J P C A M. Mikhasenko (HISKP , Uni Bonn) Ground axial vector - - PowerPoint PPT Presentation
Pole position of the a 1 ( 1260 ) Misha Mikhasenko Joint Physics Analysis Center, COMPASS @ CERN, Universit at Bonn, HISKP , Bonn, Germany CHARM 2018 Akademgorodok, Novosibirsk 23/05/2018 J P C A M. Mikhasenko (HISKP , Uni Bonn)
Misha Mikhasenko
Joint Physics Analysis Center, COMPASS @ CERN, Universit¨ at Bonn, HISKP , Bonn, Germany
CHARM 2018
Akademgorodok, Novosibirsk 23/05/2018
, Uni Bonn) Ground axial vector 25/05/2018 1 / 14
1
Introduction Hadrons in QCD Analytical structure of the scattering amplitude
2
Three pions dynamics Constrains Data
3
Extraction of the resonance parameters Fit Analytical continuation
4
Remarks COMPASS analysis CLEO analysis a1(1420) phenomenon
, Uni Bonn) Ground axial vector 25/05/2018 2 / 14
Introduction Hadrons in QCD
Quark model
color-binding,
2 ◮ Radial excitation (n), ◮ Orbital excitation (L),
many states (JPC = 0++, 1−− . . . ) are coupled to ππ. Some other to 3π system
[Amsler et al., Phys. Rept. 389, 61 (2004)]
, Uni Bonn) Ground axial vector 25/05/2018 3 / 14
Introduction Hadrons in QCD
Lattice QCD spectrum matches experimental observations well but predicts more
[Dudek et. al, Phys.Rev. D82 (2010) 034508]
π ρ a1
, Uni Bonn) Ground axial vector 25/05/2018 4 / 14
Introduction Hadrons in QCD
ππ system in the box
[EPJ Web Conf. 175 (2018)]
30 60 90 120 150 180 400 500 600 700 800 900 1000
[Wilson, D. et al.,PRD 92,(2015)]
Tracking pole position
For high mπ the ρ-becomes stable. Pole of ρ approaches real axis.
, Uni Bonn) Ground axial vector 25/05/2018 5 / 14
Introduction Analytical structure of the scattering amplitude
Breit-Wigner amplitude
Features of the complex s plane: s = E2 – the total inv.mass squared The Real axis → physical world The Imaginary axis → analytical continuation
, Uni Bonn) Ground axial vector 25/05/2018 6 / 14
Introduction Analytical structure of the scattering amplitude
Breit-Wigner amplitude
Features of the complex s plane: s = E2 – the total inv.mass squared The Real axis → physical world The Imaginary axis → analytical continuation
, Uni Bonn) Ground axial vector 25/05/2018 6 / 14
Introduction Analytical structure of the scattering amplitude
Breit-Wigner amplitude
Features of the complex s plane: s = E2 – the total inv.mass squared The Real axis → physical world The Imaginary axis → analytical continuation
Unitarity constaints for two-body scattering
ˆ S† ˆ S = ˆ I ˆ S = ˆ I + i ˆ T ˆ T − ˆ T † = i ˆ T † ˆ T. T(s, t) =
1p′ 2|ˆ
T|p1p2
Partial wave expansion − → The final form 2Im tl(s) = t∗
l (s)ρ(s)tl(s)
, Uni Bonn) Ground axial vector 25/05/2018 6 / 14
Introduction Analytical structure of the scattering amplitude
Breit-Wigner amplitude
Features of the complex s plane: s = E2 – the total inv.mass squared The Real axis → physical world The Imaginary axis → analytical continuation
Unitarity constaints for two-body scattering
ˆ S† ˆ S = ˆ I ˆ S = ˆ I + i ˆ T ˆ T − ˆ T † = i ˆ T † ˆ T. T(s, t) =
1p′ 2|ˆ
T|p1p2
Partial wave expansion − → The final form 2Im tl(s) = t∗
l (s)ρ(s)tl(s)
, Uni Bonn) Ground axial vector 25/05/2018 6 / 14
Three pions dynamics Constrains
[MM (JPAC) in preparation]
Three-body unitarity
[Eden, Landshoff et al.(2002)]
Singularity splitting:
T =
Disconnected
Connected
Final state interaction:
K = + + · · · + + . . .
