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Exzellenzcluster Universe
The virtue of precision spectroscopy : A new axial-‐vector meson
and a look behind the scenery of light meson decays
Stephan Paul for the COMPASS collaboration
TUM
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Exzellenzcluster Universe
The virtue of precision spectroscopy : A new axial-‐vector meson
and a look behind the scenery of light meson decays
Stephan Paul for the COMPASS collaboration
TUM
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Exzellenzcluster Universe
Brief Overview
• Introduction • Data-‐set and PWA analysis
– Method and Analysis Model – Results
• Light meson resonances revisited • A new meson a1(1420) • Studies of exotic 1-‐+
• How to observe decay dynamics – Example: ππ S-‐wave extraction
• Role of f0(980)
• Radiative meson-‐decays • Conclusions
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Exzellenzcluster Universe
Constituent Quarks and Mesons
f0(500) f0(980) f0(1500)
a4(2040)
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Exzellenzcluster Universe
Constituent Quarks and Mesons
f0(500) f0(980) f0(1500)
a4(2040)
π2(1880)
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Exzellenzcluster Universe
Constituent Quarks and Mesons
f0(500) f0(980) f0(1500)
a4(2040)
π2(1880)
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Exzellenzcluster Universe
Constituent Quarks and Mesons
f0(500) f0(980) f0(1500)
a4(2040)
π2(1880)
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Exzellenzcluster Universe
Constituent Quarks and Mesons
f0(500) f0(980) f0(1500)
a4(2040)
π2(1880)
2
2
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Exzellenzcluster Universe
Constituent Quarks and Mesons
Limits for light mesons
f0(500) f0(980) f0(1500)
a4(2040)
π2(1880)
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Exzellenzcluster Universe
Constituent Quarks and Mesons
Limits for light mesons
• many missing/disputed states in mass region
m ~ 2 GeV/c2
f0(500) f0(980) f0(1500)
a4(2040)
π2(1880)
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Exzellenzcluster Universe
Constituent Quarks and Mesons
Limits for light mesons
• many missing/disputed states in mass region
m ~ 2 GeV/c2
• Identification of heavy states difficult
− broad states
− large number
− overlap + mixing
f0(500) f0(980) f0(1500)
a4(2040)
π2(1880)
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Exzellenzcluster Universe
Kinematics and Isobarsgrid of t used Δm: 20 MeV/c2
generic process
what we are after
exclusive reaction
t ' = t − tmin ≈ t
m3π
t ' = t − tmin ≈ t
m3π
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Exzellenzcluster Universe
Kinematics and Isobarsgrid of t used Δm: 20 MeV/c2
t
m3π m3π
generic process
what we are after
exclusive reaction
t ' = t − tmin ≈ t
m3π
t ' = t − tmin ≈ t
m3π
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Exzellenzcluster Universe
Kinematics and Isobarsgrid of t used Δm: 20 MeV/c2
t
m3π m3π
generic process
what we are after
exclusive reaction
t ' = t − tmin ≈ t
m3π
t ' = t − tmin ≈ t
m3π
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Exzellenzcluster Universe
Kinematics and Isobarsgrid of t used Δm: 20 MeV/c2
t
m3π
t
generic process
what we are after
exclusive reaction
t ' = t − tmin ≈ t
m3π
t ' = t − tmin ≈ t
m3π
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Exzellenzcluster Universe
Kinematics and Isobarsgrid of t used Δm: 20 MeV/c2
t
m3π
t
generic process
