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

η′ − π production and search for exotic mesons at COMPASS and JLab12 Vladiszlav Pauk JPAC @ JLab MESON 2016 Krakow, Poland

O U T L I N E - 1- ‣ motivation and context: exotic states of QCD spectrum ‣ phenomenology and formalism: peripheral meson production @ GlueX & COMPASS ‣ data analysis: η π production @ COMPASS ‣ model and theoretical analysis: Regge formalism and finite-energy sum rules ( FESR ) ‣ summary and outlook: GlueX and expectations

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 - 2- ordinary hadrons ~300 states color singlets only few well-established exotic hadrons 0 + - 2 + - 1 - + J PC exotic states Dudek, et al. (2010) isovector meson spectrum from lattice QCD @ m π =700 MeV

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 - 2- ordinary hadrons ~300 states color singlets only few well-established exotic hadrons gluon excitations 0 + - 2 + - 1 - + J PC information about soft gluonic modes of QCD exotic states Dudek, et al. expected ground state (2010) exotic meson : J PC = 1 − + isovector meson spectrum from lattice QCD @ m π =700 MeV

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 - 3- decay modes π η , π η ’, π ρ , π a 1 , π b 1 , π f 1 I G J PC = 1 − 1 − +

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 - 3- decay modes π η , π η ’, π ρ , π a 1 , π b 1 , π f 1 I G J PC = 1 − 1 − + π − p → π − η p E852 , GAMS, KEK, VES decay - π 1 (1400) π η pn → η π − π 0 Crystal Barrel π − p → π − η ’ p E852 decay ︎ π η ’, π ρ π 1 (1600) π − p → π − ρ 0 p VES, E852 controversial! decay π − p → π − b 1 p E852 π 1 (2015) π b 1 , π f 1

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 - 3- decay modes π η , π η ’, π ρ , π a 1 , π b 1 , π f 1 I G J PC = 1 − 1 − + π − p → π − η p E852 , GAMS, KEK, VES decay - π 1 (1400) π η pn → η π − π 0 Crystal Barrel π − p → π − η ’ p E852 decay ︎ π η ’, π ρ π 1 (1600) π − p → π − ρ 0 p VES, E852 controversial! decay π − p → π − b 1 p E852 π 1 (2015) π b 1 , π f 1 ? COMPASS on 191 GeV pion beam π 1 (1400) π p → Xp → η (‘) π p data @ CERN π 1 (1600) GlueX on 12 GeV electron beam γ p → Xp → η (‘) π p Forthcoming data @ JLab

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- g y e r n e @ g e r a l R A π p → πη p = R A π R → πη R factorization p p Regge exchange Reggeon-particle amplitude

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- g y e r n e @ g e r a l R A π p → πη p = R A π R → πη R factorization p p Regge exchange Reggeon-particle amplitude well-defined quantum numbers for each Regge exchange discontinuity only no overlapping discontinuities in the s-channel invariant mass in invariant masses dispersion relation Reggeization at fixed t

F I N I T E E N E R G Y S U M R U L E S - 5- h y i g h r g e e n lo w e n e r g y s 1 =m( η π ) 2 N/D Regge pole t 1 s s s t 2 t reconstructed Regge s lhs h parametrization from PWA r I d s A ( s ) − A R ( s ) 0 = Cauchy integral theorem

F I N I T E E N E R G Y S U M R U L E S - 5- h y i g h r g e e n lo w e n e r g y s 1 =m( η π ) 2 N/D Regge pole t 1 s s s t 2 t reconstructed Regge s lhs h parametrization from PWA r Z N d s Im A ( s ) = N α +1 V 0 aim: first systematic analysis of peripheral production using FESR

ηπ 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 - 6- CM θ m( η π ) < 3 (GeV/c 2 ) 2 P 1 θ ~ 0 a 2 /a 4 cos θ s 0 P t θ ~ π PWA - 1 m( η π ) [GeV/c 2 ] η π vs η ’ π 5 ∙ 10 3 D-wave a 2 (1320) COMPASS coll. 2 c s / t V (2015) n a 4 (2040) e e M v 1 0 3 E 0 4 4 1 . 6 2 2 . m( η π ) [GeV/c 2 ]

ηπ 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 - 6- CM θ m( η π ) < 3 (GeV/c 2 ) 2 m( η π ) ∊ [5-6] (GeV/c 2 ) 2 P π 1 P+f 2 θ ~ 0 fwd π P a 2 /a 4 cos θ s 0 P η fwd η t θ ~ π PWA a 2 - 1 P m( η π ) [GeV/c 2 ] η π vs η ’ π 5 ∙ 10 3 D-wave a 2 (1320) COMPASS coll. 2 c s / t V (2015) n a 4 (2040) e e M v 1 0 3 E 0 4 4 1 . 6 2 2 . m( η π ) [GeV/c 2 ]

