Fp/p(t,~) = ~ 2
[Fl(t)]2
(3)
where f12 ~ 3.5 GeV -2 is the Pomeron-quark coupling, F1 (t) is the elastic form factor of the proton 3 and the Pomeron Regge trajectory is:
a(t) = 1.08 + 0.25t.
(4)
However, the true identity of the Pomeron remains a mystery, in the sense that we do not know whether it is a (virtual) manifestation of some known, or as yet undiscovered, states (perhaps they are glueballs) that lie on the Pomeron Regge trajectory. If we conjecture that this is indeed the case, how could they be observed and how could positive identifications be made? In analogy with One-Pion-Exchange (OPE) processes 4, where there is much evidence that proton scattering on virtual pions produces real pions and whose interactions look very nearly like real pionproton interactions [ 16-21], we may speculate that, under similar experimental conditions, scattering on virtual Pomerons could produce real Pomerons. This suggestion may seem surprising, given the large extrapolation from the Pomeron pole to the physical region, compared with the pion exchange case. However, the consistent evidence that Pomeron exchange dominates when no quantum numbers are exchanged, the remarkable validity of factorization and the predictability of hard scattering effects in 4m2 --28t 3 FI(/) = ~
1
(1-t/~
4 charge e x c h a n g e processes h k e p ~
momentum transfer
n or p ~
A + + , at low
138
P E Schlein/ Phystcs LettersB 332 (1994) 136-140
a)
the "~+ flux factor in the proton": d2o d(d-'--~t = 2 F~r/p( t, ~) o',~p
(6)
where, at small Itl,
n
F~r/p(t,~) = 2 × 14.6 It] ~:l 4--""-~- (t - tz2) 2 [Gl(t)]2
b)
(7)
P
,-P ~--=
}p
n,~ xn
Fig 2. (a) One-plon-exchangeprocesswith elastic ~-+p scattenng vertex, (b) the same process, but depicting the two componentsof the initial vtrtual state of the proton. The neutron with momentum fraction Xn ~s a tag for a ~r+ w~thmomentumfraction ( = 1 Xn Forward elastac scattering of the virtual ~-+ with a low momentum transfer exchange of a Pomeron ~s shown A real ~-+ emerges from that process -
-
such processes all argue that it may be useful to carry the analogy with OPE one step further and actually look for real Pomerons. During the 1960's, after Chew & Low [22] showed how measurements of scattering cross sections on unstable (virtual) targets could be obtained, extensive work was done on extrapolating measured cross sections for inclusive (charge exchange) production of neutron and A++ in p p and 7rp reactions to the onepion-exchange pole in the scattering amplitude. The Chew-Low equation for OPE in the reaction pp --~ prr+n, shown in Fig. 2 is: d2o -
2
atd----M = 4 ~ m ~
G2 Itl P~ab 4¢r (t __'~2)2 M2 a o ' ( M )
(5) where M is the invariant mass at the ~rp scattering vertex ( M = x/sT), Q is the momentum in the zrp center-of-mass, G 2 / 4 ~ = 2 × 14.6 is the pion-nucleon coupling constant at the lower vertex in Fig. 2 ( a ) , mp is the proton mass,/x is the pion mass and PLab is the beam momentum in the laboratory. The factor 2 in the numerator accounts for either beam proton being the source of the virtual pion. At high energies and large M, Eq. (5) can be rewritten as follows, using the notation of Eq. (2), to define
G l ( t ) 2 is a form factor (equal to unity at the pion pole), analogous to F1 (t) in Eq. (3). Wolf [ 16] found that G l ( t ) = (2.3 - / z 2 ) / ( 2 . 3 - t) provided rather good fits to low energy data, when used together with angular momentum barrier factors 5. As for the Pomeron case, the pion flux factor in Eq. (7) is only a property of sc and t (because sc = s'/s, there is a dependence on s only for fixed s/). In Regge language, the factor (t in Eq. (7) comes from the Regge factor [ 18,20], ~:1-2,~(/), and the propagator, 1/ (t-/.t z) 2, comes from the signature factor, because a ~ ( t ) ~ 0 at small values of t. In the OPE process of Fig. 2(a) with forward elastic ~-p scattering at the upper vertex (see Fig. 2 ( b ) ) , the virtual (exchanged) pion becomes a real pion with the low-t exchange of a Pomeron. The xn o f the final state neutron is a tag of the initial state virtual pion which has momentum fraction, ( = 1 - Xn, of the beam proton. If, in analogy with this OPE process, real Pomerons are produced in the laboratory, they would likely be unstable object(s) whose decay products are seen. The lightest of them could be a jet: = 2++ object on the Pomeron trajectory. Thus, a search for resonant structures (bumps) in invariant mass spectra and their study might reveal the Pomeron's identity. For example, Figs. 3(a,b) illustrate the following two possible processes in which real Pomerons, P, might be observed. e - p ---+ e - p ° P p ~ pp ~ pPp
