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Non-ordinary nature of light scalar mesons from Dispersion and Effective Theory: The σ/f0(500) and κ/K0*(700) case

This report discusses the non-ordinary nature of light scalar mesons, focusing on the σ/f0(500) and κ/K0*(700) cases. It explores their features, identification controversies, and the improvement brought by analyticity and effective Lagrangians.

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Non-ordinary nature of light scalar mesons from Dispersion and Effective Theory: The σ/f0(500) and κ/K0*(700) case

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  1. Phys.Rept. 658 (2016) 1 Departamento de Física Teórica and Institute of Particle & Cosmos Physics (IPARCOS) Universidad Complutense de Madrid Non-ordinary nature of light scalar mesons from Dispersion and Effective Theory: The σ/f0(500) and κ/K0*(700) case J. R. Peláez Workshop on Exotic Hadrons, Theory and Experiment at Lepton and Hadron Colliders: T.D. Lee Institute, Jiao Tong Shanghai University, June 25-27, 2019

  2. Features of ordinary mesons With only 3 light quarks, grouped in SU(3) nonets Ordinary qqMasshierarchy: Theseheavierbecause ms>>mu~md - MK*=892 MeV Mρ=770 MeV Mω=782 MeV - Mφ=1020 MeV~ss Not for light scalars! MK*=892 MeV Follow linear (J,M2) Regge trajectories Ordinary LO 1/Nc Behavior from QCD: Ordinary Linear (J,M2) trajectories with universal slope ~ 0.8-1 GeV-2 (Alsoforbaryons) Rigidrotatingrod, Stringypicture Color flux tube… CONFINEMENT J Note no scalars there Quark–antiquark quantum numbers: OK for scalar mesons. Call them non-ordinary or Criptoexotics

  3. A Light scalar nonet: /K0*(700) Non-strangeheavier!! Invertedhierarchyproblem For quark-antiquark σ/f0(500) and f0(980) are really OCTET/SINGLET mixtures  f0 a0 f0 Singlet a0(980) f0 Theextraordinaryspectroscopy of light scalars Scalar SU(3) multipletsidentification controversial Toomanyresonancesformanyyears. Butthereisanemergingpicture… 2) QM is NOT QCD 1) Mixture? 60 years of Controversy but recent relevant changes in the Review of Particle Physics: σ/f0(500) 2012 change in name and 5xreduction in uncertainties /K0*(700) 2018 change in name, 2019 makes it to the booklet. Still “needs confirmation”

  4. The real improvement: Analyticityand EffectiveLagrangians Roy/Roy-Steiner like equations.70’s Roy, Basdevant, Pennington, Petersen, 00’s Ananthanarayan, Caprini, Colangelo, Gasser, Leutwyler, Moussallam, DecotesGenon, Lesniak, Kaminski, García-Martín, JRP, Ruiz de Elvira, Yndurain, Buttiker, Moussallam, Descotes-Genon, Rodas “Unphysical” cuts implementedwithprecision. For ππ→ππ, πK→πK and ππ→KK Either as solutions or as constrains on fits.With or without ChPT. With one or more subtractions. Rigorous and precise continuation to complex plane. Difficult to relate to QCD parameters Preliminary!! K0*(800) or“kappa” becomes K0*(700) in PDG 2018 In 2019 still “Needs confirmation” Becomes f0(500) or “sigma” in PDG 2012 M=400-550 MeV Γ=400-700 MeV The f0(600) or “sigma” in PDG 1996-2010 M=400-1200 MeV Γ=500-1000 MeV

  5. Unitarized ChPT. The InverseAmplitudeMethod. General Idea Writedispersionrelation forinverse of t. PHYSICAL cut Known EXACTLY From UNITARITY Numerically dominant or resonances Calculated with ChPT To the order you want Far from poles. Approximated with ChPT Not so good for precision SubtractionConstants Approximate with Chiral Perturbation Theory To the order you want We can connect with QCD parameters 90’s Truong, Dobado, Herrero, JRP Chiral Perturbation Theory is the Low-Energy Effective Theory of QCD Extended to resonance region by unitarization Combination of Chiral Perturbation Theory and Dispersion Theory - Unitarity for elastic scattering Relation to QCD parameters Nc and mq easy through ChPT parameters Fit to data!

