SCALAR MESONS IN QCD Stephan Narison CNRS - Montpellier HEPMAD07, Antananarivo (10-15th September 2007) – p. 1/5
Light Hadrons Spectroscopy ♣ Light Quarks: u,d,s : m q ≤ Λ QCD ≈ 350 MeV ; Q u = 2 / 3; Q d = Q s = − 1 / 3 HEPMAD07, Antananarivo (10-15th September 2007) – p. 2/5
Light Hadrons Spectroscopy ♣ Light Quarks: u,d,s : m q ≤ Λ QCD ≈ 350 MeV ; Q u = 2 / 3; Q d = Q s = − 1 / 3 ♦ Light Baryons proton= uud; neutron= udd,... HEPMAD07, Antananarivo (10-15th September 2007) – p. 2/5
Light Hadrons Spectroscopy ♣ Light Quarks: u,d,s : m q ≤ Λ QCD ≈ 350 MeV ; Q u = 2 / 3; Q d = Q s = − 1 / 3 ♦ Light Baryons proton= uud; neutron= udd,... ♥ Light Ordinary Mesons ud : J PC = 0 − + ; ρ − ≡ ¯ ud : J PC = 1 −− ; π − ≡ ¯ ud : J PC = 1 ++ A 1 ≡ ¯ Well understood in QCD : associated resp. to the pseudoscalar, vector and axial-vector currents. HEPMAD07, Antananarivo (10-15th September 2007) – p. 2/5
Scalar Mesons ➳ Long standing puzzle too wide ( σ ) or • Difficult to identify experimentally : near the ¯ KK threshold ( a 0 ) . HEPMAD07, Antananarivo (10-15th September 2007) – p. 3/5
Scalar Mesons ➳ Long standing puzzle too wide ( σ ) or • Difficult to identify experimentally : near the ¯ KK threshold ( a 0 ) . • Can be produced from: φ , J / ψ , ϒ , B and D - decays γγ , ππ and π N scatterings HEPMAD07, Antananarivo (10-15th September 2007) – p. 3/5
Scalar Mesons ➳ Long standing puzzle too wide ( σ ) or • Difficult to identify experimentally : near the ¯ KK threshold ( a 0 ) . • Can be produced from: φ , J / ψ , ϒ , B and D - decays γγ , ππ and π N scatterings • Different interpretations - ordinary ¯ qq - four-quark states - gluon bound states for the I=0 HEPMAD07, Antananarivo (10-15th September 2007) – p. 3/5
qq and gluonium interpretations ¯ ➳ I=1 scalar : a 0 ( 980 ) , κ ( 800 ) • Can be explained as ¯ qq states : associated to the divergence of the QCD vector current : ψ i ( i ) ¯ ψ j J S = ( m i − m j ) ¯ HEPMAD07, Antananarivo (10-15th September 2007) – p. 4/5
qq and gluonium interpretations ¯ ➳ I=1 scalar : a 0 ( 980 ) , κ ( 800 ) • Can be explained as ¯ qq states : associated to the divergence of the QCD vector current : ψ i ( i ) ¯ ψ j J S = ( m i − m j ) ¯ ➳ I=0 scalar : σ ( 800 ) , f 0 ( 980 ) • Can be explained as 1/2 ¯ qq and 1/2 gluonium states : associated to Trace of the QCD energy-momentum tensor current : Θ µ µ = ∑ m j ¯ ψ j ¯ ψ j +( 1 / 4 ) β ( α s ) G 2 . HEPMAD07, Antananarivo (10-15th September 2007) – p. 4/5
Using QCD Spectral Sum Rules HEPMAD07, Antananarivo (10-15th September 2007) – p. 5/5
Using QCD Spectral Sum Rules Introduced by Shifman-Vainshtein-Zakharov HEPMAD07, Antananarivo (10-15th September 2007) – p. 5/5
Using QCD Spectral Sum Rules Introduced by Shifman-Vainshtein-Zakharov Improved dispersion relation : duality between measured and QCD observables HEPMAD07, Antananarivo (10-15th September 2007) – p. 5/5
Using QCD Spectral Sum Rules Introduced by Shifman-Vainshtein-Zakharov Improved dispersion relation : duality between measured and QCD observables SN-Veneziano 88, Bramon-SN 89 HEPMAD07, Antananarivo (10-15th September 2007) – p. 5/5
Using QCD Spectral Sum Rules Introduced by Shifman-Vainshtein-Zakharov Improved dispersion relation : duality between measured and QCD observables SN-Veneziano 88, Bramon-SN 89 SN 84, 96, 2005 HEPMAD07, Antananarivo (10-15th September 2007) – p. 5/5
Using QCD Spectral Sum Rules Introduced by Shifman-Vainshtein-Zakharov Improved dispersion relation : duality between measured and QCD observables SN-Veneziano 88, Bramon-SN 89 SN 84, 96, 2005 Dosch-SN 2000 HEPMAD07, Antananarivo (10-15th September 2007) – p. 5/5
Using QCD Spectral Sum Rules Introduced by Shifman-Vainshtein-Zakharov Improved dispersion relation : duality between measured and QCD observables SN-Veneziano 88, Bramon-SN 89 SN 84, 96, 2005 Dosch-SN 2000 Minkowski-Mennessier-SN-Ochs 2007 HEPMAD07, Antananarivo (10-15th September 2007) – p. 5/5
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