Light Cone Dynamics and EMC Effects in the Extraction of F_{2n} at Large Bjorken x

0.06 MB·English

by  Misak M Sargsian

Light Cone Dynamics and EMC Effects in the
Extraction of F at Large Bjorken x.
2n
Misak M. Sargsian
1 DepartmentofPhysics,FloridaInternationalUniversity,Miami,FL33199
1
0
2 Abstract. We discuss theoreticalissues related to the extractionof deep inelastic (DIS) structure
functionofneutronfrominclusiveDIS scatteringoff the deuteronat largeBjorkenx. Theoretical
n
justificationisgiventotheconsiderationofonly pncomponentofthedeuteronwavefunctionand
a
consistencywithboththebaryonicnumberandlight-conemomentumconservationsumrules.Next
J
wediscusstheEMCtypeeffectsandarguethatinallcasesrelevanttothenuclearDISreactionsat
9
large x the main issue is the medium modificationof the propertiesof boundnucleon rather than
2
thenon-nucleoniccomponentslikepions.Wegivebriefdescriptionofthecolorscreeningmodelof

] EMCandwithinthismodelweestimateuncertaintiesintheextractionoftheneutronDISstructure
h functionatlargex.Weemphasizealsothattheseuncertaintiesarerather"modelindependent"since
p anytheoreticalframeworkaccountingforthemediummodificationisproportionaltothemagnitude
-
p ofthevirtualityofboundnucleonwhichincreaseswithanincreaseofx.
e
Keywords: deep-inelasticscattering,light-conedynamics,neutronstructurefunction
h
PACS: 11.80.-m,13.60.-r,13.85.Ni
[

