Centro Brasileiro de Pesquisas Fsicas - CBPF. Rua Dr. Xavier Sigaud, 150. Dipartimento di Fisica Teorica Universita ditorino and

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1 Quark fragmentation into vetor pseudosalar mesons at LE CBF-NF-057/97 by M. Anselmino, M. Bertini 2, C. Burgard 3, F. Caruso. Quintairos Centro Brasileiro de esuisas Fsias - CBF Rua Dr. Xavier Sigaud, { Rio de Janeiro, RJ { Brazi Dipartimento di Fisia Teoria Universita ditorino INFN, Sezione di Torino, ia. Giuria, 025 Torino, Italy 2 Institut de ysiue Nuleaire de Lyon 3 CERN, E Division, CH-2 Geneva, Switzerl Abstrat Some data on te ratio of vetor to vetor + pseudosalar mesons, =( + ), te probability of eliity 0vetor states, 00 ( ), are now available from LE. Apossible relation between su two uantities teir interpretation in terms of polarized fragmentation funtions are disussed numerial estimates are given for te relative oupanies of K 0 K 0, D D, B B states. Key-words: Quark fragmentation olarization Meson prodution LE.

2 {{ CBF-NF-057/97 -Introdution Te inlusive prodution of adrons in e + e ; anniilations at LE, e ; e +! + X, allows to study te fragmentation properties of uarks su fragmentation proess is reently reeiving mu attention bot teoretially []-[4] experimentally [5], [6]. It yields information on basi non perturbative aspets of strong interations or, in ase of eavy uarks, may test existing perturbative omputations of fragmentation funtions. We onsider ere some spin dependene of partiular fragmentation proesses, namely te prodution of vetor pseudosalar mesons, teir relative abundane te probability for te vetor meson to be in a zero eliity state. Tese uantities an be related to polarized unpolarized uark fragmentation funtions teir measurement supplies basi information on te adronization proess of a uark simple statistial models for su a proess are disussed. Te uarks produed in e + e ; anniilation at LE are longitudinally polarized wit probability () of being in a eliity state te o-diagonal elements of te uark eliity density matrix () an be negleted. Te probability for a adron produed in te fragmentation of su a uark to be in a eliity state is ten given by: () = D X i D + ++ ()+D ; ;; () () were D is te polarized fragmentation funtion of a uark wit eliity into a adron wit eliity. Te unpolarized fragmentation funtion is D = 2 X D X = D : (2) E. () olds in a probabilisti seme, wit a single uark independent fragmentation in Refs. [7] [8] it as been sown tat for diagonal matrix elements tis is a good approximation tat te oerent fragmentation of te uark, witakes into aount its interation wit te, only indues orretions of p O(p T =(x s)) 2, were p T is te transverse momentum of te adron relative to te jet axis x is te fration of te uark energy arried by te adron. Let us rst onsider nal adrons wi predominantly originate from te fragmentation of only one type of uark, like mesons ontaining one eavy avour, D D, B B possibly K K at large x. Insu a ase one as: = D 00 = D ;; = D D + ++ ()+D ; ;; () i D 0 (3) i D ; + ++ ()+D ; ; ;; () + = D D + D (4)

3 {2{ CBF-NF-057/97 were sts for vetor for pseudosalar mesons. Bot above in te seuel we exploit te parity invariane of te fragmentation proess, i.e.: D 0 + = D 0 ; = D 0 D + + D ; + = D ; + D ; ; = D + D ; : (5) Notie tat for valene uarks meson wave funtions wit zero orbital angular momentum one expets D ; = D ; + =0: (6) Only 00 ( ) { via observation of te angular distribution of te vetor meson two body deays { te ratio =( + ) an be measured let us disuss wat an be learnt about te uark adronization proess from su measurements. Tese two observables do not depend on te uark polarization state, but only on te spin eliity nature of te nal meson. We dene: D + D ; D 0 D D 0 Su uantities migt depend on x. From Es. (2)-(5) we ave: : (7) 00 ( )= + (8) wi implies = = + (9) + + (0) + 00 Notie tat in pure statistial spin ounting one as =2 = () so tat 00 = 3 = 3 4 (2) te vetor meson alignment A = 2 (3 00 ; ) (3) is zero. Es. (8) (9) sow te relation between te measurable uantities 00 ( ) te parameters, wose pysial meaning is lear troug te denitions (7). E. (0) gives a relation between te probability for a uark to fragment into a vetor meson te probability fortevetor meson to ave zero eliity, in terms of te parameter : an inrease of 00 implies a derease of vie versa.

4 {3{ CBF-NF-057/97 Tere are some models in te literature wi predit a denite relation between 00. In Ref. [9] one assumes = so tat ==( + 00 ), wile in Ref. [0] one as =+ ==(2 ; 2 00 ). In ase of more tan one avour ontributing to te nal mesons, like for, te expressions of 00 beome: 00 ( )= D 0 D 0 ( + ) (4) wile E. (0) anges into = D 0 ( + ) D 0 ( + + ) (5) = D 0 D 0 ( + 00) (6) One reovers te simple results (8)-(0) not only in ase of a single avour ontributing, but also in te ase in wi do not depend on te avour. Tis migt be te ase for valene uarks. 2 - Numerial values teir interpretation To estimate te numerial values of te parameters we use data on K K 0, D D B B prodution obtained by te OAL Collaboration [6]. 00 (K ) = 0:550 0:050 (K) =0:750 0:02 for x>0:5 (7) 00 (D ) = 0:400 0:020 (D) =0:570 0:060 for x>0:2 (8) 00 (B ) = 0:360 0:092 (B) =0:760 0:090 for x>0:33 (9) were x is te energy fration of te mesons. Te ontributions from weak deays were subtrated [], were appropriate. Tis, via Es. (8)-(0), yields: K s = 0:82 0:22 D s =0:58 0:52 (20) D = :50 0:5 D =:89 0:62 (2) B b = :78 0:80 B b =0:88 0:72 (22) Te parameters ave a natural denition in terms of fragmentation funtions, but te experimental results an also be interpreted in terms of te relative oupanies of all vetor pseudovetor states [5]: let us denote by S te probability tat te fragmenting uark produes a meson wit spin S eliity let us onsider only te prodution of vetor pseudovetor mesons. Ten we ave: 00 ( )= (23)