  6. Truong ‘89, Truong,Dobado,Herrero,’90, Dobado JRP,‘93,‘96 Unitarized ChPT: TheInverseAmplitudeMethod Mass Width/2 ρ /f0(500) K*(890) (770) Simultaneously: ANALYTICITY Unitarity+Chiralexpansion when fitting data  00 GeneratesPoles of Resonances: σ/f0(500), ρ(770), /K0(800), K*(892), Similar results with coupled channels Oller, Oset, JRP, Gómez-Nicola + f0(980),a0(980) =f0(600) From 1/Nc dependence of ChPT parameters  11 UChPTpredicts 1/Nc behavior of resonance poles ρ(770)

  7. The 1/Ncexpansion and Unitarized ChPT qqbarstates: The(770): Our benchmark MN/M3 MN/M3 N/3 N/3 Nc MNc/Mphys As expected for q-qbar -iΓ/2 ΓNc/Γphys Nc We can identify quark-antiquark-likeNcbehavior Whataboutscalars?

  8. Results O(p6): the sigma Near Nc = 3 DOES NOT BEHAVE AS qqbar M becomes constant ~ 1GeV Γstartsdecreasing G. Ríos and JRP, Phys.Rev.Lett.97:242002,2006 But for Nc~ 10 tor 12 Hint of mixing with a HEAVIER qqbar component? Dominant non-qqbarcomponent near Nc=3 ROBUST Hints of possible MIXING with heavier qqbar subcomponents Dominant behavior also found in other UChPT variants (Uehara,Zheng,Oller, Nieves, Pich...) Subdominant qq component around 1 GeV also suggested in, ChQM, SD-eqs, sum-rules.... Relevant for fixing “semi-localduality” problem in non-qq mesons

  9. The 1/Ncexpansion and Unitarized ChPT. The strange resonances TheK*(892): The benchmark The/K0*(700)(=500MeV) - i /2 - i /2 MN/M3 N/3 MN/M3 N/3 As expected for q-qbar MN/M3 N/3 At odds with q-qbar Nc

  10. Another non-ordinary feature: Non-ordinary Regge trajectories J.T. Londergan, J. Nebreda, JRP, A. Szczepaniak,Phys.Lett. B729 (2014) 9-14 J.A.. Carrasco J. Nebreda, JRP, A.Szczepaniak, Phys.Lett. B749 (2015) 399 JRP, A. Rodas, EJPC 77(2017),431

  11. Extraordinary scalars: Regge Theory and Chew-Frautschi Plots All hadrons are classified in almost linear (J,M2) trajectories Indicative of confining force ALL OF THEM? Not quite Actually DIFFERENT INTERACTIONS MAY GIVE RISE TO DIFFERENT REGGE TRAJECTORIES Anisovich-Anisovich-Sarantsev-PhysRevD.62.051502 2004

  12. Dispersive parametrization of Regge pole dominated amplitudes We solve these eqs. Imposing the value of an observed pole in the second sheet LET US CHECK THE METHOD WORKS We want to CALCULATE (Not fit) the TRAJECTORIES OF RESONANCES For elastic resonances that dominate a channel, and their trajectory and residue should satisfy a system of integral equations:

  13. Results: ρ case (I = 1, J = 1) We get a prediction for the ρRegge trajectory, which is almost real Almost LINEAR α(s) ~α0+α’ s intercept α0= 0.520±0.002 slope α’ = 0.902±0.004 GeV-2 Previousstudiesfrom FITS: [1] α0= 0.5 [2] α0= 0.52 ± 0.02 [3]α0= 0.450 ± 0.005 [1] A. V. Anisovich et al., Phys. Rev. D 62, 051502 (2000) [2] J. R. Pelaez and F. J. Yndurain, Phys. Rev. D 69, 114001 (2004) [3] J. Beringer et al. (PDG), Phys. Rev. D86, 010001 (2012) [4] P. Masjuan et al., Phys. Rev. D 85, 094006 (2012) [1] α’= 0.83 GeV-2 [2] α’= 0.9 GeV-2 [4] α’= 0.87 ± 0.06 GeV-2 This is a “prediction” for the whole tower of ρ(770) Regge partners: ρ(1690) ρ(2350) …. the LINEAR behavior is a RESULT Remarkably consistent with the literature!!, (taking into account our approximations)

  14. Themethodidentifiesmanyotherordinarystates besides theρ(770): The f2(1275),f’2(1525), K*(892), K0*(1430) J.A.. Carrasco J. Nebreda, JRP, A.Szczepaniak, Phys.Lett. B749 (2015) 399 JRP, A. Rodas, EJPC 77(2017),431 Whatabout the f0(500), K0*(700)?

