How to search for doubly charmed baryons and tetraquarks

Z. Phys. A 355, 349-362 (1996) ZBTSCHRIFT FOR R-I IK A (~) Springer-Verlag 1996

How to search for doubly charmed baryons and tetraquarks Murray A. Moinester

R. & B. Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel Aviv University, 69978 Ramat Aviv, Israel (e-mail: murraym@ taupfly.tau.ac.il)

Received: 31 May 1995 Communicated by Th. Walcher

Abstract. Possible experimental searches of doubly charmed baryons and tetraquarks at fixed target experiments with high energy hadron beams and a high intensity spectrometer are considered here. The baryons are: ~¢(ccd) , ~c+(ccu), and S2c+c(ccs); and the tetraquark is T (cc5d). Estimates are given of masses, lifetimes, internal structure, production cross sections, decay modes, branching ratios, and yields. Experi- mental requirements are given for optimizing the signal and minimizing the backgrounds. This paper is designed as an experimental and theoretical review. It may therefore be of assistance in the planning for a future state-of-the-art high statistics charm experiment, in the spirit of the aims of the recent CHARM2000 workshop.

PACS: 10.14.20.Lq; 10.14.40.Lb

Introduction

The quantum chromodynamics hadron spectrum includes doubly charmed baryons: -~+ (ccd), =++ + ~cc (ccu), and J'2cc (ccs), as well as ccc and ccb, and also the corresponding antiparticles. Properties of ccq baryons were discussed by Bjorken [1], Richard [2], Fleck and Richard and Martin [3], Savage and Wise and Springer [4, 6], Kiselev et al. [7, 8], Falk et al. [9], Bander and Subbaraman [10], Stong [11], Roncaglia et al. [12], and Bagan et al. [I3]. Singly charmed baryons are an active area of current research [14--19], but there are no experimental data on the doubly charmed variety. Figure 1 shows the quark structure of all the SU(4) J=l/2 baryons, including the singly and doubly charmed baryons. A double charm state-of-the-art experiment is feasible to observe and to investigate such baryons. The required detectors and data acquisition system would need very high rate capabilities, and therefore would also serve as a testing ground for LHC detectors. Double charm physics is in the mainstream and part of the natural development of QCD research. This paper is an experimental and theoretical review, as part of the planning [20, 21] for a very high statistics fixed charm experiment, in the spirit of the recent CHARM2000 workshop [22]. The present work is a part of the March

1996 CERN COMPASS fixed target proposal: COMPASS, COmmon Muon Proton Apparatus for Structure and Spec- troscopy [23]. A Fermilab CHARM2000 experiment [24] is also possible.

The ccq baryons should be described in terms of a combi- nation of perturbative and non-perturbative QCD. For these baryons, the light q orbits a tightly bound cc pair. The study of such configurations and their weak decays can help to set constraints on phenomenological models of quark-quark forces [3, 25, 26, 27]. Hadron structures with size scales much less than l/Aqcd should be well described by perturbative QCD. This is so, since the small size assures that as is small, and therefore the leading term in the perturbative expansion is adequate. The tightly bound (cc)~ diquark in ccq may satisfy this condition. For ccq, on the other hand, the radius is dominated by the low mass q, and is therefore large. The relative (cc)-(q) structure may be described similar to mesons Qq, where the (cc) pair plays the role of the heavy antiquark. Savage and Wise [4] discussed the ccq excitation spectrum for the q degree of freedom (with the cc in its ground state) via the analogy to the spectrum of Qq mesons. Fleck and Richard [3] calculated excitation spectra (spin, orbital, radial excitations) and other properties of ccq baryons with a variety of potential and bag models, which successfully describe known hadrons. They show that the lowest radial and orbital excitations of ccq and ccs are associated with cc excitations. And these ccq states are broad since pionic transitions to the ground state are allowed. The ground state in their calculation consists of a localized (cc) diquark surrounded by a light quark, with the average distance < r(cc) > much smaller than < r(cq) >. They find that < r(cc) > increases for the radial and orbital excitations, and that the quark-diquark structure disappears. Figure 2 shows the structure of doubly charmed baryons. Badalyan [28] also described meson and baryon masses with potential models. Stong [11] emphasized how the QQq excitation spectra can be used to phenomenologically determine the QQ potential, to complement the approach taken for QQ quarkonium interactions. The ccq calculations contrast with ccc or ccb or b-quark physics, which are closer to the perturbative regime. As pointed out by Bjorken [1], one should strive to study the ~cc++c ccc baryon. Its decay properties

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' ~ + ~ _ ~ , + +

E +

~ 0

Fig. 1. The SU(4) J=l/2 baryon multiplet

V la) (b)

Fig. 2a,b. Structure of doubly charmed baryons: a Ground state and spin excitation, b Radial and orbital excitations

should be simple, since only spectator diagrams contribute to its decay. Its excitation spectrum, including several narrow levels above the ground state, should be closer to the perturbative regime. The ccq studies are a valuable prelude to such ccc efforts.

The ccq baryon is also interesting because it helps to probe QCD dynamics in a different way. One should learn new information on the basic production processes in hadron physics. The ccq studies can also help in our understanding of the structure of qqq and cqq baryons, and therefore of QCD in general. D meson structures are succesfully described [29] in terms of a central heavy c quark orbited by a light quark. But the descriptions of qqq and cqq structures are less successful. We need to better understand how protons and other baryons are built from quarks. The investigation of the ccq system may be very helpful, since this has a simpler quark structure than a proton. The ccq data should help put constraints on hadron models, improving thereby the description of cqq and qqq systems.

A tetraquark (ccftd) structure (designated here by T) was described by Richard, Bander and Subbaraman, Lipkin, Tornqvist, Ericson and Karl, Nussinov, Chow, Maonohar and Wise, Weinstein and Isgur, Carlson and Heller and Tjon, and Jaffe [2, 10, 30-33, 36-40]. Tetraquarks with only u,d,s quarks have also been extensively studied [2, 41, 43]. The doubly charmed tetraquark is of particular interest, as the calculations of these authors indicate that it may be a narrow resonance. The main reason is that binding in a 1/r quark- quark potential is proportional to the mass, which must lead to a bound state in the limit of infinite mass quarks. A less important reason for increased binding is that the kinetic energy of a high mass charmed diquark is low. Some authors [2, 10, 33, 36] compare the tetraquark structure to that of the antibaryon Ofzd, which has the coupling O~(z2d)3. In the T, the tightly bound (cc)~ then plays the role of the

(a)

~) OPE D-Meson D~- Meson

(b)

Fig. 3a,b. Two possible configurations of the tetraquark: a antibaryon, b deuson

antiquark ~). The tetraquark may also have a deuteron-like meson-meson weakly bound component, coupled to 1+, and bound by a long range one-pion exchange potential [31, 33], which corresponds to light quark exchanges in the quark picture. Such a structure has been referred to as a deuson by Tornqvist [31], since it is a deuteron-like meson-meson bound state. Figure 3 shows the two possible tetraquark configurations. A D*D narrow resonance may be more likely than a DD bound state or resonance, considering the extra binding associated with the pion exchange. The discovery of an exotic tetraquark would have far reaching consequences for QCD, for the concept of confinement, and for specific models of hadron structure (lattice, string, and bag models). Detailed discussions of exotic hadron physics can be found in recent reviews [42]. Some other exotics that can be investigated in COMPASS are: Pentaquarks uud~s, udd~s, udsds, uud~c, udd~c, uds~c [45], Hybrid q(t9 [46], usdd U÷(3100) [47], uuddss H hexaquark [48], uud- dcc Hcc hexaquark [36], qqsg or q779 C(1480) [42], ~qqqqq heptaquark [10], and glueballs [44]. But we do not discuss these various exotic hadrons in detail in this report.

