Precision Measurements and Studies of Possible Nuclear Medium Modifications of and of Separated Structure Functions F1, FL,
F2
Simona Malace (contact/spokesperson)Jefferson Lab
Joint Hall A/C Summer Meeting, June 5-6 2014
Spokespeople: D. Gaskell, C. Keppel, E. Christy, P. Solvignon
OutlineElectron β proton scattering formalism
The Parton Model and Structure Functions
The QCD Parton Model: Parton Distributions Functions (PDFs)
Nuclear Parton Distribution Functions (nPDFs)
Structure Functions from Experiment: Rosenbluth L/T separations
Experimental Status of Rosenbluth L/Ts in DIS
R and FL on proton
R in nuclei: to what degree is R modified by the nuclear medium?
How large of a nuclear medium modification of R is βsignificantβ?
Proposed measurements and their impact
Beam time request
Proposal: Motivation and Proposed Measurements
Formalism: Electron-Proton Scattering Electron-nucleon scattering: we probe the nucleon inner structure of quarks
and gluons
Lorentz invariant kinematics:
π₯=π2/2π (πΈ1βπΈ3)
π2=4πΈ1πΈ3 π ππ2(π /2)
π=πΈ1βπΈ3π¦=1β
πΈ3πΈ1
ππ=(πΈ π ,ππ)
Lorentz invariant cross section:
=
Pure magnetic structure function: reflects the probability of
photoabsorption of transversely (helicity +/- 1) polarized virtual photons
Electromagnetic structure function
Natural basis: F1(T) (transversely polarized virtual photon) and FL (longitudinally polarized virtual photon)
Formalism: The Parton Model Electron-nucleon scattering: zero order approximation = incoherent elastic
scattering off spin Β½ βquasi-freeβ quarks inside the proton (Infinite Momentum Frame)
ππππ2=
4π πΌ2ππβ2
π4 [ (1β π¦ )+ π¦2
2 ]
Elastic electron-quark scattering cross section: elementary differential cross section reflecting the interaction probability between an electron and a quark carrying a fraction x of the proton momentum
Assume there are q(x)dx quarks of type q within a proton with momenta between x and x+dx
ππππ2=
4π πΌ2ππβ2
π4 [ (1β π¦ )+ π¦2
2 ]βπ (π₯ )ππ₯
Electron-proton scattering cross section:
π2πππ₯ππ2=
4π πΌ2
π4 [ (1β π¦ )+ π¦2
2 ]β ππβ2 π (π₯ )
πΉ 2 (π₯ )=2 π₯ πΉ 1 (π₯ )=π₯βπππβ
2 π (π₯ )Bjorken Scaling
FL(x) = 0
Formalism: Corrections to the Parton Model
πΉ 2 (π₯ ,π2 )=π₯βπππβ
2 (π (π₯ )+Ξπ (π₯ ,π2))
ln()+β¦
QCD corrections to Quark-Parton Model: Bjorken scaling violations
Perturbative logarithmic corrections (leading twist) - the struck quark sits in a sea of quark-antiquark pairs and of gluons
Non-perturbative (1/Q2)n corrections (higher twist) - the struck quark communicates with the other valence quarks via gluon exchange (specific to the resonance and elastic regimes); contribution from these corrections is suppressed at high Q2
splitting functions
leading twist higher twists
Formalism: The QCD Parton Model QCD Parton Model: leading twist perturbative calculation via the factorization
theorem
IR safe hard scattering cross sections calculable in pQCD (currently to NNLO in the expansion)
Parton Distribution Functions (PDFs): IR singular (contain all collinear and soft singularities) but process independent - universal
πΉ lπ΄β (π₯ ,π ,πΌπ (π) )= βπ=π ,π
π ππ΄β(x ,ΞΌ ,πΌπ (π))β¨πΉ ππβ(π₯ ,ππ ,πΌπ (π))
πΎβ+πβπ
PDFs scale (m) transformation controlled by the pQCD evolution equation (DGLAP)
m()(β,)
QCD Parton Model: leading twist perturbative calculation via the factorization theorem
πΉ lπ΄β (π₯ ,π ,πΌπ (π) )= βπ=π ,π
π ππ΄β(x ,ΞΌ ,πΌπ (π))β¨πΉ ππβ(π₯ ,ππ ,πΌπ (π))
Formalism: The QCD Parton Model
()(β,)
From theory: the hard scattering cross sections the evolution kernel to calculate the scale dependence of the PDFs educated guess for the PDFs x functional form at some scale m = Q0 β f(x,Q0) = A0xA1(1-x)A2P(x)
From data: cross sections (or structure functions) over a wide kinematic phase space:
Formalism: The Nucleon Structure in QCD Global QCD analyses: universal PDFs have been extracted from global QCD
analyses and the pQCD Q2 evolution has been verified by experiment to high degree of accuracy
We can verify QCD sum rules; make precision determinations of as
We have a theory with predictive power
We can predict cross sections for both SM and New Physics at any energy
Higgs production at LHC dominated by the βgluon-gluon fusionβ
pQCD prediction (2013)
gluon, as induced uncertainty
PDFs become input for searches of new physics
Formalism: Nuclear PDFs Nuclear PDFs: the free proton framework is typically used to analyze nuclear
data in search of process-independent nuclear PDFs (nPDFs)
Assumptions: Factorization nPDFs obey the same evolution equations and sum rules as free PDFs Isospin symmetry: Some collaborations: neglect nuclear modifications in deuterium β¦.
