ELSEVIER Nuclear Physics B (Proc. Suppl.) 75B (1999) 231-235

I D l N ~ n ~ i H

P R O C E E D I N G S S U P P L E M E N T S

Spin Alignment in heavy and light flavour systems at OPAL Simon Robins a

aphysics Depar tment , The Technion, Haifa 32000, Israel

Spin alignment of inclusive vector mesons and longitudinal polarization of A hyperons have been measured in a sample of 4.3 million hadronic Z ° decays from the OPAL detector at LEP. Leading, light vector mesons have been found to populate preferentially the helicity-zero state, a result which has no firm theoretical explanation. The values of off-diagonal elements of the helieity density matrix are in agreement with a theory based on the Standard Model with coherent fragmentation. The longitudinal polarization of the A is well described by a model in which the constituent strange quark carries all of the hyperon spin.

1. I N T R O D U C T I O N

During LEP1 running each of the four LEP experinlents has collected ,-~ 4 million hadronic Z ° decays (Z ° --+qq). This provides a very sub- stantial sample of hadrons, produced in the clean environment of e+e - collisions, for the study of their spin properties.

At LEP1 e+e - collisions produce, via a Z ° or virtual photon, lepton or quark pairs. The pri- mary quarks produced at LEP are highly po- larized, with longitudinal polarization of -0 .91 for d-type quarks and -0 .64 for u-type quarks. The resulting par ton shower and hadronization processes mediate between the pr imary quarks and the final s tate hadrons. Various models of the hadronization process make predictions about spin effects that can be observed in final state mesons. Any spin alignment must, in part at least, arise from the dynamics of the hadroniza- tion phase. Ult imately one would hope that data on the spin alignment of vector mesons ill Z ° de- cays can shed light on the relevance of particular hadronization models.

For leading hyperons the source of spin align- ment is bet ter understood. Composed of a heavy quark and a light diquark, it is expected that the hyperon will carry all the polarization of the heavy prilnary quark it contains. At LEP1 the pr imary quark will possess only longitudinal po- larization, and thus any transverse polarization effects can be ascribed to hadronization.

At OPAL the helicity density matrices of tire vector mesons B*, D*(2010) e, ¢(1020) and K* (892) 0 have been studied. In order to increase the probability that leading particles, i.e. those containing a pr imary quark, are studied, empha- sis is placed on those mesons with a high value of xp = Pmeso,~/Pbeam, or of xE = E,,,~8on/Eb~a,n. Where statistics permit, measurements of the he- licity density matrix elements are made as a func- tion of Xp.

2. T H E H E L I C I T Y D E N S I T Y M A T R I X

The measurements of vector meson spin align- ment are extracted through measurements of the decay angles of the vector meson decay products. The spin properties of the vector mesons are de- scribed using the formalism of the helicity density matrix. The formalism of the OPAL analyses is described in detail in [1]. The helicity density matrix is a 3x3 matrix, with diagonal elements describing the relative intensity of mesons in the helicity - 1 , 0 and +1 helicity states. Thus the matrix element P00 describes the relative intensity in the helicity zero state, whilst the off-diagonal element P1-1 measures the coherence between the heticity +1 and helicity - 1 states. Convention- ally P00 =1 /3 is described as a state of no spin alignment, since implicitly f l - l -1 = P + l + l = 1/3 in this instance. In any case experiment cannot access the elements P+lnkl separately. In the case of no polarization Pi-1 --0.

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232 S. Robins~Nuclear Physics B (Iaroc. Suppl.) 75B (1999) 231-235

Analyses are performed in the helicity-beam frame, where the z-axis is the direction of the vector meson in the centre-of-mass frame, which coincides with the LEP laboratory frame. The y-axis is then the direction defined by the vector product of this z-axis with the incoming electron beam direction, and the x-axis defines a right- handed coordinate system. The angles measured in the vector meson decay are ~H and CH, the usual polar and azimuthal angles of the decay products relative to the vector meson direction.