Should only the cc~zd (D*+D °) be bound; or should the crdft (D*-D °) also be bound? The D*+D ° state, if above the DDTr threshold, would likely decay strongly to doubly charmed systems. It is easier to produce only one c~ pair, as in D * - D °. However, this state has numerous open strong decay channels. These include charmonium plus one or two pions and all the multipion states and resonances below 3.6 GeV, and it is therefore not strong interaction stable. Shmatikov [49] explicitly studied the widths and decay mechanisms of D * - D °, including some bound possibilities. In a D*+D ° search, it would be of value to also look at D * - D ° data. Even if no peak is observed, the combinato- rial backgrounds may help understand those for D*+D °.

Mass of ecq baryons and T

Bjorken [1] in 1986 estimated M(ccq) ~ 3.7-3.8 GeV for J=3/2, by assuming an "equal-spacing" rule for J=3/2 baryon masses, and by interpolating between estimated ccc and bbb masses, and those of ordinary baryons. More recently,

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Roncaglia et al. [12] used the Feynman-Hellmann theo- rem and semiempirical mass formulae to fit known hadron masses, and to estimate ccq masses, Those estimates [12] are given here to three significant figures: J2cc (ccs): 1/2+, 3.74 -t- 0.08 GeV, ~ c (ccs): 3/2+, 3.82 ~= 0.08 GeV, Zee (ccu), (ccd): 1/2+, 3.66 5:0 .07 GeV, =* (ccu), (ccd): 3/2+, 3.74 ± 0.07 GeV. ~ c c

The cc diquark is a color antitriplet with spin S=I. The spin of the third quark is either parallel 0=3/2) or anti-parallel (J=l/2) to the diquark. We see that the masses of ccq baryons with J=l /2 are expected to be lower than the J=3/2 value by roughly 80 MeV. The potential model estimates of Richard et al. [2, 3] are in agreement with these to within 30 MeV. Bagan et al. [13] studied ~e~ masses using QCD spectral sum rules, and find values some 150 MeV lower. Basdevant et al. [50] describe general relationships between meson and baryon masses, applicable also to ccq. Fleck and Richard [3] and Nussinov [33] have shown that ccq and cegd masses near 3.7 GeV are consistent with expectations from QCD mass inequalities.

Lifet ime of ccq baryons and T

The ~ce and ~cc decays may be dominated by spectator diagrams [1, 3, 14, 51-55] with lifetimes about 200 f s , roughly

=+ The main effect for ccq decays is that half of the D O or - e " there are two c quarks rather than only one that may decay. Figure 4 shows spectator decay diagrams for D o and D + decays. The figure shows why the D ÷ decay but not the D o decay is affected by interference between color allowed and color suppressed diagrams. Similar interference effects are expected for charmed baryon decays. Fleck and Richard [3] suggest that positive interference will occur between the s-quark resulting from c-decay, and the pre-existing s-quark in (2c+e. Its lifetime would then be less than that of Z ~ . Bjorken [1] and also Fleck and Richard [3] suggest that internal W exchange diagrams in the =+ decay could reduce ~ce its lifetime to around 100 f s , roughly half the lifetime of the Ac +. This diagram is shown in Fig. 5. Such considerations for charmed hadron lifetimes [14, 51-58] have been extensively discussed. The most recent calculations [59-63] of these lifetimes are based on a QCD expansion in inverse powers of m~, the charm quark mass. In the decay of each of the three ground state ccq baryons, only one additional process occurs together with the free c-quark decay (W- exchange or u-quark or s-quark interference). This should allow a much cleaner investigation of these processes and their effects on the lifetimes of ccq baryons. The lifetime of the T should be much shorter than ccq, if it is set by the D *÷ lifetime. It should be possible to determine the lifetimes of doubly charmed baryons reasonably well even without their full reconstruction. The lifetime data may then have improved statistics compared to the yields given later for completely reconstructed decays.

An interesting question is whether the binding of the cc pair leads to an increase of the ccq lifetime. The weak decay rate of a spectator c-quark has an m 5 mass dependence from phase space, where m~ is the bare charm quark mass. In quark models, the mass dependence is (m~ - #)5 if

(b} C ¢

Fig. 4a,b. Spectator decay diagrams for D o and D + mesons: a color allowed, b color suppressed

¢ C

C S } W +

( q

d u

Fig. 5. Non-spectator baryonic W-exchange diagram for ='+ decay ~ c c

the effective phase space is reduced by # MeV. Assuming that mc ~ 1.5 Gev, a binding near # = 125 MeV would then reduce the the decay rate by 35%. Such effects would be reminiscent of the changes in the decay rates for neu- trons bound in nuclei or for bound muons. Bigi [63, 64] and Eichten and Quigg [65] discussed such an increase of lifetime for the B~ + meson due to the strong be binding. On the other hand, Bigi and Uraltsev [62, 64, 66] claim that in the self-consistent 1/MQ expansion [67, 68], binding energy does not influence heavy quark lifetimes. Their result was discussed in the context of b and c decays [63] in Be, and may or may not also be relevant for baryons. One may also ask [68] whether or not the c-quark mass is large enough to justify a 1/Me2 expansion. The experimentalist approach is that data for ccq and Be lifetimes and masses are needed to test 1/MQ and phenomenological models. Increased lifetimes would of course make the experiment easier to carry out.

One expects that doubly charmed hadrons should be pre- dominantly produced near threshold in the center of mass of the colliding hadrons. They would then have sufficient energy in the laboratory frame to be conveniently observed. We give an estimate here for the lifetime boost 7 in the laboratory frame for a ccq baryon that is produced at the center of rapidity via a high energy hadron beam of momentum Pb,L and energy Eb,L interacting with a target nucleon of mass MN. We have 7 = Ec,L/Mc, where Ee,L is the laboratory energy of the produced mass Mc charm baryon. We can estimate a value for Ec,c using the invariance (with respect to a Lorentz boost in the z direction) of the light cone momentum fraction c~ = (Ec +pcz)/(Eb +Pbz) that describes the ratio of the charm baryon momentum to the beam hadron momentum. We equate a(CM) = c~(LAB), with a(CM) ~ Mc/2Ebxm and or(LAB) ..~ 2Ec,L/2Eb,L. We can express the c~ in terms of the invariant energy v~ , using the relationships s ..~ 2Eb,LMN and s ~ 4E~,cm. We have

c~(CM) ~ IYIe/v/-s and c~(LAB) ~ 2Ee,nMg/s. Finally,

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we obtain 3' ~ Ec,L/Me ~ x/s/2MN ~ x/Eb, L/2MN. For a CERN experiment with Pb ~ 400 GeV/c, one obtains 3' ~ 15, so that the expected ccq energies are near 55 GeV.

Production cross section of ccq baryons

One can consider production o f doubly charmed hadrons of momenta Pc by proton and Sigma and pion beams of momenta P#. We discuss production at different Feynman Xy- values, X: ~ Pc/Pb, evaluated with laboratory momenta. The cross sections may also depend on the projectile. For example, pion beams may be more effective than ~ ' - beams in producing high-Xf D - mesons. And baryon beams may be more effective than pion beams in producing ccq and cqq baryons at high Xf .