1
v INTRODUCTION
8
4
6 Since the pioneering experiments on deep inelastic electron scattering off the deuteron
5
atSLACinlate70’s[1]theinvestigationofthepartonicdistributionfunctions(PDFs)of
.
1
theneutronat large xis oneofthemostimportanttopicsinthehighx QCD studies.
0
The main target of the choice for the extraction of the neutron PDFs is the deuteron
1
1 andasthestudiesprogresseditbecomemoreandmoreclearthatseveralissuespurelyin
:
v nuclear physics nature should be addressed for successful exploration of DIS structure
i oftheneutron.
X
Historically, due to its simplicity the main reaction considered was the inclusive
r
a d(e,e′)X scattering of the deuteron. However new generation of semi-inclusive
experiments[2, 3, 4] present completely new framework in studies of neutron
PDFs[5, 6,7, 8, 9].
In inclusiveDIS scattering several issues pertainingto thedeuteron and the natureof
theinclusivescatteringareimportantforunambiguousinterpretationoftheneutronDIS
data. These includes appropriate descriptionof the scattering process off therelativistic
bound system,effects due to modificationof bound nucleon structureas well final state
interaction.
In this report we focus on two issues such as light-cone description of the inclusive
DISprocess involvingdeuteronand mediummodificationofneutronPDFs.
LIGHT CONE DESCRIPTION OF THE INCLUSIVE DIS
SCATTERING
Since partons have meaningful interpretation only in the infinite momentum frame or
in the light cone[10] the selfconsistent interpretation of DIS scattering off the nuclei in
thermsofpartonicdegreesoffreedomrequiresthedescriptionofthenucleiintheinfinite
momentum or light cone reference frame. In this case a bound nucleon is described by
light-conemomentuma which is Lorentz invariant quantity boosted in the direction of
infinitemomentumand has a meaningof themomentumfraction of thenucleus carried
bytheboundnucleon.
Inthecaseforthedeuteronassumingthatitconsistsofonlyprotonandneutronwecan
express the relative momentum of pn system in the light-cone through the momentum
fractiona as follows[11]:
m2 +p2
k= N t −m2 (1)
sa (2−a ) N
where momentum fractions are normalized in such a way that for stationary nucleon
a = 1. The above defined momentum k allows us to estimate the limit at which one
can consider the deuteron as consisting of proton and neutron only, For this in Fig.1
we present the Bjorken - x dependence of k for typical DIS scattering kinematics at
large x and compare it with the three momentum of the nucleon as it enters in the lab
framedescriptionofthedeuteron.Fromthefigureweobservethatatlargextherelative
momentum of pn system in the light cone is consistently less than the the one defined
in the Lab frame. This situation is important from the point of view of justification of
theapproximation in which deuteron consists of only proton and neutron. Based on the
recent observation[12] that the nucleonic component in the isosinglet pn short range
correlationdominatesinthewavefunctiontill∼650MeV/crelativemomentawewere
able to estimate that for Q2 ≥5 GeV2 and practically for whole range of large Bjorken
x ≤1 the non-nucleonic components can be safely neglected in the ground state wave
functionofthedeuteron.
Constrainingourselvesonlybytwo-nucleoncomponentofthedeuteronwavefunction
within LC approximation for the DIS structure function of the deuteron we obtain[13,
14]
FA(x,Q2) = (cid:229) 2 da d2p r LC(a ,p ) FN(x˜,Q2)n
2 a 2 ⊥ N ⊥ 2 n˜
N=1Z
M m n ′ p2
× ( d )2(1+cosd )2(z+a N )2+ ⊥ sin2d , (2)
2m q Q2 2M2
(cid:20) N N (cid:21)
where
Q2 w2 +Q2−m2
x˜ = , n˜ = N N,
2m n˜ 2m
N N
1M M
w2 = Q2+ d(p a +zq )+ dp z−p2,
N 2 2 + q + 2 + ⊥
V/c0.8
Ge
m, 0.7
u
nt
me0.6
mo
0.5
0.4
0.3
0.2
0.1
0
0.4 0.5 0.6 0.7 0.8 0.9 1
x
FIGURE1. Thedependenceofminimallight-conek(solidline)andlabframep (dashedline)relative
momentaofthe pnsysteminthedeuteronontheBjorkenx.CalculationsaredoneforQ2=5GeV2 and
w =2GeV.
N
1 M
n ′ = (p q +p q )= d p a +q z , (3)
+ − − + + q +
2m 2m
N N
(cid:2) (cid:3)
and p = E±p where z axis is defined in the direction of~q. The light-cone density
± z
matrixr LC(a ,p )canbeexpressedthroughthedeuteronwavefunctionasfollows[11]:
N ⊥
E |Y (k)|2
r LC(a ,p )= k d (4)
N ⊥ 2−a
where E = m2 +k2 and the momentum k is defined according to Eq.(1). The light-
k N
cone densityqmatrix defined above satisfies two sum rules: From baryon charge conser-
vationonehas
da
d2p r LC(a ,p )=1, (5)
a ⊥ N ⊥
Z
whilethemomentumsumrulerequires
da
d2p ar LC(a ,p )=1. (6)
a ⊥ N ⊥
Z
The above two relations are necessary conditions for self-consistency if one excludes
any non-nucleonic component in the deuteron wave function. In this respect it is inter-
estingthatwithinapproximationsinwhichthestrucknucleonistreated asvirtualinthe
lab frame of the scattering process (generally referred as virtual nucleon (VN) approxi-
mation)(see e.g.[16, 17, 18, 19, 8, 9])themomentumsumruleofEq.(6)is notsatisfied
and:
da
d2p ar VN(a ,p )<1. (7)
a ⊥ N ⊥
Z
Such a result can be interpreted as missing momentum fraction being distributed to the
unaccounteddegreesoffreedomsuchaspions.Notethatthelastsumruleisnotdirectly
satisfied in the VN model, but it can be restored if mesonic degrees of freedom are
introducedexplicitly(see e.g.Ref.[20].
The account of both sum rules, given above, within light-cone approximation leads
to a prediction for the FA/FN ratio which qualitatively contradicts the EMC effect for
2 2
x>0.5 (Fig.2). This situation however indicates that the next step in the description of
∼
DIS scattering off the nucleus should be the account of nuclear medium modifications
ofthestructurefunctionsofboundnucleon.
MEDIUM MODIFICATION EFFECTS
ThediscoveryoftheEMC effect at largexhas triggeredahugetheoreticaleffort which
has led tothedevelopmentof alarge numberof models(see, e.g., Refs. [21, 22, 23, 24,
25, 26]). One can divide these models in two groups: one in which the effect is due to
the missed non-nucleonic component (such as pion degrees of freedom) and the other
groupinwhichEMCeffectsareduetomodificationofthepropertiesofboundnucleons.
Accordingtoourdiscussionabovewebelievethatthefirstgroupcontributeslittleinthe
