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Double Pomeron Exchange from the ISR to the SSC
Nuclear Physics B (Proc. Suppl.) 12 (1990) 291-302 North-Holland
291
DOUBLE POMERON EXCHANGE FROM THE ISR TO THE SSC M. G. Albrow Rutherford Appleton Laboratory, Chi!ton, Didcot, OXI 1 0QX, United Kingdom
After a general introduction to Double Pomeron Exchange I show how the existence .of the process was demonstrated at the CERlq Intersecting Storage Rings and discuss its value there as a spectroscopic tool in meson/giueball studies. At higher collision energies as now available at the Super Proton Synchrotron and Fermilab pp Colliders it would be very interesting to study hard processes in Double Pomeron Exchange and investigate Pomeron structure. The still higher Large Hadron Collider and Superconducting Super Collider energies extend the range of this physics dramatically, possibly into the electroweak sector.
I.
INTRODUCTION If the study of diffraction or Pomeron exchange is now rather on the fringe of mainstream particle physics, then Double Pomeron Exchange (DPE) is on the fringe of the fringe! Perhaps that is ~:]ly there are few who talk about it, even at a meeting of diffraction specialists such as this. Yet it seems to me that something really rather fascinating is happening, which we do not understand, and that this is a situation which is ripe for progress either theoretical or experimental or both. Imagine you are a proton, sailing along minding your own business, when suddenly you feel a soft 50 MeV or so thump. Another proton passed by, and felt the same thing. If that is aU we will call it elastic scattering, and if the kinematics is right (high relative energy and a small--but not too small--enongh thump) we will call what hit you a 'Pomeron'--which is just a name so that we can talk about it. Let this happen again and again, and measure the distribution of the 'thump', i.e. the squared four-momentum transfer, t. Then once you suddenly see, shooting away from both thumped protons and apparently having nothing to do with either, a cloud of particles that were not there before. Where did they come from? Both protons deny losing anything or even getting excited--it looks as if the vacuum itself has been shaken up. We can check that idea by trying to 'fly by' other hadrons; we can substitute either or both protons and the ~qAnething happens, the cluster properties are invariant. The cluster is also produced with a fiat rapidity distribution within a kinematically allowed range; the vacuum is Lorentz-invariant after all and this must be expected if the produced hadrons have more to do with the vacuum than with the incident hadrons. It is as if the vacuum is full of virtual hadronic states (which we s~ely knew all along!) and that these can be made real simply by providing the necessary energy-momentum through the glancing passage of two hadrons. The analogous electromagnetic process, ntaking real a virtual • + e - (for example) pair by the glancing passage of two electrically charged p0trticles, is the 'two-photon exchange process', best studied in e + e.- colliders because the hadronic processes are suppressed. The diagram showing the DPE process is shown in fig. I. I make no apology for talking about 'Pomerons' from now on almost as if they are normal particles, which they are surely not. For all I know they may be solitonie excitations in a giuon condensate, but just as solid.state physicists may discuss phonon-phonon scattering we may talk
0920-5632/90/$03.50~) Elsevier Science Publishers B.V. (North-Holland)
292
M.G. Albrow /Double Pomerou Exchange
h2
FIGURE 1 The Double Pomeron Exchange process. Incident hadrons h: and h2 collide at c.m. energy ~ , emerging unchanged with four-momentum transfer (squared) t: and tz. A neutral hadronic cluster of mass M is produced. -
about Pomeron-Pomeron collisions. It simplifies communication. Maybe it is also useful to consider that the energy-momentum transferred by a Pomeron is shared by gluun, q and ~ constituents with structure functions gp(x) and qp(x). We can make the ansatz that it/8 useful unless future experiments show inconsistencies with that formalism or a better one is developed. The formalism developed to describe the high-energy total cross-section and elastic scattering, once scaling high-mass diffractive excitation was discovered at the Intersecting Storage Rings (ISR), unambiguously predicted DPE. The experimental confirmation was a long time coming and was rather undramatic, as the evidence was built up over the years by several experiments, mostly at the ISR. It is now, I believe, irrefutable.
2. THE REGGE FORMALISM Figure 2 is a reminder of the famous optical theorem. The very existence of inelastic processes a + b --, X, where X is any coupled state, implies and relates to elastic scattering, because it can be followed by X --, a + b. One must sum over all possible states X.
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FIGURE 2 The Optical Theorem. The total cross-section of two hadrons is proportional to the imaginary part of the forward scattering amplitude
Textbook R e u e theory describes elastic scattering in terms of exchanged virtual states which have neither well-defined mass nor weiI.deflned spin; however, the latter are related through the formula al(t) = ao ÷ a't
,
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where a is the angular momentum and t is the square of the four-momentum transfer. This is the 'Regge trajectory'; when t is positive it connects mesons of similar quantum numbers but different spins, and when t is negative it describes the energy dependence of the scattering according to do 1 ~_st~(°-2 dt - ~ IAls't)lZ" F(t) - The ~(t) is basically the product of two vertex functions ~(t), s~-: fig. 3a, and is rapidly falling, roughly like e TM for high-energy pp scatterivg. Those Regge exchanges connecti'ng families of known
(a }
