the$virtue$of$precision$spectroscopy$:$ a$new$axial7vector ... · exzellenzcluster universe...

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


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


Constituent Quarks and Mesons

f0(500) f0(980) f0(1500)

a4(2040)



f0(500) f0(980) f0(1500)

a4(2040)

π2(1880)



f0(500) f0(980) f0(1500)

a4(2040)

π2(1880)

2

2



Limits for light mesons

f0(500) f0(980) f0(1500)

a4(2040)

π2(1880)




• many missing/disputed states in mass region

m ~ 2 GeV/c2

f0(500) f0(980) f0(1500)

a4(2040)

π2(1880)




• 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)


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



t

m3π m3π

generic process

what we are after

exclusive reaction

t ' = t − tmin ≈ t

m3π

t ' = t − tmin ≈ t

m3π



t

m3π

t

generic process

what we are after

exclusive reaction

t ' = t − tmin ≈ t

m3π

t ' = t − tmin ≈ t

m3π


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


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


Fit Model -‐ Isobars

[ππ]S


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


)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%


Preliminary


)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%


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


(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


(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


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


(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


(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


(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


t dependence of mass distributions


)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


)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%


Preliminary


)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


)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%


Preliminary


)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%


Preliminary


)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%


Preliminary


)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


)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%


Preliminary

high t

low t

1++0+ρπ S 2-‐+0+ f2 π S 4++1+ ρπ G2++1+ ρπ D


t dependence of mass distributions


)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


)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%


Preliminary


)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


)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%


Preliminary


)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%


Preliminary


)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%


Preliminary


)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


)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%


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


More exotic families

f0(980)


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


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


(incoherent sum)

Preliminary

π−π+π−

and

π− π

0 π0

1++0+ f0(980) π P


)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


(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


(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


(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


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


(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


(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


(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


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)


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


! 1 resonance : a

4(2040) + non resonant term

2 resonances : π2(1670) and π


! 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


Mass dependent fits a1(1420) Fit in 11 t-‐bins

sum

t

t


Mass dependent fits a1(1420) Fit in 11 t-‐bins

sum

t

t NEW


Phase: a1(1420) Fit in 11 t-‐bins: medium t

a1’a1(1420)

a4π2

a2’

fit range


Phase: a1(1420) Fit in 11 t-‐bins: medium t

a1’a1(1420)

a4π2

a2’

fit range

NEW


COMPASS “Holography”

Reference waves

Interferometry

simultaneous fit in 11 t-‐bins

tt


Mass dependent fitsFit in 11 t-‐bins t

t

Strongly t-‐dependent spectral shape around a1(1260)

sum

JPCMε[isobar]πL


Example for t-‐dependence

t

JPCMε[isobar]πL

IntensitiesPhases

Reference wave

a1(1260) non-‐resonant

πππ COMPASS 2008


Mass dependent fitsFit in 11 t-‐bins t

t

Second high-‐mass a1’ resonance visible

sum


Mass dependent fits a2(1320) t

t

Strongly t-‐dependent interference effects high-‐mass a2’

sum a2(1320) a2’


Some Results

truly new states

PDG


Kinematic Dependence

ACCMOR COMPASS

Very Preli

minary

Global and mass-‐dependent t‘ slope parameters


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


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


Preliminary


)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


Preliminary


)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


Preliminary


)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


Preliminary


)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


Preliminary


)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


Preliminary

around a1(1260)

around π(1300)

around a1(1420)

around a1(1260)

around π(1800)

around π2(1670)

m=0

m=1


What about the building blocks

• We have solved a puzzle – but were the building blocks correct ?

ρσ

f0 f2

Deck


What about the building blocks

• We have solved a puzzle – but were the building blocks correct ?

?σ

ρ

Deck σ

ρ

Deck


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

��


Isobars: an Example

use BES parametrization: as it decays into ππ and KK (threshold effect)

f0(980) parametrization[ππ]S


Isobars: [ππ]*Sf0(980)continuum -‐ [ππ]S

fixed functional form – variable intensity/phase (2 parameters)


Isobars: [ππ]*S

replaced by ONE [ππ]*S histogram with n-‐bins


Isobars: [ππ]*S

replaced by ONE [ππ]*S histogram with n-‐bins (2n parameters determined by fit)


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


Correlation:m2π(0++) vs m3π(J

PC)

low t

high t

3π: 0-+ 3π: 2-+ 3π: 1++


Correlation:m2π(0++) vs m3π(J

PC)

low t

high t

3π: 0-+

3π: 0-+ 3π: 2-+

3π: 2-+ 3π: 1++

3π: 1++


For more Details see Talk of Fabian Krinner


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


Deck and Data6-‐+ 4-‐+

t‘


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‘


Phase of Exotic wave

• Clear phase variation seen • Variation of O(500) • Mild variation with t´1++

(-‐)1++

2++

4++

2-‐+


• 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


Photo-‐Production


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


EM-‐Transitions for Mesons

a2(1320)

M2 transition


EM-‐Transitions for Mesons

a2(1320) π2(1670)

First E2 transition observed for mesonsM2 transition


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 ?


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 !!


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)..


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


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

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