ncteq nuclear parton distributions · ncteq nuclear parton distributions a. kusina lpsc grenoble in...
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nCTEQ nuclear parton distributions
A. Kusina
LPSC Grenoble
in collaboration with:K. Kovarık, T. Jezo, F. I. Olness,I. Schienbein, J. Y. Yu, B. Clark,
J. Owens, J. Morfin, C. Keppel
Outline:
I Motivations & Introduction
I Framework
I Results
I Summary
Annual Meeting of the GDR PH-QCD15-17 December 2014, Ecole Polytechnique
Motivations: Why do we need nuclear PDFs?
I What are PDFs of boundprotons/neutrons?
I Heavy ion collisions in LHC and RHIC
I Differentiate flavors in free-proton PDFs (e.g. strange)
charged lepton DIS
F l±
2 ∼(
13
)2[d+ s] +
(23
)2[u+ c]
neutrino DIS
F ν2 ∼[d+ s+ u+ c
]F ν2 ∼
[d+ s+ u+ c
]F ν3 ∼ 2
[d+ s− u− c
]F ν3 ∼ 2
[u+ c− d− s
]1 / 20
Assumptions entering the nuclear PDF analysis
1. Factorization & DGLAP evolution
I allow for definition of universal PDFsI make the formalism predictiveI needed even if it is broken
2. PDF of nucleus can be constructed as a sum of independentproton and neutron PDFs
3. Isospin symmetry
{un/A(x) = dp/A(x)dn/A(x) = up/A(x)
4. x ∈ (0, 1) like in free-proton PDFs [instead of (0, A)]
Then observables OA can be calculated as:
OA = ZOp/A + (A− Z)On/A
With the above assumptions we can use the free proton framework toanalyze nuclear data
2 / 20
Available nuclear PDFs
I Multiplicative nuclear correction factors
fp/Ai (xN , µ0) = Ri(xN , µ0, A) ffree protoni (xN , µ0)
I Hirai, Kumano, Nagai [PRC 76, 065207 (2007), arXiv:0709.3038]
I Eskola, Paukkunen, Salgado [JHEP 04 (2009) 065, arXiv:0902.4154]
I de Florian, Sassot, Stratmann, Zurita[PRD 85, 074028 (2012), arXiv:1112.6324]
I Native nuclear PDFsI nCTEQ [PRD 80, 094004 (2009), arXiv:0907.2357]
fp/Ai (xN , µ0) = fi(xN , A, µ0)
fi(xN , A = 1, µ0) ≡ ffree protoni (xN , µ0)
3 / 20
nCTEQ framework [PRD 80, 094004 (2009), arXiv:0907.2357]
I Functional form of the bound proton PDF same as for thefree proton (∼CTEQ61 [hep-ph/0702159], x restricted to 0 < x < 1)
xfp/Ai (x,Q0) = c0x
c1(1− x)c2ec3x(1 + ec4x)c5 , i = uv, dv, g, . . .
d(x,Q0)/u(x,Q0) = c0xc1(1− x)c2 + (1 + c3x)(1− x)c4
I A-dependent fit parameters (reduces to free proton for A = 1)
ck → ck(A) ≡ ck,0 + ck,1(1−A−ck,2
), k = {1, . . . , 5}
I PDFs for nucleus (A,Z)
f(A,Z)i (x,Q) =
Z
Afp/Ai (x,Q) +
A− ZA
fn/Ai (x,Q)
(bound neutron PDF fn/Ai by isospin symmetry)
4 / 20
Data sets
I NC DIS & DYCERN BCDMS & EMC &NMCN = (D, Al, Be, C, Ca, Cu, Fe,Li, Pb, Sn, W)FNAL E-665N = (D, C, Ca, Pb, Xe)DESY HermesN = (D, He, N, Kr)SLAC E-139 & E-049N = (D, Ag, Al, Au, Be,C, Ca,Fe, He)FNAL E-772 & E-886N = (D, C, Ca, Fe,W)
I Single pion production (new)
RHIC - PHENIX & STAR
N = Au
I Neutrino (to be included later)
CHORUS CCFR & NuTeV
N = Pb N = Fe
5 / 20
Data sets: Single pion production
RHIC - PHENIX & STAR
(N = Au)
PHENIX Collaboration:[Phys.Rev.Lett. 98 (2007) 172302, nucl-ex/0610036]
STAR Collaboration:[Phys.Rev. C81 (2010) 064904, arXiv:0912.3838]
I Theory calculation:P. Aurenche, M. Fontannaz, J.-Ph. Guillet, B. A. Kniehl, M. Werlen
[Eur. Phys. J. C13, 347-355, (2000), arXiv:hep-ph/9910252]
I Fragmentation functions:J. Binnewies, Bernd A. Kniehl, G. Kramer
[Z. Phys. C65 (1995) 471-480, arXiv:hep-ph/9407347]
6 / 20
Fit details
Fit properties:
I fit @NLO
I Q0 = 1.3GeV
I using ACOT heavy quark scheme
I kinematical cuts: Q > 2GeV,W > 3.5GeV
I 708 (DIS & DY) + 32 (single π0)= 740 data points after cuts
I 16 free parameters
I 7 gluonI 7 valenceI 2 sea
I χ2 = 618, giving χ2/dof = 0.85
Error analysis:
I use Hessian method
χ2 = χ20 +
1
2Hij(ai − a0
i )(aj − a0j )
Hij =∂2χ2
∂ai∂aj
I tolerance ∆χ2 = 35 (everynuclear target within 90% C.L.)
