Frontiers of QCD with Precision nPDFs

2.7 MB·

by  Aleksander Kusina

EPJWebofConferenceswillbesetbythepublisher
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(cid:13)c Ownedbytheauthors,publishedbyEDPSciences,2016
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Frontiers of QCD with Precision nPDFs (cid:63)
2

n
a AleksanderKusina1,a,FlorianLyonnet2,b,FredrickI.Olness2,c,d,andIngoSchienbein1,e
J

6 1LPSC,UniversitéJosephFourier/CNRS-IN2P3/INPG,UMR5821,Grenoble,F-38026,France
2 2SouthernMethodistUniversity,Dallas,TX75275,USA

]
h Abstract.Searchesfornewphysicswillincreasinglydependonidentifyingdeviations
p
from precision Standard Model (SM) predictions. Quantum Chromodynamics (QCD)
-
p will necessarily play a central role in this endeavor as it provides the framework for
e the parton model. However, as we move to higher orders and into extreme kinematic
h regions, we begin to see the full complexities of the QCD theory. Recent theoretical
[ developments improve our ability to analyze both proton and nuclear PDFs across the

fullkinematicrange.ThesedevelopmentsareincorporatedintothenewnCTEQ15PDFs,
1
and we review these developments with respect to future measurements, and identify
v
5 areaswhereadditionaleffortisrequired.
1
1
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0 1 The Character and Consequences of QCD1
.
1
“QCDisourmostperfectphysicaltheory.” 2 Itsscopeiswiderangingspanningnuclearphysics,par-
0
6 ticlephysics,cosmology,andastrophysics. Italsocontainsawealthofphenomenaincluding: “radia-
1 tivecorrections,runningcouplings,confinement,spontaneous(chiral)symmetrybreaking,anomalies,
: andinstantons”[1].
v
i QCDisbothaforcewhosepropertieswewanttostudy,andalsoatoolwecanusetolinkexperi-
X
mentallymeasuredhadroniccrosssectionstotheoreticallycalculablecrosssectionsinthecontextof
ar the parton model. The basic statement of the parton model is: σA→X = fa/A ⊗(cid:98)σa→X where we fac-
torizethecomplexnon-perturbativeQCDinteractionsintothePartonDistributionFunctions(PDFs)
fa/A andthetheoreticalpartoniccrosssection(cid:98)σa→X. Here,σA→X isthephysicallymeasurablecross
section,andAcanrepresenteitheraprotonoranucleon.
Aswepushourcalculationstohigherprecisionandintoextremekinematicregions(suchaslow-
Q2 or hi/low-x) we may encounter a variety of phenomena such as those illustrated schematically
in Fig.1. While many of these phenomena can be neglected at lower orders and lower precision, if
(cid:63)BasedonworkincollaborationwithD.B.Clark,E.Godat,T.Ježo,C.Keppel,K.Kovaˇrík,J.G.Morfín,P.Nadolsky,
J.F.Owens,&J.Y.Yu. ThisworkissupportedinpartbytheU.S.DepartmentofEnergyundergrantDE-FG02-04ER41299,
andbyProjetinternationaldecooperationscientifiquePICS05854betweenFranceandtheU.S.
