Hyperon Studies at JPAC. General approach: Role of reaction theory Hyperon Studies

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1 Hyperon Studies at JPAC Who we are and what we do General approach: Role of reaction theory Hyperon Studies Adam Szczepaniak Indiana University Jefferson Lab ~jpac/index.html

2 There may be hadrons that look like but before we know this it is necessary to identify resonances

3 we need to know how to interpret peaks (Violin Resonances) b! K pj/ pj/ a resonance in??... or a reflection?

4 S-matrix principles: Crossing, Analyticity, Unitarity s M A(s,t) t t M s X A(s, t) = A l (s)p l (z s ) l Analyticity s-channel M-decay channel s-plane Crossing A l (s + i ) 6= A l (s i ) A l (s) =lim! A l (s + i ) bumps/peaks on the real axis (experiment) come from singularities in unphysical sheets Unitarity These singularities come from QCD

5 Amplitude JPAC Events, X-sections,MC QCD Predictions t A(s, t) = 1X f l (s)p l (z s )= 1X u g l (t)p l (z t ) s l= l= Amplitude analysis: based on S-matrix principles: analyticity unitarity crossing Global effort JLab/IU/GWU Physics Analysis Center

6 QCD on the Lattice : simulated scattering experiment (known kinematical function) Z(Ei= data ) = T(Ei) (infinite volume amplitude ) Ei = discrete energy spectrum of states in the lattice D.Wilson et. al in general solution of the Lusher condition requires an analytical model for T

7 JPAC : Example of Analysis Projects Light meson decays and light quark resonance ω/φ 3π, πγ (dispersive) ω 3π (Veneziano, B4) η 3π, η /f1 ηπ π, (Khuri-Treiman, B4) J/Ψ γππ Photo-production: (production models, FESR and duality) γp πp γp pk+k- (and Kp) γp π+π-p, πηp, ωp Exotica and XYZ s: π-p π-ηp & π-p π-η p (FESR) Launched in the Fall of 213 >2 analysis/papers published B Ψ π- K + u, Ψ(426) J/Ψ π+π-, Λb K- pj/ψ J/Ψ 3π, KKπ (Veneziano, B4)

8 Adam Szczepaniak (IU/JLab) Mike Pennington (JLab) Tim Londergan (IU) Geoffrey Fox (IU) Emilie Passemar (IU/JLab) Cesar Fernandez-Ramirez (Jlab Mexico) Vincent Mathieu (IU) Micheal Doering (GWU) Ron Workman (GWU) BESIII collaboration Medina Ablikim (Beijing) Ryan Mitchell, (IU) LHCb collaboration T.Skwarnicki (Syracuse) J.Rademacker, (Bristol) Vladyslav Pauk (Mainz JLab) Alessandro Pilloni (Rome JLab) Astrid Blin (Valencia) Andrew Jackura (IU) Lingyun Dai (IU/JLab Valencia) Meng Shi (JLab Beijing) Igor Danilkin (JLab Mainz) Peng Guo (IU/JLab CSU) COMPASS collaboration Mikhail Mikhasenko (Bonn) Fabian Krinner (TUM) Boris Grube (TUM) BaBar collaboration Antimo Palano (Bari) GlueX collaboration Matthew Shepherd (IU) Justin Stevens (JLab) CLAS collaboration Diane Schott (GWU/JLab) Viktor Mokeev (JLab) HASPECT Marco Battaglieri (Genova) Derek Glazier (Glasgow) Raffaella De Vita (Genoa)

9 p - p Æ p n analyticity & complex energy plane Im E E 1 6 Re E dsêdt Hmb.GeV -2 L 1 resonance pole 1 special thanks to Vincent Mathieu GeV x GeV x GeV x GeV x GeV x GeV x t HGeV 2 L

10 Hyperon Physics Bridge between light (u,d) and heavy (c,b) quark baryons Test Quark Model vs QCD (lattice) Photon couples to quarks is, glueballs, hybrids or use in associated production of K*'s and Hyperons Hyperon spectrum less understood e.g Λ(145) only recently pole positions have started to be reported by the PDG

11 Some quark model states have not been seen yet 2 -- (L=2,S=1)

12 Analyticity is a powerful constraint a s < (2GeV) 2 c cf. Bonn/Gatchina, EBAC, Julich, Giessen,GWU, Mainz, Zagreb,) R R a c low-s b s-unitarity d A a t-channel pole (cut) develops c b d high-s cf. Regge phenomenology b s > (2GeV) 2 d

13 Im A Regge (N,t) Can use cross- N ds Im A(s,t) a c channel reggeons to a c study direct channel ρ,a 2 resonances b d Im A(s,t)= Im A(s,t) b d s - u s - u K + p K - p u u d u u d