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FIGURE 3 a) Elastic scattering, b) Single diffractive excitation; one proton becomes a hadronic cluster of mass M mesons such as the R(770) all have a(t) < 1 for negative t ( for the ~r trajectory a0 is 0.:;) and we see from the above formula that their contribution to elastic scattering (or to the total cross-section) will drop with energy. However, there is one exchanged trajectory which apparently has ao just above 1.0, so the power of s is positive and at high energy the exchange of this will dominate the (rising) total cross-sectious and elastic scattering. This so-called Pomeron trajectory is also distinguished by having a much flatter slope a ' than the others: 0.25 GeV-z or so compared with 1 GeV-z for the meson trajectories. Regge exchanges can also be used to describe inelastic processes; in particular one can have a Pomeron exchange with excitation of one of the incident hadrons into a multiparticle state: single diffractive excitation (fig. 3b). It was discovered at t~e ISR in the early 1970's that this process extends up to high (for that era) masses M, namely 10 GeV or so, well above the baryon resonance region. One could then consider applying the optical theorem also to the Pomeron-proton total cross-section (the lower vertex in fig. 3b), relating that to elastic Pomeron-proton scattering in the forward direction (t = 0), and describing the latter also by Regge exchange. This results in the diagram of fig. 4 and the f o l l o ~ ~xpression for the cross-section: s do _ m~ ' ~ G t i k ( t ) ( s ~ a i ( O + a J O ) / ' M ~ ak(O) ~r d ~ l ' 16~s "] ~ k' ~ " ) ~ This could be shown to describe the data with (for high masses M) all three Regge lines i, j, k being Pomerons: this gives a cross-section which scales in MZ/s and has a mass dependence fike l / M z, and with a t-distribution for the quasi-elastic proton roughly e% half the elastic slope. This success impfied that one should be able to extend the diagram from fig. 4a to fig. 4b, with now five internal lines, corresponding to the physical process shown in fig. i. At high enough energies ~ a n d for Feynman x (x = PL/P~c) of the throughgoing hadrons close to 1.0, Pomeron exchange will dominate over other reneons, and we have the DPE process. The characteristics are that both incident hadrons have the t- and x-distributions characteristic of single diffractive excitation, and the
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FIGURE 4 a) The optical theorem is applied to the lower vertex of fig. 3b, relating the total Pp cross-section to the imaginary part of the Pp scattering amplitude, described again by Regge exchange. b) An extension of the diagram (a), implied by the formalism. If the exchanges i,j are Pomerons a non-zero imaginary forward scattering amplitude gives the PP total cross-section shown in fig. 1
produced hadron cloud can be at any rapidity including y = 0. One can thus have two large rapidity gaps in the *vent, and the central hadron system is then rather 'disconnected' from the incident hadrons - - in the hypothesis of factorization on which the above formalism is based it is independent of their flavour for example. By observing the central hadron system we could not tell whether the ha&on-ha&on collision was pp or ~rO! Other DPE characteristics are that the four-momentum transfers to the two incident hadrons are uncorrelated, as are their azimuthal scattering angles. Let us now consider the energy and mass ranges. If one simply measures the inclusive single p~u~icle spectrum for small-angle protons at high energies 0/sabove 20 GeV say) one sees the elastic peak at x = I, below which is the large peak of the diffractively scattered protons, falling off like I/M 2 where M z = s (I - x ) . This fall-off flattens out by about x = 0.95 merging into different contributions to the spectrum: protons that are fragments of diffractively excited clusters and simply non-diffractive events. A proton with x = 0.98 is highly likely to be coupled only to a Pomeron, which is not the case for one with x = 0.92. Let us take, as a rule-of-thumb, the limit x = 0.95, although there is nothing magic about this value. If now both incident hadrons emerge with xn and x, exceeding 0.95, the produced hadron cluster mass M is given by the relation M" = s (I - Xn) (I - xz) from which we find the upper limits on produced mass M given in Table I.
Table 1
Upper limit of mass range for DPE at hadron colliders
MlnaX
(GeV) ISR SPS
TeV I UNK LHC SSC
63 630 1800
3000 16000 400OO
(GeV) 3 30 90 150 800
2000
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There is an alternative rule of thumb which gives precisely the same result using rapidity gaps. The separation in rapidity between the two quasi-elastically scattered protons is approximately In s, where s is in GeVz. (The GeVz scale is given by the transverse mass, m" + I~, of the protons.) The central system will be appro~mately contained in a rapidity range of in M'. (This is only strictly true for particles with transverse mass of l GeV'.) If we demand two rapidity gaps exceeding 3 units to suppress non-Pomeron exchanges, i.e. colour exchanges or meson trajectories, then we have: in M2~, = ins - 6 , i.e.
.~ns- 6) Mm~
"
exp
The above mass ranges each have their own particular physics interest. The mass range up to about 3 GeV which could be studied .in this way at the ISR is very suitable for light meson spectroscopyand resonance studies, in particular for giueball searching. The mass region up to 30 or I00 GeV accessible with the existing pp coIliders corresponds to the ~rs'range where, for hadron-hadron collisions, parton scattering phenomena became clearly manifest. The DPE mass region up to 800 or 2000 GeV which could be reached at the Large Hadron CoIIider (LHC) and the Superconducting Super Collider (SSC) correspond to ~ v a l u e s where, for hadron-hadron collisions electroweak phenomena such as W and Z production become relevant. I shall discuss each of these regions in turn.
3.
LOW-MASS REGION AT FIXED-TARGET MACHINES AND THE ISR Double Pomeron Exchange can be thought of as 'diffractive excitation of the vacuum'. Any virtual hadron states "-'nthe vacuum can be made real by the glancing collision of the two incident hadrons, coupling via the two Pomerons. There is an important constraint on the quantum numbers allowed for such states, which must be: IOJPc = 0+0 + + , 0+2 + + , . . . , 0 + e v e n + +
.
One would therefore expect to be able to produce by this technique any giueball states with these quantum numbers. The 'quantum number f'dter' and the isolation from other hadrons are extremely useful features. The possibility that the Pomeron is predominantly giuonic may help. Experiments at the ISR in the late 1970's demonstrated many of the features of DPE [I-5] but at least in the lower part of the ISR energy range (~/~ < 30 GeV) the presence of Q, ~, and Az signals showed [6] a sizeable contamination of non..DPE. The first use of this reaction to search for giuebalis by Waldi, Schubert and Winter [7] using data from the Split Field Magnet (SFIVl),saw a clear f(1270j signal, but was rather limited in statistics (2264 w + = - events at ~/s > 53 GeV). We used the Axial Field Spectrometer (AFS) to obtain [8] a much higher statistics sample (10s ~r+ ~r- events at ~ = 63 GeV) with better mass resolution [o(M) = I0 MeV at I GeV]. The AFS was built for high transverse momentum (jet) physics; the DPE work was carried out parasitically. We added small high.precision drift chambers above and below the downstream beam-pipes. The distribution of Feynman-x for the two forward protons in the final sample peaks at x = 0.995, and 99.$% of the events have both protons above x = 0.95 (and two rapidity gaps exceeding 3). This should be almost pure DPE. The mass spectrum of the w+ w- pair is shown on a log scale in fig. $ and one sees no sign of the Q(770), which is a good monitor of the purity of the sample in terms of quantum numbers.