Consider a hadronic interaction in which two e~ pairs are produced. The two c's combine and then form a ccq baryon. Calculations for ccq production via such interactions have been recently carried out. Some ingredients to the calculations can be stated. For ccq production, one must produce two c quarks (and associated antiquarks), and they must join to form a tightly bound, small size anti-triplet pair. The two c-quarks may arise from two parton showers in the same hadron-hadron collision, or from a single patton shower, or they may be present as an intrinsic charm component of the incident hadron, or otherwise. The two c-quarks may be produced (initial state) with a range of separations and relative momenta (up to say tens of GeV/c). In the final state, if they are tightly bound in a small size cc pair, they should have relative momentum lower than roughly 1 GeV/c. The overlap integral between initial and final state diquarks de- termines the probability for the cc fusion process. The diquark should then easily combine with a q to form ccq. A ccq production calculation based on two parton showers in the same hadron-hadron collision was discussed by Levin [69]. Halzen et al. [70] gives evidence for multiple parton interactions in a single hadron collision, from data on the production of two lepton pairs in Drell-Yan experiments.

As an aid in comparing different possible calculations, one may parameterize the yield as:

o'(ccq)/o(c~) ~ k[a(e~)/o'(in.)] ~ klL (1)

Here, or(c6) is the charm production cross section, roughly 25 pb; cr(in.) is the inelastic scattering cross section, roughly 25 mb; and R is their ratio, roughly 10 -3 [71]. Here, k is the assumed "suppression" factor for joining two c 's together with a third light quark to produce ccq. Equation (1) does not represent a calculation, and has no compelling theoretical basis. It implicitly factorizes ccq production into a factor (R) that accounts for the production of a second c-quark, and a factor (k) describing a subsequent ccq baryon formation probability. Considering the overlap integral described in the preceding paragraph, one may expect k values less than unity for simple mechanisms of ccq formation. The factor R describing the production of a second charm pair may have a value greater than that given above, as discussed later in the discussion of ccq production via the intrinsic charm mechanism. With the value of R chosen, this situation would be described by a factor k> 1. Theoretical cross section calculations are needed, including the Xy-dependence of ccq

production. We will explore the experimental consequences of a ccq search for the range k=0.04-1.0, corresponding to cr(ecq)/~r(c~) ~ 10 -3 - 4 . × 10 -5. Assuming cr(er) charm production cross sections of 25 microbarns, this range corresponds to ccq cross sections of 1 - 25 nb/N.

Aoki et al. [72] reported a 2-event, large uncertainty measurement with a 7r- beam and emulsion nuclei at v/S =26 GeV for the double to single open charm pair production ratio. The DDD[9 to DD ratio was given as 10 -2. A better measurement is certainly needed. The NA3 [73] experiments measured a (k~) /o- (~) with 400 GeV/c protons and 150-280 GeV/c 7r- interacting with nuclei. NA3 reported a value of ~ 3 × 10 -4 for this ratio, with compara- ble results for the pion and proton experiments. The proton experiment had 15 5= 4 ~P~ events with a production cross section cr(~P) = 27 -4- 10 pb. We assume that the ~P~ result is relevant, even though ~ production is only a small part (~ 0.4%) of the charm production cross section, with most of the cross section leading to open charm. These two results for double charm production establish a range of values close to the value 10 -3 for R estimated above in the discussion of Eq. 1.

Brodsky and Vogt [91, 74] suggested that there may be significant intrinsic charm (IC) e~ components in hadron wave functions, and therefore also intrinsic double charm (ICC) cer~ components. The IC probability was obtained from the measurements of charm production in deep inelastic scattering. The Hoffmann and Moore analysis [75] of EMC data, including next-to-leading order (NLO) correc- tions to the IC component, but not to the extrinsic charm component, yields a 0.3% IC probability in the proton. A recent reanalysis of the EMC charm production data was carried out by Harris, Smith, and Vogt [76]. Their analysis includes the intrinsic and extrinsic charm contributions, both calculated at NLO. They found that an IC component is still needed to fit the EMC data, with a value indicated for the proton of (1.0 4- 0.6)%. Theoretical calculations of the IC component have also been reported [77]. The double intrinsic charm component can lead to ccq production, as the cc pair pre-exists in the incident hadron. One may expect that aside from the IC mechanism, ccq production will be pre- dominantly central. Intrinsic charm ccq production, with its expected high Xy distribution, would therefore be especially attractive.

Brodsky and Vogt [91] discussed double g, ko production [73] in the framework of IC. The data occur mainly at large X I , while processes induced by gluon fusion tend to be more central. They claim that the data (transverse momentum, X f distribution, etc.) suggest that k ~ production is highly correlated, as expected in the intrinsic charm picture. A recent experiment of Kodama et al. [78] searched for soft diffractive production of open charm in D D pairs with a 800 GeV proton beam and a Silicon target. The experiment set a 90% confidence level upper limit of 26 microbarns per Sili- con nucleus for diffractive charm production. Kodama et al. estimated that the total diffractive cross section per Silicon nucleus, above the charm threshold, is 12.2 mb. The ratio of these values gives an upper limit of 0.2% for the probability that above the charm threshold, a diffractive event contains a charm pair. Kodama et al. interpreted this as the upper limit on the IC component of the proton. Brodsky et al. [79]

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discuss the probability for the intrinsic charm in an incident high energy hadron to be freed in a soft diffractive interaction in a high energy hadronic collision. In their formalism, the IC probability is multiplied by a resolution factor #2/m2, w h e r e ].z 2 is an appropriate soft mass scale [79] and rac is the charm quark mass. If we take the soft scale to be of order Aqca=0.2 GeV or the p mass, one obtains a significant resolution factor suppression for charm production in a soft process. Thus, the charm fraction that should be observed in a soft hadronic or diffractive cross section should be con- siderably smaller than the intrinsic charm probability. If the suppression factor is for example 10, that would change the upper limit of the Kodama et al. experiment from 0.2% to 2%. The data would not therefore place a useful limit on the IC component. In the case of hard reactions, such as the deep inelastic lepton scattering of the EMC experiment, the suppression factor is not present. Despite the small IC probability and the suppression factor, Brodsky and Vogt [91, 74] claim that the large X i J/~ hadroproduction (NA3) data, including the A-dependence, are consistent with the IC picture. Robinett [80] calculated k~ff' production in terms of multiple parton interactions.

The IC predictions were also compared to the E791 data [81] for the leading particle effect in the observed production asymmetry for D-/D + mesons at large X f for an incident 7r- beam [74]. The data and IC and Pythia calculations [81] had qualitatively the same behaviour, with increased asymmetry at high Xf. This suggests [81] that the produced charm coalesces with the spectator valence quarks of the projectile. Figure 6 shows two possible diagrams associated with the leading particle effect for the diffractive high Xf production of D - mesons in the interaction of beam pions with target nucleons. The Pomeron exchange mechanism is shown, and the c~ pair is either present as an IC component in the initial pion, or it is produced in the final state. Al- though the detailed agreement with the data was not good for both models, neither appears to be ruled out by the data. The IC model in contrast to the Pythia model is based on the the total number of D - and D ÷ being equal [82]. A revised IC calculation should give better agreement with data [82] by making the assumption that the same number of D - and D + are produced by fragmentation, and that coalescence enhances the number of D- . The IC calculations [83] have been described in detail. A revised Pythia model calculation which gives improved agreement with the data was recently reported [84].

