Structure Functions in the NucleonStructure Functions in the Nucleon

Shunzo KumanoShunzo KumanoHigh Energy Accelerator Research Organization (KEK) High Energy Accelerator Research Organization (KEK)

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

April 25 – 26, 2008 April 25 – 26, 2008 (Talk on April 26)(Talk on April 26)

shunzo.kumano@kek.jpshunzo.kumano@kek.jphttp://research.kek.jp/people/kumanhttp://research.kek.jp/people/kumanos/os/

Ultra-high energy cosmic rays and hadron structure 2008Ultra-high energy cosmic rays and hadron structure 2008KEK, Tsukuba, JapanKEK, Tsukuba, Japan

http://www-conf.kek.jp/hadron08/crhs08/http://www-conf.kek.jp/hadron08/crhs08/

ContentsContents

1.1. Introduction Introduction Parton Distribution Functions (PDFs)• Parton Distribution Functions (PDFs)•

• • Relevant kinematical regions for ultra-high energRelevant kinematical regions for ultra-high energy y

cosmic ray interactions with atmospheric nucleicosmic ray interactions with atmospheric nuclei

2.2. Current SituationCurrent Situation • • PDFs in the nucleonPDFs in the nucleon • • Nuclear PDFsNuclear PDFs

• • Fragmentation functionsFragmentation functions

3. Summary3. Summary

IntroductionIntroduction

http://th.physik.uni-frankfurt.de/~drescher/SENECA/

Typical Air Shower Model (SENECA)

My talk is on this “hard” part.

Soft interactions are Soft interactions are discussed yesterday.discussed yesterday.

Kasahara@this workshop

In a shower modelIn a shower model ((e.g.e.g. SIBYLL) SIBYLL)R. S. Fletcher, T. K. Gaisser, P. Lipari, R. S. Fletcher, T. K. Gaisser, P. Lipari, and T. Stanev, Phys. Rev. D 50 (1994) 5710.and T. Stanev, Phys. Rev. D 50 (1994) 5710.

High-energy part is described by the following cross sectionsHigh-energy part is described by the following cross sections

SIBYLL (1994): PDFs by Eichten-Hinchliffe-Lane-Quigg (EHLQ) in 1984SIBYLL (1994): PDFs by Eichten-Hinchliffe-Lane-Quigg (EHLQ) in 1984

The PDFs at large The PDFs at large xx11 and small and small xx22 should affect should affectsimulation results of the air shower. simulation results of the air shower.

Soft and Hard processesSoft and Hard processes My talk is on hard processes.My talk is on hard processes.

• • Nuclear PDFs at small Nuclear PDFs at small xx (N, O) (N, O) • • Nucleonic and Nuclear PDFs at large Nucleonic and Nuclear PDFs at large xx (p, …, Fe) (p, …, Fe) • • Fragmentation functionsFragmentation functions

Soft Hard

~1 GeV

Hard scale (e.g. transverse momentum pT )Resonances Partons

pQCD + Parton Distribution Functions (PDFs)(+ Fragmentation Functions)

(R. Engel)

p, …, Fe N, O

Most energetic particles (namely large Most energetic particles (namely large xxF F ) contribute) contributemainly to subsequent shower development.mainly to subsequent shower development.

Quark momentum distributionsQuark momentum distributions

If the proton consists of three quarksand if they carry equal momenta

x11/3

Quarks interact by gluon exchange within the proton. 　　　　　 Momentum could be transferred.

gluon

x11/3

momentumdistribution

Momentum distributionis spread.

Meaning ofMeaning of x x (= parton momentum / parent-hadron momentum)(= parton momentum / parent-hadron momentum)

Valence and sea quarksValence and sea quarks

Sea quark

Valence quark

x1~ 0.2

momentumdistribution

A quark-antiquark pair is created through gluon.

This quark is called “sea quark”.

Definition of valence-quark distribution: qv ≡q−q

Using q =qv+ qs, we have qs=q.

Scaling violation (QScaling violation (Q2 2 dependence)dependence)

ZEUS, Eur. Phys. J. C21 (2001) 443.

small Qsmall Q22

large Qlarge Q22

1

Q2

1

Q2

gluon, qq clouds

As QAs Q2 2 becomes large, the virtualbecomes large, the virtual starts to probe the gluon, quark,starts to probe the gluon, quark,and antiquark “clouds”.and antiquark “clouds”.

