Work supported in part by Department of Energy Contract DE-AC03-76SF00515

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1 Presented at Hih-enery Physics International Euroconference on Quantum Chromodynamics (QCD 96), Montpellier, France, 4-2 Jul 996. SLAC-PUB-7295 QCD tests with polarized beams Takashi Maruyama a a Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309, USA We present three QCD studies performed by the SLD experiment at SLAC, utilizin the hihly polarized SLC electron beam. We examined particle production dierences in liht uark and antiuark hemispheres, and observed more hih momentum baryons and K, 's than antibaryons and K + 's in uark hemispheres, consistent with the \leadin particle" hypothesis. We performed a search for jet handedness in liht - and -jets. Assumin Standard Model values of uark polarization in Z 0 decays, we have set an improved upper limit on the analysin power of the handedness method. We studied the correlation between the Z 0 spin and the event-plane orientation in polarized Z 0 decays into three jets. The CP-even and T-odd triple product ~ SZ ( ~ k ~ k 2) formed from the two fastest jet momenta, k ~ and k ~ 2, and the Z 0 polarization vector SZ, ~ is sensitive tophysics beyond the Standard Model.. INTR ODUCTION Since 992 SLC has been runnin with a lonitudinally polarized electron beam, and SLD has collected approximately 50,000 hadronic Z 0 decays in 993 and 00,000 in 994/5 with averae beam polarizations of 63% and 77%, respectively. In the process e,! Z 0!, the forward-backward asymmetry A FB, uark polarization P, and Z 0 polarization P Z 0 are reatly enhanced by the lonitudinal beam polarization as shown in Table, and SLD has performed a variety of QCD studies exploitin these features. Table Expected Asymmetry and P olarization P e,= {77% P e,=+77% (u-type) {0.35 A FB (d-type) {0.49 P at cos = representin the SLD collaboration 2. LEADING P ARTICLE PRODUCTION In many framentation models, the primary uark and antiuark in Z 0! events appear in a specic hadron, and this \leadin" hadron tends to have lare momen tum. Experimentally, by separatin uark hemispheres from an tiuark hemispheres, it is possible to look for dierences in identied particle production which would be attributable to such \leadin" particles. W e de- ne a particle to be leadin if one of its constituent uarks is a primary uark, for example the u or u in e,! Z 0! uu. Then the experimental uestion is whether the inclusive properties are dierent for particles that could be \leadin" (e.. a + in a u,uark jet) and those that could not (e.. a, in a u,uark jet). To study this uestion we must: i) separate - and - jets; ii) select liht uark events (Z 0! uu; dd;ss)so as to be insensitive toheavy hadron decay products; and iii) identify particle types. W e then compare the scaled momen tum distributions of iven particles with those of their antiparticle in a pure sample of uark jets in order to determine whether the primary uark prefers a particular particle type or momen tum. The analysis used the chared tracks measured in the central drift chamber [] and in the vertex detector [2]. A set of cuts was applied to the data to select well-measured tracks, and events were reuired to be well-contained within the detec- Work supported in part by Department of Enery Contract DE-AC03-76SF0055

2 tor acceptance. Flavor tain was performed by countin the numberofwell measured tracks n si that were inconsistent with the interaction point as the oriin. Chared particle identication was performed with the Cherenkov Rin Imain Detector (CRID) [3]. Standard mass reconstruction techniues were used for neutral particle identication [4]. The lare forward-backward asymmetry due to the hihly polarized electron beam was used to separate uark from antiuark hemispheres. As the primary uarks from Z 0 decays are left handed, they tend to follow the direction of the incident left-handed fermion. The event was divided in two by a plane perpendicular to the thrust axis, and when the electron beam was left(riht)-handed, the hemisphere whose normal satised ~n ~p e > 0was labeled as the uark (antiuark) hemisphere. A cut was applied to remove events whose thrust axis failed to satisfy j cos t j > 0:2, where t is the anle between the thrust axis and the e, beam direction. The Standard Model at tree level predicts the purities of the uark- and antiuark-taed samples to be about 72% for our averae electron beam polarization of 73%. Liht uark events were selected by reuirin n si = 0. In each hemisphere, the production rates as a function of x p of identied hadrons were determined. W e combined the positively chared tracks in the -taed jets with the neatively chared tracks in the -taed jets (similarly, 's in -jets were combined with 's in jets). W e subtracted the contributions to these samples from hea vy uark events, estimated from the Monte Carlo simulation. For each hadron type h, the resultin rates were unfolded for the purity of the uark tain to obtain dierential production rates R(! h) in liht uark jets. W e dene the dierence between particle and antiparticle production rates normalized by their sum: D h = R(! h), R(! h) R(! h)+r(! h) : The systematic uncertainties on particle identication larely cancel in this variable, and the errors are dominated by statistics. Fiure shows these normalized dierences as a function of x p. For each particle type, the dierences are consistent with zero at low x p.for the 's the dierence is also consistent with zero at hih x p, whereas for the others a sinicant positive dierence is observed for x p above 0: Fiure. Normalized production dierences as a function of scaled momen tum for (a) chared pions (circles) and kaons (crosses), and (b) protons (circles) and 's (crosses). Since the baryons contain no constituent antiuarks, we interpret the steep rise in D p and D with increasin x p as an indication that baryon production is dominated by leadin particle pro-

