Attributes of molecule-like exotics in the heavy sector - Interlude on EFTs. - Observables that test the molecular hypothesis in

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1 Attributes of molecule-like exotics in the heavy sector - Interlude on EFTs - The Exotic Spectrum X(3872),Y, Z,... - Observables that test the molecular hypothesis in X(3872) X(3872)! (2S) (4040)! X(3872) (4160)! X(3872) ( ) D 0,( ) scattering - (Example of a thing that is probably not a molecule) - Candidates for molecules in the b-sector R.P. Springer Duke University Light Nuclei from First Principles 4 Oct 2012

2 E (GeV) Energy Scales Planck scale unification scale } } top quark mass hadronic nuclear atomic

3 Examples of Effective Theories Newton s laws Thermodynamics Fluid Dynamics Gravity Quantum Electrodynamics Standard Model of Nuclei and Particles

4 Attributes of Effective Field Theories (EFTs) Utilize separation of scales => create small parameter Based upon underlying (perhaps approximate) symmetries Reliable error estimates from order of calculation Systematically improvable May be used to probe unknown underlying theory May be used to simplify calculations in known theories Typically contain unknown (by the EFT) coefficients that have to be fixed via experiment or other means Coefficient fixed from any exp for which EFT is valid true for *all* observables in that EFT Typically valid only in a limited energy window

5 An Effective Quantum Field Theory for low energy light-light scattering Scales: m e 511 kev E << m e Symmetry: Lorentz invariance F µ = F µ L = 1 4 F µ F µ + c 1 m 4 e (F µ F µ ) 2 + c 2 m 4 e (F µ Fµ ) 2 F µ = A µ x A x µ c = 1 [L] = [T ] = 1 [E] = [T ] 1 = [L] 1 = c 1 E 4 m 4 e + (from J. Gasser, MENU 07)

6 gluon In the absence of a antiquark &. solution to QCD, use EFT => contains predictions of QCD as a subset % D 0 meson = cu - quark c-quark s - Symmetry (group) structure s 1 works for ground states, s 1. but we need dynamics for excited states

7 Limits of QCD where symmetries are enhanced 0 m u < m d < m s m c < m b < m t - QCD L light QCD = i (q il i/dq il + q ir i/dq ir ) (q il m ij q jr + q ir m ij q jl ) ij m q = diag(m u, m d, m s ) q il L ij q jl q ir R ij q jr L SU(3) L R SU(3) R P T m q,p

8 L heavy QCD = Q(i/D m Q)Q Q = e im Qv.x (h (Q) v p µ Q = m Qv µ + k µ h (Q) v iv.dh (Q) v + (Q) v ) small Heavy Meson Multiplets cq s l and s Q = 1/2 separately conserved D(0 )i = 00i = 1 p 2 ( "#i #"i) light k m Q HQET + D(1 ) µ i ""i, PT = HH PT 1 p ( "#i + #"i), ##i 2 heavy

9 Collect into Supermultiplets (D (0,+) 0, D s0 ) H a = 1 + /v 2 [P µ a µ P a 5 ] S a = 1 + /v 2 [P µ a µ 5 P a ] (D (0,+), D s ) (D 0,+, D s ) (D (0,+) 1, D s1 ) L = Tr[H a (iv.d ab H )H b ] + T r[s a (iv.d ab S )S b ] + g Tr[H a H b /A ba 5 ] + g Tr[S a S b /A ba 5 ] + h (Tr[H a S b /A ba 5 ] + h.c.) D + D + p µ g p. 0 f 2 = e im/f D µ = µ + V µ V µ = 1 2 ( µ + µ ) A µ = i 2 ( µ µ )

10 K. Seth, Prog. Part. Phys 67 (2012) 390.

11 Y (4660) X(4630) X,Y,Z states from Table 9, Brambilla et al Y (4360) Z(4430) + X(4350) Y (4260) Y (4274) Z 2 (4250) + Y (4008) X(3872) X(4160) Y (4140) Z 1 (4050) + X(3940) X(3915)... D D(3730) J PC 1 (1 ++ ) 0/2 ++ 0/2?+??+?

