1. Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Institut für Theoretische Physik Technische Universität Wien Denis Parganlija In collaboration with: F. Brünner and A. Rebhan (Vienna) F. Giacosa (Kielce) [Based on F. Brünner, D. Parganlija and A. Rebhan, Phys. Rev. D 91 (2015) 10, 106002 (arXiv:1501.07906 [hep-ph]) and D. Parganlija and F. Giacosa, in preparation]

2. QCD Lagrangian: Gluon bound states: Glueballs! Emergence of glueballs is analogous to that of: Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Glueballs Strong Coupling is Energy-Dependent Gluons are self-interacting Baryons (Half-Integer Spin) Mesons Integer Spin

3. Theory: distinctive mass spectrum and decay patterns Experiment: - formation/production in gluon-rich processes → annihilation, radiative decays - suppression in γγ collisions How to Recognise Glueballs Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data

4. Glueball Mass Spectrum From the Yang- Mills sector of QCD No decays Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data [C. J. Morningstar and M. J. Peardon, Phys. Rev. D 60, 034509 (1999).]

5. Glueball Decays I Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data AdS/CFT correspondence: N=4 SU(∞) supersymmetric and conformal Yang-Mills theory in 4 dim. ↔ A string theory in a 5-dim. curved (anti-de-Sitter) space (xS^5) However: QCD is neither supersymmetric nor conformal Problem resolution: AdS7 x S^4 with a compactified dimension → unwanted symmetries broken Glueballs emerge from graviton modes → Witten Model Introduction of holographic quarks via D8- and anti-D8-branes → Witten-Sakai-Sugimoto (WSS) Model Strongly Coupled Weakly Coupled Low-energy limit: supersymmetric gravity

6. Glueball Decays II Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data [WSS massive: F. Brünner and A. Rebhan, Phys. Rev. Lett. 115 (2015) 131601 (arXiv: 1504.05815 [hep-ph])] [WSS chiral: F. Brünner, D. Parganlija and A. Rebhan, Phys. Rev. D 91 (2015) 10, 106002 (arXiv:1501.07906 [hep-ph])]

7. Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data But there is a problem.

8. Glueballs will mix with non-glueball states of same quantum numbers Example: Mixing of the scalar glueball with ground-state resonances leads to results preferring f 0 (1710) or f 0 (1500) as glueball The scalar glueball can also mix with excited scalars → study in Linear Sigma Model Glueball Mixing I Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data [Cheng, Chua, Fariborz, Giacosa, Lee, Liu, Weingarten…] [Amsler, Close, Kirk, Kitamura, Morisita, Teshima…]

9. Glueball Mixing II Linear Sigma Model: an effective approach to low-energy QCD encoding (1) symmetries (chiral, dilatational, …) (2) symmetry breaking (spontaneous, explicit) Here: three-flavour LSM containing (1) ground-state scalar, pseudoscalar, vector and axial-vector states (2) excited scalar and pseudoscalar states (3) scalar glueball Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data

10. Glueball Mixing II Preliminarily: Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Experimental data (mostly PDG) Linear Sigma Model 0 ++ glueball, lattice QCD [C. J. Morningstar and M. J. Peardon, Phys. Rev. D 60, 034509 (1999).] Excited 0 ++ glueball, WSS Model [F. Brünner, et al., Phys. Rev. D 91 (2015) 10, 106002 (arXiv:1501.07906 [hep-ph])]

11. Suggestions for Antiproton Experiments Look into ππ final states starting at ~ 1.65 GeV; this should be possible via formation if not production (lighter scalars well known from other data) Look into KK final states starting at ~ 1.65 GeV Look into 4π final states starting at ~ 1.65 GeV: glueball coupling may be strong Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data

12. Summary Glueballs predicted by QCD but still not unambiguously observed in the hadron spectrum Two main candidates for the scalar glueball: f 0 (1500) and f 0 (1710) but no generally accepted preference More data is needed to identify glueballs, particularly using antiproton beams

13. Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Thank you, and please find me at Poster 39

14. The Importance of Glueballs Mass of, e.g., nucleons is generated by 1. Higgs mechanism (subdominant) 2. Strong interaction (predominant) Glueball mass is at the leading order generated only by the strong interaction Glueballs must have integer spin → they are mesons Meson spectrum is incomplete without glueballs Glueballs couple to quarkonia in vacuum → (indirect) influence on chiral restoration Relevant for PANDA @ FAIR Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data

15. Spare Slides

16. Produced in : f 0 (980) f 0 (1370) f 0 (1500) Five states up to 1.8 GeV (isoscalars) [Crystal Barrel; GAMS] Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Motivation: Data on IJ PC = 00 ++ Mesons StateMass [MeV]Width [MeV] f 0 (500) 400 - 550400 - 700 f 0 (980)990 ± 2040 - 100 f 0 (1370)1200 - 1500200 - 500 f 0 (1500)1504 ± 6109 ± 7 f 0 (1710)139 ± 8 [Crystal Barrel; OBELIX] [Columbia-Syracuse; Crystal Barrel; OBELIX] Seen in radiative decays: f 0 (980) f 0 (1500) f 0 (1710) [CMD-2; KLOE] [MARK III/Crystal Barrel; BES] [Crystal Ball; MARK II; DM2; BES] Absent/suppressed in γγ: f 0 (1500) f 0 (1710) [L3; ALEPH] [ALEPH] [Belle: contrary statement] Can theory help?

