High-Energy Hadron PhysicsHigh-Energy Hadron Physicsat J-PARC at J-PARC

Shunzo KumanoShunzo Kumano

High Energy Accelerator Research Organization High Energy Accelerator Research Organization (KEK) (KEK)

Graduate University for Advanced Studies (GUAS)Graduate University for Advanced Studies (GUAS)

May 12 – 16, May 12 – 16, 2008 (Talk on 2008 (Talk on May 16)May 16)

shunzo.kumano@kek.jpshunzo.kumano@kek.jp

http://research.kek.jp/http://research.kek.jp/people/kumanos/people/kumanos/

Sixth International Conference on Perspectives in Hadronic PhysSixth International Conference on Perspectives in Hadronic Physicsics

ITCP, Trieste, ItalyITCP, Trieste, Italy

ContentsContents

1.1. Introduction to high-energy hadron physics at J-Introduction to high-energy hadron physics at J-PARCPARC

• • Introduction to the J-PARC facility Introduction to the J-PARC facility

• • Possible projects with 30 – 50 GeV proton bePossible projects with 30 – 50 GeV proton beamam

2.2. Structure functionsStructure functions Possible roles of J-PARC projects inPossible roles of J-PARC projects in • • Unpolarized and Polarized Unpolarized and Polarized parton distribution functions (PDFs), Nuclparton distribution functions (PDFs), Nucl

ear PDFsear PDFs

• • Fragmentation functionsFragmentation functions

• • Tensor structure functionsTensor structure functions

Topics

relat

ed to

my

Topics

relat

ed to

my

studie

sstu

dies

Part IPart I

Introduction toIntroduction toHigh-Energy Hadron PhysicsHigh-Energy Hadron Physics

at J-PARCat J-PARC

J-PARC FacilityJ-PARC Facility

http://j-parc.jp/index-e.htmlhttp://j-parc.jp/index-e.html

J-PARC LocationJ-PARC Location

J-PARCJ-PARC(Japan Proton Accelerator(Japan Proton Accelerator Research Complex)Research Complex)

Joint facility of JAEA and KEK.Joint facility of JAEA and KEK.

JAEA (Japan Atomic Energy Agency)JAEA (Japan Atomic Energy Agency)

KEK (High Energy Accelerator KEK (High Energy Accelerator Research Organization)Research Organization)

Bird’s-eye viewBird’s-eye viewParticle and Nuclear Particle and Nuclear PhysicsPhysics

High-Intensity Frontier of Proton High-Intensity Frontier of Proton AcceleratorAcceleratorHigh-intensity proton beamHigh-intensity proton beam High-intensity secondary beHigh-intensity secondary beamsams(Neutrino, Kaon, Pion, Neutron (Neutrino, Kaon, Pion, Neutron …) …)

Strangeness nuclear physics (1st experiment)Exotic hadronsHadrons in nuclear mediumHard processes (50 GeV recovery)Nucleon spin (proton polarization)Quark-hadron matter (heavy ion)

Efforts are neededto get approvalfor projects afterstrangeness physics.

Theorist’s contributionsare crucial for the 2nd projects.

New nuclei with strangeness

Baryon interactions with strangeness(New aspect of low-energy QCD)

S = 0

– 1

– 2

+ 1

Ordinarynuclei

N

Z

, nuclei

nuclei

?

in nuclei

New hadronic many-body systemby extending the flavor degrees of freedom.

• No data for YY interactions

• Some data for YN interactions (~ 40)

• Plenty of data for NN interactions (~ 4,000)

J-PARC (K–, K+) for and nuclei, YN scattering

(K–, π±), (π±, K+) for nuclei, YN scattering

Aerial photograph on January Aerial photograph on January 28, 200828, 2008

Hadron facilityHadron facility

Hadron Facility in May 2007Hadron Facility in May 2007and a possible schedule for and a possible schedule for beam lines beam lines

Hadron Facility on April Hadron Facility on April 11, 200811, 2008

High-Momentum Beam Line High-Momentum Beam Line (30, 50 GeV Proto(30, 50 GeV Proton)n)

This beam line should be This beam line should be interestinginterestingfor the audience of this for the audience of this workshop.workshop.