π’π / π΄ (π₯ )=ππ / π΄ (π₯ ) ,ππ /π΄ (π₯ )=π’π /π΄ (π₯ )
Formalism: Nuclear PDFs Nuclear PDFs: the free proton framework is typically used to analyze nuclear
data in search of process-independent nuclear PDFs (nPDFs)
Example: EPS09
πβπ+π΄β π+ π= β
π=π ,π ,ππ π΄π
β(π2)βοΏ½ΜοΏ½βπ+πβπ+π (π2)Factorization:
nPDF obeying standard DGLAP
usual hard scattering cross section
nPDF: π π΄πβ (π₯ ,π2 )=π π΄πβ(π₯ ,π2) π ππβ(π₯ ,π2)
free proton PDFs
Nuclear modifications to the free proton PDFs
Data: most constraints from charged lepton scattering DIS (F2A/F2
D) but few also from Drell-Yan dilepton production on p+A and from neutral pion production on dAu and pp
Nuclear PDFs: EPS09 Not enough data to allow for an independent extraction of each parton flavor;
only 3 distributions: valence, sea, gluons
open circles: data on s2A/A/s2
D/2 from SLAC
πβπ+π΄β π+ π
Nuclear PDFs: Importance The collinear factorization framework has been used to extract universal nPDFs
by several groups
Most nPDFs extractions rely on experimental constraints from: DIS charged lepton scattering e+A/e+D Drell-Yan dileptons in p+A/p+d and RHIC d+Au/p+p very few use neutrino-nucleus DIS Whether this framework is applicable to a wider class of processes remains
to be verified
Important application of nPDFs: study of the properties of the quark-gluon plasma
DIS Structure Functions from Experiment Technically the separated L and T contributions to the total cross section are
needed to extract F1, FL, F2
Ξ= πΌ2π 2π2
πΈ β²πΈ
πΎ1βπ ,πΎ=π(1βπ₯ )
π=1/ (1+2(1+ π2
π2 )π‘ππ2(π2))
π2ππΞ©ππΈ β²=Ξ (π π (π₯ ,π2 )+ππ πΏ (π₯ ,π2 ))=Ξ ππ (1+ππ )
transversely longitudinallypolarized virtual photon cross sections
ππ (π ,πΈπ )= πΎπ4π 2πΌ
ππ (π₯ ,π2)π π³ (π ,πΈπ )=2 π₯πΎπ4 π2πΌ
π πΏ(π₯ ,π2) =AND
RA-RD needed to transition from cross sections to structure functions ratios
[1-] 1-]
Example: When transitioning from cross sections to F2 at low Q2 and moderate x, a small change (0.08) in R (~0.2) leads to few % (up to 4) change in F2
Formalism: Rosenbluth L/T Separations
),( 2QxTsintercept
),( 2QxLs
slope
The L & T contributions are separated by performing a fit of the reduced cross section dependence with e at fixed x and Q2
)Ξ΅Ο+(Ο=dEd
dLT'
21s
Requirements for precise L/T extractions:
As many e points as possible spanning a large interval from 0 to 1 as many (E, Eβ, q) settings as possible
Very good control of point-to-point systematics 1-2 % on the reduced cross section translates into 10-15 % on FL
Most precise, model-independent extractions come from dedicated experiments where all e points have been measured in a short time interval
Formalism: RA β RD Extraction
))(1
1( DAD
TD
TA
D
A RRR
=
ee
ss
ss
RA β RD and sAT/sD
T are extracted by performing a fit of the cross section ratio dependence with eβ at fixed x and Q2
DR=
ee
e1
,
Example: extraction from SLAC E140
Phys. Rev. D 86 054009 (2012)
R: small quantity (< 1)
Even a small RA β RD in absolute value could imply
non-negligible nuclear medium modifications of R
x = 0.175, Q2 = 4 GeV2
DR = 0.04 20% effect
R = 0.2
DIS Measurements of Rp: HERA R and FL structure function are determined in a model independent way from
cross section measurements at the same x and Q2 using 3 energies (Ep = 460, 575 and 920 GeV)
At HERA low to intermediate Q2
corresponds to very low x
HERA provided constraints for the gluon PDF: gluon PDF related uncertainty of the pQCD prediction for the Higgs production cross section was ~25% before HERA, after ~5%
x = 10-4 β 10-3
DIS Measurements of Rp: SLAC and JLab E140x and E99-118 (L/T dedicated experiments): R is determined in a model
independent way from cross section measurements at the same x and Q2 using multiple beam energies
Nuclear Dependence of R: Experimental Status
NMC: Phys. Lett. B 294, 120 (1992)
)(011.0)(016.0031.0 syststatRR PD
22 925.001.0 GeVQx
)(020.0)(026.0027.0 syststatRR CCa
22 420.001.0 GeVQx
Conclusion: DR consistent with zero
NMC: Nucl. Phys. B 481, 23 (1996)
)(026.0)(021.0040.0 syststatRR CSn
22 105.001.0 GeVQx
DR: positive shift?