ae-mail:[email protected]
be-mail:fl[email protected]
ce-mail:[email protected]
dPresenter
ee-mail:[email protected]
1Inthisshortpresentationweprovideonlyanabbreviatedsetofreferences.
2WhatQCDTellsUsAboutNature–andWhyWeShouldListen,byFrankWilczek.[1]
EPJWebofConferences
wearetoproperlyanalyzethenewgenerationofhigh-precisionhigh-statisticsexperiments,wemust
considerthepotentialimpactofthesemanifestationsoftheQCDtheory.
The recent performance of the LHC has exceeded expectations and produced an unprecedented
numberofeventstobeanalyzed. However,toadvanceourunderstandingoftheseprocessesandthe
inherentaspectsoftheQCDtheoryrequiresbothimprovedtheoreticaltoolsandcomplementarydata
from other experiments such as an Electron Ion Collider (EIC) and Large Hadron electron Collider
(LHeC). In the same manner that the combination of the HERA ep and Tevatron pp¯ data provided
maximumknowledgeoftheunderlyingphysics,thecombinationoftheLHCandfuturelepton-hadron
datacanfurtherexpandoursearchfornewphysicsandourunderstandingofQCD.
Tocarryoutthisprogramrequiresboththeabovedata,andalsoimprovedtheoreticaltoolstoper-
formtheanalysis. Webrieflyreviewsomeoftherecentprogress,andidentifyareaswhereadditional
effortisrequired.
1.1 NuclearPDFs
Figure1. Weschematicallyrepresentthevarietyofphenomenawhichmayenterwhenconsideringprotonand
nuclearPDFsathighprecision. WeemphasizethatthenuclearPDFsandcorrectionsareimportantforflavor
differentiation.
Historically,thenuclearPDFs(nPDFs)andtheassociatednuclearcorrectionfactorshaveplayed
a key role in the flavor differentiation of the proton PDFs. The common processes used to extract
the proton PDFs were Deeply Inelastic Scattering (DIS), Drell-Yan (DY) lepton-hadron scattering,
andjetproduction. Theseprocessesinvolvedifferentlinearcombinationsofthepartonicflavors,and
theneutrino-nucleonDISprocessesareespeciallyvaluableaswecanextractthefourquantities{FνN,
2
Fν¯N,FνN,Fν¯N}.Duetothesmallneutrinocrosssection,thesemeasurementsareusuallyperformedon
2 3 3
heavynucleartargets;hence,adetailedunderstandingofthenPDFsandtheircorrectionsareessential
toconstrainingtheflavorstructureofboththenuclearandprotonPDFs.
Tocomprehensivelyanalyzebothprotonandnucleardatainasingleunifiedframework,wehave
developedthenCTEQprojectwhichcancombinebothdatasets(includinguncertainties)intothefit.
ThenCTEQ15setofnPDFs[2]isillustratedinFig.2, andthisextendstheCTEQprotonPDFsfitsto
includethenucleardependenceacrossthefullArangefromprotonupto208Pb.
1.2 TheStrangeQuark
ToillustratethechallengesoffittingthenPDFs, inFig.3wedisplaytheeffectivenuclearcorrection
factorsRonironforneutral-currentcharged-lepton((cid:96)±)DISandcharged-currentneutrino(ν,ν¯)DIS.
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16 0.7