e-(Tr+qr-) P p
(8) (9)
In each case, P is the produced real Pomeron which then decays. In Reaction (8), which could be studied 5 For future use, the parameters m F~r/p(t, ~) should be "finetuned" to fit more recent data
P.E Schlein / Physics Letters B 332 (1994) 136-140 a)
e e
p-
.~
L
--------- x}P
Xp
139
by the measurement o f the final state proton. The Pomeron's momentum fraction could be anywhere in the range, s¢ < 0.1, which is the domain of Pomeron dominance. A required selection on momentum transfer to the Pomeron is discussed in the following paragraph. Donnachie and Landshoff [5,7] pointed out that there is significant background to Pomeron exchange due to f 2 ( 1 2 7 0 ) exchange when its momentum transfer, Itl < 0.5 GeV 2. Thus, any resonance structure seen in the system, P, in Reactions (8) and (9) would also contain states which couple to f 2 ( 1 2 7 0 ) . Requiring Itl > 0.5 GeV 2 would remove such background. We note that kinematically in Reaction (9), as in a conventional Double-Pomeron-Exchange reaction, the energy squared of the interacting Pomeron-Pomeron system, s' = s( 1 - x l ) ( 1 - x 2 ) = ss¢ls¢2, where xl and x2 are the beam momentum fractions o f the two final state protons. Although, as discussed above, one of the x values should be near unity, the other x value need not be so large and, indeed, can be summed over, with the requirements that 1 - x < 0.1. This latter point, together with the experimental resolution on x, allows a range of s t to be observed in a given spectrum. In order to arrive at some estimate of the cross section for real Pomeron production in Reaction (9), we first note that the cross section for the DoublePomeron-Exchange process at large values of s t can be written as [23]: -
b) P
~P P~ 1 p
p,
}p
Xp Big. 3 Using the same notation as in Fig. 2(b), two possible processes are shown which may produce real Pomerons (a) e - p scattering at HERA, illustrating elastm pO scattenng on a virtual Pomeron, (b) pp scattenng, dlustrating elastic proton scattenng on a virtual Pomeron See the text for a further discussion of these processes
at the H E R A e - p collider at DESY, the electron yields a photon at low Q2 which becomes a vector meson such as a p° which, in turn, elastically scatters on the Pomeron, thereby yielding a real Pomeron in the final state. In Reaction (9), a beam proton elastically scatters on a virtual Pomeron from the other beam proton. The existence in the final-state of a single real Pomeron is a special case of the normal Double-Pomeron-Exchange reaction, which contains the Pomeron-Pomeron total cross section. As discussed below, the expected cross section for this process may be estimated without knowing the Pomeron-Pomeron cross section in the low mass resonance region. The following selection criteria should enhance real Pomeron production and suppress background: Require small momentum transfer in the elastic scattering process. This will enhance the probability that a real Pomeron alone emerges from the lower vertex of the elastic scattering. In Reaction (8), this means that the final state po vector should be close to the intermediate y vector. In Reaction (9), the upper proton would have small momentum transfer with its x near unity. - The virtual Pomeron, which experiences elastic scattering at the lower end of the processes in Figs. 3(a,b), has a momentum fraction of the incident proton described by the flux factor distribution of Eq. (3). Both s¢ and t are determined -
d4o -
d~ldqd~2dtz = F e / p ( q , ~ l ) Fp/p(tz,~2) O'pp(tOtal),
(10)
where o-pp (total) is the Pomeron-Pomeron total cross section. From factorization, it can be estimated to be about 0.2 mb [23]. Since the corresponding O-ep at small s t values (for PP --* P ) is unknown, Eq. (10) can not be used to evaluate the cross section for Reaction (9). However we note, from an examination of Fig. 3 ( b ) , that this cross section may be approximately expressed as the product of the Pomeron flux factor and the cross section for Pomeron-proton elastic scattering: d2o -
d ( d t = Fp/p (t, ~ ) tr ep (elastic).