HERMES: Phys. Lett. B 567, 339 (2003)22 155.065.001.0 GeVQx
DNDHe RRRR // 143
Model-dependent extractions of RA-RD: NMC (DR extracted using Q2 dependent fit at fixed x), HERMES (one beam energy only, assumed RA/RD scales with Q2)
Nuclear Dependence of R: Experimental Status
Hint from JLab L/T separations on D and Al, C, Cu, Fe in the resonance region: R appears to be modified by the nuclear medium
E04-001/E06-109 (Hall C): paper to be submitted for publication within the next month
Model-independent extractions of RA-RD: SLAC E140 (DIS) β no Coulomb corrections applied
E04-001/E06-109 (Res Region)
Nuclear Dependence of R in DIS: Experimental Status Coulomb effects have not been accounted for in the SLAC E140 analysis (correction
is non-negligible at SLAC and JLab kinematics)
Re-analysis of combined data sets from E140 (Fe), E139 (Fe) and Hall C (Cu) at x = 0.5 and Q2 = 4 - 5 GeV2 arXiv:0906:0512
Coulomb corrections calculated within the Effective Momentum Approximation framework the eβ dependence of the cross section ratios sA/sD has been fitted to extract RA - RD
No Coulomb Corrections
DR 2s from zero
With Coulomb Corrections
βSince the nuclear dependence of R has not as yet been systematically measured, we shall test two assumptions for βRβ¦β
1) (Absolute) RA β RD = 0.04
2) (Relative) (RA β RD)/RN = 30%
Both assumptions based on NMC RSn β RC
EMC, BCDMS, NMC: e ~ 1
V. Guzey et al., PRC 86 045201 (2012)
The impact of a non-zero DR for the antishadowing region has been analyzed
Two data sets have been analyzed:
),(),(2
2
22
QxFQxF
D
A
D
A ss
SLAC: e < 1
),(),(
),(),(
22
22
21
21
QxFQxF
QxFQxF
D
A
D
AD
A
ss
Implications of Ξ π β 0
The impact of a non-zero DR for the antishadowing region
Antishadowing from longitudinal photons? Antishadowing disappears for F1 ratio,
F1A/F1DF2A/F2D
remains for F2
Implications of Ξ π β 0V. Guzey et al., PRC 86 045201 (2012)
A very well measured behaviour like the EMC effect still offers surprises β the tension between low e JLab and high e SLAC data on heavy targets
EMC slope β SRC correlation: The SRC and EMC effect: a common (as yet unknown) origin SRC: measure of some quantity like local density experienced by a nucleon in a correlated pair which gives rise to the EMC effect
If R is A-dependent this interpretation needs revisionHowever:
Does the correlation between -dREMC/dx and SRC apply the same to F2, F1, FL?
