hermes. Latest News from HERMES. E.C. Aschenauer. DESY-ZEUTHEN on
behalf of the hermes Collaboration. E.C. Aschenauer. DESY PRC October 2002.
1 ...
Latest News from HERMES E.C. Aschenauer DESY-ZEUTHEN
on behalf of the hermes Collaboration
hermes
E.C. Aschenauer
DESY PRC October 2002
1
Polarized Deep Inelastic Scattering
(E,’ p’ ) (E, p)
Important Variables:
e q
γ*
u N
u
lab
=
4EE
x
lab
z
lab
Q2 2mν Eh ν
Q
h
2
h d
π
+
π
= =
0
sin2 ( θ2 )
ν
lab
=
E − E0
y
lab
ν E
=
=
p·q p·k
α2 E 0 Cross Section: = Q2 E Lµν W µν 0 0 0 2 Lµν = 2[kµ kν + kν kµ − k · k − me gµν +ime µναβ S α (k − k 0 )β ] pµ pν µν µν 2 2 W = −g F1 x, Q + ν F2 x, Q 1 µνλσ qλ 2 2 + ν (p · qSσ − S · qpσ ) g2 x, Q +i ν Sσ g1 x, Q 1 2 2 (for spin 1) −b1 x, Q rµν + 6 b2 x, Q (sµν + tµν + uµν ) 1 1 2 2 + 2 b3 x, Q (sµν − uµν ) + 2 b4 x, Q (sµν − tµν ) d2 σ dΩdE 2
F1 ,F2 / g1 ,g2 =⇒ Unpolarized / Polarized Structure Functions NO: relativistic effects , intrinsic kT , quark masses and correlations hermes
E.C. Aschenauer
DESY PRC October 2002
2
V
+ -T
+
V
Deuterium - Tensor Polarization
T
0
Tensor Polarization: T
E/EHFS
3 Hydrogen
2
HFS MF | 1 > +1 |2> 0
MI MS +1/2 +1/2 -1/2 +1/2
Deuterium
HFS |1> |2> |3>
MF +3/2 +1/2 -1/2
MI +1 0 -1
MS +1/2 +1/2 +1/2
0 -1 |3> |4>
-3
0
2
4
-1 0
|4> |5> |6>
-1/2 -1/2 +1/2 -1/2
6
8 0 B/BCH
2
4
-3/2 -1 -1/2 0 +1/2 +1
6
1 − 3N0
=
N+ +N− −2N0 N+ +N− +N0
=
N± −2N0 N± +N0
State Vector + Vector Tensor ± Tensor 0
1
-2
=
-1/2 -1/2 -1/2
Injected |1 > +|6 > |3 > +|4 > |3 > +|6 > |2 > +|5 >
N+ N− N± N0
V 1 -1 0 0
T 1 1 1 -2
8 B/BCD
Only possible with a gas target hermes
E.C. Aschenauer
DESY PRC October 2002
3
The Tensor Polarized Structure Function b d1 q+
F1 (x) : g1 (x) : b1 (x) :
q-
Proton P 2 + − 1 e (q (x) + q i i i i (x)) 2 P 2 + − 1 e (q (x) − q i i i i (x)) 2
q0
Deuteron P 2 + − 1 0 e (q (x) + q (x) + q i (x)) i i i i 3 P 2 + − 1 e (q (x) − q i i i i (x)) 2 P 2 + − 1 0 e (2q (x) − (q (x) + q i i i i i (x))) 2
In the parton model bd 1 measures the difference in the quark momentum distributions of helicity 1 and 0 targets
hermes
E.C. Aschenauer
DESY PRC October 2002
4
AT (10-2)
Tensor Asymmetry
2
bd 1 enters in the symmetric part of Wµν −→ not sensitive to PB
0
AT -2
=
1 T
·
N+ N− N0 + −2 L0 L+ L− − 0 N+ + N− + N 0 + L L L
T: target polarization < T >= 0.83 ± 0.03 L+/−/0 : dead-time corrected luminosities
-4 10
hermes
=
(σ + +σ − )−2σ 0 σ + +σ − +σ 0
E.C. Aschenauer
-2
10
-1
x
DESY PRC October 2002
5
b2
Results on bd1 0.02
b1 = − 32 · AT · Fd 1
0.015
b1 =
0.01
· b2
with:
0.005
• Fd 1 =
0
Fd 2 = -0.005
• -0.01
1+γ 2 2·x(1+R)
Fn 2 : Fp 2 Fp 2:
1+γ 2 d 2·x(1+R) · F2 Fn p F2 (1 + F2p ) 2
NMC, Nucl. Phys. B371 (1992) 3
