Recent Experimental Results on QCD Factorization Breaking of … · 2020-06-25 · Recent...

Recent Experimental Results on QCD FactorizationBreaking of Nonperturbative Functions

Joe OsbornUniversity of Michigan

Based on work in arXiv:1609.04769, submitted to Phys. Rev. D

November 21, 2016

J.D. Osborn UMich HEP Seminar 11/21/2016 1 / 37

Outline

Why study the 3-D structure of nucleon

Physics in the transverse momentum dependent framework

RHIC, PHENIX, and two particle angular correlations

Recent results on factorization breaking

Future factorization breaking measurements


Mapping the Structure of the Proton

Historically have usedsemi-inclusivedeep-inelastic-scattering(SIDIS) and Drell-Yan(DY) as probes of hadronstructure

SIDIS measurementsshowed there is structureto the proton

Longitudinal structure ofproton in terms ofx = pquark/pproton

Well mapped out overlarge range of x and Q2


1-D Structure

Collected data has led toincredible precision forpartonic structure ofnucleons in thelongitudinal direction!

Collinear partondistribution functions(PDFs) are very wellconstrained over 4 ordersof magnitude in x

Figures taken from http://nnpdf.hepforge.org


QCD Cross Sections

To account for boundstate nature ofhadrons, cross sectionsare factorized

Nonperturbative partondistribution andfragmentationfunctions (PDFs andFFs) are used todescribe the individualpartons within a hadron

Functions arenonperturbative, mustbe constrained by data!

Taken to be processindependent anduncorrelated

σ = f1(x ,Q2)⊗f2(x ,Q2)⊗d σ̂

dt⊗Dh

q (z ,Q2)


Multidimensional Proton Structure

What does thebound-state proton looklike in terms of the quarksand gluons inside it?

PositionMomentumSpinFlavorChargeColor (!)

What about transversemomentum degrees offreedom?


1D vs. 3D Nonperturbative Functions

Historicallynonperturbative functionsare approximated as onlydependent on the collinearmomentum fraction x

In reality there must betransverse structure dueto the confined nature ofthe partons and theadditional possibility ofgluon radiation

The unintegrated kT distributions are explicitly dependent ontransverse momentum

Parton Distribution Functions: f (x)→ f (x , kT )

Fragmentation Functions: D(z)→ D(z , jT )

We can also add spin into the picture...


Transverse-Momentum-Dependent PDF Zoo

Transverse-Momentum-Dependent(TMD) PDFs

N - Nucleonq - QuarkU - UnpolarizedL - Longitudinally polarizedT - Transversely polarized

8 TMD PDFs at twist-2 describing transverse partonic structure,spin-spin, and spin-momentum correlations!

Image taken from Alexei Prokudin Spin 2016


Transverse-Momentum-Dependent Functions in Nature

Many transverse-momentum-dependentPDFs and FFs correlatespin with momentum

Beginning to reallyexplore partoniccorrelations within thenucleon! New era ofnucleon structure

Are these correlationsreally present in nature?Absolutely!

Sivers TMD PDF

arXiv:1609.07374, COMPASS at CERN



Boer Mulders TMD PDF

PRD 87, 012010(2013), HERMES at HERA



Transversity TMD PDF

PLB 717, (2012) 376, COMPASS at CERN



PRD 78, 032011 (2008), Belle at KEK

Collins TMD FF


Transverse-Momentum-Dependent Phenomenology

In the collinear framework, nonperturbative functions are taken to beuncorrelated, universal, process independent functions

In the transverse-momentum-dependent framework, it has beennecessary to re-check these assumptions

This has led to very interesting predictions...


Universality in Transverse-Momentum-Dependent Functions

Drell-Yan Semi-Inclusive DIS

Sign change in Sivers transverse-momentum-dependent PDFpredicted due to initial-state vs. final-state gluon exchange withproton remnants between Drell-Yan and semi-inclusive DIS: processdependent PDF!

Factorization of transverse-momentum-dependent PDFs andfragmentation functions still predicted to hold in these QED processes


First Measurement of Possible Modified Universality

Semi-inclusive DIS Sivers asymmetries have been measured, e.g. byHERMES and COMPASS collaborations

First measurement of Drell-Yan type process from STAR at RHIC!

Data support prediction of process dependenttransverse-momentum-dependent PDF

PRL 116, 132301(2016)


Factorization of Transverse-Momentum-Dependent Functions

Factorization is still predicted to hold in semi-inclusive DIS andDrell-Yan

σ = f1(x , kT ,Q2)⊗ f2(x , kT ,Q

2)⊗ d σ̂

dt⊗ Dh

q (z , jT ,Q2)

What about leading-order QCD processes where a colored quark orgluon is exchanged?

