Doubly Heavy Baryons

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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 Baryons

• The only experimental information about DHB gives
  SELEX collaboration
• There are several questions to SELEX results
• 1) Lifetime
• 2) 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

5
Mass spectrum
6
Potential models
Diquark approximation
Heavy Quark Symmetry
Heavy Quark-Diquark Symmetry
Simplification in (QQq) dnamics in
Born-Oppenheimer or adiabatic approximations VQ,
VQ ?ltlt Vq Two step calculation in Potential
Model
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Potential models
Three-body problem
8
Ground states mass predictions
20
20
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PM predictions
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SR and Lattice QCD

• NRQCD Sum Rules
• M(?cc)3.47??0.05 GeV
• M(?bc)6.80??0.05 GeV
• M(?bb)10.07??0.09 GeV
• Lattice QCD
• M(?cc)3.60??0.02 GeV

V. Kiselev, A.Onishchenko, A.L.
R.Lewis et al
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Spin-dependent corrections

• For heavy diquark

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Spin-dependent corrections

• Taking into account interaction with the light
  quark gives (SSdSl )

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?cc spectrum
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?bb spectrum
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Hyperfine mass splittings
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• Hyperfine splitting for ?cc
• PM ? ?(13030) MeV
• QCDEFT ?(12040) MeV
• Lat.QCD ?76.6 MeV

V. Kiselev, A.Onishchenko, A.L.
N.Brambilla et al
R.Lewis et al
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Summary

• Ground state mass predictions depend on the model
  (200 MeV)
• Uncertainties in PM are mainly connected with
  different value of heavy quark masses.
• The lightest S- and P-wave exitations of the
  diquark are quasistationar.

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Lifetimes
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OPE
Where
is standard hamiltonian of weak c-quark
transitions
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OPE

• 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
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OPE

• For example, for semileptonic decay mode

where
In numerical estimates we have used following
parameter values mc1.6 GeV ms0.45 GeV
mq0.3 GeV M(?cc)M(?cc)3.56 GeV ?MHF0.1
GeV ?diq(0) 0.17 GeV3/2
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OPE
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OPE
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Exclusive decays in NRQCD sum rules

• Semileptonic DHB decays
• Heavy Quark Spin Symmetry makes possible to
  describe semileptonic decays close to zero-recoil
  point
• HQSS put constraints on SL FF

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Exclusive decays in NRQCD sum rules
Quark loop for 3-point correlator in the baryon
decay For 1/2?1/2 transition there are 6
form-factors
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(No Transcript)
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Exclusive decays in NRQCD sum rules
These 6 FF are independent. However, in NRQCD in
LO for small recoil it is possible to obtain
following relations
Only 2 FF are not suppressed by heavy quark mass
Vector current conversation requires

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NRQCD Sum Rules

• In 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.

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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.
• Thats 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 ee-, where FM dominates, expected cross
sections at is
At SuperB, where expected luminocity is ?L1036
cm-2 s-1
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Hadronic production
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4c sector

• LO calculations for ??(4c) at
  gives
• at mc1.25 GeV
• ??s0.24
• It should be compared with
• This gives
• At Z-pole
• Main uncertainties come from errors in mc and ?s

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Violation of factorization in hadroproduction at
low pT
?cc total cross sections Tevatron
??(?cc)12 nb LHC ??(?cc)122 nb
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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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X cc final state
1) Fragmetation mechanism
M2/s corrections are neglected (M2/s ltlt1)
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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
A.Berezhnoi, A.L. K.Y. Liu, Z.G. He, K.T. Chao
Complete calculations deviate from fragmetation
calculations at M2/s terms are important
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X cc final state
3) Quark-Hadron duality
It should be compared with total sum of complete
calculations.
Q-H duality does not contradict Color Singlet
model within uncertainties in mc ?s and ??
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X cc final state
a) fragmentation approach S1
Dc?cc(z) similar to Dc?J/?(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
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X cc final state
b) Quark-Hadron duality
One inclusive cross section for vector 3c in
S1 Uncertainties are caused by errors in ?s and
? This value is close to results of complete
calculations with ?cc(0) taken from PM.
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Conclusion

• 1)
  at
• ( at LHC
  )
• 2) For lumonocity L1034 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