The components of the vector meson helicity density matr ix can then be determined by fitting the observed angular distributions. The polar de- cay angle distribution for a vector meson decaying to two psuedoscalars, is given by:

W(COSOH) = ~[(1 -P0o) + (3po0 - 1)cos 2 OH]

It can be seen that when P0o =0, the angular dis- tr ibution N(OH) ~ sin20H, and when Po0 =1, N ( ~ H ) ~ cos 2 OH. When P00 =1/3 , the case of spin alignment, the distribution is isotropic in cos 0g. Fitt ing the polar angular distribution thus yields Poo •

The azimuthal decay angle distribution is given by:

W(lal) = (2/~)[1 +2Repl_lCOS21~l]

where a = [¢g[ -- 7r/2, to exploit the symme- try properties of the distribution. Fitting the az- imuthal distribution yields Repl-1 •

Whilst no detailed hadronization models exist, the expectation is that the orientation of non- primary quarks is random, and that they have no net polarization.

3. V E C T O R M E S O N A N A L Y S E S

The analyses outlined here use 4.3M hadronic Z ° decays recorded at LEP1 between 1990 and 1995. A description of the OPAL detector can be found elsewhere [2].

The techniques used to identify the vector me- son resonances vary according to the particularly meson and channel under investigation. All res- onances however are identified by fitting peaks to the appropriate inclusive mass spectrum. The

numbers of events seen in the mass peak, after ac- ceptance correction and background subtraction, are then fitted as a function of cos ~H to yield measurements of Poo , and of CH (where statis- tics permit) to yield Repl-1 •

3.1. B*--~B 7 Events containing b hadron decays are tagged

using secondary vertex information, and low en- ergy photons (the kinematics of the decay re- stricts the photon energy to below 800 MeV/c) identified via their conversion in the material of the OPAL detector to e+e - . B mesons are in- clusively reconstructed and the B* mass derived from the invariant mass of the B meson-photon combination. A total of 1894 candidates are ob- tained, [3]. The angular distribution of the decay photons was fitted to yield a measurement Poo = 0.36 5= 0.09, consistent with no spin alignment.

3.2. D *+ --+D°Tr + Details of the slection and reconstruction of

D *+ candidates is described in[4]. D O mesons are reconstructed through their decay to K-rr + and, for the spin analysis [1], required to lie in the mass range 1.79 to 1.94 GeV. Only those D o mesons with XE > 0.2 are used in the analysis. D *+ candidates were identified through their decay to a 'slow' pion. These low momentum pions were used to identify a peak at around 145 MeV/c 2 in the spectrum of the mass difference between the D o and D *+ candidate track combinations.

Maximum likelihood fits were made to the decay angular distributions and matrix element P00 measured separately for c --+D *+, b --+D *+ and background events. The charm component thus measured contains both directly produced D *+ mesons and those from excited charm hadron decays. The results for the helicity density matrix elements for this charm component were, P0o = 0.40 + 0.02 and Repl-1 = -0.039 5= 0.014. Thus the OPAL data show evidence for spin alignment of the D *+, i.e. enhanced production of D *+ in the helicity-zero state, and a small but significant negative value of Repl-1 , indicating coherence in in the primary q~ fragmentation.

S. Robins~Nuclear Physics B (Proc. Suppl.) 75B (1999) 231-235 233

3.3. ¢(1020) ---~K+K - Charged kaons are identified using energy loss

information in the OPAL jet chamber, and the ~o.8 ¢(1020) resonance fitted to the mass spectrum of 0.7 pairs of oppositely charged kaons [1]. Measure- 0.6 ments of the helicity density matrix are made us- 0.5 ing ¢ candidates with Xp > 0.7. The mass spectra 0.4 are formed in three bins each of the azimuthal and 0.3

0.2 polar decay angles, and fits made to these mass

0A spectra to determine the number of candidates o seen as a function of decay angle. These fits yield measureinents poo = 0.54 :t: 0.08, indicating pref- erential occupation of the helicity-zero state, and Repl_l = -0.11 ~: 0.07 suggesting, as for the D *+, coherent fragmentation.

