# Presentation: 947456

## The nucleon helicity as seen by HERMES

- From g1 to G
- Patricia Liebing
- RIKEN-BNL Research Center
-  for the                       collaboration

- Annual RHIC and AGS Users Meeting, BNL, June 18-22 2007

## Outline

- Nucleon helicity structure has been studied by Hermes mainly in 3 ways
- Inclusive DIS -> g1
- Semi-inclusive DIS -> purity analysis
- High-pT hadrons with sensitivity to g
- No data with longitudinally polarized data since 2000, but
- Ongoing, refined and complementary analyses
- Analysis of unpolarized data for F2, dv/uv and FF

**Notes:**
Relying on naïve assumptions

## A Quick Reminder

- HERA ep collider at DESY (Hamburg)
- Polarized e with 27.5 GeV
- Hermes cms energy (fixed target) 7.2 GeV

## Hermes

- Internal longitudinally polarized H,D target P0._x0010_85
- Flip every 60, 90s

## g1p,d corrected (unfolded)  for instrumental smearing and QED radiative effects
Points statistically correlated
Only diagonal elements of covariance matrix shown in plots
Error bars include systematics from F2, R parametrization and Q2 evolution (within x bin)

- Points *statistically* correlated
- Only diagonal elements of covariance matrix shown in plots
- Error bars include systematics from F2, R parametrization and Q2 evolution (within x bin)

- g1 Finally Published!

- A. Airapetian et al, Phys. Rev. D 75 (2007) 012007

## Final Results on g1

## g1 Integrated

- Integrals for 0.021<x<0.9
- Integral seems to saturate at x<0.04 for Deuteron
- Use 1d to extract

## s vs. s?

- Extraction of                  ,      uses SU(2) flavor symmetry - Bjorken Sum Rule
- Extraction of                    uses SU(3) flavor symmetry
- But:                    , even with 20% SU(3) breaking while semi-inclusive Hermes data give
- Consistent?
- Negative contribution at
-     lower x<0.02?

- Published isoscalar method:
- Assumed FF from BKK
- (Phys. Rev. D 52, 4947 (1995))_x0003_

## SIDIS Asymmetries

- All asymmetries unfolded
- to correct for smearing
- and QED radiative effects

**Notes:**
All asymmetries qualitatively the same, except k-

## Analysis of SIDIS Data

- Quark polarizations obtained from DIS+SIDIS (identified pion, kaon) asymmetries on proton and deuteron, using purity formalism:
- Purities determined by MC
- Caveat: LO analysis, dependent on MC fragmentation model

- A. Airapetian et al,
- Phys. Rev D 71
- (2005) 012003

## Study of Lund Fragmentation

- LUND string fragmentation parameters are tuned by minimizing the difference of MC and data (identified) hadron multiplicities
- Find agreement within ~10% (for pions)
- But: What are the errors?
- Estimate systematic uncertainties of values extracted using LUND MC (e.g. on q/q from purity method)
- Usual method: Compare an old “historical” fit with the current one normally gives large uncertainties
- Error scan using Hessian matrix (similar to CTEQ)

## LUND Error Scan

- 2-contours in correlated
- LUND parameter space

- 2-contours in uncorrelated
- Hessian parameter space

## Result of Error Scan

- Black line = total systematic error estimate on q/q
- Grey line =  contribution from comparing old and new tunes
- Colored points = Sample q/q with parameters along 68% Hessian contour
- “True” error from LUND tune is much smaller than estimate
- But: The overall 2/ndf 20 for the best tune  MC model itself is not perfect
- Uncertainty due to “use of MC” unknown
- Studies are ongoing

## Model Dependent, Leading Order Result on g/g

- Black and green curves from pQCD fits to g1
- Red curves: Fits to HERMES high-pT hadron data using LO MC+pol. PDF model and 2 functional forms
- Red point: Average g/g from fits.

