Continuum Charged $D^{}$ Spin Alignment at $sqrt{s}$ = 10.5

a r X i v :h e p -e x /9802022v 1 26 F e

b 1998CLNS 98/1542CLEO 98-3

Continuum Charged D ?Spin Alignment at √s =10.5GeV is presented.This study using 4.72fb ?1of CLEO II data shows that there is little evidence of any D ?spin alignment.

1

G.Brandenburg,1R.A.Briere,1A.Ershov,1Y.S.Gao,1D.Y.-J.Kim,1R.Wilson,1

H.Yamamoto,1T.E.Browder,2Y.Li,2J.L.Rodriguez,2T.Bergfeld,3B.I.Eisenstein,3

J.Ernst,3G.E.Gladding,3G.D.Gollin,3R.M.Hans,3E.Johnson,3I.Karliner,3 M.A.Marsh,3M.Palmer,3M.Selen,3J.J.Thaler,3K.W.Edwards,4A.Bellerive,5 R.Janicek,5D.B.MacFarlane,5P.M.Patel,5A.J.Sado?,6R.Ammar,7P.Baringer,7 A.Bean,7D.Besson,7D.Coppage,7C.Darling,7R.Davis,7S.Kotov,7I.Kravchenko,7

N.Kwak,7L.Zhou,7S.Anderson,8Y.Kubota,8S.J.Lee,8J.J.O’Neill,8R.Poling,8 T.Riehle,8A.Smith,8M.S.Alam,9S.B.Athar,9Z.Ling,9A.H.Mahmood,9S.Timm,9

F.Wappler,9A.Anastassov,10J.E.Duboscq,10D.Fujino,10,?K.K.Gan,10T.Hart,10 K.Honscheid,10H.Kagan,10R.Kass,10J.Lee,10M.B.Spencer,10M.Sung,10A.Undrus,10,?

A.Wolf,10M.M.Zoeller,10

B.Nemati,11S.J.Richichi,11W.R.Ross,11H.Severini,11

P.Skubic,11M.Bishai,12J.Fast,12J.W.Hinson,12N.Menon,8e8e0734f111f18583d05a3fler,12

E.I.Shibata,12I.P.J.Shipsey,12M.Yurko,12S.Glenn,13Y.Kwon,13,?A.L.Lyon,13 S.Roberts,13E.H.Thorndike,13C.P.Jessop,14K.Lingel,14H.Marsiske,14M.L.Perl,14 V.Savinov,14D.Ugolini,14X.Zhou,14T.E.Coan,15V.Fadeyev,15I.Korolkov,15

Y.Maravin,15I.Narsky,15V.Shelkov,15J.Staeck,15R.Stroynowski,15I.Volobouev,15 J.Ye,15M.Artuso,16F.Azfar,16A.E?mov,16M.Goldberg,16D.He,16S.Kopp,16 G.C.Moneti,16R.Mountain,16S.Schuh,16T.Skwarnicki,16S.Stone,16G.Viehhauser,16

J.C.Wang,16X.Xing,16J.Bartelt,17S.E.Csorna,17V.Jain,17,§K.W.McLean,17 S.Marka,17R.Godang,18K.Kinoshita,8e8e0734f111f18583d05a3fi,18P.Pomianowski,18S.Schrenk,18

G.Bonvicini,19D.Cinabro,19R.Greene,19L.P.Perera,19G.J.Zhou,19M.Chadha,20

S.Chan,20G.Eigen,8e8e0734f111f18583d05a3fler,20M.Schmidtler,20J.Urheim,20A.J.Weinstein,20

F.W¨u rthwein,20D.W.Bliss,21

G.Masek,21

H.P.Paar,21S.Prell,21V.Sharma,21 D.M.Asner,22J.Gronberg,22T.S.Hill,8e8e0734f111f18583d05a3fnge,22R.J.Morrison,22H.N.Nelson,22

T.K.Nelson,22D.Roberts,22B.H.Behrens,23W.T.Ford,23A.Gritsan,23J.Roy,23 J.G.Smith,23J.P.Alexander,24R.Baker,24C.Bebek,24B.E.Berger,24K.Berkelman,24 K.Bloom,24V.Boisvert,24D.G.Cassel,24D.S.Crowcroft,24M.Dickson,24 S.von Dombrowski,24P.S.Drell,24K.M.Ecklund,24R.Ehrlich,24A.D.Foland,24 P.Gaidarev,24L.Gibbons,24B.Gittelman,24S.W.Gray,24D.L.Hartill,24B.K.Heltsley,24 P.I.Hopman,24J.Kandaswamy,24P.C.Kim,24D.L.Kreinick,24T.Lee,24Y.Liu,24 N.B.Mistry,24C.R.Ng,24E.Nordberg,24M.Ogg,24,??J.R.Patterson,24D.Peterson,24

