The Spin of the Proton_Pasquale Di Nezza_Spin Physics at HERMES___ hadronic tensor W µν Æparametrised by structure functions (Lorentz symmetry, current conservation, parity,

The Spin of The Spin of the Protonthe Proton

Pasquale Di NezzaDESY, Hamburg 18/08/05

HERHERaa MEMEasurementasurement ofof SSpinpin

Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon___Pasquale Di Nezza _________________________________________________________Spin Physics at HERMES________

Collaboration of 180 phys., 33 Inst., 12 Countries

HERHERaa MEMEasurementasurement ofof SSpinpin

Collaboration of 180 phys., 33 Inst., 12 Countries

Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon___Pasquale Di Nezza _________________________________________________________Spin Physics at HERMES________

• Introduction to polarised DIS

• Prerequisites

• Polarisedstructure functions

• The Spin of the Nucleon

fascinatedfascinated by spin …by spin …“You think you understand something? Now add spin…” -- R. Jaffe

W. Pauli

N. Bohr

Preface | Introduction to polarised DIS | Prerequisites | polarised Structure Functions | the Spin of the Nucleon___Pasquale Di Nezza_________________________________________________________Spin Physics at HERMES________

fascinatedfascinated by spin … an analogyby spin … an analogy

Speaking in this analogy our planet has an orbital angular momentum (around the sun / the nucleus) and in addition a spin angular momentum (around its own axis).

What is Spin ?What is Spin ?[www.markusehrenfried.de/science/physics/whatisspin.html]

• Stern-Gerlach (1921):

• Uhlenbeck, Goudsmit:(1925)explanation of atomic spectra


quantum number: ms=1/2

What is Spin ?What is Spin ?

Spin and Symmetry: [S.Hawkins: A brief history of time]

180ο 360ο

spin: ?21

2x360ο

math:antisymmetricwave function

spin: 2 spin: 1


is spin important ?is spin important ?

half integer SPIN

obey Pauli principle

antisymmetric under exchange

of identical particles

Fermi-Dirac statistics:Fermions MATTER

Pauli principle …


integer SPINdon’t care for Pauli principle

symmetric

Bose-Einstein statistics:Bosons

FORCES

is spin important ?is spin important ?


half integer SPIN

obey Pauli principle

antisymmetric under exchange

of identical particles

Fermi-Dirac statistics:Fermions MATTER

integer SPINdon’t care for Pauli principle

symmetric

Bose-Einstein statistics:Bosons

FORCES

Pauli principle …

how to study the proton spin ?how to study the proton spin ?

… deep-inelastic scattering (DIS)

)cos(12EE'qQlab

22 θ-=−=

,2MνQx

2lab= E'Eν

lab−=

22 MQ >>↔• “deep” high resolution:1MM 22X

µνW hadronic part of the xsectioncontains info on proton structure+ strong interaction effects

DIS cross sectionDIS cross section


µνL leptonic part of the xsectionindependent of proton structurecan be calculated explicitely

)Xepe( →σ

µνµν'4

2

'

2

WLEE

MQα

dEdd

=Ω

σ

hadronichadronic tensortensor µνWparametrised by structure functions(Lorentz symmetry, current conservation, parity, ecc.)

)Q(x,Fνpp)Q(x,FW 22νµ

21

µνµν +−= g

( ) ⎟⎠⎞

⎜⎝⎛ ⋅−⋅++ )Q(x,gqpSqSp

ν1)Q(x,gS

νqiε 22σσ

21σ

λµνλσ




21

µνµν +−= g

( ) ⎟⎠⎞


ν1)Q(x,gS

νqiε 22σσ

21σ

λµνλσ

momentum distribution of quarks

( )∑ ∑=+= −+i i iiii xqexqxqexF )(21)()(

21)( 221

QPM:




21

µνµν +−= g

( ) ⎟⎠⎞


ν1)Q(x,gS

νqiε 22σσ

21σ

λµνλσ



21)( 221

QPM:

qi(x) = Distribution Functionconnected to the probability to have a struck quark with fractional momentum x




21

µνµν +−= g

( ) ⎟⎠⎞


ν1)Q(x,gS

νqiε 22σσ

21σ

λµνλσ



21)( 221

QPM:

q+i(x) = Polarized Distribution Functionconnected to the probability to have a struck quark with fractional momentum x and spin in the same direction of the proton




21

µνµν +−= g

( ) ⎟⎠⎞


ν1)Q(x,gS

νqiε 22σσ

21σ

λµνλσ

helicity distribution of quarks

( )∑ ∑=−= −+i i i2ii2i1 (x)∆qe21(x)q(x)qe

21(x)g



21)( 221

QPM:


helicityhelicity densitiesdensities ∆∆qq


because of helicity conservation, the virtual photon can couple only to a quark of opposite helicity

23SS Nγ =+

)(2/3 xq−≈σ

by changing the orientation of target nucleon spin or the helicityof incident lepton beam we can select q+(x) or q-(x) ∆q

21SS Nγ =+

)(2/1 xq+≈σ

the nucleon spin structurethe nucleon spin structure

( )444 3444 21

1 Σsvv ∆q∆d∆u2

121

=∆++=

EMC (‘88) ∆Σ=0.123 ± ...