ξ σ{
s ξ }σ′
, Uni Bonn) Ground axial vector 25/05/2018 7 / 14
Three pions dynamics Constrains
[MM (JPAC) in preparation]
Three-body unitarity
[Eden, Landshoff et al.(2002)]
Singularity splitting:
T =
Disconnected
Connected
Final state interaction:
K = + + · · · + + . . .
ξ σ{
s ξ }σ′ T(σ′, s, σ) = Kξ(s, σ′)t(s)Kξ(s, σ)
, Uni Bonn) Ground axial vector 25/05/2018 7 / 14
Three pions dynamics Constrains
[MM (JPAC) in preparation]
Three-body unitarity
[Eden, Landshoff et al.(2002)]
Singularity splitting:
T =
Disconnected
Connected
Final state interaction:
K = + + · · · + + . . .
ξ σ{
s ξ }σ′ T(σ′, s, σ) = Kξ(s, σ′)t(s)Kξ(s, σ) 2Im t(s) = t∗(s) ρ(s) t(s),
Symmetrized quasi-two-body phase space factor
ρ(s) = 1 2
=
100 200 300 400 500 600 700 800]
2 ) 2 c (GeV/[
2 + π − π m 0.5 1 1.5]
2 ) 2 c (GeV/[
2 + π − π m 0.5 1 1.5 2 c < 100 MeV/ 2 c 1318 MeV/ − π 3 m (770) ρ, Uni Bonn) Ground axial vector 25/05/2018 7 / 14
Three pions dynamics Constrains
[MM (JPAC) in preparation]
Three-body unitarity
[Eden, Landshoff et al.(2002)]
Singularity splitting:
T =
Disconnected
Connected
Final state interaction:
K = + + · · · + + . . .
ξ σ{
s ξ }σ′ T(σ′, s, σ) = Kξ(s, σ′)t(s)Kξ(s, σ) 2Im t(s) = t∗(s) ρ(s) t(s),
Symmetrized quasi-two-body phase space factor
ρ(s) = 1 2
=
100 200 300 400 500 600 700 800]
2 ) 2 c (GeV/[
2 + π − π m 0.5 1 1.5]
2 ) 2 c (GeV/[
2 + π − π m 0.5 1 1.5 2 c < 100 MeV/ 2 c 1318 MeV/ − π 3 m (770) ρThe model: symmetrized
[Bowler, Phys.Lett.B182 (1986)] t(s) = g2 m2 − s − ig2ρ(s)/2
, Uni Bonn) Ground axial vector 25/05/2018 7 / 14
Three pions dynamics Constrains
[MM (JPAC) in preparation]
Three-body unitarity
[Eden, Landshoff et al.(2002)]
Singularity splitting:
T =
Disconnected
Connected
Final state interaction:
K = + + · · · + + . . .
ξ σ{
s ξ }σ′ T(σ′, s, σ) = Kξ(s, σ′)t(s)Kξ(s, σ) 2Im t(s) = t∗(s) ρ(s) t(s),
Symmetrized quasi-two-body phase space factor
ρ(s) = 1 2
=
100 200 300 400 500 600 700 800]
2 ) 2 c (GeV/[
2 + π − π m 0.5 1 1.5]
2 ) 2 c (GeV/[
2 + π − π m 0.5 1 1.5 2 c < 100 MeV/ 2 c 1318 MeV/ − π 3 m (770) ρThe model: symmetrized, dispersive
t(s) = g2 m2 − s − ig2 ˜ ρ(s)/2 , ˜ ρ(s) = s πi ∞
9m2
π
ρ(s′) s′(s′ − s) ds′, Im i ˜ ρ = iρ.
