Tagged Structure Functionsin Global PDF Analysis

High Energy Nuclear Physics with Spectator TaggingOld Dominion University

March 9, 2015

Wally Melnitchouk

CTEQ-JLab (CJ) collaboration: http://www.jlab.org/CJ (with A. Accardi, E. Christy, C. Keppel, P. Monaghan, J. Owens, N. Sato)

1

Inclusive particle production

σAB→CX(pA, pB) =�

a,b

�dxa dxb fa/A(xa, µ) fb/B(xb, µ)

�

n

αns (µ) σ̂

(n)ab→CX (xapA, xbpB , Q/µ)

AB → C X

A B

C

a bσ̂

X

universal functions characterize internal structure of bound state A

fa/A

xa xb

Parton distributions in nucleons

2

PDFs extracted in global QCD analyses of data fromdeep-inelastic l-h scattering; lepton-pair, weak boson& jet production in h-h scattering, ...

~ 4,000 spin-averaged data points over large range of x and Q2

(more if include A > 2 nuclear data)

Parton distributions in nucleons

3

Needed to understand basic structure of QCD bound states - and for backgrounds in searches for physics beyond the Standard Model at high-energy colliders

Q evolution feeds low x, high Q from high x, low Q 2 22

In modern fits, PDFs typically parametrized asxf(x, µ) = Nxα(1− x)β P (x)

with polynomial e.g. P (x) = 1 + �√x+ η x

PDFs extracted in global QCD analyses of data fromdeep-inelastic l-h scattering; lepton-pair, weak boson& jet production in h-h scattering, ...

Parton distributions in nucleons

4

Several groups dedicated to global PDF analysis

MSTW (Martin-Stirling-Thorne-Watt) LHC focus, strong data cuts

CTEQ (Coordinate Theoretical-Experimental Project on QCD)- CT (CTEQ-Tung et al.) LHC focus

- CJ (CTEQ-JLab) includes high x, low Q- nCTEQ nuclear PDFs

2

ABM (Alekhin-Bluemlein-Moch) LHC focus, some lower Q

JR (Jimenez-Delgado-Reya) dynamically generated from low Q 2

NNPDF “neural networks”, strong data cuts

HERAPDF only H1 & ZEUS data

most use NLO, some use NNLO (partially known)

2

Parton distributions in nucleons

5

10-4 10-3 10-2 10-1 100x

0

0.2

0.4

0.6

0.8

1

1.2

1.4

x f (

x,Q

2 )

gCJ12mid

Q2 = 10 GeV2d_

+u_

d_−u

_

d

u

s

/10

0 0.2 0.4 0.6 0.8 1x

0

0.2

0.4

0.6

0.8

gCJ12mid

Q2 = 10 GeV2

d_

+u_

d_−u_

d

u

s

Example of recent PDFs, from CJ12 analysis

Owens, Accardi, WMPRD 87, 094012 (2013)

Parton distributions in nucleons

6

CTEQ-JLab PDFsHigh-x region requires use of data at lower W & Q2

weak cut:Q > 1.3 GeV , W > 1.73 GeV

strong cut:Q > 2 GeV, W > 3.5 GeV

factor 2 increase in # of DIS data points when relaxstrong cut (excludes most SLAC, all JLab data) weak cut

W 2 = M2 +Q2 (1− x)

x

7

significant error reduction when cuts extended to low-W region

x x

High-x region requires use of data at lower W & Q2

cut0: strong cutcut3: weak cut

CTEQ-JLab PDFs

W 2 = M2 +Q2 (1− x)

x

8

higher twists usually parametrized phenomenologically

Low-Q data requires higher twist & target mass corrections2

F2(x, Q2) = FLT2 (x,Q2)

�1 +

C(x)Q2

�polynomialC(x)

x x

(no TMC ornuc.corr.)

different TMCprescriptions

significant at high-x

CTEQ-JLab PDFs

9

deuterium as “effective neutron” target,but need to correct for nuclear effects

u-quark PDF well constrained by proton data;d-quark PDF requires neutron data

Arrington, Rubin, WMPRL 108, 252001 (2012)