The most probable IC state occurs when the constituents are minimally off-shell; i.e., have the smallest invariant mass. In the rest system, this happens when the constituents are relatively at rest. In a boosted frame, this configuration corresponds to all constituents having the same velocity and rapidity [79, 85]. Most of the momentum, on the other hand, is carried by the heavy quark constituents of these Fock states. Within gauge theory (QCD, QED), particles (quarks, gluons, protons, electrons) may coalesce into bound states primarily when they are at low relative velocity. It is well known that in QED, the coalescence probability depends on the factor ~f/V, where V is the relative velocity. This factor may be large, even if the fine structure constant c~f is small. Coalescence probabilities in some QED processes were calculated by Brodsky et al. [86, 87]. The coalescence via IC in

71"- I d

¢ C

a 0

"/F- u.

b

Fig. 6a,b. Two possible diagrams associated with the leading particle effect for the diffractive high Xf production of D - mesons in the interaction of beam pions with target nucleons. The pomeron exchange mechanism is shown, and the c~ pair is either present as an intrinsic charm component in the initial pion a, or it is produced in the final state b

the leading particle effect occurs after the 7r- fluctuates into a [~dc-~) Fock state. It happens automatically when the IC Fock state is freed, if the charm and valence quarks move at approximately the same velocity and rapidity [74]. When an intrinsic double charm ICC state is freed in a soft collision, the two charm quarks should also have approximately the same velocity, so that coalescence into a cc state is likely. The two freed c's may scatter and the consequent coalescence probability should depend analagously on as(#Z)/V. The scale # depends on the exchanged momentum. When it is a soft scale, the effective coupling can be quite large [88]. The cc diquark may subsequently coalesce with a valence quark to produce ccq.

A detailed ICC ccq production cross section calculation would be of great interest. For production with pion or baryon beams, one may be able to estimate the ccq coalescence rate, using appropriate leading D data as a normalization. One characteristic of IC is an A °'7 surface dominated A-dependence, which gives an extra nuclear suppression relative to leading twist fusion processes. One should therefore measure the A-dependence of ccq production at large Xf. Comparison of the data with ICC predictions may give new perspectives on heavy and light quark wavefunctions, and also on coalescence mechanisms for producing leading particle effects.

We can describe some ingredients for a calculation of the ICC contribution to ccq production. The inelastic cross section is roughly 25 rob. Taking 0.3% for the IC component of an incident proton or pion, the naive estimate for the cc~ probability is (3. × 1 0 - 3 ) 2 = 9. × I0 -6 . Here, the probability for ICC is taken as the square of IC, which is probably

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a lower limit. Once one has one pair, the projectile Fock state is already far off-shell, and the amplitude to produce an additional heavy quark pair may only involve an extra power of c~s(m2c) [89]. Since most of the cross section at x/s = 30 GeV is at low Pt, there may also be a factor of roughly 10 loss for the resolution factor [79]. The cc pair has 3x3=9 color components, 3 color antitriplet, and 6 color sextet. If cc are unpolarized in color space in the double- intrinsic-charm Fock state (a plausible assumption), there is 1/3 probability for the antitriplet possibility. We denote the ccq coalescence probability by P. One then expects a ccq production cross section: cr = 25 × 106 × 9 x 10 -6 × 10 - j x P x 1/3 ~ 10P n b / N . For example, probabilities P of 50%-100% would lead to 5-10 nb/N cross sections. But a calculation for this probability is not yet available.

The energy dependence of ccq and cqq production cross sections is also of interest. Consider data for Ac and and ~ from WA89 [901 (330 GeV 22-) and WA62 [92] (110 GeV S - ) . The WA62 data were taken for Xf > 0.6, and an estimated large extrapolated cross section of ~rB = (5.3 :t: 2.0) #b/Be nucleus was reported. WA62 gives a cross section dependence of dcr /dX f ~ (1 - Xf ) 17+°7, while WA89 [90] finds roughly & r / d X f ~ (1 - Xf) 4"7:t:1"6:k0"6. It is possible therefore that some or most of the cross section in WA62 is via diffractive rather than central production. With the X/dependence of WA89, less than 2% of the cross section should be observed at Xf > 0.6. If the WA62 data are correct, they have much more cross section than WA89 for the same high Xf range. It leads to the surprising result that cqq (central or diflYactive) production is favored at energies closer to threshold, perhaps due to some unknown production mechanism. Cross sections at high Xf compa- rable to those of WA62 were also reported by the neutron beam experiment BIS-2 at Serpukhov [93], with beam energies up to 70 GeV. A more recent low energy neutron beam experiment at Serpukhov, EXCHARM [94], also reported clean A~ signals at XI > 0.5. However, Bunyatov and Nefedov [95] recently determined cross sections for the production of charmed particles in proton-nucleon interactions at 70 GeV from proton beam dump experiments with the IHEP-JINR neutrino detector. For the region X f > 0.5, they reported total cross sections more than two orders of magnitude lower than the values obtained by BIS-2 [93]. If these new results are correct, then charm production cross sections near threshold are consistent with expectations, and are not anomalously large. Still, it is important that an energy scan be carried out with different beam particles, to better understand the dependence of the cqq cross section on beam energy. If the charm production cross sections near threshold are low as expected, then fixed target experiments should look for ccq production at the highest possible energies.

It will be of interest to compare ccq production in hadron versus electron- positron collisions, even if COMPASS deals with hadron interactions. Following production of a single heavy quark from the decay of a Z or W boson produced in an electron-positron collision, Savage and Wise [41 discussed the expected suppression for the the production of a second heavy quark by string breaking effects or via a hard gluon. Kiselev et al. [71 calculated low cross sections for double charm production at an electron-positron collider B factory,

for ~ = 10.6 GeV. They find cr(ccq)/cr(c?.) = 7. x 10 -5. This result is inapplicable to hadronic interactions as in COM- PASS. But it demonstrates the wide interest in this subject.

A number of works [8, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105] consider the production and decay of doubly heavy hadrons (bcq, bc, bbq, ccq, etc.) via gluonic fusion and quark-antiquark annihilation in hadronic production for collider experiments at the FNAL Tevatron or CERN LHC. A COMPASS fixed target study for ccq (possibly including some Bc mesons) can be a valuable prelude to future collider studies of doubly heavy hadrons. For short lifetime ccq detection, if the cross sections are adequate, it is easier to work in a fixed-target apparatus. More recently, gluonic fusion calculations were carried out by Berezhnoi, Kiselev, Likhoded (BKL) [96] for cc diquark production in hadron collider experiments at large transverse momenta, calculated with a complete set of 36 diagrams to the fourth order of as. Such calculations may be more precise [96] than those based on the fragmentation mechanism [9]. Glu- onic and quark-antiquark collisions are included, such as 99 ~ br) and qc~ ---, bb. These processes may be followed by _gluon bremsstrahlung and splitting and annihilation b --* b 9 ~ I)99 --~ t)c~, resulting finally in bt)c& Such calculations can also give the yield of Bc (bc) mesons [6, 9, 106-113]. Similarly, one may calculate ecgg production. The gluonic component is expected to give much more contribution than quark-antiquark at 1.8 TeV, and also at lower Tevatron energies. The dependence of the cross section on the projectile is then less important. For example, in fixed target experiments with pion compared to proton beams, quark-antiquark annihilation is more likely, but should give a small contribution compared to gluon-gluon collisions.