12 Techniques/Descriptions/Strategies QCD Sum Rules Non-relativistic QCD Heavy Quark Effective Theory Heavy Hadron Chiral Perturbation Theory X-EFT Lattice Potential Models Molecule Hybrids Mixtures Tetraquark Baryonium Coupled channels Hadrocharmonium

13 Molecules: do the constituents retain their identify as hadrons? (more details in the X(3872) section) X(3872) D 0 D 0 X(3915) D 0 D 0 + D + D BGL Y (4140) D + s D s BGL Y (4260) D 0 D, (2S)f 0 (980) AN, TKGO c c, c0, c1!,d 1 D Q,LZL,YWM,R Z(4430) + D + D 0 1 LMNN/BGL X(4630) (2S)f 0 (980) GHHM Y (4660) (2S)f 0 (980) GHM BGL=Branz,Gutsche,Lyubovitskij LMNN=Lee,Miharo,Navarro,Nielsen TKGO=Torres,Kehmchandari,Gamermann,Oset AN=Albuquerque,Nielsen Q=Qiao LZL=Liu,Zeng,Li YWM=Yuan,Wang,Mo R=Rosner GH(H)M=Guo,(Haidenbauer),Hanhart,Meissner

14 X(3872) as molecule 1 p D 0 D0 + D 0 D 0 2 X(3872) J/ C = + S-wave X(3872) + J/ < 1.2 MeV Isospin issue: [X! J/ + 0 ] [X! J/ + ] = Belle 2011 PRD 84, Hanhart et al [X! J/!] [X! J/ + ] =0.8 ± 0.3 BaBar 2010 J PC =1 ++ or 2 + multipole question m D 0 D0 m X(3872) =0.16 ± 0.33 MeV

15 Like the Deuteron? Systematic NN treatment: NN-EFT (no pions) Only now it is an infinite sum of (DD + cc) or (B B ( ) + cc) etc. = C ic 2 Mp C 3 Mp A = A = 4 M [ a + ia2 p (a3 a 2 r 0 )p 2 + ] does not converge NN system: a (1 S 0 ) 1 8 MeV a (3 S 1 ) 1 36 MeV Both S-wave scattering lengths anomalously large => momentum expansion fails => reorganize to treat C s nonperturbatively A = 4 1 M 1/a + ip + with effective range: A = 4 M EM effects easily included 2 1 1/a 1 2 rp2 + ip +

16 Evidence that pionless EFT works in strong and EM sector Chen,Rupak,Savage nucl-th/ v4 180 δ NN scattering phase shift: A(q 2 ) k (MeV) FIG. 1. The phase shift δ 0 as a function of the center of mass momentum k. The dashed curve corresponds to δ (0) 0, the dotted curve corresponds to δ(0) 0 + δ (1) 0, the solid curve corresponds to δ (0) 0 + δ (1) 0 + δ (2) 0, and the dot-dashed curve is the Nijmegen partial wave analysis [35] :EM form factor of deuteron q (MeV) FIG. 3. The form factor A(q 2 ) as a function of q = q 2. The dashed curve corresponds to the leading order prediction, the dotted curve corresponds to the next-to-leading order prediction, and the solid curve corresponds to the next-to-next-to-leading order prediction, in EFT(π/).

17 X-Effective Field Theory: Fleming, Kusunoki, Mehen, van Kolck D HH PT. X(3872) 1-sum, XEFT % D (2S) Factorization theorems: Braaten/Kusunoki/Lu Rate = (phase space) C DD! f 2 niversal shallow-bound-state properties from effective range DD (r) / e theory: Braaten/Voloshin... r r B = 1 2µ D Da 2 20 MeV a 10 fm hri 12 fm

18 X(3872) D ( ) scattering Canham/Hammer/RPS IF X(3872) 1 2 (D 0 D 0 + D 0 D 0 ) m X = ( ± 0.17) MeV B X =(0.16 ± 0.36) MeV L = a 1 j=d 0,D 0, D 0, D 0 j 2µ X B X i t + 2 2m j j + X X g 2 X ( D 0 D 0 + D 0 D0) + h.c. + Integral equation: = + Results depend only on scattering length a D 0 X = 9.7a a D 0 X = 16.6a

