Bin Gong

Institute of High Energy PhysicsChinese Academy of Science

QWG08@Nara 2008.12

QCD corrections to double charmonium

production in annihilation at −+ee GeV610 .s =

Colleague: Jian-Xiong Wang

IntroductionQCD corrections to two double charmoniumproduction at the B factories

Summary

OutlineOutline

cηJ/ψee +→−+

J/ψJ/ψee +→−+

In order to remedy the huge discrepancy of J/ψ production on Tevatron, color-octet mechanism was proposed based on NRQCDBut there are still difficulties:

J/ψ photoproduction at the DESY ep collider HERAJ/ψ production at B-factoriesJ/ψ (ψ’) polarization at the Fermilab Tevatron

It seems that NLO corrections are very important!

Current experimental results on inelastic J/ψ photoproduction are adequatelydescribed by the color singlet channel alone at NLOReal correction process gives the same order and/or even largercontribution at high pt region than the LO color singlet processHigh order process gives larger contribution at high pt region than the LO color singlet process

ccJ/ψγγ →

cJ/ψcg →

IntroductionIntroduction

cηJ/ψee +→−+

LO NRQCD Prediction: 2.3-5.5 fbE. Braaten and J. Lee, Phys. Rev. D67, 054007 (2003); D72, 099901(E) (2005).K. Y. Liu, Z. G. He and K. T. Chao, Phys. Lett. B557, 45 (2003).K. Hagiwara, E. Kou and C. F. Qiao, Phys. Lett. B570, 23 (2003).

Belle : J/ c B c ≥ 2 25. 6 2. 8 3. 4 fbBABAR : J/ c B c ≥ 2 17. 6 2. 8−2.1

1.5 fb

Experimental Data:

K. Abe et al. (Belle Collaboration), Phys. Rev. Lett. 89, 142001 (2002)P. Pakhlov (Belle), arXiv:hep-ex/0412041.B. Aubert et al. (BABAR Collaboration), Phys. Rev. D72, 031101 (2005).

Such a large discrepancy challenges current understanding of charmonium production based on NRQCD.

NLO QCD Corrections: Gives a K factor of about 2Y. J. Zhang, Y. J. Gao and K. T. Chao, Phys. Rev. Lett. 96, 092001 (2006).

Relativistic Corrections: Gives another K factor of about 2G. T. Bodwin, D. Kang, T. Kim, J. Lee and C. Yu, AIP Conf. Proc. 892, 315 (2007).

Z. G. He, Y. Fan, and K. T. Chao, Phys. Rev. D75, 074011 (2007).

Combination of above corrections may resolve the large discrepancy.

Since the calculation of the NLO QCD corrections for this process is quite complicated, and plays a very important role in explaining the experimental data, we perform an independent calculation with our FDC package.

Z mOS −3C F

s4

1UV

− E ln 4 2

m c2 4

3 O

Z 2OS −C F

s4

1UV

2 IR

− 3E 3 ln 42

mc2 4 O

Z 3OS s

4 0′ − 2C A 1

UV− 1

IR− 4

3 T F1UV

− E ln 4 2

m c2 O

Z gMS − 0

2 s4

1UV

− E ln4 O

LO

NLO

0 128 2 s2e c2|R sJ /0| 2|R s

c 0| 2s−432

27m c8s112

NLO 0 1 s −0 ln 2m c

K 1s6

K 1 s −24 − 79s − 68s2

3s2s 1 f1s2 − 3s 16

2s − 4 − f 23s

2s − 2 f 3−34s3 193s2 − 342s 160

4s − 4s − 2

f 4−41s2 − 194s 64

32s − 4 f 58s2 − 21s − 8

2s − 4 f 665s2 − 302s 64

32s − 4 f7−3s2 − 4s2s − 4

a 14z1 8 − 7s

s2 s − 4 −64s4 406s3 11s2 − 335s − 120

s − 42s 12 a 92z2−8s2 − 19s 130

ss − 4

a 62z1 8 − 7s

s2 s − 4

z2−130 19s 8s2 ss − 4 −32s4 − 110s3 639s2 696s 172

s − 42s 12 a 74z1 7s − 8

s2 s − 4

80 diagrams in total

curveslower for GeV 5.1curvesupper for GeV 4.1

GeV 978.0)0(

(0)(0)(0)

GeV 10.6

GeV 3380Λ

32

(4)MS

==

=

==

=

=

c

c

s

sηs

J/ψs

mmR

RRR

s

.

c

Cross section as function of the renormalization scale The scale dependence has

not been improved when NLO QCD corrections are included.

