Scalar Mesons in Hadronic B Decays HaiYang Cheng

Scalar Mesons in Hadronic B Decays Hai-Yang Cheng (鄭海揚) Academia Sinica March 30, 2013 Cross Strait Meeting on Particle Physics and Cosmology in collaboration with Chun-Khiang Chua (蔡俊謙), Kwei-Chou Yang (楊桂周) & Zhi-Qing Zhang (張志清) 1

Scalar Mesons - Consider JP=0+ scalar mesons L=1 if they are made of qq Two nonets (nonet=octet+singlet) have been observed: n light nonet (< 1 Ge. V) I=0: (500), f 0(980), I=1/2: (800), I=1: a 0(980), n heavy nonet (> 1 Ge. V) I=0: f 0(1370), f 0(1500), f 0(1710), I=1/2: K*0(1430), I=1: a 0(1450) f 0(500) K 0*(800) f 0(980) a 0(980) mass (Me. V) 400 -550 682 29 990 20 980 20 width (Me. V) 400 -700 547 24 40 -100 50 -100 u or f 0(500) and or K 0*(800) are much broader than f 0 and a 0 u f 0 and a 0 are degenerate in mass 2

Suppose (500), f 0(980), (800) and a 0(980) form an SU(3) flavor nonet f 0 a 0 f 0 a 0 2 -quark model expt Intermediate serious problems: u How to explain the mass degeneracy of f 0(980) and a 0(980) ? u Why are and much broader than f 0 and a 0 ? , K , and a 0 q are OZI allowed, while f 0 is OZI suppressed m » a > f not borne out by experiment u How to explain a 0(980) ? s quark content in a 0(980) ? ss is an isospin singlet while a 0 is an isospin triplet 3

Four-quark picture Major difficulties with a 0 and f 0 can be circumvented in the fourquark model (Jaffe 1977) n n Mass degeneracy of f 0 and a 0 is natural ! , ! K & f 0, a 0! KK are OZI super-allowed (fall apart) , while f 0! & a 0! q are OZI allowed so that (4 -quark)>> (2 -quark) f 0(980) and a 0(980) are very close to KK threshold ) f 0(980) width is dominated by , a 0 governed by state. This explains why m » » À f » a 4

A unified picture: ♦ Scalar qq meson has a unit of orbital angular momentum ) a higher mass above 1 Ge. V f 0(1370), a 0(1450), K*0(1430) and f 0(1500)/f 0(1710) form a P-wave qq nonet with some possible mixing with glueballs, supported by lattice. ♦ Four-quark scalar meson can be lighter due to (i) absence of the orbital angular momentum barrier in S-wave 4 -quark state. (ii) a strong attraction between and ) a mass near or below 1 Ge. V -Light scalar mesons , , f 0(980), a 0(980), form an S-wave qqqq nonet The internal structure of scalars still remains controversial and not well established. Exotic light scalars have not been seen ⇒ diquark structure 5?

Mathur et al. (’ 07) Lattice 2 -quark nature for a 0(1450) & K 0*(1430) 4 -quark nature for f 0(500) & K 0*(800) Prelovsek et al. (’ 10) However, ETM (’ 12) reached an opposite conclusion for the quark content of light scalars Tetraquark mesons in large-N QCD by S. Weinberg ar. Xiv: 1303. 0342 6

B→ SP, SV Ba. Bar and Belle have measured B→ (f 0, a 0(980), a 0(1450), K 0*(1430))(P, V) l Is light scalar production suppressed in 4 -quark model ? l Can we test the quark structure of light and heavy scalar mesons ? We shall apply QCD factorization to B→SP (Beneke, Buchalla, Neubert, Sachrajda) vertex & penguin spectator int. annihilation Ironically, practical calculation can be done only in 2 -quark model for scalars Heavy meson decays can shed light on scalar structure 7

Historical remarks n QCD factorization Chua, Yang, HYC: B SP (’ 05) B SV (’ 07) Ying Li et al. (’ 12) n p. QCD Cai-Dian Lu et al. (’ 06, ’ 07) Zheng-Jun Xiao, Zhi-Qing Zhang (’ 10); Z. Q. Zhang (’ 10 -’ 12) n Naïve factorization n B S form factors sum rules: Aliev et al. , T. Huang et al. , Han et al. p. QCD: C. D. Lu et al. , Z. J. Xiao et al. 8