3 duction as x p!. If production of (K ) mesons were dominated by leadin meson production, and, (K, )were produced eually in jets containin primary u and d(s) uarks, then we would expect to observe normalized dierences of 0:22 for the mesons, due to (i) the 22:7 production ratio for Z 0! dd(ss) : Z 0!uu, and (ii) the dierent electroweak asymmetries for u- and d-type uark production. Our data are more consistent with D = 0 than D = 0:22 over the entire measured x p rane, suestin some dilution of leadin pions from resonance decays such as the 0. Our measured D K values above x p ' 0:2 are consistently above 0.22, indicatin both that i) there is leadin kaon production at hih momen tum, and ii) leadin kaons are produced more often in ss events than in uu events. 3. JET HANDEDNESS Polarized incident electrons provide an excellent opportunity to test the transport of spin throuh the hadronization process since the Standard Model predicts hih polarization of uarks from Z 0 decays with a stron dependence on polar anle and incident electron polarization. A rst measuremen t of spin-transport, usin the techniue suested by Ref. 5, was reported in Ref. 6. This measuremen t has been updated with the 994{95 SLD dataset. The simplest observable with the same transformation properties under parity inversion as spin has the form = ^t ( ~p ~p 2 ), where ^t is a unit vector alon the jet axis, correspondin to the spin direction of a lonitudinally polarized parton, and ~p and ~p 2 are the momenta of two particles in the jet chosen by some chare-independent prescription, such asj~p j> j~p 2 j.[5] A jet may be dened as left- or rihthanded if is neative or positive, respectively. The jet handedness H is then dened as the asymmetry in the number of left- and riht-handed jets: H (N <0, N >0 )=(N <0 + N >0 ). Usin the expected parton polarization P from the Standard Model, the analyzin power of the method is dened by H = P. The observed H in liht-uark jets was found to be consistent with zero, and the 95% C. L. upper limit of the analyzin power was determined to be jj < 0:033. This improves the limit in Ref. 6 by a factor of 3, and rearms that inclusiv e transportation of spin throuh the hadronization process is small. 4. TRIPLE-PR ODUCT CORRELA TION For polarized Z 0 decays to three hadronic jets one can dene the triple product S ~ Z ( k ~ k ~ 2 ), which correlates the Z 0 boson polarization vector ~S Z with the normal to the three-jet plane dened by k ~ and k ~ 2, the momen ta of the hihest- and the second-hihest enery jets, respectively. The triple product S ~ Z ( k ~ k ~ 2 )iseven under C and P reversals, and odd under T N, where T N reverses momen ta and spin vectors without exchanin initial and nal states. Since T N is not a true time-reversal operation, a non-zero value does not sinal CPT violation and is possible in a theory that respects CPT invariance [7]. Similar observables were rst proposed for direct experimental observation of the non-abelian character of QCD in e,!! [8], and in e,! [9] where p a sizable sinal is expected at c.m. eneries s below 40 GeV; no experimental measuremen ts have been performed since a lonitudinally polarized electron beam is reuired. The dierential cross section for e,! for massless uarks ma y be written [9,0] d d cos! = 9 6 [(, 3 cos2!)+a Z cos!]; () where! is the polar anle of the vector normal to the event plane with respect to the electron-beam direction, and A Z is the polarization of the Z 0 bozon alon this same direction (A Z =(P e,, A e )=(, P e, A e ), where P e, is the electronbeam polarization, dened to be neative for a left-handed beam, and A e =2v e a e =(v 2 e+a 2 e) with v e and a e the electroweak vector and axial vector couplin parameters of the electron, respectively). With ja Z j representin the manitude [], the second term is proportional to the T N - odd triple product, and appears as a forwardbackward asymmetry of the ev ent-plane normal relative to the Z 0 polarization axis. The sin and manitude of this term are dieren t for the two beam helicities.

