Table Of ContentNonperturbative Transverse Momentum Effects in Dihadron and Direct
Photon-Hadron Angular Correlations
J.D. Osborn for the PHENIX Collaboration
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109
Two-particleangularcorrelationshavelongbeenusedasanobservableformeasuringtheinitial-
state partonic transverse momentum k . Sensitivity to this small transverse momentum scale al-
T
lows nonperturbative transverse momentum dependent effects to be probed in high p dihadron
T
and direct photon-hadron correlations. The observable p , the out-of-plane transverse momen-
out
tum component from a near-side π0 or direct photon, is sensitive to initial-state k and final-state
T
fragmentationtransversemomentumj andthuscanprobenonperturbativetransverse-momentum-
T
dependenteffects. Inthetransverse-momentum-dependentframework,nearlyback-to-backparticle
production in p+p collisions with a measured final-state hadron has been predicted to break fac-
torization due to the possibility of gluon exchanges with colored remnants in the initial and final
7 states. For this reason, the interacting partons are predicted to be correlated; however, there is so
1 farnoquantitativepredictionforthemagnitudeofsucheffects. Inthi√stalk,recentmeasurementsof
0 dihadron and direct-photon hadron correlations in p+p collisions at s=510 GeV at the PHENIX
2 experiment will be presented.
n
a
I. INTRODUCTION breaking is predicted, individual TMD PDFs and TMD
J
FFs become correlated with one another and cannot be
3
written as a convolution of nonperturbative functions.
In quantum chromodynamics (QCD), parton distribu-
] The ideas behind the predicted sign change of certain
tion and fragmentation functions (PDFs and FFs) are
x TMD PDFs and factorization breaking result from the
e used to describe the long distance bound state nature of
samephysicalprocessofsoftgluonsbeingexchangedbe-
- hadrons. Historically PDFs and FFs have been taken to
p tween participants of the hard scattering and remnants
only be dependent on the longitudinal momentum frac-
e of the collision. These predictions represent major qual-
h tion x and z, respectively. In the last several decades
itative departures from purely perturbative approaches
[ this has been extended to include transverse momen-
which do not consider the remnants of the collision at
tum dependence so that the “unintegrated” transverse-
1 all.
momentum-dependent(TMD)PDFsandFFsarewritten
v
explicitlyasdependentonboththelongitudinalmomen-
1
8 tumandtransversemomentumofthepartons. Sincethe
6 framework explicitly includes small transverse momenta,
In calculations of TMD processes where factorization
0 thereevaluationofimportantprinciplesofQCDlikefac-
0 torization and universality has been necessary. is predicted to hold, the Collins-Soper (CS) equation is
. known to govern the evolution of nonperturbative func-
1 In particular, the role of color interactions due to soft
tions in a TMD framework with the hard scale of the in-
0
gluonexchangesbetweenparticipantsofthehardscatter- teraction Q2 [4, 5]. Contrary to the purely perturbative
7
ing and remnants of the interaction in collisions involv-
1 collinear DGLAP evolution equations, the CS evolution
ing a hadron have been found to have profound effects
: equation for TMD processes involves the Collins-Soper-
v regarding these principles. For example, the Sivers func-
Sterman(CSS)softfactor[6],whichcontainsnonpertur-
i
X tion, a particular TMD PDF that correlates the trans- bative contributions. The theoretical expectation from
verse spin of the proton with the orbital angular mo-
r CSSevolutionisthatmomentumwidthssensitivetonon-
a mentum of the parton, was predicted to be the same
perturbative transverse momentum should increase with
magnitude but opposite in sign when measured in semi-
the hard scale of the interaction. This can intuitively be
inclusivedeep-inelasticscattering(SIDIS)andDrell-Yan
thought of as due to an increased phase space for hard
(DY) [1]. This prediction arises from the different color
gluon radiation, and thus a broader transverse momen-
flowsthatarepossiblebetweenthesetwointeractionsdue
tum distribution. This behavior has been studied and
to the possibility of soft gluon exchanges in the initial-
confirmedinseveralphenomenlogicalanalysesofDYand
stateandfinal-stateforDYandSIDIS,respectively. Fac-
Z boson data (see e.g. [7–9]) as well as phenemonologi-
torization of the nonperturbative functions is still pre-
calanalysesofSIDISdata(seee.g.[9–11]). SincetheCS
dicted to hold in both SIDIS and DY.
