hermes
New results of exclusive φ0 and ρ0 vector meson
production at HERMES
W. Augustyniak
Andrzej Soltan Institute for Nuclear Studies, Warsaw, Poland
on behalf of HERMES Collaboration
witold.augustyniak@fuw.edu.pl
.
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.1/20
hermes
Rudiments
Spin Density Metrix Elements (SDME’s) : definitions and their determination
SDME’s and Amplitudes for ρ0 and φ vector mesons
Dependencies of SDME’s on Q2 and t’
The observables:
R=
σL
σT
the signatures of the Natural or Unnatural Parity Exchange amplitudes
Conclusions
Outlook
.
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.2/20
hermes
e + p → e′ + p′ + V : Rudiments
e
Q2
e
γ∗
V
W2
p
t
p
Kinematics:
ν = 5 ÷ 24 GeV, < ν >= 13.3 GeV,
Q2 = 0.5 ÷ 7.0 GeV2 , < Q2 >= 2.3 GeV2
W = 3.0 ÷ 6.5 GeV, < W >= 4.9 GeV,
.
xBj = 0.01 ÷ 0.35, < xBj >= 0.07
In one photon approximation
≡ γ ∗ + p → p′ + V
The amplitude of this process can be
factorized:
A = Φ∗γ ∗ →qq̄ ⊗ Aqq̄+p→qq̄+p ⊗ Φqq̄→V .
In these three steps the interaction time
(q q̄) with target is shorter than fluctuation
and formation of VM. (Collins,Frankfort
and Stirman Phys.Rev D56(1997)2982)
γ ∗ + N → ρ0 (φ) + N ′ it is good tool to
study the helicity conservation:
helicity state of γ ∗ is easy to
determine (QED)
ρ0 → π + π − decay determines the
helicity of ρ0
t′ = 0 ÷ 0.4 GeV2 , < t′ > = 0.13 GeV2
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.3/20
Exclusive ρ0 and φ Meson Production
hermes
e + p → e ′ + p ′ + ρ0 → π + π −
e + p → e′ + p ′ + φ → K + K −
The exclusive events were selected from the missing energy spectra ∆E =
Entries
ρ0
2
2
MX
−Mp
2Mp
for
:
φ.
700
600
DATA
500
DIS MC
400
300
200
100
0
-2
0
2
4
6
.
8
10 12
∆E (GeV)
The background was simulated by code MC PYTHIA.
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.4/20
ρ0 & φ-meson Spin Density Matrix
Elements (SDMEs)
hermes
α
SDMEs: rλ
′
ρ λρ
∼ ρ(V ) =
+
1
ρ(γ)T
T
λ
λ
γ
V
λ
2
V λγ
spin-density matrix of the vector meson ρ(V ) in terms of the photon matrix ρ(γ)
and helicity amplitude TλV λγ
presented according to K.Schilling and G.Wolf (Nucl. Phys. B61 (1973) 381)
α = 04, 1 − 3, 5 − 8 long. or trans. photon, λρ = −1, 0, 1 - polarization of ρ0 (φ)
measured experimentally at 5 < W < 75 GeV (HERMES,COMPASS,H1,ZEUS)
provide access to helicity amplitudes TλV λγ , which are:
extracted experimentally from SDMEs
calculated from GPDs:S.V.Goloskokov,P.Kroll arXiv:0708.3569 [hep-ph]27.08.07;
Eur.Phys.J. C 50,829 (2007) hep-ph/0601290; Eur.Phys.J. C 42,281 (2005)
hep-ph/0501242
.
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.5/20
Events
hermes
Fit of Angular Distributions Using Max.
Likelihood Method in MINUIT
π
−
lepton
scattering−plane
e’ Φ * φ
γ
e
N’
π
+
ρ
o
0.2
0.2
0.175
0.175
0.15
0.15
0.125
0.125
0.1
0.1
0.075
0.075
0.05
0.05
0.025
0.025
0
N
ρo−decay−plane
π
+
ρo −production−plane
N’
φ
π
−
θ
-2
0
0
2
Φ [rad]
-2
0
-2
0
2
φ [rad]
0.9
0.8
0.2
0.7
0.175
0.6
0.15
0.5
0.125
0.4
0.1
0.3
0.075
0.2
0.05
0.1
0.025
0
-1
-0.5
0
0.5
1
cos Θ
0
2
ψ [rad]
Simulated Events: matrix of fully reconstructed MC events from initial uniform angular
distribution
.