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Exclusive ~r'~ -
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FIGURE 5 Pion-pair spectrum from the AFS DPE experiment (~/'s"= 63 GeV) A very nice confirmation of the DPE phenomenon was provided when two beams of a-particles were collided in the ISR at ~ ffi 126 GeV, and we recorded events with both a.particles scattered (without dissociation) through a few mrad and~a-central w pair produced. Although only a few hundred events were obtained, the mass spectrum appearsTdentical to that from pp collisions at ~" ffi 63 GeV. This is shown in fig. 6. Other tests done in pp were to decrease ~ and to change the azimuthal scattering angle /,~ between the protons between 0 ° and 180°; no differences were observed.
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The most striking feature of the ~r+ g - mass distribution in fig. 5 is the dramatic drop near 1 GeV, demonstrably pure S-wave and caused by the old S*(980)--now fo(975). Resonances are not always bumps! We also had K +K- data from threshold to about 1350 MeV, enabling a coupled channel analysis to be carried out by Au, Morgan and Pennington [9]. Their analysis leads to the conclusion that the S" is really a pair of close and narrow states: St(991) which couples similarly to wT and KK and $2(988) which couples mainly to K K. Together with the broad S-wave resonances e(900) and e(1430) this is one too many for simple q~l dynamics. The additional degrees of freedom could come from giuons (glueball component?) or extra quarks, i.e. perhaps we have here a KK molecule (qqq~. Although the technique of DPE as a quantum number rflter for meson spectroscopy is now proven to be valuable we still have all these questions left unresolved. Further progress could be made with higher statistics K + K - data, with K~K] data as well as (very interesting!) ~tl and ~ spectra. I have no doubt that high-quality data on these exclusive DPE channels would be most valuable. This could be done at pp colliders; however in practice the big experiments do not want to put much time and effort into physics at the 1 GeV mass scale. There is a case for a smaller-scale experiment (e.g. Crystal Ball with forward spectrometers [10]) for this type of physics. It is also carried out at lower energies at the CERN Omega Spectrometer by experiment WA76 [11]. I show in fig. 7 their K ~ e spectrum adding data at 85 GeV/c and 300 GeV/c, and the ~h spectrum at 300 GeV/c ( ~ = 23.8 OeV). The ;~ch structure is obvious. The cross-section for exclusive central hh production in pp is quoted as 21 + 9 nb at 85 GeV/c and 18 =~. 6 nb at 300 GeV/c. If this is DPE-do,"=" ated, and hence stays up with energy and is equal in pp, it would mean that a 5 pb- t expe6ment at our colliders could collect l0 s ~h events. With such a small value of M'/~i'one could demand rapidity gaps Ay exceeding say 4 units to reduce the non-DPE background to negligible levels, and also do a partial wave analysis to unravel the spin ~ t e s . However at the Super Proton Synchrotron (SPS) fixed-target energies it is clear that other production mechanisms are important, as evidenced, for example, by a single ~ signal in the exclusive K + K - channel.
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Exclusive baryon pair production is also seen in DPE, but until now ~ : h small statistics, for example the AFS Collaboration show [8] 64 events with central pp production. It would be interesting to measure also hyperon-pair production with one, two, or three strange quark pairs. It might turn out that it is easier to produce hadrons containing more than one 'heavy' quark than in the comparable two-photon production processes e+e - -* e+e - Y Y, if the Pomeron behaves as a multi-giuon system so that gg -* Q Q can occur more than once in DPE. In this case DPE could be [12,13] a useful hunting ground for such exotic hadrons as b~ and bbc, particles which may be impossible to make and detect under any, circumstances. The idea (fig. 8) is that both Q's may be
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FIGURE 8 Possible mechanism for heavy-meson Q Q production by DPE
produced by hard processes rather than soft 'string fracture', and that the Pomeron may have a small effective size with hardish giuons close together. Donnachie and Landshoff [14] claim that the Pomeron behaves as if it couples to a single quark, like an isoscalar photon, but that may not be the case for a close pair of heavy quarks. In any case at s o m e level pairs of virtual B© mesons will be present in the vacuum, as are ~r pairs. That of course does not mean that their production will be at a detectable level! This discussion is relevant not for ISR energies but for the colliders. Making v~.rious, perhaps optimistic, assumptions Streng [13] found, for example, that at the SPS pp Collider, V~"= 630 GeV, DPE to cc~ may t)e 8-10 nb, and about half of the c~ pairs would form a charmonlum state. In the run just finished with 5 pb- t there would be some 100 DPE events with two '4' in e+e - or/z+/~ channels! (Neither UAI nor UA2 trigger on such events, however.) Similarly at ~/s = 2 TeV the cross-section for DPE -* b[g~ coulu be about 2 nb (10,000 events per year) of which 5% may be '4' + 'T' and 5% may have Bc. Figure 9 shows calculations of the PP -* 4Q cross-sections which may be compared with a total PP cross-section estimated to be 140/zb. Certainly these estimates may be very optimistic, but it would be interesting to find out! We may expect that a comparison between the central hadronic system produced in DPE and in the analogous two-photon production reaction studied in e +e- machines would be instructive. There are clear differences in the low-mass region studied up to now, a good example being that a ~r+~r+ ~r-~r- system is predominantly QQ when produced by 7~, but this is only a 15% contribution in DPE [8]. Also only I = 0 states can be produced in DPE, a restriction not holding in 7"f, the "v-coupling is proportional to the quark charges, and so on. For higher mass systems (for e +e" these will become accessible at LEP) will the topological features of the hadmnic systems differ in a way that will reveal Pomeron structures? I discuss this in the following section.
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FIGURE 9 Calculations [13] of the cross-scction for PP --~ 4Q, as a function of the total central energy M.~ -The two curves show different guesses for the giuon distribution in P
4.
DPE AT COLLIDER ENERGIES Historically the most important tool used in unravelling the structure of the proton was of course deep-inelastic lepton scattering. We were able to measure rather directly the q and q distributions, and indirectly, using the 'theory of evolution', also the gi~on ~ b - ~ o n s : Just suppose lepton beams did not existt Life would certainly have been a lot harder, but we could eventually have extracted the same information from just proton-proton (and proton-antiproton) comsions. Drd-Yan pairs of muons and electrons provide a measurement of the product of the q and q structure function. Jet pairs allow one to measure an effective structure function such as S(x) + 4/9 [q(x) + q(x)]. Direct high-pr photon-jet pairs give further constraints, being sensitive to a different mix of constituents. A systematic programme of such measurements would have taught us the q, ~I, and g structure of p and p, albeit more painfully. I suggest that a similar programme in central hadron systems produced by DPE would e l t h u teach us the structure of the Pomeron in terms of quarks and giuons or reveal inconsistencies teacbi_ng us that this way of thinking is too naive. One can also consider other routes to lenmins~ the Pomeron structure, and I do not claim that DPE studies are unique or even necessarily the best; we need all the tools we can setl One method [I$] which is potentially clean and is made possible by the advent of our first el) coIlider, the Hadron Electron Ring Accelerator, (HERA) is to measure -/P collisions with deep.inelastic elc.~.ron scattering.