D.Riley,24A.So?er,24B.Valant-Spaight,24C.Ward,24M.Athanas,25P.Avery,25

C.D.Jones,25M.Lohner,25S.Patton,25C.Prescott,25J.Yelton,25and J.Zheng25

1Harvard University,Cambridge,Massachusetts02138

2University of Hawaii at Manoa,Honolulu,Hawaii96822

3University of Illinois,Urbana-Champaign,Illinois61801

4Carleton University,Ottawa,Ontario,Canada K1S5B6

and the Institute of Particle Physics,Canada

5McGill University,Montr′e al,Qu′e bec,Canada H3A2T8

and the Institute of Particle Physics,Canada

6Ithaca College,Ithaca,New York14850

7University of Kansas,Lawrence,Kansas66045

8University of Minnesota,Minneapolis,Minnesota55455

9State University of New York at Albany,Albany,New York12222

10Ohio State University,Columbus,Ohio43210

11University of Oklahoma,Norman,Oklahoma73019

12Purdue University,West Lafayette,Indiana47907

13University of Rochester,Rochester,New York14627

14Stanford Linear Accelerator Center,Stanford University,Stanford,California94309 15Southern Methodist University,Dallas,Texas75275

16Syracuse University,Syracuse,New York13244

17Vanderbilt University,Nashville,Tennessee37235

18Virginia Polytechnic Institute and State University,Blacksburg,Virginia24061 19Wayne State University,Detroit,Michigan48202

20California Institute of Technology,Pasadena,California91125

21University of California,San Diego,La Jolla,California92093

22University of California,Santa Barbara,California93106

23University of Colorado,Boulder,Colorado80309-0390

24Cornell University,Ithaca,New York14853

25University of Florida,Gainesville,Florida32611

3

I.INTRODUCTION

There have been numerous theoretical[1–7]and experimental[8–15]studies of the frag-mentation of heavy quarks.The energy distribution and?avor dependence of heavy quark hadronization have been modeled by fragmentation functions.The role that spin plays in the hadronization process is still being investigated and is not well understood at this time [16–22].To increase the understanding of this role,a precise measurement of the probabilities of a meson being directly produced in each of the available spin states is needed.

At CLEO,the fragmentation of charm quarks can be analyzed by making measurements of primary hadrons containing charm quarks from continuum e+e?annihilations.CLEO has previously published results of charmed meson energy distributions[8]as well as the spin alignment of charged D?mesons[18].In this paper an updated measurement of the charged D?spin alignment using the entire CLEO II dataset is presented.

II.POLARIZATION,ALIGNMENT,AND P V

According to the quark model,a meson is composed of two spin1

(1)

V+P

where P and V are the respective probabilities of the meson being created in the pseudoscalar and vector states.

The helicity formalism is useful in the context of describing the angular distributions and correlations in the production and decay of particles with non-zero spin.For a particle with momentum p,the helicity is de?ned as

J· p

λ=

mesons from e+e?→γ?→cˉc are unpolarized,but it is possible for the D?mesons to be aligned.

To measure the spin alignment of a vector meson,the angular distribution of its decay products is analyzed,but because the angular distributions of theλ=1andλ=?1states are degenerate,the values ofρ11andρ?1?1cannot be distinguished and only one variable, e.g.ρ00=1?ρ11?ρ?1?1,is accessible.From the de?nition above,the vector meson is aligned ifρ00di?ers from1/3.For the case of a vector meson decaying to two pseudoscalar mesons,the angular distribution can be written

3

W(cosθ)=

,(4)

1?ρ00

the angular distribution can be expressed as

W(cosθ)=N(1+αcos2θ)(5) where N is a normalization factor equal to3/(6+2α).The value ofαcan range between?1 and+∞,where the angular distribution would be isotropic ifα=0,proportional to sin2θifα=?1and proportional to cos2θifα=∞.

Whereas the naive statistical expectation is that all four S-wave meson states are created in equal proportions,i.e.ρλλ=1

conjugate modes is implied throughout this paper).Theπ+in the D?+decay is kinematically limited to having a momentum less than456MeV/c in the lab frame of reference,and is

referred to as the“slow”pion.

All tracks used in this analysis are required to have an impact parameter within5mm of the interaction point in the plane transverse to the beam pipe and within50mm in the

direction of the beam pipe.Tracks are also required to have a momentum less than6GeV/c

and an r.m.s.residual less than1mm for their hits.Particle ID is not used since there is little gain for this particular analysis and it introduces the possibility of additional systematic

errors.For a pair of photons to be considered as a candidateπ0,they must each have an energy of at least100MeV,be within the“good”barrel of the detector(|cosθdetector|<0.71), have a shower shape in the crystal calorimeters consistent with that of a photon,combine

to be within20MeV/c2of the neutral pion mass,and have|cosθγ|<0.9,whereθγis the decay angle of the photon in theπ0rest frame,with respect to theπ0direction of motion in

the lab frame.

