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Longitudinal News from HERMES: Features and Byproducts of the D q(x) Reanalysis

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Longitudinal News from HERMES:Features and Byproducts of the Dq(x) Reanalysis

Joshua G. Rubin

University of Illinois

RHIC/AGS Users’ Meeting

June 1, 2009

A quick plug!

Dg/g at HERMES!

When you can’t measure it from scaling...

...and open-charm is nowhere to be found...

...choose a model (PYTHIA), decompose your high pT data into subprocesses, and solve for Dg/g!

Joshua Rubin - RHIC/AGS - June 1, 2009

Coming to a theatre near you!

Now Back to “The NewDq(x)”

(Watch for an upcoming publication)

Joshua Rubin - RHIC/AGS - June 1, 2009

The HERMES Experiment

Event Trigger:

Hodoscopes and Calorimeter

Gas Target:

target = 1014 nuc/cm2

>80% polarization

Tracking Chambers

e

Hadron ID:

96-97 Threshold Cerenkov (p)

98-00 RICH (p, K, P)

Lepton Hadron Separation:

Calorimeter + TRD + Preshower

Joshua Rubin - RHIC/AGS - June 1, 2009

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!

Joshua Rubin - RHIC/AGS - June 1, 2009

Experimental Asymmetry:

(A|| and A1 are related by depolarization and kinematic factors)

LO expression:

How can we get at Dq(x) then?!

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 withsemi-inclusive analysis

Take advantage of the hadrons!

The semi-inclusive version of A1:

Joshua Rubin - RHIC/AGS - June 1, 2009

- Highlights
- First ever 5-flavor Dq(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.

A. Airapetian et al. Phys. Rev., D71:012003, 2005

Though the reanalysis is not complete, it has already yielded new results!

Joshua Rubin - RHIC/AGS - June 1, 2009

New Dimensions! (zh and ph┴)

Joshua Rubin - RHIC/AGS - June 1, 2009

What’s interesting about semi-inclusive kinematic variables?

Each x-bin can be divided into z and ph┴dimensions...

Highest energy hadron & fewest string breaks

Lowest energy hadrons & most string breaks

z and ph┴ yield information about the fragmentation process...

- We’re looking at two features of this extended binning:
- Quark-hadron correlations can be enhanced in the purity-based extraction of Dq(x) by identifying leading quark and remnant containing hadrons. Work in progress...
- A1(ph┴) is interesting in itself! It yields information about the fragmentation pT and intrinsic kT.
- New result!

Joshua Rubin - RHIC/AGS - June 1, 2009

- 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.

Recent theoretical work:

- M. Anselmino, A. Efremov, A. Kotzinian, and B. Parsamyan
- Phys.Rev.D74:074015,2006.

Calculate

Construct

Assume

Joshua Rubin - RHIC/AGS - June 1, 2009

- Binned in xandph┴to hold <x> more constant within an x-bin.
- Points fit with and without ph┴ dependant term:

No significant ph┴ dependence observed

Joshua Rubin - RHIC/AGS - June 1, 2009

A More Robust Calculation of the Purity Matrix Systematic

Joshua Rubin - RHIC/AGS - June 1, 2009

- 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 c2 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 c2 minimum was not addressed at the time.

Joshua Rubin - RHIC/AGS - June 1, 2009

Correlating MC tune and Dq(x) systematic uncertainty

Purities

Dq(x)

1. Scanc2 surface around best Monte Carlo tune. Fit with quadratic Polynomial.

68% Contour

Best MC Tune

- 2. Find 68% contour. Based on two factors:
- Height of 68% of d-dimensional Gaussian Distribution.
- The height of c2 minimum to accommodate model imperfection. PDG does something like this.

c2

c2min+C

c2min

parj b

parj a

3. ComputeDq(x) along contour:

The maximum deviation of Dq(x) from the best tune is the 68% uncertainty!

Joshua Rubin - RHIC/AGS - June 1, 2009

What locations on the 68% contour should be sampled?

68% Contour

This problem is similar to fitting global PDF parameterizations… Models typically have correlatedparameters.What do those guys do?! Look at CTEQ.