ALLM97 (hep-ph 9712415) R: Phys. Lett. B250 (1990) 193
10
• no higher twist effects (b3 , b4 = 0)
1 -1
10 10
hermes
K.Bora & R.L. Jaffe Phys.Rev.D57 (1998) 6906 -4
10
-3
E.C. Aschenauer
10
-2
10
-1
x
DESY PRC October 2002
6
DVCS azimuthal asymmetries ∗ ∗ dσ ∝ |TBH |2 + |TDVCS |2 + (TBH TDVCS + TDVCS TBH )
isolate BH-DVCS interference term: • imaginary part ∝ beam helicity asymmetry: dσ ←+ − dσ →+ ∝ Im (TBH TDVCS ) e
e
∝
sin φ
• real part ∝ beam charge asymmetry: dσe+ − dσe− ∝ Re (TBH TDVCS ) ∝ cos φ ⇒ both asymmetries measured by HERMES
e’ (Detected) e
γ (Detected)
γ∗
(known)
GPD p
X (Not Detected)
y x
(known)
ST SL
P k’
θγ q
z
lepton scattering plane and the γ ∗ γ - plane
k
hermes
φ: azimuthal angle between
φ
E.C. Aschenauer
DESY PRC October 2002
7
DVCS on Nuclear Targets
Nγ / NDIS
x 10
-3
0.45 0.4
HERMES PRELIMINARY
0.35
Neon
0.3
Hydrogen
Proportional to :
Deuterium
0.25
• Charge of the Nucleus • Formfactor of the Nucleus
0.2 0.15 0.1 0.05
Mx < 1.7 GeV
0 -0.4 -0.2
0
0.2 0.4 0.6 0.8
1
1.2 1.4 2
-t (GeV )
hermes
E.C. Aschenauer
DESY PRC October 2002
8
→+
e Ne → e γ X
0.6
+
(Mx< 1.7 GeV)
→+
e d→e γX
0.6
HERMES PRELIMINARY P1 + P2 sin φ + P3 sin 2φ
0.4
0.8
ALU
0.8
ALU
ALU
DVCS SSA on Nuclear Targets (Mx< 1.7 GeV)
+
e p→e γX
P1 + P2 sin φ + P3 sin 2φ
0.2
0.2
0
0
0
-0.2
-0.2
-0.2
-0.4 P1 = 0.00 ± 0.02 (stat) P2 = -0.22 ± 0.03 (stat) P3 = 0.04 ± 0.03 (stat)
-0.6 -0.8 -1
-0.8
-2
-1
0
1
2
3
φ (rad)
P1 + P2 sin φ + P3 sin 2φ
P1 = -0.04 ± 0.02 (stat) P2 = -0.18 ± 0.03 (stat) P3 = 0.00 ± 0.03 (stat)
-0.6
= 0.20 GeV2, = 0.10, = 2.5 GeV2
-1 -3
(refined)
-0.4 P1 = -0.04 ± 0.02 (stat) P2 = -0.15 ± 0.03 (stat) P3 = 0.03 ± 0.03 (stat)
-0.6
= 0.13 GeV2, = 0.09, = 2.2 GeV2
(Mx< 1.7 GeV)
+
HERMES PREL. 2000
0.4
0.2
-0.4
→+
0.6
HERMES PRELIMINARY
0.4
0.8
-0.8
= 0.18 GeV2, = 0.12, = 2.5 GeV2
-1 -3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
φ (rad)
3
φ (rad)
Predictions by A.V. Belitsky et al. (hep-ph/0112108): Deuterium: ALU ∼ −0.13 · sin(Φ) at Q2 = 4GeV2 x = 0.1, t = −0.3GeV2 Hydrogen: ALU ∼ −0.16 · sin(Φ)
First Hint for coherent scattering on the nucleus. hermes
E.C. Aschenauer
DESY PRC October 2002
9
The 3rd Twist-2 Structure function
q
f1 =
↓
g1q =
-
↓
q
h1 =
-
↓
Unpolarized quarks and nucleons
Longitudinally polarized quarks and nucleons
Transversely polarized quarks and nucleons
vector charge: ¯ µ ψ|P S >= < P S|ψγ R1 dxq(x) − q¯(x) 0
axial charge: ¯ µ γ5 ψ|P S >= < P S|ψγ R1 dx∆q(x) + ∆¯ q (x) 0
tensor charge : ¯ µν γ5 ψ|P S >= < P S|ψσ R1 dxδq(x) − δ q¯(x) 0
q(x): spin averaged well known
∆q(x): helicity difference known
δq(x): helicity flip unmeasured
HERMES 1995-2000
HERMES 2002. . .