QPM:

Spin P

uzzle

gluons are important !

GΣ21

21

∆+∆=

don’t forget the orbital angular momentum!

gq LGL∆Σ 21

21

+∆++=SLAC, CERN, DESY: 0.2-0.4


polarisedpolarised deep inelastic scatteringdeep inelastic scattering

polarised beam

and/or

polarised target


exclusive dis

gq JJ +=

semi-inclusiveDIS

flavour separation

inclusive dis

inclusivehadrons

gq LGL∆Σ 21

21

+∆++=

Hermes @ DESYHermes @ DESY



self-polarised electrons: e



self-polarised electrons: e

Stern-Gerlach separation


how to measure how to measure xsectionsxsections //asymmetriesasymmetries


)Qx,()E'θ,( 2σσ ↔

E’ = const.

θ = const.

how to measure how to measure xsectionsxsections //asymmetriesasymmetries


)Qx,()E'θ,( 2σσ ↔

E’ = const.

θ = const.

L)Qx,N()Qx,(

22 ∆∆∝σ

how to measure ghow to measure g11virtual photon asymmetry:

)Q,(A)γ1(

1)Q,(F)Q,(

Fgγg

σσσσ

A 2||221

21

1

22

1

2321

23211 xDx

xg+

≈≈−

=+

−=


how to measure ghow to measure g11


)Q,(F)Q,(F)Q,(g)Q,(g 2param1

meas2

1

212

1 xxxx ⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛=

252 GeV101:Q −

:)Q,(F 2param1 x

0.7 - 0.000005 :x

how to measure ghow to measure g11


)Q,(F)Q,(F)Q,(g)Q,(g 2param1

meas2

1

212

1 xxxx ⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛=

252 GeV101:Q −

:)Q,(F 2param1 x

0.7 - 0.000005 :x

0

0.5

1

1.5

2

2.5

3

3.5

4

1 10 102

E143

Q2 (GeV2)

gp 1(x

,Q2 )

+c(x

)

HERMES

HERMES low-x prel.

E155 prel.

EMC

SMC

phen. fit

222 GeV101:Q −

:)Q,( 2p1 xg

0.75 - 0.006 :x

helicity distributions

(polarised quark distributions)

the integral of gthe integral of g11


( )∑ −+ −= f fff (x)q(x)qe21(x)g 21

∑ ∆= f f x)(qe21 2

sum rules for gsum rules for g11

∑∫ ∆+∆⎯⎯ →⎯=Γ q 2qQPMnp,11

0

np,1 )qq(e)(d xgx

Bjorken sum rule:(isospin symmetry)

fundamental QCD prediction

21.06a3n

1p

1 ≅=Γ−Γ

Ellis-Jaffe sum rule:∆s=0

)02.0(19.0a121)(a

365

38p(n)

1 −≅−+=Γ


sum rules for gsum rules for g11

∑∫ ∆+∆⎯⎯ →⎯=Γ q 2qQPMnp,11

0

np,1 )qq(e)(d xgx


Bjorken sum rule confirmed @ 8% C.L.

violated

∆s=0

∆∆qq from gfrom g11(x,Q(x,Q22))

∑ ∆= q 22qLO1 )Qq(x,e21)(xg

])Q,(G)Qq(x,[e21

2)( g

2qq

22q

sLO1

NLO1 CxCgxg ⊗∆+⊗∆+= ∑π

αone step further:

parameterised


∑ −= data 2stat

2calc1

meas12 )(

σχ gg

minimisation : 2χ

evaluateparameter

∆∆qq andand ∆∆G G from gfrom g11(x,Q(x,Q22))


∆uv ∆u

∆dv ∆d

∆s ∆s • ∆uv and ∆dv (quite) well determined

need more direct probes flavour separation∆G

• ∆q and ∆G weakly constraint by data

polarisedpolarised semisemi--inclusive DISinclusive DIS

π- udK- us

flavour tagging

π+ ud




π- udK- us

flavour tagging

π+ ud

∑ →⊗⊗∝f

fff zDdxqz )()()(dhqh σσ , z=Eh/ν

distributionfunction

probability that struck quarkof flavour f fragments into hadron of type h with energy fraction z

fragmentationfunction


∑ ∫∑ ∫≈

+

−=

f fff

f fff

)Q(z,Ddz)Q(x,qe

)Q(z,Ddz)Q(x,∆qe

σσσσ

)Q(x,A2h22

2h22

h23

h21

h23

h212h

1

polarised partondistribution functions !

known quantitieshadron asymmetries to be measured


particle identificationparticle identification


double radiator RICH for π / K / p separationaerogel: n=1.03C4F10: n=1.0014

Cerenkov light emission:

