CONG-FENG QIAO CONG-FENG QIAO 11HuLanHaoTe, 2010HuLanHaoTe, 2010

Pseudoscalar Quarkonium Pseudoscalar Quarkonium Exclusive Decays to Vector Meson Pair Exclusive Decays to Vector Meson Pair Cong-Feng QiaoCong-Feng Qiao Graduate University Graduate University Chinese Academy of Sciences Chinese Academy of Sciences July 20 July 20 ，， 20102010


ContentsContents

Exclusive Decays to J/Exclusive Decays to J/ΨΨ Pair Pair Exclusive Decays to Vector Meson PairExclusive Decays to Vector Meson PairBrief Summary Brief Summary

b

c


I. Exclusive Decays to J/I. Exclusive Decays to J/ΨΨ Pair Pair The lowest energy state in Υ family, the , is veThe lowest energy state in Υ family, the , is very elusive. The existence of the is a solid predry elusive. The existence of the is a solid prediction of the quark modeliction of the quark modelAbout thirty year after it spin triplet partner beiAbout thirty year after it spin triplet partner being found, recently it was observed for the first ting found, recently it was observed for the first time by Babar through Υ (3s) --> γme by Babar through Υ (3s) --> γ [Aubert, et al., Babar Collaboration, 2008][Aubert, et al., Babar Collaboration, 2008]

b

b

b

b

The The bottomoniumbottomonium energy level spectru energy level spectrumm (CLEO Collaboration July 19, 2002) (CLEO Collaboration July 19, 2002)

In recent years, the search for has been coIn recent years, the search for has been conducted at CLEO, LEP, and CDF, B-factories, usinducted at CLEO, LEP, and CDF, B-factories, using both inclusive and exclusive methodsng both inclusive and exclusive methodsIt is worth noting that both Babar and CLEO-It is worth noting that both Babar and CLEO-c measurements are indirect ones. For further sc measurements are indirect ones. For further study on physics, direct measurements on its tudy on physics, direct measurements on its decay products are necessarydecay products are necessary

b

b

Direct Search for at CDFDirect Search for at CDF [Tseng, CDF, 2002][Tseng, CDF, 2002]

J/J/J/J/ A small cluster of 7 events can be seen, A small cluster of 7 events can be seen, where 1.8 events are expected from where 1.8 events are expected from backgroundbackground If this cluster is due to decay, then thIf this cluster is due to decay, then the e product of its production cross-section product of its production cross-section and decay branching fractions are near and decay branching fractions are near the lower limit of expectation from the lower limit of expectation from Braaten et al.Braaten et al.

b

b

b

According Braaten, Fleming and Leibocich According Braaten, Fleming and Leibocich (hep-ph/0008091) , though helicity (hep-ph/0008091) , though helicity suppressed,suppressed, Which seems to be overestimated, sinceWhich seems to be overestimated, since [Maltoni and Polosa,hep-ph/0405082][Maltoni and Polosa,hep-ph/0405082]

3 5bB r [ J / J / ] 7 10 ~ 7 10

5bBr [ C C C C ] ~ 10

A recent analysis shows: A recent analysis shows: [Y.Jia, hep-ph/0611130][Y.Jia, hep-ph/0611130]

If so, such a rare decay mode perhaps will If so, such a rare decay mode perhaps will not be observed in the foreseeable future in not be observed in the foreseeable future in experimentexperiment

9bBr [ ] ( 0.9 1.4 ) 10

4.2 8b 1.9Br [ J / J / ] 2.4 10

More recently, the More recently, the J/J/J/J/procesprocess was calculated at the next-to-leading ors was calculated at the next-to-leading order accuracy and find the NLO correction der accuracy and find the NLO correction many enhance the branching fraction to tmany enhance the branching fraction to the same level of relativistic correction he same level of relativistic correction [Bin Gong, Yu Jia, and J.X.Wang, PLB, 2009][Bin Gong, Yu Jia, and J.X.Wang, PLB, 2009] However, there exists a disagreement iHowever, there exists a disagreement in this result n this result [[BragutaBraguta & & KartvelishviliKartvelishvili, arXiv:0907.2772], arXiv:0907.2772]

b

http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Braguta%2C%20V%2EV%2E%22

http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Kartvelishvili%2C%20V%2EG%2E%22

http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Kartvelishvili%2C%20V%2EG%2E%22

The radiative correction to The radiative correction to J/J/J/J/ process is recalculated by a third party. process is recalculated by a third party. Result shows there is no agreement witResult shows there is no agreement with h either initial calculation or with the either initial calculation or with the criticism criticism Nevertheless, numerical results are all Nevertheless, numerical results are all in in a similar ordera similar order [Sun, Hao, QCF, 2010][Sun, Hao, QCF, 2010]

b

Because of parity and Lorentz invariance, the decay amBecause of parity and Lorentz invariance, the decay amplitude possesses the following unique tensor structureplitude possesses the following unique tensor structure