14 g 0.6 s AA==14 20 0.8
xf1146802 xf0000....4352 AAAAAAAAAA==========91245811122706413909177 /(,)11505 000000......463752
2 0.1 0.1
100-3 10-2 x 10-1 1 0.100-3 10-2 x 10-1 1 0 103 102 101 10.0 103 102 101 1
Figure2. a)ThenCTEQ15PDFsforarangeofnuclearAvalues.[2]b)ThenPDFuncertaintybands,together
withHKN07,[3]EPS09,[4]andDSSZ.[5]
Fe]R[F200011000111...........789017890121555550000000−2 a) A=56, Z=26 1x0−1QfKSHitLPK2 =BAN5C0 G/7N e(MNVCL2O) 1 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxνFe]R[F2001100111.........890189012555500000 Axxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx=5b6, Z)=26 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx10-1QfKSitLP2 =AAxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx52C G/NeMVC2 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxHKN07 (NLOxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx)1
Figure 3. The computed nuclear correction ratio, R = FFe/FD as a function of x. Figure-a) shows the fit
2 2
usingtheneutral-currentlepton((cid:96)±N)DISdata(KP,SLAC/NMC,HKN07). Figure-b)showsthefitusingthe
charged-currentneutrino(νN)DISdata;thedataarefromtheNuTeVexperiment.SeeRef.[6]
400
300
200
100
0
-4 -2 0 2 4
y
Figure 4. a) b) The leading-order (LO) differential cross section (dσ/dy) for W+production at the Tevatron
(2 TeV) and the LHC (14 TeV) as a function of rapidity. The partonic contributions are also displayed for
{ud¯,cs¯,us¯,cd¯}. Theverticalscalesarelogarithmic. c)Thestrangequarkcontribution(yellow)asafractionof
thetotald2σ/dM/dyinpb/GeVforpptoW+productionattheLHCfor14TeVwithCTEQ6.6usingtheVRAP
programatNNLO.C.f.Ref.[7]fordetails.
TheRvaluesdiffer,andthisuncertaintythenfeedsintotheindividualflavorssuchasthestrangequark
s(x). PriortotheLHCdata,ourknowledgeof s(x)cameprimarilyfromνFeDIS,sotheuncertainty
ofthenuclearcorrectionwasanimportantconsideration. Consequently,improvementsinthenuclear
correctionfactorRwillyieldimprovedprotonPDFs.
AtthehigherenergyscalesoftheLHC,the(relatively)heavierpartonflavors(suchasthestrange)
play a more prominent role. This is illustrated in Fig.4 where we find the cs¯ → W+ contribution is
EPJWebofConferences
muchlargerthanattheTevatron(forexample)wheretheud¯processdominated.Wecanthenturnthis
issuearoundandusetheLHCdatatoimposeconstraintsonthestrangequark.[8]
Inthisinstance,thecombinationoffixed-targetνN DISdatatogetherwithLHCW/Z production
datacanimproveconstraintsofboththestrangePDFandthenuclearcorrectionfactors.
1.3 CharmandBottomQuark
0.55
N=3 N=4
f f
g(x)0.50 Nf=5
1∫dx x 00.45 Nf=6
0.40
1 5 10 50 100 5001000
μ[GeV]
Figure 5. a) Momentum fraction of the charm and bottom PDFs as a function of the scale. b) Momentum
fractionofthegluonforN ={3,4,5,6}asafunctionofthescale.
F
p+p -> γ+c+X