∂∂logQ2

q x,Q2( )g x,Q2( )

⎛

⎝⎜

⎞

⎠⎟ =

α s2π

dyyx

1∫

Pqq x / y( ) Pqg x / y( )Pgq x / y( ) Pgg x / y( )⎛⎝⎜

⎞⎠⎟

q y,Q2( )g y,Q2( )

⎛

⎝⎜

⎞

⎠⎟

DGLAP (Dokshitzer, Gribov, Lipatov, Altarelli, Parisi)

Q2 corresponds to“spatial resolution”.

Description of hard hadron interactionsDescription of hard hadron interactions

s : fa

A1 (x1,Q2 )⊗ fbA2 (x2 ,Q2 )

a ,b ,c∑ ⊗ σ (ab → cX)⊗ Dc

h (z,Q2 )

Forward process: large xF =x1 −x2 (x1 ≈1 : A1, x2 = 1)

It is important to understand:It is important to understand: • • Gluon distributions at small Gluon distributions at small xx (N, O), (N, O), • • Quark distributions at large Quark distributions at large xx (p, …, Fe), (p, …, Fe), • • Fragmentation functionsFragmentation functions

Parton distribution functionsParton distribution functions

Parton interactions (pQCD)Parton interactions (pQCD) Fragmentation functionsFragmentation functions

A1 (p, …, or Fe)

A2 (N or O)

Cosmic ray

Atmosphere

s

x2PA2

A2

x1PA1

A1

Note: 0 < x1 < A1 0 < x2 < A2

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LHC

J-PARC

HERARHIC

Ultra-high energy cosmic rays arerelated to physics small-x physics (LHC)and large-x physics (JLab, J-PARC(?)).

High-energy hadron facilities and high-energy cosmic rays High-energy hadron facilities and high-energy cosmic rays

(R. Engel, International School on AstroParticle Physics, June 30th - July 9th, 2005, Belgirate, Italy )

x1 x2

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

• s = (p1 + p2 )2

• mμμ ≥ 3 GeV

e.g. Drell-Yan: x1x2 =m mm

2

s

x :

mmm2

s

x :mmm

2

s≥

310

=0.3 J-PARC

≥ 3

200=0.02 RHIC

≥3

14000=0.0002 LHC

Large-x facility

Small-x facility

Hadron facilitiesHadron facilities

p + p(A)→ m+m−+ X (qq → m+m−)

Ultra-high energy cosmic ray interactionscould be related to LHC& JLab, J-PARC (?) physics.

x1x2 =Q2

s =

Q2

2ME for fixed tarets

For the forward reion of x1 ~1 (lare x), Q2 ~10 GeV

x2 ~10

s(G eV 2 ) =10−7 for s=(14 TeV )2

x2 ~10

2E(G eV ) =10−10 = 1 for cosm ic rays with E =1020 eV

(extrem ely sm all x)

Momentum fraction Momentum fraction x x in the forward regionin the forward region

Parton Distribution FunctionsParton Distribution Functionsin the Nucleonin the Nucleon

Motivations for studying PDFsMotivations for studying PDFs(1)(1)To establish QCDTo establish QCD

Perturbative QCDPerturbative QCD

• In principle, theoretically established in many processes.

(There are still issues on resummations and small-x physics.)

• Experimentally confirmed (unpolarized, polarized ?)

Non-perturbative QCD (PDFs)Non-perturbative QCD (PDFs)

• Theoretical models: Bag, Soliton, … (It is important that we have intuitive pictures of the nucleon.)

• Lattice: Reliable x-distributions have not been obtained.

Determination of the PDFs from experimental data. Determination of the PDFs from experimental data.

(2) For discussing any high-energy reactions, accurate PDF(2) For discussing any high-energy reactions, accurate PDFss are needed.are needed.

origin of nucleon spin:origin of nucleon spin: quark- and gluon-spin contribuquark- and gluon-spin contributionstions

exotic events at large Qexotic events at large Q22:: physics of beyond current fphysics of beyond current frameworkramework

heavy-ion reactions:heavy-ion reactions: quark-hadron matter quark-hadron matter

neutrino oscillations: neutrino oscillations: nuclear effects in nuclear effects in n n + + 1616O O

cosmology: cosmology: ultra-high-energy cosmic raysultra-high-energy cosmic rays

Recent papers on unpolarized PDFsCTEQ (uncertainties) D. Stump (J. Pumplin) et al., Phys. Rev. D65 (2001) 14012 & 14013. (CTEQ6) D. Pumplin et al., JHEP, 0207 (2002) 012; 0506 (2005) 080; 0602 (2006) 032; 0702 (2007) 053; (charm) PR D75 (2007) 054029; (strange) PRL 93 (2004) 041802; Eur. Phys. J. C40 (2005) 145; JHEP 0704 (2007) 089.

