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 – 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 “significant”?

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:

𝑥=𝑄2/2𝑀 (𝐸1−𝐸3)

𝑄2=4𝐸1𝐸3 𝑠𝑖𝑛2(𝜃 /2)

𝜗=𝐸1−𝐸3𝑦=1−

𝐸3𝐸1

𝑝𝑖=(𝐸 𝑖 ,𝑝𝑖)

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 ½ “quasi-free” quarks inside the proton (Infinite Momentum Frame)

𝑑𝜎𝑑𝑄2=

4𝜋 𝛼2𝑒𝑞❑2

𝑄4 [ (1− 𝑦 )+ 𝑦2

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

𝑑𝜎𝑑𝑄2=

4𝜋 𝛼2𝑒𝑞❑2

𝑄4 [ (1− 𝑦 )+ 𝑦2

2 ]∗𝑞 (𝑥 )𝑑𝑥

Electron-proton scattering cross section:

𝑑2𝜎𝑑𝑥𝑑𝑄2=

4𝜋 𝛼2

𝑄4 [ (1− 𝑦 )+ 𝑦2

2 ]∑ 𝑒𝑞❑2 𝑞 (𝑥 )

𝐹 2 (𝑥 )=2 𝑥 𝐹 1 (𝑥 )=𝑥∑𝑞𝑒𝑞❑

2 𝑞 (𝑥 )Bjorken Scaling

FL(x) = 0

Formalism: Corrections to the Parton Model

𝐹 2 (𝑥 ,𝑄2 )=𝑥∑𝑞𝑒𝑞❑

2 (𝑞 (𝑥 )+Δ𝑞 (𝑥 ,𝑄2))

ln()+…

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

𝐹 l𝐴❑ (𝑥 ,𝑄 ,𝛼𝑠 (𝜇) )= ∑𝑎=𝑞 ,𝑔

𝑓 𝑎𝐴❑(x ,μ ,𝛼𝑠(𝜇))⨂𝐹 𝜆𝑎❑(𝑥 ,𝑄𝜇 ,𝛼𝑠 (𝜇))

𝛾∗+𝑎→𝑋

PDFs scale (m) transformation controlled by the pQCD evolution equation (DGLAP)

m()(’,)

QCD Parton Model: leading twist perturbative calculation via the factorization theorem

𝐹 l𝐴❑ (𝑥 ,𝑄 ,𝛼𝑠 (𝜇) )= ∑𝑎=𝑞 ,𝑔

𝑓 𝑎𝐴❑(x ,μ ,𝛼𝑠(𝜇))⨂𝐹 𝜆𝑎❑(𝑥 ,𝑄𝜇 ,𝛼𝑠 (𝜇))

Formalism: The QCD Parton Model

()(’,)

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 – 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 “gluon-gluon fusion”

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 ….

𝑢𝑛 / 𝐴 (𝑥 )=𝑑𝑝 / 𝐴 (𝑥 ) ,𝑑𝑛 /𝐴 (𝑥 )=𝑢𝑝 /𝐴 (𝑥 )

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

𝜎❑𝑙+𝐴→ 𝑙+ 𝑋= ∑

𝑖=𝑞 ,𝑞 ,𝑔𝑓 𝐴𝑖

❑(𝜇2)⊗�̂�❑𝑙+𝑖→𝑙+𝑋 (𝜇2)Factorization:

nPDF obeying standard DGLAP

usual hard scattering cross section

nPDF: 𝑓 𝐴𝑖❑ (𝑥 ,𝑄2 )=𝑅 𝐴𝑖❑(𝑥 ,𝑄2) 𝑓 𝑝𝑖❑(𝑥 ,𝑄2)

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

𝜎❑𝑙+𝐴→ 𝑙+ 𝑋

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

Γ= 𝛼2𝜋 2𝑄2

𝐸 ′𝐸

𝐾1−𝜀 ,𝐾=𝜈(1−𝑥 )

𝜀=1/ (1+2(1+ 𝜈2

𝑄2 )𝑡𝑎𝑛2(𝜃2))

𝑑2𝜎𝑑Ω𝑑𝐸 ′=Γ (𝜎 𝑇 (𝑥 ,𝑄2 )+𝜀𝜎 𝐿 (𝑥 ,𝑄2 ))=Γ 𝜎𝑇 (1+𝜀𝑅)

transversely longitudinallypolarized virtual photon cross sections

𝑭𝟏 (𝒙 ,𝑸𝟐 )= 𝐾𝑀4𝜋 2𝛼

𝜎𝑇 (𝑥 ,𝑄2)𝑭 𝑳 (𝒙 ,𝑸𝟐 )=2 𝑥𝐾𝑀4 𝜋2𝛼

𝜎 𝐿(𝑥 ,𝑄2) =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

)εσ+(σ=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, E’, 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 – RD Extraction

))(1

1( DAD

TD

TA

D

A RRR

=

ee

ss

ss

RA – RD and sAT/sD

T are extracted by performing a fit of the cross section ratio dependence with e’ 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 – 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 – 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) – 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 e’ 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

“Since the nuclear dependence of R has not as yet been systematically measured, we shall test two assumptions for ∆R…”

1) (Absolute) RA – RD = 0.04

2) (Relative) (RA – RD)/RN = 30%

Both assumptions based on NMC RSn – 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 Δ 𝑅≠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 Δ 𝑅≠0V. Guzey et al., PRC 86 045201 (2012)

A very well measured behaviour like the EMC effect still offers surprises – the tension between low e JLab and high e SLAC data on heavy targets

EMC slope – 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 Δ 𝑅≠0

We propose to extract Rp, RD - Rp, RA – 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 – 0.5% (depending on the target) in a W2 bin of 0.1 GeV2

Proposal: Central Kinematics

(E, E’, q)

SHMS has a large momentum “bite”: 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 – 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 – 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 – 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