**A lot of the analysis is in the determination of the **
**systematic error and  the mean x**

## From Measurements ...

******g/g=0: asymmetry is due to quarks only! **
**Gluons become important for the cross section (asymmetry) above p****T********1 GeV**

- “Antitagged” data:
- Scattered lepton not in the acceptance
- pT measured w/respect to beam axis
- Curves from MC+asymmetry model using
- g/g(x)=0: central
- g/g(x)=-1: upper
- g/g(x)=+1: lower

## (More Asymmetries)

- “Tagged” inclusive charged hadrons
- Scattered lepton detected
- Q2>0.1 GeV2, W2>4 GeV2
- pT w/respect to virtual photon

- Inclusive Pairs of charged hadrons
- No regard to scattered lepton
- All charge combinations
- pT w/respect to beam axis
- pT(h1,h2)>0.5 GeV
- Plotted vs. lower cut on:

## ... via MC information ...

- Fractions of contributing subprocesses
- From PYTHIA 6.2 model
- Tuned and adapted for HERMES data (see later)
- Their asymmetries
- Initial state partons
- Kinematics of the hard subprocess
- Scale, x, pT
- Subprocess kinematics of hard processes with gluons in the nucleon in initial state    -> Signal

## ... and an Asymmetry Model

- Event-by-event calculation from MC kinematics, flavors, subprocess type
- Hard processes: Use pol. LO PDF (GRSV 2000)
- Hard resolved photon processes: Use 1/2(maximal+minimal) scenarios from GRS
- Soft processes: Use assumptions
- A=0 for exclusive/diffractive processes
- A~A1(low x) from world data for soft nondiffractive (“low-pT”)
- Vary PDFs/assumptions for syst. error

## (Fractions and Asymmetries)

**Subprocess Fraction**

**Subprocess Asymmetries**
**(using GRSV std.)**

- VMD (elast.+diffr., low-pT) decreasing w/pT
-  DIS increasing with pT
-  QCDC/QCD2->2(q) increasing with pT
-  Signal processes are PGF and
- QCD2>2(g) (resolved photon)

- DIS increasing with pT (x) - positive
-  QCDC/QCD2->2,VMD flat and small
-  Important for background asymmetry!
- |PGF| increasing with pT - negative
-  QCD2->2(g) opposite to PGF, small

- Antitagged, charge combined
- Deuteron data

## ... to g/g

- Once we know everything necessary: How do we get g/g out of this?

- x-range covered by data (unpolarized): 0.07<x<0.7

## Methods for g/g Extraction

- Methods for g/g Extraction

- Method I:
- Factorize
- Assumes
- No sign change in â(x)
- “flat” g/g(x)
- No information on <x> of measurement
- Gives average g/g over covered x range (0.07<x<0.7)

- Method II:
- Fit: find a g/g(x) such that
- Assumes functional form for g/g(x)
- Only small range in pT
- Gives g/g(x) and average x of measurement

## g/g From Method I

-  Results for different data samples agree within statistics
-  Dominating sample: Deuteron antitagged -> Used for Method II and syst. error analysis (charge combined)

- _h__+__,h__-__ antitagged:_
- 4 points between
- 1.05<pT<2.5 GeV
- _h__+__,h__-__ tagged:_
- 1 point for
- pT>1 GeV
- _Pairs_:
- 1 point for
-                    GeV2

- Only statistical errors!

## g/g from method II

- Light shaded area: range of data
- Dark shaded area: fit center of gravity

**Fit results**

- g/g from method II

- Final 2 functions used are polynomials with 1(2) free parameters
- Fix:
- g/gx for x0 and
- g/g1 for x1    (Brodsky et al.)
- |g/g(x)|<1 for all x
- Difference between functions is a systematic uncertainty
- 2/ndf5 due to highest pT point
- Model syst. not included in fit
- 1-2 parameter function is too smooth

## PYTHIA 6.2 has been tuned
Fragmentation parameters for Q2>1 GeV2
VMD Model for Q2>0.1 GeV2

Get fair agreement in tagged region (Q2>0.1 GeV2) when integrating over pT

- Fragmentation parameters for Q2>1 GeV2
- VMD Model for Q2>0.1 GeV2
- Get fair agreement in tagged region (Q2>0.1 GeV2) when integrating over pT

**Tagged region:**
- Comparison of cross sections for charged hadrons (:in HERMES acceptance:)

- How Good is the Model?

## How Good is the Model Really?

- The very same tuned PYTHIA fails to describe cross sections vs. pT
- For both tagged and antitagged regions
- Consistent with missing NLO corrections in MC

**Antitagged region:** Comparison of cross sections of charged hadrons (:in HERMES acceptance:)

**Application of k-factor to relevant processes in MC gives better agreement with data**

## LO MC vs. NLO pQCD

- Why can we not (yet) use NLO pQCD calculations to extract g/g?
- Example: simple PGF process (LO)
- Magenta curves are what LO pQCD would give
- Dashed curves are for intrinsic kT is included (0.4 GeV)
- Solid curves are intrinsic and fragmentation pT (0.4 GeV) included