, Uni Bonn) Ground axial vector 25/05/2018 7 / 14
Three pions dynamics Data
Axial vector states below 2 GeV
Dominated by 3π scattering
◮ ρπ
∼ 60% − 80%
◮ σπ
∼ 5% − 10%
◮ f2π
∼ < 5%
K ¯ Kπ < 3%
, Uni Bonn) Ground axial vector 25/05/2018 8 / 14
Three pions dynamics Data
Axial vector states below 2 GeV
Dominated by 3π scattering
◮ ρπ
∼ 60% − 80%
◮ σπ
∼ 5% − 10%
◮ f2π
∼ < 5%
K ¯ Kπ < 3%
τ − → π−π+π− ν
τ− W− ν π− π+ π−
V-A
V-A: Vector (1−−) or Axial (1++) Isospin 1 due to the charge Negative G-parity ⇒ positive C-parity ⇒ JPC = 1++
, Uni Bonn) Ground axial vector 25/05/2018 8 / 14
Extraction of the resonance parameters Fit
[data from ALEPH, Phys.Rept.421 (2005)]
0.0 0.5 1.0 1.5 2.0 2.5
d /ds (a. u. / 0.025 GeV2)
ALEPH(3 ) 1 2 3
s M2
3 (GeV2)
χ2 function
χ2(c, m, g) = ( D − M(c, m, g))T C−1
stat(
D − M(c, m, g)),
, Uni Bonn) Ground axial vector 25/05/2018 9 / 14
Extraction of the resonance parameters Fit
[data from ALEPH, Phys.Rept.421 (2005)]
0.0 0.5 1.0 1.5 2.0 2.5
d /ds (a. u. / 0.025 GeV2)
ALEPH(3 ) SYMM SYMM-DISP
0.0 2.5 5.0
res./err.
2/n. d. f. = 93.5/99
1 2 3
s M2
3 (GeV2)
0.0 2.5 5.0
res./err.
2/n. d. f. = 663.20/99
χ2 function
χ2(c, m, g) = ( D − M(c, m, g))T C−1
stat(
D − M(c, m, g)),
, Uni Bonn) Ground axial vector 25/05/2018 9 / 14
Extraction of the resonance parameters Fit
[data from ALEPH, Phys.Rept.421 (2005)]
0.0 0.5 1.0 1.5 2.0 2.5
d /ds (a. u. / 0.025 GeV2)
ALEPH(3 ) SYMM SYMM-DISP
0.0 2.5 5.0
res./err.
2/n. d. f. = 93.5/99
1 2 3
s M2
3 (GeV2)
0.0 2.5 5.0
res./err.
2/n. d. f. = 663.20/99
χ2 function
χ2(c, m, g) = ( D − M(c, m, g))T C−1
stat(
D − M(c, m, g)),
Breit-Wigner mass and width
The BW mass is given by Re[t−1(m2)] = 0 The BW width ⇐ Im[g2/t(m2)] = mΓBW
Preliminary results: ma1(1260)
BW
= (1.246 ± 0.003) GeV, Γa1(1260)
BW
= (0.394 ± 0.005) GeV.
, Uni Bonn) Ground axial vector 25/05/2018 9 / 14
Extraction of the resonance parameters Analytical continuation
Re [
1] (GeV2)Im [
1] (GeV2)Complex plane ( s m )2 4m2 pole
Unitarity cut Corner path Intergal end pointsAnalytical continuation
|t−1
II
(s)| =
g2 − i ˜ ρ(s) 2 + ρ(s)
Analytical continuation of ρ(s) ρ(s) ∼ (√s−mπ)2
4m2
π
dσ 2π Uρ(σ) λ1/2(s, σ, m2
π)
s Error propagation using bootstrap analysis.
, Uni Bonn) Ground axial vector 25/05/2018 10 / 14
Extraction of the resonance parameters Analytical continuation
0.5 1.0 1.5 2.0 2.5 3.0
Re[s] (GeV2)
0.00
Im[s] (GeV2)
Complex s plane in the QTB DISP model First sheet Second sheet
0.3 0.6 0.9 1.2 1.5Re [
1] (GeV2)Im [
1] (GeV2)Complex plane ( s m )2 4m2 pole
Unitarity cut Corner path Intergal end pointsAnalytical continuation
|t−1
II
(s)| =
g2 − i ˜ ρ(s) 2 + ρ(s)
Analytical continuation of ρ(s) ρ(s) ∼ (√s−mπ)2
4m2
π
dσ 2π Uρ(σ) λ1/2(s, σ, m2
π)
s Error propagation using bootstrap analysis.