ηπ 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 - 6- CM θ m( η π ) < 3 (GeV/c 2 ) 2 m( η π ) ∊ [5-6] (GeV/c 2 ) 2 P π 1 P+f 2 θ ~ 0 fwd π P a 2 /a 4 cos θ + s 0 P η fwd η t θ ~ π PWA a 2 - 1 P m( η π ) [GeV/c 2 ] = Σ even waves η π vs η ’ π (D+G-waves) 5 ∙ 10 3 D-wave a 2 (1320) COMPASS coll. 2 c s / t V (2015) n a 4 (2040) e e M v P 1 0 3 E ~ A( θ )+A(- θ ) 0 4 4 1 . 6 2 2 . m( η π ) [GeV/c 2 ]

ηπ 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 - 6- CM θ m( η π ) < 3 (GeV/c 2 ) 2 m( η π ) ∊ [5-6] (GeV/c 2 ) 2 P π 1 P+f 2 θ ~ 0 fwd π P ? cos θ — s 0 P η fwd η t θ ~ π PWA a 2 - 1 P m( η π ) [GeV/c 2 ] = Σ odd waves η π vs η ’ π (P-wave) 5 ∙ 10 3 ? P-wave COMPASS coll. 2 c exotic state s / t V (2015) n e e M v P 1 0 3 E A( θ ) - A(- θ ) ~ 0 4 4 1 . 6 2 2 . m( η π ) [GeV/c 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 - 7- Single-Regge limit P Double-Regge limit P+f 2 P a 2 PWE for pomer 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 - 7- N J ( s 1 ) Single-Regge X λ 0 ( θ ) e i λφ D J ( s 1 ) d J s 1 =m( η π ) 2 A = K R ( s ) limit J, λ P s =(CoM energy) 2 cos θ = a 0 + b 0 t 1 + ct 2 1 Gottfried-Jackson angles cos φ = a + bs 2 s t 1 - (beam mom. transfer) 2 Double-Regge limit P+f 2 s 1 =m( η π ) 2 forward π amplitude A R t = K R ( s 1 , t 1 ) R ( s 2 ) V ( ω ) P s 2 =m(p η ) 2 cos ω ≈ s 1 s 2 Toller angle u 1 - (beam mom. transfer) 2 s a 2 forward η amplitude A R PWE for pomer u = K R ( s 1 , u 1 ) R ( s 2 ) 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 - 8- conservation of parity partial-wave amplitudes A L → K L A L and angular momentum Z threshold behavior A L = A ( Ω ) Y L ( Ω ) d Ω K L ∼ q L q L - orbital angular momentum q = ( s 1 − ( m π + m η ) 2 )( s 1 − ( m π − m η ) 2 ) Pomeron exchange contribution A ∼ s 1 e α 0 t log s 1 asymptotic behavior of the P-wave 1 A 1 ∼ log s 1 PWE for pomer

C O N S T R A I N T S A N D E X P E C TAT I O N S - 8- conservation of parity partial-wave amplitudes A L → K L A L and angular momentum Z threshold behavior A L = A ( Ω ) Y L ( Ω ) d Ω K L ∼ q L q L - orbital angular momentum q = ( s 1 − ( m π + m η ) 2 )( s 1 − ( m π − m η ) 2 ) Pomeron exchange contribution ? A ∼ s 1 e α 0 t log s 1 0.2 asymptotic behavior of the P-wave P-wave: 0.1 1 L=1 A 1 ∼ log s 1 PWE for pomer 0 normalization constrained 1 2 3 4 5 (m π +m η ) 2 s 1 [GeV/c 2 ] by sum rules

F I N I T E - E N E R G Y S U M R U L E - 9- FESR for forward-backward asymmetry N Z X d s 1 Im A even/odd ( s 1 ) = N α R V R R 0 antisymmetric combination: symmetric combination: exotic non-exotic odd partial waves even partial waves exchanges: P+f 2 - a 2 exchanges: P+f 2 +a 2

F I N I T E - E N E R G Y S U M R U L E - 9- FESR for forward-backward asymmetry N Z X d s 1 Im A even/odd ( s 1 ) = N α R V R R 0 antisymmetric combination: symmetric combination: exotic non-exotic odd partial waves even partial waves exchanges: P+f 2 - a 2 exchanges: P+f 2 +a 2 expansion in powers of s 2 /s N Z C ( i ) L ( N ) V ( i ) X d s 1 Im A L ( s 1 ) = R V ( i ) ⇣ s 2 ⌘ i X V ( ω ) = R,i 0 s i stabilize coherent contributions from truncated PW series larger angular momenta

S U M M A R Y & O U T L O O K - 10 - γ γ γ photoproduction ρ ω @ GlueX ρ + π ρ ρ γ p → Xp → π η p p p p

S U M M A R Y & O U T L O O K - 10 - γ γ γ photoproduction ρ ω @ GlueX ρ + π ρ ρ γ p → Xp → π η p p p p ‣ 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

S U M M A R Y & O U T L O O K - 10 - γ γ γ photoproduction ρ ω @ GlueX ρ + π ρ ρ γ p → Xp → π η p p p p ‣ 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 expectations ‣ non-trivial correlation between production of exotic states and violation of exchange degeneracy ‣ sensitivity to the gluon component of η ’