2c β1mcβp

βn1cos

−=⇒=ϑ

particle identificationparticle identification


quark/antiquark/anti--quark quark helicityhelicity distributionsdistributions

∑ ∫∑ ∫≈

+

−=

f fff

f fff

)Q(z,Ddz)Q(x,qe

)Q(z,Ddz)Q(x,∆qe

σσσσ

)Q(x,A2h22

2h22

h23

h21

h23

h212h

1



needs at least six independent asymmetry sets A1h(x) to determine six unknown helicity distributions: ∆u, ∆u, ∆d, ∆d, ∆s, ∆s

PURITY is an unpolarised quantity

)Q,(qq

(z)Ddz)Q(x,q'e

(z)Ddz)Q(x,qe)Q(x,A 2

'h22

h222h

1

),(hqP

xf f f'f'

fff

zx

∆⋅= ∑ ∑ ∫

∫44444 344444 21


(x) )A,A,A,A,(AA Kd1,d1,p1,d1,p1,±±±

= ππr

(x) 0ss,

ss,

dd,

dd,

uu,

uuQ ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

∆∆∆∆∆∆=

r

measured measured hadronhadron asymmetriesasymmetries

h+

π-

π+

h-

inclproton

deuteron

h+

h-

π+

π-

K+

K-


K− us all sea objects

π-h-incl

x

x

puritiespuritiesconditional probability that γ* hits a quark of flavour q

when hadron of type h was detected

u u d sd sπ+

K+

π−

K−


quark/antiquark/anti--quark quark helicityhelicity distributionsdistributionsu quarks large positive polarisation


quark/antiquark/anti--quark quark helicityhelicity distributionsdistributionsu quarks large positive polarisation


d quarks negative polarisation


sea quark (u, d, s ,s) compatible with 0

no indication for ∆s < 0

- - -

u quarks large positive polarisation


d quarks negative polarisation

where do we standwhere do we standthe (spin) structure of the nucleon …


H1, ZEUS,++

HERMES, ++

HERMES, COMPASS:first glimpse

HERMESCERNRHIC

?

don’t forget the orbital angular don’t forget the orbital angular momentummomentum

gq LGL∆Σ 21

21

+∆++=

hard exclusive processes…


polarisedbeam

and/or

polarisedtarget γexclusive dis

exclusivity @HERMESexclusivity @HERMES

e+

missing mass technique:

Mx2=(p+q−Pγ,π )

2

σ(Mx)~0.8 GeV


detected

detectedNOT detected



Mx2=(p+q−Pγ,π )

2

σ(Mx)~0.8 GeV


detected


e+



Mx2=(p+q−Pγ,π )

2

σ(Mx)~0.8 GeV


detected


2005++2005++

e+

Generalized Parton Distributions

Quantum number of final state selects different GPDs:Vector mesons (ρ, ω, φ): H EH EPseudoscalar mesons (π, η): H E H E DVCS (γ) depends on H, E, H, EH, E, H, E~~ ~~

~~ ~~

“Tomographic” Images of the Proton’s Quark Content

(In the Infinite Momentum Frame)

transversely polarized target1Impact parameter:-t

b = T

where do we stand where do we stand the (spin) structure of the nucleon …


H1, ZEUS,++

HERMES, ++

HERMES:first glimpse

HERMESCERNRHICSLAC

? UPCOMING:HERMESJLab?

transversitylecture by its own

HERMESCERNRHICJLabKEK

…ecc.

the nucleon puzzle is goingthe nucleon puzzle is goingto be completedto be completed

Still fascinated by Spin ?Still fascinated by Spin ?

Thank you !Thank you !

___Pasquale Di Nezza_________________________________________________________Spin Physics at HERMES________

HERa MEasurement of SpinHERa MEasurement of Spinfascinated by spin …What is Spin ?What is Spin ?What is Spin ?is spin important ?is spin important ?how to study the proton spin ?DIS cross sectionhadronic tensorhadronic tensorhadronic tensorhadronic tensorhadronic tensorhelicity densities Dqthe nucleon spin structurepolarised deep inelastic scatteringhow to measure xsections /asymmetrieshow to measure xsections /asymmetrieshow to measure g1how to measure g1how to measure g1how to measure g1the integral of g1sum rules for g1sum rules for g1Dq and DG from g1(x,Q2)polarised semi-inclusive DISpolarised semi-inclusive DISpolarised semi-inclusive DISparticle identificationparticle identificationquark/anti-quark helicity distributionsquark/anti-quark helicity distributionsmeasured hadron asymmetriespuritiesquark/anti-quark helicity distributionsquark/anti-quark helicity distributionsquark/anti-quark helicity distributionswhere do we standdon’t forget the orbital angular momentumexclusivity @HERMESexclusivity @HERMESexclusivity @HERMESGeneralized Parton Distributionswhere do we stand

Documents

The Spin of the Proton___Pasquale Di Nezza_____Spin Physics at HERMES_____ hadronic tensor W µν Æparametrised by structure functions (Lorentz symmetry, current conservation, parity,

The Spin of the Proton_Pasquale Di Nezza_Spin Physics at HERMES___ hadronic tensor W µν Æparametrised by structure functions (Lorentz symmetry, current conservation, parity,