Nuclear parton distribution functions and their effects on sin 2 W anomaly
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Transcript of Nuclear parton distribution functions and their effects on sin 2 W anomaly
Nuclear parton distribution functions and their effects on sin2W anomaly
Shunzo Kumano, Saga University
[email protected], http://hs.phys.saga-u.ac.jp
12th International Workshops on Deep Inelastic Scattering (DIS04)
Strbske Pleso, Slovakia, April 14-18, 2004
Refs. npdf: (1) M. Hirai, SK, M. Miyama, Phys. Rev. D64 (2001) 034003
(2) M. Hirai, SK, T.-H. Nagai, hep-ph/0404093
sin2W : (1) SK, Phys. Rev. D64 (2001) 034003
(2) research in progress (T.-H. Nagai)
April 15, 2004
Contents
PurposesDetermination of Nuclear Parton Distribution Functions (NPDFs)
(1) used data, 2 analysis method (2) results
Nuclear modification effects on NuTeV sin2W
(1) Paschos-Wolfenstein (PW) relation (2) valence-quark modification effects
on the PW relation and sin2W
Why nuclear parton distribution functions?
(1)Basic interest to understand nuclear structure in the high-energy region, Determination of sin2W
perturbative & non-perturbative QCD
sin2W in neutrino scattering (NuTeV)
(2) Practical purpose to describe hadron cross sections precisely
heavy-ion reactions: quark-gluon plasma signature
long-baseline neutrino experiments: nuclear effects in + 16O
Parametrization of
Nuclear Parton Distribution Functions
Code for the obtained NPDFs
could be obtained from
http://hs.phys.saga-u.ac.jp/nuclp.html
Nuclear modificationNuclear modification of F2
A / F2D is
well known in electron/muon scattering.
F2
A = e i2
ix q i(x) + q i(x)
A
0.7
0.8
0.9
1
1.1
1.2
0.001 0.01 0.1 1
EMC
NMC
E139
E665
shadowingoriginal
EMC finding
Fermi motion
x sea quark valence quark
Functional form of wi(x,A)
f iA(x) = wi(x,A) f i(x), i = uv, dv, q, g
first, assume the A dependence as 1/A
then, use
wi(x,A) = 1 + (1–1 /A) a i+b i x+c i x2+d i x
3
(1 – x ) i
a i, b i, c i, d i, i: parameters to be determined by 2 analysis
Fermi motion: 1
(1 – x ) i as x 1 if i > 0
Shadowing: wi(x 0, A) = 1 + (1–1 /A) a i < 1
Fine tuning: b i, c i, d i
Experimental data
(1) F2A / F2
D
NMC: 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’
NMC: Be / C, Al / C, Ca / C, Fe / C, Sn / C, Pb / C, C / Li, Ca / Li
(3) DYA /
A’
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
Q2 (
GeV
2 )
x
NMC (F2A/F2
D)
SLAC
EMC
E665
BCDMS
HERMES
NMC (F2A/F2
A')
E772/E886 DY
Analysis conditions
parton distributionsin the nucleon
MRST01 (QCD=220
MeV)
Q2 point at whichtheparametrizedPDFs are defined: Q2=1Ge V2
usedexperimentaldata: Q21Ge V2
totalnumber of data: 951
606(F2A /F2
D) +293(F2A /F2
A') + 52(Drell–Yan )
subroutinefor the 2 analysis: CERN– Minuit
2 = (Ridata –R i
calc)2
( idata)2
i
R = F2A
F2D, F2
A
F2A' ,
DYpA
DYpA ' , i
data = (isys )2 + (i
stat)2
Comparison with F2Ca/F2
D & DYpCa/ DY
pD data
(Rexp-Rtheo)/Rtheo at the same Q2 points
0.7
0.8
0.9
1
1.1
1.2
0.001 0.01 0.1 1
F2C
a /F2D
x
EMC
NMC
E136
E665
Q2= 5 GeV2
-0.2
0
0.2
0.001 0.01 0.1 1
x
EMC
NMC
E139
E665
Ca/D
0.7
0.8
0.9
1
1.1
1.2
0.03 0.1 1
x
E772
Q2= 50 GeV2
-0.2
0
0.2
