Transverse quark spin distributions in the nucleon Hidekazu Tanaka - - PowerPoint PPT Presentation

Transverse quark spin distributions

in the nucleon

Hidekazu Tanaka

for HERMES collaboration Tokyo Institute of Technology, Department of Physics Spin puzzle Deep Inelastic Scattering Single-spin asymmetry Recent results from HERMES

Spin Puzzle Spin Puzzle

1 2 = 1 2   G  Lq  Lg

Gluon spin distribution

 ≡u d  u  d s  s

Quark helicity distribution

G

Unknown ....

LqLg

Orbital angular momenta

• f quark and gluon

 ~ 0.2−0.3

Known now in measuring

Parton Distribution Functions Parton Distribution Functions

Quark helicity (known) Quark density (well known) Quark transversity (unmeasured!) Gluon distributions PDFs describe the nucleon structure

What is Quark Transversity ? What is Quark Transversity ?

q − q = ??

Transversity δq describes transverse quark polarization in the transversely polarized nucleon.

i

=

?? quark polarization in the long. pol. nucleon

q q

Non-realtivestic limit ; q − q = 0 quark polarization in the trans. pol. nucleon

q

Yet Another Quark Distribution Yet Another Quark Distribution

Other quark distribution is “Sivers function” . The Sivers function describes unpolarized quark in the transversely polarized nucleon. The Sivers function is related to quark orbital angular momentum. ??

f 1T

⊥

f 1T

⊥  x

quark momentum distribution in unpol. nucleon

q x

quark momentum distribution in trans. pol. nucleon

L

f 1T

⊥  x

The HERMES Experiment The HERMES Experiment

q

f 1T

⊥

L

Sivers function Transversity

Deep Inelastic Scattering is the best tool to access to both distribution functions

Semi-inclusive

(Hadron coincidence measurement with the scattered lepton)

Deep Inelastic Scattering (DIS) Deep Inelastic Scattering (DIS)

Fragmentation Inclusive

(Only scattered lepton is measured)

Unmeasured lepton nucleon

x : Quark momentum fraction

Q, q PM ,0

: Target mass : Virtual photon 4-momentum

M Q  : Virtual photon energy



*

(Bjorken scaling parameter)

qx Dz

: Fractional energy of produced hadron

z

Transversely Polarized DIS Transversely Polarized DIS

Lepton Scatt. Plane Hadron Prod. Plane

Two Azimuthal angles

S 

: Angle between and L.P. : Angle between L.P. and H.P.

 S ⊥

 k ,  k

'

 q  phad

: Lepton momentum : Hadron momentum : Virtual photon momentum

Single Target-spin Asymmetry Single Target-spin Asymmetry

d 



d 



Unpolarized Transversely

polarized

A = d 

−d  

d 

d   e





∗

e

∗

T U T U Sivers asymmetry Collins asymmetry

A ≡ AUT

Collins sinS 

AUT

Sivers sin−S

AUT

Collins ∝ qx H 1 ⊥ z

AUT

Sivers ∝

f 1T

⊥ x D1z

Sivers function Transversity

d 

 ,  π production

cross-section

Fragmentation Function Fragmentation Function

Collins FF Unpolarized FF

AUT

Collins ∝ qx H 1 ⊥ z

AUT

Sivers ∝

f 1T

⊥ x D1z

π π

Collins FF describes fragmentation of pol. quark into unpol hadron (Unknown) Normal unpol. fragmentation (Well known)

Properties of the Asymmetry Properties of the Asymmetry

Collins Asymmetry Sivers Asymmetry

AUT

Collins ∝ qx H 1 ⊥ z

AUT

Sivers ∝

f 1T

⊥ x D1z

Transversity (Polarized PDF) Collins FF (Polarized FF) Sivers function (Unpolarized PDF) Orbital angular momenta ↓ & T U

A ≡ AUT

Collins sinS 

AUT

Sivers sin−S

Sivers Asymmetry Measured at HERMES Sivers Asymmetry Measured at HERMES

π+ π- π0 Asymmetries are small, but is slightly positive at low x.

AUT

Sivers 

Beam : (27.6 GeV) Target : Hydrogen About 5 months data taking

e



〈Q

2〉 ~ 2.5GeV 2

0.2z0.7

0.023x B0.4

Gray band indicates possible effects of exclusive vector meson.

AUT  x ∝ f 1T

⊥  x ∫dz D1z

AUT z ∝∫dx f 1T

⊥ x D1z

xB : Quark momentum fraction z : Fractional energy of produced hadron

π+ π- π0

Collins Asymmetry Measured at HERMES Collins Asymmetry Measured at HERMES

AUT

Collins  ≥0

AUT

Collins  −≤0 ; Large negative

; Small positive

AUT  x ∝  q x ∫dz H 1

⊥ z

AUT z ∝∫dx qx H 1

⊥ z

AUT

Collins  0 ≤0 ; Negative

π+ π- π0

Conclusion Conclusion

Tow new quark distributions are important to understand the nucleon structure.

• Transversity : a probe of a relativistic nature of

the nucleon.

• Sivers function : related to quark orbital angular

momentum. To investigate those functions, several experiments (HERMES, COMPASS, RHIC-spin) are now running. HERMES provided their preliminary results on single spin asymmetry of π production in DIS.