A rough estimation of the charmed baryon production in...
Transcript of A rough estimation of the charmed baryon production in...
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A rough estimation of the charmed baryon production in perturbative QCD
H. Kawamura (KEK)
Sep.10, 2013 Discussion at KEK Tokai
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Hydrogen Target
π−
Κ+
π−
20 GeV/c π− Beam
Dispersive Focal Plane
High-resolution, High-momentum Beam Line D*− Spectrometer
-π p−*D
*cY
-π
-π+K
Missing Mass Spectrum
Missing Mass Spectroscopy
Measure D*-
Charmed Baryon Spectroscopy Noumi-san
Λc Σ
c(245
5)
Σc(2
520)
Λc(2
625)
Λc(2
765)
Λc(2
880)
Λc +
0.8
GeV
πΣc DN D*N
Λc(2
595)
Σc(2
800)
Λc(2
940)
Λc +
1.0
GeV
3
Signal: 1 nb/Yc* :~1000 events Sensitivity: ~0.1 nb (3σ, Γ∼0.1 GeV)
Λc 1/2+
Σc(2455) 1/2+
Σc(2520) 3/2+
Σc(2800) ??
Λc(2595) 1/2-
Λc(2625) 3/2-
Λc(2880) 5/2+
Λc(2940) ??
DN
πΛc
(GeV/c2)
D*N
2.3
2.4
2.7
2.9
2.6 πΣc
2.8
πΛc
Expected Spectrum in the (π,D*-) reaction Noumi-san
How much is σ(π-p→D*-Yc*)? • No observation
– the upper limit: 7 nb (68% CL) • We want to know:
– A plausible estimation of the cross section • Coupling Constant/ Form Factor
– possible ambiguity of the estimation: Lower Limit • Validity of SUF(4), analogy of the strangeness production, …
– How it changes in excited state • What we can learn from the measurement
– If it is much beyond that we expected…
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Noumi-san
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1 2
0( ) ( )M s
du u uQu
φ α×∫
PQCD for exclusive processes
• Perturbative QCD O.K., if . 2, , QCDs t u Λ
2, ,( ) | H( (s))
QCDA B s C Ds t u
M A B C D φ φ α φ φΛ
+ → + = × × × ×
light-cone distribution amplitude
parton scattering amplitude
Lepage, Brodsky, PRD22(1989)2157
H
meson baryon u
1 u−
( )M uφu
1 u v− −
v ( , )B u vφ
• How much energy (s,t,u) is needed to justify the use of PQCD ?
Ans. it depends not only on energies but also on the behavior of distribution amplitude , etc. .
Typical momentum integral: 2 , ,Q s t u
Even if Q2 is large, uQ2 is not necessary large (depends on the shape of . ) Mφ
Aφ
Bφ
Cφ
Dφ
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• Some hints on PQCD applicability to exclusive processes
(1) Pion transition form factor
γ
*γ 2 2Q q= −
(2) Pion EM form factor
With quite an elaborated framework, i.e., “k_t factorization” & “Sudakov resummation”, the contribution from the perturbative region is dominant when
20 2 3GeV QCDQ ≥ Λ ≈ −
PQCD O.K. for 3GeV?Q ≥
From Belle experiment
Theoretical study Q
p2
2
If ( ) small in the dominant
region, PQCD is O.K.s p
pα
Li & Sterman (1992)
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( )cm n 2
dσ 1 f θdt s −=
p nγ π ++ → +
Exclusive photoproduction at Jefferson Lab.