GRV (GRV98) M. Glück, E. Reya, and A. Vogt, Eur. Phys. J. C5 (1998) 461. --- no update

MRST A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne, (MRST2001, 2002, 20033) Eur. Phys. J. C23 (2002) 73; Eur. Phys. J. C28 (2003) 455; (theoretical errors) Eur. Phys. J. C35 (2004) 325; (2004) PL B604 (2004) 61; (QED) Eur. Phys. J. C39 (2005) 155; PL B636 (2006) 259; (2006) PRD73 (2006) 054019; hep-ph/0706.0459.

Alekhin S. I. Alekhin, PRD68 (2003) 014002; D74 (2006) 054033.

BB J. Blümlein and H. Böttcher, Nucl. Phys. B774 (2007) 182-207.

NNPDF S. Forte et al., JHEP 0205 (2002) 062; 0503 (2005) 080; 0703 (2007) 039.

H1 C. Adloff et al., Eur. Phys. J. C 21 (2001) 33;

ZEUS S. Chekanov et al., Eur. Phys. J. C42 (2005) 1.

It is likely that I miss some papers!

Recent activities uncertainties NNLO QED s – s charm

Parton distribution functions are determined by fitting various experimental data.

g electron/muon: m + p→ m + X neutrino: nm + p→ m + X

Drell-Yan: p+ p→ m+m−+ X ⋅⋅⋅

(1) assume functional form of PDFs at fixed Q2 (≡Q02 ) :

e.. fi(x,Q02 )=Aix

ai (1−x)βi (1+ix),

where i =uv, dv, u, d , s,

(2) calculate oβservaβles at their experim ental Q2 points.(3) then, the param eters Ai, a i, βi, iare determ ined so as

to m inim ize c 2 in com parison with data.

Available data for determining PDFs(Ref. MRST, hep/ph-9803445)

Used data for MRST01(Ref. MRST, hep/ph-0110215)

€

MW1= F1 , νW2 = F2 , νW3 = F3 , x = Q2

2p⋅q , y = p⋅qp⋅k

€

dσ ν ,ν CC

dx dy =GF

2 (s − M 2)2π (1+Q2 / MW

2 )2 x y2F1CC + 1− y − M x y

2 E ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ F2

CC ± x y 1− y2

⎛ ⎝ ⎜

⎞ ⎠ ⎟ F3

CC ⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

N

X

q

p W

nm

m –

+

Determination of each distribution Valence quark

€

12 [F3

νp +F3ν p]CC = uv +dv + s−s +c −c

M = 11+Q2 / MW

2 GF

2 u( ′k , ′l ) m (1−5) u(k,l) <X|JmCC |p,lp >

dsd ′E dW =

GF2

(1+Q2 / MW2 )2

′k32p 2E

Lmn Wmn

nm + p → μ − + X

Lmn =8 km ′k n + kn ′k m −mnk⋅ ′k + ie mnrskr ′ks⎡⎣ ⎤⎦ where e0123 =+1

Wmn =−W1 mn −qmqn

q2

⎛⎝⎜

⎞⎠⎟ +W2

1MN

2 pm −p⋅qq2 qm⎛

⎝⎜⎞⎠⎟ pn −

p⋅qq2 qn⎛

⎝⎜⎞⎠⎟ +

i2MN

2 W3emnrs prqs

Note: Issue of nuclear correctionsin CCFR/NuTeV (n+Fe)unless we will have a n factory.

Sea quarke/m scattering

Drell-Yan (lepton-pair production)

(q1) q1

q2

m–

m+

(q2)

projectile target

F2N =

F2p + F2

n

2=

518

x u+u + d + d( )+218

x u+u + d + d( )

=518

xV +418

xS if q distriβutions are flavor sym m etric

p1 + p2 → m+m−+ X

ds ∝ q(x1) q(x2 )+ q(x1) q(x2 )

ds ∝ qV (x1) q(x2 )at large xF =x1 −x2

q(x2 ) can be obtained if qV (x1) is known.

Gluon

scaling violation of F2

∂∂ lnQ2( )

qs x, t( )g x, t( )

⎛⎝⎜

⎞⎠⎟

=α s2π

dyyx

1∫

Pqq x / y( ) Pqg x / y( )Pgq x / y( ) Pgg x / y( )⎛⎝⎜

⎞⎠⎟

qs y, t( )g y, t( )

⎛⎝⎜

⎞⎠⎟

at small x ∂F2

∂ lnQ2( )≈10 as

27pG

jet productionK. Prytz, Phys. Lett. B311 (1993) 286.