For the D0→K?π+mode,the D0is reconstructed by taking all possible pairs of oppositely charged tracks in an event,assigning the kaon mass to one and the pion mass to the other(or vice versa),adding their four-momenta,and then calculating the invariant mass.The D?+is reconstructed by adding the four-momentum of a candidate slowπ+in the event to the four-momentum of the candidate D0.The mass di?erence,?M,between the candidate D0and D?+is required to be within2.5MeV/c2of the world-average mass di?erence of145.42MeV/c2[28].

The D0is spinless and the decay products have an isotropic angular distribution.How-ever,due to the jet-like nature of continuum events,the background from random track combinations tends to have cosφK??1,whereφK is the decay angle of the K?in the D0 rest frame,relative to the D0motion in the lab frame.A requirement that cosφK≥?0.9is added to improve the signal-to-background ratio.

For the D0→K?π+π0mode,the four-momentum of a candidateπ0is added to the four-momenta of two oppositely charged tracks to form candidate D0’s in the event.Mass di?erence and kaon decay angle requirements are the same as described above.

IV.FITTING

To test models that predict that the alignment varies as a function of the momentum of the D?+,the data are broken up into six x+bins in the range0.25to1.0,where x+is a Lorentz-invariant variable de?ned as

x+≡P(D?)+E(D?)

E2beam?M2D?+and M D?+is the world-average value for the mass of a D?+.

For each x+range,a sideband subtraction is performed.The sideband region is from 9MeV/c2to12MeV/c2above the mean of the?M peak and the ratio for the sideband subtraction is determined by?tting the data with a bifurcated double Gaussian for the signal plus a background function A+B(?M)1/2+C(?M)3/2and integrating the background shape

6

for the signal and sideband regions.The?ts used to determine the sideband ratios are shown in Figures1and2.

The sideband-subtracted M(Kπ)data is?t for each x+bin with a double Gaussian for

the signal region plus a?rst-order polynomial background.1Each of these x+bins is broken up into?ve equal cosθbins,whereθis the angle de?ned in Section II.To prevent the?tted

signal shape from having large?uctuations due to lower statistics in some cosθbins,the D0

mass peak is?t for each cosθbin with the ratios of areas and widths of the double Gaussian ?xed to those found when?tting the mass peak in that momentum range for the entire cosθ

spectrum.

V.EFFICIENCIES

It is important to understand the relative e?ciencies of detecting a D?+in the various

cosθbins.In the lowest momentum bins,for example,the e?ciency decreases as cosθapproaches one because of the increased di?culty in measuring the track of a slow pion that

is emitted in the direction opposite the D?direction in the lab frame.Detection e?ciency as a function of x+and cosθwas measured by analyzing Monte Carlo data with a GEANT-based

detector simulation.

Monte Carlo events were generated using the Lund Jetset7.3program,where the e+e?annihilation was required to result in a cˉc pair with one of the charm quarks hadronizing to

a D?+that decays to D0π+with D0→K?π+(π0),while no constraints were placed on the other charm quark.The D?mesons were produced such that their decay to D0π+had an

isotropic angular distribution in the rest frame of the D?+.

VI.RESULTS

The?ts of the sideband subtracted M(Kπ)and M(Kππ0)distributions for all scaled

momentum ranges are shown in Figures3and4.2The e?ciency-corrected angular distribu-tions for both decay modes were combined in each x+bin with a weighted average and are shown in Figure5,where they have each been normalized to unit area and?t with Eq.(5).

The values ofαresulting from these?ts as well as the?ts for each of the two decay modes treated separately are listed in Table I.Figure6shows the combined results forαplotted as a function of momentum as well as the theoretical curves suggested by Suzuki[23]and Cheung and Yuan[24].Table II lists the values ofρ00as calculated from the measurement ofαfor each scaled momentum bin.Averaging the cosθdistributions over all momenta and then?tting gives a valueˉα=?0.028±0.026,corresponding toˉρ00=0.327±0.006.

