Investigating different tetraquark structures for X(3872)

Transcription

1 Investigating different tetraquark structures for X(387) QCD 10 15th International QCD conference 8/06-03/07/10 M. Nielsen Universidade de São Paulo S. Narison, F.S. Navarra

2 X(387) KEK (PRL91(003)) very narrow state observed in the decay: B ± K ± (J/ψπ + π ) confirmed by CDF, D0, BaBar Belle ± 0.60 ± 0.50 MeV/c + BaBar (B ) ± 0.60 ± 0.10 MeV/c 0 BaBar (B ) ± 1.0 ± 0.0 MeV/c D ± 3.10 ± 3.00 MeV/c CDF old ± 0.70 ± 0.40 MeV/c CDF new (preliminary) ± 0.16 ± 0.19 MeV/c old average ± 0.39 MeV/c new average ± 0. MeV/c o o m(d )+m(d *) ± 0.36 MeV/c X(387) Mass Measurements MX = (387.0 ± 0.39) MeV Γ <.3 MeV X(387) γj/ψ C =+ not seen in e + e X(387) J P 1 angular distribution favors J PC = X(387) Mass ( MeV/c ) c c spec. for J PC = P 1 (3990) (Barnes & Godfrey, PRD69 (004)) 3 3 P 1 (490)

3 X J/ψπ + π π 0 X J/ψπ + π 1 strong isospin and G parity violation M(D 0 D 0 ) = (3871 ± 1) X(387): molecular (D 0 D 0 + D 0 D 0 ) state (Swanson, Close, Voloshin, Wong...) Maiani et al. (PRD71 (05)) tetraquark J PC =1 ++ states ±

4 + 0 J/ψπ π π X X J/ψπ + π strongisospin isospin G 1 strong andand G parit parity violation 0 not 0 be easily explained as a cc state X(387) can 0 0 D ) = (3871 ± 1) M (D M (D D ) = (3871 ± 1) Tetraquark state? 0 D 0 + D 0 D 0 ) state X(387): molecular state (Swanson, Close, Voloshin, Wong...) X(387) : molecular (D (Close Page PLB57(004)) 387) : molecular (D D + D D ) and state (Close and Page PLB57(0 + or 1++ Tornqwist (ZPC61(94)) predict a D D molecule with J P CP= 0 C = 1++ states: Maiani et al. (PRD71 (05)) tetraquark J P C + nqwist (ZPC61(94)) predict a D D molecule with J =0 Xq = [cq]s=1 [c q ]S=0 + [cq]s=0 [c q ]S=1 or 1 molecular and tetraquark interpretations differ by the way quarks are organized in the state PRL97, 1600 (06) Mbelle = 3875.±0.7±0.8 PRD77,rate (08) production for a pure molecule should be two orders of magnitude Mbabar = ±1.1±0.5 smaller than exp. (Bignamini et. al., higher masses than X J/ψππ PRL103(09)16001) p.5/35 Xu +Xd

5 QCD Sum Rule Fundamental Assumption: Principle of Duality Π(q) =i d 4 xe iq.x 0 T [j(x)j (0)] 0 Theoretical side Phenomenological side

6 QCD Sum Rule Fundamental Assumption: Principle of Duality Π(q) =i d 4 xe iq.x 0 T [j(x)j (0)] 0 Theoretical side Phenomenological side Theoretical side Π(q) =i d 4 xe iq x 0 T [j(x)j (0) 0 = n C n (Q )Ôn Phenomenological side Π(q )= ds ρ(s) q s + iɛ +

7 ρ(s) =λ δ(s m )+ρ cont (s) 0 j H = λ. ρ cont (s) =ρ OP E (s)θ(s s 0 ) s 0 : continuum parameter Π phen (Q ) Π OP E (Q ) inverse Laplace (Borel) transform λ e m /M = s0 s min ds e s/m ρ OP E (s)

8 ρ(s) =λ δ(s m )+ρ cont (s) 0 j H = λ. ρ cont (s) =ρ OP E (s)θ(s s 0 ) s 0 : continuum parameter Π phen (Q ) Π OP E (Q ) inverse Laplace (Borel) transform λ e m /M = s0 s min ds e s/m ρ OP E (s) Good Sum Rule Borel window such that: pole contribution > continuum contribution good OPE convergence good Borel stability

9 m = s0 ds e s/m s ρ OP E (s) s min s0 ds e s s/m ρ OP E (s) min QCD sum rules calculation for X(387) Matheus, Narison, MN, Richard: PRD75 (07) [ j µ = iɛ abcɛ dec [(q T a Cγ 5 c b )( q d γ µ C c T e ) + (q T a Cγ µ c b )( q d γ 5 C c T e )]