We now quote some results from the cc diquark (and ~ ) production calculations of BKL [96] and of DSS (Donch- eski, Steegborn, Stong) [97]. They assume that following cc production, the produced diquark forms a ccq with prac- tically unit probability, with the ccq carrying the total diquark momentum. They calculate rapidity distributions for ccq production with Pt > 5 G e V / c in collider experiments. BKL and DSS point out that the ccq cross section strongly depends on the heavy diquark wave function at the origin. BKL use a Coulombic wave function, an approximation that is improved by DSS due to the evaluation in realistic po- tentials. One may correct for this effect by multiplying the BKL estimate for ccq by a factor 4 [96]. The DSS calculation used the fragmentation mechanism, which is shown [103] to be adequate for Tevatron experiments above Pt = 5 GeV/c. BKL claim that the fragmentation mechanism un- derestimates the cross sections, compared to their complete calculation. BKL first estimate cc production cross sections for gluonic subprocess energies of 15 - 100 GeV. They use the CTEQ1 parametrization [114] for the structure function of the proton. They integrate over the gluonic luminosity in the colliding proton and antiproton, for all energies of the gluonic subprocesses. They find the hadronic cross section for ccq to be 0.13 nb for the baryons at v G = 1.8 TeV, transverse momentum Pt > 5 GeV, rapidity lY] < 1. Inte- grating over rapidity and all Pt, they find 1.4 nb. Including the factor of 4 diquark wave function correction gives an estimated total cross section at 1.8 TeV of 5.6 nb. At a 500 GeV/c beam energy fixed-target experiment, corresponding

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to x/s ~ 30 GeV, production cross sections with Pt > 5 GeV/c should be negligible. Most ccq hadrons will defi- nitely be produced at much lower Pt. BKL also evaluated [96] the gluonic contribution to the proton-proton production cross section of cc-diquark at v/~ = 30 GeV. At realistic diquark wave functions, BKL found [96] the total cross section equal to only 1 pb. This is two orders of magnitude lower than one obtains by an extrapolation from 1.8 TeV to 30 GeV, assuming that the produced e e ~ mass is near 6 GeV, and taking the same energy dependence given by Schub et al. [115] for kV production. The BKL calculation apparently has a strong threshold effect, associated with the extra c~ production. However, their calculations may have large uncertainties, and needs to be tested against existing data. A crucial test of the BKL formalism is double if/hadroproduction. How well does their leading twist approach account for the NA3 data [73], particularly the X f distribution and normalization? Does it do as well as the IC calculation?

Considering all estimates and uncertainties described above, we will give yields in COMPASS using estimated lower and upper limits of 1 nb/N and 25 nb/N for the ccq production cross section.

Decay modes and branching ratios of ccq baryons

The semileptonic and nonleptonic branching ratios of ccq baryons were estimated by Bjorken [1] in 1986. He uses a statistical approach to assign probabilities to different decay modes. He first considers the most significant particles in a decay, those that carry baryon or strangeness number. Pions are then added according to a Poisson distribution. The Bjorken method and other approaches for charm baryon decay modes are described by Klein [16]. Sanchis-Lozano [5] studied semi-leptonic decays of doubly heavy baryons. Savage and Springer [6] examined the flavor SU(3) predictions for the semileptonic and nonleptonic ccq weak decays. They give tables of expected decay modes, where the rates for different modes are given in terms of a few reduced ma- trix elements of the effective hamiltonian. In this way, they also find many relationships between decay rates of different modes. Savage and Springer discuss the fact that the SU(3) predictions for the decay of the D-mesons can be understood only by including the effects of final state interactions [116]. They suggest that FSI effects should be much less important for doubly charmed baryons (ccq) compared to charmed mesons.

We describe some decay chains considered by Bjorken [1].. For ccq decays, Bjorken in 1986 estimated [l] that roughly 40% are semi-leptonic and 60% are hadronic. Con- sidering that the D O semi-leptonic decay rate [17] is given as 17%, one may instead estimate 17% semi-leptonic and 83% hadronic for ccq decays. Bigi evaluates semileptonic decay rates for c quarks [62, 63] in B~ and D O in a i/m~ expansion. Such calculations are not available for ccq decays. Bjorken estimates that as many as one-third of the hadronic decays lead to final states with all charged hadrons. We quote from Bjorken's decay rate estimates. For the =++ ~ c c ,

+ + - - + A c T i " . one may have ~c,-~++ ~ Sc / ( 7r followed by Z~ ++ --+ + +

A Ac+Tr+K-Tr + final state was estimated by Bjorken [1] to have a 5% branching ratio. Bjorken also estimated:

=++ ~ =+ + (1.5%); =++ =++ ~ D°ATr+rc ÷ (5%); -co _cTr _ ~ ~ C C ~o + + _~++ ___, A-~K-Tr+Tr + =~Tr 7r (4.5%); -,~-++ ~ D+ATr + (3%); _c~ (5%); sL L ~ S2c %÷ (5%); s2L ~ n%+~+~ -- (4%); sL L

- - + - - + +

•-D+Tr ÷ (2%); Y2c+~ ---, -~cK 7r (1.5%); ~c~ -0T1- + ÷ (4%); =+ ~ - + + - (2%); ~cc _~Tr , - ~ c I X 7"( ~ ~ * c ~-tcTr 7"f "~+ ~ "~'0 +

=+ ~ A+cK-Tr + (3%); (1.5%); =+ ~ D + A (2.5%); ~ ~ C C

=+÷ - + (2.5%); ++ --+ =÷ --~ D + K - p (1%); ~2~ ++ ~ ~cc K 7r ~ c ~ ~ c c ~ + - - + + + + : ' ~ / ( 7r 7r (5%); ~2~+~+~ --~ ~2~7r (5,5%). Following the decay of one of the two c quarks, the resulting state has typically a singly charmed baryon or meson, which may also decay hadronically or semileptonically. The decay event therefore has either two hadronic, two semi-leptonic, or mixed decays. The experiment should identify the two secondary vertices. The decay topologies should satisfy a suitable COM- PASS charm trigger, with reasonable efficiency. However, for events with no neutrino in the final state, the mass resolution will be superior.

Can one distinguish experimentally between the production of the ccq 1/2+ ground and excited 3/2+ states? Consid- ering that the 3/2+ to 1/2+ mass difference for ccq baryons is expected [2, 3, 12] to be roughly 80 MeV, the 3/2+ states would decay electromagnetically to the 1/2+ states, in a two- body decay. The physics of charmed baryons with J=3/2+ was discussed recently by Rosner [117]. Kubantsev [118] described for ccq decay in FNAL E781, how the coincidence detection of the GeV decay gamma ray, together with the weak decay products of the 1/2+ decay, can distinguish 1/2+ from 3/2+ production. Such a gamma-ray coincidence technique was reported by CERN WA89 [90] in their low staffs- tics observation of the symmetric 112+ ~ charmed baryon, which is expected [12, 119] to decay electromagneticatly to the antisymmetric 1/2+ =+ The WA89 search focussed on ~c- mass difference plots of -+ -+ with the M(7= c) -M(= c), starting sample of events (both signal and sidebands) in which the 1/2+ =+ is observed. Searches for 3/2+ ccq states can also ~ C

benefit from such a mass difference analysis. The subtrac- tion technique for a two-body decay removes many errors, and yields improved energy resolution compared to plots of

=+) the total invariant mass M(7, ~c or M(7 , ccq). Sideband subtractions can also help remove some of the backgrounds. Similar mass difference analyses were done by WA89 [90] for ~c --~ A~Tr. The mass difference technique (D* trick) was described originally for D* ~ DTr [120].

Decay modes and branching ratios of the T

The U = i + c c ~ d T structure may be a direct four-quark bound state, or a D*+D ° bound deuson. It can have a narrow width, since it can not decay directly to DD, which can only couple to 0 ÷, 1 - , 2 +. For the deuson case, the binding is via a 7r + exchange potential, which is twice that of a 7r ° exchange potential. Consequently, the ccl2d D * + D ° may be bound, even while the ccftC, D * ° D ° and c c d d D * + D + are not [33]. Due to the (D*-D-Tr) mass difference of only 5.7 MeV, the exchange potential acts at very long range [31, 33]. The heavy c quarks make the kinetic energy of these quarks in the T small, thereby increasing the chances for binding. Here we consider the likely decays of a D * + D ° state, described as a binding of a virtual D* and a D. One can search for the decays T ~ 7r D D and T ~ 7 D D, as discussed by

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Nussinov [33]. The pion or gamma are emitted at the primary interaction point, where the virtual D* decays immediately. The two D mesons decay downstream, with the 7-ray and the two D's nearly co-linear in the laboratory frame [33]. The D* decay branching ratios [17] are 99% for 7rD and 1% for q,D, where these values depend strongly on the (D*-D- 7r) mass difference. If the T has a D*D structure, the mass of the virtual D* may be lower than that of a real D*. In that case, one expects different branching ratios for T decay to DDTr versus DDT, compared to D* decay to DTr versus D'~ [33]. If the T mass is below the DDTr threshold, only electromagnetic decay would be possible.

