Likhoded A.K.

IHEP, Protvino, Russia

SuperB as a factory of Doubly Charmed Baryons?

Double-charmed BaryonsThe only experimental information about DCB gives SELEX

collaboration:

There are several questions to SELEX results:

1) Lifetime

2) Cross sections

Theoretical information about DCB:

1) Mass spectrum

2) Life time and leading decay modes

3) Cross section

*

*

3443MeV,

3520MeV,

3541MeV,

cc

cc

cc

ccd M

ccd M

ccu M

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

Double-charmed BaryonsMass spectrum theoretical predictions:

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.

Sum Rules

Lattice QCD

Spin-dependent potential

Hyperfine splitting

PM:

QCDEFT

Lat.QCD

Double-charmed Baryons

3.47 GeV, (without HF splitting)ccM

3.600GeV 20MeVccM

*cc ccM M

130MeV 30 MeV

120MeV 40 MeV

76.6MeV

[N.Brambilla et al]

[R.Lewis et al]

[R.Lewis et al]

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

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

Excited states spectrum

Lifetimes of DCB

(*)

(*)

(*) (*)1

2cc

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

In 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

Lifetimes of DCB

For example, for semileptonic decay mode

where

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

In numerical estimates we have used following parameter values:

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

M(++cc)=M(+

cc)=3.56 GeV MHF=0.1 GeV

|diq(0)| = 0.17 GeV3/2

Lifetimes of DCB

0.43ps, 0.12pscc cc

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

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

These 6 f.f. 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 w G w

Only 2 f.f. are not suppressed by heavy quark mass:

1 1V A IWG G w

In the case of zero recoil IW(1) is determined from Borell transfromation

For transition

For calculation of exclusive widths one can adopt pole model

Production of cc-baryons

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.

Similar to cc-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 J/cc and cc final states. In this case only one uncertainty remains – the of squared wave functions at origin.

3cc cc

4c-sectorLO calculations for (4c) at gives

at mc=1.25 GeV

s=0.24

It 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

2

cR

c

2~ 2.3 10ZR

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

1) Fragmetation mechanism

e

e

X

c

c

2

23

02 2 1

27c X s

RJD z z

m

2 XEz

s

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

X cc final state

2) 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]

X cc final state

3) Quark-Hadron duality

2sing

2

280fbD

c

m

ccccm

d e e cc c cdm

dm

1.25GeVcm 0.24s 0.5GeV

S=1

sing204fbd e e cc c c

S=0

sing76fbd 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

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

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

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

Dixi

~ 100fbcce e X 10.6GeVs

~ 122nbcce e X