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Model independent extraction ofneutron structure functions
from deuterium data.
Svyatoslav Tkachenko
University of South Carolina
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Structure functionsand parton distribution functions
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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
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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
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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
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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
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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.
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Spectator tagging
(aka pinpointing the low-momentum part of the deuteron wave function)
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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
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“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
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“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.
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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.
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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
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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%
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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”)
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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
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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
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Extracted F2n (analyses comparison)
(preliminary)
▼ - Analysis 1
■ - Analysis 2
Simulation in PWIA spectator picture
CTEQ-JLab band
Systematic errors shown for analysis 1
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Extracted F2n/F2
p (N. Baillie)
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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
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Conclusions
• Preliminary analysis does not contradict spectator model
• Technically different analyses of BoNuS data converge
• Analysis note review underway
• BoNuS12 proposal approved