The T decays to 7rDD and ")'DD may be useful for a search, if these branching ratios are sufficiently large. For the quasi-two-body decay channel T --+ ~ + (DD), to the extent that the relative DD mass is small, one may expect improved resolution by using the D* mass difference technique. For events in which DD coincidences are observed, one looks for a peak in the mass difference M(TDD)-M(DD). One should get better resolution for the reconstruction of the T mass for the pion decay channel. If the T has a mass higher than DD*, it may be a narrow resonance, not strong-interaction stable. In that case, one may search for a peak in the reconstructed DD* mass spectrum.

A search for the T would be an extremely difficult experiment. The expected cross section is very low. The com- bined branching ratio for the decay of the two D's to charged particle decay channels is low. The event reconstruction efficiency would be low for events with the two D-decay vertices, considering that there may also be decay vertices from particles with anticharmed quarks. How well can one unambiguously assign charged tracks to the different vertices? Still, even a measure of the open charm double D cross section would be of interest.

General experimental considerations

Charm experiments usually use vertex detectors consisting of many planes of silicon micro-strips with thousands of channels. Some of the planes are upstream of the target for beam tracking. These detectors allow a high efficiency and high resolution for reconstruction of both primary (production) vertex and secondary (decay) vertex. The position resolution of the vertex detectors is typically better than 300 microns in the beam direction. By measuring the yield of a particle as a function of the separation between the two vertices, the lifetime of the particle is obtained. This is possible as long as the lifetime is not so short, such that the separation of vertices becomes ambiguous. Other major components in charm experiments are several magnetic spectrometers with track detectors for track reconstruction and for momentum analysis, Cherenkov counters for particle identification (PID), and electromagnetic and hadronic calorimeters. Muon detectors and transition radiation detectors (TRD) for electron separation are included for studies of leptonic decays. The invariant mass resolution for typical charm masses in such spectrometers is about 7 MeV, and COMPASS expects better for decay channels leading to charged particles. Different spectrometers are sensitive to different regions of Feynman X f values.

TARGET

v2/

Fig. 7. Example of an event in which --*+ is produced in the target and ~cc decays at secondary vertex V1. The resulting ~,e + subsequently decays at vertex V2

In hadronic production, the charm states produced are preponderantly charm mesons at low Xf. Future experiments are planned to obtain higher yields of charmed hadrons. Increased charm sensitivity can be achieved as in E781 [121] by using higher integrated beam intensi- ties, and higher efficiency detector systems. E781 also will use a trigger condition that identifies a secondary vertex, and also requires positive particles with momentum greater than 15 GeV/c. This should enhance the high-Xf acceptance (XI > 0.t), and give higher quality events. A good charm trigger [121] can produce an enriched sample of such high Xf charm baryons with a significantly lower number of events written to tape or disk. CHARM2000 experiments will also require charm enhancement triggers [34, 35]. The E781 [121] and CHARM2000 experiments [23, 24] complement each other in their emphasis on different XI regions, incident particle types, statistics and time schedules.

High quality particle identification (PID) for the largest possible energy range of the outgoing particles is important for reducing backgrounds associated with incorrect identification of tracks. In E781, this will be available via ring imaging Cherenkov (RICH) and TRD PID systems. These and other experimental techniques to reduce backgrounds are described in more detail in ref. [22].

The backgrounds are not only events from the primary vertex, but also from the decays of the hadrons associated with the two associated ~ quarks produced together with the two c quarks. One may expect that the requirement to see two related, sequential secondary vertices, or to see a doubly charged particle, may provide a significant reduction in background levels. A typical doubly charmed decay event is shown in Fig. 7. To correctly reconstruct the ~ccz'++ mass from this event, one must consider the invariant mass of

~++ decay. One must the ~dr~÷ + pair that arises from the ~ use the vertex information to reject mass combinations of a produced singly charmed baryon such as --+ and a 7r + not ~ C C '

arising from - -~ decay. ~ C C

High energies are needed for studies of high mass, and short lifetime baryons. Thereby, one may produce high energy doubly charmed baryons. The resulting large lifetime boost improves separation of secondary and primary vertices, and improves track and event reconstruction. COM- PASS with 300-450 GeV protons and pions [23] should be sufficiently high. Although beam line constraints may limit initial COMPASS studies to 300 GeV or lower, the higher energies will be eventually required for a complete ccq experiment.

Depending on the backgrounds, one may require separation distances of secondary from primary vertices of approximately 1-4 o-, where cr is the longitudinal tracking resolu-

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tion. The requirement for two charm vertices in ccq decays may reduce backgrounds somewhat, so that this separation distance cut may be less stringent than in the case of cqq studies. For a lifetime of 100 f s , with a laboratory lifetime boost of 15, the distance from the production point to the decay point is around 450 microns. E781 can attain roughly 300 micron beam-direction resolution for X f =0.2, with a 650 GeV beam, and 20 micron strip silicon detectors. For lower X f events, the resolution deteriorates due to multiple scattering, and there is little gain in using narrower strips. COMPASS aims to achieve 150 micron resolution for X f > 0.1, about 50% of the charm events.

The target design is very important. To achieve a high interaction rate and still have acceptable multiple scattering effects, the total target thickness should be less than 2% interaction length, corresponding to about 3 mm of Cop- per. Low A targets would minimize multiple scattering, but Copper is advantageous due to an A 1/3 charm production enhancement. The optimum target design and thickness for double charm is being studied via Monte Carlo simulation, and is discussed below also in connection with trigger requirements.

Some bqq production and decay, with two secondary vertices, may be observed in COMPASS. Such events are themselves of great interest, and must also be considered as background to ccq production. The bqq and ccq events may be distinguished by the larger bqq lifetime, and the higher transverse energy released in the b decay. It is not the primary aim of COMPASS to study bqq baryons. Fixed target experiments at CERN have only a very small number of candidate bqq baryon events at a center of mass energy around 30 GeV [122].

Tr igger considerat ions

The roughly 5% interaction length target in FNAL E781 is divided into about five segmented 1% targets separated_by about 1 cm, such that the primary charm production vertex is in a target segment while the secondary charm decay vertex is between target segments. One can identify charm candidates by requiring that at least one decay particle from a short lived parent have a sufficiently large impact param- eter or transverse miss distance S relative to the primary interaction point in the target. The definition of S is shown in Fig. 8. The transverse miss distance (S) is obtained via extrapolation of tracks that are measured with a high resolution detector close to the target. This quantity is a quasi- Lorentz invariant. Consider a relativistic unpolarized parent baryon or a spin zero meson that decays into a daughter that is relativistic in the parent's center of mass frame. Cooper [123] has shown that the average transverse miss 'distance is S ~ 7rc~-/2. For example, Ae with c~- ~ 60 microns should have S ~ 90 microns, and ~c with c~- ~ 18 microns ( r ~ 60 fs) [90, 124] should have S ~ 30 microns. The E781 on-line filter cut is on the sum of the charged decay products of the doubly charmed baryon and the singly charmed baryon daughter's decay products. The trigger requires positive particles with momenta P> 15 GeV/c, and at least one of these must have S>30 microns [121]. Tracks from the primary vertex are typically rejected by the cut on S. With a vertex

