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Review of Light Scalars: From Confusion to Precision

This review focuses on the progress made in understanding light scalars, specifically the σ or f0(500), f0(980), κ or K(800), and a0(980) mesons. The motivation, experimental data, and theoretical models are discussed to improve our understanding of these particles. The use of analyticity and effective Lagrangians in combination with Chiral Perturbation Theory are also explored.

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Review of Light Scalars: From Confusion to Precision

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  1. Departamento de Física Teórica II. Universidad Complutense de Madrid Review of light scalars: fromconfusiontoprecision J. R. Peláez 10th International Conferenceon Quark Confinement and the Hadron Spectrum QCHSX TU Munich. October 8th 2012

  2. Outline 1) ScalarMesons: motivation & perspective 2) Theσor f0(500) I willfocusonprogresssince QCHS2010, namelyafter PDG2010 Followingtwopoints of view: 3) The f0(980) 4) Theκor K(800)and a0(980) i) PDG Consensual, conservative 5) Summary ii) My own Probablyclosertothedominant view in thecommunity workingon light scalars

  3. I=0, J=0  exchangeveryimportantfornucleon-nucleonattraction!! Crude Sketch of NN potential: From C.N. Booth Motivation: Thef0(600)orσ, half a centuryaround Scalar-isoscalar fieldalreadyproposedby Johnson & Teller in 1955 Sooninterpretedwithin “Linear sigma model” (Gell-Mann) or Nambu JonaLasinio - likemodels, in the 60’s.

  4. Thelongstandingcontroversy Theσ, controversial sincethe 60’s. “notwellestablished” 0+ state in PDG until 1974 Removed from 1976 until 1994. Back in PDG in 1996, renamed “f0(600)” Thereason: TheσisEXTREMELY WIDE and has no “BW-resonancepeak”. Usuallyquotedbyitspole: The “kappa”: similar situationtotheσ, butwithstrangeness. Stillout of PDG “summarytables” Narrowerf0(980), a0(980) scalarswellestablishedbutnotwellunderstood. Even more states: f0(1370), f0(1500), f0(1700), notforthisreview

  5. Motivation: The role of scalars The f0’s havethevacuum quantum numbers. Relevantforspontaneous chiral symmetrybreaking. Glueballs: Featureof non-abelian QCD nature Thelightestoneexpectedwiththese quantum numbers Non ordinarymesons? Tetraquarks, molecules, mixing… SU(3) classification. Howmanymultiplets? Invertedhierarchy? Whylesser role in thesaturation of ChPT parameters? First of allitisrelevanttosettletheirexistence, mass and width

  6. Outline 1) ScalarMesons: motivation & perspective 2) Theσor f0(500)

  7. Theσuntil 2010: the data   1) FromN scattering  Initialstatenotwelldefined, modeldependentoff-shellextrapolations (OPE, absorption, A2exchange...) Phaseshiftambiguities, etc...  N N Systematicerrors of 10o !! Example:CERN-Munich 5 different analysis of same pn data !! Grayeret al. NPB (1974) 2) FromKe (“Kl4 decays”) Geneva-Saclay(77), E865 (01) Pions on-shell. Very precise, but00-11. Unfortunately….NN insensitivetodetails… needothersources Definitelynot a Breit-Wigner 2010 NA48/2 data

  8. Theσuntil 2010: the data 3) Decaysfromheaviermesons Fermilab E791, Focus, Belle, KLOE, BES,… “Production” from J/Ψ, B- and D- mesons, and Φradiativedecays. VerygoodstatisticsClear initialstates and differentsystematicuncertainties. Strong experimental claimsforwide and light  around 500 MeV “Strong” experimental claimsforwide and light  around 800 MeV Veryconvincingfor PDG, but personal caveatsonparametrizationsused, whichmayaffecttheprecision and meaning of the pole parameters PDG2002: “σwellestablished” However, since1996 until 2010 stillquoted as Mass= 400-1200 MeV Width= 600-1000 MeV ?

  9. PDG uncertaintiesfrom 1996 until 2010 Clear room for Improvement

  10. Part of theproblem: Thetheory Manyoldan new studiesbasedoncrude/simple models, Strongmodeldependences Suspicion: Whatyouput in iswhatyougetout??

  11. Example: Polesfrom sameexperiment!! PDG uncertaintiesca. 2010

  12. Part of theproblem: Thetheory Manyoldan new studiesbasedoncrude/simple models, Strongmodeldependences Suspicion: Whatyouput in iswhatyougetout?? Even experimental analysisusing WRONG theoreticaltoolscontributetoconfusion (Breit-Wigners, isobars, K matrix, ….) Lesson: Forpolesdeep in thecomplexplane, thecorrectanalyticproperties are essential Analyticityconstraints more powerful in scattering Dispersiveformalisms are themost precise and reliable AND MODEL INDEPENDENT