hermes
E.C. Aschenauer
DESY PRC October 2002
10
Characteristics of Transversity • Non-relativistic quarks: ∆q(x) = δq(x) ⇒ δq probes relativistic nature of quarks • Angular momentum conservation ⇒ Transversity has no gluon component ⇒ different Q2 evolution than ∆q(x) • q and q¯ contribute with opposite sign to δq(x) ⇒ predominantly sensitive to valence quark polarization • Bounds: ⇒ |δq(x)| ≤ q(x) ⇒ Soffer bound: |δq(x)| ≤ 12 [q(x) + ∆q(x)] • Transversity distribution CHIRAL ODD ⇒ No Access In Inclusive DIS
hermes
E.C. Aschenauer
+ X +
DESY PRC October 2002
11
How can one measure Transversity? Need another chiral-odd object! δq(x) accessible in semi-inclusive DIS X ep→ehX = f H→q ⊗ σ eq→eq ⊗ Dq→h σ q
⇓ chiral-odd DF
⇓ chiral-odd FF
Study SSA with a transversely polarized target at HERMES 1. ep↑ −→ e0 πX
⇐ Favorite Process Collins,93, Kotzinian,95, Mulders et al,96
2. ep↑ −→ e0 Λ↑ X 3. ep↑ −→ e0 ππX
hermes
E.C. Aschenauer
Baldracchini,82, Jaffe,96 Jaffe et al,97
DESY PRC October 2002
12
First glimpse on Transversity ?! 0.04
1 N + (φ) − N − (φ) · AU L (φ) = hP i N + (φ) + N − (φ)
P1 * sin φ P1 * sin φ + P2 * sin 2φ
→
0.02 AUL(φ)
Longitudinal polarized deuteron target
e d → e π+ X
0
-0.02
P1 = 0.012 ± 0.002 P2 = 0.004 ± 0.002
0.04
Q
0
-0.02
1 − y ∼ 0.15
y x ST
P1 = 0.021 ± 0.005 P2 = 0.009 ± 0.005
0.04 →
0.02 AUL(φ)
ST ∝ sin Θγ '
2M x p
0.02 AUL(φ)
ST transverse component of target spin w.r.t. virtual photon:
→
e d → e π0 X
e d → e π- X
0
-0.02 SL
P1 = 0.006 ± 0.003 P2 = 0.001 ± 0.003
P
θγ q
0.04
φ
→
z
k
0.02 AUL(φ)
k’
ed→eK X +
0
-0.02
P1 = 0.013 ± 0.006 P2 = -0.005 ± 0.006
longitudinal polarized hydrogen target
π 0 : hep-ex/0104005, π ± : hep-ex/9910062 hermes
E.C. Aschenauer
-0.04
-π
-π/2
0 φ (rad)
π/2
DESY PRC October 2002
π 13
0.08
→
+
ed→eπ X → + ep→eπ X
0.06
sinφ Moments
UL
Asinφ
0.04 0.02 0 -0.02 -0.04 0.08
→
0
ed→eπ X → 0 ep→eπ X
0.06
UL
Asinφ
0.04 0.02 0
Original predictions by Collins:
-0.02 -0.04 0.08
→
-
→
+
• Proton Target Larger for π + , π 0 than for π − (u-quark dominance ) • Raise with xbj (valence quark dominance) • Grow with p⊥ , peak around 1 GeV
ed→eπ X → ep→eπ X
0.06
UL
Asinφ
0.04 0.02 0 -0.02 -0.04 0.08
ed→eK X
0.06
UL
Asinφ
0.04
H1⊥ ( D1
0.02 0 -0.02
Mc Mh Mc2 +p2⊥
with Mc '1 GeV)
• First SSA for Kaons
-0.04 0
0.1
0.2
x
hermes
∝
E.C. Aschenauer
0.3 0
0.25
0.5
0.75
Pt [GeV/c]
1
0.2
0.3
0.4
0.5
0.6
0.7
z
DESY PRC October 2002
14
Attempt of Interpretation • observe non-vanishing hsin φi-moments • hsin 2φi-moment small (consistent with zero) Attribute asymmetry to Collins fragmentation and Transversity: − ST hsin φi Asin φ ∼ SL hsin φi U L U T U L Longitudinally polarized in experiment (along beam direction) hsin φiU L ∼
1 Q
hsin φiU T ∼
P
hsin 2φiU L ∼ hermes
E.C. Aschenauer
⊥(1),q
2 q e q q (hL (x)H1
P
⊥(1),q
q 2 e xh 1 (x)H1 q q
P
⊥(1),q
2 q eq xh1L
⊥(1),q
(z) − z1 h1L
(z) ⊥(1),q
(x)H1
L/T polarized in theory (along γ ∗ direction) ˜ (x)H(z))
but ST ∼
1 Q
like twist-3
(z) DESY PRC October 2002
15
Data - Theory 0.1
→
ed→eπX 0.06
π
+
π
-
π
0
→
ed→eπX
HERMES PRELIMINARY →
+
ed→eK X
0.06
0.2