5 {4{ CBF-NF-057/97 wit In terms of previous parameters = Te data (7)-(9) give: = + 0 (24) = + ; =: (25) = = (26) (K )=0:34 0:06 0 (K )=0:4 0: (K) =0:25 0:0 (27) (D )=0:34 0:04 0 (D )=0:23 0: (D) =0:43 0:06 (28) (B )=0:49 0:09 0 (B )=0:27 0: (B) =0:24 0:09 (29) in agreement wit Es. (20)-(22) (26). Simple spin ounting would give =0:5 0 = 0 0 =0: Comments onlusions We ave sown ow te simultaneous measurements of te ratio of vetor to vetor + pseudovetor mesons 00 ( ) supply basi information on te fragmentation of uarks su information does not depend on te eliity of te uark, but on te spin eliity of te nal meson. Some data are available for K, D B mesons in some ases sow lear deviations from simple statistial spin ounting preditions of oter models. Su information ould be of ruial importane for te orret formulation of uark fragmentation Monte Carlo programs, wi at te moment widely assume simple relative statistial probabilities. Let us onsider our results, Es. (20)-(22) (27)-(29). For strange mesons te data agree wit spin ounting in te amountofk versus K, but, among vetor mesons, eliity zero states seem to be favoured tese are in absolute te most abundantly produed, 0 (K )=0:4. For armed mesons bot values of D D ounting values (), suggesting a prevalene of pseudosalar states, 0 0 dier from te spin (D) =0:43,, among vetor mesons, of eliity 0 states tey also disagree wit te models of Refs. [9] [0], wi, respetively, predit = = +. Te eavy b-mesons, instead, are produed in good agreement wit statistial spin ounting rules, as one expets. Data from LE are still being analyzed. For tis kind of study it is important tat te prodution rates for te salar vetor mesons te results on spin alignment are presented on te same footings, i.e., wit te same uts on te saled energies a onsistent subtration of te ontributions from weak deays. It will be interesting to determine te parameters te relative spin state oupanies S for oter mesons, like. Tere migt be some ommon features to all ligt uark fragmentation proesses, leading to te same vetor pseudovetor state oupany probabilities for K K.

6 {5{ CBF-NF-057/97 It would also be wortwile to study te dependene of tese probabilties on te saled energy of te mesons. Also, te degree of universality of uark fragmentation ould be tested by studying te same uantities disussed ere in oter proesses, like meson prodution in lepton-adron or poton-adron interations or in ; adronadron ollisions. It would also be interesting to ompare data on te prodution of spin /2 spin 3/2 baryons. Some non perturbative aspets of strong interations an only be takled by gatering experimental information looking for patterns regularities wi migt allow te formulation of orret penomenologial models. Aknowledgements We would like to tank George Laerty for elpful disussions. M. Bertini, F. Caruso. Quintairos would like to tank te Department of Teoretial ysis of te Universita ditorino for te kind ospitality F.C. is grateful to INFN to CN of Brazil for nanial support.q. is grateful to te CN.

7 {6{ CBF-NF-057/97 Referenes [] M. Anselmino, M. Bertini, F. Murgia. Quintairos, e-rint Arive: ep-p/ , to appear in Z. ys. C. [2] D. Boer, R. Jaob.J. Mulders, e-rint Arive: ep-p/ [3] A.D. Adamov G.R. Goldstein, e-rint Arive: ep-p/ [4] J. Binnewies, e-rint Arive: ep-p/ [5] C. Burgard, Measurements of te rodution of Carm Hadrons wit te OAL detetor at LE, roeedings of te 996 DF Conferene, Minneapolis, to be publised in World Sienti. [6] OAL Collaboration, R. Akers et al., Z. ys. C67 (995) 389 OAL Collaboration, G. Alexer et al., Z. ys. C72 (996) OAL Collaboration, K. Akersta et al., Z. ys. C74 (997) 43 OAL Collaboration, K. Akersta et al., Z. ys. C74 (997) 437 OAL Collaboration, K. Akersta et al., CERN preprint CERN-E/97-093, submitted to Z. ys. C OAL Collaboration, K. Akersta et al., CERN preprint CERN-E/97-094, submitted to ys. Lett. B OAL Collaboration, K. Akersta et al., Identied Carged artile rodution in Quark Gluon Jets, ontributed paper to te XIII International Symposium on Lepton- oton Interations, Hamburg, 997, L-296. [7] M. Anselmino,. Kroll B. ire, Z. ys. C29 (985) 35 [8] A. Anselm, M. Anselmino, F. Murgia M. Ryskin, JET Lett. 60 (994) 496 [9] A.F. Falk M.E. eskin, ys. Rev. D49 (994) 3320 [0] J.F. Donogue, ys. Rev. D9 (979) 2806 [] We ave interpolated te arged kaon rates to x>0:5 using a t to te dierential ross setion listed in [6]. We subtrated te ontributions from arm bottom events to te prodution of strange mesons using te JETSET [3] model, assigning systemati errors to tis subtration as determined in [2]. [2] OAL Collaboration, K. Akersta et al., CERN preprint CERN-E/97-063, submitted to Z. ys. C. [3] T. Sjostr, Comp. ys. Comm. 82 (994) 74.