SU(6)

hard gluons

S=0 diquarksdifferent modelsof deuteron

CTEQ-JLab PDFs

10

Effect of nuclear corrections & statistics

0 0.2 0.4 0.6 0.8 1x

0.7

0.8

0.9

1

1.1

1.2

1.3

u / u

ref

no deuteronPDF + nuclear errorPDF error only

0 0.2 0.4 0.6 0.8 1x

00.20.40.60.81

1.21.4

1.61.82

d / d

ref

no deuteronPDF + nuclear errorPDF error only

significant uncertainties in u for x > 0.8, d for x > 0.6

CTEQ-JLab PDFs

11

0 0.2 0.4 0.6 0.8 1x

0.7

0.8

0.9

1

1.1

1.2

1.3

u / u

ref

CJ12midCT10MSTW08ABKM09

Q2 = 100 GeV2

increase in PDF error from more realistictreatment of nuclear corrections

reduction of error from larger database

CTEQ-JLab PDFs

0 0.2 0.4 0.6 0.8 1x

0.4

0.6

0.8

1

1.2

1.4

1.6

d / d

ref

CJ12midCT10MSTW08ABKM09

Q2 = 100 GeV2

Effect of nuclear corrections & statistics

12

0 0.2 0.4 0.6 0.8 1x

0

0.2

0.4

0.6

0.8

1

d / u

CJ12midCT10MSTW08ABKM09

• with same functionalform for u & d, most PDF fits assume either0 or for limitx → 1∞

CTEQ-JLab PDFsEffect of nuclear corrections & statistics

13

flexible parametrizationfor behaviorx → 1

CJ12min: WJC-1 + mild off-shell (0.3% nucleon swelling)CJ12mid: AV18 + medium off-shell (1.2% swelling)CJ12max: CD-Bonn + large off-shell (2.1% swelling)

*

allows finite, nonzerox = 1 limit

•

•

d/u → 0.22

± 0.20 (PDF)

± 0.10 (nucl)

. d → d + a xb u

0 0.2 0.4 0.6 0.8 1x

0

0.2

0.4

0.6

0.8

1

d / u

CJ12minCJ12midCJ12max

*

CTEQ-JLab PDFsEffect of nuclear corrections & statistics

Owens, Accardi, WMPRD 87, 094012 (2013)

14

Large-x PDF uncertainties have implications for colliders

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

A W

yW

LHCCJ (min nuclear)CJ (max nuclear)

0

0.2

0.4

0.6

0.8

1

0 1 2 3yW

TevatronCDF Data

pp,√s = 7 TeV

pp,√s ≈ 2 TeV

Brady, Accardi, WM, OwensJHEP 1206, 019 (2012)

e.g. asymmetryW±

rapidity y =1

2ln

�E + pzE − pz

�

15

sensitive tod at high x

Large-x PDF uncertainties have implications for colliders

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

A W

yW

LHCCJ (min nuclear)CJ (max nuclear)

0

0.2

0.4

0.6

0.8

1

0 1 2 3yW

TevatronCDF Data

pp,√s = 7 TeV

pp,√s ≈ 2 TeV

Brady, Accardi, WM, OwensJHEP 1206, 019 (2012)

e.g. asymmetryW±

rapidity y =1

2ln

�E + pzE − pz

�

favors smalleroff-shell effect

16

CJ15 PDFsNew CJ15 analysis includes several new theoretical developments (better treatment of heavy quarks; off-shell corrections to valence and sea distributions; improved d / u parametrization)and new data sets (D0 W asymmetries; BONuS )

_ _

Fn2 /F

d2

Explore whether new data can constrain PDFs,and nuclear corrections, at large x

Kulagin, Petti, NPA 765, 126 (2006)Owens et al., PRD 87, 094012 (2013)

vary off-shell “rescaling” parameterwithin “spectator diquark” model

λ = ∂ logΛ2

∂p2

minimize as a function of χ2 λ

17

CJ15 PDFsMinimum total for different deuteron wave functionand off-shell models

χ2

models 2-15: λ = {−0.9%,−0.8%, ...,+0.4%}

minimum total χ2

18

CJ15 PDFsNuclear EMC effect in the deuteron for differentnuclear models

} spectatoroff-shellmodel

larger off-shell effects for larger , and for KP modelλ

enhancement at x ~ 0.2 in KP model

19

CJ15 PDFsSLAC deuteron data favor smaller off-shell corrections,disfavor (hardest) WJC-1 wave function

