The x + (5568) from QCDSR

Transcription

1 The x + (5568) from QCDSR Marina Nielsen Universidade de São Paulo

2

3 Lots of X, Y and Z states observed by BaBar, Belle, BESIII, CDF, CLEOIII, CLEO-c, CMS, D0 and LHCb Collaborations many not confirmed states, many candidates for exotic states

4 Exotic States if X(3872!!ISRY(4260,4008?)!!ISR J/" #+ #- PRL 99, , 548 fb-1 bservation X Glueball Hybrids New e structur M=4008 Tetraquarks 1% % X J/ψπ + π Y(4260 ) "! for calibration MC X(3872) can not No enhancement in D(*) D(*): PRL 98, M 0(D0 0 D 0 ) = M (D D ) = ( D 0 + X(3872) : molecular (D 0 0? X(3872): X(3872)molecular : molecular (D D + D 0 D Te theor. review: (ZPC61(94)) predict Tornqwist (ZPC61(94)) predict a D Da D D molec PR 429, 243 Tornqwist Maiani et al. 5.1% % Molecules.7% % 5.4% % + 0 J/ψπ π π (PRD71 (05)) tetr Xq = [cq]s=1 Pentaquarks Texto MeV Friday, June 22, 2012 MeV ev MeV PRL97, (06) MeV s: Friday, June 22, % CL 2 solutions with con/distructive interf. Friday, June 22, 2012 domingo, 11 de setembro de ev Mbelle = ±0.7±0.8 PRL97, (06) Mb

5 + Belle, - BaBar, + to now BESIII, CLEO-c and LHCb?) -ISR Up Y(4260,4008?) J/ J/ ISR ISR charged charmonium states 99, , 548 fbreported PRL 99, , 548 fb-1 PRL 99, , 548 fb servation +(4430) +(4050) +(4250) Z Z Z 1 EUROPEAN ORGANIZATION FOR NUCLEAR2 RESEARCH (CERN) , , 548 fb Y( Y( )?+ J/ New ICHEP 08, 413 fb-1 No enhancement in e r u t c stru D(*) D(*): PRL 98, M=4008 Zc+(3900)? theor. MC review: theor. review: PRPRL , , 548 fbpr 429, , 243 No enhancement in? theor. review: 4 26 PR 0) 429, [hep-ex] 23 Feb 2012 D(*): PRL 98, M2( (2S) ), (GeV2 ) III -1 M2(K0 ) ?) ISR J/ Zc (3885) ICHEP 08, 413 No enhancement in fb-1 D(*) D(*): PRL 98, Zc+(4025)? Zc+(4020) sys system Detailed study of K Det Detailed study of K before theor. review: 2013 PR 429, at J/, (2S) loo looking at J/, (2S) looking : III? III III ) plot M(K D 2(K0 ) 1) S, P, M(K ) plot D wave intensity M2(K0 )1) S, P,M(K M con contributions, K K Zc+(4200) K 2) K 2) K is parameterized K - in K X(4140) state MeV MeV + + MeV B MeV J/ K decays M (K ) M2(K+ ) -1 PRL 99, , 548 fb the Search for K No enhancement in MeV D(*) D(*): PRL 98, MeV -1 ICHEP 08, 413 fb LHCb-PAPER February 21, 2012 M2( (2S) ), (GeV2 ) New o enhancement in e r u t c u r t s D(*): PRL 98, M= in Bfor -0 -K search BaBar Z(4430) sea BaBar search forbabar Z(4430) J/ CERN-PH-EP M2( (2S) ), (GeV2 ) for calibration 4260) M2(K ) evreview: ev ev theor. and (2S) distributions and and (2S) distributions J/ J/ J/ MeVPR 429, 243Y MeV MeV (4260) MeV K*(892) background (from K ) + background BW (free mass (from &K background (from K ) + BW (free mass & width) MeV MeV MeV re MeV - (likeno - (2S ev -ev - Belle), ev No signal in J/ in signal in ~2 J/ in (like No signal in J/ (like in Belle), ~2 in (2S) : w e ev %domingo, CL 11 densetembro on/di2 solutions with con/dide 16 No enhancement inthe LHCb collaboration possible structure: tetraquarks or molecules re P

6 molecular and tetraquark interpretations differ by the way quarks are organized in the state Meson molecule Tetraquark state larger than normal mesons compact state