( 11 )
140
P E. Schlem/Phystcs Letters B 332 (1994) 136-140
If we assume that o-l,p(elastic) is about 15% of o-ep (total), the cross section for Reaction (9) should be about 15% of the total pp single-diffractive cross section, which is described by Eq. ( 1 1 ) , using o-pp(total). Experiment UA8 [24] has recently obtained a value, o-pp(total) ,-, 3 mb, from measurements o f Reaction ( 1 ) using the Pomeron flux factor o f Eq. ( 3 ) . Thus, o-pp (elastic) :-, 0.5 mb can be used to evaluate Eq. ( 11 ). A complete program to isolate and identify possible states on the Pomeron Regge trajectory will require the study of different reactions, such as Eqs. (8) and ( 9 ) . The observed states should be consistently found in different reactions to which the above criteria are applied, and the observed cross sections should be in reasonable agreement with expectations. If the basic ideas discussed in this Letter are correct and the complete program o f studying states in the manner outlined here is carried out, perhaps it will be possible to finally solve the mystery o f the Pomeron's identity. Experiments WA91 and WA76 at the CERN-SPS have reported [25] evidence for a state X ( 1 9 0 0 ) with 1 ( j e c ) = 0 (2 ++) in the Double-Pomeron-Exchange reaction, Eq. ( 9 ) . Although this mass corresponds to a possible lowest mass state on the Pomeron Regge trajectory (obtained by solving Eq. (4) for t when c~(t) = 2), it would be premature to identify X ( 1 9 0 0 ) as that state. There are many tests to make; the state would have to be observed in several reactions and in other experiments and it must also survive the t cut discussed above, to suppress background from f2 (1270) exchange. Furthermore, its cross section should be compatible with Eq. ( 1 1 ) . Finally, we emphasize that, as demonstrated by Experiment UA8 [8,9], the diagrams in Figs. l ( a ) and 3 illustrate that triggering on protons with Xp > 0.9 and It] > 0.5 GeV 2 effectively defines a Pomeron beam, just as a neutron with large-xn and low t in Fig. ( 2 ) ( b ) effectively tags a beam o f virtual 7r+. The possibility o f tagging such protons at the CERN Large Hadron Collider has recently been studied by K. Eggert and A. Morsch [26] and looks very promising. In addition, the ZEUS experiment at H E R A has installed neutron counters [27] at small angles in order to study hard scattering processes with virtual pions. It is a pleasure to acknowledge several valuable discussions with Peter Landshoff.