3.4. K*(892) ° --+K+K 7= The inclusive K±K ~= mass spectrum is formed

to yield a high statistics sample of K* (892) 0 de- cays [5]. The high statistics enable measurements to be made in six bins of decay angle for twelve ranges of xp. The results are shown in Figure 1, where a clear change in the values of both Po0 and Repl_l can be seen to occur for Xp > 0.3.

The results of the OPAL measurements of the Poo for vector meson are summarised in Figure 2. There is clear evidence of a preference for the helicity-zero state for the D*, ~b and K* mesons. The measurements of Repl_l at high xp show sig- nificant negative values, sugesting coherent frag- mentation.

A prediction has been made [6] of the ratio of off-diagonal to diagonal elements of the helicity density matr ix elements for the K *°. This model assumes final state qq interactions (i.e. coherence in the fragmentation), Standard Model couplings in the e+e - -~qq interaction and low meson trans- verse momentum to the parent jet. This predic- tion is that R e p l _ l / ( 1 - poo) "~ -0.10, and the OPAL measurement for xp >0.3 is -0 .19 + 0.05, in reasonable agreement with this prediction.

4. L A M B D A H Y P E R O N P O L A R I Z A - T I O N

The longitudinal polarization, PL, of a hyperon can be measured using the angular distribution of

~=Z 0.3

0.2

0.1

0

' " . . . . . I . . . . I . . . . I . . . . I ' " " ' 1 . . . . I . . . . I . . . . I ' ' '

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-0.1

-0.2

-0,3 0

' ' ' 1 ' ' ' ' 1 . . . . I . . . . I . . . . I ' ' 1 ' ' ' 1 . . . . I . . . . '1 ' ' ' ' I '

. . . . . . . . . . . . . .

, , 1 . . . . . . . I . . . . I . . . . I . . . . I . . . . I . . . . I . . . . t . . . .

0.1 0.2 0.3 0.4 0.5 0.6 8.7 0.8 0.9

Figure 1. The helicity desnity matrix elements, Po0 and Repl-1 , measured in the decay K*(892) ° --+K+K ~ as a function of xp. The error bars are statistical and systematic combined in quadra- ture, with the tick marks indicating the statistical errors alone.

the decay products. For the decay A --+p 7r, this decay angular distribution is:

W(cos 0") ,-, 1 + aAPL cos0*

where cos 8" is the A - p angle in the centre-of- mass frame, and aA is the A decay parameter. Transverse polarization, PT, can be measured in an identical way by fitting the same function to cos ¢p, where Cp is the angle to the plane formed by the A and the event thrust axis.

Both the longitudinal and transverse polariza- tion have been measured using A hyperons re- constructed in OPAL data. The measured values are:

X p

234 £ Robins~Nuclear Physics B (Proc. Suppl.) 75B (1999) 231-235

B~

D,

¢(1020)

- 0 -

K'(892) °

OPAL

c-->D*, Xp> 0.2

- Xp> 0.7

e. Xp> 0.7

I I I

0.2 0.4 0.6 0.8 Poo

~ 0,8 i

0.7

0,6

0.5

0.4

0.3

0.2

0,1

t)

-0A

OPAL

......... ::::: ::o'::Lo%, I / • O P A L data / / / ~

/ i

X E

Figure 2. A summary of OPAL measurements of P00 in vector meson decays. The dashed line shows the expectation in the case of case of no spin alignment, P00 =1/3.

Figure 3. Measured longitudinal A polarization as a function of XE. The curves show a comparison with the J E T S E T Monte Carlo, and a modified JETS ET using the popcorn scheme according to Gustafson and Hakkinen.

X E > 0.3, P~ = -32.9 =t: 7.6% PT >0.3 GeV/c, P~ : 0.9 + 0.9%

Figure 3 shows these data as a function of XE, compared with the prediction of the JETSET7.4 Monte Carlo, with the default popcorn baryon production scheme [7] and the modified popcorn scheme of Gustafson and Hakkinen [9]. In both cases the J E T S E T Monte Carlo was tuned to the OPAL data (see [10]).

Tile modified baryon production scheme is an a t tempt to determine appropriately the amount of polarization expected in hyperons fi'om each of several different sources. It is assumed in this scheme that directly produced A hyperons will carry all tile polarization of the primary s quark.