Binned Maximum Likelihood Method: 8 × 8 × 8 bins of cos (Θ), φ, Φ. Simultaneous fit of 23
α = W (Φ, φ, cos Θ) for data with negative and positive beam helicity
SDMEs rij
(< |Pb | >= 53.5%, Ψ = Φ − φ)
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.6/20
hermes
Function for the Fit of 23 SDME rijα
W(cos Θ, φ, Φ) = W unpol + W long.pol ,
Wunpol
" (cos Θ, φ, Φ) =
√
04 ) + 1 (3r 04 − 1) cos2 Θ − 2Re{r04 } sin 2Θ cos φ − r04 sin2 Θ cos 2φ
− r00
00
1−1
10
2
“
”
√
2
2
2
1
1
1
1
- ǫ cos 2Φ r11 sin Θ + r00 cos Θ − 2Re{r10 } sin 2Θ cos φ − r1−1 sin Θ cos 2φ
“√
”
2
2
2
2Im{r10 } sin 2Θ sin φ + Im{r1−1 } sin Θ sin 2φ
- ǫ sin 2Φ
”
“
p
√
2
2
2
5
5
5
5
+ 2ǫ(1 + ǫ) cos Φ r11 sin Θ + r00 cos Θ − 2Re{r10 } sin 2Θ cos φ − r1−1 sin Θcos2φ
#
”
“
p
√
2Im{r610 } sin 2Θ sin φ + Im{r61−1 } sin2 Θ sin 2φ ,
+ 2ǫ(1 + ǫ) sin Φ
"
“√
”
√
3
2
long.pol.
3
3
2
W
(cos Θ, φ, Φ) = 8π2 Pbeam
1−ǫ
2Im{r10 } sin 2Θ sin φ + Im{r1−1 } sin Θ sin 2φ
”
“√
p
2
7
7
2Im{r10 } sin 2Θ sin φ + Im{r1−1 } sin Θ sin 2φ
+ 2ǫ(1 − ǫ) cos Φ
#
”
“
p.
√
2
8 sin2 Θ + r 8 cos2 Θ − 2Re{r8 } sin 2Θ cos φ − r8
+ 2ǫ(1 − ǫ) sin Φ r11
1−1 sin Θ cos 2φ
00
10
3
8π 2
1
(1
2
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.7/20
SDMEs and Amplitudes for:ρ0 , φ
hermes
HERMES PRELIMINARY
∗
A- SCHC γL
|T11 |2
ρ0L
γT∗
ρ0T
→
and
→
2
04 ∝ r 1
∝ 1 − r00
1−1 ∝ -Im{r1−1 }
∗ , ρ0
γL
T
5 } ∝ -Im{r 6 }
∗
Re{T00 T11 } ∝ Re {r10
10
8
7
∗
Im {T11 T00 } ∝ Im {r10 } ∝ Re{r10 }
B- Interference:
γT∗ → ρ0L
∗ } ∝ Re{r 04 }
Re{T11 T01
10
2
1
∝ Re {r10 } ∝ Im{r10 }
∗ } ∝ r5
Re {T01 T00
00
2
1
|T01 | ∝ r00
∗ } ∝ Im{r 3 }
Im {T01 T11
10
8
∗
Im {T01 T00 } ∝ r00
C- Spin Flip:
∗ → ρ0
γL
T
6
5 ∝ r5
∗
Re {T10 T11 } ∝ r11
1−1 ∝ Im{r1−1 }
8
8
∗ } ∝ Im {r 7
Im {T10 T11
1−1 } ∝ r11 ∝ r1−1
D-Spin Flip:
.