References [1] For reviews, see e g.' K. Gouhanos, Phys Rep. 101 (1983) 169; G Albert and G Goggi, Phys. Rep. 74 (1981) 1, AB Kaidalov, Phys. Rep. 50 (1979) 157; U Amaldi, M Jacob and G. Matthiae, Ann Rev. Nucl. Sci 26 (1976) 385. [2] A.B. Kaldalov and K.A. Ter-Mamrosyan, Nucl. Phys. B 75 (1974) 471, R.L. Cool et al, Phys. Rev Lett. 47 (1981) 701 [3] A.M. Smith et al, lR608 Collaboration], Phys Lett. B 163 (1985) 267, B 167 (1986) 248 [4] A. Brandt et al, [UA8 Collaboration], Proceedings of the 1991 Joint lntemaUonal Lepton-Photon Symposium & Europhyslcs Conference on High Energy Physics, World Scientific (ed S Hegarty, K. Potter and E. Quercigh - 1992) 741; see also. PV Landshoff, 1bid., 365 [5] A Donnachle and PV Landshoff, Nucl. Phys B 244 (1984) 322, B 267 (1985) 690 [6] G Ingelman and P Schleln, Phys Lett B 152 (1985) 256 17] A Donnachleand PV Landshoff, Nucl Phys B 303 (1988) 634, Phys. Lett B 191 (1987) 309 [8] R. Bonmo et al, [UA8 Collaborataon], Phys. Lett B 211 (1988) 239 19] A Brandt et al, [UA8 Collaboration], Phys Lett B 297 (1992) 417. [10] M Derrick et al., [ZEUS Collaboration], Phys. Lett. B 315 (1993) 481, see also DESY 94-063 (April 1994). [ 11 ] H1 Collaboration, paper presented at Moriond Conference (March 1994), to be published (1994). [121 H Fritzsch and KH Streng, Phys. Lett. B 164 (1985) 391 [13] E.L. Berger et al, Nucl Phys B 286 (1987) 704 [14] K. Eggert [UA1 Collaboration] m Proc Elastic and Diffractwe Scattering - 1987, (ed K. Goulianos, Editions FronUeres, 1988) 1. [15] P. Brunl and G. Ingelman, Phys. Lett B 311 (1993) 317 [16] G Wolf, Phys Rev. Lett. 19 (1967) 925, Phys. Rev 182 (1969) 1538 [17] E Colton et al, Phys. Rev Lett. 21 (1968) 1548, Phys. Rev D 1 (1970) 373; D 2 (1970) 2108. [18] EL. Berger et al, Phys. Rev. Lett 20 (1968) 964. [19] Z. Mmg Ma et al, Phys. Rev. Lett. 23 (1969) 342 [20] E Colton et al., Phys Rev D 3 (1971) 1063. 121] GG Arakelyan, KG Boreskov and AV Turbmer, Sov J Nucl Phys. 41 (1985) 651 [22] G.F Chew and FE Low, Phys. Rev 113 (1959) 1640 [23] P Landshoff (private communication- 1994) [24] A Brandt et al, [UA8 Collaboration], to be pubhshed (1994) [251 TA. Armstrong et al., [WA76 Collaboration], Phys Lett B 228 (1989) 536; S Abatzls et al, [WA91 Collaboration], CERN/PPE 94-28 [26] K. Eggert and A. Morsch (private communication - April 1994) [27] G. Wolf (private communcatlon - 1994).
ELSEVIER
On the possible observation of real Pomerons Peter E. Schlein 2 Umverstty of Cahforma, Los Angeles, CA 90024, USA 1 Recewed 23 April 1994 Editor: R. Gatto
Abstract Recent experimental (UA8) and phenomenological developments in Pomeron-exchange processes (diffraction) indicate that the Pomeron behaves hke a quasi-real state(s) within the proton. Observed cross sections in proton-proton collisions are a product of a Pomeron flux factor in the proton and a Pomeron-proton cross section. We compare this situation with the wellknown One-Pion-Exchange (OPE) processes, where a virtual (exchanged) pion becomes a real pion in the laboratory. In that case, observed cross sections can also be expressed as a product of a flux factor for a pion within the proton and a pion-proton cross section. In analogy with OPE, we suggest that it may be possible to produce real Pomerons in the laboratory. We suggest a number of reactions which may be used experimentally for this purpose, and discuss selection procedures and strategies.
