Mesons beyond the quark-antiquark picture: glueballs, hybrids, tetraquarks - part 1 - Francesco Giacosa

Transcription

1 Mesons beyond the quark-antiquark picture: glueballs, hybrids, tetraquarks - part 1-55 Cracow School of Theoretical Physics 20 28/6/2015, Zakopane, Poland

2 Outline The Lagrangian of QCD and its symmetries What is a meson? Conventional mesons and nonconventional mesons Experiments Panoramic of candidates of non-connventional mesons Summary

3 The Lagrangian of QCD and its symmetries Born Died Giuseppe Lodovico Lagrangia 25 January 1736 Turin 10 April 1813 (aged 77) Paris

4 The QCD Lagrangian Quark: u,d,s and c,b,t R,G,B q q q q i G = = i i i R B ; i u,d,s,... 8 type of gluons (RG,BG, ) A a ; a = 1,..., µ 8

5 Feynman diagrams of QCD Quark Quark Gluon Gluon Gluon-quark-antiquark vertex 3-gluon vertex 4-gluon vertex

6 Trace anomaly: the emergence of a dimension Chiral limit: m i = 0 is a classical symmetry broken by quantum fluctuations (trace anomaly) Dimensional transmutation Λ Y M M e V α ( µ = Q) = S 2 g (Q) 4π * Effective gluon mass: m gluon = 0 mgluon MeV Gluon condensate: a a, µν GµνG 0

7 Flavor symmetry q i q i Gluon-quark-antiquark vertex. It is democratic! The gluon couples to each flavor with the same strength q U i ij q j + U U (3) U U = 1 V

8 Chiral symmetry q i, R q i, R q i, L q i, L q = q + q i i, R i, L 1 5 q = (1 + γ ) q i, R i q = (1 γ ) q i, L i 2 R L q = q + q U q + U q i i,r i,l ij j,r ij j,l U ( 3) SU (3) R U (3) = U (1) U (1) L R + L R L R SU (3) L In the chiral limit (mi=0) chiral symmetry is exact

9 Spontaneous breaking of chiral symmetry U ( 3) SU (3) SU (3) R U (3) L = U (1) R + L U (1) R L R L SSB : SU(3) SU(3) SU(3) R L V= R+ L Chiral symmetry Flavor symmetry q i q i = q i, Rq + q, i, Lq i L i, R 0 * m mu md 5 MeV m 300 MeV m m ρ meson proton 2m 3m * *

10 Symmetries of QCD: summary SU(3)color: exact. Confinement: you never see color, but only white states. Dilatation invariance: holds only at a classical level and in the chiral limit. Broken by quantum fluctuations (trace anomaly) and by small quark masses SU(3)RxSU(3)L: holds in the chiral limit, but is broken by nonzero quark masses. Moreover, it is spontaneously broken to U(3)V=R+L U(1)A=R-L: holds at a classical level, but is also broken by quantum fluctuations (chiral anomaly)

11 What is a meson?

12 Hadrons No colored state has been seen. Confinement: physical states are white and are called hadrons. Hadrons can be: Mesons: bosonic hadrons Baryons: fermionic hadrons

13 Definition of mesons: WIkipedia???

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18 Meson Definition(s): 1) A meson is a strongly interacting particle with integer spin. 2) A meson is a strongly interacting particle with zero baryon number. A meson is not necessarily a quark-antiquark state

19 Conventional mesons Quark: u,d,s, R,G,B Quark-antiquark bound states: conventional mesons color = 1 / 3 ( R R + B B + GG )

20 Conventional mesons/2 Surely, with quark-antiquark states we can understand a lot of QCD, but definitely not everything. r L, r S P = ( 1 ) L C = ( 1 ) L + S r L, r S r J = r L + r S J PC

21 Exotic quantum numbers Not all quantum numbers are permitted for a quark-antiquark states. PC J = 0, 1, 2,... are exotic quantum numbers. Short ex: show it is so! P = ( 1 ) C = ( 1 ) r r r J = L + S L L + S

22 PC + L = S = 0 J =0 pseudoscalar mesons + π = u d space : L = 0 spin : S = 0 R R + BB + GG π = du space : L = 0 spin : S = 0 RR + BB + GG 0 π = = = + + uu dd space : L 0 spin : S 0 RR BB GG Flavor symmetry: the 3 pions have the same mass. + K = u s sp ace : L = 0 spin : S = 0 R R + BB + G G... 0 D u c sp ace : L 0 spin : S 0 R R BB G G... = = = + +

23 PC L = 0, S = 1 J =1 vector mesons + ρ = u d space : L = 0 spin : S = 1 R R + BB + G G... * + K (892) u s sp ace : L 0 spin : S 1 R R BB G G... = = = + + *0 D = u c space : L = 0 spin : S = 1 R R + BB + G G... j / Ψ = cc space : L = 0 spin : S = 1 R R + BB + G G

24 PC ++ L = S = 1 J =0 scalar mesons σ = u u + d d sp ace : L = 1 sp in : S = 1 R R + BB + G G corresp onds to the resonan ce f (1 370) χ (1S) = cc space : L = 1 spin : S = 1 R R + BB + G G c 0

25 PDG quark-antiquark listing/1

26 PDG quark-antiquark listing/2

27 Chiral models: the basic idea

28 Spontaneous symmetry breaking at the meson level 0 π = π 1 2(uu dd) neutral pion σ 1 2(uu + dd) f 0(1370) Chiral transformation: σ π V 2 m 0 λ = σ + π + σ + π 2 4 ( 2 2 ) ( 2 2 ) 2 m < 0 Mexican hat 2 0 SSB: σ uu + dd 0

