1

A rough estimation of the charmed baryon production in perturbative QCD

H. Kawamura (KEK)

Sep.10, 2013 Discussion at KEK Tokai

2

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…

4

Noumi-san

5

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)

7

( )cm n 2

dσ 1 f θdt s −=

p nγ π ++ → +

Exclusive photoproduction at Jefferson Lab.

n pγ π −+ → +

7

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

14/13

* ( )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