10 m = s0 ds e s/m s ρ OP E (s) s min s0 ds e s s/m ρ OP E (s) min QCD sum rules calculation for X(387) Matheus, Narison, MN, Richard: PRD75 (07) [ j µ = iɛ abcɛ dec [(q T a Cγ 5 c b )( q d γ µ C c T e ) + (q T a Cγ µ c b )( q d γ 5 C c T e )] Condensate/RHS s 0 1/ = 4.17 GeV Pert + m q + <qq> + <g G > + m q <qq> + m 0 <qq> + <qq> + m 0 <qq> Contribution/(Pole+Continuum) (%) s 0 1/ = 4. GeV Continuum Pole M (GeV ) M (GeV )

11 M X (GeV) s 0 1/ = 4.1 GeV s 0 1/ = 4. GeV M (GeV ) can construct a current based on diquarks in the triplet configuration, with symmetric spin distrib [cq] S=1 [ c q] S=0 +[cq] S=0 [ c q] S=1, as proposed in ref. Therefore, the corresponding lowest-dimension int lating operator for describing X q as a tetraquark st given by: j (q,di) m X = (3.9 [(qa T Cγ ± 5c 0.13) b )( q d γ µ GeV C c T e ) µ = iɛ abcɛ dec +(q T a Cγ µ c b )( q d γ 5 C c T e )], where q denotes a u or d quark. On the other hand, we can construct a current de ing X q as a molecular D D state: molecular current (MN, j µ (q,mol) Navarra, (x) = Lee, 1 [ arxiv: ) ( q a (x)γ 5 c a (x) c b (x)γ µ q b (x)) j µ (q,mol) (x) = 1 [ ] ( q a (x)γ 5 c a (x) c b (x)γ µ q b (x)) ( q a (x)γ µ c a (x) c b (x)γ 5 q b (x)) In general, other four-quark operators with 1 + possible. For example, starting from the simple cha diquark states given in Table II, another tetraquar rent with J PC =1 ++ can be constructed by comb similar result for the mass

12 double-ratio sum rules: r mol/3 = M mol M 3

13 double-ratio sum rules: r mol/3 = M mol M r mol/ s 0 =4.1 GeV s0 =4.3 GeV M (GeV) differences smaller than 0.01%

14 J/! X c c q Problem: decay width X J/ψππ ~ 50 GeV q V (Navarra, MN, PLB639 (06)7)

15 X c q c q J/! V Problem: decay width X J/ψππ ~ 50 GeV (Navarra, MN, PLB639 (06)7) to test if the width depends on the color combination of the diquarks: diquark-antidiquark in the color sextet configuration (6-6) j µ 6 = i [(q T a Cγ 5λ S ab c b)( q d γ µ Cλ S de ct e ) +(q T a Cγµ λ S ab c b)( q d γ 5 Cλ S de ct e )]

16 X c q c q J/! V Problem: decay width X J/ψππ ~ 50 GeV (Navarra, MN, PLB639 (06)7) to test if the width depends on the color combination of the diquarks: diquark-antidiquark in the color sextet configuration (6-6) j µ 6 = i [(q T a Cγ 5λ S ab c b)( q d γ µ Cλ S de ct e ) +(q T a Cγµ λ S ab c b)( q d γ 5 Cλ S de ct e )] similar result for the mass s0 =4.15 GeV r 6(mol)/ r mol/3 r 6/ "(GeV! )

17 τ =1/M =0.4 GeV 1.01 r 6(mol)/ r mol/3 r 6/ s0 (GeV)

18 τ =1/M =0.4 GeV 1.01 r 6(mol)/ r mol/3 r 6/ ( ) s0 (GeV) c J/! X c q Γ(X J/ψππ) 6 50 MeV q V

19 to avoid fall apart mechanism ( g Λ) j µ mol λ = eff ( cλ a γ µ c)( qλ a γ 5 q)

20 to avoid fall apart mechanism ( g Λ) j µ mol λ = eff ( cλ a γ µ c)( qλ a γ 5 q) r mol " () s 0 =3.9 GeV s0 =5.0 GeV !!"#$ %!& '

21 r mol λ /ψ = M mol λ M ψ s 0 =6.0 GeV s0 =5.0 GeV 1.3 s 0 =3.9 GeV 1. r mol " (# !!"#$ %!& '

22 r mol λ /ψ = M mol λ M ψ s 0 =6.0 GeV s0 =5.0 GeV 1.3 s 0 =3.9 GeV r mol " (# r mol λ /ψ M mol λ 3.53 GeV !!"#$ %!& '

23 r 3/ψ = M 3 M ψ s 0 =6.0 GeV s0 =5.0 GeV 1.3 s 0 =3.9 GeV 1. r 3/" !!"#$ %!& '

24 r 3/ψ = M 3 M ψ s 0 =6.0 GeV s0 =5.0 GeV 1.3 s 0 =3.9 GeV 1. r 3/" r 3/ψ M GeV !!"#$ %!& '

25 Conclusions By studying only the mass of X(387) one can not stablish its structure Molecular (DD*) and tetraquark ( ) lead to too large decay width [cq][ c q] currents Colored J/ψ-π molecular current gives the correct decay width but, maybe, small mass More studies are necessary to reach a definite conclusion