Color present in both the initial and final state - therefore soft gluonexchange possible in both the initial and final state


Factorization of Transverse-Momentum-Dependent Functions

Factorization breakingpredicted in a transverse-momentum-dependent(TMD) framework forp + p → h1 + h2 (PRD 81,094006 (2010))

TMD nonperturbativefunctions no longer defined -partons are quantummechanically correlatedacross colliding hadrons!

Consequence of soft gluonexchanges in both the initialand final state

Predicted modifieduniversality of certain TMDPDFs and factorizationbreaking from same physicalprocess - consequences ofcolor flow in action!

Consequence of QCD as anon-Abelian gauge theory


Looking for Factorization Breaking

An obvious way to look foreffects is by comparingmeasurement to acalculation which assumesfactorization

Problem: calculationsrequire good knowledge ofthe transverse-momentum-dependent nonperturbativefunctions. Collinear pQCDcalculations still have∼10-40% errors

What about observingchange of functions with thehard scattering scale?

PRD 91, 032001 (2015)

PRD 80, 111108 (2009)


Collins-Soper-Sterman (CSS) Evolution

CSS evolution first published in 1985. Similar to DGLAP evolution equation,but includes small transverse momentum scale

Has been used to successfully describe global Drell-Yan and Tevatron Z0

cross sections

Clear qualitative prediction - momentum widths sensitive to nonperturbativetransverse momentum increase with increasing hard scale

Due to increased phase space for hard gluon radiation

PRD 67, 073016 (2003)


Drell-Yan/Z and Semi-Inclusive DIS in CSS Evolution

Measurements show thatDrell-Yan andsemi-inclusive DIS followtheoretical prediction -widths rise with hardscattering scale

The theoretical evolutionprediction comes directlyout of the derivation fortransverse-momentum-dependentfactorization

SIDIS - Eur. Phys. J. C(2013) 73,2531

2 [GeV/c]2Q1 2 3 4 5 6 7 8

2 [G

eV/c

]⟩

2 Tp⟨

0.15

0.2

0.25

0.3

0.35

0.4

0.20<z<0.250.30<z<0.350.40<z<0.50

+ h-

h

]2 [GeV/cµµM0 5 10 15 20 25

[GeV

/c]

⟩Tp⟨

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

= 21 GeV, PRL 38,1334sp+C, = 25 GeV, PRD 23,604sp+Cu,

= 44 GeV, PRL 47,12sp+p, = 62 GeV, PRL 47,12sp+p,

FNAL fixed target DY


Drell-Yan/Z and Semi-Inclusive DIS in CSS Evolution

Phenomenological studiesconfirm that Drell-Yan andsemi-inclusive DIS followtheoretical prediction

The evolution predictioncomes directly out of thederivation for transverse-momentum-dependent(TMD) factorization

If TMD factorization,then CSS evolution. Ifnot CSS evolution,then not TMDfactorization!

Drell-Yan and semi-inclusiveDIS clearly follow theoreticalprediction

DY/Z - PLB 633, 710 (2006)

SIDIS - PRD 89, 094002 (2014)


Direct Photons and Dihadrons

Direct photon-hadron anddihadron correlations bothpredicted to be sensitive tofactorization breaking effectsin PHENIX

Assuming factorization,direct photon-hadrons probethree nonperturbativefunctions, while dihadronsprobe four

Direct photons offer one lessavenue for gluon exchangein the final-state:fewer/different effects?


Relativistic Heavy Ion Collider - RHIC at Brookhaven National Laboratory


PHENIX Detector

PHENIX central arms

∆φ ∼ π|η| <0.35

ElectromagneticCalorimeter (PbSc/PbGl)provides isolated directphoton and π0 → γγdetection

Drift Chamber (DC) andPad Chambers (PC)provide nonidentifiedcharged hadron detection