what we are after
exclusive reaction
t ' = t − tmin ≈ t
m3π
t ' = t − tmin ≈ t
m3π
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Exzellenzcluster Universe
Kinematics and Isobarsgrid of t used Δm: 20 MeV/c2
t
m3π
t
generic process
what we are after
exclusive reaction
t ' = t − tmin ≈ t
m3π
t ' = t − tmin ≈ t
m3π
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Exzellenzcluster Universe
First Impressions Motivation for Isobar Model
m22π
)2c System (GeV/+π-π-πMass of the 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
5 M
eV/
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
610× (COMPASS 2008) p+π-π-π → p-π
m22π
m2 2 π
m2 2 π
ρρ
f2(1270) Prelim
inary
Prelim
inary
Prelim
inary
Prelim
inary
f0(980)
isobar model
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Exzellenzcluster Universe
Partial wave analysis
What is PWA ? !Describe population in 5-‐dimensional phase space in πππ by model • Define a set of quantum numbers JPC • Define a set of possible decay channels for each JPC (X- → isobar + π; isobar→ππ ) : wave (88 waves used)
– each such “wave” has a pre-‐determined population in phase space – each wave may have alignment of J described by quantum number M
• For each bin of 20 MeV/c2 mass of πππ: determine which coherent combination of waves fits distribution best
• Obtain spin-‐density matrix • Describe spin density matrix (submatrix) by model containing
resonances and non-‐resonant contributions connecting all mass bins • Determine resonance parameters
step
1step
2
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Exzellenzcluster Universe
Fit Model -‐ Isobars
[ππ]S
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Exzellenzcluster Universe
Major wavesMajor waves
mass independent fits minimal M = (0,1) waves
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
610× Sπ(770) ρ +0++1−1
2c/2 1.000 GeV≤ t' ≤0.100 32.65%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
10
20
30
40
50
310× Sπ(1270)
2f +1+−2−1
2c/2 1.000 GeV≤ t' ≤0.100 0.87%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
5
10
15
20
25
30
310× Gπ(770) ρ +1++4−1
2c/2 1.000 GeV≤ t' ≤0.100 0.76%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
0.5
1
1.5
2
2.5
3
610× p)−)π(3→p−πCOMPASS 2008 ( Sπ(770) ρ +0++1
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
0.5
1
1.5
2
610× p)−)π(3→p−πCOMPASS 2008 ( Dπ(770) ρ +1++2
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
10
20
30
40
50
310× p)−)π(3→p−πCOMPASS 2008 ( Gπ(770) ρ +1++4 (scaled)+π−π−π, 0π0π−π
2/c20.100 < t' < 1.000 GeV(incoherent sum)
Preliminary
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
0.05
0.1
0.15
0.2
0.25
0.3
610× p)−)π(3→p−πCOMPASS 2008 ( Sπ(1270) 2 f+0+−2
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
JPCM
JPCM ε isobar[ ]πL
1++M + ρ[ ]πS2++M + ρ[ ]πD2−+M + f2 (1270)[ ]πS4++M + ρ[ ]πG
1++M + f0 980( )%& '(πP0−+M + f0 980( )%& '(πS
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Exzellenzcluster Universe
Major wavesMajor waves
mass independent fits minimal M = (0,1) waves
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
0.5
1
1.5
2
2.5
3
610× p)−)π(3→p−πCOMPASS 2008 ( Sπ(770) ρ +0++1
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
0.5
1
1.5
2
610× p)−)π(3→p−πCOMPASS 2008 ( Dπ(770) ρ +1++2
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
10
20
30
40
50
310× p)−)π(3→p−πCOMPASS 2008 ( Gπ(770) ρ +1++4 (scaled)+π−π−π, 0π0π−π
2/c20.100 < t' < 1.000 GeV(incoherent sum)
Preliminary
