Meson spectroscopy at VES and COMPASS D. Ryabchikov Institute for - - PowerPoint PPT Presentation
Meson spectroscopy at VES and COMPASS D. Ryabchikov Institute for High Energy Physics, Protvino; Technische Universit at M unchen D. Ryabchikov (IHEP, TUM E18) Meson spectroscopy at VES and COMPASS 27.02.2019 1 / 21 OUTLINE Two
Institute for High Energy Physics, Protvino; Technische Universit¨ at M¨ unchen
Meson spectroscopy at VES and COMPASS 27.02.2019 1 / 21
Two flagship reactions for VES and COMPASS experiments: π−N → π−π−π+N and π−N → π−π0π0N Methods of the analysis:
The mass-independent PWA with established isobars Isospin relations between π−π−π+ and π−π0π0 amplitudes Two parametrizations of PWA density matrix: rank=1 and unlimited rank with extracting the Largest-Eigenvalue-Eigenvector (LEV) Resonance-model fits Analysis with free parametrization of ππ-isobars
Results of the analysis:
Mass-independent PWA for VES with established shapes of ππ-isobars, comparison of isospin relations between π−π−π+ and π−π0π0 (VES and COMPASS) Selected results for resonance model fits (COMPASS) Comparison of PWA with rank=1 and unlimited rank with extracting the Largest-Eigenvalue-Eigenvector (VES) Selected results for analysis with free parametrization of ππ-isobars (COMPASS)
Meson spectroscopy at VES and COMPASS 27.02.2019 2 / 21
Meson spectroscopy at VES and COMPASS 27.02.2019 3 / 21
Meson spectroscopy at VES and COMPASS 27.02.2019 4 / 21
VES
pbeam = 29 GeV/c Nucleus Be target, no detection of the recoil particle Momentum transferred squared 0 < t′ < 1 GeV2/c2 π−Be → π−π−π+Be 87x106 events π−Be → π−π0π0Be 32x106 events
COMPASS
pbeam = 190 GeV/c LiH target, Recoil Proton Detector Momentum transferred squared 0.1 < t′ < 1 GeV2/c2 π−p → π−π−π+p 46x106 events π−p → π−π0π0p 3.5x106 events
Meson spectroscopy at VES and COMPASS 27.02.2019 5 / 21
S J PCM ε
target recoil
ε = +: natural ε = parity exchange parity exchange −: unnatural
X
L 1 2
Rππ π π π π
+ − − −(beam)
(bachelor)
Reggeon exchange, naturality η = PR(−1)J R Gottfried-Jackson frame: SCM of X: ZGJ p∗
beam, YGJ = [
p∗
recoilx
p∗
beam]
Reflectivity basis for system of mesons: |JMε >= |JM > −εP(−1)J−M|J − M > At high beam energies: reflectivity ε equal to naturality η unpolarised target: ε = ±1 states do not interfere
Meson spectroscopy at VES and COMPASS 27.02.2019 6 / 21
Mass-independent PWA events density: I(m, t′, τ) =
Nr
T ε
i,r(m, t′)ψε i (m, τ)
+ FLAT The decay amplitudes ψε
i (τ) are enumerated by their quantum numbers
i, ε = JPCMε [isobar] π L and have no free parameters Transition amplitudes T ε
ir(m, t′) fitted independently in each (m, t′) - bin
Events density expressed through spin-density matrix: I(m, t′, τ) =
ρε
i,j(m, t′)ψε i (m, τ)ψε∗ j (m, τ),
ρε
i,j = Nr
T ε
i,rT ε ∗ j,r
For COMPASS data Nr = 1 is chosen, for VES - two models are tried: Nr = 1 and unlimited rank and extracting Eigenvector with Largest Eigenvalue
Meson spectroscopy at VES and COMPASS 27.02.2019 7 / 21
Decay amplitudes for I=1 of 2π isobar (i.e. ρπ) in case of I(3π) = 1 are connected:
2( 1 √ 2[(π− (1)π+)π− (2) + (π− (2)π+)π− (1)]) ↔ −
