motivation and context: exotic states of QCD spectrum phenomenology - - PowerPoint PPT Presentation

Vladiszlav Pauk MESON 2016 Krakow, Poland

η′− π production and search for exotic mesons at COMPASS and JLab12

JPAC @ JLab

O U T L I N E

• motivation and context: exotic states of QCD spectrum
• phenomenology and formalism: peripheral meson production

@ GlueX & COMPASS

• data analysis: ηπ production @ COMPASS
• model and theoretical analysis: Regge formalism and

finite-energy sum rules (FESR)

• summary and outlook: GlueX and expectations
• 1-

1- + 2+ - 0+ -

Q C D S P E C T R U M A N D E X O T I C H A D R O N S

• rdinary hadrons

exotic hadrons color singlets isovector meson spectrum from lattice QCD @ mπ=700 MeV

~300 states

• nly few

well-established

Dudek, et al. (2010)

• 2-

JPC

exotic states

1- + 2+ - 0+ -

• rdinary hadrons

exotic hadrons color singlets isovector meson spectrum from lattice QCD @ mπ=700 MeV

~300 states

• nly few

well-established

Dudek, et al. (2010)

• 2-

gluon excitations

JPC

information about soft gluonic modes of QCD

exotic states

expected ground state exotic meson: JPC = 1−+

Q C D S P E C T R U M A N D E X O T I C H A D R O N S

• 3-

S E A R C H E S F O R H Y B R I D S I N P E R I P H E R A L P R O D U C T I O N

IGJPC = 1−1−+ πη, πη’, πρ, πa1, πb1, πf1 decay modes

pn → ηπ−π0

• π−p → π−ηp

π1(1400) π1(2015)

• 3-

S E A R C H E S F O R H Y B R I D S I N P E R I P H E R A L P R O D U C T I O N

Crystal Barrel ︎πη’, πρ π1(1600)

E852, GAMS, KEK, VES

E852 πb1, πf1 IGJPC = 1−1−+ πη, πη’, πρ, πa1, πb1, πf1 decay modes πη decay decay decay π−p → π−η’p π−p → π−ρ0p VES, E852 controversial! E852 π−p → π−b1p

pn → ηπ−π0

• π−p → π−ηp

data

π1(1400) π1(2015) γp→Xp→η(‘)πp GlueX on 12 GeV electron beam @ JLab πp→Xp→η(‘)πp COMPASS on 191 GeV pion beam @ CERN

• 3-

Forthcoming data

S E A R C H E S F O R H Y B R I D S I N P E R I P H E R A L P R O D U C T I O N

Crystal Barrel ︎πη’, πρ π1(1600)

E852, GAMS, KEK, VES

E852 πb1, πf1 IGJPC = 1−1−+ πη, πη’, πρ, πa1, πb1, πf1 decay modes πη decay decay decay π−p → π−η’p π−p → π−ρ0p VES, E852 controversial! E852 π−p → π−b1p π1(1400) π1(1600)

?

P E R I P H E R A L P R O D U C T I O N I N R E G G E M O D E L

• 4-

R

Reggeon-particle amplitude factorization Regge exchange

R p p

Aπp→πηp = R AπR→πη

@

l

a

r

ge

e

n

er

g y

P E R I P H E R A L P R O D U C T I O N I N R E G G E M O D E L

• 4-

R

Reggeon-particle amplitude factorization no overlapping discontinuities in invariant masses Regge exchange

R p p

Aπp→πηp = R AπR→πη

@

l

a

r

ge

e

n

er

g y

well-defined quantum numbers for each Regge exchange dispersion relation at fixed t Reggeization discontinuity only in the s-channel invariant mass

F I N I T E E N E R G Y S U M R U L E S

• 5-

reconstructed from PWA

s t 2

r h s lhs Regge pole N/D

h

igh

en

er

gy

low en

e

rg

y

Regge parametrization

s t 1 t s

s1=m(ηπ)2

0 = I ds A(s) − AR(s)

Cauchy integral theorem

F I N I T E E N E R G Y S U M R U L E S

aim: first systematic analysis

• f peripheral production using FESR
• 5-

Z N ds Im A(s) = N α+1V

reconstructed from PWA

s t 2

r h s lhs Regge pole N/D

h

igh

en

er

gy

low en

e

rg

y

Regge parametrization

s t 1 t s

s1=m(ηπ)2

D-wave ηπ vs η’π

COMPASS coll. (2015)

s t

a2/a4

a2 (1320) a4 (2040)

E v e n t s 4 M e V / c

2

1 03

5∙103

1 . 6 2 2 . 4

m(ηπ) < 3 (GeV/c2 )2

cos θ

• 1

1

P θ

m(ηπ) [GeV/c2] m(ηπ) [GeV/c2]

P θ~0 θ~π CM

• 6-

PWA

P H E N O M E N O L O G Y O F P R O D U C T I O N AT C O M PA S S

ηπ

D-wave ηπ vs η’π

COMPASS coll. (2015)

P+f2 a2

s t

a2/a4

a2 (1320) a4 (2040)

fwd η

E v e n t s 4 M e V / c

2

1 03

5∙103

1 . 6 2 2 . 4

m(ηπ) < 3 (GeV/c2 )2

cos θ

• 1

1

η

π

fwd π

P

m(ηπ) ∊ [5-6] (GeV/c2 )2

θ

m(ηπ) [GeV/c2] m(ηπ) [GeV/c2]

P P P θ~0 θ~π CM

• 6-

PWA

P H E N O M E N O L O G Y O F P R O D U C T I O N AT C O M PA S S

ηπ

D-wave ηπ vs η’π

COMPASS coll. (2015)