7 X ± (5568): most recent acquisition arxiv: p X ± (5568)! B 0 s ± M = (5567.8±2.9±1.2) MeV Γ = (21.9±6.4±3.5) MeV stat. significance 5.1σ

8 LHCb and CMS: no structure is found from B s 0 π + from threshold up to 6000 MeV arxiv: ICHEP2016 talk

9 from D. Zieminska, ICHEP2016 talk

10 a Theoretical calculations a QCD sum rules: quark models: Agaev et al., arxiv: ; Chen et al., arxiv: ; Wang, arxiv: ; Chen et al., arxiv: ; Zanetti et al., arxiv: ; Agaev et al., arxiv: ; Dias et al., arxiv: ; Albuquerque et al., arxiv: ;... Wang & Zhu, arxiv: ; Liu et al., arxiv: ; Xiao & Chen, arxiv: ; Stancu, arxiv: ; Lu & Dong, arxiv: ; Chen & Ping, arxiv: ; Maiani et al., arxiv: ;... coupled channels: Albaladejo et al., arxiv: rescattering effects: Liu & Li., arxiv: more general arguments: Burns & Swanson, arxiv: ; Guo et al., arxiv:

11 X ± (5568) Tetraquark state Agaev et al., arxiv: ; Chen et al., arxiv: ; Wang, arxiv: ; Tang & Qiao, arxiv: BK molecular state Agaev et al., arxiv: ; Xiao & Chen, arxiv: ; Albaladejo et al., PLB757 mass not compatible with 4-q or mol. Burns & Swanson, arxiv: ; Guo et al., arxiv: ; Zanetti et al., arxiv: ; Wang & Zhu, arxiv: ; Chen & Ping, arxiv: ; Maiani et al., arxiv: ; Lu & Dong, arxiv: ; Albuquerque et al., arxiv:

12 Burns & Swanson (arxiv: ): could the signal be due to the fact that D0 detector cannot detect π 0 at low transverse momentum?

13 Burns & Swanson (arxiv: ): could the signal be due to the fact that D0 detector cannot detect π 0 at low transverse momentum? consider the weak decay: B + c! B 0 s +! B 0 s + [ 0 ] it naturally gives rise to a kink in the B s0 π + spectrum near 5570 MeV

14 Burns & Swanson (arxiv: ): could the signal be due to the fact that D0 detector cannot detect π 0 at low transverse momentum? consider the weak decay: B + c! B 0 s +! B 0 s + [ 0 ] it naturally gives rise to a kink in the B s0 π + spectrum near 5570 MeV What about LHCb and CMS detectors?

15 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 quark level quark and gluon degrees of freedom Wilson OPE Phenomenological side hadron level hadron parameters (masses, couplings, form-factors,...) dispersion relation phen i OPE i

16 phen = 2 1 m 2 q 2 + continuum coupling current-state OPE (q 2 )= Z 1 s min ds OPE (s) s q 2, OPE (s) = 1 Im[ OPE ]

17 phen = 2 1 m 2 q 2 + continuum coupling current-state OPE (q 2 )= Z 1 s min ds OPE (s) s q 2, OPE (s) = 1 Im[ OPE ] continuum = s 0 ds ρop E (s) s q 2 {

18 phen = 2 1 m 2 q 2 + continuum coupling current-state OPE (q 2 )= Z 1 s min ds OPE (s) s q 2, OPE (s) = 1 Im[ OPE ] s 0 : continuum parameter continuum = s 0 ds ρop E (s) s q 2 Π { phen (Q 2 ) Π OPE (Q 2 ) valid at small Q 2 valid at large Q 2

19 To improve the matching Borel transform Borel Transform { eliminates subtraction terms suppresses higher order condensates increases importance pole contribution λ 2 e m2 /M 2 = s0 s min ds e s/m 2 ρ OPE (s)

20 To improve the matching Borel transform Borel Transform { eliminates subtraction terms suppresses higher order condensates increases importance pole contribution λ 2 e m2 /M 2 = s0 s min ds e s/m 2 ρ OPE (s) m 2 = s 0 ds s s min s 0 ds s min OPE (s) e i s/m 2 OPE (s) e i s/m 2

21 Good Sum Rule Borel window such that: pole contribution > continuum contribution good OPE convergence good Borel stability OPE side: condensates up to dimention 6 quark condensate gluon condensate mixed condensates four-quark condensate