n pγ π −+ → +
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90s
θ °
−
=
∝7
90s
θ °
−
=
∝
11s−∝ d p nγ + → +
2 3GeVQ ≥ −
Onset of counting rule
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• at J-PARC * * cp D Yπ − −+ → +
20GeVEπ =
−π *−D
p * cY
( )uπφ
( , )p v wφ ( , )cY v wφ ′ ′
( )D uφ ′
*
1 2 1 2
( )
= ( ) ( , ) ( , , , , ( )) ( ) ( , ) c
P i i s D
p D
u v v H u u v v u v vπ
σ π
φ φ α µ φ φ
− −
Λ
+ → + Λ
′ ′ ′′ ′× × × ×
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*
1 2 1 2
( )
= ( ) ( , ) ( , , , , ( )) ( ) ( , ) c
P i i s D
p D
u v v H u u v v u v vπ
σ π
φ φ α µ φ φ
− −
Λ
+ → + Λ
′ ′ ′′ ′× × × ×
( )uπφ
pion u
1 u−
( )uπφ
( ) 6 (1 )as u u uπφ = −
Pion’s light-cone distribution amplitude (LCDA)
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1 2( , )p x xφ
{
}
1 2 3
5 1
5
5
0 ( ) ( ) ( ) ( )
( ) ( ( )) ( )4
( ) ( ) ( )
( ) ( ( )) ( )
ijk i i k
N
i
i
u z u z u z N pf pC N p V z p
p C N p A z p
p C N p T z p
α β γ
αβ γ
αβ γ
νµν αβ µ γ
ε
γ
γ
σ γ γ
= /
+ /
−
1x2x
3 1 21x x x= − −
1
1 2 3 1 2 30( ) (1 ) ( )ii x zp V
iV zp dx dx dx x x x e xδ φ− ∑= − − −∫
Proton LCDA
B-meson LCDA in HQET
Light-like vector :
Wilson line :
Decay constant :
HQET field :
velocity of B meson
Scale : renomalization scale of operators
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Heavy meson DA in HQET
Heavy quark limit
Grozin, Neubert (97) HK,Kodaira,Tanaka,Qiao (01)
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OPE for B meson LCDA
OPE with 1-loop coeff. functions up to dim.5 operators
dim.3
dim.4
dim.5
• Valid in the small t region. • 3 HQET parameters
HK,Tanaka (09)
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OPE + NP ansatz
HK,Tanaka, PLB673(2009)201
Consistent with QCD sum rule
Grozin,Neubert (97) • dependence is small.
• Inputs
( )2 21 GeV 0.11 0.06 GeVλ = ±E
( )2 21 GeV 0.18 0.07 GeVλ = ±H
( )1.5 GeV,1.5GeV 0.65 0.06 GeVΛ = ±SF
Short distance mass in the “shape function scheme”
Neubert (05)
cf. Lee, Neubert (’07) OPE up to dim.4, mom. space
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* ( )D
φ ω
*0 (0) ( ) ( , )
1 1 Tr ( ) ( ( ) ( )) 2 2 2+ − +
Γ
+ /= + − Γ//
v
D D
h q tn D p
f M vt t t n
ε
φ φ φ ε
HQ spin symmetry → { }* * ,,( ), ( )D BD B
φ ω φ ω
All commonly given by ( )+φ ω
vector meson
pol. vector
leading DA *D( )φ ω
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( )φ ω± A simple parametrization by Grozin & Neubert (1996).
0 020 0
1( ) , ( )e eω ω
ω ωωφ ω φ ωω ω
− −
+ −= =Light-cone sum rule
02 0.3GeV3
ω = Λ ≈
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1 2( , )φ ω ωΛ
[ ]
1 2
5 1 2
0 (0) ( ) ( ) ( )
1 ( ) ( , )2 2
ijk i i kv c
c
h u t n d t n p
f M v C v t t
α β γ
αβγ
ε
γ φΛ ΛΛ
Λ
+ /= Λ
1 1 2 2
1 2
1 2 1 2 1 20 01 ( )
0 0
( , )= ( , )
= ( , )
it it
i t u t u
t t d d e
d due u
ω ω
ω
φ ω ω φ ω ω
ω ω φ ω
∞ ∞ − −Λ Λ
∞ − +Λ
∫ ∫∫ ∫
1 1 k v u vω ω+ + += =
2 2 k v u vω ω+ + += =
u
dc
Evolution eq. + LC sum rule:
Ball, Braun, Gardi (2008)
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( , , , , ( )) i i sH u u v v α µ′′
Hard Part
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Comments
• Large number of diagrams. ↔ Connected diagrams with 4 gluon lines connecting 5 fermion lines
• Uncertainty of LCDAs
• Final State Interaction
• Scale uncertainty