  15. We CALCULATE the f0(500) trajectory • Londergan, Nebreda,JRP, Szczepaniak PLB 729 (2014) 99 Fromtheirpolesonly, using a dispersiveformalism Theρ(770) trajectory comes outalmost-real and linear, consistentwithordinarytrajectories The f0(500) trajectoryisnoteven real and muchsmaller (anotherscale at play) No evidentReggepartnersforthe f0(500), explainingwhyitisnot in linear fits and disfavors a predominant quarkonium nature

  16. Ifnot-ordinary… Whatthen? Can weidentifythedynamics of theσ and κtrajectories? Not quiteyet… but…

  17. Plotingthetrajectories in thecomplex J plane… Striking similarity with Yukawa potentials at low energy: V(r)=−Ga exp(−r/a)/r Our result is mimicked with a=0.5 GeV-1 to compare with S-wave ππscatteringlength 1.6 GeV-1 “a” rather small !!! Ordinaryρtrajectory Non-ordinaryσtrajectory The extrapolation of our trajectory also follows a Yukawa but deviates at very high energy

  18. For the kappa we find a very similar behavior: JRP, A. Rodas, EJPC 77(2017),431 Compared to: V(r)=−Ga exp(−r/a)/r Similar order of magnitude for range aππ=0.5 GeV-1 aπK=0.33 GeV-1 aππ/ aπK ~1.52 Maybe aMM scales as inverse of reduced mass µπK /µππ=1.57

  19. Several approachessupporting a non-ordinarynature of thelightestscalars - Tetraquarkmodels Jaffe, Fariborz, Schechter, Sannino, Giacosa, Riquer, Polosa, t’Hooft, Maiani, Isidori,… - Extended orunitarized LSM. Schechter, Fariborz,Black,Sannino, Giacosa, Scadron,… - Unitarized Quark Models: Pole doubling, Relatively similar pole trajectories Van Baveren, Rupp, Bugg… -Sum rules Nielsen, Navarra, Lee, Hosaka, Jido, Oka… - Lattice Alford, Jaffe, Kunihiroet al., Mathur et al. Dudek, Edwards, Thomas, Wilson.,Bali et al., - SchwingerDyson /BetherSalpeter from quarks and gluons: Roberts, Fisher, Eichmann, Williams - UnitarizedChiralPerturbationTheory/ChiralUnitaryApproachand theNcbehavior JRP, Oller, Oset, Nieves, Ruiz Arriola, Pich … - Non-ordinary Regge behavior Nebreda, JRP, Szczepaniak, Carrasco, Rodas… For a FANTASTIC sigma review… From controversy to precision on the sigma meson: a review on the status of the non-ordinary f0(500) resonance. J.R.P. Phys.Rept.658 (2016).

  20. Summary Part 1: Existence and parameters After 60 years of controversy, a low-mass and very wide σ/f0(500) has been well-established (even @PDG) with relatively precise parameters Good data and MODEL-INDEPENDENT DISPERSIVE methods were essential to establish its parameters The κ/K0*(700) now in similar situation as the σ/f0(500) in 2010. Additional preliminary DISPERSIVE DETERMINATION confirms its parameters. Expect more changes @PDG soon. Part 2: Nature and classification From ChPT: light scalars do NOT followordinarybehavior. Theσmayhave a subdominantqqcomponentwith M1 GeV Quark massdependencepredicted. Dispersive CALCULATION of Regge trajectories: Ordinary linear trajectories for ρ, K*, f2, f2’ and K0*(1430). Buttheσ/f0(500) andκ/K0*(700) do not fit into ordinary Regge trajectories. Both similar behavior. Scales typical of meson physics

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