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

Q 2 = 2 Ge V 2

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 PDFCTEQ6

q(x)q(x) at large at large xx

g(x)g(x) at small at small xx

(unknown)(unknown)22

for cosmic-ray studiesfor cosmic-ray studies

““gluon saturation”gluon saturation”

There are also large nuclearThere are also large nuclearcorrections in these regions.corrections in these regions.

Issue of Issue of qq (x)(x) in the “nucleon” at large in the “nucleon” at large xx from from nn-Fe (≠nucleon) scattering-Fe (≠nucleon) scattering

0

0.2

0.4

0.6

0.8

1

0.00001 0.0001 0.001 0.01 0.1 1

x

Q 2 = 2 Ge V 2

xg/5

xd

xu

xs

xuv

xdv

Most people believe that valence-quarkMost people believe that valence-quarkdistributions are well determined, distributions are well determined, but it may not.but it may not.

Of course, gross functional forms arefixed by dx∫ uv(x)=2, dx∫ dv(x)=1which are oβtained from ep =1, en =0.

CCFR, NuTeV experimentsCCFR, NuTeV experiments

n , ν

Huge Fe target (690 ton)Huge Fe target (690 ton)

E =30 ~500 G eV…… ““Nucleonic” PDFs have beenNucleonic” PDFs have been

obtained by assuming that nuclear obtained by assuming that nuclear corrections are the same as thosecorrections are the same as thosein the charged-lepton (e, in the charged-lepton (e, mm) scattering.) scattering.

M. Tzanov M. Tzanov et al. et al. (NuTeV), (NuTeV), Phys. Rev. D 74 (2006) 012008.Phys. Rev. D 74 (2006) 012008.

Nuclear corrections in iron Nuclear corrections in iron (A=56, Z=26)(A=56, Z=26)Charged-lepton scatteringCharged-lepton scattering

Neutrino scatteringNeutrino scattering Base-1 Base-1 remove CCFR data • remove CCFR data • • • incorporate deuteron correctionsincorporate deuteron correctionsBase-2 Base-2 corresponds to CTEQ6.1M with s≠sbarcorresponds to CTEQ6.1M with s≠sbar • • include CCFR data include CCFR data Charged-lepton correction factorsCharged-lepton correction factors are appli are applied.ed. • • s≠sbars≠sbar

Using current nucleonic PDFs, they (and MRST)Using current nucleonic PDFs, they (and MRST)obtained very different corrections from obtained very different corrections from charged-lepton data.charged-lepton data.

However, it depends on the analysis method forHowever, it depends on the analysis method fordetermining nucleonic (determining nucleonic (≠≠ nuclearnuclear) PDFs.) PDFs.

Large uncertainties onLarge uncertainties onpossible nuclear correctionspossible nuclear corrections

I. Schienbein I. Schienbein et al. et al. (CTEQ)(CTEQ),,PRD 77 (2008) 054013.

Nuclear Nuclear Parton Distribution FunctionsParton Distribution Functions

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

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1

EMCNMCE139E665

q-qbar fluctuation of photon (+ recombination)

Nuclear binding (+ Nucleon modification)

Fermi motionof the nucleon

x Explained in Saito’s talk

Could affectCould affectcosmic-ray studiescosmic-ray studies

Nuclear modifications of structure function Nuclear modifications of structure function FF22

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) s DYA / s DY

A’ 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 (F2

A

/F2

D

)

SLAC

EMC

E665

BCDMS

HERMES

NMC (F2

A

/F2

A'

)

E772/E886 DY

NMC (F2

D

/F2

p

)

Functional formFunctional formIf there were no nuclear modificationIf there were no nuclear modification

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

, dvA x( )=wdv x,A( )

Zdv x( )+ Nuv x( )A

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

A, d A x( )=wq x,A( )

Zd x( )+ Nu x( )A

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

A x( )=w x,A( ) x( )

→ uA x( ) =Zu x( ) + Nd x( )

A, d A x( ) =

Zd x( ) + Nu x( )A

un =d p ≡d, d n =up ≡u

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

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

at at QQ22==1 GeV1 GeV2 2 (( QQ002 2 ))

0.7

0.8

0.9

1

1.1

1.2

0.03 0.1 1

x

E772

Q

2

= 50 GeV

2

LO

NLO

HH

H

H

HH

H

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1

x

EMC

NMC

H E136

E665

Q

2

= 10 GeV

2

Comparison with FComparison with F22CaCa/F/F22

DD & & ssDYDYpCapCa/ / ssDYDY

pDpD data data

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

DD, , ssDYDYpCapCa/ / ssDYDY

pDpD

H

H

H HHH HF 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 experimentsResults & Future experiments

0.4

0.6

0.8

1

1.2

0.001 0.01 0.1 1

x

LONLO

uv

Q 2 = 1 GeV 2

JLab

nFactoryMINARnA

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)

