Phenomenology, Theoretical interpretation Heavy Scalar octet. m s 1.45 GeV Glueballs spectra

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1 Outline 1 Scalar Mesons Phenomenology, Theoretical interpretation Heavy Scalar octet. m s 1.45 GeV Glueballs spectra Light Scalar octet. m s < 1 GeV 1 B MM, M = P, S, V, A, B PS, results B 3P Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, 21 1 / 15

2 Phenomenology, Theoretical interpretation Scalars. m S < 1.8 GeV 1 19 Scalar mesons (J PC = ++ ): κ = K (8), a (98), σ = f (5), f (98), K (143), a (145), f (137), f (15), f (171) 2 Seems two multiplets (m S < 1.8 GeV): HSM (m S 1.5 GeV) and LSM (m S.5 1 GeV) 3 Heavy quark decays (B PS, D P(S 2P), J/ψ X2π, ). τ-decays (τ ν τ 2P). Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, 21 2 / 15

3 Heavy Scalar octet. J PC = ++, n 2s+1 L J = 1 3 P m S 1.45 GeV. q q a K K + a f (15),f (137) K (143) K (143) a + (145) Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, 21 3 / 15

4 Heavy Scalar octet. J PC = ++, n 2s+1 L J = 1 3 P 1 Quark Model/Lattice: only one qq n 2s+1 L J = 1 3 P : HSM 2 m S 1.5 GeV (degenerate!, like P, V, ), Q = m R /Γ R 1. f.5 GeV. 3 Phenomenology/Lattice predictions (H. Cheng, Giacosa). f (15) f > oct. = 1 6 ( ūu > + ds > ) 2 3 ss > f (137) f > sing. = 1 3 ( ūu > + dd > + ss > ) f (17) G >= Scalar Glueball 4 Mixing angles: θ o singlet-glueball, θ 12 θ 23 2 o singlet-octet and octet-glueball. Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, 21 4 / 15

5 Glueballs spectra Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, 21 5 / 15

6 Light Scalar octet. J PC = ++, n 2s+1 L J = 1 1 S (?) m S < 1 GeV. qq q q (?) κ κ + (7) a f (98), σ κ κ (7) a + (98) Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, 21 6 / 15

7 Light Scalar octet. J PC = ++, n 2s+1 L J = 1 1 S (?) m S < 1 GeV. qq q q (?) 1 Other octet: m S = [.5 1] GeV. 1 Real world S >= a 4q > +b 2q > +c 2qg > +. 2 LSM: 4q, too wide (Q = m R /Γ R 1!) 3 σ Higgs of Chiral Symmetry. 2 Future information from Lattice, B PS, Charm decays. Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, 21 7 / 15

8 b-decays B MM, M = P, S, V, A, Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, 21 8 / 15

9 H eff. B MM, M = P, S, V, A, H eff = G F 2 [λ uq (C 1 O u 1 + C 2O u 2 ) λ tq ( 1 )] C i O i + C g O g + h. c. i=3 O1 u = ( qu) L(ūb) L O2 u == (ūu) L( qb) L O 3 = ( qb) L ( q q ) L O 4 = ( q b) L ( qq ) L q q O 5 = ( qb) L ( q q ) R O 6 = 2 ( q b) S P ( qq ) S+P q q O 7 = 3 2 ( qb) L e q ( q q ) R O 8 = 3 e q ( q b) S P ( qq ) S+P q q O 9 = 3 2 ( qb) L e q ( q q ) L O 1 = 3 2 q e q ( q b) L ( qq ) L q O g = O 11 = gsm b [ q σ 8π 2 µν t a G a µν b] R O γ = em b [ q σ 8π 2 µν F µν b] R = O 7 Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, 21 9 / 15

10 B PS B K π, K η A B π K λ us a 1 X B λ π ts K [ ( a 4 (a 6 a 8 /2)rχ )X K B π ] + 2λ ts a 6 m K m B fk F B π (mk 2 ) Γ(B Γ(B K π ) K π ) 2 r χ 2m 2 K /m b m s. λ q q = V q bv q q, λ ts =.42, λ us =.1 K X = < B π K X = < B π K ( sd) L >< π ( db) L B >= f K K ( sd) S+P >< π ( db) S P B >= r χ 2 X K (m 2 B m2 π)f B π (m 2 K B π Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, 21 1 / 15

11 B f K [ [ ] ( ) A B K S λ usa 1 X K B S λ ts a 4 + a 1 (a6 eff. + a 8 )rχ K X K B S ( 2a 6 a 8 3 ) ] 32 a 11 X S s + B K λ ts ( 2a 6 a a 11 2λ ts a 6 m K Γ(B K S ) Γ(B ) m B fk F B π K π ) m S m B f s S F B K (m 2 S ) (mk 2 ) f s S fk X S s B K = < S ss >< K sb B >= m S f s S m 2 B m2 K m b m s F B K (m 2 S ) Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, / 15

12 A B π a + λ ud a 1 X B π a + ( + [ ( λ td a 4 + a 1 (a 6 + a 8 )mπ 2 ˆm(m b + m u ) ) 2(a 3 a 5 ) + a 4 (a 6 a 8 /2)m 2 B m u (m b + m d ) ) X B π a + ] X B (a + π ) u Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, / 15

13 B PS Decay HFAG B exp. NFA QCDF PQCD π a + < π f (π + π ) < π a < K f (π + π ) 9(1) 17(3) , 34 K a < K f (π + π ) 11(2) 11(in) 13 22, 28 π a + (145) < K + a (145) < 3.1 < K f (137) < 1.7 K f (15) < π K + (K + π ) 5(9) 5(9) π + K (K + π ) 47(5) 47(5) 47 (in) ηk + 16(3) 16(3) 7 π K 26(1) 26(1) ηk 1(2) 1(2) 8 Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, / 15

14 B PS Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, / 15

15 Carlos Ramirez (Universidad Industrial de Santander) Scalar Mesons October 22, / 15

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