λ = −0.9% λ = +0.4%

20

deuteronwave function

LC momentum distribution(“smearing function”)

21

0 0.5 1 1.5 2 2.5 3yW

0

0.2

0.4

0.6

0.8

1A W

D0CJ15CJ15 (KP off-shell)

CJ15 PDFs

PRL 112, 151803 (2014)

D0 W-asymmetry data disfavor large nucleonoff-shell corrections at high x

larger asymmetry at high rapidity corresponds tosmaller d-quark PDF (smaller EMC effect) at high x

σW+ − σW−σW+ + σW−

∼ 1− d/u

1 + d/u

22

CJ15 PDFs

λ = −0.9% λ = +0.4%

PRL 112, 151803 (2014)

D0 W-asymmetry data disfavor large nucleonoff-shell corrections at high x

23

CJ15 PDFsBONuS data favor larger nucleon off-shellcorrections (and harder deuteron wave function)

Fn2 /F

d2

improvement in with KP model� 5% χ2

24

CJ15 PDFsIs improvement from specific kinematics?χ2

calculated larger at high x with KP modelFn2 /F

d2

25

CJ15 PDFs

calculated larger at high x with KP modelFn2 /F

d2

Is improvement from specific kinematics?χ2

26

3 4 5 6

W 2 (GeV2)

0

0.2

0.4

0.6

0.8

F 2n / F

2d

BONuSCJ15CJ (no-BONuS fit)

Q2 = 4.0 GeV2

3 4 5 6

W 2 (GeV2)

0

0.2

0.4

0.6

0.8

F 2n / F

2d

BONuSCJ15CJ15 (no-BONuS fit)

Q2 = 3.4 GeV2

3 4 5 6

W 2 (GeV2)

0

0.2

0.4

0.6

0.8

F 2n / F

2d

BONuSCJ15CJ15 (no-BONuS fit)

Q2 = 2.9 GeV2

3 4 5 6

W 2 (GeV2)

0

0.2

0.4

0.6

0.8

F 2n / F

2d

BONuSCJ15CJ15 (no-BONuS fit)

Q2 = 2.4 GeV2

3 4 5 6

W 2 (GeV2)

0

0.2

0.4

0.6

0.8

F 2n / F

2d

BONuSCJ15CJ15 (no-BONuS fit)

Q2 = 2.0 GeV2

3 4 5 6

W 2 (GeV2)

0

0.2

0.4

0.6

0.8

F 2n / F

2d

BONuSCJ15CJ15 (no-BONuS fit)

Q2 = 1.7 GeV2

CJ15 PDFsCD-Bonn & λ=−0.7%

slightly larger neutron (hence d-quark) with BONuSF2

27

Outlook“BONuS6” data demonstrated how spectator taggingcan be used to constrain PDFs; impact not dramatic... “BONuS12” promises to extend range to x ~ 0.85 with reduced experimental & minimal nuclear uncertainties

28

OutlookParallel effort in global analysis of spin-dependent PDFs Jefferson Lab Angular Momentum (JAM) Collaboration (Nobuo Sato, A. Accardi, J. Ethier)

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8

x

xΔu+

xΔd+

ref.+ smear+ TMC+ HT

-1-0.8-0.6-0.4-0.2

0 0.2 0.4 0.6 0.8

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7

x

Δu+/u+

Δd+/d+

Q2 = 1 GeV2

Jimenez-Delgado, Accardi, WMPRD 89, 034025 (2014)

currently assessing impact of new JLab6 data(eg1b, eg1-DVCS, d2n, ...)

full JAM15 analysis will include SIDIS & RHIC-spin data

29

0

0.1

0.2

0.3

0.4

0.5

0.2 0.4 0.6 0.8

x

Δd+ Q2 = 1 GeV2

0

0.05

0.1

0.15

0.2

0.25

0.2 0.4 0.6 0.8

rela

tive

erro

r

x

Δu+

JAM +12 GeV

Upcoming 12 GeV experiments will measure inclusiveand semi-inclusive polarization asymmetries up to x ~ 0.8

will significantly reduce PDF uncertainties at large x(~ 70% for x ~ 0.6-0.8)

Outlook

30

The End

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