measurements of r and the longitudinal and transverse structure functions in the nucleon resonance...
TRANSCRIPT
Measurements of R and the Longitudinal and Transverse Structure Functions in the Nucleon Resonance Region and Quark-Hadron Duality
Rolf Ent, DIS2004
-Formalism: R, 2xF1, F2, FL
-E94-110: L/T Separation at JLab-Quark-Hadron Duality
-Or: Why does DIS care about the Resonance Region?-If time left: Duality in nuclei/g1
-Summary
Inclusive Inclusive e + p e’ + X scattering scattering
Single Photon Exchange
Elastic Resonance DIS
Alternatively:
)(' LT
dEd
d
onpolarizati allongitudin relative : ε
photons virtualpolarizedely transversofflux :Where
)/)2/(tan2/( 212'
MFFdEd
dmott
12xF
FR L
T
L
)2/(sin4
)2/(cos42
22
Emott 122
22
2)4
1( xFFQ
xMFL
Resonance Region L-Ts Needed ForResonance Region L-Ts Needed For
Extracting spin structure functions from spin asymmetries
/2 –
3/2
1/2
+ 3/2
A1 =
g
1
=
1/2 –
3/2
A1
A1
2T
=F
1(A
1 – A
2)
1 + 2From measurements of F
1 and A
1
extract 1/2
and 3/2
!
(Get complete set of transverse helicity amplitudes)
R (for R small)
_~
_~F
2(1 + R)
1 + R(Only insensitive to R if F2 in relevant (x,Q2)
region was truly measured at = 1)
G0
SOS
HMS
E94-110 Experiment performed at JLab-Hall C
JLab-HALL CJLab-HALL C
Shielded Detector Hut
Superconducting Dipole
Superconducting Quadrupoles
Electron Beam
Target Scattering Chamber
HMS
SOS
Thomas Jefferson National Accelerator Facility
Rosenbluth SeparationsRosenbluth Separations Hall C E94-110: a global survey of longitudinal strength in the resonance region…...
T
L +T
= L T/
(polarization of virtual photon)
Thomas Jefferson National Accelerator Facility
Spread of points about the linear fits is Gaussian with ~ 1.6 % consistent with the estimated point-point experimental uncertainty (1.1-1.5%)
a systematic “tour de force”
Hall C E94-110: a global survey of longitudinal strength in the resonance region…...
Rosenbluth SeparationsRosenbluth Separations
Thomas Jefferson National Accelerator Facility
World's L/T Separated Resonance DataWorld's L/T Separated Resonance Data
(All data for Q2 < 9 (GeV/c)2)
R = L/T
<
R = L/T
<
Thomas Jefferson National Accelerator Facility
World's L/T Separated Resonance DataWorld's L/T Separated Resonance Data
Now able to study the Q2 dependence of individual resonance regions!
Clear resonant behaviour can be observed!
Use R to extractF2, F1, FL
(All data for Q2 < 9 (GeV/c)2)
R = L/T
<
R = L/T
E94-110 Rosenbluth Extractions of R E94-110 Rosenbluth Extractions of R ● Clear resonant behaviour is observed in R for the first time!
→ Resonance longitudinal component NON-ZERO.
→ Transition form factor extractions should be revisited.
● Longitudinal peak in second resonance region at lower mass than S 11(1535 MeV)
→ D13(1520 MeV) ? P11(1440 MeV)?
● R is large at low Q high W (low x)
→ Was expected R → 0 as Q2 → 0
→ R → 0 also not seen in recent SLAC
DIS analysis (R1998)
Kinematic Coverage of ExperimentKinematic Coverage of Experiment
● Rosenbluth-type separations where possible (some small kinematic evolution is needed)
● Iteratively fit F2 and R over the entire kinematic range.
2 Methods employed for separating Structure Functions:
R = (d/) =(W
2,Q2) + L(W2,Q2)
Also perform cross checks with elastic and DIS (comparing with SLAC data)
L-T Separated Structure FunctionsL-T Separated Structure Functions
Good agreement between methods ( model available for use!) Very strong resonant behaviour in F
L!