14 _ PWA for KN Model the amplitude Fit to data Analytically continue to complex values of energy to search for poles Partial-wave analysis (Lmax= 5), Coupled channels, Unitarity Analyticity: Right threshold behavior (angular momentum barrier), Resonances and backgrounds are incorporated byhand through K matrices In the range 2.19<s<4.7 GeV2 (8 data points, 75 data points, 5 data points) We fit the KSU analysis singleenergy partial waves [Zhang et al., PRC 88, 3524 (215)] Caveat: we lose correlations among partial waves Cesar Fernandez Ramirez et al., arxiv: [hep-ph]

15 S` = I +2i [C`(s)] 1/2 T`(s)[C`(s)] 1/2 T`(s) = K 1 (s) i `(s) 1 [i `(s)] kk = s s k Z 1 s k [C`(s)] kk s s s ds s k k =, KN,, (1385), (152),,, K N, (1232),, Resonance Background [K a (s)] kj = x a k M a M 2 a s xa j [K b (s)] kj = x b k M b M 2 b + s xb j Generates pole in the 2nd Riemann sheet Generates pole in the real axis for s< in the1st Riemann sheet

16 Phase Space/Analicticity [C`(s)] kk = q k(s) q apple q 2 k (s)r 2 1+q 2 k (s)r2 ` Right threshold behavior Angular momentum barrier Right high-energy behavior r =1 fm (interaction radius) [q k (s)] 2 = m 1m 2 s k [s s k ] Z 1 [i `(s)] kk = s s k [C`(s )] kk s k s s p (` ) ds s s k = a a` (`) apple (`)(s sk ) p s k s 1+a (s s k ) ([1 + a(s s `a`+1/2 k )] 2 F 1 [1,`+1/2, 1/2, 1/a(s k s)] i [3 + 2` + a(s s k )] 2 F 1 [1,`+1/2, 1/2, 1/a(s k s)]) Valid for l real and bigger than -1/2 16

17 Partial Waves 1 S 1.7 P 1.6 P 3.8 D K N K N K N K N K N π Σ K N π Σ Im s (GeV 2 ) Λ(145) Λ(167) Λ(2) Λ(16) Λ(171) Λ(181) Pole positions Im s (GeV 2 ) Λ(189) Λ(152) Λ(169) Pole positions s (GeV 2 ) s (GeV 2 ) s (GeV 2 ) s (GeV 2 )

18 Partial Waves.4 P 13.2 D 13.4 D 15.2 F 15 K N K N K N K N K N π Σ K N π Σ K N π Λ K N π Λ Pole positions Pole positions Im s (GeV 2 ) Σ(167) Im s (GeV 2 ) Σ(1775) Σ(1915) s (GeV 2 ) s (GeV 2 ) s (GeV 2 ) s (GeV 2 )

19 1 Pole Positions πλ πσ KN ππσ πσ * πλ * K ησ K * N Σ(167) Σ(156) Γ p (MeV) Σ(1915) πσ ππλ Λ(145) KN Λ(152) Λ(169) Λ(16) πσ * Λ(171) Λ(167) ηλ Λ(182) Λ(183) Λ(211) 5 S 1 P 1 P 3 6 D 3 D 5 F 7 5 F 7 G physical axis M p (MeV) K * N Λ(181) Λ(2) Λ(189) Λ(22) Λ(21) Λ(25) physical axis Γ p (MeV) 2 Σ(177) Σ(1775) Σ(2) Σ(23) 3 S 11 P 11 P 13 D 13 4 D 15 F 15 F 17 G 17 Σ(27) M (MeV)

20 Resonances as Regge Poles near the resonance pole 1GeV 2 T l 1 (m 2 l s) = 1 l (l m 2 l + s) if l = + m 2 l than T l l 1 (s) with (s) = + s In general T = T (l, s) and a pole corresponds to a trajectory in the l,s space A pole in s at a fixed integer l is connected to another pole at a different integer l

21 KN! KN Unnatural parity J Natural parity 7/2 Λ(21) KN! Λ(183) 5/2 Λ(182) Λ(211) Λ(189)? P3 (169) 3/2 Λ(152) Λ(169)? threshold effect Λ(167) Λ(145) 1/2 Λ(1116) Λ(16)? (171) Λ(181) P Re[s p ] (GeV 2 )

22 Unnatural parity J Natural parity Σ(23) 7/2 Σ(1775) 5/2 Σ(1385) 3/2 Σ(167)? 1/2 Σ(1192) Re[s p ] (GeV 2 ) (3 *) Σ(194) nobody gets it, but there is a gap in Ragge trajectory