Fragmentation FunctionsFragmentation Functions

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

Fragmentation FunctionFragmentation Function

Fragmentation function is defined by

e+

e–

, Z

q

q

h

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

Fh (z,Q2 ) =1

s tot

ds(e+e−→ hX)dz

s tot =total hadronic cross section

z ≡Eh

s/ 2=2EhQ

=EhEq

, 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 ) =coefficient function

Dih(z,Q2)=fram entation function of hadron h from a parton i

Calculated in perturbative QCDCalculated in perturbative QCDNon-perturbative (determined from experiments)

Momentum (energy) sum ruleMomentum (energy) sum rule

Dih z,Q2( )= proβaβility to find the hadron h from a parton i

with the enery fraction z

Energy conservation: dz z

0

1

∫

h∑ Di

h z,Q2( )=1

h =p + , p 0 , p −, K+ , K0 , K0 , K−, p, p, n, n, ⋅⋅⋅

Simple quark model: p +(ud ), K+(us), p(uud), ⋅⋅⋅

Favored fragmentation: Dup+

, Ddp+

, ...

(from a quark which exists in a naive quark m odel)

Disfavored fram entation: Ddp+

, Dup+

, Dsp+

, ...

(from a quark which does not exist in a naive quark m odel)

Favored and disfavored fragmentation functionsFavored and disfavored fragmentation functions

Experimental data for pionExperimental data for pion

# of data

TASSOTCPHRSTOPAZSLDSLD [light quark]SLD [ c quark]SLD [ b quark]ALEPHOPALDELPHIDELPHI [light quark]DELPHI [ b quark]

12,14,22,30,34,44292958

91.2

91.291.291.2

291824

292929292222171717

s (GeV)

Total number of data ： 264

0

20

40

60

80

100

0 0.2 0.4 0.6 0.8 1z

TASSO

TPC

HRS

TOPAZ

SLD

ALEPH

OPAL

DELPHI

1E-3

1E-2

1E-1

1E+0

1E+1

1E+2

1E+3

0 0.2 0.4 0.6 0.8 1z

SLDALEPHOPALDELPHI

Q = MZ

Fp±(z,Q2 )=

1s tot

ds(e+e−→ p ±X)dz

Typical data for pionTypical data for pion

-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

luon

u quark

c quark β quark

Q2 = 2 GeV2

Q2 = 2 GeV2 Q2 = 2 GeV2

Q2 = 10 GeV2 Q2 = 100 GeV2

KKPAKK Kretzer

HKNS

s quark

DSS

Fragmentation functionsFragmentation functions

z =phpc

~phs / 2

Gluon and light-quark fragmentation functions have large uncertainties.

Global analysisresults

Large differences between the functions of various analysis groups.

ss pc

ph

Expected Belle dataExpected Belle data

s =10.58 GeV

R. Seidl (RIKE-BNL), talk at ECT* in February, 2008

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PDG2007The Belle will provide accurateThe Belle will provide accuratefragmentation functions fragmentation functions at low energy in the near future.at low energy in the near future.

e+ + e−→ h± + X

Our works related to this talk Our works related to this talk

(1) Nuclear PDFs(1) 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 (2007) 06520C 76 (2007) 06520

7.7.

(2) Fragmentation functions(2) Fragmentation functions M. Hirai, SK, T.-H. Nagai, and K. Sudoh, M. Hirai, SK, T.-H. Nagai, and K. Sudoh, Phys. Rev. D75 (2007) 094Phys. Rev. D75 (2007) 094

009.009.

(3)(3) Hadron Physics at J-PARCHadron Physics at J-PARC SK, Nucl. Phys. A782 (2007) 442.SK, Nucl. Phys. A782 (2007) 442.

SummarySummary

Communications between cosmic-ray physicistsCommunications between cosmic-ray physicistsand hadron physicists are needed for developingand hadron physicists are needed for developinga reliable interaction model.a reliable interaction model.

Hard interactions are discussed in my talk.Hard interactions are discussed in my talk.

In order to understand the shower profile, namely to determinIn order to understand the shower profile, namely to determine e energy and composition of primary cosmic rays, it should be energy and composition of primary cosmic rays, it should be important to studyimportant to study

Nucleonic and Nuclear PDFs at small Nucleonic and Nuclear PDFs at small xx (LHC) (LHC)

Nucleonic and Nuclear PDFs at large Nucleonic and Nuclear PDFs at large xx (JLab, J-P (JLab, J-PARC, …)ARC, …)

Fragmentation functions (Belle, …)Fragmentation functions (Belle, …)

The End

The End