New results from2012/2013

√s=510 GeV

p+p runs


Angular Correlation Observables

Direct photon-hadron production

Dihadron production

pout = passocT sin ∆φ


∆φ Correlations for π0-h± and Direct γ-h±

-1 0 1 2 3 4 50

0.5

<15 GeV/ctrig

T12<p

<2 GeV/cassocT

1<p

-1 0 1 2 3 4 50

0.1 <15 GeV/ctrig

T12<p

<4 GeV/cassocT

3<p

-1 0 1 2 3 4 50

0.1

<15 GeV/ctrig

T12<p

<10 GeV/cassocT

5<p

-1 0 1 2 3 4 50

0.5

<12 GeV/ctrig

T9<p

<2 GeV/cassoc

T1<p

-1 0 1 2 3 4 50

0.1

<12 GeV/ctrig

T9<p

<4 GeV/cassoc

T3<p

-1 0 1 2 3 4 50

0.1

<12 GeV/ctrig

T9<p

<10 GeV/cassoc

T5<p

PHENIX

-1 0 1 2 3 4 50

0.5

<9 GeV/ctrig

T8<p

<2 GeV/cassocT

1<p

-1 0 1 2 3 4 50

0.1

<9 GeV/ctrig

T8<p

<4 GeV/cassocT

3<p

=510 GeVsp+p at

|<0.35η|

-1 0 1 2 3 4 50

0.1

<9 GeV/ctrig

T8<p

<10 GeV/cassocT

5<p

±-hγIsolated Direct ±-h0π

Underlying Event

[rad]φ∆

-1 [

rad

]φ∆dd

Ntr

igN

1

Two jet structure visible for π0-h±, isolation cut on near side for direct γ-h±

Direct γ-h± probes smaller jet energy due to emerging from hard scattering at LO


√〈p2

out〉 Extracted from Fits to ∆φ Correlations

[GeV/c]trig

Tp

4 5 6 7 8 9 10 11 12 13 14

[GeV

/c]

⟩2 ou

t p⟨

0

1

2

3

4

5±-hγ

|<0.35η|

=510 GeVsp+p at

PHENIX

±-h0π<3 GeV/cassoc

T2<p

<4 GeV/cassocT

3<p

√〈p2

out〉 characterizes away-side jet width in momentum space

Decreases with hard scattering scale ptrigT , opposite of semi-inclusiveDIS and Drell-Yan!

Sensitive to perturbative and nonperturbative kT and jT ; fits are toentire away-side jet


pout Distributions

pout shows twodistinct regions:Gaussian and powerlaw

Gaussian fits clearlyfail past ∼1.3GeV/c

Indicates transitionfromnonperturbative toperturbative kT andjT

[GeV/c]out

p-8 -6 -4 -2 0 2 4 6 8

-1 [G

eV/c

]ou

tdpdN

trig

N1

-1110

-1010

-910

-810

-710

-610

-510

-410

-310

-210

-110

1

10

PHENIX

=510 GeVsp+p at

|<0.35η|

3π4<φ∆<3

π2

<10 GeV/cassocT

0.7<p

±-h0π 4-5

)-1 5-6 (x10)-2 6-7 (x10)-3 7-8 (x10)-4 8-9 (x10

)-5 9-12 (x10)-6 12-15 (x10

[GeV/c]trigT

p

±-hγ

Note: Curves are Kaplan andGaussian fits, not calculations!!


Gaussian Widths of pout

Extract Gaussian widthsof pout vs. ptrigT , hardscattering scale

Sensitive to onlynonperturbative kT andjT in the nearlyback-to-back region∆φ ∼ πGaussian widths decreasewith ptrigT also, consistent

with√〈p2

out〉 andopposite of semi-inclusiveDIS and Drell-Yan!

[GeV/c]trig

Tp

4 5 6 7 8 9 10 11 12 13 14

Gau

ssia

n W

idth

[GeV

/c]

0.45

0.5

0.55

0.6

0.65±-h0π

±-hγ Linear Fit±-h0π

Linear Fit±-hγ<10 GeV/cassoc

T0.7<p

PHENIX

|<0.35η|=510 GeVsp+p at


PYTHIA p+p Event Simulation

To make a comparison,used PYTHIA eventgenerator simulation

PYTHIA reproducesexpectation from CSSevolution in Drell-Yanover large range of Mµµ

]2 [GeV/cµµM5 10 15 20 25 30

Gau

ssia

n W

idth

[GeV

/c]

1

2

3

PYTHIA Perugia0 SimulationDrell-Yan Dilepton

>1 GeV/clepT

p|<0.35η|

=510 GeVsp+p at

]2 [GeV/cµµM20 30 40 50 60 70 80 90 100

Gau

ssia

n W

idth

[GeV

/c]

