Model independent extraction ofneutron structure functions

from deuterium data.

Svyatoslav Tkachenko

University of South Carolina

Structure functionsand parton distribution functions

Structure Functions and Moments

• Precise PDFs at large x needed as input for LHC– Large x, medium Q2 evolves to medium x, large Q2

• Moments can be directly compared with OPE (twist expansion), Lattice QCD and Sum Rules– All higher moments are weighted towards large x

PDF uncertainties(CTEQ-JLab)

From Accardi et al, arXiv.org:1102.3686v1

Structure Functions and Resonances

• Precise structure functions in Resonance Region constrain nucleon models[Separate resonant from non-resonant background; isospin decomposition]

• Needed as input for spin structure function data, radiative corrections,…

• Compare with DIS structure functions to test duality

To extract d/u ratio, we need neutron data.

F2n

F2p

14d /u

4 d /u

Extracting structure function ratio is model dependent and the results from the same data set might differ a lot depending on the model applied for analysis.

d

u

4 F2n F2 p 1

4 F2n F2 p

Large x - Large Nuclear Effects

• Even simple “Fermi Smearing” leads to significant dependence on D wave function

• Different models for off-shell and “EMC” effects lead to large additional variations

• Contributions from MEC, (1232) and “exotic” degrees of freedom unknown

• FSI?

Deuteron wave function model dependence

R – ratio of deuteron and nucleon F2 structurefunctions

From Accardi et al, arXiv.org:1102.3686v1

Bound neutron… Free neutron…

How can we study free neutron structure without free neutrons available?

Emulate them with nuclear targets: – In 3He, due to fortuitous cancellation of proton spins,

we can study neutron spin structure.

– If we can find observables that are mostly sensitive to the low-momentum part of the deuteron wave function, we can treat the nucleons as quasi-free and thus study neutrons.

Spectator tagging

(aka pinpointing the low-momentum part of the deuteron wave function)

Spectator Tagging

pS E S ,p S ; S ES

p S ˆ q

M D /2

pn MD ES ,p S ;

n 2 S

W 2 M 2 2M Q2

W *2 pn q 2 pn pn 2 (MD Es )

p n

q Q 2

M *2 2M(2 S ) Q 2

x Q 2

2 pnq

Q 2

2M (2 S ) *

E = 4.223 GeV

e

p

n <Q2> = 1.19 (GeV/c)2

“Rules” for the spectator.Final state interactions.

The momentum and angular dependence of the ratio of spectral functions with andwithout FSI effects. Blue boxes mark preferred kinematics – regions where FSI havesmaller effect.

Ciofi degli Atti and Kopeliovich, Eur. Phys. J. A17(2003)133

“Rules” for the spectator.“Off-shellness” depends on the spectator momentum magnitude.

Ratio of the bound to free F2 neutron structure functions vs spectator momentum. Model by W.Melnitchouk. Preferred kinematics denoted by blue box.

Rules for the spectator.Summary.

Low momentum spectatorsPS < 100 MeV/c

Minimize uncertainty due tothe deuteron wave function and on-shell extrapolation. O (1%) correction.

Backward kinematicsθqp > 110o

Minimize effects from FSI andtarget fragmentation.O (5%) correction.

Validation of the spectator tagging method (BoNuS experiment)

• Check angular dependence of effective (bound) structure functions in comparison with PWIA spectator model

• Check spectator momentum dependence of effective (bound) structure functions in comparison with PWIA spectator model

Low Spectator Momenta - Nearly Free Neutrons ?

*BoNuS = Bound Nucleon Scattering

**RTPC = Radial Time Projection Chamber

Radial TPC (view from downstream)

e-backwards p

The Experiment

BoNuS

Region

VIPs

0.07 0.2 GeV/c

D (r p )

2

CLAS

20%

Bonus Radial Time Projection Chamber.(Detector system for slow protons)

•Thin-walled gas target (7 atm., room temperature)

•Radial Time Projection Chamber (RTPC) with Gaseous Electron Multipliers (GEMs)

•4 - 5 Tesla longitudinal magnetic field (to suppress Möller electrons and to measure momentum)

•3-dimensional readout of position and energy loss (“pads”)

Spectator momentum dependence (preliminary)

Ratio to simulation Effective F2n

Simulation uses PWIA spectator model, radiative effects, full model of RTPC and CLAS.P. Bosted and M.E. Christy F2

n model is used.

78 MeV/c 93 MeV/c

110 MeV/c 135 MeV/c

78 MeV/c 93 MeV/c

110 MeV/c 135 MeV/c

Backwards angles (cos θpq < -0.2) data are shown

Angular dependence(preliminary)

78 MeV/c 93 MeV/c

110 MeV/c 135 MeV/c

Q2 = 1.66 (GeV/c)2

W* = 1.73 GeV

• No significant deviations from PWIA (ps<100 MeV/c), first 2 panels

• Possible θ dependence at higher momenta

Extracted F2n (analyses comparison)

(preliminary)

▼ - Analysis 1

■ - Analysis 2

Simulation in PWIA spectator picture

CTEQ-JLab band

Systematic errors shown for analysis 1

Extracted F2n/F2

p (N. Baillie)

Plans for 12 GeV

BoNuS

E12-06-113E12-06-113

• Data taking of 35 days on D2 and 5 days on H2 with L = 2 · 10

34 cm-2 sec-1

• Planned BoNuS detector DAQ and trigger upgrade

• DIS region with – Q 2 > 1 GeV

2/c 2

– W *> 2 GeV

– ps < 100 MeV/c

– pq > 110°

• Largest value for x* = 0.80 (bin centered x* = 0.76)

• Relaxed cut of W *> 1.8 GeVgives max. x* = 0.83

CLAS12CentralDetector

Conclusions

• Preliminary analysis does not contradict spectator model

• Technically different analyses of BoNuS data converge

• Analysis note review underway

• BoNuS12 proposal approved