General comments on J-PARC projectsGeneral comments on J-PARC projectswith 30 – 50 GeV proton beamwith 30 – 50 GeV proton beam

Refs. My talks on “Possible Hadron Physics at J-PARC”Refs. My talks on “Possible Hadron Physics at J-PARC”

in Trieste (2006)in Trieste (2006) http://www.pg.infn.it/hadronic06http://www.pg.infn.it/hadronic06//

in Ghent (2007)in Ghent (2007) http://inwpent5.ugent.be/workshophttp://inwpent5.ugent.be/workshop07/07/

in Mito (2008)in Mito (2008) http://j-parc.jp/NP08/

J-PARC workshops on hadron physicsJ-PARC workshops on hadron physics

• • J-PARC-HS05, J-PARC-HS05, http://www-conf.kek.jp/J-PARC-HS05/program.http://www-conf.kek.jp/J-PARC-HS05/program.htmlhtml

• • J-PARC-NP07, J-PARC-NP07, http://www-conf.kek.jp/NP_JPARC/program.htmhttp://www-conf.kek.jp/NP_JPARC/program.htmll

• • J-PARC-NP08, J-PARC-NP08, http://j-parc.jp/NP08/http://j-parc.jp/NP08/

Haron Physics at J-PARCHaron Physics at J-PARC

Strangeness nuclear physics (1st experiment)

Exotic hadrons

Hadrons in nuclear medium

Hard processes (50 GeV recovery)

Nucleon spin (proton polarization)

Quark-hadron matter (heavy ion)Need major

upgrades

Next projec

ts

1st projec

t(also )

My talk is related to

Kaon and pion beams

Proton beam

Hadron physics with 30 – 50 GeV proton bHadron physics with 30 – 50 GeV proton beam eam

30 GeVJ/ productionTransition: Hadron Quark degrees of freedomHadron interactions in nuclear mediumShort-range NN interactionsGPDs…50 GeVDrell-Yan (unpolarized PDFs)Single spin asymmetriesTensor structure at 50 GeV (Spin-1 hadrons)Fragmentation functions (Hadron productions)…Proton-beam polarizationDrell-Yan: Double asymmetries (Polarized PDFs)Complimentary to RHIC-Spin (large-x physics)…

x1 x2

J-PARC: s =10GeVRHIC: s=200GeVLHC: s=14TeV

• s = (p1 + p2 )2

• mμμ ≥ 3 GeV

e.g. Drell-Yan: x1x2 =mμμ

2

s

x :

mμμ2

s

x :mμμ

2

s≥

310

=0.3J-PARC

≥3

200=0.02RHIC

≥3

14000=0.0002LHC

Large-x facility(Medium-x)

Small-x facility

Hadron Hadron facilitiesfacilities

p + p(A)→ μ+μ−+ X(qq→ μ+μ−)

Flavor asymmetric antiquark Flavor asymmetric antiquark distributions: u / d distributions: u / d

J-PARC proposal, M. Bai et al. (2007)

http://www.acuonline.edu/academics/cas/physics/research/e906.html

E866

E906

J-PARC

This project is suitable for probing “peripheral structure” of the nucleon.

J.-C. Peng’s talkJ.-C. Peng’s talk

SK, Phys. Rep. 303 (1998) 183;G. T. Garvey and J.-C. Peng,Prog. Part. Nucl. Phys. 47 (2001) 203.

Elastic Scattering: A+B Elastic Scattering: A+B C+D at large p C+D at large pTT

Brodsky@J-PARC-HS05Brodsky@J-PARC-HS05

L.Y. Zhu et al., PRL 91 (2003) 022003

γp → π +n H. Gao

s7 dσdt

Transition from hadron degrees of freedomto quark-gluon d.o.f.

Constituent counting rule

dσdt

(AB→ CD) : s2−n f(θc.m.)

n = nA + nB + nC + cD

(total number of interacting elementary particles)

J-PARC: p + p p + p

Color TransparencyColor Transparency

Brodsky, Strikman@J-PARC-HS05Brodsky, Strikman@J-PARC-HS05

Investigate pInvestigate p AA pp pp (A-1)(A-1)

At large momentum transfer, a small-size component At large momentum transfer, a small-size component of the hadron wave function should dominate. This of the hadron wave function should dominate. This small-size hadron could freely pass through small-size hadron could freely pass through nuclear medium. nuclear medium. (Transparent)(Transparent)

Nuclear transparency: T =σ A

AσN

Hadron size ~ 1 / hard scale

Color transparency: T larger, as the hard scale larger

(BNL-EVA) J. Aclander et al., (BNL-EVA) J. Aclander et al., PRC 70 (2004) 015208PRC 70 (2004) 015208

““Probe of dynamics of elementary reactions”Probe of dynamics of elementary reactions”

Possibility at J-PARC

Incident energy (GeV)Incident energy (GeV)1010 3030 505000

0.40.4

0.80.81212CC

(p,2p) at J-PARC

T

Generalized Parton Distributions (GGeneralized Parton Distributions (GPDs)PDs) GPDs are defined as correlaGPDs are defined as correla

tiontionof off-forward matrix.of off-forward matrix.