2( 1 √ 2[(π−π0 (1))π0 (2) + (π−π0 (2))π0 (1)])
Same dalitz-plot structure → N(π−π0π0):N(π−π−π+)=1:1 Decay amplitudes for I=0 of 2π isobar (i.e. f0π or f2π) channels are always connected :
3( 1 √ 2[(π− (1)π+)π− (2) + (π− (2)π+)π− (1)]) ↔ −
3((π0 (1)π0 (2))π− )
Different Dalitz-plot structure. Narrow isobar and m(3π) >> misob + mπ → N(π−π0π0):N(π−π−π+)=0.5:1 Case of broad, overlapping isobars for π−π−π+ - ratio can be siginficantly larger
All corresponding relative phases in π−π0π0 and π−π−π+ are equal - in case of appropriate choosing of directions of ”spin analyzers” - π−- direction in 2π center-of-mass for both systems
Meson spectroscopy at VES and COMPASS 27.02.2019 8 / 21
VES COMPASS
1-(1++)0+ rho pi S
GeV Events/ 20 MeV 500 1000 1500 2000 2500 3000 3500 4000 x 10 3 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 summed over t fit1 fit2
)
2
(GeV/c
−
) π (3
m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
intensity (per 40 MeV/c 0.5 1 1.5 2 2.5 3
6
10 × p)
−
) π (3 → p
−
π COMPASS 2008 ( S π (770) ρ
+ + +
1
+
π
−
π
−
π , π π
−
π
2
/c
2
0.100 < t' < 1.000 GeV (incoherent sum)
Preliminary
Meson spectroscopy at VES and COMPASS 27.02.2019 9 / 21
VES COMPASS
1-(2++)1+ rho pi D
GeV Events/ 20 MeV 500 1000 1500 2000 2500 3000 3500 4000 x 10 2 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 summed over t fit1 fit2
)
2
(GeV/c
−
) π (3
m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
intensity (per 40 MeV/c 0.5 1 1.5 2
6
10 × p)
−
) π (3 → p
−
π COMPASS 2008 ( D π (770) ρ
+
1
+ +
2
+
π
−
π
−
π , π π
−
π
2
/c
2
0.100 < t' < 1.000 GeV (incoherent sum)
Preliminary
Meson spectroscopy at VES and COMPASS 27.02.2019 10 / 21
VES COMPASS
φ(1-(2++)1+ rho pi D - 1-(1++)0+ rho pi S GeV Degrees
50 100 150 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 t=0-0.015 GeV2
)
2
(GeV/c
−
) π (3
m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 phase (degree)
50 100 150 200 p)
−
) π (3 → p
−
π COMPASS 2008 ( S) π (770) ρ
+ + +
1 − D π (770) ρ
+
1
+ +
(2 φ
+
π
−
π
−
π , π π
−
π
2
/c
2
0.100 < t' < 0.116 GeV
2
/c
2
0.100 < t' < 0.113 GeV
Preliminary
The relative phases between waves containing 3π-resonances do not depend on beam energy and t′
Meson spectroscopy at VES and COMPASS 27.02.2019 11 / 21
VES COMPASS
rho pi Natur= +
GeV Events/ 20 MeV 500 1000 1500 2000 2500 3000 3500 4000 4500 x 10 3 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 summed over t fit1 fit2
)
2
(GeV/c
−
) π (3
m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
intensity (per 40 MeV/c 1 2 3 4 5
6
10 × p)
−
) π (3 → p
−
π COMPASS 2008 ( =+1) ε spin total ( π (770) ρ
+
π
−
π
−
π , π π
−
π
2
/c
2
0.100 < t' < 1.000 GeV (incoherent sum)
Preliminary
The ε = +1 dominates over ε = −1 (latest also do not show isospin relations)
Meson spectroscopy at VES and COMPASS 27.02.2019 12 / 21
VES COMPASS
1-(2-+)0+ f2 pi S
GeV Events/ 20 MeV 1000 2000 3000 4000 5000 x 10 2 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 summed over t fit1 fit2
)
2
(GeV/c
−
) π (3
m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