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These are events with quasi-elastically scattered e and p with central hadron production. The process is a hybrid between DPE in pp and 77 in e +e - , and was discussed by C. Peroni at this conference. Another method advocated by Ingelmann and Sehlein [16] is to study single diffractive excitation of high-mass systems and compare them with final states from pp colHsions at ~ = M; the comparison between Pp and pp should reveal P / p differences, and we already know the proton structure. This has the advantages of having existing data, a higher cross-section and higher available masses, only one large rapidity gap being needed rather than two. Despite the different advantages of these other methods, the sym_metry of the PP initial state in DPE is a nice feature. Observing Drell-Yan # +# - pairs would be a sure sign of q and q content, which could then be measured by simple deconvolution. (A picture of Pomerons as purely gluonic is surely unphysical, as q's and q's must evolve at QZ > 0.) The mass spectrum up to 12-15 GeV is of course particularly rich in structure with the J / ~ family and the T family--perhaps their signal: continuum ratio is enhanced compared with normal hadron colHsions, from gg -~ T + anything. One may need of the order of 10s DPE events with mass M exceeding 20 GeV or so to start this game. An efficient run at the Fermilab Collider with I0 pb- i should allow this. A related subject with higher cross-sections is that of soft real photon production (Pr < 200 MeV/c or so) and low-mass e +epairs, which are not well understood in hadron-hadron colHsions. The study of jets and event topology in DPE requires special care, because psendorapidity gap triggers cause a strong bias. In the view of the Pomeron as a multiconstituent object, a typical high-pr jet DPE event will also have 'beam fragment jets' along the t-channel axis and will thus have four jets altogether. Some hadrons will go in the beam direction. The distinction between true rapidity y and pseudorapidity ~ is important here. At Fcrmilab with 900 GeV beams the beam particle rapidity is 7.6. A 5 GeV pion at 0 ° has y = 4.3 and is thus more than 3 units of y from the diffractively scattered p, even though vl = oo. Topoiogy studies should thus not use T-gap triggers but rather y-gap selection, or more easily measure both scattered beam particles and select x > 0.95. Having done that, do we see: i) Predominantly 'beam jets', as in typical inelastic hadron-hadron colHsions? ii) Plus the emergence of two high-l>r jets--which we can use to measure effective structure functions--or rather only the two high-pT jets as one sees in ?~, colHsions? iii) Sometimesthree high-pr jets (no doubtl)? iv) Sometimes four--as can F,e ~nade either by double gluon bremsstrahlung or double parton scattering (DPS) with two 2 --* 2 processes. If the latter can be seen and separated it allows a me~.surement of the effective transverse size of the Pomeron. From the smallness of the total Pomeron-Pomeron cross-section We may expect an enhanced (DPS) four-jet fraction (unless it is due to transparency rather than size, which seems unlikely). This study in DPE probably requires high statistics with central masses of the order of I00 GeV or more, so may have to wait for future coHiders. The large collider experiments naturally concentrate on the electroweak and hard scattering phenomena and have not yet seriously attempted to look at this physics, although (or rather becansel) the cross-sections are quite large. Perhaps this will change.
5.
THE I~JTURE SUPER COLLIDERS
Given that we have not yet studied DPE at ~'above 100 GeV it is certainly very presumptious to even think of it at the much higher LHC and SSC energies of the future. So this section will be short. However~ let us risk another wild speculation. At the SSC with both protons above x = 0.95 we are able to stretch DPE masses up to 2000 GeV, well into the electroweak sector and in fact just where we
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are now for pp collisions at Fermilab. Of course single W and Z production would be interesting to measure, as a high-mass Drell-Yan type process. Much more dramatic is a prediction [17] of dkect and strong W + W - and Z°Z° production by Pomerons in Alan White's Critical Pomeron theory. Here with two flavours of colour sextet quarks q6 in addition to the normal six flavours of colour triplet quarks, we have the pair-production diagrams shown in fig. 10a, just like DPE ~r pair-production in the old days (fig. 10b). Just as that was a clean source of information on lnr
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scattering, through final-state interactions, allowing glueball searches etc., so this, if true, would be a clean source of information on WW and ZZ scattering phase shifts, etc. Maybe this is how the strongly interacting systems of Intermediate Vector Bosons (IVBs) above I TeV will be studied:
I should llke to thank Alan White and the other organizers of this very enjoyable meeting.
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REFERENCES 1) M. Della Negra et al., Phys. Lett. 65B (1976) 394. 2) L. Baksay et al., Phys. Lett. 61B (1976) 89. 3) H. DeKerret et al., Phys. Lett. 68B (1977) 385. 4) D. Drijard et al., Nucl. Phys. B143 (1978) 61. 5) J.C.M. Armitage et al., Phys. Lett. 82B (1979) 149. 6) J. Timmer, Ph.D. Thesis, Univ. Utrecht (1978). 7) R. Waldi, K.R. Schubert and K. Winter, Z. Phys. C18 (1983) 301. 8) T..~kesson et al. (AFS Collaboration), Nucl. Phys. B264 (1986) 154. 9) K.L. Au, D. Morgan and M.R. Pennington, Phys. Rev. D35 (1987) 1633. 10) P. Schlein, private communications. 11) T.A. Armstrong et al., Phys. Lett. 221B (1989) 221; preprint CERN-EP/89-22 (submitted to Phys. Lett. 13). 12) M.G. Albrow, Talk presented at the Workshop on Physics in the 90's at the SPS Collider, Zinal, June 1985. 13) K.H. Streng, Phys. Lett. B 166 (1986) 443 ; Phys. Lett. BITI (1986) 313. 14) A. Donnachie and P.V. Lr.tndshoff, Nucl. Phys. B244 (1984) 322. A. Donnachie and P.V. Landshoff, Nucl. Phys. B267 (1985) 690. 15) A. Donnachie and P.V. Landshoff, Phys. Lett. BI91 (1987) 309. 16) G. lngelmann and P. Schlein, Phys. Lett. 15213(1985) 256. 17) A.R. White, in Hadronic Multiparticle Production, ed. P. Carruthers (World Scientific, Singapore, 1988), p. 351 and talk at this conference.