, Uni Bonn) Ground axial vector 25/05/2018 10 / 14
Extraction of the resonance parameters Analytical continuation
1.19 1.20 1.21 1.22 1.23
Pole mass Re sp (GeV)
Pole width 2Im sp (GeV)
syst.uncert stat.uncert. m 10 MeV m + 10 MeV fit till 2 GeV main fit 0.3 0.6 0.9 1.2 1.5 Re [
1] (GeV2)Im [
1] (GeV2)Complex plane ( s m )2 4m2 pole
Unitarity cut Corner path Intergal end pointsAnalytical continuation
|t−1
II
(s)| =
g2 − i ˜ ρ(s) 2 + ρ(s)
Analytical continuation of ρ(s) ρ(s) ∼ (√s−mπ)2
4m2
π
dσ 2π Uρ(σ) λ1/2(s, σ, m2
π)
s Error propagation using bootstrap analysis.
m(a1(1260))
p
= (1.208 ± 0.004) GeV, Γ(a1(1260))
p
= (0.569 ± 0.012) GeV.
Systematic studies: variation of ρ-shape variation of fit range
, Uni Bonn) Ground axial vector 25/05/2018 10 / 14
Extraction of the resonance parameters Analytical continuation
0.5 1.0 1.5 2.0 2.5 3.0
Re[s] (GeV2)
0.00
Im[s] (GeV2)
Complex s plane in the QTB DISP model First sheet Second sheet
0.3 0.6 0.9 1.2 1.5Re [
1] (GeV2)Im [
1] (GeV2)Complex plane ( s m )2 4m2 pole
Unitarity cut Corner path Intergal end pointsAnalytical continuation
|t−1
II
(s)| =
g2 − i ˜ ρ(s) 2 + ρ(s)
Analytical continuation of ρ(s) ρ(s) ∼ (√s−mπ)2
4m2
π
dσ 2π Uρ(σ) λ1/2(s, σ, m2
π)
s Error propagation using bootstrap analysis.
m(a1(1260))
p
= (1.208 ± 0.004) GeV, Γ(a1(1260))
p
= (0.569 ± 0.012) GeV.
Systematic studies: variation of ρ-shape variation of fit range
, Uni Bonn) Ground axial vector 25/05/2018 10 / 14
Extraction of the resonance parameters Analytical continuation
0.5 1.0 1.5 2.0 2.5 3.0
Re[s] (GeV2)
0.00
Im[s] (GeV2)
Complex s plane in the QTB DISP model First sheet Second sheet
0.3 0.6 0.9 1.2 1.5Re [
1] (GeV2)Im [
1] (GeV2)Complex plane ( s m )2 4m2 pole
Unitarity cut Hook path Intergal end pointsAnalytical continuation
|t−1
II
(s)| =
g2 − i ˜ ρ(s) 2 + ρ(s)
Analytical continuation of ρ(s) ρ(s) ∼ (√s−mπ)2
4m2
π
dσ 2π Uρ(σ) λ1/2(s, σ, m2
π)
s Error propagation using bootstrap analysis.
m(a1(1260))
p
= (1.208 ± 0.004) GeV, Γ(a1(1260))
p
= (0.569 ± 0.012) GeV.