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
0.05
0.1
0.15
0.2
0.25
0.3
610× p)−)π(3→p−πCOMPASS 2008 ( Sπ(1270) 2 f+0+−2
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
compare: π−π+π− and : π−π0π0
JPCM
JPCM ε isobar[ ]πL
1++M + ρ[ ]πS2++M + ρ[ ]πD2−+M + f2 (1270)[ ]πS4++M + ρ[ ]πG
1++M + f0 980( )%& '(πP0−+M + f0 980( )%& '(πS
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Exzellenzcluster Universe
t dependence of mass distributions
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
0.05
0.1
0.15
0.2
0.25610×
Sπ(770) ρ +0++1−12c/2 0.113 GeV≤ t' ≤0.100
40.45% (COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
10
20
30
40
50
310× Sπ(770) ρ +0++1−1
2c/2 0.724 GeV≤ t' ≤0.449 15.94%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16610×
Dπ(770) ρ +1++2−12c/2 0.724 GeV≤ t' ≤0.449
17.28% (COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
2
4
6
8
10
12
14
16
18
20
310× Sπ(1270)
2f +0+−2−1
2c/2 0.724 GeV≤ t' ≤0.449 5.39%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
0.5
1
1.5
2
2.5
3
3.5
310× Gπ(770) ρ +1++4−1
2c/2 0.724 GeV≤ t' ≤0.449 1.12%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
10
20
30
40
50
310× Dπ(770) ρ +1++2−1
2c/2 0.113 GeV≤ t' ≤0.100 3.39%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
10
20
30
40
50310×
Sπ(1270) 2
f +0+−2−12c/2 0.113 GeV≤ t' ≤0.100
6.46% (COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
00.20.40.60.8
1
1.21.41.61.8
2
2.22.4
310× Gπ(770) ρ +1++4−1
2c/2 0.113 GeV≤ t' ≤0.100 0.49%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
high t
low t
1++0+ρπ S 2-‐+0+ f2 π S 4++1+ ρπ G2++1+ ρπ D
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Exzellenzcluster Universe
t dependence of mass distributions
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
0.05
0.1
0.15
0.2
0.25610×
Sπ(770) ρ +0++1−12c/2 0.113 GeV≤ t' ≤0.100
40.45% (COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
10
20
30
40
50
310× Sπ(770) ρ +0++1−1
2c/2 0.724 GeV≤ t' ≤0.449 15.94%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16610×
Dπ(770) ρ +1++2−12c/2 0.724 GeV≤ t' ≤0.449
17.28% (COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
2
4
6
8
10
12
14
16
18
20
310× Sπ(1270)
2f +0+−2−1
2c/2 0.724 GeV≤ t' ≤0.449 5.39%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
0.5
1
1.5
2
2.5
3
3.5
310× Gπ(770) ρ +1++4−1
2c/2 0.724 GeV≤ t' ≤0.449 1.12%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
10
20
30
40
50
310× Dπ(770) ρ +1++2−1
2c/2 0.113 GeV≤ t' ≤0.100 3.39%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
0
10
20
30
40
50310×
Sπ(1270) 2
f +0+−2−12c/2 0.113 GeV≤ t' ≤0.100
6.46% (COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c System (GeV/−π+π−πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2 cN
umbe
r of E
vent
s / (
20 M
eV/
00.20.40.60.8
1
1.21.41.61.8
2
2.22.4
310× Gπ(770) ρ +1++4−1
2c/2 0.113 GeV≤ t' ≤0.100 0.49%
(COMPASS 2008) p−π+π−π → p−π
Preliminary
high t
low t
1++0+ρπ S 2-‐+0+ f2 π S 4++1+ ρπ G2++1+ ρπ D
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
0.1
0.2
0.3
0.4
0.5
610× p)−)π(3→p−πCOMPASS 2008 ( Sπ(770) ρ +0++1
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 0.116 GeV2/c20.100 < t' < 0.113 GeV
Preliminary
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
0.05
0.1
0.15
0.2
0.25
0.3610× p)−)π(3→p−πCOMPASS 2008 (
Sπ(770) ρ +0++1 (scaled)+π−π−π, 0π0π−π
2/c20.285 < t' < 0.395 GeV2/c20.262 < t' < 0.326 GeV
Preliminary
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Exzellenzcluster Universe