After a lengthy calculation, we obtain:After a lengthy calculation, we obtain: [Sun, Hao, QCF, 2010][Sun, Hao, QCF, 2010]

with the real and imaginary parts reading as with the real and imaginary parts reading as

in small mc limitin small mc limitThe double and single logarithmic terThe double and single logarithmic terms agree with Gong et al. result, but not tms agree with Gong et al. result, but not the finite termshe finite terms

With the following in putsWith the following in puts

we havewe have

In the light-cone formalism, the leading twist teIn the light-cone formalism, the leading twist term has no contribution to the rm has no contribution to the J/J/J/J/proceprocessssWe expand the LCDA projector in momentum spWe expand the LCDA projector in momentum space given by Beneke and Feldmann(2001) to twist-ace given by Beneke and Feldmann(2001) to twist-4, which yields more terms than what employed b4, which yields more terms than what employed by Braguta et al.y Braguta et al.

Higher twist contributionsHigher twist contributions

b

With the asymptotic form for twist-2 With the asymptotic form for twist-2 distribution amplitudes, i.e.distribution amplitudes, i.e.

The analytical decay amplitude turns The analytical decay amplitude turns to be pretty simple, it readsto be pretty simple, it reads

Here,Here,

and decay constants and can and decay constants and can be obtained through experiment and be obtained through experiment and NRQCDNRQCD , ,

Then the numerical result readsThen the numerical result reads

Theoretically, the description of Theoretically, the description of VVVV process is a long-standing unsolved process is a long-standing unsolved problemproblemPerturbatively, this process is helicity Perturbatively, this process is helicity suppressedsuppressed

c

II. Exclusive Decays to Vector Meson PairII. Exclusive Decays to Vector Meson Pair c


Experiment measurement on Experiment measurement on VVV V processes processes

K12 is a kinematical factorK12 is a kinematical factor

c

There were lots of theoretical investigations There were lots of theoretical investigations on on this issue in the literature, e.g.this issue in the literature, e.g.

In light-cone distribution formalism we calculIn light-cone distribution formalism we calculate this process, up to the next-to-leading order ate this process, up to the next-to-leading order in twist expansionin twist expansionIn addition to the asymptotic form, the LCDA In addition to the asymptotic form, the LCDA form in terms of Gegenbauer polynomials is alsform in terms of Gegenbauer polynomials is also taken into account in our calculationo taken into account in our calculation

We find We find

The results are in disagreement with tThe results are in disagreement with the experiment measurements he experiment measurements [Sun, Hao, QCF, 2010][Sun, Hao, QCF, 2010]


To further study the nature of recently observed state To further study the nature of recently observed state direct measurement of its decay products is necessary direct measurement of its decay products is necessaryWith in the pQCD and factorization scheme, we have calcWith in the pQCD and factorization scheme, we have calculated the helicity suppressed processulated the helicity suppressed process J/ J/J/J/at at next-to-leading ordernext-to-leading orderOur result confirms the existence of double logarithm,Our result confirms the existence of double logarithm, however, others terms differs from what in the literature, however, others terms differs from what in the literature, though numerical difference is not bigthough numerical difference is not big

b

c

III. Brief SummaryIII. Brief Summary


In the light cone formalism, expanding the LIn the light cone formalism, expanding the LCDAs of final vector mesons to twist-4, we finCDAs of final vector mesons to twist-4, we find that the higher twist terms contribute more d that the higher twist terms contribute more to the decay width than what from the NLO to the decay width than what from the NLO correctionscorrectionsAccording to our twist-4 calculation, the braAccording to our twist-4 calculation, the branching fraction of nching fraction of J/ J/J/J/process can process can be as large as 10^-6, which enables the direct be as large as 10^-6, which enables the direct search of in Tevatron Run II or LHCsearch of in Tevatron Run II or LHC

b

b

b


In the light cone formalism we have calculated the prIn the light cone formalism we have calculated the process ocess J/ J/J/J/ in next-to-next-leading order in t in next-to-next-leading order in twist expansionwist expansionResult shows that the higher twist DAs indeed violate Result shows that the higher twist DAs indeed violate the helicity conservation rules, however it still deviatthe helicity conservation rules, however it still deviate a lot from the experimental measuremente a lot from the experimental measurementThis means that the perturbative description of This means that the perturbative description of V VV V is not enough, and some non-perturbative mechaniis not enough, and some non-perturbative mechanism may play important rolessm may play important roles

c

c


Thank you for Thank you for

your attentionyour attention

Contents

Documents

Transcript of Contents