Decays constants Consider interpolating current dependent For neutral f 0, , a 00, f. S=0 due to C invariance finite-energy sum rule, or NLJ model ⇒ Du, Li, MZ Yang (QCD sum rule) ⇒ HYC, KC Yang (sum rule) ⇒ Typical scalar decay constant is above 300 Me. V ! 9

Light-cone distribution amplitudes (LCDAs) twist 2: twist 3; s, For neutral scalars , f 0, a 00, 10 dx S(x)=0 S(x)= - S(1 -x). For neutral scalars f 0, a 00, , B 0=0 and only odd C’s contribute. In general, B 0( )=[m 1( )-m 2( )]/m. S B is either zero or small of order 0 md-mu or ms-mu, contrary to pseudoscalar case where B 0=1. 10

For Bm, it can be evaluated using QCD sum rules ⇒ B 1=-0. 78 0. 08, B 3=0. 02 0. 07 a 0 at =1 Ge. V for a 0(980) , , …. 11

Two scenarios We consider two scenarios for treating a 0(1450) & K*0(1450) in sum rules: n scenario 1: , a 0(980), f 0(980) lowest lying qq states, K*0(1430), a 0(1450), f 0(1500) first excited states 2 -quark states for all scalars n scenario 2: K*0(1430), a 0(1450), f 0(1500) lowest lying qq states first excited states lie between 2. 0 2. 3 Ge. V 4 -quark states for light scalars & 2 -quark ones for others 12

B→ K 0*(1430)( , ’) QCDF p. QCD Expt (10 -6) B- K 0*- 17. 9+12. 8 -13. 8 33. 8+17. 6 -13. 5 15. 8 3. 1 B- K 0*- ’ 9. 3+60. 0 -9. 8 77. 5+32. 5 -26. 1 5. 2 2. 1 B 0 K 0 * 16. 1+12. 3 -13. 1 28. 4+14. 9 -11. 6 9. 6 1. 9 B 0 K 0* ’ 8. 7+49. 0 -9. 1 74. 2+31. 3 -25. 3 6. 3 1. 6 In B PP decays, Br(B K ’) Br(B K ). It is other way around when K is replaced by K 0*(1430)

B→ K 0*(1430)( , , ) QCDF p. QCD Expt (10 -6) B- K 0 * - 39. 0+64. 9 -71. 6 B- K 0*- 0 14. 8+7. 7 -3. 3 8. 4+4. 1 -3. 2 B 0 K 0*- + 36. 3+18. 7 -7. 4 10. 5+4. 0 -2. 6 28. 0 11. 6 B 0 K 0 * 0 21. 5+10. 6 -4. 6 4. 8+1. 5 -1. 0 27. 0 5. 4 B- K 0*- 21. 5+11. 4 -6. 0 7. 4+3. 7 -2. 7 24. 0 5. 1 B 0 K 0 * 21. 9+12. 0 -6. 0 9. 3+4. 3 -3. 7 27. 0 5. 4 B- K 0*- 3. 8+11. 2 -1. 7 17. 3+52. 8 -13. 1 7. 0 1. 6 B 0 K 0 * 3. 7+5. 6 -0. 6 16. 9+52. 2 -13. 0 3. 9 0. 8 12. 1+4. 8 -3. 1 QCDF is in good agreement with experiment 14

B→ K 0*(1430) QCDF p. QCD B - K 0 * - 12. 9+39. 0 -10. 4 30. 9+12. 5 -9. 2 B - K 0 * 0 7. 4+20. 4 -5. 6 21. 6+8. 5 -6. 6 B 0 K 0*- + 13. 8+38. 8 -10. 7 B 0 K 0 * 0 5. 6+19. 1 -4. 3 Ba. Bar Belle 32. 0+10. 8 -6. 0 51. 6+7. 2 -7. 7 31. 6+12. 4 -9. 3 27. 8 4. 1 49. 7+7. 8 -9. 0 10. 7+4. 1 -3. 2 7. 0 1. 2 n Some discrepancy between Ba. Bar & Belle n Weak annihilation contributions are large enough to account for the discrepancy between theory & experiment. However, this will destroy the agreement between theory & expt for B K 0*( , ’, , , ) n Isospin relations: (K*-0 +)= (K*00 -), (K*00 0)= (K*00 -)/2 The latter is violated. 15