evolutionequationcomesdirectlyoutofthederivationof
In p+p collisions where two nearly back-to-back TMD factorization [12], it then follows that a promising
hadrons are measured, soft gluon exchanges are pos- avenue to potentially observe factorization breaking ef-
sible in both the initial and final state since there is fectsistostudypossibledeviationsfromCSSevolutionin
color present in both the initial and final states. In processes where factorization breaking is predicted such
this process, factorization breaking was predicted in a as dihadron and direct photon-hadron angular correla-
TMDframework[2,3]. Forprocesseswherefactorization tions in p+p collisions.
2
II. DIHADRON AND DIRECT photon or near-side hadron. Measuring the azimuthal
PHOTON-HADRON ANGULAR angular separation between the near-side trigger particle
CORRELATIONS and away-side associated particle allows calculating p
out
with the following equation:
Dihadron and direct photon-hadron angular correla-
tions are both predicted to be sensitive to factorization pout =paTssocsin∆φ (1)
breaking effects because there are hadrons in both the
initial and final states, thus the potential for soft gluon The results presented were measured by the PHENIX
exchangesinboththeinitialandfinalstatesexists. Addi- collaboration at the Relativistic Heavy Ion Collider at
tionally these processes can be treated in a TMD frame- Brookhaven National Lab. The PHENIX detector cov-
workwhenthetwoparticlesarenearlyback-to-backand ers a pseudorapidity interval of |η| < 0.35, and has two
have large p ; a hard scale is defined with the large p armswhichintotalspananazimuthalregionof∆φ∼π.
T T
of the particles and the process is also sensitive to the Leadscintillatorandleadglasselectromagneticcalorime-
convolution of initial-state and final-state small trans- tersprovidemeasurementsofisolateddirectphotonsand
verse momentum scales k and j . Here k refers to neutral pions via their two photon decay. To measure
T T T
the initial-state partonic transverse momentum due to away-sideparticles,thePHENIXdetectoremploysadrift
theconfinednatureofthepartonsandsoftorhardgluon chamber and pad chamber tracking system that mea-
radiation, and j refers to the final-state fragmentation sures nonidentified charged hadrons. These results were
T
transversemomentumduetosoftorhardgluonradiation measured from p+p collisions at a center-of-mass energy
√
in the hadronization process. of s = 510 GeV, and were recently submitted to the
arXiv [13].
(a)
III. RESULTS
Figure 2 shows the measured per-trigger yields as a
function of ∆φ for both π0-hadron and direct photon-
hadron correlations. The π0-hadron correlations show
(b) the expected two jet structure, with two peaks that are
nearly back-to-back around ∆φ ∼ 0 and ∆φ ∼ π. The
nearsideofthedirectphoton-hadroncorrelationsisomit-
ted due to the presence of an isolation cut on the di-
rect photons; thus the near side is not physically inter-
FIG.1. Aschematicdiagramshowingeventhard-scattering pretable. Additionally, the away-side jets are sensitive
kinematics for (a) dihadron and (b) direct photon-hadron to the effects of kT broadening, so they are the yields of
processes in the transverse plane. Two hard scattered par- interest. The direct photon-hadron yields have a smaller
tons with transverse momenta pˆtrig and pˆassoc are acoplanar yield than the π0-hadron yields due to the direct photon
T T
due to the initial-state partonic k , given by |(cid:126)k1 +(cid:126)k2|. The emerging from the hard scattering at leading order; thus
T T T
scattered partons result in two fragmented hadrons that are thedirectphoton-hadroncorrelationsprobeasmallerjet
additionally acoplanar due to the final-state transverse mo- energy than the π0-hadron correlations.
