the spin structure function g 1 and qcd fits to the g 1 world data

Lara De Nardo PacSpin2007

The spin structure function gThe spin structure function g11 and and QCD fits to the gQCD fits to the g11 world data world data

Lara De NardoLara De NardoTRIUMF/DESYTRIUMF/DESY


OutlineOutline

Definition of g1

Review of recent g1 dataHERMESCOMPASSCLAS

Review of recent fits to g1

LSSAACBBCOMPASS

Some ideasConclusions


Inclusive Inclusive DDeep eep IInelastic nelastic SScatteringcattering

L is exact in QED

npNSNSG qCGCCeg ,2

1

npNSqe ,2

2

1 in LO QCD

'

2

E

WL


param.kin.fact.measuredparam.

kinematicfactors

Measured Inclusive AsymetriesMeasured Inclusive Asymetries

measured DIS cross section

inclusive asymmetry:

)2,(

22

2)2,(

||2

2

28

4

24

1

21

1)2,(1

Qxgy

QxAQx

unpol

y

Q

yy

Qxg

Measured at HERMES, withPzz=0.83±0.03Azz~0.01 zzd

d

AF

b

2

3

1

1


gg11 World Data World Data

D

P,D


HERMES resultsHERMES results0.0041 < x < 0.9

0.18 GeV2 < Q2 < 20 GeV2

Correction for smearing and radiative effects introduces statistical correlationsStatistical uncertainties are diagonal elements of covariance matrixSystematic unc. are dominted by target and beam polarization

Phys.Rev.D75(2007)012007Phys.Rev.D75(2007)012007


theory

IntegralsIntegralsSaturation in the deuteron integral is assumed

Q2=5 GeV2, NNLO in MS scheme

from hyperon beta decay (a8=0.586±0.031)

theory

ωD=0.05±0.01

from neutron beta decaya3=1.269±0.003

(use only Q2>1GeV2 data)

Use only deuteron data!


COMPASS resultsCOMPASS results

Phys.Lett.B647(2007)330Phys.Lett.B647(2007)330

At low Q2 only measurements from SMC and COMPASS10 times lower statistical error than SMC

QQ22<1 GeV<1 GeV22

0.0005<x<0.020.0005<x<0.02

2002-2003 data


COMPASS resultsCOMPASS results

Phys.Rev.D75(2007)012007Phys.Rev.D75(2007)012007

A1 compatible with zero for x<0.05No tendency towards negative values at low x (as in SMC)

2002-03-04 data89M events

0.78GeV0.78GeV2 2 < <Q< <Q22> < 55.3GeV> < 55.3GeV22

0.003<x<0.70.003<x<0.7

aa00= 0.35 = 0.35 ± 0.03(stat) ± 0.05 (syst)± 0.03(stat) ± 0.05 (syst)

at 3GeVat 3GeV22


Data on gData on g11nn

g1n negative everywhere except at

very high-x

Recent HERMES results indicate that low-Q2 data tends to zero at low-x

does not support earlier conjecture of strong decrease for 0x

pd

D

n ggg 111

2

31

2


AA11 World Data World Data

21

121 1 A

F

gA

1

1

F

g


CLASCLAS

Phys.Lett.B641(2006)11

E155fit

400 points for p and 1654 for d! (633 for Q2>1GeV2 and W>2GeV)Clear decrease of asymmetries with decreasing Q2

CLAS fit at Q2=10GeV2


gg11 QCD fits QCD fitsg1 QCD fits are models for q(x,Q2) obtained by fitting inclusive world data on g1 :

nqnq

nqn n

pppp ,.....,..,,.........,....., 11

1 1

1get

2

2112 )(

data

datafit

data

gg

minimize

Calculate g1fit at the Q2 of all data points: )),((),( 22

1 iii

fit CQxqQxg

DGLAP: iii Pq

Q

q

2 to go from Q20 to Q2

data

),....,(),( 120

inq

iii ppfQxq

Start from model at initial Q2=Q20:

minimize jdatafit

datai

datafit ggjigg ))(,cov()( 11112

(for HERMES data)

, qpNS, qn

NS, Goruv, dv, q, G (need assumption on the sea)


Evolution of Statistical UncertaintiesEvolution of Statistical Uncertainties

Statistical uncertainties are given by:

Calculable exactly at Q20 since the functional form of q is known at Q2

0.