22 QCDSR calculation for X + (5568) mass Khemchandani, MN, Zanetti: arxiv: tetraquark current with J P = 0 + Z j X = " abc " dec u T a C 5 b b dd 5 C s T e Te (q) =i d 4 xe iq.x h0 j X (x) j X (0) 0i T (x) =f S u (x)s d ( x)s s (x)s b ( x)

23 QCDSR calculation for X + (5568) mass Khemchandani, MN, Zanetti: arxiv: tetraquark current with J P = 0 + Z j X = " abc " dec u T a C 5 b b dd 5 C s T e Te (q) =i d 4 xe iq.x h0 j X (x) j X (0) 0i T (x) =f S u (x)s d ( x)s s (x)s b ( x) OPE for the quark propagator

24 Khemchandani, MN, Zanetti: arxiv: pole dominance s 0? In general s 0 =(m X +0.5 GeV) 2

25 Khemchandani, MN, Zanetti: arxiv: pole dominance s 0? In general s 0 =(m X +0.5 GeV) 2 m X =(5.58 ± 0.17)GeV

26 Khemchandani, MN, Zanetti: arxiv: pole dominance s 0? In general s 0 =(m X +0.5 GeV) 2 m X =(5.58 ± 0.17)GeV a OPE convergence? a

27 pole dominance

28 pole dominance a No OPE convergence for s 0 <46 GeV 2 a

29

30 OPE convergence

31 OPE convergence pole dominance

32 m X =(6.39 ± 0.10)GeV not compatible with X(5568) mass, but

33 m X =(6.39 ± 0.10)GeV not compatible with X(5568) mass, but not excluded by LHCb data

34 a Decay width X ± B s0 π ± Dias, Khemchandani, Martínez Torres, MN, Zanetti: arxiv: j B 0 s = i b a 5 s a j X = " abc " dec u T a C 5 s b bd 5 C d T e j 5µ = d a µ 5 u a Problem: due to Fierz transf. tetraquark currents can be written as a sum of molecular currents with trivial color = X 0 configurations g 0 ba s a db 0 u b } mesons j X = " abc " dec u T a C 5 s b bd 5 C d T e } tetraquark

35 with mesonic currents the decay can proceed directly through the fall apart in its components X + X b c d q s c u q u B 0 s J/ψ π + V fall apart decays should not be possible with tetraquark currents with color entanglement a How to solve this problem? a

36 with mesonic currents the decay can proceed directly through the fall apart in its components X + X b c d q s c u q u B 0 s J/ψ π + V fall apart decays should not be possible with tetraquark currents with color entanglement a How to solve this problem? a B 0 s X + b s require color exchange during the decay

37 If X + (5568) is a genuine tetraquark state, only color-conected diagrams will contribute OPE side Phen. side B 0 s X + b s from the 2-point QCDSR

38 If X + (5568) is a genuine tetraquark state, only color-conected diagrams will contribute OPE side Phen. side B 0 s X + b s from the 2-point QCDSR coupling constant

39 OPE side: u 0 = M 2 X very stable in the range: 1.0 apple M 2 apple 2.2 GeV 2

40 Dias, Khemchandani, Martínez Torres, MN, Zanetti: arxiv: Phen. side OPE side =

41 Dias, Khemchandani, Martínez Torres, MN, Zanetti: arxiv: Phen. side OPE side = using m X =5568 MeV we get:

42 using the results from a trustable QCDSR: m X =(6.39±0.10) GeV and s 0 =(48±2) GeV 2 we get: (X ± (5568)! B 0 s ± ) = (20.4 ± 8.7) MeV (X ± (6390)! B 0 s ± ) = (30.1 ± 8.6) MeV but this is not the total width since there are more open channels now (BK, B*K*, B s + )!

43 using the results from a trustable QCDSR: m X =(6.39±0.10) GeV and s 0 =(48±2) GeV 2 we get: (X ± (5568)! B 0 s ± ) = (20.4 ± 8.7) MeV (X ± (6390)! B 0 s ± ) = (30.1 ± 8.6) MeV but this is not the total width since there are more open channels now (BK, B*K*, B s + )! compatible with exp. width, but...

44 Conclusions Lots of exotic states in the last years: a new spectroscopy? Discovery of X+ (5568) represents a challenge We need better bounds in the experimental reports