Those A particles that are decay products of heav- ier baryons will carry some fraction of the primary s quark spin. A primary u or d quark loses its po- larization when it becomes a constituent of a A hyperon.

Agreement of both the default and modified J E T S E T predictions with data is good. No signif- icant transverse polarization has been observed.

5. SUMMARY

5.1. V e c t o r m e s o n sp in a l i g n m e n t Spin alignment of in leading vector mesons has

been observed at OPAL, and a preference seen for occupation of the helicity-zero state, i.e. P0o >

S. Robins~Nuclear Physics B (Proc. Suppl.) 75B 0999) 231-235 235

1/3. No model fully describes this behaviour. Whilst a simple statistical 'spin counting' [11] model fits the B'measurements, this model con- strains p00 to be below 0.5 - clearly contradicted by the OPAL data. A QCD inspired model [12] that treats hadronization as a process of soft gluon emission predicts po0 = 0, whilst a naive model [11] of vector meson production arising from a helicity conserving process q -~qV sug- gests P00 = 1.

In the string model of LUND [13], which has been used with great success to describe many phenomenon observed at the LEP experiments, there is no mechanism that can produce spin aligmnent of vector mesons. Similarly the widely used cluster model of HERWIG [14], whilst de- scribing LEP data rather well in general fails to make a prediction of vector meson spin alignment. These results thus await theoretical interpreta- tion.

The OPAL measurement of negative values of the off-diagonal element of the helicity density matrix element, Repl-1 , is consistent with co- herence in primary qq production and fragmenta- tion. A recent theory [6] predicts numerical val- ues for the K *°, arising from Standard Model ex- pectations, that are in reasonable agreement with OPAL measurements.

5.2. A polarization The results of OPAL measurements of the lon-

gitudinal A hyperon polarization are entirely con- sistent with a sinple model in which all of the pri- mary quark polarization is transferred to the final state hyperon during hadronization. No evidence of transverse polarization is seen.

tion), Z. Phys. C73, 379 (1997). 5. K. Ackerstaff et al. (The OPAL Collabora-

tion), Phys Lett. B412, 210 (1997). 6. M. Ansehnino, M. Bertini, F. Murgia and P.

Quintaros, 'Off-diagonal helicity density ma- trix elements for vector mesons produced at LEP', preprint hep-ph/9704420, to appear in Eur. Phys. Jour. 5,I. Anselmino, 'Spin effects in vector meson production at LEP', procs. Cracow Epiphany conference on spin effects in particle physics, Aeta Phys. Polon., B29 1469 (1998).

7. B. Andersson et al., Physica Scripta 32, 574 (1985).

8. T. SjSstrand, Comp. Phys. Commun. 39,346 (1986) T. SjSstrand and M. Bengtsson, Comp. Phys. Commun. 43,367 (1987) T. SjSstrand, CERN write-up, CERN- TH.7112/93, (1993).

9. P. Eden and G Gustafson, Z. Phys C75, 41 (1997). P. EdSn, 'A program for baryon generation and its applications to baryon fragmentation in DIS', Lund preprint: LU TP 96-29.

10. R. Akers et al., (The OPAL Collaboration), Z. Phys C69, 543 (1996).

11. J. F. Donoghue, Phys. Rev. D19, 2806 (1979). 12. J. E. Augustin and F. M. Renard, Nucl. Phys.

B162, 341 (1980). 13. B. Andersson, G. Gustafson, G Ingelman and

T. Sj6strand, Phys. Rep. 97, 31 (1983). 14. G. Marchesini et al., Comp. Phys. Commun.

67, .465 (1992).

R E F E R E N C E S

1. G. Alexander et al. (Tile OPAL Collabora- tion), Z. Phys. C74, 437(1997)

2. K. Ahmet et al., (The OPAL Collaboration), Nucl. Instrum. Methods A305, 275 (1991).

3. K. Ackerstaff et al. (The OPAL Collabora- tion), Z. Phys. C74, 413 (1997).

4. R. Akers et al. (The OPAL Collaboration), Z. Phys. C67, 27 (1995) G. Alexander et al. (The OPAL Collabora-