Joshua G. Rubin
University of Illinois
SPIN 2008
October 9, 2008
Joshua G. Rubin
University of Illinois
SPIN 2008
October 9, 2008
The new q(x) at HERMES
Joshua Rubin - SPIN2008 - October 9, 2008 2/18
Var. Description SIDIS Requirements
x Light Cone Momentum Fraction of Parton
Q2 Negative Squared Photon Momentum Q2 > 1 GeV2
W2 Final State Invariant Mass W2 > 10 GeV2
pTHadron transverse momentum w.r.t. q-vector
ZhEnergy Fraction carried by Hadron h 0.2 < zh < 0.8
Deep-Inelastic Scattering and DIS Kinematics at HERMES
• 27.6 GeV positron beam on deuterium gas
target
• ~ 53% Beam Polarization
• ~ 82% Target Polarization
Thanks Halzen & Martin!
Thanks Halzen & Martin!
Joshua Rubin - SPIN2008 - October 9, 2008 3/18
q(x) and How to Measure it
LO expression:
q
q(x)F(x)g xqe
xF(x)A )(
)(2
1 2
11 1
1
NN
NNA||N
N
Experimental Asymmetry:
(A|| and A1 are related by depolarization and kinematic factors)
How can we get at
q(x) then?!
q
hq
q
hqq
q
hqq
h
xq
xqzxP
zDxqe
zDxqe
A)(
)(),(
)()('
)()(
''
2'
2
1
Purity is probability that hadron h came from quark flavor q.
Use correlation between struck quark and observed hadrons to flavor-tag events
Extract quark contributions with semi-inclusive analysis
The semi-inclusive version of A1:
Take advantage of the hadrons!
Joshua Rubin - SPIN2008 - October 9, 2008 4/18
To jog the memory... “The Long Paper”
A. Airapetian et al. Phys. Rev., D71:012003, 2005Highlights
First ever 5-flavor q(x) extraction
9 x-bins for valence quarks, 7 for sea quarks
Rigorous unfolding procedure developed which removes detector and radiative smearing without assuming smoothness
Room for Improvement
Overlooked low-momentum deuterium data
Semi-inclusive kinematic dimensions unexplored. i.e. zh, ph┴
Bin-to-bin correlations and absence of smoothness assumption causes apparent error bar inflation
An attempt was made to overestimate the difficult-to-compute purity matrix systematic uncertainty. It was hoped that the subject could be revisited with more rigor.
Though the reanalysis is not complete, it has already yielded new results!Though the reanalysis is not complete, it has already yielded new results!
Joshua Rubin - SPIN2008 - October 9, 2008 5/18
New Dimensions! (zh and ph┴)
New Dimensions! (zh and ph┴)
Joshua Rubin - SPIN2008 - October 9, 2008 6/18
Low-z Mid-z High-z
Low-ph┴Leading
Mid-ph┴Standard
High-ph┴Remnant
Highest energy hadron & fewest
string breaks
Highest energy hadron & fewest
string breaks
Lowest energy hadrons & most
string breaks
Lowest energy hadrons & most
string breaks
Each x-bin can be divided into z and ph┴ dimensions...
z and ph┴ yield information about the fragmentation process...
What’s interesting about semi-inclusive kinematic variables?
We’re looking at two features of this extended binning:
1. Quark-hadron correlations can be enhanced in the purity-based extraction of q(x) by identifying leading quark and remnant containing hadrons. Work in progress...
2. A1(ph┴) is interesting in itself! It yields information about the fragmentation pT and intrinsic kT.
New result!
We’re looking at two features of this extended binning:
1. Quark-hadron correlations can be enhanced in the purity-based extraction of q(x) by identifying leading quark and remnant containing hadrons. Work in progress...
2. A1(ph┴) is interesting in itself! It yields information about the fragmentation pT and intrinsic kT.
New result!
Joshua Rubin - SPIN2008 - October 9, 2008 7/18
What is ph┴ of a final state hadron good for?
M. Anselmino, A. Efremov, A. Kotzinian, and B. Parsamyan
Phys.Rev.D74:074015,2006.
• ph┴ is interesting, but complicated!
• It is a convolution of fragmentation pT (string breaks) and intrinsic kT (PDFs)
• Any flavor dependence of kT unknown
• Important for transverse momentum dependences (TMDs)
• x and ph┴ are not completely independent variables… apparent ph┴ dependence can result from different <x> in each ph┴ bin.
ConstructConstruct
AssumeAssume
Recent theoretical work:Recent theoretical work:
CalculateCalculate
Joshua Rubin - SPIN2008 - October 9, 2008 8/18
P + 11.8 11.7
P - 13.7 13.3
d + 37.1 35.6
d - 22.4 21.9
d K+ 27.6 27.5
d K- 25.2 23.6
A1(x, ph┴ ) – New Result!
)15(2
321
NDF
pCxCC hhhh )16(2
21
NDF
xCC hhAh
1
No significant ph┴
dependence observed
• Binned in x and ph┴ to hold <x> more constant within an x-bin.
• Points fit with and without ph┴ dependant term:
Joshua Rubin - SPIN2008 - October 9, 2008 9/18
Addressing Error Bar Inflation:
Covariance and Smoothness
Addressing Error Bar Inflation:
Covariance and Smoothness
Joshua Rubin - SPIN2008 - October 9, 2008 10/18
The bin-to-bin unfolding procedure used in the long q(x) paper for A1(x):
• Corrects radiative and detector smearing by tracking MC event bin migration
• Makes no assumption of smoothness
Side-effect:
• Statistical errors correlated and considerably larger than those of raw asymmetry
Bo
rn B
ins
(j)
Kinematic Unfolding and the Interpretation of Uncertainties
When A1 is fit with a smooth function and statistical covariance is taken into account (blue band), inflated uncertainties are reduced.
