semihard processes at j-parc and belle in qcd...「加速器を用いた重力研究2017」11/30,...

Semihard processes at J-PARC and Belle in QCD

Kazuhiro Tanaka (Juntendo U/KEK)

activities @J-PARC branch on high-energy hadron physics

検討会「高エネルギー QCD・核子構造」 7/7, KEK Tokai, Room 116

世話人：熊野俊三、澤田真也、田中和廣、谷田聖、．．．

http://indico2.riken.jp/indico/conferenceDisplay.py?confId=2573

・ RHICのUltrapheripheral collision (UPC)の成果

・ RHIC/LHCのUPCおよびKEKB/ILCでの２光子衝突の物理

・ KEKBのチャームバリオン生成

「核子質量の起源と組成」 9/1, KEK Tsukuba, Honkan Room 322

世話人：熊野俊三、田中和廣

http://j-parc-th.kek.jp/workshops/2017/09-01/

・核子質量の起源と組成

・ J-PARCでの媒質中質量変化

・ KEKBでの２光子衝突

「加速器を用いた重力研究2017」 11/30, KEK Tokai, Room 116

世話人：熊野俊三、溝口俊弥、三部勉、村田次郎


・加速器を用いた重力研究

・極冷中性子やミューオンを用いた実験

・重力源としてのクォーク・グルーオンのエネルギー運動量テンソルが関わる

反応に関して理論・実験の双方から

KEK東海研究会

Generalized Parton Distribution (GPD)

p p

x x ( , , )( , , )

H x tE x t

( , , )

( , , )

H x t

E x t


p p

x x ( , , )( , , )

H x tE x t

( , , )

( , , )

H x t

E x t

† (0) () )( ( ) p z N pN)( xi pzd ez GPD


d4dQ2dxBdtd~ |TDVCS + TBH|2

DVCS BH

Eo = 11 GeV Eo = 6 GeV Eo = 4 GeV

BH

DVCS

TBH : real, given by elastic form factors

TDVCS: complex, determined by GPDs

Accessing GPDs through polarized DVCS

i zpxd ez † (( ) ( ) )0) ( zN p N p† (0) (( ) 0) ( ) p N pN

p p

p p

xp p

x x ( , , )( , , )

H x tE x t

( , , )( , , )

H x tE x t

2t

† (0) () )( ( ) p z N pN

p p

)( xi pzd ez

2 P GPD

Projected quark densities in impact parameter

Contribution of EContribution of H+E

p p

x x ( , , )( , , )

H x tE x t

( , , )

( , , )

H x t

E x t



† (0) () )( ( ) p z N pN)( xi pzd ez

p p

x x ( , , )( , , )

H x tE x t

( , , )( , , )

H x tE x t

( ) ( ' )1| (0) ( )| ( ) ( ) ( )( , , ) ( )2 2

( , , )i Pzx i p pd e p p u p u pH x t E x ut p u pP

z zM

( 555

) 1| (0 ( , , ) ( ,) ( )| ( ) ( ) ( ) ( )2 2

, ( ') )x zi Pd e p p u p pz H x t E xp u p u pt u pP

zM

2p pP

2 P GPD

( ) 21 2 4

gT q iD q F F F

( )( )

, , ,

2

, ,

| | ( ) ( ) ( )2

( ) ( ) ( )

[

]

q g q g q gN

q g q g NN

P ip T p u p A t P B tm

gD t C t m g u pm

2

2

p pP

p pt

( ) ( ) 0q gC t C t 0T

0 0 1q gA A | | 2p T p p p

0p p ( ,0,0) ( ) , ( ,0,0) ( ).q qH x q x H x q x

1 12 2

1 1( , , ) ( ) 4 ( ) , ( , , ) ( ) 4 ( )q q

q q q qdxxH x t A t D t dxxE x t B t D t

2 ·0 , 02 ·

ntP n

1

1( ) (0)qdxxq x A

( ' )1| ( ) ( )| (2

( , , ) ( ,) ( ) ( ) ( )2 2

)2

,i q qPx z i p pd e p q q p u p uH x t E xp u p u pP

z z tM

z

555 ( , , ) ( , , ) ( ' )1| ( ) ( )| ( ) ( ) (

22)