- Cross sections

- pT (of the hard subprocess) and x distributions

## What Does This Result Tell Us?

- Despite the obvious shortfalls stick with LO MC
- Includes effects of intrinsic transverse momentum (kT) and transverse momentum acquired in fragmentation (pT(frag))
- Impact on cross section larger than NLO correction
- pT<->x relation changes
- Result is in LEADING ORDER, with model uncertainties
- Scale variation 1/2*scale - 2*scale (NLO effects!)
- Variation of kT and pT(frag) within range allowed by HERMES and world SIDIS (pT<1 GeV) data
- Variation of crucial PYTHIA parameters
- Variation of (pol. and unpol.) PDFs and low-pT asymmetry
- Variation of functional form for g/g(x) (for Method II)

## What Does That Look Like?

**Method I**

- Uncertainties from each group
- PYTHIA params.
- PDFs
- low-pT asym.
-    summed linearly to “Models” uncertainty
- Conservative approach
- Experimental (stat.+syst.) added in quadrature
- syst. uncertainty from 4% scaling uncertainty 14% on g/g

## Back To The Final Result

- For an accurate g/g extraction:
- Need NLO MC and/or NLO pQCD with initial/ final state radiation effects (resummation?)
- From our results:
- g/g is (likely) mostly small
- Need to combine all available data to get a better picture

## Summary

- Hermes has collected a wealth of unpolarized and longitudinally polarized data on H and 2D targets
- Analyses are being refined, including more and more understanding of the data (experimentally) and the physics (theoretically)
- E.g.,LUND parameter tuning and error scan
- “Overload” purity method for q, including 0, k0, asymmetries
- More multiplicities to come (maybe Fragmentation functions)
- G results soon to be published

## BACKUP

## Pythia simulates the total ep (*p) cross section using a mixture of different subprocesses
VMD (exclusive, diffractive, soft nondiffractive, hard nondiffractive)
Anomalous (                ) processes
Direct photon processes (QCDC, PGF)
LO DIS 

- VMD (exclusive, diffractive, soft nondiffractive, hard nondiffractive)
- Anomalous (                ) processes
- Direct photon processes (QCDC, PGF)
- LO DIS

- Pythia: Reminder

## MC vs. LO QCD

-  Comparison of LO cross section for hard subprocesses from pQCD (M. Stratmann) and MC (no JETSET, Kretzer FF instead)
- Magenta lines: Results from varying scale
- Scale definition different for MC and calculation

## g/g Extraction: Cuts 

- g/g Extraction: Cuts

- Cuts are defined to balance statistics with sensitivity (S/B ratio)
- Also possible systematics under consideration
- Important: Correlation between measured pT and hard pT (x, scale)

## Systematics: PDFs

- Standard PDFs used:
- CTEQ5L(SaS2) for Pythia (unpol., Nucleon(Photon))
- GRSV std./GRV98 for q/q going into asymmetries
- Variation:
- GRV98(GRS) for Pythia (unpol, Nucleon(Photon))
- GS-B/GRV94, BB2006/CTEQ5L for q/q(nucleon) going into asymmetries
- Error:
- For Pythia (unpol) the difference is taken as a 1 error
- For q/qI(nucleon) the maximum difference is taken as a 1 error

## Systematics: Asymmetries

- Besides PDFs, there are 2 more sources of uncertainties
- Asymmetry of “low-pT” VMD process
- Std: Alow-pT=Ainclusive (from fit to g1/F1)
- Variation: Alow-pT=0 (!asymmetric error!)
- Unknown polarized photon PDFs needed for hard resolved processes
- Std: Arithmetic mean of maximal and minimal scenarios of Glück et. al., Phys. Lett. B503 (2001) 285
- Variation: maximal and minimal scenarios (symmetric, 1 error)

## Systematics: pT smearing

- Initial state (intrinsic kT of partons in nucleon and photon) and final state (fragmentation) radiation generate additional pT with respect to the collinear “hadron pT” ,            .
- Huge effects on measured cross sections, and the correlation between measured pT and hard subprocess pT , and x
- Also large effects on subprocess fractions
- See Elke’s study in the paper draft
- Std.: kT (0.4 GeV) and pTFragm. (0.4 GeV) from 2 minimization
- Variation: 1 error from 2 minimization (0.04/0.02 GeV)

## Systematics: Scale Dependence

- Scale in Pythia was varied by factors 1/2 and 2
- Same variation for asymmetry calculation
- Error: Maximum difference to std. is taken as 1 uncertainty

## Systematics: Cutoffs

- A number of cutoffs in Pythia (to avoid double counting) can influence subprocess fractions
- Most important one: PARP(90) sets the dividing line between
- PGF/QCDC and hard resolved QCD
- Hard and soft (low-pT) VMD
- Std: Default Pythia (0.16)
- Variation:  0.14-0.18 (from comparing Pythia LO cross section with theory LO cross section)

## Systematics: Method 2

- An additional uncertainty is assigned for Method 2 due to the choice of functional shape
- Std: Function 1 (1 free parameter)
- Variation: Function 2 (2 free parameters)
- Error = difference (!asymmetric!)