intensity (per 40 MeV/c 0.1 0.2 0.3 0.4 0.5 0.6 0.7
6
10 × p)
−
) π (3 → p
−
π COMPASS 2008 ( S π (1270)
2
f
+ + −
2
+
π
−
π
−
π , π π
−
π
2
/c
2
0.100 < t' < 1.000 GeV (incoherent sum)
Preliminary
Meson spectroscopy at VES and COMPASS 27.02.2019 13 / 21
VES
1-(1++)0+ f0(980) pi P
GeV Events/ 20 MeV 5000 10000 15000 20000 25000 30000 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 summed over t fit1 fit2)
2
(GeV/c
−) π (3
m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 )
2
intensity (per 40 MeV/c 2 4 6 8 10 12 14 16 18 20 22 24
3
10 × p)
−
) π (3 → p
−
π COMPASS 2008 ( P π (980) f
+ + +
1 (scaled)
+
π
−
π
−
π , π π
−
π
2
/c
2
0.100 < t' < 1.000 GeV (incoherent sum)
Preliminary
φ(1-(1++)0+ f0(980) pi P - 1-(1++)0+ rho pi S GeV Degrees)
2
(GeV/c
−) π (3
m 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 phase (degree)
100 200 p)
−
) π (3 → p
−
π COMPASS 2008 ( S) π (770) ρ
+ + +
1 − P π (980) f
+ + +
(1 φ
+
π
−
π
−
π , π π
−
π
2
/c
2
0.100 < t' < 0.116 GeV
2
/c
2
0.100 < t' < 0.113 GeV
Preliminary
Meson spectroscopy at VES and COMPASS 27.02.2019 14 / 21
VES
1-(0-+)0+ f0(980) pi S
GeV Events/ 20 MeV 200 400 600 800 1000 1200 x 10 2 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 summed over t fit1 fit2]
2
c GeV/
[
π 3
m
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)
2
c Intensity / (20 MeV/
20 40 60 80 100 120 140
3
10 × (COMPASS 2008) p
+
π
−
π
−
π → p
−
π S π (980) f
+ + − 2
) c < 1.000 (GeV/ t' 0.100 < Mass-independent fit Mass-dependent fit resonant non-resonant
]
2
c GeV/
[
π 3
m
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
[deg] φ δ − φ ∆
200 − 150 − 100 − 50 − 50 100 150 200
] S π (770) ρ
+ + +
1 [ − ] S π (980) f
+ + −
[
2
) c < 0.113 (GeV/ t' 0.100 < ° = 140 φ δ
Clear π(1800) signal, no π(1300)-signal
Meson spectroscopy at VES and COMPASS 27.02.2019 15 / 21
VES
1-(4++)1+ rho pi G
GeV Events/ 20 MeV 2000 4000 6000 8000 10000 12000 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 summed over t fit1 fit2]
2
c GeV/
[
π 3
m
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
)
2
c Intensity / (20 MeV/
5 10 15 20 25 30
3
10 × (COMPASS 2008) p
+
π
−
π
−
π → p
−
π G π (770) ρ
+
1
+ +
4
2
) c < 1.000 (GeV/ t' 0.100 < Mass-independent fit Mass-dependent fit resonant non-resonant
]
2
c GeV/
[
π 3
m
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
[deg] φ δ − φ ∆
200 − 150 − 100 − 50 − 50 100 150 200
] S π (1270)
2
f
+ + −
2 [ − ] G π (770) ρ
+
1
+ +
4 [
2
) c < 0.262 (GeV/ t' 0.220 < ° 11.9 − = φ δ
M = 1980 ± 10, Γ = 300 ± 40 MeV/c2 M = 1935+11
−13, Γ = 0.333+10 −21 MeV /c2
Meson spectroscopy at VES and COMPASS 27.02.2019 16 / 21
Coherent part of the density matrix R is the largest part of the matrix which has rank 1 and behaves like vector of amplitudes. Let R =
d
ek ∗ Vk ∗ V +
k
where ek is k-th eigenvalue Vk is k-th eigenvector Let e1 ≫ e2 > . . . > ed > 0. Leading term RL is coherent part of density matrix and RS is the rest (incoherent part). This decomposition is stable w.r.t. variations
R = RL + RS, RL = e1 ∗ V1 ∗ V +
1 ,
RS =
d
ek ∗ Vk ∗ V +
k
Experience shows that resonances tend to concentrate in RL.