Bjorken variable

Momentum transfer squared

ξ = p+ − ′p +

p+ + ′p + =−Δ+

2P+

t =Δ2

dz−

4π∫ eixP+z− ′p (−z / 2)γ + (z / 2) p

z+=0, rz⊥=0=

12P+ H(x,ξ,t)u( ′p )γ +u(p) + E(x,ξ,t)u( ′p )

iσ +αΔα

2Mu(p)

⎡

⎣⎢

⎤

⎦⎥

dz−

4π∫ eixP+z− ′p (−z / 2)γ +γ5 (z / 2) p

z+=0, rz⊥=0=

12P+

%H(x,ξ,t)u( ′p )γ +γ5u(p) + %E(x,ξ,t)u( ′p )γ5Δ

+

2Mu(p)

⎡

⎣⎢

⎤

⎦⎥

x =

Q2

2p⋅q

Skewdness parameter

P =

p+ ′p2

,Δ = ′p −p

pp′′= p= p ++ΔΔpp

kk

qq qq ––ΔΔk+qk+q

kk ++ΔΔ

tt == ΔΔ 22

γγ ** γγ

Forward limit: PDFs H(x,ξ,t) ξ=t=0 = f (x), %H(x,ξ,t)

ξ=t=0=Δf (x)

There is no analog in E and %E.First moments: Form factorsdx H(x,ξ,t)∫ =F1(t), dxE(x,ξ,t)∫ =F2 (t)

dx %H(x,ξ,t)∫ =GA(t), dx %E(x,ξ,t)∫ =GP (t)

Dirac and Pauli form factors Dirac and Pauli form factors FF1 , 1 , FF22

Axial and Pseudoscalar form factors Axial and Pseudoscalar form factors GGA A

, , GGPPSecond moments: Angular momentaSum rule: Jq =

12

dxx Hq(x,ξ,t=0)+ Eq(x,ξ,t=0)⎡⎣ ⎤⎦∫ ,J q =12Δq+ Lq

xξ − xξ− − x ξ+ xξ − x ξ+ x ξ−

1− ξ− ξ0 1

( )0, 0x x xξ ξ ξ ξ− < < + > − <

( )1 0, 0x x xξ ξ ξ< < + > − >( )1 0, 0x x xξ ξ ξ− < < + < − <

Emission of quark with momentum fraction x+ξAbsorption of quark with momentum fraction x-ξ

Emission of quark with momentum fraction x+ξEmission of antiquark with momentum fraction ξ-x

Emission of antiquark with momentum fraction ξ-xAbsorption of antiquark with momentum fraction -x-ξ

GPDs in different GPDs in different xx regions and GPDs at J-PARC regions and GPDs at J-PARC

x

Meson distribution amplitude

Quark distribution

Antiquark distribution

π

p

p

Bp GPDs

qq

GPDs at J-PARC:GPDs at J-PARC:SK, M. Strikman, K. SudoSK, M. Strikman, K. Sudoh, in progress.h, in progress.

t ? mN2

Short-range NN interactionShort-range NN interaction • • Short-range repulsive core, Tensor forceShort-range repulsive core, Tensor force • • Quark degrees of freedomQuark degrees of freedom • • Cold dense nuclear matter, Neutron starCold dense nuclear matter, Neutron star

Ciofi degli Atti@J-PARC-NP07Ciofi degli Atti@J-PARC-NP07

E. Piasetzky et al.,E. Piasetzky et al.,PRL97 (2006) 162504PRL97 (2006) 162504

Strikman@INPC07Strikman@INPC07

Nuclei do not collapse Nuclei do not collapse Short-range repulsive core Short-range repulsive corerr

V(r)V(r)

Nucleon size r ≈ 0.8 fmNucleon size r ≈ 0.8 fmAverage nucleon separation in a nucleus: R ≈ 2 fm ~ 2rAverage nucleon separation in a nucleus: R ≈ 2 fm ~ 2rThe short-range part is important as the density becomes largerThe short-range part is important as the density becomes larger (neutron star).(neutron star).

0.4 fm0.4 fm

A(p, 2pN)X experiment for short range correlationA(p, 2pN)X experiment for short range correlation

initialinitial finalfinal

pp nn

pp

pp

Single spin asymmetrySingle spin asymmetry A

N=σ ↑ −σ ↓

σ ↑ +σ ↓

g Collins effect

AN : δTq⋅H1⊥(Transversity×Collinsfragmentationfunction)

–

Nucleon Quark

– –

The Sivers function describes The Sivers function describes unpolarized quarkunpolarized quarkin the transversely polarized nucleon.in the transversely polarized nucleon.