Systematic studies: variation of ρ-shape variation of fit range
, Uni Bonn) Ground axial vector 25/05/2018 10 / 14
Extraction of the resonance parameters Analytical continuation
0.5 1.0 1.5 2.0 2.5 3.0
Re[s] (GeV2)
0.00
Im[s] (GeV2)
Complex s plane in the QTB DISP model First sheet Second sheet
0.3 0.6 0.9 1.2 1.5Re [
1] (GeV2)Im [
1] (GeV2)Complex plane ( s m )2 4m2 pole
Unitarity cut Hook path Intergal end pointsAnalytical continuation
|t−1
II
(s)| =
g2 − i ˜ ρ(s) 2 + ρ(s)
Analytical continuation of ρ(s) ρ(s) ∼ (√s−mπ)2
4m2
π
dσ 2π Uρ(σ) λ1/2(s, σ, m2
π)
s Error propagation using bootstrap analysis.
m(a1(1260))
p
= (1.208 ± 0.004) GeV, Γ(a1(1260))
p
= (0.569 ± 0.012) GeV.
Systematic studies: variation of ρ-shape variation of fit range
, Uni Bonn) Ground axial vector 25/05/2018 10 / 14
Extraction of the resonance parameters Analytical continuation
0.5 1.0 1.5 2.0 2.5 3.0
Re[s] (GeV2)
0.00
Im[s] (GeV2)
Complex s plane in the QTB DISP model First sheet Second sheet
0.3 0.6 0.9 1.2 1.5Re [
1] (GeV2)Im [
1] (GeV2)Complex plane ( s m )2 4m2 pole
Unitarity cut Hook path Intergal end pointsAnalytical continuation
|t−1
II
(s)| =
g2 − i ˜ ρ(s) 2 + ρ(s)
Analytical continuation of ρ(s) ρ(s) ∼ (√s−mπ)2
4m2
π
dσ 2π Uρ(σ) λ1/2(s, σ, m2
π)
s Error propagation using bootstrap analysis.
m(a1(1260))
p
= (1.208 ± 0.004) GeV, Γ(a1(1260))
p
= (0.569 ± 0.012) GeV.
Systematic studies: variation of ρ-shape variation of fit range
, Uni Bonn) Ground axial vector 25/05/2018 10 / 14
Extraction of the resonance parameters Analytical continuation
0.5 1.0 1.5 2.0 2.5 3.0
Re[s] (GeV2)
0.00
Im[s] (GeV2)
Complex s plane in the QTB DISP model First sheet Second sheet a1(1260) pole Spurious pole
0.3 0.6 0.9 1.2 1.5Re [
1] (GeV2)Im [
1] (GeV2)Complex plane ( s m )2 4m2 pole
Unitarity cut Hook path Intergal end pointsThe reason of the spurious pole
ρ(s) ∼ (√s−mπ)2
4m2
π
dσ 2π Uρ(σ) λ1/2(s, σ, m2
π)
s
Not every pole is the resonance
, Uni Bonn) Ground axial vector 25/05/2018 11 / 14
Extraction of the resonance parameters Analytical continuation
0.5 1.0 1.5 2.0 2.5 3.0
Re[s] (GeV2)
0.00
Im[s] (GeV2)
adjusted sQTB DISP1p model First sheet Second sheet a1(1260) pole
2/n. d. f. = 1103/99
0.3 0.6 0.9 1.2 1.5Re [
1] (GeV2)Im [
1] (GeV2)Complex plane ( s m )2 4m2 pole
Unitarity cut Hook path Intergal end pointsThe reason of the spurious pole
ρ(s) ∼ (√s−mπ)2
4m2
π
dσ 2π Uρ(σ) λ1/2(s, σ, m2
π)
s
Not every pole is the resonance
Can we find the model without the pole
Denoting ˆ t(s) = t(s)/s
2Imˆ t(s) = ˆ t∗(s) (sρ(s))ˆ t(s),
New model
c/(Pk(s) − ig2sˆ ρ(s)/2) P1(s) = m2 − s does not fit the data
, Uni Bonn) Ground axial vector 25/05/2018 11 / 14
Extraction of the resonance parameters Analytical continuation
0.5 1.0 1.5 2.0 2.5 3.0
Re[s] (GeV2)
0.00
Im[s] (GeV2)
adjusted sQTB DISP2p model First sheet Second sheet a1(1260) pole Second pole
2/n. d. f. = 66.4/99
0.3 0.6 0.9 1.2 1.5Re [
1] (GeV2)Im [
1] (GeV2)Complex plane ( s m )2 4m2 pole
Unitarity cut Hook path Intergal end pointsThe reason of the spurious pole
ρ(s) ∼ (√s−mπ)2
4m2
π
dσ 2π Uρ(σ) λ1/2(s, σ, m2
π)
s
Not every pole is the resonance
Can we find the model without the pole
Denoting ˆ t(s) = t(s)/s
2Imˆ t(s) = ˆ t∗(s) (sρ(s))ˆ t(s),
New model
c/(Pk(s) − ig2sˆ ρ(s)/2) P1(s) = m2 − s does not fit the data P2(s) = s(m2 − s) + h gives a good fit and the same pole
, Uni Bonn) Ground axial vector 25/05/2018 11 / 14
Remarks
Three-body unitarity is important for hadron spectroscopy
◮ both experimental and lattice ◮ The light 1++ sector is the first place to study it
We found a class of models which can satisfy unitarity exactly:
◮ Factorization and final state interaction.