B a 0(980)P QCDF p. QCD Expt B- a 00 K - 0. 34+1. 10 -0. 16 3. 5 1. 2 <3. 0 B- a 0 - K 0 0. 08+2. 20 -0. 11 6. 9+2. 4 -2. 1 <4. 6 B 0 a 0+ K - 0. 34+2. 35 -0. 05 9. 7+3. 3 -2. 8 <2. 2 B 0 a 00 K 0 0. 05+0. 90 -0. 02 4. 7+1. 4 -1. 5 <9. 2 B- a 0 0 - 4. 9 0. 6 2. 8+0 -1. 3 <6. 9 B- a 0 0 0. 70+0. 31 -0. 22 0. 41+0 -0. 23 <1. 7 B 0 a 0 + - 5. 3+1. 7 -1. 3 0. 86 0. 17 B 0 a 0 - + 0. 58+0. 64 -0. 25 0. 51 0. 12 B 0 a 0 4. 7+2. 3 -1. 37 0. 21 B 0 a 0 0 0 1. 0+0. 5 -0. 3 0. 51+0. 12 -0. 11 - n n <3. 7 Production of a 0(980) in B decays has not been seen p. QCD predicts too large Br(B a 0 K) compared to experiment + QCDF a 0+ - a 0 K-, it is other around in p. QCD a 0 - + should be highly suppressed relative to a 0+ - 16

B→ a 0(980) _ n B 0 a 0 - + is highly suppressed relative to a 0+ - (not true in p. QCD) a 0 + self -tagging -6 consistent with expt’l limit 3. 7 10 (Belle) ! If expt’l Br ~ 1 10 -6, it may indicate a 4 -quark nature for a 0(980) No extra diagrams for 4 -quark a 0(980) production 17

Scenario 1 is ruled out a 0(1450) is a lowest-lying 2 -quark state If a 0(1450)+ - & a 0(980)+ - are seen at the level of 1 10 -6 ⇒ low lying 2 -quark content for a 0(1450) and 4 -quark structure for a 0(980) production has been seen in D decays e. g. D 0→K 0 a 00, K-a 0+ in D 0→K+K-K 0 Br(B 0 a 0+(980)½-) is predicted to be 23£ 10 -6 by QCDF. A measurement of this mode may give first observation of a 0(980) production in B decays 18

B f 0(980)K In 2 -quark model, f 0(980) is not a pure ss state due to (i) (J/ →f 0 )/ (J/ →f 0 ) 0. 4, (ii) similar widths of f 0 & a 0 so that f 0 is not OZI suppressed relative to a 0 a mixing between f 0 and |f 0(980) =cos |ss +sin |nn with nn=(uu+dd)/ 2 Fig. (a) is suppressed due to cancellation between a 4 & a 6 penguin terms and small non-strange quark content in f 0(980) B f 0 K rate is sensitive to the scalar decay constant of f 0, recalling that 19

o Large rates of f 0(980)K & f 0(980)K* can be fitted with 20 without power corrections from penguin corrections to central values LHCb (’ 13) measured Br(B 0 J/ f 0(980))Br(f 0(980) + -) | |<30 o 20

n Does the agreement between theory & experiment imply a 2 -quark nature for f 0(980) ? n Is B f 0 K further suppressed if f 0(980) is a bound state of four quarks ? additional diagrams ⇒ (nonfactorizable) The relevant diagrams are double but they involve nonfactorizable diagrams not so amenable. Form factor is also beyond conventional QM f 0 K rate is not necessarily suppressed in 4 -quark scenario for f 0(980) 21

Conclusions u Except for B K 0*(1430)¼, B SP & B SV can be accommodated in QCDF without introducing 1/mb power corrections from penguin annihilation to central values u Scenario 1 is ruled out for a 0(1450) & K 0*(1430) they are lowest lying qq states light scalars are most likely 4 -quark states 22