More exotic families
f0(980)
![Page 26: The$virtue$of$precision$spectroscopy$:$ A$new$axial7vector ... · Exzellenzcluster Universe The$virtue$of$precision$spectroscopy$:$ A$new$axial7vector$meson$ and$ alook$behind$the$scenery$of$](https://reader031.vdocuments.site/reader031/viewer/2022011916/5fdc3a0799479e00bc46e78c/html5/thumbnails/26.jpg)
Exzellenzcluster Universe
Waves involving f0(980)2-‐+0+ f0(980) π D0-‐+0+ f0(980) π S
π−π+π−
and
π− π
0 π0
1++0+ f0(980) π P
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Exzellenzcluster Universe
Waves involving f0(980)2-‐+0+ f0(980) π D0-‐+0+ f0(980) π S
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
24
68
10
121416
1820
2224
310× p)−)π(3→p−πCOMPASS 2008 ( Pπ(980) 0 f+0++1
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
π−π+π−
and
π− π
0 π0
1++0+ f0(980) π P
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Exzellenzcluster Universe
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
0.05
0.1
0.15
0.2
0.25
0.3
610× p)−)π(3→p−πCOMPASS 2008 ( Pπ S)ππ (+0++1
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
0.02
0.04
0.06
0.08
0.1
0.12
610× p)−)π(3→p−πCOMPASS 2008 ( Sπ S)ππ (+0+−0
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
20
40
60
80
310× p)−)π(3→p−πCOMPASS 2008 ( Dπ S)ππ (+0+−2
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
1++0+[ππ]S π P 0-+0+[ππ]S π S 2-+0+[ππ]S π D
Waves involving [ππ]Sπ−π+π−
and
π− π
0 π0
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Exzellenzcluster Universe
2-‐+0+ f0(980) π D0-‐+0+ f0(980) π S
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
0.05
0.1
0.15
0.2
0.25
0.3
610× p)−)π(3→p−πCOMPASS 2008 ( Pπ S)ππ (+0++1
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
0.02
0.04
0.06
0.08
0.1
0.12
610× p)−)π(3→p−πCOMPASS 2008 ( Sπ S)ππ (+0+−0
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
)2 (GeV/c−)π(3m0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)2in
tens
ity (p
er 4
0 M
eV/c
0
20
40
60
80
310× p)−)π(3→p−πCOMPASS 2008 ( Dπ S)ππ (+0+−2
(scaled)+π−π−π, 0π0π−π2/c20.100 < t' < 1.000 GeV
(incoherent sum)
Preliminary
1++0+[ππ]S π P 0-+0+[ππ]S π S 2-+0+[ππ]S π D
Waves involving [ππ]Sπ−π+π−
and
π− π
0 π0
1++0+ f0(980) π P
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Exzellenzcluster Universe
Model for Spin Density Matrix
Two types of contributions
p
p
π-‐ π+
π-‐
ρ, σ
π-‐
Resonance
������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
p
nπ-‐π+
p
pπ-‐
������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
π+
Deck
ρ, σ
π-‐
π-‐
Describe the results obtained independently in different mass bins by a model • select physics contributions • fit to spin density matrix (not only to simple mass spectra)
![Page 31: The$virtue$of$precision$spectroscopy$:$ A$new$axial7vector ... · Exzellenzcluster Universe The$virtue$of$precision$spectroscopy$:$ A$new$axial7vector$meson$ and$ alook$behind$the$scenery$of$](https://reader031.vdocuments.site/reader031/viewer/2022011916/5fdc3a0799479e00bc46e78c/html5/thumbnails/31.jpg)
Exzellenzcluster Universe
Use only lowest M = 0,1 waves (so far) This work: 6 waves Model: 2 resonances : a
1(1260) and a
1´ + non resonant term
! 2 resonances : a
2(1320) and a
2´ + non resonant term
! 1 resonance : a
4(2040) + non resonant term
2 resonances : π2(1670) and π
2´ + non resonant term
! 1 resonance : a
1(1420) + non resonant term
1 resonance : π (1800) + non resonant term !!
– 231 mass distributions with 23100 data points – 352 free parameters
!!