Free parameters are constrained using ALEPH data (where is Belle, BES data !?). Analytical continuation:
◮ requires an accurate integral path deformation. ◮ The pole of the a1(1260) resonance was found.
The spurious pole
The dynamics in the channel requires strong influence of the left singularities (the threshold region is important). Systematic studies are ongoing.
, Uni Bonn) Ground axial vector 25/05/2018 12 / 14
Remarks
Thanks to
, Uni Bonn) Ground axial vector 25/05/2018 12 / 14
Remarks
, Uni Bonn) Ground axial vector 25/05/2018 12 / 14
Remarks COMPASS analysis
a1(1260) at COMPASS
[COMPASS, PRD 95 (2017)]
Low P virtuality ptarget precoil π− π− π+ π− P
, Uni Bonn) Ground axial vector 25/05/2018 13 / 14
Remarks COMPASS analysis
a1(1260) at COMPASS
[COMPASS, PRD 95 (2017)]
High P virtuality ptarget precoil π− π− π+ π− P
, Uni Bonn) Ground axial vector 25/05/2018 13 / 14
Remarks COMPASS analysis
a1(1260) at COMPASS
[COMPASS, PRD 95 (2017)] ]
2
c GeV/
[
π 3
m 0.5 1 1.5 2 2.5 )
2
c Intensity / (20 MeV/ 0.1 0.2
6
10 ×
S π (770) ρ
+ + +
1
2
) c < 0.113 (GeV/ t' 0.100 < Model curve Resonances
ptarget precoil π− π− π+ π− P
π− π− π+ π− P (ππ)
+
π− π− π+ π− P (ππ)
mBW = 1.299+0.012
−0.028 GeV
ΓBW = 0.380 ± 0.080 GeV
COMPASS Model
Partial wave analysis to isolate 1++ sector. Coherent addition of the short and the long range diagrams ⇒ (no unitarity)
, Uni Bonn) Ground axial vector 25/05/2018 13 / 14
Remarks COMPASS analysis
a1(1260) at COMPASS
[COMPASS, PRD 95 (2017)] ]
2
c GeV/
[
π 3
m 0.5 1 1.5 2 2.5 )
2
c Intensity / (20 MeV/ 0.05 0.1 0.15 0.2
6
10 ×
S π (770) ρ
+ + +
1
2
) c < 0.144 (GeV/ t' 0.127 < Model curve Resonances
ptarget precoil π− π− π+ π− P
π− π− π+ π− P (ππ)
+
π− π− π+ π− P (ππ)
mBW = 1.299+0.012
−0.028 GeV
ΓBW = 0.380 ± 0.080 GeV
COMPASS Model
Partial wave analysis to isolate 1++ sector. Coherent addition of the short and the long range diagrams ⇒ (no unitarity)
, Uni Bonn) Ground axial vector 25/05/2018 13 / 14