The Collins fragmentation function describes a The Collins fragmentation function describes a fragmentation of polarized quarkfragmentation of polarized quarkinto unpolarized hadron.into unpolarized hadron.

g Sivers effect

AN : f1T⊥ ⋅D1(Siversfunction×Unpolarizedfragmentation)

Probe of angularProbe of angularmomentummomentum

The transversity distribution describes The transversity distribution describes transverse quark polarizationtransverse quark polarizationin the transversely polarized nucleon.in the transversely polarized nucleon.

(No polarized proton beam is needed!)(No polarized proton beam is needed!)

Burkardt@J-PARC-HS05

Higher-twistQiu, Sterman; Koike@J-PARC-HS05

Part IIPart II

Parton Distribution FunctionsParton Distribution Functionsandand

Fragmentation FunctionsFragmentation Functions

in connection with J-PARCin connection with J-PARC

Unpolarized Parton Distribution Functions (PDFs) in the nucleonUnpolarized Parton Distribution Functions (PDFs) in the nucleon

The PDFs could be obtained from http://durpdg.dur.ac.uk/hepdata/pdf.html

0

0.2

0.4

0.6

0.8

1

0.00001 0.0001 0.001 0.01 0.1 1

x

Q2

= 2 Ge V2

xg/5

xd

xu

xs

xuv

xdv

Valence-quarkdistributions

Gluon distribution / 5

PDF uncertaintyPDF uncertainty

CTEQ5M1

MRS2001

CTEQ5HJ

CTEQ6 (J. Pumplin et al.), JHEP 0207 (2002) 012

u d

g

other PDF

CTEQ6

Important x region for finding an “exotic event” in a high-pT region at LHCJ-PARC x region

If processes are well understood theoreticallyIf processes are well understood theoreticallyincluding pQCD terms, J-PARC measurementsincluding pQCD terms, J-PARC measurementsare important for finding new physics at LHCare important for finding new physics at LHCor possibly in cosmic rays.or possibly in cosmic rays.

Nuclear Nuclear

Parton Distribution Parton Distribution FunctionsFunctions

http://research.kek.jp/people/kumanos/nuclp.html

Experimental data: Experimental data: total number = 1241total number = 1241

(1) F2A / F2

D 896 data NMC: p, He, Li, C, Ca SLAC: He, Be, C, Al, Ca, Fe, Ag, Au EMC: C, Ca, Cu, Sn E665: C, Ca, Xe, Pb BCDMS: N, Fe HERMES: N, Kr

(2) F2A / F2

A’ 293 data NMC: Be / C, Al / C, Ca / C, Fe / C, Sn / C, Pb / C, C / Li, Ca / Li(3) σDYA / σDYA’ 52 data E772: C / D, Ca / D, Fe / D, W / D E866: Fe / Be, W / Be

1

10

100

500

0.001 0.01 0.1 1

x

NMC (F

2

A

/F

2

D

)

SLAC

EMC

E665

BCDMS

HERMES

NMC (F

2

A

/F

2

A'

)

E772/E886 DY

NMC (F

2

D

/F

2

p

)

Functional formFunctional form

If there were no nuclear If there were no nuclear modificationmodification

Isospin symmetryIsospin symmetry ：：

Take account of nuclear effects by Take account of nuclear effects by wwi i (x, A)(x, A)

uvA x( ) =wuv

x,A( )Zuv x( ) + Ndv x( )

A, dv

A x( ) =wdvx,A( )

Zdv x( ) + Nuv x( )A

uA x( ) =wq x,A( )Zu x( ) + Nd x( )

A, dA x( ) =wq x,A( )

Zd x( ) + Nu x( )A

sA x( ) =wq x,A( )s x( )

gA x( ) =wg x,A( )g x( )

→ uA x( ) =Zu x( ) + Nd x( )

A, d A x( ) =

Zd x( ) + Nu x( )

A

un =dp ≡d, dn =up ≡u

Nuclear PDFs “per nucleon”Nuclear PDFs “per nucleon”

AuA x( ) =Zup x( ) + Nun x( ), AdA x( ) =Zdp x( ) + Ndn x( )p=proton,n=neutron

at at QQ22==1 GeV1 GeV2 2 ((

QQ002 2 ))

Functional form of Functional form of wwi i (x, A)(x, A)

fiA (x,Q0

2 ) =wi (x,A) fi (x,Q02 )i =uv, dv, u, d, s, g

wi (x, A) =1+ 1−1Aα

⎛⎝⎜

⎞⎠⎟

ai +bix+ cix2 +dix

3

(1−x)β

Nuclear charge: Z =A dx23

uA −uA( )−13

dA −dA( )−13

sA −sA( )⎡⎣⎢

⎤⎦⎥∫ =A dx

23

uvA −

13

dvA⎡

⎣⎢⎤⎦⎥∫

Baryonnumber:A=A dx13

uA −uA( ) +13

dA −dA( ) +13

sA −sA( )⎡⎣⎢

⎤⎦⎥∫ =A dx

13uv

A +13

dvA⎡

⎣⎢⎤⎦⎥∫

Momentum:A=A dx uA +uA +dA +dA + sA + sA + g⎡⎣ ⎤⎦∫=A dx uv

A +dvA + 2 uA +dA + sA( ) + g⎡⎣ ⎤⎦∫

Three constraintsThree constraints

xx

A simple function = cubic polynomialA simple function = cubic polynomial

Note: The regionNote: The region x x > 1 cannot > 1 cannot be described by this parametrbe described by this parametrization.ization.