EMC effect:
Implications of Ξ π β 0
We propose to extract Rp, RD - Rp, RA β RD, for C, Cu, Au, F1, FL, F2 in a model independent fashion in a x range from 0.1 to 0.6 and Q2 from 1 to 5 GeV2
to cover the antishadowing and most of the EMC effect regions
For each L/T extraction (black stars) we would use:
both Hall C spectrometers, SHMS and HMS up to 6 beam energies: 4 standard (4.4, 6.6, 8.8, 11 GeV) and 2 non-standard (5.5 and 7.7 GeV) D, Cu targets for all kinematics shown; H, C, Au at select kinematics
Statistical goal: 0.2 β 0.5% (depending on the target) in a W2 bin of 0.1 GeV2
Proposal: Central Kinematics
(E, Eβ, q)
SHMS has a large momentum βbiteβ: we will collect a wealth of data within the spectrometers acceptance
Besides the model-independent L/T separations at the central kinematics, we can perform minimally model-dependent L/Ts within the spectrometers acceptance
Proposal: Kinematics
Proposal: Backgrounds and Corrections Charge-Symmetric Background
Radiative Corrections
Largest contribution 20% (less at most kinematics); the background will be measured with same spectrometer as the signal
Elastic/quasielstic radiative effects: < 20%; total radiative effects within 40% To test our understanding of external radiative corrections we will take
measurements on a 6% r.l. Cu target at x = 0.25, 0.275 and 0.4
Pion Background Upper limits on p/e ratio: < 2% contamination Much smaller at most settings
We will take additional measurements to constrain/verify Coulomb corrections procedure
At fixed e we expect sAu/sD to scale with Q2, any measured variation would be mostly due to Coulomb corrections
Coulomb Corrections
Proposal: Impact for Rp
We plan to map the x and Q2 dependence of Rp independently
Without our proposed measurements very few model-independent, true Rosenbluth L/Ts at low to moderate x and Q2
Proposal: Impact for RD-Rp
We plan to map the x and Q2 dependence of RD-Rp independently
Without our proposed measurements very few model-independent, true Rosenbluth L/Ts at low to moderate x and Q2
Impact for Rp and RD-Rp: Summary We will pin down in detail the x and Q2 dependence of Rp in a kinematic region where
the contribution to the structure functions coming from R is not negligible We will extend the RD β Rp measurements to higher Q2 and verify whether the difference
between RD and Rp previously observed at Q2 < 1.5 GeV2 disappears at higher Q2 as the very few points from SLAC indicate
Proposal: Impact for FL The FL structure function has strong sensitivity to the nonperturbative initial state
distribution of gluons First few orders of the Nachtmann proton FL moments
calculated from data to test pQCD calculations Phys. Rev. Lett. 110, 152002 (2013)
Our proposed measurements (not shown here) would provide constraints for the integrals at low to intermediate x between Q2 of 1 and 5 GeV2 with very similar precision as E94110 (black circles)
Proposal: Impact for RA-RD We plan to map the x and Q2 dependence of RA-RD independently by measuring on a
Copper target
We will use C and Au to measure RA-RD at select kinematics to check primarily the A-dependence of possible medium modifications of R
Proposal: Impact for RA-RD Existing data have shown that there is not a huge effect on R induced by the nuclear
medium Recent analyses have shown that a huge effect is NOT needed to change the way we
think about the origin of the antishadowing or about the EMC effect (a 30% change would be sufficient, for example)
The quality and quantity of existing data is not sufficient to pin down nuclear effects with a high level of precision
We propose to measure via true, model-independent Rosenbluth L/Ts RA-RD in one dedicated experiment and set the most precise constraints to date on possible nuclear medium modifications of R we would map the x and Q2
dependence separately
we would map a possible A dependence
Proposal: Impact for sA/sD
Our data can be used to constrain/verify the universality of the nuclear modification as seen in sA/sD in charged lepton scattering and could be included in nPDF fits
Our proposed measurements are shown only at central kinematics; due to the large acceptance of SHMS/HMS constraints from our data would extend to lower and higher x than shown
Proposal: Beam Time Request β 22 PAC daysProduction time per target
Beam time request for all activities
We use H and D to extract Rp, RD-Rp and structure functions We use D and Cu to measure medium
modifications of R and their possible dependence with x and Q2
We use D, C, Au to measure medium modifications of R and their A dependence
We allocated time for: systematic checks background measurements measurements to constrain Coulomb corrections configuration changes
We need a total of 22 PAC days
Summary Theoretical and experimental efforts over the past decades have produced a robust framework
for studying the free nucleon structure and its dynamics in terms of quark and gluon distributions and their fundamental interactions
Work is being done to apply a similar framework to the study of the nucleon structure when bound in nuclei
The predictive power of the pQCD Parton Model allows for studies of unexplored physics (within SM) or new physics, beyond the SM
DIS Charged lepton scattering measurements of cross sections and structure functions played/plays a major role in this endeavor
Accessing F1,2,L or F2A/F2
D requires the knowledge of R and the current status of experimental determinations of this quantity shows that more model-independent Rosenbluth L/T separations are needed for free and bound nucleons
Recent analyses have shown that even modest medium modifications of R allowed by the existing low-precision data could change the way we think about the origin of the antishadowing region or the EMC effect
We propose to extract Rp, RD - Rp, RA β RD, for C, Cu, Au, F1, FL, F2 in a model independent fashion in a x range from 0.1 to 0.6 and Q2 from 1 to 5 GeV2 to cover the antishadowing and most of the EMC effect regions
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