mentum perpendicular to the jet axis j . For (b) direct
photon-hadrons only one away-side jet fraTgyment is produced The measured pout per-trigger yields are shown in
Fig. 3 for both π0-h± and direct photon-h± angular cor-
since the direct photon is colorless. The transverse momen-
relations. Theopenpointsshowthedistributionsforπ0-
tumcomponentperpendiculartothetriggerparticle’saxisis
hadron correlations while the filled points show the dis-
labeled as p .
out
tributionsforthedirectphoton-hadroncorrelations. The
distributions are constructed for only away-side charged
Figure 1 shows a kinematic diagram in the transverse
hadrons that are sensitive to initial-state k and final-
plane for both dihadron (top) and direct photon-hadron T
state j . The p distributions show two distinct re-
(bottom)events. Atleadingorderthehardscatteredpar- T out
gions; at small p ∼ 0 where the particles are nearly
tonsareexactlyback-to-back, butduetoinitial-statek out
T
thepartonsareacoplanarbysomeamount|(cid:126)k1+(cid:126)k2|. The back-to-back a Gaussian shape can be seen, while at
T T larger p a power law shape is clear. These two shapes
fragmentation process introduces an additional trans- out
indicate a transition from nonperturbatively generated
verse momentum component j which is assumed to be
Ty transverse momentum due to soft gluon emission in the
Gaussian distributed about the parton axes such that
(cid:112) (cid:113) Gaussian region to perturbatively generated transverse
(cid:104)j2(cid:105) = 2(cid:104)j2 (cid:105). The transverse momentum compo-
T Ty momentum due to hard gluon emission in the power law
nentperpendiculartothetriggerparticle’saxisislabeled region. ThedistributionsarefitwithaGaussianfunction
asp andissensitivetoinitialandfinalstatek andj , atsmallp andaKaplanfunctionovertheentiredistri-
out T T out
where the trigger particle refers collectively to the direct bution. The Gaussian function clearly fails at p ∼1.3
out
3
p+p at s=510 GeV 0.1 Isolated Direct g -h–
0.5
|h |<0.35 p 0-h–
8<ptrig<9 GeV/c 0.1 Underlying Event
T
1<passoc<2 GeV/c 8<ptrig<9 GeV/c 8<ptrig<9 GeV/c
T T T
3<passoc<4 GeV/c 5<passoc<10 GeV/c
T T
0 0 0
-1 0 1 2 3 4 5 -1 0 1 2 3 4 5 -1 0 1 2 3 4 5
0.1
0.5
PHENIX
1
-] trig 0.1
d 9<p <12 GeV/c
a T trig
N [rf 1<paTssoc<2 GeV/c 93<<ppTass<oc1<24 G GeeVV/c/c 9<ptTrig<12 GeV/c
dDd T 5<passoc<10 GeV/c
g T
1Ntri
0 0 0
-1 0 1 2 3 4 5 -1 0 1 2 3 4 5 -1 0 1 2 3 4 5
0.1
0.5
trig
12<p <15 GeV/c
T 0.1 trig
1<passoc<2 GeV/c 12<pT <15 GeV/c 12<ptrig<15 GeV/c
T 3<passoc<4 GeV/c T
T 5<passoc<10 GeV/c
T
0 0 0
-1 0 1 2 3 4 5 -1 0 1 2 3 4 5 -1 0 1 2 3 4 5
D f
[rad]
FIG.2. Pertriggeryieldsofchargedhadronsasafunctionof∆φareshowninseveralptrig andpassoc binsforbothπ0-hadron
T T
and direct photon-hadron correlations. The near side yield of the isolated direct photon-hadron correlations is not shown due
tothepresenceofanisolationcut. Theblueandredsolidlinesshownontheaway-sidesofthedistributionsarefitstoextract
(cid:112)
the quantity (cid:104)p2 (cid:105).