23 On the nature of Λ(145) Puzzle since the 6 s Quantum numbers those of a uds state Constituent quark models fail to reproduce the mass 155 MeV [Capstick, Isgur, PRD 34, 289 (1986)] 1524 MeV [Löring, Metsch, Petry, EPJA 1, 447 (21)] Amplitude analysis of KN scattering and πσk + data finds two poles [Mai, Meiβner, EPJA 51, 3 (215)] i MeV i MeV Lattice says: KN molecule [Hall et al., PRL 114, 1322 (215)] Lattice says: three-quark state [Engel et al., PRD 87, 3452 (213); PRD 87, 7454 (213)] Regge phenomenology [Fernandez-Ramirez et al., arxiv: (215)] Quark-diquark models obtain one Λ(145) with the right energy 143 MeV [Santopinto, Ferretti, PRC 92, 2522 (215)] 146 MeV [Faustov, Galkin, PRD 92, 545 (215)]

24 Λ(145)

25 Re Im Unnatural parity J Natural parity Unnatural parity J Natural parity Λ(22) 7/2 Λ(21) Λ(22) 7/2 Λ(21) Λ(183) 5/2 Λ(182) Λ(183) 5/2 Λ(182) 3/2 + 3/2 Λ(152) 3/2 + 3/2 Λ(152) 1/2 Λ(145) a Λ(145) b 1/2 Λ(1116) Λ(145) b Λ(145) a Λ(1116) R(s p ) (GeV 2 ) I(s p ) (GeV 2 ) (a) resonances. (a) resonances. Unnatural parity J Natural parity Unnatural parity J Natural parity Σ(23) 7/2 Σ(21) Σ(23) 7/2 Σ(21) Σ(1775) 5/2 Σ(1915) Σ(1775) 5/2 Σ(1915) Σ(1385) 3/2 Σ(167) Σ(1385) 3/2 Σ(167) 1/2 Σ(1192) 1/2 Σ(1192) R(s p ) (GeV 2 ) I(s p ) (GeV 2 ) (b) resonances. FIG. 1. (color online). Chew Frautschi plot for the the leading and Regge trajectories. Dashed lines are displayed to guide the eye. 25 (b) resonances. FIG. 2. (color online). Projections of the leading and Regge trajectories onto the ( =(s p ), J) plane. Dashed lines are displayed to guide the eye.

26 Compare fits - a, - b, - c a (145) = 1429 b (145) = i MeV 9i MeV Λa(145) is closer to the normal trajectory

27 Summary New, analytical model for hyperon spectrum Need to incorporate Regge constraints in direct channel as a constraint on, eg, K-matrix matrix poles in cross channels, as constrained on p.w. extraction, Λ(145): One more piece to the puzzle (more confusion?)

28 TABLE II. Summary of pole masses (M p =Re s p )andwidths( p = 2Im s p ) in MeV. Our poles are depicted in Fig. 5 unless they have a very large imaginary part. In [2] the (152) pole was obtained at (M p =1518.8, p =17.2). Ref. [5] implements two models labeled as KA and KB (see text). I stands for isospin, for naturality, J for total angular momentum, P for parity, and for orbital angular momentum. For baryons, = +, natural parity, if P =( 1) J 1/2 and =, unnatural parity, if P = ( 1) J 1/2 where P stands for parity. Resonances marked with are unreliable themselves due to systematics and lack of good-quality 2 /dof. Resonances marked with are most likely artifacts of the fits. Λ * This work KSU from [3] KA from [5] KB from [5] PDG [1] I J P M p p M p p M p p M p p Name Status 1 2 S ± ± (145) **** ± ± (167) **** (18) *** 1983 ± ± (2) * 243 ± ± P ± ± (16) *** 1685 ± ± (171) * 1835 ± 1 18 ± ± ± (181) *** P ± ± ± ± (189) **** D ± ± (152) **** ± ± (169) **** 251 ± ± (25) * 2133 ± ± 28 (2325) * 5 2 D ± ± (183) **** ± ± F ± ± (182) **** ± ± (211) *** + F ± ± (22) * G ± ± (21) ****

29 TABLE III. Summary of pole masses (M p =Re s p )andwidths( p = 2Im s p ) in MeV. Our poles are depicted in Fig. 5 unless they have a very large imaginary part. Notation is the same as in Table II. Resonances marked with are unreliable themselves due to systematics and lack of good-quality 2 /dof. Σ* This work KSU from [3] KA from [5] KB from [5] PDG [1] I J P M p p M p p M p p M p p Name Status S (162) * (175) *** 1813 ± ± (19) * ± ± (2) * P ± ± (156) ** (166) *** ± ± (177) * (188) ** P ± ± ± ± D (158) * ± 7. 26± (167) **** (194) *** D 1744 ± ± (1775) **** 1952 ± ± F ± ± (1915) **** ± ± (27) * 7 1 F ± ± (23) **** G 2177 ± ± (21) *