S o m e o f the m o s t interesting and remarkable phen o m e n a in strong interaction physics occur in reactions w h i c h have b e a m - l i k e particles in the final states. O n e such reaction is:
a) Xp
p{~ p, + p ~
p f -q- X -q- charge c o n j u g a t e
(1)
w h e r e the final state " r e c o i l " proton, p f , with b e a m m o m e n t u m fraction xp > 0.9, contains the valence quarks f r o m the incident b e a m proton. Thus, the incident ~ interacts with the residual soft ( 1 - Xp) c o m p o n e n t o f the incident proton and yields the system X, w h i c h has squared invariant mass s I = s(1 - Xp) (see Fig. 1). S i n c e the 1960's [ 1], the (1 - X p ) " o b j e c t " w h i c h mediates these so-called inelastic diffraction reactions (as well as elastic scattering) has been identified as the P o m e r o n R e g g e trajectory.
1 Supported by U.S National Science Foundauon Grant PHY9303454. 2 E-mall address: [email protected] CH
',
I-Xp
b)
s
P
p
P
Fig. l. (a) The mmal state momentum vectors in the overall center-of-mass of Reaction (1) The p interacts with the soft ( l - xp ) component of the inittal state proton. The observed final state (spectator) proton has Xp > 0 9; (b) the t-channel exchange diagram version of the reaction. The ( 1 -- Xp) component of the initial state proton is labeled as the Pomeron and s ~ = s(1 - Xp).
0370-2693/94/$07 00 (~) 1994 Elsevier Science B V. All rights reserved SSDI 0370-2693 ( 94 ) 00659-U
P.E. Schlein / Physws Letters B 332 (1994) 136-140
When the momentum transfer to the proton is small, the observed (inclusive) momentum distribution is approximately described by [1] do-~d(1 - X p ) ,,, 1/( 1 -Xp). Although the most likely value of ( 1 - x p ) is near zero, at high energies the X-system which resuits from the Pomeron-p collision (for (1 - xp) < 0.1 ) can have quite large invariant mass, v/s7. Although early attempts were made [ 1,2] to extract values for the Pomeron-proton cross section from data on Reaction ( 1), only in the last decade have details of the Pomeron-proton interaction begun to emerge from experiments. It now seems that the Pomeron behaves like a quasi-real object(s) in the proton. Surprising "beam jets" are seen in the Pomeronproton rest frame in Reaction (1), both in exclusive final states [3] and inclusively [4]. These have been interpreted as evidence for Pomeron single-quark interactions, whose existence had been argued earlier by Donnachie and Landshoff [5]. Ingelman & Schlein [6] suggested that, if the Pomeron had partonic structure and s t were large enough, hard-scattering phenomena might be observable in Reaction ( 1). To calculate predictions for jet production, they took factorization literally in Reaction ( 1 ) and assumed that the observed cross section would be a product of two independent probabilities. One is the probability to find a Pomeron in a given state, the effective structure function of the Pomeron in the proton. The second is the cross section for Pomeron-proton hard scattering, whose QCD calculation requires the additional assumption that the Pomeron is a quasi-real object inside the proton with some internal structure. The hard scattering takes place between a parton in the Pomeron and a patton in the p, with a cross section trep. Using the notation of Donnachie & Landshoff [7] with ~ = 1 - Xp, the observed cross section may be written as: d2o -
d(dt = Fp/p( t, ~) O'pp,
(2)
where Fp/p (t, ~:) is the structure function (or flux factor) of the Pomeron, P, in the proton, t is the momentum transfer to the exchanged Pomeron and ~: is its momentum fraction of the beam. The subsequent observation [8,9] by experiment UA8 of jets in Reaction (1) with normal QCD properties, and with approximately the expected cross sec-
137
tion, established a partonic structure of the Pomeron and lent credibility to the quasi-real nature of the Pomeron inside a proton. The Pomeron's structure seems hard [9], like (1 - x) l, with evidence for an additional 8-function-like component. Whether the Pomeron is dominated by quarks or gluons is not yet known, although future Pomeron studies in e - p collisions at HERA [ 10,11 ] and comparison of diffractive production of bb pairs [ 12-14] and W ± or Z ° [7,15] should shed light on this question. Our best empirical knowledge of the flux factor of the Pomeron in the proton is that given by Donnachie & Landshoff [ 5 ] from their extensive studies of elastic and diffractive data: 9fl 2 ~l--2a(t)
Fp/p(t,~) = ~ 2
[Fl(t)]2
(3)
where f12 ~ 3.5 GeV -2 is the Pomeron-quark coupling, F1 (t) is the elastic form factor of the proton 3 and the Pomeron Regge trajectory is:
a(t) = 1.08 + 0.25t.