0.03 0.1 1
x
E772
Ca/D DY
Comparison with R=F2A/F2
A’ data: (Rexp-Rtheo)/Rtheo are shown
-0.2
0
0.2
0.001 0.01 0.1 1
NMC
E139
-0.2
0
0.2
0.001 0.01 0.1 1
NMC
-0.2
0
0.2
0.001 0.01 0.1 1
E139
-0.2
0
0.2
0.001 0.01 0.1 1
x
EMC
NMC
E139
E665
He/D
Be/D
Li/D
C/D
-0.2
0
0.2
0.001 0.01 0.1 1
BCDMS HERMES
-0.2
0
0.2
0.001 0.01 0.1 1
E139
E49
-0.2
0
0.2
0.001 0.01 0.1 1
EMC
NMC
E139
E665
-0.2
0
0.2
0.001 0.01 0.1 1
x
BCDMS
E87
E139
E140
Ca/D
Al/D
N/D
Fe/D
Comparison with R=DYpA/ DY
pA’ (Rexp-Rtheo)/Rtheo are shown
-0.1
0.1
0.3
0.01 0.1 1
E772
-0.2
0
0.2
0.01 0.1 1
-0.2
0
0.2
0.01 0.1 1
x
E866
C/D DY
Ca/D DY
Fe/Be DY
-0.2
0
0.2
0.01 0.1 1
-0.2
0
0.2
0.01 0.1 1
-0.3
-0.1
0.1
0.01 0.1 1
x
Fe/D DY
W/D DY
W/Be DY
Nuclear corrections of PDFs with uncertainties
0.7
0.8
0.9
1
1.1
1.2
0.001 0.01 0.1 1
x
Ca
Q2 = 1 GeV2
valence-quark
0.4
0.6
0.8
1
1.2
1.4
0.001 0.01 0.1 1
x
antiquark
0
0.5
1
1.5
2
0.001 0.01 0.1 1
x
gluon
Nuclear Effects on sin2W
Nuclear modification difference
between uvA and dv
A
sin2W anomaly
Paschos-Wolfenstein relation R– =
NCN – NC
N
CCN – CC
N = 12
– sin2W
Difference between nuclear modifications of uV and dV: v(x) =
wdV(x) – wuV
(x)
wdV(x) + w uV
(x)
RA
– =NC
A – NCA
CCA – CC
A=
{1 – (1 – y)2} [ (uL2 – uR
2){uvA(x) + cv
A(x)} + (dL2 – dR
2){dvA(x) + sv
A(x)}]
dvA(x) + sv
A(x) – (1 – y)2{uvA(x) + cv
A(x)}
Others: sin2W = 1 mW2/mZ
2 = 0.2227 0.0004
NuTeV: sin2W = 0.2277 0.0013 (stat) 0.0009 (syst)
N = isoscalar nucleon
Nuclear effects are in the weight functions: wuvand wdv
uVA(x) = wuV
(x)Z uV(x) + N dV(x)
A, dV
A(x) = wdV(x)
Z dV(x) + N uV(x)A
NuTeV target: 56Fe (Z = 26, N = 30), not isoscalar nucleus nuclear effects should be carefully taken into account
Neutron excess and a related function: n= N – Z
A, n(x) = n
uV(x) – dV(x)
uV(x) + dV(x)
Expand in v, n, s, c << 1 not so obvious: SK, PRD 66 (2002) 111301, research in progress
R A– =
(12
– sin2 W) {1 + v(x) n(x)} + 13
sin 2 W{v(x) + n(x)}
+ (12
– 23
sin 2 W) s(x) + (12
– 43
sin 2 W) c(x)
1 + v(x)
n(x) +
1 + (1 – y) 2
1 – (1 – y)2{
v(x) +
n(x)} +
2{s(x) – (1 – y)2 c(x)}
1 – (1 – y) 2
RA
– = 12
– sin2W + O(v) + O( n) + O( s) + O( c)
0
0.02
0.04
0.06
0.08
0.001 0.01 0.1 1x
20 GeV2
1 GeV2 56
Fe
prelim
inar
y
G. P. Zeller et al. Phys. Rev. D65 (2002) 111103.
NuTeV kinematics
at Q2=20 GeV2
PDFs NuTeV PDFs (*)
xuVA = wu v
Z xuv + N xdv
A=
Z uvp* + N uvn
*
A
xdVA = wd v
Z xdv + N xuv
A=
Z dvp* + N dvn
*
A
uvp* =wuv
xu v , u vn* =wu v
xdv , dvp* =wdv
xd v , d vn* =wd v
xuv
uv* = uvp
* – dvn* = – v (wu v
+ wd v) xuv
dv* = dvp
* – uvn* = + v (wu v
+ wd v) xdv
sin2W = – dx { F [uv*, x] uv
* + F [dv*, x] dv
* } = of the order of NuTeV deviation large error (preliminary!)
Summary
(1) 2 analysis for the nuclear PDFs, and their uncertainties. Valence quark: well determined except for the small-x regio
n. Antiquark: determined at small x, large uncertainties at medium and large x. Gluon: large uncertainties in the whole-x region.
(2) We provide nuclear PDFs for general users. http://hs.phys.saga-u.ac.jp/nuclp.html.
(3) Effects on NuTeV sin2W progress (esp. error estimate) possibly (sin2W ) = 0.00X 0.00X with a large error