291
DOUBLE POMERON EXCHANGE FROM THE ISR TO THE SSC M. G. Albrow Rutherford Appleton Laboratory, Chi!ton, Didcot, OXI 1 0QX, United Kingdom
After a general introduction to Double Pomeron Exchange I show how the existence .of the process was demonstrated at the CERlq Intersecting Storage Rings and discuss its value there as a spectroscopic tool in meson/giueball studies. At higher collision energies as now available at the Super Proton Synchrotron and Fermilab pp Colliders it would be very interesting to study hard processes in Double Pomeron Exchange and investigate Pomeron structure. The still higher Large Hadron Collider and Superconducting Super Collider energies extend the range of this physics dramatically, possibly into the electroweak sector.
I.
INTRODUCTION If the study of diffraction or Pomeron exchange is now rather on the fringe of mainstream particle physics, then Double Pomeron Exchange (DPE) is on the fringe of the fringe! Perhaps that is ~:]ly there are few who talk about it, even at a meeting of diffraction specialists such as this. Yet it seems to me that something really rather fascinating is happening, which we do not understand, and that this is a situation which is ripe for progress either theoretical or experimental or both. Imagine you are a proton, sailing along minding your own business, when suddenly you feel a soft 50 MeV or so thump. Another proton passed by, and felt the same thing. If that is aU we will call it elastic scattering, and if the kinematics is right (high relative energy and a small--but not too small--enongh thump) we will call what hit you a 'Pomeron'--which is just a name so that we can talk about it. Let this happen again and again, and measure the distribution of the 'thump', i.e. the squared four-momentum transfer, t. Then once you suddenly see, shooting away from both thumped protons and apparently having nothing to do with either, a cloud of particles that were not there before. Where did they come from? Both protons deny losing anything or even getting excited--it looks as if the vacuum itself has been shaken up. We can check that idea by trying to 'fly by' other hadrons; we can substitute either or both protons and the ~qAnething happens, the cluster properties are invariant. The cluster is also produced with a fiat rapidity distribution within a kinematically allowed range; the vacuum is Lorentz-invariant after all and this must be expected if the produced hadrons have more to do with the vacuum than with the incident hadrons. It is as if the vacuum is full of virtual hadronic states (which we s~ely knew all along!) and that these can be made real simply by providing the necessary energy-momentum through the glancing passage of two hadrons. The analogous electromagnetic process, ntaking real a virtual • + e - (for example) pair by the glancing passage of two electrically charged p0trticles, is the 'two-photon exchange process', best studied in e + e.- colliders because the hadronic processes are suppressed. The diagram showing the DPE process is shown in fig. I. I make no apology for talking about 'Pomerons' from now on almost as if they are normal particles, which they are surely not. For all I know they may be solitonie excitations in a giuon condensate, but just as solid.state physicists may discuss phonon-phonon scattering we may talk
0920-5632/90/$03.50~) Elsevier Science Publishers B.V. (North-Holland)
292
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FIGURE 1 The Double Pomeron Exchange process. Incident hadrons h: and h2 collide at c.m. energy ~ , emerging unchanged with four-momentum transfer (squared) t: and tz. A neutral hadronic cluster of mass M is produced. -
about Pomeron-Pomeron collisions. It simplifies communication. Maybe it is also useful to consider that the energy-momentum transferred by a Pomeron is shared by gluun, q and ~ constituents with structure functions gp(x) and qp(x). We can make the ansatz that it/8 useful unless future experiments show inconsistencies with that formalism or a better one is developed. The formalism developed to describe the high-energy total cross-section and elastic scattering, once scaling high-mass diffractive excitation was discovered at the Intersecting Storage Rings (ISR), unambiguously predicted DPE. The experimental confirmation was a long time coming and was rather undramatic, as the evidence was built up over the years by several experiments, mostly at the ISR. It is now, I believe, irrefutable.
2. THE REGGE FORMALISM Figure 2 is a reminder of the famous optical theorem. The very existence of inelastic processes a + b --, X, where X is any coupled state, implies and relates to elastic scattering, because it can be followed by X --, a + b. One must sum over all possible states X.
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FIGURE 2 The Optical Theorem. The total cross-section of two hadrons is proportional to the imaginary part of the forward scattering amplitude
Textbook R e u e theory describes elastic scattering in terms of exchanged virtual states which have neither well-defined mass nor weiI.deflned spin; however, the latter are related through the formula al(t) = ao ÷ a't
,
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where a is the angular momentum and t is the square of the four-momentum transfer. This is the 'Regge trajectory'; when t is positive it connects mesons of similar quantum numbers but different spins, and when t is negative it describes the energy dependence of the scattering according to do 1 ~_st~(°-2 dt - ~ IAls't)lZ" F(t) - The ~(t) is basically the product of two vertex functions ~(t), s~-: fig. 3a, and is rapidly falling, roughly like e TM for high-energy pp scatterivg. Those Regge exchanges connecti'ng families of known
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FIGURE 3 a) Elastic scattering, b) Single diffractive excitation; one proton becomes a hadronic cluster of mass M mesons such as the R(770) all have a(t) < 1 for negative t ( for the ~r trajectory a0 is 0.:;) and we see from the above formula that their contribution to elastic scattering (or to the total cross-section) will drop with energy. However, there is one exchanged trajectory which apparently has ao just above 1.0, so the power of s is positive and at high energy the exchange of this will dominate the (rising) total cross-sectious and elastic scattering. This so-called Pomeron trajectory is also distinguished by having a much flatter slope a ' than the others: 0.25 GeV-z or so compared with 1 GeV-z for the meson trajectories. Regge exchanges can also be used to describe inelastic processes; in particular one can have a Pomeron exchange with excitation of one of the incident hadrons into a multiparticle state: single diffractive excitation (fig. 3b). It was discovered at t~e ISR in the early 1970's that this process extends up to high (for that era) masses M, namely 10 GeV or so, well above the baryon resonance region. One could then consider applying the optical theorem also to the Pomeron-proton total cross-section (the lower vertex in fig. 3b), relating that to elastic Pomeron-proton scattering in the forward direction (t = 0), and describing the latter also by Regge exchange. This results in the diagram of fig. 4 and the f o l l o ~ ~xpression for the cross-section: s do _ m~ ' ~ G t i k ( t ) ( s ~ a i ( O + a J O ) / ' M ~ ak(O) ~r d ~ l ' 16~s "] ~ k' ~ " ) ~ This could be shown to describe the data with (for high masses M) all three Regge lines i, j, k being Pomerons: this gives a cross-section which scales in MZ/s and has a mass dependence fike l / M z, and with a t-distribution for the quasi-elastic proton roughly e% half the elastic slope. This success impfied that one should be able to extend the diagram from fig. 4a to fig. 4b, with now five internal lines, corresponding to the physical process shown in fig. i. At high enough energies ~ a n d for Feynman x (x = PL/P~c) of the throughgoing hadrons close to 1.0, Pomeron exchange will dominate over other reneons, and we have the DPE process. The characteristics are that both incident hadrons have the t- and x-distributions characteristic of single diffractive excitation, and the