Evidence of different resonances contributing in different channels?
Thomas Jefferson National Accelerator Facility
First observed ~1970 by Bloom and Gilman at SLAC by comparing resonance production data with deep inelastic scattering data
. Integrated F2 strength in Nucleon Resonance region equals strength under scaling curve. Integrated strength (over all ’) is called Bloom-Gilman integral
Shortcomings:
• Only a single scaling curve and no Q2 evolution (Theory inadequate in pre-QCD era)
• No L/T separation F2 data depend on assumption of R = L/T
• Only moderate statistics
Duality in the F2 Structure Function
’ = 1+W2/Q2
Q2 = 0.5 Q2 = 0.9
Q2 = 1.7 Q2 = 2.4
F 2
F 2
Thomas Jefferson National Accelerator Facility
First observed ~1970 by Bloom and Gilman at SLAC
Now can truly obtain F2 structure function data, and compare with DIS fits or QCD calculations/fits (CTEQ/MRST)
Use Bjorken x instead of Bloom-Gilman’s ’
Bjorken Limit: Q2, Empirically, DIS region is
where logarithmic scaling is observed: Q2 > 5 GeV2,
W2 > 4 GeV2
Duality: Averaged over W, logarithmic scaling observed to work also for Q2
> 0.5 GeV2, W2 < 4 GeV2, resonance regime
(note: x = Q2/(W2-M2+Q2) JLab results: Works
quantitatively to better than 10% at such low Q2
Duality in the F2 Structure Function
Numerical Example: Resonance Region F2
w.r.t. Alekhin Scaling Curve(Q2 ~ 1.5 GeV2)
Thomas Jefferson National Accelerator Facility
Duality in FDuality in FTT and F and FLL Structure Functions Structure Functions
Duality works well for both FT and FL above Q2 ~ 1.5 (GeV/c)2
MRST (NNLO) + TMMRST (NNLO)
AlekhinSLACE94-110
Also good agreement with SLAC L/T Data
Thomas Jefferson National Accelerator Facility
Quark-Hadron Duality
complementarity between quark and hadron descriptions of observables
Hadronic Cross Sectionsaveraged over appropriate
energy range
hadrons
Perturbative Quark-Gluon Theory
=
At high enough energy:
quarks+gluons
Can use either set of complete basis states to describe physical phenomena
But why also in limited local energy ranges?
If one integrates over all resonant and non-resonant states, quark-hadron duality should be shown by any model. This is simply unitarity.However, quark-hadron duality works also, for Q2 > 0.5 (1.0) GeV2, to better than 10 (5) % for the F2 structure function in both the N- region and the N-S11 region!(Obviously, duality does not hold on top of a peak! -- One needs an appropriate energy range)
One resonance + non-resonant background
Few resonances + non-resonant background
Why does local quark-hadron duality work so well, at such low energies?
~ quark-hadron transition
Confinement is local ….
Thomas Jefferson National Accelerator Facility
Quark-Hadron Duality – Theoretical Efforts
N. Isgur et al : Nc ∞ qq infinitely narrow resonances qqq only resonances
Distinction between Resonance and Scaling regions is spuriousBloom-Gilman Duality must be invoked even in the Bjorken Scaling region
Bjorken Duality
One heavy quark, Relativistic HO
Scaling occurs rapidly!
Q2 = 5
Q2 = 1
F. Close et al : SU(6) Quark ModelHow many resonances does one needto average over to obtain a completeset of states to mimic a parton model?56 and 70 states o.k. for closureSimilar arguments for e.g. DVCS and semi-inclusive reactions
u
Thomas Jefferson National Accelerator Facility
Duality ‘’easier” established in Nuclei
The nucleus does the averaging for you!
EMC EffectFe/D
ResonanceRegion Only
( F
e/
D)
IS
(= x corrected for M 0)
Nucleons haveFermi motionin a nucleus
Thomas Jefferson National Accelerator Facility
CLAS: N- transition region turns positive at Q2 = 1.5 (GeV/c)2 Elastic and N- transition cause most of the higher twist effects
… but tougher in Spin Structure Functions
g1p
CLAS EG1
Pick up effects of both N and (the is not negative enough….)