Published asymmetries from HERMES long q(x) paper fit with: A1
h (x) = C1 + C2 x
Joshua Rubin - SPIN2008 - October 9, 2008 11/18
Fits to the Quark Polarizations
Helicity densities fitted with xq(x) = C1 xc2 (1-x)c3
• Data points have rigorous model-independent uncertainties (and associated covariance)
• Fits give a more reasonable impression of the true statistical significance of the data taking into account covariance and (reasonably) assuming smooth physics
• Statistical covariance is crucial when interpreting data. Fit uncertainty can be overestimated without including covariance (pink band). Fit central values are affected as well.
Do utilize provided covariance info when interpreting data!
(Simulated data points for illustrative purposes only!)(Simulated data points for illustrative purposes only!)
Joshua Rubin - SPIN2008 - October 9, 2008 12/18
A More Robust Calculation of the
Purity Matrix Systematic
A More Robust Calculation of the
Purity Matrix Systematic
Joshua Rubin - SPIN2008 - October 9, 2008 13/18
Tuning JETSET, the Fragmentation Monte Carlo
• Purity matrices, which encode the correlation between struck quark flavor and observed hadron type, are generated using a JETSET Monte Carlo.
• JETSET is an implementation of the Lund-string phenomenological fragmentation model based on ~12 tunable parameters.
• These parameters are tuned by minimizing a 2 comparison of MC to data multiplicities.
• In the existing publication, the systematic uncertainty related to this tune was conservatively overestimated by comparing several tunes that poorly describe multiplicities in the HERMES kinematic regime. This was a major source of uncertainty in the publication.
• The (unlikely) possibility of correlated parameters creating an ambiguous 2 minimum was not addressed at the time.
Joshua Rubin - SPIN2008 - October 9, 2008 14/18
2
parj a parj
b
Best MC Tune
min
min+C
1. Scan 2 surface around best Monte Carlo tune. Fit with quadratic Polynomial.
2. Find 68% contour. Based on two factors:
• Height of 68% of d-dimensional Gaussian Distribution.
• The height of 2 minimum to accommodate model imperfection. PDG does something like this.
3. Compute q(x) along contour:
The maximum deviation of q(x) from the best tune is the 68% uncertainty!
Correlating MC tune and q(x) systematic uncertainty
68% Contour
q(x)
Purities
Joshua Rubin - SPIN2008 - October 9, 2008 15/18
What locations on the 68% contour should be sampled?
(J. Pumplin et al., JHEP 07 (2002) 012)
This problem is similar to fitting global PDF parameterizations… Models typically have correlated parameters. What do those guys do?! Look at CTEQ.
• A & B are correlated parameters. The minimum in one depends on the location of the other
• Compute Hessian matrix of second derivatives to find uncorrelated directions
68% Contour
Extract q(x) where uncorrelated parameter vectors cross 68% certainty contour. The greatest deviations represent
q(x) tune systematic uncertainty.
Joshua Rubin - SPIN2008 - October 9, 2008 16/18
•Blue ellipses represent 68% contour
•Colored lines represent uncorrelated parameter directions
•Blue ellipses represent 68% contour
•Colored lines represent uncorrelated parameter directions
Jetset/Lund 2 surface in
Fragmentation Parameter Basis
Scan the 2 surface around the best Monte Carlo tune.
• Correlations are quite clear between parameters
• Generate and diagonalize the matrix of 2nd derivatives to find linear combinations that are uncorrelated
The real thing…
Joshua Rubin - SPIN2008 - October 9, 2008 17/18
Revised q(x) uncertainty estimate
u
d
u
d
s
x
Published q(x) total systematic
Publishedq(x) MC systematic
Difference between q(x) on 68% contour along Hessian vectors and at the 2 minimum.
We can move the gray estimate down to the highest colored point!
In most bins, the tune-related systematic can
be greatly reduced.
Joshua Rubin - SPIN2008 - October 9, 2008 18/18
Concluding Remarks
• A1(ph┴ ) -- A first look at this interesting quantity
– No dependence was observed.
– Can we differentiate sources of ph┴ ? Can we learn something about flavor-dependence of intrinsic kT? Can we learn something meaningful about fragmentation?
• Fits will compliment the new q(x) data:
– Unfolded data points provide assumption-free presentation of the data, but suffer from apparent inflation of error bars and statistical covariance.
– The addition of fit curves give a more reasonable impressions of statistical significance
• Improved fragmentation model tune uncertainty
– Uncertainty appears to be considerably smaller than published
– Robust Hessian approach properly handles correlated parameters
Joshua Rubin - SPIN2008 - October 9, 2008 21/18
From: Harut Avakian, “Studies on transverse spin effects at JlabStudies on transverse spin effects at Jlab”,QCD Structure of the Nucleon June 12-16, 2006, Rome
What do we know about A1(ph┴) so far?
CLAS sees clear ph┴ dependence of A1
CLAS sees clear ph┴ dependence of A1
• Some care was taken to correct for the varying x-dependence in in each ph┴ -bin.
• CLAS result is at a significantly lower W and higher x than HERMES