Structure Functions in the Structure Functions in the Nucleon Nucleon Shunzo Kumano Shunzo 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) April 25 – 26, April 25 – 26, 2008 (Talk on 2008 (Talk on April 26) April 26) [email protected][email protected]http://research.kek.jp/peopl http://research.kek.jp/peopl e/kumanos/ e/kumanos/ Ultra-high energy cosmic rays and hadron structure 20 Ultra-high energy cosmic rays and hadron structure 20 08 08 KEK, Tsukuba, Japan KEK, Tsukuba, Japan http://www-conf.kek.jp/hadron08/crhs08/ http://www-conf.kek.jp/hadron08/crhs08/
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Structure Functions in the Nucleon Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS) April.
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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)
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.
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( )⎛⎝⎜
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
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)
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
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, …)