DISkinematicsat largex. Moreoverit can be shownthatin theLC approximationeven
ifpionswillcarry sizablelightconemomentumfraction itwillnotbeaccessibleinDIS
measurement[27].
The important characteristics of the models in the second group is that the extent of
modification depends on the magnitude of virtuality of the bound nucleon. In this case
as it followsfrom Fig.1 one expects that withan increase ofx the mediummodification
oftheDISstructurefunctionwillbemoreand moreimportant.
To estimate the expected magnitude of the effects in the extraction of large x neu-
tron structure function from inclusive DIS scattering off the deuteron we calculate the
mediummodificationbasedononeof"secondgroup"models:thecolorscreeningmodel
ofRef.[23, 13].
This model is based on the observation that the most significant EMC effect is
observed in the range of x corresponding to high momentum components of the quark
distribution in the nucleon and therefore the EMC effect is expected to be mostly
sensitivetothenucleonwavefunctionconfigurationswherethreequarksarelikelytobe
close together. Such small size configurations are referred as point-like configurations
(PLC). It is then assumed that for large x the dominant contribution to FN(x,Q2)
2
is given by PLC of partons which, due to color screening, interact weakly with the
other nucleons. Because of this the optimally bound configuration of nucleons will
have suppressed contribution from the PLC component of nucleon wave function. The
suppression of PLC in a bound nucleon is assumed to be the main source of the EMC
effect in inclusiveDIS and the suppression factor is calculated in perturbation series of
theparameter:
hU i
k = A (8)
D E
(cid:12) A(cid:12)
(cid:12) (cid:12)
(cid:12) (cid:12)
(cid:12) (cid:12)
1.15 1.3
2Q) 4He 2Q) 56Fe
(x,C1.1 JLAB (x,C
M M1.2
E SLAC LC E LC
R1.05 R
1 1.1
0.95
1
0.9
0.85 0.9
0.8
0.8
0.75
0.7 0.7
0.4 0.6 0.8 0.4 0.6 0.8
x x
FIGURE 2. The x dependence of EMC ratios. Solid line light-cone approximation without medium
modifications. Dashed area corresponds to LC calculations with EMC effects calculated according to
color screening model. Largest effect correspondsto D E =0.6 GeV and smallest - D E =1 GeV. The
A
dataarefromRefs.[29,30].
where hU i is the average potential energy per nucleon and D E ≈ M∗−M ∼ 0.6÷
A A
1GeV isthetypicalenergy fornucleon excitationswithinthenucleus.
To calculate the deformation of the quark wave function in the bound nucleon due to
suppression of the probability of PLC in the bound nucleon and then to account for it
inthecalculationofFA(x,Q2)oneneedstointroducethenuclearpotentialwithexplicit
2
quark degrees of freedom in it:V(R ,y,y ). Then using this potential to reevaluate the
ij i j
potential energy U that enters into Schrödinger equation for the nuclear ground state
wavefunctionin theform:
U(R )= (cid:229) hf (y)f (y )|V(R ,y,y ,y,y )|f (y)f (y )i, (9)
ij N i N j ij i j i j N i N j
yi,yj,yi,yj
where f (y) is the free nucleon wave function. Uesineg for thee unpeerturbed nuclear
N i e e
wave function the solution of the Schrödinger equation with U(R ), one can treat
ij
(U −V)/D E ), as a small parameter to calculate the dependence of the probability to
A
find a nucleon in a PLC on the momentum of the nucleon inside the nucleus. Such
a calculation allows to estimate the suppression of the probability to find a PLC in a
boundnucleonascomparedtothesimilarprobabilityforafreenucleon.IntheDIScross
section the PLC suppressioncan be represented as a suppressionfactor d (k2) which is
A
multiplicativetothenucleonstructurefunctionFN(x˜,Q2)intheLCconvolutionformula
2
ofEq.(2)[23]
1 1
d (p2)= = ,
A (1+k )2 [1+(p2/M+2e )/D E ]2
A A
(10)
f/f2n2p00..89
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9
x
FIGURE 3. The x dependence of extracted F2n ratios from the DIS deuteron data[31]. Circles - LC
F2p
model,lowersquaresminimalEMCeffectuppersquaresmaximalEMCeffects.
where k is the momentum of the bound nucleon in the light cone. Finally the x depen-
dence of the suppression effect is based on the assumption that the PLC contribution in
the nucleon wave function is negligibleat x<0.3, and gives the dominant contribution
∼
at x > 0.5. We use a simple linear fit to describe the x dependence between these two
∼
valuesofx [28].
UsingtheaboveestimateofthesuppressionfactorwepresentinFig.2thecomparison
of our calculations for D E ≈M∗−M ∼0.6÷1 GeV with the old SLAC[29] and new
A
JLab[30] data. These comparisons also demonstrate that the LC calculation without
mediummodificationdisagreesstronglywiththemeasured EMCratios.
EXTRACTION OF THE NEUTRON DIS STRUCTURE FUNCTION
Withintheabovedescribed theoreticalmodel weperform theextractionofneutron DIS
stricture function F (x) with the similar procedure used in Ref.[1]. In the estimates in
2n
whichEMCeffectsaretakenintoaccountwefirst modifytheprotonstructurefunction,
smear it by Fermi motion and then subtract from the deuteron data. After correcting
by nucleon motion effects we modify back the extracted neutron structure functions to
reconstruct "free" F for neutron. The results are presented in Fig.3, which indicates
2n
thatlarger is x moreimportantare nuclearmodification effects dueto large virtualityof
nucleons(seeFig.1)involvedinDIS scattering.
CONCLUSION AND OUTLOOK
It can be shown that other models of EMC based on the modification of structure
function of nucleon exhibit similardependence on the momentum (virtuality) of bound
nucleon[14, 15]. As a result one expects that the uncertainty in the extraction of large x
DIS structure functions of the neutron from inclusive scattering off the deuteron to be
rather "model independent". This emphasizes further the urgency of understanding the
originand extentofEMCeffects relevanttolargex kinematics.
ACKNOWLEDGMENTS
Many thanks to Mark Strikman and Leonid Frankfurt for many years of collaboration
onstudiesofnuclearDISandEMCeffects.ThisworkissupportedbytheUnitedStates
DepartmentofEnergy GrantunderContract DE-FG02-01ER-41172.
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