Analysis conditionsAnalysis conditions

· Nucleonic PDFs:MRST98 [ QCD = 174 MeV (LO), 300 MeV (NLO) ]

· Total number of data ： 1241 ( Q2≧1 GeV2 )

896 (F2A/F2

D) + 293 (F2A/F2

A´) + 52 (Drell-Yan)

· Subroutine for 2 analysis ： CERN-Minuit

2min ( /d.o.f.) = 1653.3 (1.35) ….. LO = 1485.9 (1.21) ….. NLO

2 =Ri

data − Ritheo( )

2

σ idata( )

2i

∑σ i

data = σ isys

( )2

+ σ istat

( )2

R =F2

A

F2D ,

F2A

F2′A ,

σ pA

σ p ′A

· Total number of parameter ：12

· Error estimate ： Hessian method

δF(x)[ ]2

= Δχ 2 ∂F(x)

∂ξ ii, j∑ H ij

−1 ∂F(x)

∂ξ j

H ij =Hessian

ξi =parameter

0.7

0.8

0.9

1

1.1

1.2

0.03 0.1 1

x

772E

Q

2

=50GeV

2

LO

NLO

H

H

H

H

H

H

H

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1

x

EMC

NMC

HE136

E665

Q

2

= 10 GeV

2

Comparison with FComparison with F22CaCa/F/F22

DD & & σσDYDYpCapCa/ / σσDYDY

pDpD datadata

(R(Rexpexp-R-Rtheotheo)/R)/Rtheo theo at the same Qat the same Q22 points points R= FR= F22CaCa/F/F22

DD, , σσDYDYpCapCa/ / σσDYDY

pDpD

H

H

H HHH H

F F

F

F

F

-0.2

0

0.2

0.001 0.01 0.1 1

x

EMC

NMC

H E139

F E665

-0.2

0

0.2

x

E772

NLO analysisNLO analysisLO analysisLO analysis

Results & Future experiments

0.4

0.6

0.8

1

1.2

0.001 0.01 0.1 1

x

LO

NLO

uv

Q 2 = 1 GeV

2

JLab

FactoryMINARA

0.4

0.6

0.8

1

1.2

0.4

0.6

0.8

1

1.2

0.001 0.01 0.1 1

x

q

gluon

FermilabJ-PARC

RHICLHC

RHICLHC

FermilabJ-PARCGSI

eLICeRHIC

eLICeRHIC

E866

E906

J-PARC

J-PARC proposalJ. Chiba et al. (2006)

(HKN07)(HKN07)

Polarized Polarized

Parton Distribution Parton Distribution FunctionsFunctions

http://spin.riken.bnl.gov/aac/http://spin.riken.bnl.gov/aac/

1

2=12

Δuv + Δdv + Δqsea( )

Δ1 24 44 34 4 4

+ ΔG + Lq + Lg

Nucleon Nucleon SpinSpin

Naïve Quark Model

Δ =Δuv + Δdv =1

Δ ≈0.1~0.3

Almost none of nucleon spinis carried by quarks!

Nucleon Spin:

QCD

Sea-quarks and

gluons?

Gluon: ΔGSea-quarks:Δqsea

Recent data indicate ΔG is small at x ~ 0.1.

Orbital angular momenta ?

L

q, L

g

Future experiments

Electron / muon scattering

Current polarized data arekinematically limited.

1

10

100

0.001 0.01 0.1 1

x

E130(p)

E143(p)

E155(p)

EMC(p)

SMC(p)

HERMES(p)

E143(d)

E155(d)

SMC(d)

E142(n)

E154

HERMES(n)

(GeV2

)

g1 data

(from H1 and ZEUS, hep-ex/0502008)

F2 data

x =

Q2

2p⋅q;

Q2

ys

fixed target: min(x) =Q2

2MNElepton

≤1

2Elepton(GeV)

ifQ2 ≥1GeV2

for Elepton (SMC) =190GeV,min(x) =1400

=0.003

region of g1 data(from AAC04)