2

GeV 5.1

/sμ

mc

=

=

More details of this work can be found in Phys. Rev. D77, 054028 (2008).

The K factor becomes larger as center-of-mass energyincreases, which indicates that it is more difficult toobtain the convergent result from the pQCD withoutthe resummation of terms as the center-of-mass energy goes higher.

)ln( 2cs/m

Cross section and K factor as function of center-of-mass energy

J/ψJ/ψee +→−+

LO NRQCD prediction indicates that the cross section of this process is larger than that of J/ψ+ηc production by a factor of 1.8, but no evidence for this process was found at the B factories.

G. T. Bodwin, J. Lee and E. Braaten, Phys. Rev. D90, 162001 (2003); 95, 239901(E) (2005).

K. Abe et al. (Belle Collaboration), Phys. Rev. D70, 071102 (2004).

The discrepancy of J/ψ+ηc production may be resolved by including higher order corrections, how about this one?

36 NLO diagrams remain in total. And there are six-point integrals in diagrams of groups (b) and (d) .

All six-point scalar integrals can be reduced to several five-pointscalar integrals.Most five-point scalar integrals can further be reduce to four-pointscalar integrals except that five of them need to be integrated directly.E 0 1

2 p1 p2 , 12 p 2 − p1, 1

2 p 3 , − 12 p 3 , 0, 0, 0, mc , m c

ns.integratioscalar in theappear variablealsobut ˆ bleonly variaNot t s

1 dt d 0

dt 1 s Ks, t

0 1 s Ks

There is no gluon in LO diagrams, thus we have:The result is independent of renormalization scheme of gluon fieldand QCD gauge coupling constant.

. scaleation renormaliz theoft independen is )ˆ( μsKZmOS −3C F

s4

1UV

− E ln 4 2

m c2 4

3 O

Z2OS −C F

s4

1UV

2IR

− 3E 3 ln 4 2

m c2 4 O

GeV 1.5for GeV 944.0)0(

1371GeV 10.6

GeV 3380Λ

32

(4)MS

==

==

=

cs mR

/αs

.

The K factor ranges from -0.314 to 0.253, strongly depending onthe renormalization scale, which indicates a large uncertainty. Even though, we can find that NLO QCD corrections greatly decreasethe cross section, and may explain why this channel have not beenobserved at the B factories.

2

GeV 1.5d

dd

dK

)cos(LONLO

/sμ

mxσ

xσ

x

c

/

=

=

=

= θ

At the peak along the beam direction |x|=1, the NLO QCD corrections decrease the differential cross section lesser, which makes the peak even sharper.

Differential cross section as a function of |x|. θisthe angle between J/ψand the beam.

2

GeV 1.5

/sμ

mc

=

=

The NLO QCD corrections become smaller as the center-of-mass energy increases.

More details of this work can be found in Phys. Rev. Lett. 100, 181803 (2008).

Cross section and K factor as function of center-of-mass energy

The NLO QCD corrections to J/ψ+ηc production at the B factories are calculated. A K factor of about 2 is obtained. It decreases the discrepancy between LO theoretical predictions and experimental measurements, and confirm the result given by Y. J. Zhang, Y. J. Gao and K. T. Chao analytically.

The NLO QCD corrections to The NLO QCD corrections to J/J/ψψ+ + J/J/ψψproduction at the B production at the B factories are calculated. We find that the cross section at factories are calculated. We find that the cross section at NLO is greatly decreased. When combined with the results NLO is greatly decreased. When combined with the results for for J/J/ψψ++ηηcc production, and also relativistic corrections of production, and also relativistic corrections of two channels, we can explain why this channel have not been two channels, we can explain why this channel have not been observed at B factories while observed at B factories while J/J/ψψ++ηηcc have.have.

SummarySummary

Thanks！