1++ 0+ρ π S
2-‐+ 0+ f2 π S4++ 1+ ρ π G2++ 1+ ρ π D
1++ 0+ f0(980) π P0-‐+ 0+ f0(980) π S
Mass-‐dependent fit
JPCMε[isobar]πL
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Exzellenzcluster Universe
Mass dependent fits a1(1420) Fit in 11 t-‐bins
sum
t
t
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Exzellenzcluster Universe
Mass dependent fits a1(1420) Fit in 11 t-‐bins
sum
t
t NEW
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Exzellenzcluster Universe
Phase: a1(1420) Fit in 11 t-‐bins: medium t
a1’a1(1420)
a4π2
a2’
fit range
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Exzellenzcluster Universe
Phase: a1(1420) Fit in 11 t-‐bins: medium t
a1’a1(1420)
a4π2
a2’
fit range
NEW
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Exzellenzcluster Universe
COMPASS “Holography”
Reference waves
Interferometry
simultaneous fit in 11 t-‐bins
tt
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Exzellenzcluster Universe
COMPASS “Holography”
Reference waves
Interferometry
simultaneous fit in 11 t-‐bins
tt
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Exzellenzcluster Universe
COMPASS “Holography”
Reference waves
Interferometry
simultaneous fit in 11 t-‐bins
tt
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Exzellenzcluster Universe
COMPASS “Holography”
Reference waves
Interferometry
simultaneous fit in 11 t-‐bins
tt
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Exzellenzcluster Universe
Mass dependent fitsFit in 11 t-‐bins t
t
Strongly t-‐dependent spectral shape around a1(1260)
sum
JPCMε[isobar]πL
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Exzellenzcluster Universe
Example for t-‐dependence
t
JPCMε[isobar]πL
IntensitiesPhases
Reference wave
a1(1260) non-‐resonant
πππ COMPASS 2008
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Exzellenzcluster Universe
Mass dependent fitsFit in 11 t-‐bins t
t
Second high-‐mass a1’ resonance visible
sum
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Exzellenzcluster Universe
Mass dependent fits a2(1320) t
t
Strongly t-‐dependent interference effects high-‐mass a2’
sum a2(1320) a2’
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Exzellenzcluster Universe
Some Results
truly new states
PDG
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Exzellenzcluster Universe
Kinematic Dependence
ACCMOR COMPASS
Very Preli
minary
Global and mass-‐dependent t‘ slope parameters
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Exzellenzcluster Universe
Kinematic Dependence
)2 System (GeV/c+π -π -πMass of the 0.5 1 1.5 2 2.5
Rat
io
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2 p (COMPASS 2008)+π-π-π →p -π
Very Preli
minary
COMPASS
Global and mass-‐dependent t‘ slope parameters Ratio of Integrals
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Exzellenzcluster Universe
t‘ Dependence (mass-‐indep)
)2c/2 (GeVt'Squared Four-Momentum Transfer 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
)2 c/2N
umbe
r of E
vent
s / (
GeV
610
710
810 Sπ(770) ρ +0++1−1
2c 1.300 GeV/≤ π3m ≤1.100 2−)c 0.02) (GeV/± = (12.03 b
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c/2 (GeVt'Squared Four-Momentum Transfer 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
)2 c/2N
umbe
r of E
vent
s / (
GeV
510
610
710
Sπ S
]ππ [+0+−0−12c 1.300 GeV/≤ π3m ≤1.100 2−)c 0.07) (GeV/± = (22.13 b
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c/2 (GeVt'Squared Four-Momentum Transfer 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
)2 c/2N
umbe
r of E
vent
s / (
GeV
410
510
610
710 Sπ
S]ππ [+0+−0−1
2c 1.900 GeV/≤ π3m ≤1.700 2−)c 0.05) (GeV/± = (11.95 b
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c/2 (GeVt'Squared Four-Momentum Transfer 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
)2 c/2N
umbe
r of E
vent
s / (
GeV
510
610
710 Sπ(770) ρ +1++1−1
2c 1.300 GeV/≤ π3m ≤1.100 2−)c 0.03) (GeV/± = (15.69 b
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c/2 (GeVt'Squared Four-Momentum Transfer 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
)2 c/2N
umbe
r of E
vent
s / (
GeV
410
510
610 Pπ(980) 0f +0++1−1
2c 1.580 GeV/≤ π3m ≤1.380 2−)c 0.1) (GeV/± = (10.5 b
(COMPASS 2008) p−π+π−π → p−π
Preliminary
)2c/2 (GeVt'Squared Four-Momentum Transfer 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
)2 c/2N
umbe
r of E
vent
s / (
GeV
510
610
710
Sπ(1270) 2
f +0+−2−12c 1.760 GeV/≤ π3m ≤1.560
2−)c 0.03) (GeV/± = (9.84 b
(COMPASS 2008) p−π+π−π → p−π
Preliminary
around a1(1260)
around π(1300)
around a1(1420)
around a1(1260)
around π(1800)
around π2(1670)
m=0
m=1
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Exzellenzcluster Universe
What about the building blocks
• We have solved a puzzle – but were the building blocks correct ?