out
(cid:112)
while the Kaplan function accurately describes the tran- entire away-side jet region, (cid:104)p2 (cid:105) is sensitive to both
out
sition from Gaussian behavior to power law behavior. perturbatively and nonperturbatively generated k and
T
j . While it is dominated by nonperturbatively gener-
To search for effects from factorization breaking, a T
atedtransversemomentumsincethemajorityofcharged
comparison to the expectation from CSS evolution must
hadronsareinthenearlyback-to-backregionp ∼0or
be made using momentum widths which are sensitive to out
∆φ ∼ π, an observable that is sensitive to only nonper-
nonperturbativetransversemomentum. Tomakeacom-
turbatively generated transverse momentum is the most
parison, two different momentum widths were extracted
ideal for comparisons to CSS evolution.
from the measured correlations. Figure 4 shows the root
mean square of pout as a function of ptTrig, which is ex- Since the Gaussian fits to the pout distributions are
tracted from fits to the entire away-side jet region in taken in only the nearly back-to-back region, the widths
Fig.2. Theaway-sidefitscanbeseeninFig.2asredand oftheGaussianfunctionsaremomentumwidthsthatare
(cid:112)
blue solid lines around ∆φ ∼ π. The values of (cid:104)p2 (cid:105) sensitive to only nonperturbative transverse momentum.
out
clearly decrease for both the π0-hadron correlations and Figure 5 shows the measured Gaussian widths as a func-
direct photon-hadron correlations, which is the opposite tion of the interaction hard scale ptrig for both direct
T
of what is predicted from CSS evolution. The direct photon-hadron and π0-hadron correlations. Similarly to
(cid:112)
photon-hadron correlations show a stronger dependence the values of (cid:104)p2 (cid:105) from Fig. 4, the Gaussian widths
out
than the π0-hadron correlations in the same region of decrease as a function of the hard scale, which is the
ptrig. Since the values of (cid:112)(cid:104)p2 (cid:105) are extracted from the opposite of the prediction from CSS evolution. The di-
T out
4
1
-] 10 g -h– p 0-h– ptrig [GeV/c]
c p+p at s=510 GeV T
/ 4-5
V
e 1 |h |<0.35 5-6 (x10-1)
N [G out1100--21 203p.7<<D pf a<s4s3op c<10 GeV/c 678---789 (((xxx111000---234)))
dp T 9-12 (x10-5)
d 10-3 12-15 (x10-6)
g
1Ntri 10-4 PHENIX
10-5
10-6
10-7
10-8
10-9
10-10
10-11
-8 -6 -4 -2 0 2 4 6 8
p [GeV/c]
out
FIG. 3. Per trigger yields of charged hadrons as a function of p are shown in several ptrig bins for both π0-h± and direct
out T
photon-h± correlations. ThedistributionsarefitwithaGaussianfunctionatsmallp andaKaplanfunctionovertheentire
out
range. The Gaussian fit clearly fails after ∼1.3 GeV/c, indicating a transition from nonperturbatively generated k and j to
T T
perturbatively generated k and j .
T T
V/c] 5 |h |<0.35 g -h– p 0-h– panydthπia0-h[1a4d]rownascoursreedlattioonsismaunladtestduidreyctthpehoetvoonlu-htiaodnroonf
[Ge 4 p+p at s=510 GeV 2<paTssoc<3 GeV/c momentumwidthswiththehardscaleoftheinteraction.
æut PHENIX 3<passoc<4 GeV/c The Perugia0 [15] tune was used since it was tuned to
2po T
Æ 3 Tevatron Z boson data at small pT; therefore it should
adequatelyreproduceeventswithasmallamountoftotal
p . pythiadirectphotonanddijeteventswereproduced
T
2 andthep distributionswereconstructeddirectlyfrom
out
the simulation in exactly the same way that they were
1 measuredindata. Althoughthemagnitudeofthewidths
from the simulation is roughly 15% different in each bin,
the simulation remarkably nearly reproduces the mea-
0
4 5 6 7 8 9 10 11 12ptrig [1G3eV/c1]4 sured evolution of the Gaussian widths as seen in Fig. 5.