Meson spectroscopy at VES and COMPASS 27.02.2019 17 / 21
VES, rank=1 VES, unlimited rank, LEV
1-(2++)1+ rho pi D
GeV Events/ 20 MeV 500 1000 1500 2000 2500 3000 3500 4000 x 10 2 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 summed over t fit1 fit22+D1+ RHO(770)
500 1000 1500 2000 2500 3000 3500 4000 x 10 2 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 summed over t fit1 fit21-(2-+)0+ f2 pi S
GeV Events/ 20 MeV 1000 2000 3000 4000 5000 x 10 2 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 summed over t fit1 fit22-S0+ F2(1270)
500 1000 1500 2000 2500 3000 3500 4000 4500 x 10 2 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 summed over t fit1 fit2Meson spectroscopy at VES and COMPASS 27.02.2019 18 / 21
Decay amplitude with established isobars: The decay amplitude ψε
i (τ) contains angular part and π−π+ isobar Breit-Wigner
function and is bose-symmetrized by swapping (1) ↔ (3) in π−
(1)π+ (2)π− (3) system:
ψε
i (τ) = Aε i (Ω12, Ω∗ 1)BWj(i)(m12) + Aε i (Ω32, Ω∗ 3)BWj(i)(m32)
Decay amplitudes with freed isobars: The fixed amplitude of π−π+ isobar is replaced by sum of step-like functions with complex coefficients: BW (m)j →
β ωj,βΠβ(m)
In that case [isobar] → (ππ)s and wave notation is JPCMε (ππ)s π L The full free-isobarred amplitude for JPCMε sector: FJPMε(τ) =
k
JPMε,k(Ω12, Ω∗ 1)Πβ(m12) + Aε JPMε,k(Ω32, Ω∗ 3)Πβ(m32)
k
ΨJPMε,k,β(τ) where k sums over different L, s for fixed JPMε We found linear dependences inside the set of free-isobaric decay amplitudes ˆ ΨJPMε,k,β(τ), called zero modes. For two amplitudes:0−+(ππ)SπS and 0−+(ππ)PπP - one real-valued function of zero mode found. For one amplitude: 1−+(ππ)PπP - one zero mode.
Meson spectroscopy at VES and COMPASS 27.02.2019 19 / 21
0.5 1.0 1.5 2.0 mπ−π+ [GeV/c2] 2 4 6 Intensity [Events/(GeV/c2)] ×106 1−+1+[ππ]1−−πP 1.58 < m3π < 1.62 GeV/c2 0.326 < t′ < 1.000 (GeV/c)2 6.0%
Corrected zero mode Uncorrected zero mode Fixed shape
0.5 1.0 1.5 2.0 2.5
m3π [GeV/c2]
0.5 1.0 1.5 2.0
m2π [GeV/c2] 1−+1+[ππ]1−−πP Preliminary 0.326 < t′ < 1.000(GeV/c)2
15000 30000 45000 60000 75000 90000 105000
−2 −1 1 Re(Tbin)
1/2 ×103 −1 1 2 Im(Tbin)
1/2 ×103 1−+1+[ππ]1−−πP 1.58 < m3π < 1.62 GeV/c2 0.326 < t′ < 1.000 (GeV/c)2 6.0%
Corrected zero mode Uncorrected zero mode Fixed shape
0.5 1.0 1.5 2.0 2.5
m3π[GeV/c2]
1 2
Intensity [Events/40 MeV]
×104
1−+1+[ππ]1−−πP 0.326 < t′ < 1.000(GeV/c)2
Fixed isobars Freed isobars
Meson spectroscopy at VES and COMPASS 27.02.2019 20 / 21
Analysis of 3π states in VES and COMPASS shows the dominance of diffractive production mechanism for both beam energies and different t′-ranges:
The positive reflectivity dominates for both beam energies The isospin relations between π−π−π+ and π−π0π0 demonstrate 1:1 and for f π have 0.5:1 Relative phases match for corresponding pairs of waves in π−π−π+ and π−π0π0 The relative phases between resonant 3π waves do not depend on beam energy and on t′
VES has compatible statistics of π−π−π+ and π−π0π0 and enhanced production of JPCMε = 1++0+ states:
perspective study of a1(1420)-phenomenon in both 3π-final states perspective to perform ”free-isobarred” analysis in both 3π-final states
COMPASS analysis with freed isobars was first time performed for JPCMε = 1−+1+(ππ)Pπ P:
The continuous ambiguities were resolved by applying Breit-Wigner model for (ππ)P freed amplitude The obtained (ππ)P model-independent amplitude is well described by ρ(770) Breit-Wigner
Meson spectroscopy at VES and COMPASS 27.02.2019 21 / 21