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Doubly Heavy Baryons

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Title: Doubly Heavy Baryons


1
Doubly Heavy Baryons
  • Likhoded A.K.
  • IHEP, Protvino, Russia

2
Contents
  • Introduction
  • Mass spectrum
  • Decays
  • Production
  • Conclusion

3
Double-heavy Baryons
  • The only experimental information about DHB gives
    SELEX collaboration
  • There are several questions to SELEX results
  • 1) Lifetime
  • 2) Cross sections

4
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
7
Potential models
Three-body problem
8
Ground states mass predictions
20
20
9
PM predictions
10
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
11
Spin-dependent corrections
  • For heavy diquark

12
Spin-dependent corrections
  • Taking into account interaction with the light
    quark gives (SSdSl )

13
?cc spectrum
14
?bb spectrum
15
Hyperfine mass splittings
20
  • 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
16
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.

17
Lifetimes
18
OPE
Where
is standard hamiltonian of weak c-quark
transitions
19
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
20
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
21
OPE
22
OPE
23
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

24
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
25
(No Transcript)
26
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

27
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

28
NRQCD Sum Rules
29
Production of ??cc-baryons
30
  • 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.

31
  • 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.

32
Fragmentation mechanism
e.g.
33
In ee-, where FM dominates, expected cross
sections at is
At SuperB, where expected luminocity is ?L1036
cm-2 s-1
34
Hadronic production
35
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

36
Violation of factorization in hadroproduction at
low pT
?cc total cross sections Tevatron
??(?cc)12 nb LHC ??(?cc)122 nb
37
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

38
Backup slides
39
X cc final state
1) Fragmetation mechanism
M2/s corrections are neglected (M2/s ltlt1)
40
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
41
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 ??
42
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
43
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.
44
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
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