  13. The 60’s and early 70’s: Strongconstraintson amplitudes fromANALYTICITY in theform ofdispersionrelations Butpoor input onsomeparts of theintegrals and poorknowledge/understanding of subtractionconstants = amplitudes at lowenergyvalues The 80’s and early 90’s: Development of Chiral PerturbationTheory (ChPT). (Weinberg, Gasser, Leutwyler) Itistheeffectivelowenergytheory of QCD. Providesinformation/understandingonlowenergy amplitudes The 90’s and early 2000’s: Combination of Analyticity and ChPT (Truong, Dobado, Herrero, Donoghe, JRP, Gasser, Leutwyler, Bijnens, Colangelo, Caprini, Zheng, Zhou, Pennington...) The real improvement: Analyticity and Effective Lagrangians

  14. Analyticity and Effective Lagrangians: twoapproaches Unitarized ChPT(Truong, Dobado, Herrero, JRP, Oset, Oller, Ruiz Arriola, Nieves, Meissner, …) Use ChPT amplitudes insideleftcut and subtractionconstants of dispersionrelation. Relatively simple, althoughdifferentlevels of rigour. Generatesallscalars Crossing (leftcut) approximated… so, notgoodforprecision

  15. Why so muchworriesabout “theleftcut”? Itiswrongtothink in terms of analyticity in terms of Leftcutdueto Crossedchannels ρ σ Sincethepartial wave isanalytic ins…. Forthe sigma, theleftcut relativelyclose and relevant ρ σ

  16. Analyticity and Effective Lagrangians: twoapproaches Unitarized ChPT 90’s Truong, Dobado, Herrero, JRP, Oset, Oller, Ruiz Arriola, Nieves, Meissner,… Use ChPT amplitudes insideleftcut and subtractionconstants of dispersionrelation. Relatively simple, althoughdifferentlevels of rigour. Generatesallscalars Crossing (leftcut) approximated… , notgoodforprecision Roy-like and GKPY equations. 70’s Roy, Basdevant, Pennington, Petersen… 00’s Ananthanarayan, Caprini, Colangelo, Gasser, Leutwyler, Moussallam, DecotesGenon, Lesniak, Kaminski, JRP… Leftcutimplementedwithprecision . Use data onallwaves + highenergy . Optional: ChPT predictionsforsubtractionconstants Themost precise and modelindependent pole determinations f0(600) and κ(800) existence, mass and width firmlyestablishedwithprecision Forlong, wellknown forthe “scalarcommunity” Yettobeacknowledgedby PDG…. By 2006 very precise Roy Eq.+ChPT pole determinationCaprini,Gaser, Leutwyler

  17. PDG uncertaintiesca. 2010 Data after2000, bothscatteringand production Dispersive- modelindependentapproaches Chiral symmetrycorrect Yettobeacknowledgedby PDG….

  18. Somerelevant DISPERSIVE POLE Determinations (afterQCHS-2010, also “according” to PDG) GKPY equations = Roy likewithonesubtraction García Martín, Kaminski, JRP, YndurainPRD83,074004 (2011) R. Garcia-Martin , R. Kaminski, JRP, J. Ruiz de Elvira, PRL107, 072001(2011). Includeslatest NA48/2 constrained data fit .Onesubtractionallows use of data only NO ChPT input butgoodagreementwithprevious Roy Eqs.+ChPTresults. Roy equationsB. Moussallam, Eur. Phys. J. C71, 1814 (2011). An S0 Wave determination up to KK thresholdwith input fromprevious Roy Eq. works Analytic K-Matrixmodel G. Mennesier et al, PLB696, 40 (2010)

  19. Theconsistency of dispersiveapproaches, and alsowith previousresultsimplementing UNITARITY, ANALTICITY and chiral symmetryconstraintsbymanyotherpeople … (Ananthanarayan, Caprini, Bugg, Anisovich, Zhou, IshidaSurotsev, Hannah, JRP, Kaminski, Oller, Oset, Dobado, Tornqvist, Schechter, Fariborz, Saninno, Zoou, Zheng, etc….) Has ledthe PDG toneglectthoseworksnotfullfillingtheseconstraints alsorestrictingthesampletothoseconsistentwith NA48/2, Togetherwiththelatestresultsfrom heavy mesondecays Finallyquoting in the 2012 PDG edition… M=400-550 MeV Γ=400-700 MeV More than 5 times reduction in themassuncertainty and 40% reductiononthewidthuncertainty Accordingly THE NAME of theresonanceischangedto… f0(500)

  20. DRAMMATIC AND LONG AWAITED CHANGE ON “sigma” RESONANCE @ PDG!! The f0(600) or “sigma” in PDG 1996-2010 M=400-1200 MeV Γ=500-1000 MeV Becomes f0(500) or “sigma” in PDG 2012 M=400-550 MeV Γ=400-700 MeV To my view… stilltoo conservative, but quite animprovement

  21. Actually, in PDG 2012: “Note on scalars” And, at therisk of beingannoying…. Now I findsomewhatboldtoaveragethoseresults, particularlytheuncertainties 8. G. Colangelo, J. Gasser, and H. Leutwyler, NPB603, 125 (2001). 9. I. Caprini, G. Colangelo, and H. Leutwyler, PRL 96, 132001 (2006). 10. R. Garcia-Martin , R. Kaminski, JRP, J. Ruiz de Elvira, PRL107, 072001(2011). 11. B. Moussallam, Eur. Phys. J. C71, 1814 (2011).