Remarks COMPASS analysis
a1(1260) at COMPASS
[COMPASS, PRD 95 (2017)] ]
2
c GeV/
[
π 3
m 0.5 1 1.5 2 2.5 )
2
c Intensity / (20 MeV/ 0.05 0.1 0.15
6
10 ×
S π (770) ρ
+ + +
1
2
) c < 0.189 (GeV/ t' 0.164 < Model curve Resonances
ptarget precoil π− π− π+ π− P
π− π− π+ π− P (ππ)
+
π− π− π+ π− P (ππ)
mBW = 1.299+0.012
−0.028 GeV
ΓBW = 0.380 ± 0.080 GeV
COMPASS Model
Partial wave analysis to isolate 1++ sector. Coherent addition of the short and the long range diagrams ⇒ (no unitarity)
, Uni Bonn) Ground axial vector 25/05/2018 13 / 14
Remarks COMPASS analysis
a1(1260) at COMPASS
[COMPASS, PRD 95 (2017)] ]
2
c GeV/
[
π 3
m 0.5 1 1.5 2 2.5 )
2
c Intensity / (20 MeV/ 0.05 0.1 0.15
6
10 ×
S π (770) ρ
+ + +
1
2
) c < 0.262 (GeV/ t' 0.220 < Model curve Resonances
ptarget precoil π− π− π+ π− P
π− π− π+ π− P (ππ)
+
π− π− π+ π− P (ππ)
mBW = 1.299+0.012
−0.028 GeV
ΓBW = 0.380 ± 0.080 GeV
COMPASS Model
Partial wave analysis to isolate 1++ sector. Coherent addition of the short and the long range diagrams ⇒ (no unitarity)
, Uni Bonn) Ground axial vector 25/05/2018 13 / 14
Remarks COMPASS analysis
a1(1260) at COMPASS
[COMPASS, PRD 95 (2017)] ]
2
c GeV/
[
π 3
m 0.5 1 1.5 2 2.5 )
2
c Intensity / (20 MeV/ 20 40
3
10 ×
S π (770) ρ
+ + +
1
2
) c < 0.724 (GeV/ t' 0.449 < Model curve Resonances
ptarget precoil π− π− π+ π− P
π− π− π+ π− P (ππ)
+
π− π− π+ π− P (ππ)
mBW = 1.299+0.012
−0.028 GeV
ΓBW = 0.380 ± 0.080 GeV
COMPASS Model
Partial wave analysis to isolate 1++ sector. Coherent addition of the short and the long range diagrams ⇒ (no unitarity)
, Uni Bonn) Ground axial vector 25/05/2018 13 / 14
Remarks CLEO analysis
Partial wave analysis: combined fit with 7 waves. 5 isobars ρ, ρ(1450), f2(1270), σ, f0(1370). significant contribution of K ∗ ¯ K
Main fit results
ma1 ≈ 1.33 GeV, Γa1(ma1) ≈ 0.814 GeV, Branching fractions:
◮ Br(a1 → ρπ) ≈ 60%, ◮ Br(a1 → σπ) ≈ 20%, ◮ Br(a1 → f0(1370)π) ≈ 7%, ◮ Br(a1 → K ⋆ ¯
K) ≈ 2.2%.