2 2( )q qi zPxd e p q q p u pp u p u p u p

Pz z H x t x p

Mz E t

( ) 21 2 4

gT q iD q F F F

( )( )

, , ,

2

, ,

| | ( ) ( ) ( )2

( ) ( ) ( )

[

]

q g q g q gN

q g q g NN


gD t C t m g u pm

2

2

p pP

p pt

( ) ( ) 0q gC t C t 0T

0 0 1q gA A | | 2p T p p p

( ) 21 2 4

gT q iD q F F F

( )( )

, , ,

2

, ,

| | ( ) ( ) ( )2

( ) ( ) ( )

[

]

q g q g q gN

q g q g NN


gD t C t m g u pm

2

2

p pP

p pt

( ) ( ) 0q gC t C t 0T

0 0 1q gA A | | 2p T p p p

1 1(0) (0) (0) (0)2 2q q g gA B A B

0 0 0q gB B

| | 1| 2

iipS J pS S

pS pS

312

ijki jkMJ d x x x TM T

0p p ( ,0,0) ( ) , ( ,0,0) ( ).q qH x q x H x q x

1 12 2

1 1( , , ) ( ) 4 ( ) , ( , , ) ( ) 4 ( )q q


2 ·0 , 02 ·

ntP n

1

1( ) (0)qdxxq x A

1

1

1 1( , , ) ( , , ) ( ) ( )2 2

q qq qdxx H x t E x t A t B t

( ' )1| ( ) ( )| (2

( , , ) ( ,) ( ) ( ) ( )2 2

)2


z z tM

z

555 ( , , ) ( , , ) ( ' )1| ( ) ( )| ( ) ( ) (

22)


Pz z H x t x p

Mz E t

( ) 2 1 2 4

q g

gT q iD q F F F

T T

( ) 21 2 4

gT q iD q F F F

( )( )

, , ,

2

, ,

| | ( ) ( ) ( )2

( ) ( ) ( )

[

]

q g q g q gN

q g q g NN


gD t C t m g u pm

2

2

p pP

p pt

( ) ( ) 0q gC t C t 0T

0 0 1q gA A | | 2p T p p p

0p p ( ,0,0) ( ) , ( ,0,0) ( ).q qH x q x H x q x

1 12 2

1 1( , , ) ( ) 4 ( ) , ( , , ) ( ) 4 ( )q q


2 ·0 , 02 ·

ntP n

( ' )1| ( ) ( )| (2

( , , ) ( ,) ( ) ( ) ( )2 2

)2


z z tM

z

555 ( , , ) ( , , ) ( ' )1| ( ) ( )| ( ) ( ) (

22)


Pz z H x t x p

Mz E t








KEK東海研究会

angular momentum distribution

mass & energydistribution

force & pressure

distribution

Gravitational form factors can be accessed through GPDs

1 2

11 2

1

( , , ) ( ) 4 ( )

( , , ) ( ) 4 ( )

qq q

qq q

dxxH x t A t D t

dxxE x t B t D t

p p

x x ( , , )( , , )

H x tE x t

( , , )

( , , )

H x t

E x t

| ( ) ( |2 2

)2

i Pzxd e p q qz z z p

1 ( ) (( , ) ),q ut p

Px p uH

( ' )( ) (2

, )( , )q i p pu p uE ptM

x

p p

x x ( , , )( , , )

H x tE x t

( , , )

( , , )

H x t

E x t




DVCS BH


BH

DVCS




Kumano san’s talk

“UPC”








KEK東海研究会

p p

x x ( , , )( , , )

H x tE x t

( , , )

( , , )

H x t

E x t





2QCDs t -

41

High momentum beam line at J-PARC

• Primary beam (proton)

• Secondary beam (pion)

E = 15-20GeV

Hadron Facility at J-PARC

p

p, d, A

35 2 1

30GeV ( 50GeV?)10 cm s

EL

High-momentum beamline 30 GeV proton

~15-20 GeV unseparated (mainly pions)

0°extraction angle

high intensitynot too high energy

best suited to study meson-induced hard exclusive processes

1/ ad s

[GeV ]c

Pion-induced Drell-Yan process

N N exclusive


N X inclusive

N N exclusive


N N exclusive


DVCS BH


BH

DVCS




† (0) () )( ( ) p z N pN)( xi pzd ez

p p

x x ( , , )( , , )

