Doubly Heavy Baryons

Doubly Heavy Baryons

Likhoded A.K.IHEP, Protvino, Russia

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Contents Introduction Mass spectrum Decays Production Conclusion

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Double-heavy BaryonsThe only experimental information about DHB

gives SELEX collaboration:

There are several questions to SELEX results:1) Lifetime2) Cross sections

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Theoretical information about DHB:1) Mass spectrum

Potential Models (two step calculation) QCD Sum Rules QCD Effective field theory Lattice QCD

2) Life time and leading decay modes OPE Exclusive decays in NRQCD sum rules

3) Cross section Perturbative QCD + nonrelativistc ME

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Mass spectrum

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Potential modelsHeavy Quark Symmetry

q

Q 1

QCD

QCDQm

Diquark approximationDiquark approximation

Simplification in (QQ’q) dnamics in Born-Oppenheimer or adiabatic approximations:

VQ,VQ’ << Vq

Two step calculation in Potential Model

Heavy Quark-Diquark Symmetry

q

1

QCD

QQ

QCD2 vmvmm QQQ

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Potential modelsThree-body problemThree-body problem

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Ground states mass predictions

[20]

[20]

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PM predictions for ground state cc-diquark 3c are

+

* +

3478MeV, 1S1S 1/2

3610MeV, 1S1S 3/2

cc

cc

M

M

~ 40MeVM

[V. Kiselev, A.Onishchenko, A.L.]

Metastable state (2P1S) ½-(3702) have L=1, S=0 for diquark.

Transitions to the ground state (L=0, S=1) requires simultaneous change of orbital momentum and spin.

PM predictions

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SR and Lattice QCD NRQCD Sum Rules

M(cc)=3.470.05 GeVM(bc)=6.800.05 GeVM(bb)=10.070.09 GeV

Lattice QCDM(cc)=3.600.02 GeV

[V. Kiselev, A.Onishchenko, A.L.]

[R.Lewis et al]

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Spin-dependent correctionsFor heavy diquark:

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Spin-dependent correctionsTaking into account interaction with

the light quark gives (S=Sd+Sl )

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cc spectrum

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bb spectrum

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Hyperfine mass splittings

[N.Brambilla et al]

[R.Lewis et al]

[V. Kiselev, A.Onishchenko, A.L.]

Hyperfine splitting for cc: PM: =(130±30) MeV QCDEFT =(120±40) MeV Lat.QCD =76.6 MeV

[20]

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Summary1) Ground state mass predictions

depend on the model (~200 MeV)2) Uncertainties in PM are mainly

connected with different value of heavy quark masses.

3) The lightest S- and P-wave exitations of the diquark are quasistationar.

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Lifetimes

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OPE

(*)

(*)

(*) (*)12cc

cc

cc ccMT

4Im 0eff effd x T H x HT

Where

is standard hamiltonian of weak c-quark transitions

1 1

* . .2 2

Feff uq cq

GH V V C O C O h c

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OPEIn decays of heavy quarks released energy is

significant, so it is possible to expand Heff in the series of local operators suppressed by inverse powers of heavy quark mass

spectator

Pauli interference

EW scattering

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OPEFor example, for semileptonic decay mode

2 52

3

2(*) (*) (*) (*)

2

,192

, ,2

F cc cs

c cc v v cc c cc v v cc c c cc

G mV

iDK v c c v G v c G c v E G K

m

where

In numerical estimates we have used following parameter values:

mc=1.6 GeV ms=0.45 GeV mq=0.3 GeV

M(++cc)=M(+

cc)=3.56 GeV MHF=0.1 GeV

|diq(0)| = 0.17 GeV3/2

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OPE

0.43ps, 0.12pscc cc

16%, 4%,cc ccBr l X Br l X

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OPE

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Exclusive decays in NRQCD sum rules Semileptonic DHB decaysHeavy Quark Spin Symmetry makes possible to describe

semileptonic decays close to zero-recoil point

HQSS put constraints on SL FF

2 2 2 2b c b cq m m m m

2 2 2

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b c l

b c

m m mm m

'v v

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Exclusive decays in NRQCD sum rules