)cov(),(),(),()( ,2222

jijij i

q ppQxdp

qdQx

dp

qdQx

kdp

d

Gdt

ddt

d

qdt

dNS NSqP 1

GPP 32

GPP 54

The derivatives of the distributions evolve just like the distributions!One has to take into account the fact that e.g. G does not dependon the parameters only at Q2

0!For details on the unc. calculations in Mellin space see BB paper

iiidp

GdP

dp

dP

dp

Gd

dt

d

54

iiidp

GdP

dp

dP

dp

d

dt

d

32

X-space


COMPASS’06COMPASS’06

x space x space Mellin spaceMellin space

Positivity imposed to s and g (asym. errors)

Q2=3GeV2

A negative g is needed at low-x in order to represent data


LSS’06LSS’06

4

4

2

22

1

),(),(

QQ

QxhQxg HT

exp2

1

21

21

exp

21

21

),(

),(),(

),(

),(

QxF

QxgQxg

QxF

Qxg HTLT

),(),( 20

20 QxxfxAQxfx MRST

iiii

Initial parameterization:

Higher twist terms included in the fit:

Gsduf vv ,,,

New data:Low Q2 CLAS dataCOMPASS data (large Q2)

4

42

2

22

12

1 ),(),(),(Q

MQxh

Q

MQxgQxg TMCpQCDLT

)(),( in

ip xhxh

i=1,…,5: 10 parameters+6 for PDs (=8-2 for sum rules)

E.Leader et al.,Phys.Rev.D75(2007)074027


LSS06: Impact of CLAS dataLSS06: Impact of CLAS data

Number of data points: 190 823

Plots from D.Stamenov’s talk at DIS07

Low-Q2 data increases precision in the determination of HTPDF accuracy is also improved(it has to be noted that other groups (BB) have not found such a strong signal for HT)


CLAS12 expectationsCLAS12 expectations

EG1: 0.05 <Q2<3.5GeV2(2001)

EG12: 0.5<Q2<7 GeV2(2012?)

xG

x(u+u) x(d+d)

xs

CLAS12LSS06(with EG1)

LSS05 Q2=2.5GeV2

EG1 improves u, d, s, G

CLAS12 will particularly improve G

12 GeV upgrade

K.Griffionen, DIS07


LSS06: Impact of COMPASS dataLSS06: Impact of COMPASS data

Number of data points: 823 826

Effect of new data is negligible

Old:Phys.Lett.B612(2005)154

New:Phys.Lett.B647(2007)8(2.5 times larger statistics) Data at large Q2 does not impact HT

Differently from what found by COMPASS, g1

d is almost insensitive to the sign of g, but depends on the HT terms


LSS06 vs COMPASS06LSS06 vs COMPASS06Same 2 for the three solutions

The solution with G>0 is pushed to zero at low-x, in order to explain g1d data almost zero

(it would make g1d more negative)

Differences between the two fits interpreted as due to HT terms missing in COMPASS06

LSS’06

G<0

G>0

G<0

G>0


Impact of HERMES dataImpact of HERMES data

G=0.320.32±±0.47 0.47 0.22 0.22 ±±0.39 (stat)0.39 (stat).

The effect on the other parton distributions is much less visible

∆∆ =0.22 =0.22 ± ± 0.11 0.11 ± ± 0.05(exp) 0.05(exp) ± ± 0.06(theo)0.06(theo)

(test done with BB code,Nucl.Phys.B636(2002)225)

Thanks to H.Böttcher

Without HERMES g1d

With HERMES g1d


AAC06AAC06

M.Hirai et al., Phys.Rev.D74(2006)014015

Fit A: DIS A1 + PHENIX dataFit B: DIS A1

0LLA

Positivity imposed11 free parametersError bands with

NPAR 2qsdu

),()]([),( 20

9820 QxfxxkxQxf GRV

iiiiii

Gqduf vv ,,,

Hermes data is described better (red) when G is included in g1 G should be positive in the region 0.033<x<0.065Remaining discrepancies described by LSS with HT:

dzzCz

xG

z

xg G

G

)(1


AAC06AAC06

Resulting distributions compared to previous analyses


AAC-low-xAAC-low-x0LLA is dominated by gg scattering at small pT

It depends on no sign dependence!