2

3

4

5PYTHIA Perugia0 SimulationDrell-Yan Dilepton

>4 GeV/clepT

p|<0.35η|

=510 GeVsp+p at


PYTHIA Event Simulation

[GeV/c]out

p-5 -4 -3 -2 -1 0 1 2 3 4 5

-1 [G

eV/c

]ou

tdpdN

trig

N1

-910

-810

-710

-610

-510

-410

-310

-210

-110

1

10

±-h0π 4-5

)-1 5-6 (x10)-2 6-7 (x10)-3 7-8 (x10)-4 8-9 (x10

)-5 9-12 (x10)-6 12-15 (x10

PYTHIA Perugia0 Simulation

=510 GeVsp+p at <10 GeV/cassoc

T0.7<p

3π4<φ∆<

3π2

|<0.35η|

±-hγ [GeV/c]trig

Tp

Can construct poutdistributions fordirect photons anddihadrons inPYTHIA as well fordirect comparison

PYTHIA replicatesthe nonperturbativeto perturbativetransition in thepout distributions


PYTHIA Event Simulation

PYTHIA alsoreplicates thenegative slope ofthe gaussian widthsin γ−hadron andπ0−hadron!

Magnitudes ofwidths fromPYTHIA show∼15% differencefrom data despiteslope beingreplicated

[GeV/c]trig

Tp

4 5 6 7 8 9 10 11 12 13 14

Gau

ssia

n W

idth

[GeV

/c]

0.5

0.6

0.7

0.8 Linear Fit±-h0πPHENIX

Linear Fit±-hγPHENIX Linear Fit±-h0πPYTHIA

Linear Fit±-hγPYTHIA

|<0.35η|=510 GeVsp+p at <10 GeV/cassoc

T0.7<p

±-h0πPHENIX ±-hγPHENIX

±-h0πPYTHIA Perugia0 ±-hγPYTHIA Perugia0


PYTHIA Simulation

WHY does PYTHIA replicate both increasing behavior in p+p → `¯̀ anddecreasing behavior in p+p →h+X??

Unlike analytical pQCD calculation, PYTHIA forces all particles to colorneutralize in the event, including remnants

PYTHIA allows initial and final state soft gluon exchanges!

PYTHIA authors confirm that it is plausible that PYTHIA would besensitive to such effects

Image taken from http://home.thep.lu.se/ torbjorn/talks/karlsruhe10a.pdf


Relations to Other QCD Studies?

Color coherence studies atthe Tevatron

Phys. Rev. D 50, 5562 (1994) (CDF)Phys. Lett. B 414, 419-427 (1997) (D0)

Color coherence studies atthe LHC

Eur. Phys. J. C74 (2014) no.6,2901


Future Measurements

Recent RHIC run in 2015delivered one of the mostunique data sets toPHENIX and STAR

RHIC collided p↑+p,p↑+Au, and p↑+Al at√s = 200 GeV

PHENIX recorded ∼10xthe amount of

√s = 200

GeV data from previousanalysis

Possibility to comparep+p at

√s = 200 and

510 GeV

Possibility to comparep+p to p+A (strongergluon fields in nucleus??)

Does transverse spinchange anything??


Future Measurements - sPHENIX

Future detector at RHIC,sPHENIX, has beenproposed

Dedicated jet detector atRHIC

Golden measurement - γ-jet

Allows full kinematic eventreconstruction


Conclusions

Extending the knowledge of nucleon structure from 1 dimension to 3dimensions (and more!)

Transverse-momentum-dependent nucleon structure offers a richerdescription of the nucleon with many interesting phenomenologicalpredictions

Factorization breaking has been predicted in hadronic collisions wherea final-state hadron is measured in atransverse-momentum-dependent framework

PHENIX has just released the first measurement studying thesepredicted effects - arXiv:1609.04769

Data show the opposite evolution trend in the nonperturbativemomentum widths from semi-inclusive DIS and Drell-Yan, wherefactorization is predicted to hold

More measurements planned in the future... stay tuned!


Back Up


√s=200 GeV Results from PHENIX

Previous PHENIX resultat√s=200 GeV with

larger errors (Phys. Rev.D 82, 072001 (2010))

Next step: analyze recentRun 15

√s=200 GeV

p+p and p+A data fromRHIC!