I eigenvalues span 10 orders ofmagnitude → require numericalprecision
I use noise reducing derivatives
7 / 20
nCTEQ RESULTS
(preliminary)
8 / 20
nCTEQ results
Kr/D
Ag/D C/Li
Cu/D
W/B
e
Li/D
Fe/C
Fe/D
Al/C
Al/D
dAu/
pp N/D
Fe/B
e
C/D
Xe/D
Ca/C
Ca/D
He/D
Pb/D
Pb/C
Be/D
Be/C
Sn/C
Au/D
Ca/L
i
W/D
Sn/D
0.0
0.5
1.0
1.5
2.0
2.5
chi2
/dof
122 7
27
28
11
1433
14
3 32
28
28 47
2 21
26
32
3
14
3
14111 3
7
9
8
chi2 over no. of degrees of freedom per nuclear target
9 / 20
nCTEQ results
Nuclear PDFs (Q = 10GeV)
xfPbi (x,Q)
Compare nCTEQ fits:
I with π0 data (violet)
I without π0 data (gray)
10 3 10 2 10 1 1x0
5
10
15
20
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
nCTEQ no PionnCTEQ with Pion
nCTEQ with π0
nCTEQ no π0
PREL
IMIN
ARY
10 / 20
nCTEQ results
Nuclear correction factors(Q = 10GeV)
Ri(Pb) =fPbi (x,Q)
fpi (x,Q)
Compare nCTEQ fits:
I with π0 data (violet)
I without π0 data (gray)
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
=(
,)/
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
=(
,)/
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
=(
,)/
(,
)nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
=(
,)/
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
nCTEQ no PionnCTEQ with Pion
nCTEQ with π0
nCTEQ no π0
PREL
IMIN
ARY
11 / 20
nCTEQ results
Nuclear correction factors(Q = 10GeV)
Ri(Pb) =fPbi (x,Q)
fpi (x,Q)
I different solution ford-valence & u-valencecompared to EPS09 & DSSZ
I sea quark nuclear correctionfactors similar to EPS09
I nuclear correction factorsdepend largely on underlyingproton baseline
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
=(
,)/
(,
)
EPS09DSSZHKN07nCTEQ with Pion
10 3 10 2 10 1 1x
EPS09DSSZHKN07nCTEQ with Pion
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
=(
,)/
(,
)
EPS09DSSZHKN07nCTEQ with Pion
10 3 10 2 10 1 1x
EPS09DSSZHKN07nCTEQ with Pion
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
=(
,)/
(,
)
EPS09DSSZHKN07nCTEQ with Pion
10 3 10 2 10 1 1x
EPS09DSSZHKN07nCTEQ with Pion
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
=(
,)/
(,
)
EPS09DSSZHKN07nCTEQ with Pion
10 3 10 2 10 1 1x
EPS09DSSZHKN07nCTEQ with Pion
nCTEQ
HKN07
EPS09
DSSZ
PREL
IMIN
ARY
12 / 20
nCTEQ results
Nuclear PDFs (Q = 10GeV)
x fPbi (x,Q)
I nCTEQ d-valence &u-valence solution betweenHKN07 & EPS09
I nCTEQ features largeruncertainties than previousnPDFs
I better agreement betweendifferent groups (nPDFs don’tdepend on proton baseline)
10 3 10 2 10 1 1x0
5
10
15
20
(,
)
nCTEQ with PionHKN07EPS09DSSZ
10 3 10 2 10 1 1x0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8nCTEQ with PionHKN07EPS09DSSZ
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(,
)
nCTEQ with PionHKN07EPS09DSSZ