Quark loop for 3-point correlator in the baryon decay

For 1/21/2 transition there are 6 form-factors:

1 2 3 5 1 2 3V I V F V A I A F A

F F I I F Ip J p u p G v G v G G v G v G u p

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Exclusive decays in NRQCD sum rulesThese 6 FF are independent. However, in NRQCD in LO for small recoil it is possible to obtain following relations:

1 2 3 1,V V V IW A IWG G G G

Only 2 FF are not suppressed by heavy quark mass:

1 1V A IWG G

Vector current conversation requires

1 1IW

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NRQCD Sum RulesIn the case of zero recoil IW(1) is determined from Borell

transfromation

For calculation of exclusive widths one can adopt pole model

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NRQCD Sum Rules

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Production of cc-baryons

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In all papers it was assumed, that

This is quite reasonable assumption in the framework of NRQCD, where, for example, octet states transforms to heavy quarkonium. Analogously, we have to assume, that dissociation of (cc)3 into DD is small.

3cc cc

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Similar to quarkonium production cross sections factorizes into hard (pertubative) and soft (non-pertubative) parts.

In both cases second part is described by wave function of bound state at origin.

That’s why it is reasonable to compare, for example, J/cc and cc final states. In this case only one uncertainty remains – the of squared wave functions at origin.

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Fragmentation mechanism

e.g.

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In e+e-, where FM dominates, expected cross sections at is

10.6GeVs

5~ 7 10cc

cc

2( ) ~ 7 10 pbcc

At SuperB, where expected luminocity is L=1036 cm-2 s-1

* 5~ 7 10ccN

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Hadronic production

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4c sectorLO calculations for (4c) at gives

at mc=1.25 GeV s=0.24It should be compared with

This gives

At Z-pole

Main uncertainties come from errors in mc and s

10.6GeVs

372fbe e cccc

tot cc

1.03nbe e cc

44~ 3.7 10

2c

Rc

2~ 2.3 10ZR

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Violation of factorization in hadroproduction at low pT

cc total cross sections:Tevatron: (cc)=12 nbLHC : (cc)=122 nb

3~10bc

cc

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Conclusion• Double heavy quark pair

production is a new battle field (see, e.g. B-factories)

• Test of fragmentation approximation in production

• NRQCD factorization• Properties of weak decays

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Backup slides

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1) Fragmetation mechanism

X cc final state , / , 1 , ',c cX cc J P

e

e

X

c

c

2

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02 2 127c X s

RJD z z

m

2 XEz

s

M2/s corrections are neglected (M2/s <<1)

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X cc final state2) Complete calculations (with M2/s corrections)

(c) = 40 (49) fb,

(J/) = 104 (148) fb,

( c0) = (48.8) fb

( c1) = (13.5) fb

( c2) = (6.3) fb

Complete calculations deviate from fragmetation calculations at

M2/s terms are important

10.6GeVs

[A.Berezhnoi, A.L.]

[K.Y. Liu, Z.G. He, K.T. Chao]

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X cc final state3) Quark-Hadron duality

2sing

2

280fbD

c

m

ccccm

d e e cc c cdm

dm

1.25GeVcm 0.24s 0.5GeV

S=1sing204fbd e e cc c c

S=0sing76fbd e e cc c c

Q-H duality does not contradict Color Singlet model within uncertainties in mc s and

It should be compared with total sum of complete calculations.

tot 216fbQQ

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X cc final state

a) fragmentation approach

S=1 Dccc(z) similar to DcJ/(z)

Difference in wave functions |J/ (0)|2 and |cc(0)|2

Again, similar to J/ case, at complete calculations for vector (cc)3 -diquark are needed

10.6GeVs

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X cc final state

b) Quark-Hadron duality

One inclusive cross section for vector 3c in S=1

Uncertainties are caused by errors in s and

This value is close to results of complete calculations with cc(0) taken from PM.

~115 170fbcc c c

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Conclusion1) at ( at LHC )

2) For lumonocity L=1034 cm-2 s-1 it gives ~104 cc-baryons per year

3) Taking into account Br ~10-1 in exclusive modes we expect 103 cc events per year

~100fbcce e X 10.6GeVs

~122nbcce e X