Joshua G. Rubin University of Illinois SPIN 2008 October 9, 2008 Joshua G. Rubin University of...

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!


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!


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!


New Dimensions! (zh and ph┴)

New Dimensions! (zh and ph┴)


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!


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


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:


Addressing Error Bar Inflation:

Covariance and Smoothness

Addressing Error Bar Inflation:

Covariance and Smoothness


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


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!)


A More Robust Calculation of the

Purity Matrix Systematic

A More Robust Calculation of the

Purity Matrix Systematic


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.


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


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.


•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…


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.


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


Backup slides…Backup slides…


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

Joshua G. Rubin University of Illinois SPIN 2008 October 9, 2008 Joshua G. Rubin University of...

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