γT∗ → ρ0−T
∗ } ∝ r 04 ∝ r 1
Re{T1−1 T11
11
1−1
3
∗
Im {T1−1 T11 } ∝ Im {r1−1 }
E- Double Spin Flip:
Witold Augustyniak, SINS
04
1 - r 00
1
2 r1-1
2
-2 Im r1-1
5
2√2 Re r 10
6
-2√2 Im r 10
7
2√2 Im r 10
8
2√2 Re r 10
04
2 Re r 10
1
-2 Re r 10
2
2 Im r 10
5
1/√2 r 00
1
-r 00
3
2 Im r 10
8
-1/√2 r 00
5
√2 r 11
5
-√2 r1-1
6
√2 Im r1-1
7
-√2 Im r1-1
8
√2 r 11
8
-√2 r1-1
04
r 1-1
1
r 11
3
Im r1-1
ρ0 proton, <Q2>=1.9 GeV2, <W>=5 GeV
φ proton and deuteron
A: γ*L →VL0 & γ*T →VT0
B: Interference γ*L →VL0 & γ*T →VT0
C: γ*T →VL0
D: γ*L →VT0
E: γ*T →V0-T
-0.2
0
0.2
0.4
0.6
scaled SDME value
=⇒ Hierarchy of ρ0 amplitudes:
|T00 | ∼ |T11 | ≫ |T01 | > |T10 | &
|T1−1 |, (0 → L, 1 → T )
=⇒ φ meson SDMEs are consistent
with SCHC, |T00 | ∼ |T11 |
th
Frascati, October 9 , 2007
– p.8/20
Dependencies of φ meson SDME’s on Q2
hermes
0.2
0.1
0
0.4
0.2
1
0
0
-0.1
1
1
0.15
1
0.06
0.1
0.5
0.02
-0.015
0
0.25
-0.11
-0.09
1
1
1
1
The SDME’s dependencies on
Q2 for
0.2
-0.2
proton and deuteron data.
0
0
0.15
bars represent the total, the inner ones
-0.4
-0.1
1
-0.1
1
0.1
1
The outer
1
0.19
the statistical errors.
-0.1
0
0.06
-0.2
-0.07
-0.1
1
1
0.16
1
0.25
0
0
0
0
-0.5
-0.16
-0.25
1
1
0.2
-1
1
1
0.45
0.24
0
-0.08
0.5
0
0
-0.2
1
.
-0.45
1
Witold Augustyniak, SINS
-0.4
1
1
Frascati, October 9th , 2007
– p.9/20
hermes
0.6
Dependencies of φ meson SDME’s on t’
0.09
0.05
0.1
0.015
0.4
-0.015
0
0
0.25
0.5
0
-0.06
0
0.25
0.5
-0.08
0
0.25
0.5
0
0.1
0.4
0.1
-0.01
0.2
0
-0.12
0
-0.1
0.25
0.5
.
-0.2
0
0.25
0.5
0
0.25
0.5
0
0.25
0.5
0.03
0
0.25
0.5
proton and deuteron data.
0.2
-0.2
-0.025
0
0.25
0.5
-0.08
0
0.25
0.5
0.09
The outer
bars represent the total, the inner ones
0
-0.4
The SDME’s dependencies on t’ for
0.2
0
0.25
0.5
0
0.25
0.5
0.1
0
0.25
0.5
0
0.25
0.5
0
0.25
0.5
0.05
the statistical errors.
-0.15
0.01
-0.01
-0.2
-0.07
0
0.25
0.5
0
0.25
0.5
-0.07
0.16
0.25
0.4
0.5
0
0
0.1
0
-0.16
0
0.25
0.5
-0.25
0
0.25
0.5
-0.2
0
0.25
0.5
-0.5
0.3
0.4
0.4
0.3
0
0.1
0.1
0
-0.3
0
0.25
.
0.5
-0.2
0
0.25
0.5
Witold Augustyniak, SINS
-0.2
0
0.25
0.5
-0.3
Frascati, October 9th , 2007
– p.10/20
φ Longitudinal-to-Transverse
Cross-Section Ratio
2
HERMES PRELIMINARY
04
R
ep(d)→e´φp(d)
proton and deutron, <W>=5 GeV
04
04
= r 00 /ε(1-r 00)
hermes
Comparison of commonly measured:
Cornell, <W>=2.1 GeV
R04 =
ZEUS, <W>=75 GeV
1.5
σL
σT
=
04
1 r00
,
ǫ 1−r04
00
where:
P
04 =
{ǫ|T00 |2 +}/σtot
r00
σtot = ǫσL + σT
H1, <W>=75 GeV
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
2
4
2
Q (GeV )
.
=⇒ R04 for φ meson at HERMES is in good agreement with world data.