17. Main production channels for low-energy mesons: Glueballs should be produced in produced in radiative decays absent from γγ collisions supernoumerous to a nonet What is the status in the scalar sector? Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Production of Mesons [Crystal Barrel; OBELIX] [Axial Field Spectrometer Collaboration; Ames-Bologna-CERN-Dortmund- Heidelberg-Warsaw Collaboration; GAMS; WA76; WA91; WA102; LHCb] [CMD-2; MARK-III; Crystal Ball; KLOE; BES; BES II; BES III; Belle; Belle-II] [CERN-Cracow-Munich Collaboration; CERN-Munich Collaboration; E791; WA76; GAMS] [U. Wiedner, Excited QCD Winter Workshop (Sarajevo, 2013)]

18. Two approaches to Low-Energy QCD Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data QCD First principles: Lattice scalars very broad, extrapolation problems Light-front wave functions holography input, no calculation of decays Bethe-Salpeter Equations have to be non-truncated Chiral Perturbation Theory Linear Sigma Model [Wilson; Dürr, Fodor, Gregory, Irving, Katz, Lang, Mohler, Morningstar, Peardon, Prelovsek, …] [Brodsky, Pauli, Pinsky, Teramond, …] [Eichmann, Fischer, Krassnigg, Nicmorus, Oset, Roberts, Williams, …] Effective theories and models: Based on 1. Chiral symmetry and/or 2. Constituent quarks Holographic QCD

19. Holographic QCD Dual (Type-IIA) string theory with infinitely many D4- branes (N c → ∞) Compactification of a dimension x 4 → x 4 + 2π/M KK on a thermal-like circle breaks supersymmetry Antisymmetric boundary conditions for adjoint fermions: masses ~ M KK No gauge symmetry to protect adjoint scalars: masses ~ M KK Effectively 5-dim. YM theory for scales below M KK ↔ conjectured to be dual to QCD Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data M KK : Kaluza-Klein mass

20. Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data However: 1. Scale matching was perfomed for the 2 ++ state → results differ for another choice of the scale-fixing observable 2. No decay widths were calculated

21. Sakai-Sugimoto Model A holographic framework first applied for systems with chiral quarks; can be used for studies of glueball dynamics as well Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data [Sakai and Sugimoto 2005]

22. Sakai-Sugimoto Model Calculations are performed using DBI (Dirac-Born-Infeld) action for D8 branes: Determining the scale and one free parameter: This implies e.g. Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data radial coordinate field strength for with the interpretations: (PDG: 2.5) (PDG data: 0.19) [T. Sakai and S. Sugimoto, Prog. Theor. Phys. 113, 843 (2005); 114, 1083 (2006)]

23. Glueballs in Sakai-Sugimoto Model Scale fixed by the rho mass Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data 1487 MeV, dilaton F. Brünner, D. Parganlija and A. Rebhan, Phys. Rev. D 91 (2015) 10, 106002 (arXiv:1501.07906 [hep-ph]

24. Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Scalar Ambiguities How many scalar states exist between 1.7 GeV and 1.8 GeV? [M. Ablikim et al. (BES II Collaboration), Phys. Lett. B 603, 138 (2004) and Phys. Lett. B 607, 243 (2005)] StateMass [MeV]Width [MeV] f 0 (500) 400 - 550400 - 700 f 0 (980)990 ± 2040 - 100 f 0 (1370)1200 - 1500200 - 500 f 0 (1500)1504 ± 6109 ± 7 f 0 (1710)139 ± 8

25. Assume that they are the same resonance Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Scalar Ambiguities [M. Ablikim et al. (BES II Collaboration), Phys. Lett. B 603, 138 (2004) and Phys. Lett. B 607, 243 (2005)] What is the structure of the additional resonance?

26. Scalars Pseudoscalars Resonances Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Vectors Axial-Vectors

27. Excited Scalars and Pseudoscalars Lagrangian Linear Sigma Model with Excited Scalar Sates Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data E E E E E E E E E E E E E E E E E E E E E E E E Very preliminary: m ~ 1.8 GeV for the excited scalar

28. Extended Linear Sigma Model Results with two flavours + glueball Results with three flavours + glueball Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data [S. Janowski, D. Parganlija, F. Giacosa and D. H. Rischke, PR D 84 (2011) 054007] [S. Janowski, F. Giacosa and D. H. Rischke, PR D 90 (2014) 114005] Most of the literature does not contain all degrees of freedom relevant for the (complicated) glueball dynamics Inclusion of new degrees of freedom can drastically change old conclusions

29. Non-Extrapolated Results Two-Pion Decay Four-Pion Decay Data: Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Quite narrow! [D. Parganlija, arXiv:1208.0204 BES Collaboration (2006), arXiv: hep-ex/0603048] [D. Parganlija, arXiv:1208.0204 WA102 Collaboration (1999), arXiv: hep-ex/9907055]

30. Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Tensor Glueball

31. Tensor Decays Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Heavy tensor glueball is quite broad: Γ total ~ 370 MeV Γ total ~ 820 MeV Note #1: there may be quarkonium admixtures Note #2: 4π the strongest channel for the tensor

32. How close is N c = 3 to N c = ∞? Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data [G. Bali et al. (2013)] [B. Lucini and M. Teper (2001)]

33. Denis Parganlija (Vienna UT) Scalar Glueball, Excited Scalar Mesons and Importance of Antiproton Data Scalar Ambiguities States up to 1.8 GeV (PDG) StateMass [MeV]Width [MeV] f 0 (500) 400 - 550400 - 700 f 0 (980)990 ± 2040 - 100 f 0 (1370)1200 - 1500200 - 500 f 0 (1500)1504 ± 6109 ± 7 f 0 (1710)139 ± 8 f 0 (1790) PANDA can confirm or disprove this!