ρσ
f0 f2
Deck
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Exzellenzcluster Universe
What about the building blocks
• We have solved a puzzle – but were the building blocks correct ?
?σ
ρ
Deck σ
ρ
Deck
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Exzellenzcluster Universe
New Paths to Meson Decays
• Select JPC via PWA • For each JPC and mass-‐bin in 3π :
– determine composition and shapes of 2π isobars – complex couplings – non-‐resonant contributions (via t-‐dependence)
p
p
π-‐ π+
π-‐
ρ, ρ3 , f0 , f2
π-‐
Resonances
p
p
p
π-‐π+
Deck
π-‐
π-‐ρ, ρ3 , f0 , f2
p
p
π-‐
π-‐ π+π-‐
ρ, σ
ρ, σ
FSI
������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
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Exzellenzcluster Universe
Isobars: an Example
use BES parametrization: as it decays into ππ and KK (threshold effect)
f0(980) parametrization[ππ]S
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Exzellenzcluster Universe
Isobars: [ππ]*Sf0(980)continuum -‐ [ππ]S
fixed functional form – variable intensity/phase (2 parameters)
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Exzellenzcluster Universe
Isobars: [ππ]*Sf0(980)continuum -‐ [ππ]S
fixed functional form – variable intensity/phase (2 parameters)
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Exzellenzcluster Universe
Isobars: [ππ]*S
replaced by ONE [ππ]*S histogram with n-‐bins
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Exzellenzcluster Universe
Isobars: [ππ]*S
replaced by ONE [ππ]*S histogram with n-‐bins (2n parameters determined by fit)
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Exzellenzcluster Universe
Isobars: [ππ]*S
replaced by ONE [ππ]*S histogram with n-‐bins (2n parameters determined by fit)
3π:
at π(1800) 0−+ → [ππ ]S
*πS
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Exzellenzcluster Universe
Correlation:m2π(0++) vs m3π(J
PC)
low t
high t
3π: 0-+ 3π: 2-+ 3π: 1++
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Exzellenzcluster Universe
Correlation:m2π(0++) vs m3π(J
PC)
low t
high t
3π: 0-+
3π: 0-+ 3π: 2-+
3π: 2-+ 3π: 1++
3π: 1++
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Exzellenzcluster Universe
Correlation:m2π(0++) vs m3π(J
PC)
low t
high t
3π: 0-+
3π: 0-+ 3π: 2-+
3π: 2-+ 3π: 1++
3π: 1++
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Exzellenzcluster Universe
For more Details see Talk of Fabian Krinner
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Exzellenzcluster Universe
Spin Exotic 1-‐+
• Wave is dominated by Deck-‐Background • We simulate Deck (ACCMOR + Modifications) • Project contributions onto COMPASS wave set • Normalize intensity to data for for each wave and sum over t‘ • Bench mark quality on waves w/o resonances at „low mass“ • Test on exotic wave
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Exzellenzcluster Universe
Deck and Data6-‐+ 4-‐+
t‘
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Exzellenzcluster Universe
Deck and Exotic 1-‐+
Low values of t‘ : • Mostly non-‐resonant production • Good description by Deck mode !