T It is plausible that pythia could be sensitive to the ef-
(cid:112) fects from factorization breaking due to the way a p+p
FIG.4. Theextractedvaluesof (cid:104)p2 (cid:105)areshownasafunc-
out event is processed. Unlike a standard perturbative QCD
tionoftheinteractionhardscaleptrig forbothπ0-hadronand
T calculation, pythia forces all particles to color neutral-
direct photon-hadron correlations. The momentum widths
ize in the event. This includes allowing initial and final-
decrease with the interaction hard scale, which is opposite
the prediction from CSS evolution. stategluoninteractions,whicharethenecessaryphysical
mechanism for factorization breaking and are addition-
ally necessary to color neutralize all of the objects in the
event.
rect photon-hadron widths show a stronger dependence
on ptrig than the π0-hadron widths, similar to the values
T
(cid:112)
of (cid:104)p2 (cid:105).
out
Since theoretical calculations were not available,
5
eV/c] 0.8 PPHHEENNIIXX pg -0h-h– – PPHHEENNIIXX pg -0h-h– –L Linineeaar rF Fitit bnaetnwtseeonf pthaertcicoilpliasniotnsianrethpeohssairbdles,claetatdeirninggtaonndotvheel croelmor-
G PYTHIA Perugia0 p 0-h– PYTHIA p 0-h– Linear Fit flows throughout the entire scattering process. Nearly
dth [ 0.7 PYTHIA Perugia0 g -h– PYTHIA g -h– Linear Fit back-to-backdihadronanddirect√photon-hadronangular
Wi |h |<0.35 correlations in p+p collisions at s =510 GeV from the
n p+p at s=510 GeV PHENIX experiment at the Relativistic Heavy Ion Col-
sia 0.7<paTssoc<10 GeV/c liderweremeasuredtoprobepossibleeffectsfromfactor-
s 0.6
u izationbreaking[13]. Thetransversemomentumcompo-
a
G
nentperpendiculartothenear-sidetriggerparticle, p ,
out
was used to compare predictions from CSS evolution.
0.5 CSS evolution, which comes directly out of the deriva-
tion of TMD factorization [12], predicts that momentum
widths sensitive to nonperturbative transverse momen-
4 5 6 7 8 9 10 11 12 13 14
ptrig [GeV/c] tum should increase with increasing hard scale due to
T the broadened phase space for perturbatively generated
FIG. 5. The measured and pythia simulated Gaussian gluon radiation. This dependence has been observed in
phenomenologicalfitstobothDYandSIDISdata[7–11].
widths from the p distributions are shown as a function
out
of the hard scale ptrig. The widths, sensitive to only nonper- The measured correlations at PHENIX show the op-
T
turbativetransversemomentum,decreasewithptrig. Surpris- posite dependence from the prediction of CSS evolution;
T
ingly,pythianearlyreplicatestheevolutionbehaviorforboth momentum widths in hadronic collisions where at least
the direct photon-hadron and π0-hadron correlations despite one final-state hadron is measured decrease with the in-
a ∼15% difference in the magnitude of the pythia widths. teractionhardscaleptrig [13]. Remarkably,pythiarepli-
T
cates this behavior in both direct photon-hadron corre-
lations and π0-hadron correlations. While pythia cer-
tainly does not consider effects from factorization break-
IV. CONCLUSION ing as it relies on collinear factorization, the necessary
physical mechanism that results in the predicted factor-
ization breaking is present in pythia; gluon exchanges
In hadronic collisions where at least one final-state with the remnants are possible in a pythia simulated
hadronismeasured,factorizationbreakinghasbeenpre- event since all colored objects are forced to color neu-
dicted in a TMD framework. When color is present in tralizeinanygivenevent,unlikeastandardperturbative
both the initial and final states, soft gluon exchanges QCD calculation.
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