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FIGURE 4 a) The optical theorem is applied to the lower vertex of fig. 3b, relating the total Pp cross-section to the imaginary part of the Pp scattering amplitude, described again by Regge exchange. b) An extension of the diagram (a), implied by the formalism. If the exchanges i,j are Pomerons a non-zero imaginary forward scattering amplitude gives the PP total cross-section shown in fig. 1
produced hadron cloud can be at any rapidity including y = 0. One can thus have two large rapidity gaps in the *vent, and the central hadron system is then rather 'disconnected' from the incident hadrons - - in the hypothesis of factorization on which the above formalism is based it is independent of their flavour for example. By observing the central hadron system we could not tell whether the ha&on-ha&on collision was pp or ~rO! Other DPE characteristics are that the four-momentum transfers to the two incident hadrons are uncorrelated, as are their azimuthal scattering angles. Let us now consider the energy and mass ranges. If one simply measures the inclusive single p~u~icle spectrum for small-angle protons at high energies 0/sabove 20 GeV say) one sees the elastic peak at x = I, below which is the large peak of the diffractively scattered protons, falling off like I/M 2 where M z = s (I - x ) . This fall-off flattens out by about x = 0.95 merging into different contributions to the spectrum: protons that are fragments of diffractively excited clusters and simply non-diffractive events. A proton with x = 0.98 is highly likely to be coupled only to a Pomeron, which is not the case for one with x = 0.92. Let us take, as a rule-of-thumb, the limit x = 0.95, although there is nothing magic about this value. If now both incident hadrons emerge with xn and x, exceeding 0.95, the produced hadron cluster mass M is given by the relation M" = s (I - Xn) (I - xz) from which we find the upper limits on produced mass M given in Table I.
Table 1
Upper limit of mass range for DPE at hadron colliders
MlnaX
(GeV) ISR SPS
TeV I UNK LHC SSC
63 630 1800
3000 16000 400OO
(GeV) 3 30 90 150 800
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There is an alternative rule of thumb which gives precisely the same result using rapidity gaps. The separation in rapidity between the two quasi-elastically scattered protons is approximately In s, where s is in GeVz. (The GeVz scale is given by the transverse mass, m" + I~, of the protons.) The central system will be appro~mately contained in a rapidity range of in M'. (This is only strictly true for particles with transverse mass of l GeV'.) If we demand two rapidity gaps exceeding 3 units to suppress non-Pomeron exchanges, i.e. colour exchanges or meson trajectories, then we have: in M2~, = ins - 6 , i.e.
.~ns- 6) Mm~
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The above mass ranges each have their own particular physics interest. The mass range up to about 3 GeV which could be studied .in this way at the ISR is very suitable for light meson spectroscopyand resonance studies, in particular for giueball searching. The mass region up to 30 or I00 GeV accessible with the existing pp coIliders corresponds to the ~rs'range where, for hadron-hadron collisions, parton scattering phenomena became clearly manifest. The DPE mass region up to 800 or 2000 GeV which could be reached at the Large Hadron CoIIider (LHC) and the Superconducting Super Collider (SSC) correspond to ~ v a l u e s where, for hadron-hadron collisions electroweak phenomena such as W and Z production become relevant. I shall discuss each of these regions in turn.
3.
LOW-MASS REGION AT FIXED-TARGET MACHINES AND THE ISR Double Pomeron Exchange can be thought of as 'diffractive excitation of the vacuum'. Any virtual hadron states "-'nthe vacuum can be made real by the glancing collision of the two incident hadrons, coupling via the two Pomerons. There is an important constraint on the quantum numbers allowed for such states, which must be: IOJPc = 0+0 + + , 0+2 + + , . . . , 0 + e v e n + +
.
One would therefore expect to be able to produce by this technique any giueball states with these quantum numbers. The 'quantum number f'dter' and the isolation from other hadrons are extremely useful features. The possibility that the Pomeron is predominantly giuonic may help. Experiments at the ISR in the late 1970's demonstrated many of the features of DPE [I-5] but at least in the lower part of the ISR energy range (~/~ < 30 GeV) the presence of Q, ~, and Az signals showed [6] a sizeable contamination of non..DPE. The first use of this reaction to search for giuebalis by Waldi, Schubert and Winter [7] using data from the Split Field Magnet (SFIVl),saw a clear f(1270j signal, but was rather limited in statistics (2264 w + = - events at ~/s > 53 GeV). We used the Axial Field Spectrometer (AFS) to obtain [8] a much higher statistics sample (10s ~r+ ~r- events at ~ = 63 GeV) with better mass resolution [o(M) = I0 MeV at I GeV]. The AFS was built for high transverse momentum (jet) physics; the DPE work was carried out parasitically. We added small high.precision drift chambers above and below the downstream beam-pipes. The distribution of Feynman-x for the two forward protons in the final sample peaks at x = 0.995, and 99.$% of the events have both protons above x = 0.95 (and two rapidity gaps exceeding 3). This should be almost pure DPE. The mass spectrum of the w+ w- pair is shown on a log scale in fig. $ and one sees no sign of the Q(770), which is a good monitor of the purity of the sample in terms of quantum numbers.
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Exclusive ~r'~ -
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FIGURE 5 Pion-pair spectrum from the AFS DPE experiment (~/'s"= 63 GeV) A very nice confirmation of the DPE phenomenon was provided when two beams of a-particles were collided in the ISR at ~ ffi 126 GeV, and we recorded events with both a.particles scattered (without dissociation) through a few mrad and~a-central w pair produced. Although only a few hundred events were obtained, the mass spectrum appearsTdentical to that from pp collisions at ~" ffi 63 GeV. This is shown in fig. 6. Other tests done in pp were to decrease ~ and to change the azimuthal scattering angle /,~ between the protons between 0 ° and 180°; no differences were observed.