V) DØ, L = 1.0 fb -1 yγyjet > 0 √ S =1.96 TeV
e int
G 10 yγyjet < 0
pb/ γ+c+X 1 ηγηQ>0
jetγγ) (dydy(dpT1100-1-21 γ+b+X NCµRLT,(FOEx,f3=Q Q. 0 p6C)γT.D6M p(pb/GeV)Tγ0.01 CBSeTHaEP-lQSik Ie6C .I6 CmM modoedlel
3⁄ σd10-3 |yγ| < 1.0 (x1.0) d/dσ
|yjet| < 0.8 (x0.3)
10-4 pTjet > 15 GeV (x0.1)
0 20 40 60 80 100 120 140 0.00010 50 100 150 200
pγ (GeV) p (GeV)
T Tγ
Figure 6. a) Cross section for associated production of γ and c/b.[9] b) Same with an intrinsic charm
component.[10]
Considering the heavier charm and bottom quarks, these enter the PDF for energy scales above
the quark mass values; as the c and b PDFs are primarily produced by gluon splitting (g → cc¯ and
g→bb¯),theseaffectthemomentumfractioncarriedbythegluon(c.f.,Fig.5).
While we generally assume that there is no primordial component of the c and b PDFs for en-
ergyscalesbelowthequarkmass,ithasbeenpostulatedthattherecouldbeanadditional“intrinsic”
componentwhichwouldbeaddedtotheusual“extrinsic”component(whichcomesfromgluonsplit-
ting).Thereareanumberofmeasurementswherethe“intrinsic”componentcouldmanifestitself;see
Ref.[11]forarecentreview.
Fig.6-ashowsthedataforγ+c → X isabovethetheorypredictionatthelargest pγ values; an
T
γ
additional“intrinsic”component(Fig.6-b)canshiftthetheoryinthedirectionofthedataatlarge p .
T
6thInternationalconferenceonPhysicsOpportunitiesatElectron-Ioncolliders(POETIC6)
Whilethisobservationisintriguing,additionalprecisionandanalysisisrequiredtodefinitivelyclaim
evidenceofan“intrinsic”component.
Onarelatedtopic,recenttheoreticalworkdemonstratedthat(toagoodapproximation)theevolu-
tionoftheintrinsicheavyquarkcomponentisgovernedbynon-singletevolutionequationswhichcan
bedecoupledfromtheevolutionoftheremainingPDFs.[12]Theobservationallowsan(approximate)
intrinsiccomponenttoeasilybeincludedwithanycalculationwithouttheneedforaspeciallyevolved
PDFset; thisgreatlysimplifiesourabilitytosearchfor, andplaceconstraintsupon, intrinsiccharm
andbottomcomponentsofthenucleon.
1.4 HigherOrderCalculations
1.25
1.20 α(6)/α(3) 2.0 x=10-5
S S
1.15 1.5
1.10 αS(5)/αS(3) b(x)1.0 x=10-4
α(4)/α(3) x0.5 x=10-3
1.05 S S
α(3)/α(3) 0.0
1.00 S S
1 5 10 50 100 500 1000 3 5 7 10
μ[GeV] μ [GeV]
Figure7. a)Ratiosofα (µ)forN ={3,4,5,6}. b)Thediscontinuityintheb-quarkPDF f (x,µ)atNNLOvs.
s F b
µforx={10−3,10−4,10−5}.
Recentadvancesintheautomationofhigherordercalculationshavetremendouslyincreasedthe
breadthofprocesseswhichareavailableatNNLOandbeyond. Aswemovetothesehigherorders,
our PDFs and α (µ) functions are discontinuous3 when we shift the number of flavors from N to
s F
N +1; c.f. Fig.7. AnelegantpropertyofQCDisthatdespitethe(fixedorder)discontinuityofthe
F
PDFsandα ,thediscontinuityofanyphysicalquantitywillsystematicallydecreaseorderbyorderin
s
pOe(rαtuk+rb1)a.tiTohnisthiesocreyr;tatihnaltyisatroemsaayr,kaatbolerdreesrukltw. ehavetherelation: σ (cid:39) fNF ⊗σˆNF = fNF+1⊗σˆNF+1+
s
1.5 IncisiveAnalysisTools
Finally, as we advance our analysis methods it is important to develop new tools and metrics that
caninsightfullyandeffectivelyconveytheessenceofthephysics. InFig.8wedisplaythecorrelation
cosine cosφ vs. x for a variety of experiments. The plot effectively conveys which experiments
influence the PDFs in different x regions, and how they are correlated. To emphasize this point we
compare the u-valence (left) with the flipped d-valence figure (right); by flipping the figure we see
thatu-valenceandd-valenceareanti-correlated. Thus,asthefitworkstofindaminimumχ2value,it
hastobalancetheseexperimentaldatasetswhicharepullingtheu-valenceandd-valenceinopposite
directions.
3αs(µ)hasdiscontinuitiesatorderαs(µ)3,butthesearenotapparentinFig.7-a.
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D
E
P
P
I
L
F
Figure8. Correlationmeasures(cosφ)foru-valence(left)andd-valence(right)forleadatQ=10GeV. Eight
selected experiments are highlighted with symbols. To emphasize the anti-correlation between u-valence and
d-valencewehaveflippedthed-valenceplotvertically.SeeRef.[2]fortheoriginalfiguresandadditionaldetails.
1.6 Conclusions
Recenttheoreticaldevelopmentsprovideimprovedprecisionforbothprotonandnucleartargetsacross
a wide kinematic range. Further improvements will rely on a combination of additional theoretical
advances, and a broad range of experimental measurements. The prospect of future data from EIC
andLHeCfacilitieswouldbeavaluablecomplementtotheLHCandadvancebothoursearchfornew
physicsandourunderstandingofQCD.
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