6x luminosity in Run 15p+p, as well as first resultfrom p+A

Can also look attransverse spindependence in Run 15! 2 < passocT < 5


√s=200 GeV Results from RHIC

Previous PHENIX resultat√s=200 GeV to lower

ptrigT (PRD 81, 012002(2010))

Shows√〈p2

out〉 over lower

range of ptrigT

Also can plot away-sidewidth in angular space -same trend over largerange of ptrigT

[GeV/c]trig

Tp

2 4 6 8 10 12 14

[GeV

/c]

⟩2 ou

tp⟨

0

0.5

1

1.5

<5 GeV/c (PRD 74, 072002)assoc

T, 1.4<p±-h0π


T, 2<p±-h0π


T, 2<p±-h0π


T, 2<p±-hγIsolated Direct

=200 GeVsp+p at |<0.35η|

[GeV/c]trig

Tp

5 10 15 20 25 30 35

Aw

ay-s

ide

Wid

th [r

ad]

0.2

0.3

0.4

0.5

0.6 <3 GeV/c (PRL 104, 252301)assoc

T 2<p±-h0π


T 1.4<p±-h0π

<17 GeV/c (PRL 112, 122301)assoc

T 0.2<p±jet-h

=200 GeVsp+p at


〈zT 〉 with Gaussian Widths

〈zT 〉 ptrigT correction wasalso applied to Gaussianwidths vs. ptrigT

〈zT 〉 more or less amountsto a scale factor of 2difference in the slope

[GeV/c]jetT

p6 8 10 12 14 16 18 20 22 24

Gau

ssia

n W

idth

[GeV

/c]

0.45

0.5

0.55

0.6

0.65±-h0π

±-hγ Linear Fit±-h0π

Linear Fit±-hγ<10 GeV/cassoc

T0.7<p

PHENIX

|<0.35η|=510 GeVsp+p at


√〈p2

out〉 vs. pjetT

[GeV/c]jet

Tp

6 8 10 12 14 16 18 20 22 24

[GeV

/c]

⟩2 ou

t p⟨

0

1

2

3

4

5±-hγ

|<0.35η|

=510 GeVsp+p at

PHENIX

±-h0π<3 GeV/cassoc

T2<p

<4 GeV/cassocT

3<p

Examined√〈p2

out〉 as a function of pjetT as well

pjetT = ptrigT for direct photons

pjetT = ptrigT /〈zT 〉 for π0s, with 〈zT 〉 estimated using PYTHIA

〈zT 〉 =ptrigT

p̂trigT

The√〈p2

out〉 distributions almost form a continuous function?


More about Color Coherence

Radiation“drags” coloraway from vertex

Destructive interferenceoccurs away from emittedgluons

Soft radiation inhibited incertain areas

Leads to certain regionsof phase space wheregluons constructively ordestructively interfere

See the followingreferences

Phys. Rev. D 50,5562(1994)Phys. Lett. B 414(1997) 419-427Dokshitzer, Yuri.Basics of PerturbativeQCD (EditionsFrontieres, 1991)Chapters 4,5,9


SIDIS and e+e− Annihilation Momentum Widths

PRD 61, 014003

Z. Phys. C 21:37


Partonic Contributions to Processes at LO

[GeV/c]0π

Tp

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Fra

ctio

nal C

ontr

ibut

ion

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1g+g→g+gq+q→q+qq+g→q+g

qq+→g+g

+X0π→p+p|<0.35η|=510 GeVs

CTEQ6L1 PDFs at LO

(a)

π0 contribution changesfrom gluon dominated atlow pT to mix of quarkand gluons at high pT

[GeV/c]γT

p2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Fra

ctio

nal C

ontr

ibut

ion

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

+qγ→q+g

+gγ→qq++Xγ→p+p

|<0.35η|=510 GeVs

CTEQ6L1 PDFs at LO

(b)

Direct photoncontribution dominatedby QCD Comptonscattering at all pT

NLO corrections small atmidrapidity (Phys. Lett.B 140,87)


Analysis Methods

Correlated π0−h± orisolated γ−h± are collectedand corrected with:

Charged hadronefficiencyAcceptance correction

Direct photons undergoadditional statisticalsubtraction to remove decayphoton background,estimated with Monte Carloprobability functions

Isolation and tagging cutsremove decay photonbackground and NLOfragmentation photons

Probability for a π0 to decay to aphoton which could not be tagged

with 5 < pT < 7 GeV/c in PHENIX

Y isodir =

1

R isoγ − 1

(R isoγ Y iso

inc − Y isodec

)PRD 82,072001 (2010)PRC 80,024908 (2009)


R isoγ Measurement at

√s=510 GeV

R isoγ measured for

statistical subtraction ofisolated decay photoncontribution

Rγ measured in PHENIXand corrected by taggingand isolation efficiencies

R isoγ >1 indicates isolated

direct photon production [GeV/c]γ

Tp

7 8 9 10 11 12 13 14

iso

γR

1

1.2

1.4

1.6

1.8

2

2.2

PHENIX

=510 GeVsp+p at |<0.35η|

R isoγ =

Rγ

(1− εtagdec)(1− εnisodec )

N isoinc

Ninc


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