2

g

g

Fit 3: allow for negative g in the low-x region

To explain the negative at pT=2.38GeV a negative gluon is needed for 0.06<x<0.2 No change is observed in the quark distributionsThe negative g does not reside in the Fit-1 error band!

The uncertainties depend on the error band!!Error due to functional form not included in uncertainties

0LLA


Comparisons with existing Comparisons with existing G measurementsG measurements

AAC06 LSS06

The precision of the data is not yet able to discriminate among various functions

New HERMES analysis that supercedes the old one will be presented by N.Bianchi

COMPASS06


(Not so) Random (Not so) Random issuesissues

on QCD fits on QCD fits


Results Stability Results Stability Up to three minima have recently been seen with similar values of 2.

Test the stability and accuracy of the methods using MonteCarlo pseudo-data generated from a chosen set of polarised parton distributions compare then with the fit results.

LSS’06


Statistical UncertaintiesStatistical UncertaintiesAt least two groups (BB and AAC) report statistical uncertainties inflated by They cannot be directly compared to those of other groups.

NPAR

(These inflated uncertainties do not correspond to what is normally understood as statistical uncertainty, obtained as the standard deviation of the distribution of results derived by fitting a large number of MC data sets resembling the experimental data sets, but with each data point fluctuating independently according to the experimental statistical uncertainty)

2

pi

pj

22=1 defines the 1 uncertainty for single parameters

2~NPAR is the 1 uncertainty for the NPAR parameters to be simultaneously located inside the hypercontour(normally used for unknown systematics, see CTEQ, MRST….)

NPAR=number of parameters


Normalization UncertaintiesNormalization UncertaintiesSome groups attempt to account for the (substantial) syst. unc. common to an entire data set for one experiment by adding it incoherently in quadrature to the uncertainty in each data point.It can be accounted for correctly with a 2 penalty term, see BB:

Norm. unc. quoted by expt.

Fitted normalization

02

iN

2,11

2

,1

21

2

,1,1,1,1

/1

/

datak

n

j

theorj

i

n

k

datak

datak

theork

theork

i

ggN

ggggN

data

data

The normalizations can also be calculated analytically at each step, without increasing the number of parameters in the fit:

exp

1 12

,1

2

,1,1

2

22 1n

i

n

jdataji

theorj

dataji

i

i

data

gN

ggN

N

N

One can get even more fancy and consider the experimental systematic uncertainties:

Si can also be calculated analytically at each step

dataksysi

datak

datak gSgg ,1,1,1


Symmetric Sea Symmetric Sea Assumption: new results Assumption: new results

from COMPASSfrom COMPASS

The estimated v is 2.5stat away from the symmetric sea scenario

HERMES, Q2=2.5GeV2


The new g1 data from HERMES, COMPASS and CLAS provide new insights into the polarised quark distributions.

At the moment still other data (like for AAC or semi-inclusive asymmetries for De Florian et al.) has to come in aid of QCD fits in order to pin down the gluon distribution

For more precise data on G from scaling violations of g1, proposed e-p colliders e-LIC and eRHIC

The latest QCD fits look at various aspects of q (AAC:gluon, LSS:HT…)It would be nice to have one comprehensive analysis with all these features:

HT calculationStatistical error band calculation

explicitely state which 2 choice was made and possibly provide results with the two choices

Propagation of systematic uncertaintiesFit NS to test the Bjorken Sum Rule

Fit s

……

And last by not the least, I’d like to thank all the people that knowingly or not provided me with their plots!

ConclusionsConclusions

0LLA


ss

J.Blümlein et al.,Nucl.Phys.B774(2007)182

QCD fits are a powerful way to extract s(M2Z ).

While a variety of results exist in unpolarised DIS (up to N3LO), only sparse information is available from fits to g1 data, with large errors

the spin structure function g 1 and qcd fits to the g 1 world data

Documents

g1d data

initial q2

deuteron data

gev2 q2

b6472007330at low q2

data points

g1 world data lara

fitting inclusive world