J J

!P Bc

T 6 / . - /

,I" t -

Fig. 8. The transverse miss distance S: A charmed hadron is produced at the interaction point IP, and propogates with velocity ~e. It decays at a secondary vertex V, and a daughter hadron is emitted with velocity ]3d at an angle 0 with respect to ~c- The miss distance S to the IP is shown with respect to a dashed line that is extrapolated back to the interaction coordinate

detector with 20 micron strips, the E781 resolution in S in a Monte Carlo simulation is about 4 microns for very high momenta tracks. For simulated events in E781 with a 15 GeV track, the transverse miss-distance resolution deteriorates to about 9 microns, due to multiple scattering [125]. And the resolution gets even worse for yet lower momenta tracks. Considering errors not included in the Monte Carlo simulation (allignment, etc.), the actual experimental resolution will likely be worse than the values cited above. At lower momenta, backgrounds should increase, since the S- cut less effectively separates charm tracks from the primary interaction tracks. The S-trigger miss distance condition is satisfied on average for particles with cT > 18 microns (T > 60 fs). For particles with shorter lifetimes, the trigger efficiency decreases. Monte Carlo simulations show that FNAL E781 may achieve [126] acceptable yields and signal to background for S2e detection, with lifetime ~- ~ 60 fs. The computational miss-distance trigger of E781 limits that experiment to 2 MHz beam rates. COMPASS DAQ will allow a 25 MHz beam rate, and data will be read out into memory using pipelined front end electronics with built in sparsification. This should allow the use of a computational miss-distance filter prior to the decision to write data to tape or disk. Although E781 projects less target interactions than COMPASS, it will have the advantage of collecting data some years earlier.

Due to the high beam rates projected for COMPASS, the computational miss-distance trigger cannot be used as a first stage trigger or filter. One must first implement first stage hardware charm decay triggers that can operate at the expected high rates. One possibility follows the approach of the open charm experiment E791, based on the fact that charm events show a larger total transverse energy Et than background events. For single charm, E791 showed [35] that requiring a minimum Et of 7-8 GeV reduces backgrounds by a factor 3-4 with an efficiency of about 75% for charmed hadrons. This approach needs to be explored for doubly charmed hadrons, which should be characterized by yet larger transverse energies. Requiring a minimum Et of 10 GeV may for example selectively enrich the double charm sample, hopefully reducing backgrounds [35] by as much as a factor of 10.

A second hardware tagging possibility uses a multiplicity jump trigger [127] downstream of the interaction target. This is intended to be sensitive to an increase in the number of charged tracks (within a fiduciat decay volume closed at two

358

\IL c ' l

;2~ iil

,~' L ] I ( ( ) [ I i

i ( : O l l l l I c q ' b

i (-)r l I ill'' i ,

! , I l ! i i ' l ' ,

' , l l , ' L

( l l ] . ' : h e ' d ' I s i i i i

r

~i 13o::I:: , \< ' l i ve ,

Ii 'i

H [ 1 1 / ] [ I

! ,i

L

,<-:i '1':~

\It

:1

!

Fig. 9. Schematic of the target area, including multiplicity Cherenkov detectors MUC1 and MUC2

ends by thin quartz Cherenkov detectors) following one or more charm decays. COMPASS may use 7 Copper targets of 400 microns each, interleaved with 150 micron Silicon detectors, all stacked tightly together. The silicon detectors are used to identify the target segment of the primary interaction. The design is well matched to long lived charmed hadrons that exit the target, and decay downstream in a fiducial volume between the Cherenkov detectors of the multiplicity jump trigger. In COMPASS, the tracking detectors are placed after the first multiplicity jump Cherenkov detector, starting about 3 mm downstream of the Copper/Silicon target assem- bly, where the decay volume between the Cherenkov detectors is filled with about fifteen 150 micron silicon planes. The thin silicon tracking detectors, spaced l mm apart, allow one to identify secondary vertices. A schematic drawing of the target area is shown in Fig. 9. With this target design, for very short lived ccq andsubsequent singly charged hadrons, the primary and first of the secondary vertices may both be positioned inside the Copper/Silicon target assem- bly. The silicon detectors are then used to identify the target segment of the primary interaction, and also the position of the secondary vertex. A multiplicity jump charm trigger may still be implemented associated with a secondary vertex further downstream from a longer lived singly charmed hadron from ccq decay, or associated with hadrons arising from one of the two 6 quarks. An event that would register in the multiplicity jump trigger is shown in Fig. I0.

Kwan and Halling [127] reported encouraging results for a multiplicity jump trigger, using thin quartz Cherenkov detectors, However, such a trigger for high rate beams has not yet been used in a complete experiment, and still requires research and development. The Cherenkov detectors solve two problems that make it unfeasible to detect the multiplicity jump using energy loss measurements in thin scintillation detectors. The first problem is that the large fluctuations in the energy loss of singly charged particles do not allow a clean separation of multiplicities if many tracks cross the detectors. The second problem is that target frag- ments stopping in the first detector give Large signals, which simulates a negative multiplicity jump. Both of these prob-

charm decay

n = 5 n = 7

b e a m

Target MUC 1 Silicon MUC 2 10-15 Ixm

Fig. 10. Schematic of the charm multiplicity trigger operation, showing a typical charm decay event

lems are avoided by using Cherenkov detectors. The multiplicity jump trigger with thin quartz Cherenkov detectors would be sensitive to events with X/ > -.1, which is effectively an "open" trigger X f-acceptance. Most of the charm events accepted will then be mainly associated with charm mesons near Xf=O, since these dominate the cross section in hadronic processes. However, low-Xl events may have high backgrounds, since it is more difficult to separate them from non-charmed events, due to poor vertex resolution and other problems. For higher X f events, one obtains a sample of doubly charmed baryons with improved reconstruction probability because of kinematic focussing and lessened multiple scattering and improved particle identification. The backgrounds with the multiplicity jump trigger are due to secondary interactions in the Cherenkov interaction detectors and in the silicon tracking detectors inside the decay volume; due to gamma rays from a primary interaction that convert afterwards to electron-positron pairs; and due to V ° decays. COMPASS estimated that the rejection ratio of such non- charmed events, for longed lived singly charmed hadrons, would be sufficiently high (better than >5:1), to allow the trigger to achieve its needed purpose of reducing the accepted event rate to manageable values.

For ccq, the silicon tracking detectors may also be used as the active interaction targets. In this application, the multiplicity jump trigger can not be used, and one may rely instead on the transverse energy trigger. One may require that only one track, the beam track, enter the fiducial "target" volume after the first Cherenkov detector, as determined by the pulse height in this detector. Since the silicon target/detectors are spaced 1 mm apart, the secondary vertices may be observed between silicon segments. The complete experimental trigger may include the multiplicity jump trigger (associated with the Copper targets) and the transverse energy trigger (associated with either the Silicon and Copper targets). The total target thickness than includes the Copper and Silicon.

We should also consider trigger and filter options that further enhance the yield of doubly charmed hadrons. One may build a trigger that requires several particles with high transverse momentum, since this may be more likely for doubly charmed hadrons. For ='-~+, Bjorken [1] suggested using a detector which triggers (or filters) on a doubly charged (four times minimum ionizing) particle. Bjorken [1] also de-

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scribes triggers for observing semi-leptonic decay, based on tri-muon detection for Y2c+c+c and di-muon detection for ccq. With Et at 7 GeV, one may also require coincidence with a single muon. These specialized triggers require further study. The yield estimates given below are based on non-leptonic charm triggers designed for singly charmed baryons.