## Mean values, syst. and stat. errors in Method I are independent between pT points

They are correlated in Method II (band)

- They are correlated in Method II (band)

-  Error bars/bands: stat. and total errors (including exp. systematics from polarization measurements (4%))
-  For Method 2 the errors are dominated by high statistics points

**Method I**

**Method I/Method II**

- What Does That Look Like?

## Modifying/Tuning PYTHIA

- Changes to the VMD model in PYTHIA
- The Q2 slope of the total
- (resolved) *p cross section:
- The parametrization of
- The –VM couplings
- The angular distribution of the
- 0 decay products
- And implementing QED radiative corrections ...

**Notes:**
Not only understand, but also modify Pythia
VMD important contribution to data

## BACK UP

## NLO QCD Analysis of SIDIS Data 

- D. de Florian et al.
- Phys.Rev. D71 (2005) 094018

- NLO QCD Analysis of SIDIS Data

- Fit to inclusive and Hermes/SMC SIDIS asymmetries
- With error analysis
- Additional input: Fragmentation functions
- SIDIS data constrain sea quark densities better
- Uncertainties still very large

- Results very sensitive to choice of fragmentation function
- Need more precise FF from data

## NLO SIDIS Fit Errors

## Unpolarized Data

- Knowledge of unpolarized input to PDF fits very important
- SIDIS multiplicities of identified hadrons (together with e+e--data from BELLE+LEP) provide valuable information for new, more precise Fragmentation functions
- Understanding the unpolarized cross section (e.g., F2) helps evaluating the validity of pQCD assumptions

- Sorry, later ...

## Extraction of multiplicities at HERMES

- Correction for RICH efficiency
- and misidentification

- Unpolarized H and D data

- MC input

- Unfolding of smearing and
- QED radiative effects
- Acceptance correction

- Evolution to common Q2

- Multiplicities at Q2=2.5, 25 GeV2

## SIDIS Multiplicities (Pions)

- VMD correction large at z>0.7
- +/ - ratio 1.2

- Multiplicities on Proton

## SIDIS Multiplicities (Kaons) 

- VMD correction small
- k+/ k- ratio 2

- Watch the scale!

- Multiplicities on Proton

## SIDIS Multiplicities vs. Q2

- Pions

- Kaons

## Model Independent Extraction of s

- Model Independent Extraction of s

- The deuteron inclusive and charged kaon asymmetries are isoscalars:_x0013_

- }

- }

## Inclusive and Charged Kaon Asymmetries

- Asymmetries measured on deuteron,
- unfolded to correct for smearing, PID efficiency (RICH)
- and QED radiative effects

## Model Independent Extraction of s

- From A1incl and A1k we can extract Q and S assuming only
- Isospin invariance
- Charge conjugation symmetry of FF
- Use charged kaon multiplicities to get DQk and DSk
- Use CTEQ6LO for unpolarized PDFs

**Notes:**
Could use MC or FF to get Fragmentation function, but use our own data

## Charged Kaon Multiplicities

- Multiplicities measured on deuteron, unfolded to correct for smearing, PID efficiency (RICH) and QED radiative effects

- Very large difference between FF fit to data and Kretzer (PRD 62 054001 (2000)) or KKP (Nucl. Phys. B582, 514(2000)) predictions
- Have to regard light quark suppression in k fragmentation

## Results for Q(x) and S(x)

- Comparison with Previous
- Hermes Results

- Results on S(x) consistent with published 5 parameter fit
- Statistical and systematic uncertainties significantly reduced
- Polarized strange quark density consistent with 0
- No hint that it is negative

- Published isoscalar method:
- Assumed FF from BKK
- (Phys. Rev. D 52, 4947 (1995))_x0003_

## MC and data vs. pT Q2>0.1

- Cross section on deuteron,
- within Hermes acceptance
- Semi-inclusive hadrons, pT
- measured w.r.t.  direction