  22. Unfortunately, tokeeptheconfusion the PDG stillquotes a “Breit-Wignermass” and width… No comments…

  23. A precise  scatteringanalysishelpsdeterminingthe • and f0(980) parametersand isusefulforany hadronic processcontainingseveral pions in the final state A dispersiveapproachtoπ π scattering: Motivation Thedispersiveapproachismodelindependent. Justanalyticity and crossingproperties Determine theamplitude at a givenenergyeveniftherewere no data precisely at thatenergy. Relate different processes Increase the precision The actual parametrization of the data isirrelevantonce insideintegrals.

  24. S0 wave below 850 MeV R. Garcia Martin, JR.Pelaez and F.J. Ynduráin PRD74:014001,2006 Conformal expansion, 4 terms are enough. First, Adler zero at m2/2 Average of N->N data sets withenlargederrors, at 870- 970 MeV, wherethey are consistentwithin 10oto 15o error. We use data on Kl4 includingthe NEWEST: NA48/2 results Getrid of K → 2 Isospin correctionsfrom GassertoNA48/2 ItdoesNOT HAVE A BREIT-WIGNER SHAPE Tinyuncertainties dueto NA48/2 data

  25. UNCERTAINTIES IN Standard ROY EQS. vs GKPY Eqs Why are GKPY Eqs. relevant? One subtraction yields better accuracy in √s > 400 MeV region Roy Eqs. GKPY Eqs, smaller uncertainty below ~ 400 MeV smaller uncertainty above ~400 MeV

  26. S0 wave: from UFD to CFD Onlysizablechange in f0(980) region

  27. Outline 1) ScalarMesons: motivation & perspective 2) Theσor f0(500) 3) The f0(980)

  28. DIP vs NO DIP inelasticityscenarios Longstandingcontroversybetweeninelasticity data sets : (Pennington, Bugg, Zou, Achasov….) Some of them prefer a “dip” structure… ... whereasothers do not GKPY Eqs. disfavorsthe non-dipsolutionGarcía Martín, Kaminski, JRP, YndurainPRD83,074004 (2011) Garcia-Martin , Kaminski, JRP, Ruiz de Elvira, PRL107, 072001(2011) Confirmationfrom Roy Eqs. B. Moussallam, Eur. Phys. J. C71, 1814 (2011)

  29. Somerelevantrecent DISPERSIVE POLE Determinations of the f0(980) (afterQCHS-2010, also “according” to PDG) GKPY equations = Roy likewithonesubtraction García Martín, Kaminski, JRP, YndurainPRD83,074004 (2011) Garcia-Martin , Kaminski, JRP, Ruiz de Elvira, PRL107, 072001(2011) Roy equationsB. Moussallam, Eur. Phys. J. C71, 1814 (2011). Thedipsolutionfavorssomewhathighermassesslightlyabove KK threshold and reconcileswidthsfromproduction and scattering

  30. Thus, PDG12 made a smallcorrectionforthe f0(980) mass & more conservativeuncertainties

  31. Outline 1) ScalarMesons: motivation & perspective 2) Theσor f0(500) 3) The f0(980) 4) Theκor K(800)and a0(980) No changesonthe a0 mass and width at the PDG forthe a0(980)

  32. Commentsontheminoradditionstothe K(800) @PDG12 Still “omitttedfromthesummarytable” since, “needsconfirmation” But, all sensible implementations of unitarity, chiral symmetry, describingthe data find a pole between 650 and 770 MeVwith a 550 MeVwidthorlarger. As forthe sigma, and themostsoundeddetermination comes from a Roy-Steinerdispersiveformalism, consistentwithUChPTDecotesGenon et al 2006 Since 2009 twoEXPERiMENTALresults are quotedfrom D decays @ BES2 Surprisingly BES2 gives a pole position of But AGAIN!! PDG goesongivingtheirBreit-Wignerparameters!! More confusion!! Fortunately, the PDG mass and widthaverages are dominatedbythe Roy-Steinerresult

  33. Summary For quite some time nowthe use of analyticity, unitarity, chiral symmetry, etc… to describe scattering and production data has allowedtoestablishtheexistence of light theσ and κ Thesestudies, togetherwith more reliable and precise data, haveallowedfor PRECISE determinations of light scalar pole parameters The PDG 2012 edition has FINALLY acknowledgedtheconsistency of theory and experiment and therigour and precision of thelatestresults, fixing, to a largeextent, theveryunsatisfactorycompilation of σresults Unfortunately, sometraditionalbutinadequateparametrizations, longagodiscardedbythespecialists, are stillbeingused in the PDG fortheσ and theκ I expect a more“cleaning up” in the PDG forotherscalarresonancessoon

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