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Departamento de Física Teórica II. Universidad Complutense de Madrid

Departamento de Física Teórica II. Universidad Complutense de Madrid. Review of light scalars. J. R. Peláez. Light Meson Dynamics – Institüt für Kernphysik Mainz – 11-02-2014. Outline. No need for motivation at this workshop. 1) The σ or f0(500).

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Departamento de Física Teórica II. Universidad Complutense de Madrid

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  1. Departamento de Física Teórica II. Universidad Complutense de Madrid Review of light scalars J. R. Peláez Light Meson Dynamics – InstitütfürKernphysikMainz – 11-02-2014

  2. Outline No needformotivation at thisworkshop 1) Theσor f0(500) I willfocusonprogresssince PDG2010 Followingtwopoints of view: 2) The f0(980) 3) Theκor K(800)and a0(980) i) PDG Consensual, conservative 4) Summary ii) My own Probablyclosertothedominant view in thecommunity workingon light scalars 5) Nature and classification. Reggetrajectory of the f0(500)

  3. 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. Firstproposedtoexplain NN attraction, but NN insensitivetodetails. Needothersources Definitelynot a Breit-Wigner 2010 NA48/2 data

  4. 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 ?

  5. PDG uncertaintiesfrom 1996 until 2010 Clear room for Improvement

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

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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

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

  14. Somerelevant DISPERSIVE POLE Determinations (after 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)

  15. 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)

  16. 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

  17. 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).

  18. 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.

  19. 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

  20. 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

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

  22. Unfortunately, the PDG stillquotes “Breit-Wignerparameters”, withconsequenceslikethis I knowthere are verysmartpeople at the PDG tryingtofight this BW nonsense

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

  24. “sigma” Summary 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

  25. Outline 1) Theσor f0(500) 2) The f0(980)

  26. 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)

  27. Somerelevantrecent DISPERSIVE POLE Determinations of the f0(980) (after QCHS-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

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

  29. Outline 1) Theσor f0(500) 2) The f0(980) 3) Theκor K(800)and a0(980) No changesonthe a0 mass and width at the PDG forthe a0(980)

  30. 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

  31. 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 Butwiththeaddition of new memberstothe PDG I expect a more“cleaning up” in the PDG forotherscalarresonancessoon

  32. Outline 1) ScalarMesons: motivation & perspective 2) Theσor f0(500) 3) The f0(980) 4) Theκor K(800)and a0(980) 5) Nature and classification. • Reggetrajectory of the f0(500) • In collaborationwithJ.Nebreda, A. Szczepaniak and T. Londergan • Phys. Lett. B 729 (2014) 9–14

  33. ReggeTheory and Chew-FrautschiPlots Anotherfeature of QCD as a confiningtheory isthathadrons are classified in almost linear (J,M2) trajectories Roughly, this can beexplainedby a quark-antiquark pairconfined at theends of a string-like/flux-tubeconfiguration. Thetrajectories can alsobeunderstood fromtheanalyticextensiontothecomplex angular momentumplane (ReggeTheory) However, light scalars, and particularlythe f0(500) do notfit in. Anisovich-Anisovich-Sarantsev-PhysRevD.62.051502 4

  34. Reggetrajectoryfrom a single pole Londergan, Nebreda, JRP, Szczepaniak , In progress Anelasticpartial wave amplitudenear a Regge pole reads Whereαisthe “trajectory” and βthe “residue” Iftheamplitudeisdominatedbythe pole, unitarity implies: Imposingthethresholdbehavior q2l and otherconstraints fromtheanalyticextensiontothecomplexplane, This leads to a set of dispersionrelationsconstrainingthetrajectory and residue Thescalar case reqires a smallmodificationtoincludethe Adler zero

  35. Reggetrajectoryfrom a single pole Londergan, Nebreda, JRP, Szczepaniak , In progress Whenweiterativelysolvethepreviousequations fittingonlythe pole and residue of theρ(770) obtainedfromthemodelindependent GKPY approach… Werecover a fairrepresentation of theamplitude Butwealsoobtain a “prediction” fortheRegge rho trajectory, whichis: 1) Almost real 2) Almost linear: α(s) ~α0+α’ s THIS IS A RESULT, NOT INPUT 3) Theinterceptα0= 0.52 4) Theslopeα’ = 0.913 GeV-2 Remarkablyconsistentwiththeliterature, takingintoaccountourapproximations

  36. Reggetrajectoryfrom a single pole Londergan, Nebreda, JRP, Szczepaniak , In progress Sincetheapproachworksremarkablywellforthe rho, werepeat itforthe f0(500). Wefitthe pole obtainedfrom GKPY to a single pole-Reggelikeamplitude Againwerecover a fairrepresentation of theamplitude, evenbetterthanforthe rho And weobtain a “prediction” fortheRegge sigma trajectory, whichis: 1) NOT real 2) NOT evidently linear 3) Intercept 4) Slope Twoorders of magnitudeflatterthanotherhadrons The sigma does NOT fitthe usual classification

  37. Results: σ vs. ρtrajectories Usingthesamescale…. No evident Reggepartners forthe f0(500)

  38. Ifnot-ordinary… Whatthen? Can weidentifythedynamics of thetrajectory? Not quiteyet… but…

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

  40. Summary • Analytic constraints on Reggetrajectories as integral equations • Fitting JUST the pole position and residue of an isolated resonance, • yields its Regge trajectory parameters • ρ trajectory: COMES OUT LINEAR, with universal parameters • σ trajectory: NON-LINEAR. • Trajectory slope two orders of magnitude smaller • No partners. • If we force the σ trajectory to have universal slope, data description ruined • At low energies, striking similarities with trajectories of Yukawa potential

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