Jet Final States in WW Pair Production and Colour Screening in the QCD Vacuum

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1 April 988 LU TP 88-4 Jet Final States in WW Pair Production and Colour Screening in the QCD Vacuum Gösta Gustafson, Ulf Pettersson Department of Theoretical Physics, University of Lund, Sölvegatan 4A, S Lund, Sweden and P.M. Zerwas* Inst. for Theor. Physics, RWTH Aachen, Aachen, W. Germany Abstract: Hadron distributions are analyzed for W pair production in e e colliders, e e - WW - qq'oq'. They are compared for independent WW fragmentation and quark exchange pairing where qq' and Qq' form (colour singlet) jets. These distributions can give essential information on the QCD vacuum and the confinement mechanism. * Supported in part by the W. German Bundesministerium fiir Forschung und Technologie.

2 Jet Final States in WW Pair Production 2 Since the first pioneering paper on jets in high energy e e annihilation [l], the description of jetty hadron final states in short-distance processes has steadily been improved. While the foraation of jets by bunches of high energy hadrons is well described in the basic independent jet fragmentation model [2], that helped establish gluon jets [3] as a cornerstone of QCD, more subtle effects like the distribution of low energy hadrons in the angular range between the quark and the gluon jets were predicted in the string picture [4] and experimentally confirmed subsequently [s]. This string picture is suggested, see e.g. [e], as an outgrowth of the non-perturbative domain of QCD that has recently received some support in lattice analyses of the shape [7] and the breaking [s] of flux tubes between quarks. The "string effect", a natural consequence of Lorentz boosts in this picture, has also been derived, however, in a perturbative approach as a consequence of coherence effects in soft gluon emission [9]. Hadrons are produced by the separation of the colour charges within a colour singlet system. In the perturbative approach this is described by the coherent emission fro* the charges in the colour singlet. However, in some cases colour singlets can be formed in different ways. A very important question is then over how large a distance the colour charges radiate gluons coherently. At some distance this coherence will be destroyed by the screening from the vacuum condensate. In the string picture hadrons are formed by breaking the string stretched between the colour charges. The corresponding problem is then at which distance between the colour charges the geometry of the string configuration is determined. If the QCD vacuum behaves like a superconductor thers are two possibilities [lo]. If it is like a type I superconductor the string should correspond to - flux tube, similar to an elongated bag, with a more or less homogenous colour electric field. The diameter of the flux tube should be of the order of fm (a typical hadron bag diameter) and we expect that the geometry of the fluxtube is determined only when the separation of the colour charges has reached this order of magnitude. However, if the vacuum is like a type II superconductor the string would correspond to a vortexline with a thin core which is surrounded by an exponentially falling electric field. The diameter of this field would be about fm, but the size of the core could be much smaller. In this case the geometry of the string would be determined already when the separation has reached the core size.

3 Jet Final States In WW Pair Production 3 In this note we will show that this problem can nicely be studied in the analysis of WW pair production in e e~ annihilation*. WW pairs that will be produced almost at rest in e e collisions at LEP2 [4], decay with a probability of into hadnn jets. The jets are initiated by two quark-antiquark pairs in the femto-universe at distances << fm. (the indices i,j -,2,3 running over the three quark colours). Each of the quark pairs qq' and QQ' is generated in a colour singlet state, suggesting the independent hadronization of both pairs. This procedure, followed in all analyses so far, is physically convincing when the W's are produced at high energies and decay well separated from each other. However, at LEP2 this separation is not very large, growing up to -. fm only when the total e e energy increases from threshold to 2 GeV. (Even at an energy of /2 Te" the flight distance remains less than /4 fm.) The separation in time between the two decays is also rather small with an average around. fm. When the W's decay close to each other, however, also the qö' and Qq' can pair to colour singlets and thus form two fragmenting systems. Solely based on the group structure the relative probability for this configuration is /9, where the terms dropped are octet qq and Qq' states in which t>.e colour forces between quarks and antiquarks are repulsive. However the hadronization mechanism can alter this probability and other results are also conceivable. If the vacuum is like a type II superconductor with a very thin core, then it could b«possible that the strings or the fragmenting singlet systems are fixed at distances even shorter than the W flight distances. In this case the * WW production in e e annihilation has several advantages over weak decays like B J/T+X [ll,2] from which some information can be extracted, (i) The initial state is free of colour fields whereas the b quark decays in the colour field of the spectator quark. (This problem is even more severe in charm decays that cannot be understood at all by r.aive colour counting arguments [l3]); (ii) The distance can be varied by varying the total e e cm energy and the opening angles between the quark pairs, whereas the naked current quarks in B decays are initially coupled at a fixed distance - "' fm. extending to - ~' fm by glon corrections.