H x tE x t

( , , )( , , )

H x tE x t

2p pP

2 P

JLab, HERMES, COMPASS,…

GPD

( ) ( ' )1| (0) ( )| ( ) ( ) ( )( , , ) ( )2 2


z zM

( 555

) 1| (0 ( , , ) ( ,) ( )| ( ) ( ) ( ) ( )2 2


zM

† (0) () )( ( ) p z N pN)( xi pzd ez

p p

x x ( , , )( , , )

H x tE x t

( , , )( , , )

H x tE x t

2p pP

2 P

JLab, HERMES, COMPASS,…

M

GPD

( ) ( ' )1| (0) ( )| ( ) ( ) ( )( , , ) ( )2 2


z zM

( 555

) 1| (0 ( , , ) ( ,) ( )| ( ) ( ) ( ) ( )2 2


zM

DVMP@JLabexDY@J-PARC


N N exclusive

T. Sawada, W.C. Chang, S. Kumano, J.C. Peng, S. Sawada, KT,

2 2 ** 2 2 2 2 2 2em

2 8 2

4( ) (1 ) | | 2 Re | |27 4

( )du du du dud tp n fdQ dt Q M

H H E E

1 1

0 1

8 ( ) ( , , ) ( , , )3 4 (1 )

du d us d uu e edu dx H x t H x tu u x i x i

H

2 25 GeVQ

PRD93, 114034 (’16)

T. Sawada, W.C. Chang, S. Kumano, J.C. Peng, S. Sawada, KT, PRD93, 114034 (’16)

feasibility with E50 spectrometer at J-PARC T. Sawada, W.C. Chang, S. Kumano, J.C. Peng, S. Sawada, KT,

PRD93, 114034 (‘16)

feasibility with E50 spectrometer at J-PARC T. Sawada, W.C. Chang, S. Kumano, J.C. Peng, S. Sawada, KT,

PRD93, 114034 (’16)


N N exclusive


2 2 ** 2 2 2 2 2 2em

2 8 2

4( ) (1 ) | | 2 Re | |27 4


H H E E

1 1

0 1

8 ( ) ( , , ) ( , , )3 4 (1 )


H

2 25 GeVQ

PRD93, 114034 (’16)


N N exclusive


N N exclusive

QCD factorization formula

2 2small ( )t q q

@Belle, Babar

2 2small ( )t q q

@Belle, Babar

2 2small ( )t q q


LO in QCD factorization

“exclusive DY”


2 2 ** 2 2 2 2 2 2em

2 8 2

4( ) (1 ) | | 2 Re | |27 4


H H E E

1 1

0 1

8 ( ) ( , , ) ( , , )3 4 (1 )


H

2 25 GeVQ

PRD93, 114034 (’16)

@Belle, Babar

2 2small ( )t q q



“exclusive DY”

67

“Feynman mechanism”

68

“Feynman mechanism”“nonfactorizable”

69



Nonfactorizable mechanisms should be suppressed at Q2→∞ Brodsky, Lepage, Chernyak,…

Collins, Strikman, …

2( )F Q

2( )F Q

“nonfactorizable” Feynman mechanism


74



75

“nonfactorizable” mechanism

q q

p p

5 2 2

q m

76


q q

p p

2 2q m

77


q q

p p

5 2 2

q m

78


q q

p p

5 2 2

q m

79


q q

p p

5 2 2

q m

( , , ), ( , , )H x t E x t

@Belle, Babar

2 2small ( )t q q



“exclusive DY”


2 2 ** 2 2 2 2 2 2em

2 8 2

4( ) (1 ) | | 2 Re | |27 4


H H E E

1 1

0 1

8 ( ) ( , , ) ( , , )3 4 (1 )


H

2 25 GeVQ

PRD93, 114034 (’16)

82


q q

p p

5 2 2

q m

( , , ), ( , , )H x t E x t

83


q q

p p

5 2 2

q m

dispersion relation

( , , ), ( , , )H x t E x t

84


q q

p p

5 2 2

q m

dispersion relationquark-hadron duality

( , , ), ( , , )H x t E x t

KT, arXiv:1703.02190, 1709.01063

85( , , ) ( , , ) ( , , )du u dH x t H x t H x t

( , , ) ( , , )du duu de H x t e H x t

5( ) ( )u p u p

Light-cone QCD SR (LCSR)