(J. Pumplin et al., JHEP 07 (2002) 012)

- 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

Extract Dq(x) where uncorrelated parameter vectors cross 68% certainty contour. The greatest deviations represent Dq(x) tune systematic uncertainty.

Joshua Rubin - RHIC/AGS - June 1, 2009

The real thing…

- Scan the c2 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

Jetset/Lund c2 surface in Fragmentation Parameter Basis

- Blueellipses represent 68% contour
- Coloredlines represent uncorrelated parameter directions

Joshua Rubin - RHIC/AGS - June 1, 2009

Revised Dq(x) uncertainty estimate

Published Dq(x) total systematic

PublishedDq(x) MC systematic

Difference between Dq(x) on 68% contour along Hessian vectors and at the c2 minimum.

We can move the old estimate down to the highest colored point!

In most bins, the tune-related systematic can be greatly reduced.

x

Joshua Rubin - RHIC/AGS - June 1, 2009

- Hadron charge difference asymmetries...
- Complete Semi-Inclusive Longitudinal Double-Spin Asymmetries binned simultaneously in x, z, and ph┴
(of potentially more interest to the community than a modest improvement in the precision of Dq(x), right?!)

...if you trust the following fragmentation function symmetry:

(On the deuteron)

Similar to isoscalar Ds(x) extraction...

Joshua Rubin - RHIC/AGS - June 1, 2009

- A1(ph┴ ) -- A first look at this interesting quantity
- No dependence was observed.
- Can we differentiate sources ofph┴ ? Can we learn something about flavor-dependence of intrinsic kT? Can we learn something meaningful about fragmentation?

- Improved fragmentation model tune uncertainty
- Uncertainty appears to be considerably smaller than published
- Robust Hessian approach properly handles correlated parameters

- New Goodies Soon!
- Hadron Charge Difference Asymmetries Alternative (Duv+Ddv)/(uv+dv)
- Final A1h(x,z, ph┴ ) numbers to be made available on Durham.

- Look out for a Dg/g publication from HERMES soon!

Joshua Rubin - RHIC/AGS - June 1, 2009

Extra slides…

Joshua Rubin - RHIC/AGS - June 1, 2009

Addressing Error Bar Inflation: Covariance and Smoothness

Joshua Rubin - RHIC/AGS - June 1, 2009

Published asymmetries from HERMES long Dq(x) paper fit with:

A1h (x) = C1 + C2 x

Born Bins (j)

- The bin-to-bin unfolding procedure used in the long Dq(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

When A1 is fit with a smooth function and statistical covariance is taken into account (blue band), inflated uncertainties are reduced.

Joshua Rubin - RHIC/AGS - June 1, 2009

- Helicity densities fitted with xDq(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!)

Joshua Rubin - RHIC/AGS - June 1, 2009

Joshua Rubin - RHIC/AGS - June 1, 2009

What do we know about A1(ph┴) so far?

From: Harut Avakian, “Studies on transverse spin effects at Jlab”,

QCD Structure of the Nucleon June 12-16, 2006, Rome

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 thanHERMES

Joshua Rubin - RHIC/AGS - June 1, 2009

The Gluon Polarization

(Thanks Elke!)

Joshua Rubin - RHIC/AGS - June 1, 2009

- Q2 Scaling of Asymmetries
Limited Q2 coverage (when compare to unpolarized case!). Gluon polarization poorly constrained

- Golden channels. i.e. Isolate a single process involving a gluon with a known cross section– e.g. open charm isolates photon-gluon fusion.
Not enough statistics at HERMES kinematics

- Model the Spectrum of Processes at high pT
- Enhances perterbative gluon signal processes
- Suppresses soft processes
Use Monte Carlo (PYTHIA) to do this!

Joshua Rubin - RHIC/AGS - June 1, 2009

PGF

VMD

Anomalous-q

Joshua Rubin - RHIC/AGS - June 1, 2009

Joshua Rubin - RHIC/AGS - June 1, 2009

Joshua Rubin - RHIC/AGS - June 1, 2009

Joshua Rubin - RHIC/AGS - June 1, 2009