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5nCTEQ with PionHKN07EPS09DSSZ
10 3 10 2 10 1 1x0.0
0.2
0.4
0.6
0.8
1.0
(,
)
nCTEQ with PionHKN07EPS09DSSZ
10 3 10 2 10 1 1x0.0
0.2
0.4
0.6
0.8
1.0
nCTEQ with PionHKN07EPS09DSSZ
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(,
)
nCTEQ with PionHKN07EPS09DSSZ
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
nCTEQ with PionHKN07EPS09DSSZ
nCTEQ
HKN07
EPS09
DSSZ
PREL
IMIN
ARY
13 / 20
nCTEQ vs. EPS09
nCTEQ
xup/Av (Q0) = x
cu1 (1 − x)cu2 e
cu3 x(1 + ecu4 x)
cu5
xdp/Av (Q0) = x
cd1 (1 − x)cd2 e
cd3x(1 + ecd4 x)
cd5
cuvk
= cuvk,0
+ cuvk,1
(1 − A
−cuvk,2)
cdvk
= cdvk,0
+ cdvk,1
(1 − A
−cdvk,2)
EPS09
up/Av (Q0) = Rv(x,A, Z)uv(x,Q0)
dp/Av (Q0) = Rv(x,A, Z) dv(x,Q0)
Rv =
a0 + (a1 + a2x)(e−x − e−xa ) x ≤ xab0 + b1x + b2x
2 + b3x3 xa ≤ x ≤ xe
c0 + (c1 − c2x)(1 − x)−β xe ≤ x ≤ 1
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
(,
)
nCTEQNP14EPS09
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7nCTEQNP14EPS09
nCTEQnCTEQ with const.on uval, dvalEPS09
we set: {cdv1 = cuv1
cdv2 = cuv214 / 20
nCTEQ results: F2 ratios
Structure function ratio
R =FFe2 (x,Q)
FD2 (x,Q)
I good data description
I despite different u-valence &d-valence ratios are similar toEPS09
0.01 0.1 1x
0.80
0.85
0.90
0.95
1.00
1.05
1.10
R[F
l±A
2]
Q2 =5GeV2
nCTEQ - l±AHKN07EPS09
0.01 0.1 1x
0.80
0.85
0.90
0.95
1.00
1.05
1.10
R[F
l±A
2]
Q2 =20GeV2
nCTEQ - l±AHKN07EPS09
PRELIMINARY
15 / 20
nCTEQ results: π0 production
Pion production, ratio
RπdAu =1
2Ad2σdAuπ /dpTdy
d2σppπ /dpTdy
I good data description,however big experimentaluncertainities do not allow forstrong constraints on PDFs
I despite different u-valence &d-valence ratios are similar toEPS09
2 4 6 8 10 12 14 16pT [GeV]
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
RdAu
nCTEQ
EPS09NLO
PHENIX 2007 π0
STAR 2010 π0
16 / 20
nCTEQ results: gluon and π0 production
Cosine of the correlation angle:
10-3 10-2 10-1 100
x
1.0
0.5
0.0
0.5
1.0
cosφ
Correlation between g PDF and χ2 of fitted experiments at Q=10.0 GeV
512051215122512351245125
512651275129513151325135
513651375138513951405141
51435156515751585159phenix
520152025203520452055206
5160starNEW5101510251035104
510551065107510851115112
51135114511551165119
cosφ(X,Y ) =~∇X · ~∇Y4∆X∆Y
Effective χ2 change: ∆χ2eff
10-3 10-2 10-1 100
x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
∆χ
2 eff
Effective χ2 for g PDF at Q=10.0 GeV for (207, 103) nucleus
512051215122512351245125
512651275129513151325135
513651375138513951405141
51435156515751585159phenix
520152025203520452055206
5160starNEW5101510251035104
510551065107510851115112
51135114511551165119
17 / 20
Summary
I We have updated the nCTEQ error PDFs (still preliminary).
