NRQCD Prediction for the Polarization of the Jpsi Produced from b-decay

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MADPH-96-959NRQCD Prediction for the Polarization of the J/ψProduced from b-decay Sean Fleming Department of Physics,University of Wisconsin,Madison,WI 53706,USA Presented at the Meeting of the Division of Particles and Fields,August 1996,in Minneapolis.The work presented here is based upon a recent paper a done in collaboration with Oscar F.Hern′a ndez,Ivan Maksymyk,and H′e l`e ne Nadeau.The NRQCD predictions for the polarization of the J/ψproduced in b →J/ψ+X ,as well as the helicity-summed production rate are presented.2tr G μνG μν+ ˉΨ?i D Ψ?+ψ? iD 0+D 22m Q χ+···(1)where G μνis the gluon ?eld-strength tensor,Ψ?is the Dirac spinor ?eld for a light quark,D μ=?μ+igA μis the gauge-covariant derivative (with g be-

ing the QCD coupling constant),m Q is the heavy quark mass,and ψand χare 2-component ?elds that annihilate heavy quarks and create heavy anti-quarks respectively.Color and spin indices on the ?elds have been suppressed.Eq.1describes a fully relativistic ?eld theory for the light degrees of freedom coupled with a Schr¨o dinger ?eld theory for the heavy quarks and antiquarks.The relativistic e?ects of full QCD are reproduced through additional terms represented by the ···in Eq.1.In principle there are in?nitely many terms.However,using NRQCD v -scaling rules it is possible to retain only those that contribute through a given order in v .

The NRQCD factorization formalism is a rigorous derivation within NRQCD of a factored form for quarkonium production and decay rates.A central result

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is that inclusive quarkonium production cross sections must have the form

σ(A+B→H+X)= n F n

d cosθ ψ→μ+μ?(θ) ∝1+αcos2θ,(3) wher

e the polar angleθis de?ned in the J/ψrest frame for which the z-axis is aligned with the direction o

f motion of the J/ψin the lab.

The branching ratio for b→J/ψ+X is calculated using a matching procedure2.One obtains3

BR(b→J/ψ+X)=

0.002 Oψ1(3S1) +0.1 Oψ8(3S1) +0.2 Oψ8(1S0) +0.6 Oψ8(3P0)

Beneke and Rothstein5and Braaten and Chen6have developed techniques for deriving the production rates of quarkonia with speci?ed helicities.Apply-ing their methods one obtains an expression for the polarization parameter3?0.39 Oψ1(3S1) ?17 Oψ8(3S1) +52 Oψ8(3P0) /m2c α=

6.E.Braaten and Y.-Q.Chen,Phys.Rev.D54,3216(1996).

7.R.M.Barnett et al.,Phys.Rev.D54,1(1996).

8.P.Cho and A.K.Leibovich,Phys.Rev.D53,6203(1996);G.T.Bodwin,

D.K.Sinclair and S.Kim,preprint(hep-lat/9605023);J.Amundson,S.

Fleming,and I.Maksymyk,preprint(hep-ph/9601298).

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