29 The donkey of Buridan Jean Buridan (in Latin, Johannes Buridanus) (ca after 1358) Picture taken from A. Pich, arxiv: [hep-ph], Cern-Claf Lecture on The Standard model of electroweak interactions

30 Hadronic Experiments

31 Hadronic experiments Proton-proton (WA79,WA102,LHC) Electron-positron (Belle, Babar,BES,KLOE, ) J/ψ c c G

32 Photoproduction: Compass at Cern GlueX AND CLAS12 AT Jlab (start soon)

33 Proton-antiproton (Lear,Fermilab, and in the future: Panda)

34 The PANDA experiment

35 Formation process: the energy range in PANDA p + p X then X decays in something else (pions,kaons, ) Antiproton moves, proton at rest r 2 E = q + m p 2 p m = 2 m ( m + E ) X p p p Short ex: show that it is so! r U s i n g q = G e V : m = G e V X

36 Theoretical expectations

37 Non-conventional mesons: theoretical expectations 1) Glueballs 2) Hybrids Compact diquark-antidiquar states 3) Four-quark states Molecular states (a type of dynamical generation) Companion poles (another type of dynamical generation)

38 Glueball spectrum from quenched lattice QCD The missing pieces of the mesonic spectrum: the glueballs. Where are they?

39 Hybrid mesons: lattice predictions for 1^-+ hybrids at about 2 GeV See for instance the review: C. Meyer and E. Swanson, Hybrid Mesons,'' Prog.\ Part.\ Nucl.\ Phys.\ {\bf 82} (2015) 21 [arxiv: [hep-ph]]. (Many) tetraquark states are predicted in various models. Actually even too many See for instance: D. Ebert et al, Excited heavy tetraquarks with hidden charm, Eur. Phys. J. C 58 (2008) 399 [arxiv: [hep-ph]].

40 Non-quarkonium candidates: light sector

41 The light scalar mesons a 0 (980) k (800 ) f (980) f (500) 0 0 PC J = They (most probably!) are not quark-antiquark states!!!

42 The light scalars can be interpeted as tetraquark state A tetraquark is the bound state of two diquarks An example of good diquark is: qq = Space: L = 0 Spin : ( f : ( ud du) c : ( RB BR) + Example: a (980 ) = 0 -[d,s][u,s] (and not ud )

43 J PC ++ = 0 M < 1 GeV Tetraquark interpretation I = 1 a (980) 0 [ u, s][ d, s], [ u, s][ d, s], ([ u, s][ u, s] [ d, s][ d, s]) 1 I = k (800 ) 2 [ u, [ u, d d ][ d, s], ][ u, s], [ u, d ][ d, s], [ u, d ][ u, s] I = 0 0 f (500) f (980) 0 [ u, d][ u, d] ([ u, s][ u, s] + [ d, s][ d, s])

44 J PC ++ = 0 M < 1 GeV Molecular interpretation I = 1 a (980) 0 KK bound-state 1 I = k (800 ) 2 I = 0 0 f (500) f (980) 0 πk bound-state ππ bound-state KK bound-state

45 Scalars above 1 GeV and scalar glueball candidate f0(1370) is compatible with a quark-antiquark substructure. Yet, a large glueball component is expected in f0(1500) and/or in f0(1710). Latest studies actually point toward f0(1710) as being predominantly gluonic.

46 Pseudoscalar glueball: candidates Up to now we do not know where it is. A light pseudoscalar glueball was not found yet. Here also the candidates are not so easily found. η(1405) and η(1475) (but much lighter than the lattice value of 2.6 GeV) X(2370) (BES)

47 Tensor glueball: candidate Here it is fog The resonance fj(2220) could be a candidate, if J=2 will be confirmed.

48 Two states with exotic quantum number J PC + = 1 Π1(1400) Π1(1600) What are they? They cannot be quark-antiquark states, but they could be hybrid (but mass too low w.r.t. lattice) or they could be four-quark states

49 Pseudoscalar glueball Up to now we do not know where it is. A light pseudoscalar glueball was not found yet. Here also the candidates are not so easily found. η(1405) and η(1475) (but much lighter than the lattice value of 2.6 GeV) X(2370) (BES)

50 Non-quarkonium candidates: charmonium sector

51 X,Y states

52 Z states From M. Kavatsyuk for BES, eqcd 2015

53 X(3872) X(3872) PC MX = ± 0.2 MeV, Γ =1.3 ± 0.6 MeV, J = 1 ++ Various works (see Brambilla et al, EPJ C (2011) 71): tetraquark or molecular states the most probable intepretations. (Mass too light when compared to quark-antiquark predictions) Possibilities: tetraquark? a D-D* molecular state? It could arise due to mesonic loops as a companion pole. The starting seed state is a regular charm-anticharm object. Loops do the rest.

54 Other unclarified states: open-charm sector

55 D*S0(2317) D*S0(2317): too light to be a P + J = 0, Mass = ± 0.6 MeV cs, cs quarkonium. It is a good candidate to be a molecular state / dynamically generated state In arxiv: we find that the quarkonium state of 2.47 GeV and a very large width. Loop effects and companion pole?

56 Summary Confinement: hadrons Mesons: not only quark-antiquark states. Glueballs: the still missing link. They are yet to be found. States beyond quark-antiquark: light scalar mesons amd related topics. Region of charm-anticharm states: experimental proof of non-quarkonium states, but different models exist.

57 Thank You

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