Spin asymmetry A1 ; g1

2x 1+ R( )F2

R ≡FL

2xF1=

F2 −2xF12xF1

General strategies for determining General strategies for determining polarized PDFspolarized PDFs

g1(x,Q2 ) =12

eq2

q∑ dy

yx

1

∫ Δq(x / y,Q2 ) + Δq(x / y,Q2 )⎡⎣ ⎤⎦ δ(1−y) +αs(Q

2 )2π

ΔCq(y) +⋅⋅⋅⎡

⎣⎢

⎤

⎦⎥

+12

eq2 dy

yx

1

∫ Δg(x / y,Q2 ) nf

αs(Q2 )

2πΔCg(y) +⋅⋅⋅

⎡

⎣⎢

⎤

⎦⎥ eq

2 =1nf

eq2

q∑

Leading Order (LO)

Next to Leading Order (NLO)ΔCq (ΔCg ) = quark (gluon) coefficient function

F2 (x,Q2 ) =x eq2

q∑ dy

yx

1

∫ q(x / y,Q2 ) +q(x / y,Q2 )⎡⎣ ⎤⎦ δ(1−y) +αs(Q

2 )2π

Cq(2)(y) +⋅⋅⋅

⎡

⎣⎢

⎤

⎦⎥

+ x eq2 dy

y

x

1

∫ g(x / y,Q2 ) nf

αs(Q2 )

2πCg

(2)(y) +⋅⋅⋅⎡

⎣⎢

⎤

⎦⎥

Unpolarized PDFs

Parton distribution functions

Parton interactionsFragmentation functions

Description of π0 production

Δσ : Δfa(xa,Q2 )⊗ Δfb(xb,Q

2 )a,b,c∑

⊗ Δσ (ab→ cX)⊗ Dcπ (z,Q2 )

g + g→ q(g) + XprocessesaredominantatsmallpT q+ g→ q(g) + XatlargepT

The The ππ00 production process is suitable production process is suitablefor finding the gluon polarization for finding the gluon polarization ΔΔg.g.

Situation of polarized PDSituation of polarized PDFsFs

Gluon and antiquark distributions have large uncertainties at large x.

-0.2

0

0.2

0.4

0.6

0.001 0.01 0.1 1

06AAC

GRSV

BB

LSS

-0.04

-0.03

-0.02

-0.01

0

0.01

0.001 0.01 0.1 1

x

x Δ (g x )

Q

2

=1GeV

2

x Δ (q x )

J-PARC

0

0.1

0.2

0.3

0.4

0.5

0.001 0.01 0.1 1

-0.2

-0.1

0

0.001 0.01 0.1 1

x

06AAC

GRSV

BB

LSS

x Δ u

v

( x )

x Δ d

v

( x )

Q

2

=1GeV

2

Fragmentation Fragmentation FunctionsFunctions

http://research.kek.jp/people/kumanos/ffs.htmlhttp://research.kek.jp/people/kumanos/ffs.html

Purposes of investigating fragmentation functionsPurposes of investigating fragmentation functions

Semi-inclusive reactions have been used for investigating

・ origin of proton spin

re +

rp→ ′e +h+ X(e.g.HERMES),

rp+

rp→ h+ X(RHIC-Spin)

A + ′A → h+ X(RHIC,LHC)・ properties of quark-hadron matters

Quark, antiquark, and gluon contributions to proton spin

(flavor separation, gluon polarization)

Nuclear modification

(recombination, energy loss, …)

σ = fa(xa,Q2 )⊗ fb(xb,Q

2 )a,b,c∑

⊗ σ (ab→ cX)⊗ Dcπ (z,Q2 )

Fragmentation FunctionFragmentation Function

Fragmentation function is defined by

e+

e–

γ, Z

q

q

h

Fragmentation: hadron production from a quark, antiquark, or gluon

Fh (z,Q2 ) =1

σ tot

dσ(e+e−→ hX)dz

σ tot =totalhadroniccrosssection

z ≡Eh

s / 2=2Eh

Q=

Eh

Eq, s=Q2

Variable Variable zz• • Hadron energy / Beam energyHadron energy / Beam energy• • Hadron energy / Primary quark energyHadron energy / Primary quark energy

A fragmentation process occurs from quarks, antiquarks, and gluons,A fragmentation process occurs from quarks, antiquarks, and gluons,so that so that FFhh is expressed by their individual contributions: is expressed by their individual contributions:

F h(z,Q2 ) =

dyyz

1∫

i∑ Ci

zy,Q2⎛

⎝⎜⎞

⎠⎟Di

h(y,Q2 )

Ci (z,Q2 ) =coefficientfunction

Dih(z,Q2 ) =fragmentationfunctionofhadronhfromapartoni

Calculated in perturbative QCDCalculated in perturbative QCD

Non-perturbative (determined from experiments)

Comparison with pion dataComparison with pion data

1E-3

1E-2

1E-1

1E+0

1E+1

1E+2

1E+3

0 0.2 0.4 0.6 0.8 1

z

SLD

ALEPH

OPAL

DELPHI

Q = MZ

-1-0.5

00.5

1

0 0.2 0.4 0.6 0.8 1

z

Fπ±(z,Q2 ) =

1σ tot

dσ(e+e−→ π ±X)dz

Our NLO fitwith uncertainties

Fπ±(z,Q2 )data−Fπ±

(z,Q2 )theory

Fπ±(z,Q2 )theory

Rational difference between data and theory

Our fit is successful to reproduce the pion data.