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The most striking feature of the ~r+ g - mass distribution in fig. 5 is the dramatic drop near 1 GeV, demonstrably pure S-wave and caused by the old S*(980)--now fo(975). Resonances are not always bumps! We also had K +K- data from threshold to about 1350 MeV, enabling a coupled channel analysis to be carried out by Au, Morgan and Pennington [9]. Their analysis leads to the conclusion that the S" is really a pair of close and narrow states: St(991) which couples similarly to wT and KK and $2(988) which couples mainly to K K. Together with the broad S-wave resonances e(900) and e(1430) this is one too many for simple q~l dynamics. The additional degrees of freedom could come from giuons (glueball component?) or extra quarks, i.e. perhaps we have here a KK molecule (qqq~. Although the technique of DPE as a quantum number rflter for meson spectroscopy is now proven to be valuable we still have all these questions left unresolved. Further progress could be made with higher statistics K + K - data, with K~K] data as well as (very interesting!) ~tl and ~ spectra. I have no doubt that high-quality data on these exclusive DPE channels would be most valuable. This could be done at pp colliders; however in practice the big experiments do not want to put much time and effort into physics at the 1 GeV mass scale. There is a case for a smaller-scale experiment (e.g. Crystal Ball with forward spectrometers [10]) for this type of physics. It is also carried out at lower energies at the CERN Omega Spectrometer by experiment WA76 [11]. I show in fig. 7 their K ~ e spectrum adding data at 85 GeV/c and 300 GeV/c, and the ~h spectrum at 300 GeV/c ( ~ = 23.8 OeV). The ;~ch structure is obvious. The cross-section for exclusive central hh production in pp is quoted as 21 + 9 nb at 85 GeV/c and 18 =~. 6 nb at 300 GeV/c. If this is DPE-do,"=" ated, and hence stays up with energy and is equal in pp, it would mean that a 5 pb- t expe6ment at our colliders could collect l0 s ~h events. With such a small value of M'/~i'one could demand rapidity gaps Ay exceeding say 4 units to reduce the non-DPE background to negligible levels, and also do a partial wave analysis to unravel the spin ~ t e s . However at the Super Proton Synchrotron (SPS) fixed-target energies it is clear that other production mechanisms are important, as evidenced, for example, by a single ~ signal in the exclusive K + K - channel.
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Exclusive baryon pair production is also seen in DPE, but until now ~ : h small statistics, for example the AFS Collaboration show [8] 64 events with central pp production. It would be interesting to measure also hyperon-pair production with one, two, or three strange quark pairs. It might turn out that it is easier to produce hadrons containing more than one 'heavy' quark than in the comparable two-photon production processes e+e - -* e+e - Y Y, if the Pomeron behaves as a multi-giuon system so that gg -* Q Q can occur more than once in DPE. In this case DPE could be [12,13] a useful hunting ground for such exotic hadrons as b~ and bbc, particles which may be impossible to make and detect under any, circumstances. The idea (fig. 8) is that both Q's may be
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FIGURE 8 Possible mechanism for heavy-meson Q Q production by DPE
produced by hard processes rather than soft 'string fracture', and that the Pomeron may have a small effective size with hardish giuons close together. Donnachie and Landshoff [14] claim that the Pomeron behaves as if it couples to a single quark, like an isoscalar photon, but that may not be the case for a close pair of heavy quarks. In any case at s o m e level pairs of virtual B© mesons will be present in the vacuum, as are ~r pairs. That of course does not mean that their production will be at a detectable level! This discussion is relevant not for ISR energies but for the colliders. Making v~.rious, perhaps optimistic, assumptions Streng [13] found, for example, that at the SPS pp Collider, V~"= 630 GeV, DPE to cc~ may t)e 8-10 nb, and about half of the c~ pairs would form a charmonlum state. In the run just finished with 5 pb- t there would be some 100 DPE events with two '4' in e+e - or/z+/~ channels! (Neither UAI nor UA2 trigger on such events, however.) Similarly at ~/s = 2 TeV the cross-section for DPE -* b[g~ coulu be about 2 nb (10,000 events per year) of which 5% may be '4' + 'T' and 5% may have Bc. Figure 9 shows calculations of the PP -* 4Q cross-sections which may be compared with a total PP cross-section estimated to be 140/zb. Certainly these estimates may be very optimistic, but it would be interesting to find out! We may expect that a comparison between the central hadronic system produced in DPE and in the analogous two-photon production reaction studied in e +e- machines would be instructive. There are clear differences in the low-mass region studied up to now, a good example being that a ~r+~r+ ~r-~r- system is predominantly QQ when produced by 7~, but this is only a 15% contribution in DPE [8]. Also only I = 0 states can be produced in DPE, a restriction not holding in 7"f, the "v-coupling is proportional to the quark charges, and so on. For higher mass systems (for e +e" these will become accessible at LEP) will the topological features of the hadmnic systems differ in a way that will reveal Pomeron structures? I discuss this in the following section.
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4.
DPE AT COLLIDER ENERGIES Historically the most important tool used in unravelling the structure of the proton was of course deep-inelastic lepton scattering. We were able to measure rather directly the q and q distributions, and indirectly, using the 'theory of evolution', also the gi~on ~ b - ~ o n s : Just suppose lepton beams did not existt Life would certainly have been a lot harder, but we could eventually have extracted the same information from just proton-proton (and proton-antiproton) comsions. Drd-Yan pairs of muons and electrons provide a measurement of the product of the q and q structure function. Jet pairs allow one to measure an effective structure function such as S(x) + 4/9 [q(x) + q(x)]. Direct high-pr photon-jet pairs give further constraints, being sensitive to a different mix of constituents. A systematic programme of such measurements would have taught us the q, ~I, and g structure of p and p, albeit more painfully. I suggest that a similar programme in central hadron systems produced by DPE would e l t h u teach us the structure of the Pomeron in terms of quarks and giuons or reveal inconsistencies teacbi_ng us that this way of thinking is too naive. One can also consider other routes to lenmins~ the Pomeron structure, and I do not claim that DPE studies are unique or even necessarily the best; we need all the tools we can setl One method [I$] which is potentially clean and is made possible by the advent of our first el) coIlider, the Hadron Electron Ring Accelerator, (HERA) is to measure -/P collisions with deep.inelastic elc.~.ron scattering.
