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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

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

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)

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

a4(2040)

π2(1880)

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

a4(2040)

π2(1880)

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 m3π

generic process

what we are after

exclusive reaction

t ' = t − tmin ≈ t

m3π m3π

generic process

what we are after

exclusive reaction

t ' = t − tmin ≈ t

generic process

what we are after

exclusive reaction

t ' = t − tmin ≈ t

generic process

what we are after

exclusive reaction

t ' = t − tmin ≈ t

generic process

what we are after

exclusive reaction

t ' = t − tmin ≈ t

First Impressions Motivation for Isobar Model

)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

r of E

610× (COMPASS 2008) p+π-π-π → p-π

m2 2 π

f2(1270) Prelim

Prelim

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

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

r of E

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

r of E

310× Sπ(1270)

2f +1+−2−1

2c/2 1.000 GeV≤ t' ≤0.100 0.87%

Preliminary

r of E

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

ity (p

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

ity (p

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

ity (p

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

ity (p

610× p)−)π(3→p−πCOMPASS 2008 ( Sπ(1270) 2 f+0+−2

(incoherent sum)

Preliminary

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

ity (p

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

ity (p

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

ity (p

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

ity (p

610× p)−)π(3→p−πCOMPASS 2008 ( Sπ(1270) 2 f+0+−2

(incoherent sum)

Preliminary

compare: π−π+π− and : π−π0π0

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

r of E

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

r of E

310× Sπ(770) ρ +0++1−1

2c/2 0.724 GeV≤ t' ≤0.449 15.94%

Preliminary

r of E

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

r of E

310× Sπ(1270)

2f +0+−2−1

2c/2 0.724 GeV≤ t' ≤0.449 5.39%

Preliminary

r of E

310× Gπ(770) ρ +1++4−1

2c/2 0.724 GeV≤ t' ≤0.449 1.12%

Preliminary

r of E

310× Dπ(770) ρ +1++2−1

2c/2 0.113 GeV≤ t' ≤0.100 3.39%

Preliminary

r of E

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

r of E

00.20.40.60.8

1.21.41.61.8

2.22.4

310× Gπ(770) ρ +1++4−1

2c/2 0.113 GeV≤ t' ≤0.100 0.49%

Preliminary

high t

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

t dependence of mass distributions

r of E

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

r of E

310× Sπ(770) ρ +0++1−1

2c/2 0.724 GeV≤ t' ≤0.449 15.94%

Preliminary

r of E

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

r of E

310× Sπ(1270)

2f +0+−2−1

2c/2 0.724 GeV≤ t' ≤0.449 5.39%

Preliminary

r of E

310× Gπ(770) ρ +1++4−1

2c/2 0.724 GeV≤ t' ≤0.449 1.12%

Preliminary

r of E

310× Dπ(770) ρ +1++2−1

2c/2 0.113 GeV≤ t' ≤0.100 3.39%

Preliminary

r of E

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

r of E

00.20.40.60.8

1.21.41.61.8

2.22.4

310× Gπ(770) ρ +1++4−1

2c/2 0.113 GeV≤ t' ≤0.100 0.49%

Preliminary

high 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

ity (p

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

ity (p

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−

π− π

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

ity (p

121416

310× p)−)π(3→p−πCOMPASS 2008 ( Pπ(980) 0 f+0++1

(incoherent sum)

Preliminary

π−π+π−

π− π

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

ity (p

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

ity (p

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

ity (p

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−

π− π

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

ity (p

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

ity (p

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

ity (p

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−

π− π

1++0+ f0(980) π P

Model for Spin Density Matrix

Two types of contributions

π-‐ π+

π-‐

ρ, σ

π-‐

Resonance

��

nπ-‐π+

pπ-‐

��

ρ, σ

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

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

a1’a1(1420)

fit range

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

a1’a1(1420)

fit range

COMPASS “Holography”

Reference waves

Interferometry

simultaneous fit in 11 t-‐bins

Reference waves

Interferometry

Reference waves

Interferometry

Reference waves

Interferometry

Mass dependent fitsFit in 11 t-‐bins t

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

JPCMε[isobar]πL

Example for t-‐dependence

JPCMε[isobar]πL

IntensitiesPhases

Reference wave

a1(1260) non-‐resonant

πππ COMPASS 2008

Mass dependent fitsFit in 11 t-‐bins t

Second high-‐mass a1’ resonance visible

Mass dependent fits a2(1320) t

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

sum a2(1320) a2’

Some Results

truly new states

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

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

r of E

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

r of E

]ππ [+0+−0−12c 1.300 GeV/≤ π3m ≤1.100 2−)c 0.07) (GeV/± = (22.13 b

Preliminary

)2 c/2N

r of E

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

r of E

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

r of E

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

r of E

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)

What about the building blocks

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

What about the building blocks

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

Deck σ

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)

π-‐ π+

π-‐

ρ, ρ3 , f0 , f2

π-‐

Resonances

π-‐π+

π-‐

π-‐ρ, ρ3 , f0 , f2

π-‐

π-‐ π+π-‐

ρ, σ

��

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]*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)

at π(1800) 0−+ → [ππ ]S

Correlation:m2π(0++) vs m3π(J

high t

3π: 0-+ 3π: 2-+ 3π: 1++

high t

3π: 0-+

3π: 0-+ 3π: 2-+

3π: 2-+ 3π: 1++

3π: 1++

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-‐+

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‘

Phase of Exotic wave

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

(-‐)1++

2-‐+

• What about previous analysis performed by BNL, Dzerba and VES ? • We have used their wave-‐set and their range of t´

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

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

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

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

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