The DELPHI data deviate from our fit at large z.

-0.5

0

0.5

1

1.5

-0.5

0

0.5

1

1.5

-0.5

0

0.5

1

1.5

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1z

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1z

gluon

u quark

c quark b quark

Q2=2GeV2

Q2=2GeV2 Q2=2GeV2

Q2=10GeV2 Q2=100GeV2

KKPAKK Kretzer

HKNS

s quark

DSS

Fragmentation functionsFragmentation functionsat J-PARCat J-PARC

s =xaxbs~(0.4)2 (10GeV)2

s =0.4 ⋅10 =4GeV

z~pT

s / 2=

pT

2~1(largez)

ss

J-PARCJ-PARC

Gluon and light-quark fragmentation functions have large uncertainties.

Global analysisresults for π

Large differences between the functions of various analysis groups.

Exotic hadron searchExotic hadron search

by fragmentation by fragmentation functionsfunctions

ff00(980) as an example (980) as an example

Criteria for determining Criteria for determining ff00 str structure by its fragmentation funcucture by its fragmentation functionstionsPossible configurations of f0 (980)

(1) ordinary u,d - meson 1

2(uu + dd)

(2)strangemeson,ss

(3)tetraquark(KK),12(uuss + ddss)

(4)glueballgg

Contradicts with experimental widths

Γtheo( f0 → ππ) =500 −1000MeV? Γexp =40 −100MeV

Γtheo( f0 → γγ) =1.3−1.8keV? Γexp =0.205keV

Contradicts with lattice-QCD estimate

mlattice( f0 ) =1600MeV? mexp =980MeV

Discuss 2nd moments and functional forms (peak posiDiscuss 2nd moments and functional forms (peak positions)tions)of the fragmentation functions for of the fragmentation functions for ff00 by assuming by assumingthe above configurations, (1), (2), (3), and (4).the above configurations, (1), (2), (3), and (4).

Tensor Structure at High-Tensor Structure at High-EnergiesEnergies

For Spin-1 HadronsFor Spin-1 HadronsNote: Proton-beam polarization is not needed. Polarized deuteron target is enough at J-PARC!

http://www-conf.kek.jp/J-PARC-HS05/program.htmlhttp://www-conf.kek.jp/J-PARC-HS05/program.html

StructurStructureeFunctionFunctionss(in e (in e scattering)scattering)

PartoPartonnModelModel

F1 ∝ dσ

g1 ∝ dσ ↑,+1( )−dσ ↑,−1( )

b1 ∝ dσ 0( )−dσ +1( ) +dσ −1( )

2

q↑H x,Q2( )⎡⎣ ⎤⎦

F1 =12

ei2

i∑ qi +qi( ) qi =

13

qi+1 +qi

0 +qi−1( )

g1 =12

ei2 Δqi + Δqi( )∑ Δqi = qi↑

+1 − qi↓+1

b1 =12

ei2 δqi +δqi( )

i∑ δqi = qi

0 −qi

+1 + qi−1

2

Tensor Structure in High-energy ReactTensor Structure in High-energy Reactions ions (Note: No polarized proton beam is needed!)(Note: No polarized proton beam is needed!)

L. L. Frankfurt and M. I. Strikman, NP A405 (1983) 557.P. Hoodbhoy, R. L. Jaffe, and A. Manohar, NP B312 (1989) 571.

Spin asymmetries

ALL =ea2 Δqa xA( )Δqa xB( ) + Δqa xA( )Δqa xB( )⎡⎣ ⎤⎦a∑

ea2 qa xA( )qa xB( ) +qa xA( )qa xB( )⎡⎣ ⎤⎦a∑

ATT =sin2θ cos 2φ( )1+ cos2θ

ea2 ΔTqa xA( )ΔTqa xB( ) + ΔTqa xA( )ΔTqa xB( )⎡⎣ ⎤⎦a∑

ea2 qa xA( )qa xB( ) +qa xA( )qa xB( )⎡⎣ ⎤⎦a∑

AUQ0=

ea2 qa xA( )δqa xB( ) +qa xA( )δqa xB( )⎡⎣ ⎤⎦a∑ea2 qa xA( )qa xB( ) +qa xA( )qa xB( )⎡⎣ ⎤⎦a∑

Note: δ ≠transversityinmynotation

Tensor Structure in Proton-Tensor Structure in Proton-Deuteron Drell-Yan Deuteron Drell-Yan (Note: No polarized proton beam is needed!)(Note: No polarized proton beam is needed!)