Projected yields for CERN COMPASS

For COMPASS with proton and pion beams, one may rely on previous measurements done with similar beams. The open charm production cross section at SPS energies is roughly 25 #b. Taking Eq. 1 with a suppression factor of k= 0.04- 1.0, we have cr(ccq) ,~ 1 - 2 5 nb/N. We assume a measured branching ratio B= 10% for the sum of all ccq decays; this being 50% of all the decays leading to only charged particles. We also assume a measured B = 20% for the sum of all cqq decays, this being roughly the value achieved in previous experiments. With these branching ratios, we estimate a - B B = 1. - 25. x 0.2 x 0.1 = 0 . 0 2 - 0.5 nb/N. If k > 1.0, the expected cross sections would be yet higher.

For COMPASS, we now evaluate the rate of reconstructed ccq events. The yields expected to observe two un- correlated charmed hadrons may be about 10 times higher, and will also be of interest. The expectations are based on a beam of 5. x 10 v per spill, assuming 240 spills per hour of effective beam, or 1.2 x 101°/hour. For a 4000 hour run (2 years), and a 2% interaction target, one achieves roughly 1012 interactions per target nucleon. We assume that ~r(charm) --- 25 #b and ~r(in) = 25 mb for a proton target, and take a charm production enhancement per nucleon of A 1/3 (with mass A ~ 64 for COMPASS). One then obtains a high sensitivity of 1.5 x l05 charm events for each nb per nucleon of effective cross section (for nucleons in A 64 nuclei), where c%ff = ~rt3Be. Here e is the overall efficiency for the experiment. Fermilab E781 with 650 GeV pion and ,C- beams is scheduled for 1996-98, for roughly 10 times less interactions. This experiment may therefore observe some ccq baryons before COMPASS, as described in recent reports [128, 129]. The COMPASS proposal [23] describes plans starting 1999 to achieve roughly ten times more reconstructed charm events than Fermilab E781. The charm sensitivity of E781 is described in detail elsewhere [45, 121]. A futuristic option for ccq studies is a possible Fermilab CHARM2000 experiment [24], aiming at 108 reconstructed charmed hadrons.

We consider also the expected COMPASS efficiency for ccq events, by comparison to E781 estimated [121] cqq efficiencies. Our rough efficiency estimates must eventually be superceded by detailed Monte Carlo simulations of the efficiencies, but that effort goes beyond the objectives of the present review. The E781 efficiencies for cqq decays include a tracking efficiency of 96% per track, a trigger efficiency averaged over X I (for accepted Xf > 0.1) of roughly 18%, and a signal reconstruction efficiency of roughly 50%. These E781 Monte Carlo simulations [121] gave an average global efficiency of ~ 8%, by considering relatively strong signals from the ~ 200 fs lifetime decay A + --~ p/ i ' -Tr +, and the ~ 350 fs lifetime decay ~+ --+ ~-Tr+Tr - , The ~c charm baryons were assumed [121] to be produced with a

cross section of the form dcr/dXf = (1 - Xf ) 4"2, an assumption which is built into the estimation of the trigger efficiency. For heavy ccq production, it is likely that this distribution would shift to lower Xf (corresponding to an exponent greater than 4.2). This is so since the event has two charmed and two anticharmed quarks, and they all must share the available momentum. As a consequence, both the trigger and reconstruction efficiencies would be lower.

The signal reconstruction efficiency depends strongly on the ability of the track finding algorithm [130] to efficiently and unambiguously identify tracks in a given event from the hit data in the vertex detectors. Events with higher charged particle multiplicites (as for ccq) may have overlapping hits in some vertex detector planes, and are more difficult to deal with. Reconstruction efficiencies are also low for low X f events. High Xf events suffer less multiple scattering, and have improved efficiencies, since the resulting tracks are more nearly straight line, which leads to less ambiguities in the track finding. We therefore consider COMPASS events only with Xf > 0.1, corresponding also to the E781 lower limit of acceptance. The reconstruction efficiency should in any case be lower for double charm events. Including the tracks associated with the anti-charmed particles, and assuming an average of three charged tracks per charmed particle decay, ccq events may have a very high multiplicity of charged tracks. Such events are much more complex, not just twice as complex as single charm events. Some losses in reconstruction efficiency are due to extra ambiguities in track finding due to the secondary reactions that may occur in the vertex detectors, since these reactions increase the charged particle multiplicity of an event. Since doubly charmed events have a higher charged particle multiplicity in any case, they also should have a higher probability for such secondary reactions. And they also have lower efficiencies due to the tracking efficiency of 96% per track.

One may expect the vertex to be tagged more often (roughly a factor of two) for double charm compared to single charm. This would lead to a higher trigger efficiency. It is encouraging that using the COMPASS proposed type of vertex detector, multivertex events from beauty production were successfully reconstructed [122]. For lifetimes smaller than 60 fs, which is possible for ccq, the trigger efficiency would be reduced. Also, for a weak ccq signal, tighter analysis cuts with resulting lower efficiencies may be required in order to achieve the optimum signal to noise ratio.

Considering all the effects discussed, we make a conser- vative estimate here that the E781 trigger efficiencies for ccq and cqq events are roughIy the same. But we anticipate a loss in (reconstruction • tracking) efficiency for double compared to single charm, and further losses due to the short lifetime of double charm. We make an optimistic guess that the overall average ccq efficiency may be as high as e ~ 2%, 25% of the expected E781 value for cqq detection. Given the larger uncertainties in the expected cross section and backgrounds, this level of precision may be adequate for the purposes of initial rough estimations. Considering all the unknown vari- ables, the actual experimental global efficiency may however be significantly lower than the 2% estimate.

The expected sensitivity for COMPASS was given above as 150 charm events/(pb/N) of effective cross section. For crBB ~ 20-500 pb/N, one has o-~ff < 0 . 4 - 10. pb/N,

360

and therefore an upper limit of N(ccq) ~ 60-1500 events for COMPASS. This is the maximum total expected yield for ccu,ccd,ccs production for ground and excited states.

Conclusions

The observation of doubly charmed baryons or T would make possible a determination of their lifetimes and other properties. The expected low yields and short lifetimes make double charm hadron research an experimental challenge. The discovery and subsequent study of the ccq baryons or T should lead to a deeper understanding of the heavy quark sector. This status report will hopefully encourage the active participation of others in the theoretical and experimental studies needed to understand this subject.

Special thanks are due to I. Bigi, S. Brodsky, P. Cooper, L. Frankfurt, B. Kopeliovich, S. Nussinov, S. Paul, B. Povh, J. Russ, and M. D. Sokoloff for stimulating discussions and encouragement. Thanks are also due to D. Ashery, J. Appel, A. V. Berezhnoi, C. Brown, E. Chudakov, M. Donch- eski, I. Dunietz, F. Dropmann, J. Engelfried, S. Gavin, J. Gmnhaus, R. Hagedorn, D. Kaplan, V. V. Kiselev, K. Konigsmann, M. Kubantsev, S. Kwan, L. Landsberg, E. Levin, A. K. Likhoded, H. J. Lipkin, B. Muller, E. Piasetzky, M. Procario, C. Quigg, J. M. Richard, J. L. Rosner, M. A. Sanchis-Lozano, M. M. Sargsyan, M. Savage, H. W. Siebert, R. Vogt, T. Walcher, R. Werding, and M. Zavertiev lbr helpful discussions. Figures 1,2,3,9,10 are from the CERN COMPASS proposal. This work was sup- ported by the U.S.-Israel Binational Science Foundation (B.S.F.), Jerusalem, Israel.

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How to search for doubly charmed baryons and tetraquarks