2

2

2

22ˆ 1 1

B

B

mM

MBm q M

L e

2th

0 2: qxQ

quark-hadron duality

0

2

2 1 B

x Qxx Meg dx

f

2( , , )HC x Q

86

2BM

2GeV

(Borel parameter)

from LCSR

KT, arXiv:1703.02190, 1709.01063

87

2 GeVt

4pb/GeV

*2 ( )d p n

dQ dt

2 25 GeVQ

0.2 20.2 GeVt

0LCSR ( )sO

2factorization ( )sO

0LCSR ( )sO


2 2 *2 2 2 2 2 2em

8 2

4 (1 ) | | 2 Re | |27 4

( )du du du dutfQ M

H H E E

2

ddQ dt

KT, arXiv:1703.02190, 1709.01063


2 2 ** 2 2 2 2 2 2em

2 8 2

4( ) (1 ) | | 2 Re | |27 4


H H E E

1 1

0 1

8 ( ) ( , , ) ( , , )3 4 (1 )


H

2 25 GeVQ

PRD93, 114034 (’16)

@Belle, Babar

2 2small ( )t q q

“exclusive DY”


90



91

2 GeVt

4pb/GeV

*2 ( )d p n

dQ dt

2 25 GeVQ

0.2 20.2 GeVt

0LCSR ( )sO


0LCSR ( )sO


2 2 *2 2 2 2 2 2em

8 2

4 (1 ) | | 2 Re | |27 4

( )du du du dutfQ M

H H E E

2

ddQ dt

KT, arXiv:1703.02190, 1709.01063

Summary IexDY ( ) GPDs

interplay of soft/hard QCD mechanism

soft nonfactorizable mechanism (SNM)

LCSR2t

2h ( 0.7 GeV, , ) H E q

5

0s

SNM ＞ QCD factorization2s



2QCDs t -

“UPC”

2QCDs t -

( )2 1 cos2st = =- -

0k -k

kk -

( ), , k k -

2Q “Impact factor”

2 2t Δ̂= -2QCDs t -

2 2 20 3k k k^-

light-cone expansion

0

kk -

( ), , k k -

“Impact factor”

2 2t Δ̂= -

2Q0

)( )(

T

L

g uu

kk -

( ), , k k -

“Impact factor”

2 2t Δ̂= -0for T

2

log Qt

2Q0

)( )(

T

L

g uu

“UPC”

kk -

( ), , k k -

“Impact factor”

2 2t Δ̂= -0for T

2

log Qt

2Q0

)( )(

T

L

g uu

kk -

( ), , k k -

“Impact factor”

2 2t Δ̂= -

2Q

1up

nonfactorizable for 0T

IR divergent!

0

2

log Qt

)( )(

T

L

g uu

kk -

( ), , k k -

“Impact factor”

2 2t Δ̂= -

2Q

1up

nonfactorizable for 0T

IR divergent!

0

2

log Qt

)( )(

T

L

g uu

end-point behaviors: 0, 1u ( ) (1 )L u u u - ( ) 1Tg u

2QCDs t -

( )1 cos2st =- -

0 0, TL k -k

kk -

( ), , k k -

“Impact factor”

2 2t Δ̂= -

0T

2Q

IR divergent!0for T

2

log Qt

)( )(

T

L

g uu

kk -

( ), , k k -

“Impact factor”

2 2t Δ̂= -

0T

2Q

2 2QCDQ

( )Tg u

kk -

( ), , k k -

“Impact factor”

2 2t Δ̂= -

0T

22

2 20

( ) mdmQ m

2

22

2 2 2 2

( )thm

V

a mdmQ m Q m

k k -

( )

2 0Q

0T

2Q

2 2QCDQ

( )Tg u

kk -

( ), , k k -

2 2QCDQ

“Impact factor”

0T

2 2QCDQ

22

2 20

( ) mdmQ m

2

22

2 2 2 2

( )thm

V

a mdmQ m Q m

k k -

( )

2 0Q

0T

LCSR (quark-hadron duality)