4 Jet Final States in WW Pair Production 4 probability for the recoupled configurations would be suppressed. If the vortex core is larger or if the vacuum is like a type I superconductor, then the quarks would be allowed to exchange colour via soft gluons until their separation has leached a critical value, which may be of the order of fm. The probability for the recoupled configurations qq' and Qq' is then enhanced. It is possible that strings are formed more easily between nearest neighbours in phase space in order to minimize the potential energy* thus increasing the probability for the recoupled configuration*. The phenomenological consequences of the qq* and Qq' pairings are striking when the angles between the q and Q', etc.. are small, (i) Since the coloursinglet invariant masses are then much smaller than /s/2. the particle multiplicities will be reduced compared with the independent WW fragmentation picture, (ii) Energy and particle flow into the large angle segment of the event will almost be negligible, (iii) This is also reflected in the rapidity distribution with respect to the axis z cutting the small angle in two. He have analyzed these effects foe WW pair production near threshold more quantitatively by means of a Monte Carlo program [is], developed to describe hadron production in the e e» qq continuum. This program is based on a perturbative cascade formulated in terms of colour dipoles [l6] followed by string fragmentation [7]. The model reproduces well experimental data in the PETRA-PEP energy range. At \igher energies it gives a somewhat larger central multiplicity than programs based on other parton cascades (e.g. ref [l8]). However this difference is not essential for the conclusions in this analysis. * A similar situation occurs in the decay B * J/f+X via the process b * cw ccs. Without colour exchange the cs pair always forms a colour singlet while the cc pair forms a colour singlet (needed to build up a J/) with probability /9. The experimental branching ratio is about % [ll]. Theoretical estimates based on the assumption that colour can easily be exchanged by soft gluons, thus neglecting the suppression factor /9, tend to give larger values 3-5 % [l2]. On the other hand, some calculations which include this factor and also short distance QCD effects give.3-.5 %, i.e. even less than the experimental vali_e. Thus we conclude that at these small initial distances recoupling is possible and that its probability seems to be somewhat larger than (but still compatible with) the "natural" estimate above. However it is not as large as it would be if colour could be freely exchanged by soft

5 Jet Final States in WW Pair Production 5 Our results Cor the multiplicities and the particle flow and rapidity distributions are displayed in Tab. and Pig. 2. While the particle multiplicities are independent of the jet angles for independent WW fragmentation, very low multiplicity events are predicted for qq' pairings at small angle. For comparison, the multiplicity in the non WW, qq continuum final states is listed in the 3"* column. In Fig. 2, particle flows and rapidity distributions are compared, at an angle of 3 between the jets, for independent WW fragmentation and the competing qq' pairings. Note that In the case of qq' pairings the large angle segment between the jets is completely depleted from particles. Most remarkable are the differences in the rapidity distributions which are almost flat for independent WW fragmentation whereas they are strongly peaked for qq' pairings. These features all coincide with naive kinematical expectations for both cases. The differences in the distributions increase with decreasing angle, and they get washed out for large angles. Because we want to determine a small admixture of the recoupled pairings it is important that the difference between the two configurations is seen not only in the average but also on an event-by-event basis. To demonstrate this, the distribution in the number of particles within the rapidity range yj<2 for events with an opening angle of 3 between q and Q' is shown in Fig. 3. We note that the two event classes are very well separated. For smaller opening angles the separation is even larger. Our conclusions can be summarized in the following points. (i) Quark exchange pairing implies that final state distributions in WW» jets near threshold will differ from the naive expectations derived from independent WW fragmentation. Precision tests of W properties must ta<e this complication into consideration. (ii) Nonperturbative effects are likely to modify the probability resulting from mere colour counting for the quark exchange pairing, and the valje i? related to the colour screening length in the QCD vacuum condensate.

6 Jet Final States in WW Pair Production (iii) The difference between events originating from quark exchange pairing and "normal" events is large enough to allow a separation on an event by event basis. The possible variation of the different fractions with the total center of mass energy (i.e. with the separation of the W's) and with the angle between the jets will give important information about the QCD vacuum and the confinement phenomenon. Acknowledgement - P.Z. thanks B. Andersson for the ware hospitality extended to him during a stay at Lund University. We are grateful to B. Andersson, H. Bengtsson, J. Kiihn, L. Sehgal, T. Sjöstrand and T. Walsh for illuminating discussions.

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9 Jet Final States in WW Pair Production Table. Multiplicities in the fragmentation of WW + qq'qq' depending on the quai k pairings, and compared with continuum qq events, a denotes the angle between q and Q*. a Independent WW fragm. Quark exchange pairing qq continuum Figure captions.. Jets in e e > WW * qq'qq' near threshold; (a) independent WW fragmentation, (b) qq" and Qq' quark exchange pairing. 2. Particle flow and rapidity distribution (with respect to the thrust axis) for: (a) independent WW fragmentation, (b) quark exchange pairing and (c) qq continuum events. The angle between q and Q' is chosen to be Distribution in number of particles with rapidity y < 2 toe independent WW fragmentation (dashed line) and quark exchange pairings (solid line). The angle between q and Q' is 3. (a) ib) Fig

10 (a) C. J 45 i J v J 225 vv 27C : 6 (b) (c) Particle flow Fig. 2 Rapidity distribution No. of particles with 3 degrees FIG, 3-2<y<2