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.11/20
Natural Parity Exchange in φ Meson
Leptoproduction
hermes
0.5
0.5
HERMES PRELIMINARY
ep(d)→e´φp(d)
HERMES PRELIMINARY
ep(d)→e´φp(d)
0
0
04
U1 = 1 -
-0.5
0.2
04
r00
+
04
2r1-1
-
1
2r1-1
-
04
1
1
0.6
0.7
U1 = 1 - r00 + 2r1-1 - 2r1-1 - 2r11
1
2r11
-0.5
0.2
0
0
5
5
5
-0.2
0.5
-0.2
0.5
0
0
-0.5
U3 =
8
r1-1
+
5
U2 = r1-1 + r11
U2 = r1-1 + r11
8
8
r11
0.7 0.8 0.9 1
2
3
0
4
2
8
U3 = r1-1 + r11
-0.5
0.1
2
Q (GeV )
0.2
0.3
0.4
0.5
0.8
0.9
1
2
-t´ (GeV )
U 1 = 0.02 ± 0.07stat ± 0.16syst
U 2 = −0.03 ± 0.01stat ± 0.03syst
U 3 .= −0.05 ± 0.11stat ± 0.07syst
=⇒
no UPE for φ meson production, as expected
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.12/20
Dependencies of ρ0 meson SDME’s on Q2
hermes
0.075
0.5
0
0.05
0
INDICATIONS:
0.4
0.025
-0.05
∗
green: SCHHC - γL
-0.05
0.3
1
1
0.4
1
0.1
1
0.1
0
∗
yellow: Single Flip - γT
∗
grid: Single Flip - γL
0.05
0.3
→ VL , γT∗ → VT
0
→ VT
∗
blank: Double Flip - γT
-0.05
0
0.2
→ VL
→ V−T
-0.1
1
1
0.2
1
1
0.2
-0.2
0
0.175
0.1
-0.3
0.15
-0.05
1
1
1
1
0.025
0.025
0
-0.14
.
0
-0.16
-0.025
-0.18
1
1
Witold Augustyniak, SINS
1
Frascati, October 9th , 2007
– p.13/20
Dependencies of ρ0 meson SDME’s on t’
hermes
0.05
0.1
0.05
0.5
0
0
0.05
INDICATIONS:
0.4
0
0.2
0
0
0.2
∗
green: SCHHC - γL
-0.05
-0.05
0
0.2
0
0.2
0.1
0.1
0
0.3
→ VL , γT∗ → VT
∗
yellow: Single Flip - γT
∗
grid: Single Flip - γL
0.05
0
→ VT
∗
blank: Double Flip - γT
-0.05
0.2
→ VL
→ V−T
0
-0.1
0
0.2
-0.1
0
0.2
0
0.2
0
0.2
0
0.2
0.025
0.2
0.2
-0.2
0
0.175
0.1
-0.025
-0.3
0.15
0
0.2
0
0.2
-0.14
0.025
-0.16
0
-0.18
-0.025
0
0.2
0
0.2
0.02
.
0
0
0.2
0
Witold Augustyniak, SINS
0.2
Frascati, October 9th , 2007
– p.14/20
ρ0 Longitudinal-to-Transverse
Cross-Section Ratio
hermes
R=σL/σT
Comparison of commonly measured:
HERMES PRELIMINARY ⟨W⟩=5 GeV
proton
deuteron
R04
1
CLAS ⟨W⟩=2.1 GeV
DESY ⟨W⟩=2.6 GeV
CORNELL ⟨W⟩=3.5 GeV
NMC ⟨W⟩=14 GeV
COMPASS PREL.⟨W⟩=14 GeV
E665 ⟨W⟩=18 GeV
10
ZEUS ⟨W⟩=50 GeV
H1 ⟨W⟩=75 GeV
-1
10
-1
1
.
10
04
1 r00
= ǫ 1−r04 ,
00
P
04 =
{ǫ|T00 |2 + |T01 |2 + |U01 |2 }/σtot ,
r00
σtot = ǫσL + σT ,
P
σT = {|T11 |2 + |T01 |2 + |T1−1 |2 +|U11 |2 } ,
P
σL = {|T00 |2 + 2|T10 |2 } .
Due to the helicity-flip and unnatural parity amplitudes R04 depends on kinematic conditions,
and is not identical to R ≡ |T00 |2 /|T11 |2 at
SCHC and NPE dominance.