High values of t‘ : • Resonance appears • Resonance dominates our highest t‘
t‘
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Exzellenzcluster Universe
Phase of Exotic wave
• Clear phase variation seen • Variation of O(500) • Mild variation with t´1++
(-‐)1++
2++
4++
2-‐+
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Exzellenzcluster Universe
• What about previous analysis performed by BNL, Dzerba and VES ? • We have used their wave-‐set and their range of t´
VES
BNL Dzierba
COMPASS w
ith „old“ wave -‐set
• Good agreement • Intensity • Phases
• Spurious maximum around 1.1 GeV/c2 universal
Consistency with previous work
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Exzellenzcluster Universe
Photo-‐Production
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Exzellenzcluster Universe
Radiative Width
• Study resonances with electromagnetic probe – similar to photo-‐production of Δ+ off protons – radiative transitions of charmonia
• Use π as “target” excited by photon beam – π instable: inverse kinematics – Coulomb field of heavy nucleus acts as photon target
u
Identify photo-‐production via spin alignment M = 1 at low t´ < 10-3 GeV2/c2
!σ Photo ≈ e
−bphotot´
σ diffract ≈ t 'M ⋅e−bdiff t´'
→ M = 1 is suppressed in diffraction
bphoto >> bdiffract
use Pb-‐target
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Exzellenzcluster Universe
EM-‐Transitions for Mesons
a2(1320)
M2 transition
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Exzellenzcluster Universe
EM-‐Transitions for Mesons
a2(1320) π2(1670)
First E2 transition observed for mesonsM2 transition
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Exzellenzcluster Universe
Conclusion
• Establish new “2D” fit method to perform PWA in m3π and t !
• Find new iso-‐vector state a1(1420) – Ma1(1420) = 1412-‐1422 MeV/c2 , Γa1(1420) = 130-‐150 MeV/c2 – decay into f0(980)π in relative P-‐wave – coupling seems exclusively f0(980)π
– Nature of a1(1420) ? Isospin partner of f1(1420) (considered to be exotic) ? Dynamically generated through a1(1260) ⟷ KK* ⟷ f0 (980)π channel ?
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Exzellenzcluster Universe
Conclusion
• Developed new method to establish shape of isobar-‐spectrum – first application: [ππ]S*:
• Shows strong dependence on m3π and on JPC of mother wave – Reveals information on scalar isobars (measure phases in decays) !
Open Path to Dalitz-‐plot analysis using PWA from PWA identified states
!Needs high statistics !!
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Exzellenzcluster Universe
Prospects• Mass dependent fits to 25-‐20 waves simultaneously (or more)
– Obtain reliable values for mass, width, branching ratios – Identify nature of light meson spectrum and resolve ambiguities !
• Extend de-‐isobarred analysis to (ππ)L=0,1,2
!• Simultaneous physics description of M2π , M3π , φ2π , t
!• Joint fits for: π−π+π− and π−π0π0 (possibly also include VES data)
!• Other final states 5π, πηη, KK(nπ)..
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Exzellenzcluster Universe
Mass-‐dependent Fit
Will soon release results from 13-‐wave fit !• Intense systematic studies of resonance
parameters • Publish range and not Gaussian errors
Very Preli
minary
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Exzellenzcluster Universe
Mass-‐dependent Fit
Will soon release results from 13-‐wave fit !• Intense systematic studies of resonance
parameters • Publish range and not Gaussian errors
Very Preli
minary
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Exzellenzcluster Universe
Conclusion II
• Study of a1(1260) – Observe “various components” of a1(1260) with different t-‐dependencies:
• Sort out higher excitations of a1 , a2
• Radial excitation of π – π(1800) well known: COMPASS observes decay into f0(980)π and f0(1500)
• Orbital excitation of π – π2 (1670) well known: COMPASS observes decay into f2(1270) π
no evidence so far for strong coupling into [ππ]S*π
– π2 (1880) : Clear signal observed in f2π and f0π • Radiative decays:
– First observation of a mesonic E2 transition : π2(1670) → π γ – Good / reasonable agreement with calculations