( )2

0

2 2

21

1 ( )( ) ( )( ) 12

2B

V

B

auMM

T

m u

u

v Tg ug uu

u eda eΔ̂

--æ ö¶ ÷ç ÷ç ÷ç ÷ç ¶è ø

µ -ò

2 2QCDQ

( )Tg u

ρ meson WFs (1 ) 2 1u u u = - - = -

( ) 3/2 22

0,2,4,

3( ) 6 1 (2 1) 6 (1 ) 1 (5 1)2L n n

n

u u u a C u u u a =

æ ö÷ç= - - = - + - + ÷ç ÷çè øå

2 0.18 0.10a =

( )L u( ) ( )vTg u ( ) ( )a

Tg u

( ) 1/21

0,2,4,

( ) () 2 1)(vT n n n

n

Gg G C uu -=

= - -å

( )( )( )

3/21

0,2,4,

( ) 8 1 (2( 1)1 2

)a nnT

n

n

G Gu u C u

n ng u +

=

-= - -

+ +å

Ball, Braun, Koike, KT (’98)

kk -

( ), , k k -

2 2QCDQ

“Impact factor”

0T

2 2QCDQ

22

2 20

( ) mdmQ m

2

22

2 2 2 2

( )thm

V

a mdmQ m Q m

k k -

( )

2 0Q

0T


( )2

0

2 2

21

1 ( )( ) ( )( ) 12

2B

V

B

auMM

T

m u

u

v Tg ug uu

u eda eΔ̂

--æ ö¶ ÷ç ÷ç ÷ç ÷ç ¶è ø

µ -ò

2 2QCDQ

( )Tg u

2BM

2GeV

(Borel parameter)

a21 GeVt

23 GeVt 25 GeVt 210 GeVt

from light-cone sum rule

KT

kk -

( ), , k k -

2 2QCDQ

“Impact factor”

0T

2 2QCDQ

22

2 20

( ) mdmQ m

2

22

2 2 2 2

( )thm

V

a mdmQ m Q m

k k -

( )

2 0Q

0T


( )2

0

2 2

21

1 ( )( ) ( )( ) 12

2B

V

B

auMM

T

m u

u

v Tg ug uu

u eda eΔ̂

--æ ö¶ ÷ç ÷ç ÷ç ÷ç ¶è ø

µ -ò

2 2QCDQ

( )Tg u

0T

k k -

( )

2 0Q 2

2

222

22

( )thV

m

maQ m

dmQ m

0T

2 2QCDQ

23 GeVt 210 GeVt

2GeV 2Q 2GeV

2Q

2QCDs t -

( )1 cos2st =- -

0 0, TL k -k

2 [ nb GeV ]TLddt

2100 GeVs

23 GeVt

2GeV 2Q

0L

2Q

k k -

2 0Q

k k -

( ) 0

T2QCDs t -

2cos

2 [ nb GeV ]TLddt

0 GeVQ

5 GeV3 GeV1 GeV

KT

1 2M M “ ”

1M

2M

0 0L T First QCD prediction for

kk -

( ), , k k -

0T

2 2QCDQ

2 2QCDQ

( )Tg u

kk -

( ), , k k -

0T

2 0Q

0T

2 2QCDQ

2 2QCDQ

pom nVMD ero

( )Tg u

kk -

( ), , k k -

0T

2 0Q

0T

2 2QCDQ

2 2QCDQ

2

22

2 2 2 2

( )thm

V

a mdmQ m Q m

( )

22

0

22 ( ) 1( )

1 122

( )( )V a u

M uMm

vTu

Te g ug u euu

a dΔ̂-

-æ ö¶ ÷ç ÷ç ÷ç ÷ç ¶è øµ -ò

0T

k k -

( )

2 0Q

pom nVMD ero

)( )(

T

L

g uu

Summary II

allows us to obtain ``interpolating formula’’ between pQCD for and

LCSR for theγ→ρ0 impact factor

k k -

( )

2 0Q

0T

2 2QCDQ 2pomeronVMD for 0 Q

first QCD prediction for 0 0L T TLd

dt0T

0L

Kumano san ’s talk


DVCS BH


BH

DVCS




Goto san’s talk

“UPC”

Goto san’s talk

semihard processes at j-parc and belle in qcd...「加速器を用いた重力研究2017」11/30,...

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