(4)
However, the true identity of the Pomeron remains a mystery, in the sense that we do not know whether it is a (virtual) manifestation of some known, or as yet undiscovered, states (perhaps they are glueballs) that lie on the Pomeron Regge trajectory. If we conjecture that this is indeed the case, how could they be observed and how could positive identifications be made? In analogy with One-Pion-Exchange (OPE) processes 4, where there is much evidence that proton scattering on virtual pions produces real pions and whose interactions look very nearly like real pionproton interactions [ 16-21], we may speculate that, under similar experimental conditions, scattering on virtual Pomerons could produce real Pomerons. This suggestion may seem surprising, given the large extrapolation from the Pomeron pole to the physical region, compared with the pion exchange case. However, the consistent evidence that Pomeron exchange dominates when no quantum numbers are exchanged, the remarkable validity of factorization and the predictability of hard scattering effects in 4m2 --28t 3 FI(/) = ~
1
(1-t/~
4 charge e x c h a n g e processes h k e p ~
momentum transfer
n or p ~
A + + , at low
138
P E Schlein/ Phystcs LettersB 332 (1994) 136-140
a)
the "~+ flux factor in the proton": d2o d(d-'--~t = 2 F~r/p( t, ~) o',~p
(6)
where, at small Itl,
n
F~r/p(t,~) = 2 × 14.6 It] ~:l 4--""-~- (t - tz2) 2 [Gl(t)]2
b)
(7)
P
,-P ~--=
}p
n,~ xn
Fig 2. (a) One-plon-exchangeprocesswith elastic ~-+p scattenng vertex, (b) the same process, but depicting the two componentsof the initial vtrtual state of the proton. The neutron with momentum fraction Xn ~s a tag for a ~r+ w~thmomentumfraction ( = 1 Xn Forward elastac scattering of the virtual ~-+ with a low momentum transfer exchange of a Pomeron ~s shown A real ~-+ emerges from that process -
-
such processes all argue that it may be useful to carry the analogy with OPE one step further and actually look for real Pomerons. During the 1960's, after Chew & Low [22] showed how measurements of scattering cross sections on unstable (virtual) targets could be obtained, extensive work was done on extrapolating measured cross sections for inclusive (charge exchange) production of neutron and A++ in p p and 7rp reactions to the onepion-exchange pole in the scattering amplitude. The Chew-Low equation for OPE in the reaction pp --~ prr+n, shown in Fig. 2 is: d2o -
2
atd----M = 4 ~ m ~
G2 Itl P~ab 4¢r (t __'~2)2 M2 a o ' ( M )
(5) where M is the invariant mass at the ~rp scattering vertex ( M = x/sT), Q is the momentum in the zrp center-of-mass, G 2 / 4 ~ = 2 × 14.6 is the pion-nucleon coupling constant at the lower vertex in Fig. 2 ( a ) , mp is the proton mass,/x is the pion mass and PLab is the beam momentum in the laboratory. The factor 2 in the numerator accounts for either beam proton being the source of the virtual pion. At high energies and large M, Eq. (5) can be rewritten as follows, using the notation of Eq. (2), to define
G l ( t ) 2 is a form factor (equal to unity at the pion pole), analogous to F1 (t) in Eq. (3). Wolf [ 16] found that G l ( t ) = (2.3 - / z 2 ) / ( 2 . 3 - t) provided rather good fits to low energy data, when used together with angular momentum barrier factors 5. As for the Pomeron case, the pion flux factor in Eq. (7) is only a property of sc and t (because sc = s'/s, there is a dependence on s only for fixed s/). In Regge language, the factor (t in Eq. (7) comes from the Regge factor [ 18,20], ~:1-2,~(/), and the propagator, 1/ (t-/.t z) 2, comes from the signature factor, because a ~ ( t ) ~ 0 at small values of t. In the OPE process of Fig. 2(a) with forward elastic ~-p scattering at the upper vertex (see Fig. 2 ( b ) ) , the virtual (exchanged) pion becomes a real pion with the low-t exchange of a Pomeron. The xn o f the final state neutron is a tag of the initial state virtual pion which has momentum fraction, ( = 1 - Xn, of the beam proton. If, in analogy with this OPE process, real Pomerons are produced in the laboratory, they would likely be unstable object(s) whose decay products are seen. The lightest of them could be a jet: = 2++ object on the Pomeron trajectory. Thus, a search for resonant structures (bumps) in invariant mass spectra and their study might reveal the Pomeron's identity. For example, Figs. 3(a,b) illustrate the following two possible processes in which real Pomerons, P, might be observed. e - p ---+ e - p ° P p ~ pp ~ pPp
e-(Tr+qr-) P p
(8) (9)
In each case, P is the produced real Pomeron which then decays. In Reaction (8), which could be studied 5 For future use, the parameters m F~r/p(t, ~) should be "finetuned" to fit more recent data
P.E Schlein / Physics Letters B 332 (1994) 136-140 a)
e e
p-
.~
L
--------- x}P
Xp
139
by the measurement o f the final state proton. The Pomeron's momentum fraction could be anywhere in the range, s¢ < 0.1, which is the domain of Pomeron dominance. A required selection on momentum transfer to the Pomeron is discussed in the following paragraph. Donnachie and Landshoff [5,7] pointed out that there is significant background to Pomeron exchange due to f 2 ( 1 2 7 0 ) exchange when its momentum transfer, Itl < 0.5 GeV 2. Thus, any resonance structure seen in the system, P, in Reactions (8) and (9) would also contain states which couple to f 2 ( 1 2 7 0 ) . Requiring Itl > 0.5 GeV 2 would remove such background. We note that kinematically in Reaction (9), as in a conventional Double-Pomeron-Exchange reaction, the energy squared of the interacting Pomeron-Pomeron system, s' = s( 1 - x l ) ( 1 - x 2 ) = ss¢ls¢2, where xl and x2 are the beam momentum fractions o f the two final state protons. Although, as discussed above, one of the x values should be near unity, the other x value need not be so large and, indeed, can be summed over, with the requirements that 1 - x < 0.1. This latter point, together with the experimental resolution on x, allows a range of s t to be observed in a given spectrum. In order to arrive at some estimate of the cross section for real Pomeron production in Reaction (9), we first note that the cross section for the DoublePomeron-Exchange process at large values of s t can be written as [23]: -
b) P
~P P~ 1 p
p,
}p
Xp Big. 3 Using the same notation as in Fig. 2(b), two possible processes are shown which may produce real Pomerons (a) e - p scattering at HERA, illustrating elastm pO scattenng on a virtual Pomeron, (b) pp scattenng, dlustrating elastic proton scattenng on a virtual Pomeron See the text for a further discussion of these processes
at the H E R A e - p collider at DESY, the electron yields a photon at low Q2 which becomes a vector meson such as a p° which, in turn, elastically scatters on the Pomeron, thereby yielding a real Pomeron in the final state. In Reaction (9), a beam proton elastically scatters on a virtual Pomeron from the other beam proton. The existence in the final-state of a single real Pomeron is a special case of the normal Double-Pomeron-Exchange reaction, which contains the Pomeron-Pomeron total cross section. As discussed below, the expected cross section for this process may be estimated without knowing the Pomeron-Pomeron cross section in the low mass resonance region. The following selection criteria should enhance real Pomeron production and suppress background: Require small momentum transfer in the elastic scattering process. This