Thomas Jefferson National Accelerator Facility
Hint of overall negative g1n even in resonance region at Q2 = 1.2 (GeV/c)2
Duality works better for neutron than proton? – Under investigation
… but tougher in Spin Structure Functions (cont.)
g1n
SLAC E143: g1p and g1
d data combined
SummarySummary
Performed precision inclusive cross section measurements in the nucleon resonance region (~ 1.6% pt-pt uncertainties)
R exhibits resonance structure (first observation) Significant longitudinal resonant component observed.
Prominent resonance enhancements in R and FL different from those in transverse and F2 Quark-hadron duality is observed for ALL unpolarized
structure functions. Quarks and the associated Gluons (the Partons) are tightly bound in Hadrons
due to Confinement. Still, they rely on camouflage as their best defense:a limited number of confined states acts as if consisting of free quarks Quark-Hadron Duality, which is a non-trivial property of QCD, telling usthat contrary to naïve expectation quark-quark correlations tend to cancelon average
Observation of surprising strength in the longitudinal channel at Low Q2 and x ~ 0.1
Thomas Jefferson National Accelerator Facility
. Moments of the Structure Function Mn(Q2) = dx xn-2F(x,Q2)
If n = 2, this is the Bloom-Gilman duality integral!
. Operator Product Expansion
Mn(Q2) = (nM02/ Q2)k-1 Bnk(Q2)
higher twist logarithmic dependence
. Duality is described in the Operator Product Expansion as higher twist effects being small or canceling
DeRujula, Georgi, Politzer (1977)
QCD and the Operator-Product Expansion
0
1
k=1
Thomas Jefferson National Accelerator Facility
Example: e+e- hadrons
Textbook Example
Only evidence of hadrons produced is narrow states oscillating around step function
R =
E99118
Preliminary: Still R = 0.1 point-to-point(mainly due to bin centering assumptions to x = 0.1)
Model Iteration Procedure Model Iteration Procedure
Starting model is used for input for radiative corrections and in bin-centering the data in θ
σexp is extracted from the data
Model is used to decompose σ exp into F2exp and Rexp
Q2 dependence of both F2 and R is fit for each W2 bin
to get new model
Example SF Iteration Example SF Iteration
Q2
Q2
Measurements at different ε are inconsistent ⇒
started with wrong splitting of strength!
Consistent values of the separated structure functions for all ε !
Iteration results in shuffling of strength
Point-to-Point Systematic Uncertainties for E94-110
Total point-to-Total point-to-point systematic point systematic uncertainty for uncertainty for E94-110 is 1.6%.E94-110 is 1.6%.
Experimental Procedure and CS ExtractionExperimental Procedure and CS Extraction
Cross Section ExtractionCross Section Extraction● Acceptance correct e- yield bin-by-bin (δ, θ).
●Correct yield for detector efficiency.
● Subtract scaled dummy yield bin-by-bin, to remove e- background from cryogenic target aluminum walls.
● Subtract charge-symmetric background from π0 decay via measuring e+ yields.
●bin-centering correction.
● radiative correction.
W2 (GeV2)
Elastic peak not shown
At fixed Ebeam, θc, scan E’ from elastic to DIS. (dp/p =+/-8%, dθ =+/-32 mrad)
Repeat for each Ebeam, θc to reach a range in ε for each W2, Q2.
QCD and the Parton-Hadron Transition
Hadrons Q < s(Q) > 1
Constituent Quarks Q > s(Q) large
Asymptotically Free Quarks Q >> s(Q) small
One parameter, QCD,~ Mass Scale or Inverse Distance Scale where as(Q) = infinity
“Separates” Confinement and Perturbative Regions
Mass and Radius of the Proton are (almost) completely governed by
QCD213 MeV
One parameter, QCD,~ Mass Scale or Inverse Distance Scale where as(Q) = infinity
“Separates” Confinement and Perturbative Regions
Mass and Radius of the Proton are (almost) completely governed by
QCD and the Parton-Hadron Transition
QCD213 MeV