=⇒ Second order contribution of spin-flip amplitudes to R04
Q [GeV ]
2
2
=⇒ HERMES ρ0 data on R04 are suggestive to R(W)-dependence
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.15/20
hermes
Unnatural Parity Exchange (UPE) in ρ0
Leptoproduction
Natural-parity exchange: interaction is
mediated by a particle of ‘natural’ parity:
vector or scalar meson:
J P = 0+ , 1− e.g. ρ0 , ω, a2
Unnatural parity exchange is mediated by
pseudoscalar or axial meson:
J P = 0− , 1+ , e.g. π, a1 , b1 → only
quark-exchange conribution
No interference between NPE and UPE
contributions on unpolarized target
Extracted from SDMEs:
U 2 + iU 3 ∝ (U11 + U1−1 ) ∗ U10
5 + r5
U 2 = r11
1−1
p: U 2 = −0.012 ± 0.006stat ± 0.012syst
d: U 2 = −0.008 ± 0.0046stat ± 0.010syst
5 + r5
U 3 = r11
1−1
p: .U 3 = −0.020 ± 0.050stat ± 0.007syst
d: U 3 = −0.021 ± 0.038stat ± 0.011syst
Witold Augustyniak, SINS
U 1 ∝ ǫ|U10 |2 + 2|U11 + U1−1 |2
04 + 2r 04 − 2r 1 − 2r 1
U 1 = 1 − r00
1−1
11
1−1
2
p: U 1 = 2|U11 | =
0.132 ± 0.026st ± 0.053syst
d: U 1 = 0.094 ± 0.020st ± 0.044syst
p+d: U 1 = 0.109 ± 0.037tot
=⇒ Indication on hierarchy of ρ0 UPE amplitudes:
|U11 | ≫ |U10 | ∼ |U01 |
Frascati, October 9th , 2007
– p.16/20
hermes
Conclusions
.
→ φ0L (ρ0L ) and γT∗ → φ0T (ρ0T ), are dominant for both ρ and φ.
2
2
2
2
04 ), r 1
SDME’s: (1 − r00
1−1 , Im r1−1 , depend on Q i.e ∼ 1/(Q + mv ).
∗
The transitions γL
∗
Helicity-Flip transition γT
→ ρ0L :
04 } ,Re{r 1 }
Observed only for ρ. Regular dependence of three elements belonging to this set: Re {r10
10
5 are nicely seen. In the case of r 1 and Im {r 2 } dependencies are less pronaunced.
and r00
10
00
∗
Helicity-Flip transition γL
→ ρ0T :
Very weak oscilating near zero.
∗
Double Helicity-Flip transition γT
→ ρ0−T : Very weak indication of the dependence on Q2 .
Dependence on target (H, D): not observed.
Only natural-Parity Exchange: only in the case of φ.
Unnatural-Parity Exchange: only in the case of ρ.
Comparisons with other measurements: Good agreement. For measurements with higher W small
differences are seen due .
.
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.17/20
hermes
OUTLOOK
Determine SDME’s for samples with polarized target.
.
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.18/20
hermes
END ADDITIONAL SLIDES
.
.
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.19/20
Dependencies of ρ0 meson SDME’s on Q2
hermes
0.8
0.15
r04
00
04
0.1 Re{r10}
0.6
0.05
0.05
0.4
0
0.2
-0.05
1
10
1
0
0
-0.1
-0.2
0
-0.1
-0.05
r100
1
10
0.025
1
10
0.04
0.02
1
-0.05
-0.05
r51-1
-0.1
-0.05
1
10
0.1
0.3
0.05
-0.05
1
0.15
10
0.2
0.1
0.175
0.05
0.15
10
0.05
10
5
Re{r10
}
0.125
1
10
0.1
6
Im{r10
}
2
Im{r10
}
1
0.225
r500
0
1
10
0
r11-1
0.2
r511
r111
1
0.4
10
-0.025
-0.4
-0.05
0.1
0
-0.2
-0.3
0
0.2
1
Re{r10
}
-0.1
0.05
2
Im{r1-1
}
0.05
0
10
0.1
0.1
r04
1-1
1
10
ZEUS 1995
6
Im{r1-1
}
H1
0
-0.02
-0.04
-0.15
.
1
10
-0.2
p HERMES Prel.
0
The SDME’s as function of
Q2 . For HRMES data recived
at W=5.GeV for proton and
deuteron targets as well as H1
and ZEUS data at W=75 GeV.
=⇒
Several SDMEs
2
04 , r 1
(r00
1−1 , Im(r1−1 ...) indicate
possible W -dependence,
in addition to Q2 -dependence
d HERMES Prel.
1
10
1
10
Q2 (GeV2)
Witold Augustyniak, SINS
Frascati, October 9th , 2007
– p.20/20