will enhance the probability that a real Pomeron alone emerges from the lower vertex of the elastic scattering. In Reaction (8), this means that the final state po vector should be close to the intermediate y vector. In Reaction (9), the upper proton would have small momentum transfer with its x near unity. - The virtual Pomeron, which experiences elastic scattering at the lower end of the processes in Figs. 3(a,b), has a momentum fraction of the incident proton described by the flux factor distribution of Eq. (3). Both s¢ and t are determined -
d4o -
d~ldqd~2dtz = F e / p ( q , ~ l ) Fp/p(tz,~2) O'pp(tOtal),
(10)
where o-pp (total) is the Pomeron-Pomeron total cross section. From factorization, it can be estimated to be about 0.2 mb [23]. Since the corresponding O-ep at small s t values (for PP --* P ) is unknown, Eq. (10) can not be used to evaluate the cross section for Reaction (9). However we note, from an examination of Fig. 3 ( b ) , that this cross section may be approximately expressed as the product of the Pomeron flux factor and the cross section for Pomeron-proton elastic scattering: d2o -
d ( d t = Fp/p (t, ~ ) tr ep (elastic).
( 11 )
140
P E. Schlem/Phystcs Letters B 332 (1994) 136-140
If we assume that o-l,p(elastic) is about 15% of o-ep (total), the cross section for Reaction (9) should be about 15% of the total pp single-diffractive cross section, which is described by Eq. ( 1 1 ) , using o-pp(total). Experiment UA8 [24] has recently obtained a value, o-pp(total) ,-, 3 mb, from measurements o f Reaction ( 1 ) using the Pomeron flux factor o f Eq. ( 3 ) . Thus, o-pp (elastic) :-, 0.5 mb can be used to evaluate Eq. ( 11 ). A complete program to isolate and identify possible states on the Pomeron Regge trajectory will require the study of different reactions, such as Eqs. (8) and ( 9 ) . The observed states should be consistently found in different reactions to which the above criteria are applied, and the observed cross sections should be in reasonable agreement with expectations. If the basic ideas discussed in this Letter are correct and the complete program o f studying states in the manner outlined here is carried out, perhaps it will be possible to finally solve the mystery o f the Pomeron's identity. Experiments WA91 and WA76 at the CERN-SPS have reported [25] evidence for a state X ( 1 9 0 0 ) with 1 ( j e c ) = 0 (2 ++) in the Double-Pomeron-Exchange reaction, Eq. ( 9 ) . Although this mass corresponds to a possible lowest mass state on the Pomeron Regge trajectory (obtained by solving Eq. (4) for t when c~(t) = 2), it would be premature to identify X ( 1 9 0 0 ) as that state. There are many tests to make; the state would have to be observed in several reactions and in other experiments and it must also survive the t cut discussed above, to suppress background from f2 (1270) exchange. Furthermore, its cross section should be compatible with Eq. ( 1 1 ) . Finally, we emphasize that, as demonstrated by Experiment UA8 [8,9], the diagrams in Figs. l ( a ) and 3 illustrate that triggering on protons with Xp > 0.9 and It] > 0.5 GeV 2 effectively defines a Pomeron beam, just as a neutron with large-xn and low t in Fig. ( 2 ) ( b ) effectively tags a beam o f virtual 7r+. The possibility o f tagging such protons at the CERN Large Hadron Collider has recently been studied by K. Eggert and A. Morsch [26] and looks very promising. In addition, the ZEUS experiment at H E R A has installed neutron counters [27] at small angles in order to study hard scattering processes with virtual pions. It is a pleasure to acknowledge several valuable discussions with Peter Landshoff.
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