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