3100199-009
103 102 101 1 3 2 1 0.6 1.0 1.4 1.8 0.8 1.6 2.4 3.2 ( b )
I
s (GeV2) (s) (GeV)
tot K*K charge 3 neutral 3 3
m (GeV)
3
N / m (0.025 GeV) 1 103 1.4 ( a ) 1.3 1.5
, Uni Bonn) Ground axial vector 25/05/2018 13 / 14
Remarks a1(1420) phenomenon
[PRL 115 (2015) 082001]
a1(1420) phenomenon
total
1++All+ 0-+All+ 1-+All+ 2++All+ 2-+All+ 0.5 1.0 1.5 2.0 2.5 100000 200000 300000 400000 m3π(GeV) Intensity/(40MeV) π-p→π-π-π+p (COMPASS 2008) 1++0+ f0π P-wave 0.100< t'< 0.113(GeV2)
, Uni Bonn) Ground axial vector 25/05/2018 14 / 14
Remarks a1(1420) phenomenon
[PRL 115 (2015) 082001]
a1(1420) phenomenon
1++All+ 1++0+(ππ)SπP 1++0+f0πP 0.5 1.0 1.5 2.0 2.5 50000 100000 150000 200000 250000 300000 m3π(GeV) Intensity/(40MeV) π-p→π-π-π+p (COMPASS 2008) 1++0+ f0π P-wave 0.100<t'<0.113(GeV2) 1.1 1.5 1.9 2500
, Uni Bonn) Ground axial vector 25/05/2018 14 / 14
Remarks a1(1420) phenomenon
[PRL 115 (2015) 082001]
a1(1420) phenomenon
1++All+ 1++0+(ππ)SπP 1++0+f0πP 0.5 1.0 1.5 2.0 2.5 50000 100000 150000 200000 250000 300000 m3π(GeV) Intensity/(40MeV) π-p→π-π-π+p (COMPASS 2008) 1++0+ f0π P-wave 0.100<t'<0.113(GeV2) 1.1 1.5 1.9 2500
]
2
c GeV/
[
π 3
m 1 1.2 1.4 1.6 1.8 2 2.2 )
2
c Intensity / (20 MeV/ 5 10 15 20 25
3
10 × P π (980) f
+ + +
1
2
) c < 1.0 (GeV/ t' 0.1 < (1) Model curve (1420) resonance
1
a (2) (3) Non-resonant term (3) (2) (1)
]
2
c GeV/
[
π 3
m 1 1.2 1.4 1.6 1.8 2 2.2 Phase [deg] 200 − 100 − 100 200 G π (770) ρ
+
1
+ +
4 − P π (980) f
+ + +
1
2
) c < 0.113 (GeV/ t' 0.100 <
2
) c < 0.189 (GeV/ t' 0.164 <
2
) c < 0.724 (GeV/ t' 0.449 <
, Uni Bonn) Ground axial vector 25/05/2018 14 / 14
Remarks a1(1420) phenomenon
[PRL 115 (2015) 082001]
a1(1420) phenomenon
1++All+ 1++0+(ππ)SπP 1++0+f0πP 0.5 1.0 1.5 2.0 2.5 50000 100000 150000 200000 250000 300000 m3π(GeV) Intensity/(40MeV) π-p→π-π-π+p (COMPASS 2008) 1++0+ f0π P-wave 0.100<t'<0.113(GeV2) 1.1 1.5 1.9 2500
]
2
c GeV/
[
π 3
m 1 1.2 1.4 1.6 1.8 2 2.2 )
2
c Intensity / (20 MeV/ 5 10 15 20 25
3
10 × P π (980) f
+ + +
1
2
) c < 1.0 (GeV/ t' 0.1 < (1) Model curve (1420) resonance
1
a (2) (3) Non-resonant term (3) (2) (1)
]
2
c GeV/
[
π 3
m 1 1.2 1.4 1.6 1.8 2 2.2 Phase [deg] 200 − 100 − 100 200 G π (770) ρ
+
1
+ +
4 − P π (980) f
+ + +
1
2
) c < 0.113 (GeV/ t' 0.100 <
2
) c < 0.189 (GeV/ t' 0.164 <
2
) c < 0.724 (GeV/ t' 0.449 <
Not something ordinary
Does not fit to the radial excitation trajectory Too close to ground state a1(1260) Width narrower than ground state Mass is very close to the K ∗ ¯ K thereshold
, Uni Bonn) Ground axial vector 25/05/2018 14 / 14
Remarks a1(1420) phenomenon
Enhancement in COMPASS data π p → 3π p
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 (GeV)
2
+π
M 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 (GeV)
2
+π
M
< 1.5 GeV}
π 3
Dalitz plot, {1.4 GeV < M π 3 COMPASS 2008 p
+
π
→ p π
1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 (GeV)
π 3
M 10000 20000 30000 40000 50000 60000 70000 Entries/(20 MeV)
"f
Data 87 waves P-wave π f
+ ++
1
COMPASS 2008 p
+
π
→ p π
A simple cut on the Dalitz plot (f0 band) enhances bump in M3π Partial wave analysis proves that the origin is the a1(1420).
, Uni Bonn) Ground axial vector 25/05/2018 14 / 14