4 Recently Brandenbur, Dixon, and Shadmi have investiated Standard Model T N -odd contributions of the form S ~ Z ( k ~ k ~ 2 )atthez 0 resonance [0]. The triple product vanishes identically at tree level [7], but non-zero contributions arise from hiher-order processes such as those shown in Fi. 2: (a) QCD rescatterin of massive uarks [9], (b) QCD trianle of massive uarks [2], and (c) electroweak rescatterin via W and Z exchane loops. Due to various cancellations these contributions are found to be very small at the Z 0 resonance and yield values of the correlation parameter jj < 0,5. Because of this backround-free situation, measurement of the cross section () is sensitive tophysics processes beyond the Standard Model that ive 6= A (a) γ, Z γ, Z (c) Z W, Z Fiure 2. Representative Feynman diarams of hiher-order interactions with non-vanishin contributions to the triple product: (a) QCD rescatterin (m 6= 0 is reuired), (b) trianle diaram via uark annihilation (m 0 6= 0 is reuired), and (c) electroweak rescatterin. In the analysis [3] the hadronic event selection and three-jet reconstruction were based on the topoloy of enery depositions in the liuid aron calorimeter, takin advantae of its lare solid-anle coverae. The eciency for selectin (b) ' hadronic events was estimated to be 922%, with a backround in the selected sample of 0:40:2%, dominated by Z 0! +, and Z 0! e, events. To measure the triple-product correlation for e,!, three-jet events were selected and the three momen tum vectors of the jets were reconstructed usin the \Durham" jet alorithm [4]. Planar three-jet events were selected by reuirin exactly three reconstructed jets to be found with a jet-resolution parameter value of y c =0.005, the sum of the anles between the three jets to be reater than 358, and that each jet contain at least two clusters. A total of 44,683 events satised these criteria. The jet eneries were calculated by usin the measured jet directions and solvin the three-body kinematics assumin massless jets, and w ere then used to label the jets such that E >E 2 >E 3. For each event the reconstructed jet vectors were used to determine the vector normal to the jet plane and its polar anle!, from which the measured distribution of cos! was derived. A bin-by-bin correction factor (j cos!j), for detector acceptance and initial-state radiation, was determined from Mon te Carlo simulations. The cos! distribution is described by d d cos! = 9 6 [(, 3 cos2!) + A Z (, 2 P mis (j cos!j)) cos!];(2) where P mis is the probability of incorrectly orderin the enery of the three jets such that the sin of the cos! term is incorrect. Fi. 3 shows the corrected cos! distribution separately for leftand riht-handed beam events in the 994/5 data sample. A T N -odd contribution would appear as a forward-backward asymmetry, of opposite sin between the left- and riht-handed events. No asymmetry is apparen t. A maxim um-likelihood t of E. 2 to the cos! distributions from the 993 and 994/5 samples yielded = The T N -odd contribution is consistent with zero within the statistical error and the 95% C.L. limits are calculated to be,0:022 << 0:039. Anumber of systematic checks were performed. The analysis was performed on two Monte Carlo samples with sim ulated T N -odd values; in both

5 /N d/n/dcosω P < 0 P > cosω SLD A02 Fiure 3. Polar-anle distribution of the jet-plane normal with respect to the electron-beam direction with (a) left-handed and (b) riht-handed electron beam. The solid curve is the best t to the combined data samples. cases was measured to be consistent with the input value within the statistical error. The dependence of the value on the jet-ndin alorithm and the jet-resolution parameter w as examined. The analysis was also performed usin only chared tracks measured in the central drift chamber. In each case the T N -odd contribution was found to be consistent with zero within the statistical error. 5. Summary We have shown three measuremen ts that exploit the SLC beam polarization and the SLD capabilities. Wehave measured production rates of, K, p=p, K 0 and 0 = 0 in liht uarkand anti-uark jets, and observed leadin baryon and kaon production. We have searched inclusively for spin transport throuh hadronization, and set limits on jet handedness. Finally, we have measured the T N -odd correlation in polarized Z 0 decays to three-jets. W e nd the correlation to be consistent with zero and set 95% C.L. limits on beyond-the-standard-model T N - odd contributions to Z 0 decays to three-jets of,0:022 <<0:039. This work was supported by Department of Enery Contract No. DE-AC03-76SF0055. REFERENCES. M.D. Hildreth et al., Nucl. Inst. Meth. A367 (995). 2. C. J. S. Damerell et al., Nucl. Inst. Meth. A288 (990) T. J. Pavel, Ph.D. dissertation, Stanford University, in preparation. 4. K.G. Baird, Ph.D. Thesis, Ruters University, 996, SLAC-R-483 (996). 5. O. Nachtmann, Nucl. Phys. B27 (977) 34. A. V. Efremov et al., Phys. Lett. B284 (992) K. Abe et al., Phys. Rev. Lett. 74 (995) A. De Rujula et al., Nucl. Phys. B35, 365 (97). 8. A. De Rujula et al., Nucl. Phys. B46, 50 (978). 9. K. Fabricius et al., Phys. Rev. Lett. 45, 867 (980), and J. G. Korner et al., Phys. Lett. 94B, 207 (980). 0. A. Brandenbur, L. Dixon, and Y. Shadmi, Phys. Rev. D53, 264 (996).. The value of depends on the parameter that determines the jet m ultiplicity of events, and is not a universal constant. 2. K. Haiwara et al., Nucl. Phys. B358, 80 (99). 3. K. Abe et al., Phys. Rev. Lett. 75, 473 (996). 4. S. Catani et al., Phys. Lett. B263, 49 (99).