Light Flavoured Scalar Resonances: Current Status and Perspectives

1. Departamento de Física Teórica II. Universidad Complutense de Madrid Present status of Light Flavoured ScalarResonances J. R. Peláez 7th Intl. Workshopon Chiral Dynamics CD12 . Thomas Jefferson NationalAcceleratorFacility. August 9th 2012

2. Outline 1) ScalarMesons: motivation &perspective 2) Theσor f0(500) I willfocusonprogress sincelast CD2009 orafter 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 ( situationca. 2002) 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. Stilloutof PDG “summarytables” Narrowerf0(980), a0(980) scalarswellestablishedbutnotwellunderstood. Even more states: f0(1370), f0(1500), f0(1700)

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? Whylesserrole 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 VeryconvincingforPDG, 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 uncertaintiesca. 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?? Evenexperimental 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 ChPT90’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-likeequations. 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. SomerelevantDISPERSIVE POLE Determinations (after2009, 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. Theconsistencyof dispersiveapproaches, and alsowith previousresultsimplementing UNITARITY, ANALTICITYand 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, Togetherwiththelatestresultsfromheavy 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, butquite 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… I have no words…

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

24. 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) ConfirmationfromRoy Eqs. B. Moussallam, Eur. Phys. J. C71, 1814 (2011)

25. Somerelevantrecent DISPERSIVE POLE Determinations of the f0(980) (after CD2009, 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

26. Thus, PDG12 madea smallcorrectionforthe f0(980) mass & more conservativeuncertainties

27. 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)

28. Commentsontheminoradditionstothe K(800) @PDG12 Still“omitttedfromthesummarytable”since, “needsconfirmation” But, allsensible implementations of unitarity, chiral symmetry, describingthe data finda pole between 650 and 770 MeVwith a 550 MeVwidthorlarger. As forthesigma, and themostsoundeddetermination comes froma Roy-Steinerdispersiveformalism, consistentwithUChPTDecotesGenon et al 2006 Since 2009 twoEXPERiMENTALresults are quotedfrom D decays @ BES2 Surprisingly BES2 gives a pole position of But AGAIN!! PDG goesongivingBreit-Wignerparameters!! More confusion!! Fortunately, thePDG massand widthaverages are dominatedbythe Roy-Steinerresult

29. 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

30. SPARE SLIDES

31. Scalar SU(3) multipletsidentification controversial Toomanyresonancesformanyyears…. Butthereisanemergingpicture + Another heavier scalar nonet: A Light scalar nonet: (800) K(1400) Non-strangeheavier!! Invertedhierarchyproblem For quark-antiquark f0(600) and f0(980) are really octet/singlet mixtures  f0(980) f0 a0 Singlet f0singlet a0(980) a0(1475) f0 The light scalarcontroversy. Thetheoryside... classification + glueball f0 Enoughf0stateshavebeenobserved: f0(1370), f0(1500), f0(1700). Thewholepictureiscomplicatedby mixture betweenthem (lots of workshere)

32. The light scalarcontroversy. Thetheoryside... NON-ORDINARY nature Tetraquarks(Jaffe ’77) .Solvestheinvertedhierarchyproblem (issueswith chiral symmerty and excess of states), PROBLEM WITH SEMILOCAL DUALITY  Modified quark-antiquark modelswithmesoninteractions Van Beveren, Rupp Molecules(Achasov, Jülich-Bonn, Oller-Oset) are also NON-ORDINARY,… Mayalsohaveproblemwithsemi-local duality Somepeopleclaim/claimedsome of these did/do notexist , liketheκ(800) the f0(1370), etc… (Pennington, Minkowski, Ochs, Narison… σ as glueball supporters in general) By ORDINARY we mean quark-antiquark, butthere are otherpossibilities

33. Final Result: Analyticcontinuationtothecomplexplane f0(980) f0(600) Roy Eqs. Pole: Residue: GKPY Eqs. pole: Residue: Wealsoobtaintheρ pole:

34. Onthe use of BW and otherstuff • Thus, ifyouinsist in usingwhateveryouwanttofityour data…. • REFRAINfrommakingPhysicalor POLE interpretationsunlessyou are sureyourparametrizationsmakesense in thecomplexplane (analyticity), are unitary, etc… • Itmightbeusefultomakeitpublic and availableforothersbecauseyouwanttoparametrizethe data somehow so thatanybody can use it, compare toit, etc… Fine… but.

35. A precise  scatteringanalysiscan helpdeterminingthe • and f0(980) parametersand isusefulforForm • Factorscontainingseveral 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.

36. Structure of calculation: Example Roy and GKPY Eqs. Both are coupledchannelequationsfortheinfinitepartialwaves: I=isospin 0,1,2 , l =angular momentum0,1,2,3…. DRIVING TERMS (truncation) Higher waves and High energy SUBTRACTION TERMS (polynomials) KERNEL TERMS known Partial wave on real axis ROY: 2nd order More energy suppressed Very small GKPY: 1st order Less energy suppressed small Similar Procedure forFDRs “OUT” “IN (from our data parametrizations)” =?

37. 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

38. 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

39. Lesson to learn: Despite using Very reasonable parametrizations with lots of nice properties, yielding nice looking fits to data… They are at odds with FIRST PRINCIPLES crossing, causality (analyticity)… And of course, toextrapolatetothecomplexplane ANLYTICITY isessential

40. DIP vs NO DIP inelasticity scenarios GKPY S0 waved2 Now we find large differences in CFD UFD 850MeV< e <1050MeV 992MeV< e <1100MeV Dip 1.02 No dip 3.49 Other waves worse and data on phase NOT described Dip 6.15 No dip 23.68 Improvement possible? No dip (enlarged errors) 1.66 But becomes the “Dip” solution No dip (forced) 2.06

41. Comparisonwithotherresults:The f0(600) orσ

42. Comparisonwithotherresults:The f0(600) orσ OnlysecondRiemann sheetreachable withthisapproach

43. Summary “Dipscenario” forinelasticityfavored Simple and easy to use parametrizations fitted to  scattering DATA CONSTRAINED by FDR’s+ Roy Eqs+ 3 GKPY Eqs GKPY Eqs. pole: Residue: σand f0(980) polesobtainedfromDISPERSIVE INTEGRALS MODEL INDEPENDENT DETERMINATION FROM DATA (and NO ChPT).

44. UFD

45. WhenfittingalsoZakharov data

46. 1973 1987 1972 1979 ’95 model by one of the authors of PDG review Most confusion due to using MODELS (with questionable analytic properties)