E v e n t s / 0.5 (M e V / c 2

)

M = M (K )

FIG.1.D ??D mass di?erence for the D 0→Kπdecay mode for the six x +ranges a)

0.25

8

E v e n t s / 0.5 (M e V / c 2

)

M = M (K

)

FIG.2.D ??D mass di?erence for the D 0→Kππ0decay mode for the ?ve x +ranges a)0.45

9

E v e n t s / 5 (M e V / c 2

)

E v e n t s / 5 (M e V / c 2

)

(GeV / c 2

)

M (K )0

FIG.4.M (Kππ0)after sideband subtraction for the ?ve x +ranges a)0.45

D 0→K ?π+D 0→K ?π+π0

Combined

Con?dence x +

Events α

Events α

α

Level(%)

cos

FIG.5.Normalized cos θdistributions in the six x +ranges for the D 0→K ?π+and D 0→K ?π+π0decay modes combined.The solid squares are the e?ciency-corrected yields for each cos θbin in the speci?ed x +range.These distributions are ?t with the function W (cos θ)=0.4N (1+αcos 2θ),where the factor of 0.4is the bin width and N =3/(6+2α).x +ρ00

X +I

I

√

Collaboration

HRS290.18±0.080.371±0.016 TPC29-0.14±0.17±0.030.301±0.042±0.007 SLD910.019±0.378±0.5820.34±0.08±0.13 OPAL910.33±0.110.40±0.02 CLEO I.510.50.08±0.07±0.040.351±0.015±0.008 CLEO II10.5-0.028±0.0260.327±0.006 TABLE III.Results forˉαandˉρ00found by various collaborations.

Similar analyses have been done by the HRS,TPC,SLD and OPAL collaborations [16,17,21,20],as well as by CLEO using a previous data set[18].The average values of αandρ00in each study are presented in Table III.

VII.SYSTEMATIC ERROR

Many possible sources of absolute systematic uncertainty,such as the overall track-?nding e?ciency,do not have a signi?cant e?ect on this analysis because the extraction ofαin each momentum range involves only the relative comparisons of the same measured quantity, namely the yield of the D0decays,in the di?erent bins of cosθ.The remaining sources of uncertainty will therefore be related to extracting the yield and the e?ciency as a function of cosθ.The e?ects of the various sources of systematic error are shown in Figure7while the methods used to determine these errors are described below.

The Monte Carlo contribution to the systematic error was accounted for by including the error in the Monte Carlo e?ciencies in the calculations of the yields.To investigate the systematic error associated with the?tting function,the analysis was done using a single Gaussian rather than a double Gaussian to?t the signal peaks.Likewise,to investigate the systematic error associated with the choice of range for the sideband subtraction,the analysis was done using a sideband region from6MeV/c2to9MeV/c2above the nominal D??D mass di?erence rather than9MeV/c2to12MeV/c2above the nominal value.The e?ect of the mass di?erence requirement was investigated by constraining the mass di?erence to be within1.25MeV/c2of the PDG value rather than2.5MeV/c2.The systematic e?ects of the cosθbinning were studied by using six equal cosθbins rather than?ve.The di?erences between the resulting values ofαand the central value were all summed in quadrature as an estimate of the systematic error and are included in the error bars shown in Figure6.

A small linear component in the angular distribution can easily be seen in Figure5for the range0.65

VIII.INTERPRETATION OF RESULTS

We have measured the spin alignment of all D?mesons produced in e+e?→qˉq interac-√

tions at

Result

Fitting Shape

Mass Difference Cut FIG.7.The results from the systematic error studies for the six x +bins a)0.25

does not come from a decaying B meson,we cannot determine any other details about the production hierarchy.From a theoretical standpoint,we are particularly interested in the D?mesons that are produced directly in the e+e?collision,but we cannot distinguish these from secondary D?’s resulting from decays of charm mesons with L>0.[29–31].

The most prominent excited charm mesons,which are commonly referred to as D??mesons,consist of a charm quark and a light anti-quark with relative orbital angular mo-mentum L=1.They are categorized into four states with spin-parity J P=0+,1+,1+, and2+.A0+state decay to D?πis forbidden due to spin-parity conservation while other D?modes are expected to be suppressed.When a2+state decays through a D?channel,it can only produce a D?meson with a helicity of±1in the2+rest frame,while the1+states only decay through D?channels and favor a helicity of0in the1+rest frame.From the measurements available[32,33],we estimate that16-20%of D?mesons observed at CLEO could be daughters of a D??meson,not including the contribution from D??s mesons.

Although the favored helicities of D?’s from the decays of2+and1+charm states partially cancel,it is probable that these D?’s are aligned in their production rest frame,i.e.the rest frame of the parent D??.It is expected that any e?ect would be most noticeable for the highest x+bins which has the largest correlation between the D?4-momentum in the lab frame and the D?4-momentum in the D??rest frame.If the4-momenta in the two reference frames are uncorrelated,as tends to be the case for the lower x+bins,any alignment of D?’s from D??’s would not be noticeable in the lab frame.

Due to the current lack of information about the production and decay of P-wave charm meson states,we can only state that D??decays could have a signi?cant e?ect on this D?spin alignment measurement in at least some of the x+bins.

IX.CONCLUSION

This analysis is the most precise measurement of the spin alignment of D?+mesons to date.The data,without any corrections for D??e?ects on the measurements,agree well with the statistical model expectation that the J z=0state has a1

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