I nCTEQ PDFs features larger uncertainties but they are stillunderestimated.
0.01 0.1 1x
0.80
0.85
0.90
0.95
1.00
1.05
1.10
R[F
l±A
2]
Q2 =5GeV2
nCTEQ - l±AHKN07EPS09
I To have reliable estimate of nuclear corrections we needmore data (LHC lead run can help).
I Nuclear component important not only for heavy ioncollisions, but also for the free-proton analysis.
18 / 20
Summary
Plans for future:
I Official release of current analysis
I Among other things analyse LHC data, e.g. [CMS PAS HIN-13-007]
labη
-2 -1 0 1 2
)-+
N+
)/(N
--N+
(N
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
CMS Preliminary = 5.02 TeVNNspPb
-1L = 34.6 nbDataCT10EPS09
Ch
arg
easy
mm
etry
I Sensitive to ud ratio should
help to distinguishmodification for u and d
labη
0 0.5 1 1.5 2 2.5
)la
bη
(--)/
Nla
bη
(+-N
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4CMS Preliminary
= 5.02 TeVNNspPb -1L = 34.6 nb
DataCT10EPS09
ν + -
l→ -W
labη
0 0.5 1 1.5 2 2.5
)la
bη
(-+)/
Nla
bη
(++N
1
1.5
2
2.5
3 CMS Preliminary = 5.02 TeVNNspPb
-1L = 34.6 nbDataCT10EPS09
ν + + l→ +WF
orw
ard
/bac
kw
ard
asym
met
ry
19 / 20
xPb ∼ (0.003, 0.2), xp ∼ (0.001, 0.07)
Thank You
BACKUP SLIDES
21 / 20
Gluon fragmentation functions problem
Charged hadrons production in CMS and ALICE[Nucl. Phys. B 883 (2014) 615, arXiv:1311.1415]; [arXiv:1408.4659]
(to hard gluon to hadron FF)
22 / 20
Variables: DIS of nuclear target eA→ e′X
I DIS variables in case on nucleons
in nucleus
{Q2 ≡ −q2
xA ≡ Q2
2 pA·q
I pA – nucleus momentumI xA ∈ (0, 1) – analog of Bjorken variable
(fraction of the nucleus momentum carried by a nucleon)
I Analogue variables for partons:
I pN = pAA – average nucleon momentum
I xN ≡ Q2
2 pN ·q = AxA – parton momentum fraction withrespect to the avarage nucleon momentum pN
I xN ∈ (0, A) – parton can carry more than the averagenucleon momentum pN .
23 / 20
ee′
q
A X
Correlation cosine
cosφ(X,Y ) =~∇X · ~∇Y4∆X∆Y
~∇X · ~∇Y =1
2
∑ipdf
(X
(+)ipdf−X(−)
ipdf
)(Y
(+)ipdf− Y (−)
ipdf
)
∆X =
√√√√∑ipdf
(X
(+)ipdf−X(−)
ipdf
)2
In the considered case:
cosφ(g(x,Q), χ
2(iexp)
)=∑ipdf
(g(+)ipdf
(x) − g(−)ipdf
(x)
)(χ2 (+)ipdf
(iexp) − χ2 (−)ipdf
(iexp)
)√√√√∑
i′pdf
(g(+)
i′pdf
(x) − g(−)
i′pdf
(x)
)2√√√√∑
i′′pdf
(χ2 (+)
i′′pdf
(iexp) − χ2 (−)
i′′pdf
(iexp)
)2
24 / 20
Another measure of correlations: Effective χ2 change
∆χ2eff (iexp, X) =
∑ipdf
1
2
(∣∣∣∣χ2 (+)ipdf
(iexp) − χ2 (0)ipdf
(iexp)
∣∣∣∣ +
∣∣∣∣χ2 (−)ipdf
(iexp) − χ2 (0)ipdf
(iexp)
∣∣∣∣)
×
X
(+)ipdf
−X(−)ipdf√√√√∑
i′pdf
(X
(+)
i′pdf
−X(−)
i′pdf
)2
2
25 / 20