P+f2 a2

+

s t

a2/a4

a2 (1320) a4 (2040)

fwd η

E v e n t s 4 M e V / c

2

1 03

5∙103

1 . 6 2 2 . 4

m(ηπ) < 3 (GeV/c2 )2

cos θ

• 1

1

η

π

fwd π

P

m(ηπ) ∊ [5-6] (GeV/c2 )2

θ

m(ηπ) [GeV/c2] m(ηπ) [GeV/c2]

P P P

= Σ even waves (D+G-waves)

P

θ~0 θ~π

~

A(θ)+A(-θ) CM

• 6-

PWA

P H E N O M E N O L O G Y O F P R O D U C T I O N AT C O M PA S S

ηπ

P-wave

exotic state

P+f2 a2

—

s t

cos θ

• 1

1

P θ

m(ηπ) [GeV/c2]

P P P

= Σ odd waves (P-wave)

ηπ vs η’π

E v e n t s 4 M e V / c

2

1 03

5∙103

1 . 6 2 2 . 4

m(ηπ) [GeV/c2]

P

η

π

~

COMPASS coll. (2015)

CM

fwd η fwd π

θ~0 θ~π

• 6-

?

A(θ)-A(-θ)

P H E N O M E N O L O G Y O F P R O D U C T I O N AT C O M PA S S

?

PWA

ηπ

m(ηπ) < 3 (GeV/c2 )2 m(ηπ) ∊ [5-6] (GeV/c2 )2

S I N G L E A N D D O U B L E R E G G E L I M I T S

PWE for pomer

• 7-

Single-Regge limit Double-Regge limit

P+f2 a2 P P P

S I N G L E A N D D O U B L E R E G G E L I M I T S

PWE for pomer

• 7-

s1=m(ηπ)2 s2=m(pη)2 s=(CoM energy)2

cos φ = a + bs2 s cos θ = a0 + b0t1 + ct2

1

t1 - (beam mom. transfer)2

cos ω ≈ s1s2 s

Toller angle

A = K R(s) X

J,λ

NJ(s1) DJ(s1) dJ

λ0(θ)eiλφ

Gottfried-Jackson angles

u1 - (beam mom. transfer)2 s1=m(ηπ)2

Single-Regge limit Double-Regge limit forward π amplitude forward η amplitude

P+f2 a2 P P

AR

t = K R(s1, t1)R(s2)V (ω)

AR

u = K R(s1, u1)R(s2)V (ω)

P

C O N S T R A I N T S A N D E X P E C TAT I O N S

conservation of parity and angular momentum

PWE for pomer

• 8-

Pomeron exchange contribution

AL = Z A(Ω) YL(Ω) dΩ

threshold behavior

KL ∼ qL A1 ∼ 1 log s1 A ∼ s1eα0t log s1

asymptotic behavior of the P-wave

q = q (s1 − (mπ + mη)2)(s1 − (mπ − mη)2)

AL → KLAL

partial-wave amplitudes L - orbital angular momentum

C O N S T R A I N T S A N D E X P E C TAT I O N S

conservation of parity and angular momentum

PWE for pomer

• 8-

Pomeron exchange contribution

1 2 3 4 5 0.1 0.2

s1 [GeV/c2] (mπ+mη)2

AL = Z A(Ω) YL(Ω) dΩ

threshold behavior

KL ∼ qL A1 ∼ 1 log s1 A ∼ s1eα0t log s1

asymptotic behavior of the P-wave normalization constrained by sum rules

q = q (s1 − (mπ + mη)2)(s1 − (mπ − mη)2)

P-wave: L=1 AL → KLAL

?

partial-wave amplitudes L - orbital angular momentum

F I N I T E - E N E R G Y S U M R U L E

FESR for forward-backward asymmetry

• 9-

symmetric combination: non-exotic even partial waves exchanges: P+f2+a2 antisymmetric combination: exotic

• dd partial waves

exchanges: P+f2-a2

N

Z ds1 Im Aeven/odd(s1) = X

R

N αRVR

F I N I T E - E N E R G Y S U M R U L E

expansion in powers of s2/s FESR for forward-backward asymmetry

• 9-

symmetric combination: non-exotic even partial waves exchanges: P+f2+a2 antisymmetric combination: exotic

• dd partial waves

exchanges: P+f2-a2 truncated PW series

N

Z ds1 Im AL(s1) = X

R,i

C(i)

L (N)V (i) R

V (ω) = X

i

V (i) ⇣s2 s ⌘i

N

Z ds1 Im Aeven/odd(s1) = X

R

N αRVR

coherent contributions from larger angular momenta stabilize

S U M M A R Y & O U T L O O K

photoproduction @ GlueX

γ γ γ p p p

ρ ω

γp→Xp→πηp

ρ ρ ρ + π

• 10 -

S U M M A R Y & O U T L O O K

• construct fitting functions for the single- and double-diffractive regime using

Regge formalism; parametrize the low-energy amplitude within N/D formalism

• extract the parameters of the reggeon-particle amplitude
• analyze correlation between low- and high-energy regions using FESR

photoproduction @ GlueX

γ γ γ p p p

ρ ω

γp→Xp→πηp

ρ ρ ρ + π

• 10 -

S U M M A R Y & O U T L O O K

• construct fitting functions for the single- and double-diffractive regime using

Regge formalism; parametrize the low-energy amplitude within N/D formalism

• extract the parameters of the reggeon-particle amplitude
• analyze correlation between low- and high-energy regions using FESR

photoproduction @ GlueX

• non-trivial correlation between production of exotic states and violation of

exchange degeneracy

• sensitivity to the gluon component of η’

expectations

γ γ γ p p p

ρ ω

γp→Xp→πηp

ρ ρ ρ + π

• 10 -