δqi = qi0 −

qi+1 + qi

−1

2

F. E. Close and SK, PRD42, 2377 (1990)

only in S-waveonly in S-wavebb11 = 0 = 0

bb11 for spin-1 particles for spin-1 particles1st measurement of b1:(HERMES) A. Airapetian et al., PRL 95 (2005) 242001.Polarized proton-deuteron Drell-

Yan(Theory) S. Hino and SK, PR D 59 (1999) 094026, D 60 (1999) 054018. (Experiment) None J-PARC

Unique advantage of J-PARC (δqmeasurement)

AUQ0large xF( ) ≈

ea2qa xA( )δqa xB( )

a∑ea2qa xA( )qa xB( )

a∑

dx∫ b1D(x) =0 +

19δQ+δQ( )sea

Gottfried: dx

xF2p (x)−F2

n(x)⎡⎣ ⎤⎦∫ =13+23

dx u−d⎡⎣ ⎤⎦∫

Unpolarized proton+ Tensor polarized deuteron

Our works related to this talkOur works related to this talk (1) Overview on “Possible Hadron Physics at J-PARC”(1) Overview on “Possible Hadron Physics at J-PARC” SK, Nucl. Phys. A782 (2007) 442.SK, Nucl. Phys. A782 (2007) 442.

(2) ubar/dbar(2) ubar/dbar SK, Phys. Rep. 303 (1998) 183.

(3) Nuclear PDFs(3) Nuclear PDFs M. Hirai, SK, and M. Miyama, Phys. Rev. D 64 (2001) 034003;M. Hirai, SK, and M. Miyama, Phys. Rev. D 64 (2001) 034003; M. Hirai, SK, and T.-H. Nagai, Phys. Rev. C 70 (2004) 044905; M. Hirai, SK, and T.-H. Nagai, Phys. Rev. C 70 (2004) 044905; C 76 C 76

(2007) 065207.(2007) 065207.

(4) Polarized PDFs(4) Polarized PDFs, , Asymmetry Analysis Collaboration (AAC)Asymmetry Analysis Collaboration (AAC) Y. Goto Y. Goto et al.et al., Phys. Rev. D 62 (2000) 034017;, Phys. Rev. D 62 (2000) 034017; M. Hirai, SK, N. Saito, Phys. Rev. D 69 (2004) 054021; M. Hirai, SK, N. Saito, Phys. Rev. D 69 (2004) 054021; D D 74 (2006) 74 (2006)

014015.014015.

(5) Global analyses for FFs of (5) Global analyses for FFs of ππ, K, , K, andand p p + their uncertainties+ their uncertainties M. Hirai, SK, T.-H. Nagai, and K. Sudoh, M. Hirai, SK, T.-H. Nagai, and K. Sudoh, Phys. Rev. D75 (2007) 0Phys. Rev. D75 (2007) 0

94009;94009; Exotic hadron search by using FFs Exotic hadron search by using FFs e.g.e.g. for for ff00(980)(980) M. Hirai, SK, M. Oka, and K. Sudoh, M. Hirai, SK, M. Oka, and K. Sudoh, Phys. Rev. D77 (2008) 017504.Phys. Rev. D77 (2008) 017504.(6) Sum rule for (6) Sum rule for bb11(x)(x) F. E. Close and SK, F. E. Close and SK, Phys. Rev. D 42 (1990) 2377.Phys. Rev. D 42 (1990) 2377. General formalism for polarized proton+deuteron Drell-Yan General formalism for polarized proton+deuteron Drell-Yan S. Hino and SK, S. Hino and SK, Phys. Rev. D 59 (1999) 094026; D 60 (1999) 054018.Phys. Rev. D 59 (1999) 094026; D 60 (1999) 054018.

SummarySummary

I introduced some topics. More contributioI introduced some topics. More contributionsnsare needed for the hadron project at J-PARCare needed for the hadron project at J-PARC!! Need to discuss possible topics with 30 GeNeed to discuss possible topics with 30 GeV, V, 50 GeV, and 50 GeV polarized proton beams.50 GeV, and 50 GeV polarized proton beams.

J-PARC will be an important facilityJ-PARC will be an important facilityin hadron and nuclear physics communities.in hadron and nuclear physics communities.

In high-energy hadron physicsStructure functions of hadronsFragmentationHadron interactions in nuclear mediumShort-range NN interactionsHadron Quark degrees of freedomHadron spin…

The End

The End