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These are events with quasi-elastically scattered e and p with central hadron production. The process is a hybrid between DPE in pp and 77 in e +e - , and was discussed by C. Peroni at this conference. Another method advocated by Ingelmann and Sehlein [16] is to study single diffractive excitation of high-mass systems and compare them with final states from pp colHsions at ~ = M; the comparison between Pp and pp should reveal P / p differences, and we already know the proton structure. This has the advantages of having existing data, a higher cross-section and higher available masses, only one large rapidity gap being needed rather than two. Despite the different advantages of these other methods, the sym_metry of the PP initial state in DPE is a nice feature. Observing Drell-Yan # +# - pairs would be a sure sign of q and q content, which could then be measured by simple deconvolution. (A picture of Pomerons as purely gluonic is surely unphysical, as q's and q's must evolve at QZ > 0.) The mass spectrum up to 12-15 GeV is of course particularly rich in structure with the J / ~ family and the T family--perhaps their signal: continuum ratio is enhanced compared with normal hadron colHsions, from gg -~ T + anything. One may need of the order of 10s DPE events with mass M exceeding 20 GeV or so to start this game. An efficient run at the Fermilab Collider with I0 pb- i should allow this. A related subject with higher cross-sections is that of soft real photon production (Pr < 200 MeV/c or so) and low-mass e +epairs, which are not well understood in hadron-hadron colHsions. The study of jets and event topology in DPE requires special care, because psendorapidity gap triggers cause a strong bias. In the view of the Pomeron as a multiconstituent object, a typical high-pr jet DPE event will also have 'beam fragment jets' along the t-channel axis and will thus have four jets altogether. Some hadrons will go in the beam direction. The distinction between true rapidity y and pseudorapidity ~ is important here. At Fcrmilab with 900 GeV beams the beam particle rapidity is 7.6. A 5 GeV pion at 0 ° has y = 4.3 and is thus more than 3 units of y from the diffractively scattered p, even though vl = oo. Topoiogy studies should thus not use T-gap triggers but rather y-gap selection, or more easily measure both scattered beam particles and select x > 0.95. Having done that, do we see: i) Predominantly 'beam jets', as in typical inelastic hadron-hadron colHsions? ii) Plus the emergence of two high-l>r jets--which we can use to measure effective structure functions--or rather only the two high-pT jets as one sees in ?~, colHsions? iii) Sometimesthree high-pr jets (no doubtl)? iv) Sometimes four--as can F,e ~nade either by double gluon bremsstrahlung or double parton scattering (DPS) with two 2 --* 2 processes. If the latter can be seen and separated it allows a me~.surement of the effective transverse size of the Pomeron. From the smallness of the total Pomeron-Pomeron cross-section We may expect an enhanced (DPS) four-jet fraction (unless it is due to transparency rather than size, which seems unlikely). This study in DPE probably requires high statistics with central masses of the order of I00 GeV or more, so may have to wait for future coHiders. The large collider experiments naturally concentrate on the electroweak and hard scattering phenomena and have not yet seriously attempted to look at this physics, although (or rather becansel) the cross-sections are quite large. Perhaps this will change.
5.
THE I~JTURE SUPER COLLIDERS
Given that we have not yet studied DPE at ~'above 100 GeV it is certainly very presumptious to even think of it at the much higher LHC and SSC energies of the future. So this section will be short. However~ let us risk another wild speculation. At the SSC with both protons above x = 0.95 we are able to stretch DPE masses up to 2000 GeV, well into the electroweak sector and in fact just where we
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are now for pp collisions at Fermilab. Of course single W and Z production would be interesting to measure, as a high-mass Drell-Yan type process. Much more dramatic is a prediction [17] of dkect and strong W + W - and Z°Z° production by Pomerons in Alan White's Critical Pomeron theory. Here with two flavours of colour sextet quarks q6 in addition to the normal six flavours of colour triplet quarks, we have the pair-production diagrams shown in fig. 10a, just like DPE ~r pair-production in the old days (fig. 10b). Just as that was a clean source of information on lnr
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scattering, through final-state interactions, allowing glueball searches etc., so this, if true, would be a clean source of information on WW and ZZ scattering phase shifts, etc. Maybe this is how the strongly interacting systems of Intermediate Vector Bosons (IVBs) above I TeV will be studied:
I should llke to thank Alan White and the other organizers of this very enjoyable meeting.
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REFERENCES 1) M. Della Negra et al., Phys. Lett. 65B (1976) 394. 2) L. Baksay et al., Phys. Lett. 61B (1976) 89. 3) H. DeKerret et al., Phys. Lett. 68B (1977) 385. 4) D. Drijard et al., Nucl. Phys. B143 (1978) 61. 5) J.C.M. Armitage et al., Phys. Lett. 82B (1979) 149. 6) J. Timmer, Ph.D. Thesis, Univ. Utrecht (1978). 7) R. Waldi, K.R. Schubert and K. Winter, Z. Phys. C18 (1983) 301. 8) T..~kesson et al. (AFS Collaboration), Nucl. Phys. B264 (1986) 154. 9) K.L. Au, D. Morgan and M.R. Pennington, Phys. Rev. D35 (1987) 1633. 10) P. Schlein, private communications. 11) T.A. Armstrong et al., Phys. Lett. 221B (1989) 221; preprint CERN-EP/89-22 (submitted to Phys. Lett. 13). 12) M.G. Albrow, Talk presented at the Workshop on Physics in the 90's at the SPS Collider, Zinal, June 1985. 13) K.H. Streng, Phys. Lett. B 166 (1986) 443 ; Phys. Lett. BITI (1986) 313. 14) A. Donnachie and P.V. Lr.tndshoff, Nucl. Phys. B244 (1984) 322. A. Donnachie and P.V. Landshoff, Nucl. Phys. B267 (1985) 690. 15) A. Donnachie and P.V. Landshoff, Phys. Lett. BI91 (1987) 309. 16) G. lngelmann and P. Schlein, Phys. Lett. 15213(1985) 256. 17) A.R. White, in Hadronic Multiparticle Production, ed. P. Carruthers (World Scientific, Singapore, 1988), p. 351 and talk at this conference.