19 Three body cross section vs scattering length! [a 2 ] D-X (L=0) D * -X (L=0) D-X (L<7) D * -X (L<7) k [1/a] LHC possibilities: B c 10 7 per week BB final state interactions (bb) 0.4 mb (bbbb) 5 fb

20 X(3872) (2S) Mehen/RPS MeV factorization XEFT + HBChPT D 0 (2S) Hu, Mehen g 2 2 GeV 3/2 Guo et al., D 0 D 0( ) - J =( c (2S), (2S)) (X(3872)! (2S) ) tot > 0.03 (BaBar, PDG) H a (D a,d a); a =1, 2, 3 ) (X(3872)! (2S) ) > 0.04 MeV

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22 X(3872) as 2 + : =0.08

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24 (4040) X(3872) g 2! g 2 ; c 1! c 1 E 165 MeV Suppose g-like terms dominate: M(X) 2 > 0.09 GeV 3 D 0 from (X(3872)! (2S) ) ( g 2 ) 2 < 0.63 GeV 3 from width of (4040) (4040) D 0 ( g 2 ) GeV 3 from quark model hep-ph/ ) [ (4040)! X(3872) ] ( ) MeV

25 (4160)! X(3872) n (2s+1) L J =1 3 D 1 J PC =1 r J ij = 1 3 i j + j i 2 ij L = iḡ 2 Tr apple J ij H i j H + c 2 Tr J ij H i E j H +h.c = 3 c ḡ Preliminary Margaryan Mehen RPS -1.0

26 An example of possible exotics that appear not to be molecules

27 Open Charm cu, cd, cs ****** ****** =D*K = DK D s (1968) D(1875) D s (2112) D (2007) D s0 (2317) D 0 (2308) D s1 (2460) D 1 (2438) exotic quark model threshold J P *****

28 m c 1 +, 2 + D (0,+) 1 D s1 D (0,+) 2 D s2 m u, m d, m s 0 0 +, 1 + D (0,+) 0 D s0 D (0,+) 1 D s1 0, 1 D (0,+) D s D (0,+) D s Corrections : (m q, p) (, m Q ) SU(3)? D D D s D s D s1 D s0 140MeV

29 Electromagnetic Decays of 0 + s and 1 + s D s0 (2317) D s D s0 (2317) D s 0 < (CLEO) Ds1(2460) D s Ds1 (2460) D s 0 < 0.16 D s1(2460) D s D s1 (2460) D s 0 = (Belle) (BaBar) L em = e 4 [H a S b µ F µ Q ba ] Q = 1 corrections : QCD m c m s 30% 2 ( Q + Q )

30 D s0, D s1 as molecules? K K D ( ) D ( ) (D s1 D s ) = 8g2 2 s D ( ) D s ( ) 3f 2 (D s1 D s ) = 4g2 2 3f 2 (D s0 D s ) = 4g2 2 f 2 m D m Ds m 3 Ds1 m D m Ds m 3 Ds1 m D m Ds m 3 Ds0 D K (0) 2 E D K (0) 2 E DK (0) 2 E m Q 2 : 1 : 3 phase space 1.57 : 1 : R 1.58 cf. to exp. limits

31 Strong Decay of Molecules Predicts (±30%) : problem ratios molecular hypothesis disfavored D s1 D s D s1 D s 0 = 3.23 D s1 D s D s1 D s 0 = 2.21 D s0 D s D s0 D s 0 = 2.96 (exp < 0.16) (exp 0.44) (exp < 0.059) (D s1 D s 0 ) = 3(m K + E 0) 2 4 f 4 2 m D m Ds m 3 Ds1 D K (0) 2 p 0 (D s0 D s 0 ) = 3(m K + E 0) 2 4 f 4 2 m Dm Ds m 3 D s0 DK (0) 2 p 0

32 b Exotics above threshold - Belle hybrid bbg disturbed (5S) molecule Y b (1 ) Y (4260) analog Z b (10610) ± ± (5S)! ( + [bb]) Z b (10650) ± ± (5S)! ( + [bb]) Y b (10888) ± e + e! ( + (ns)) Eidelman, Heltsley, Hernandez-Rey, Navas, Patrignani

33 Z b as a molecule HQET predicts additional states (Voloshin... ) W 0 = 1 (0 + )= bb 0 lt p 3 Z b =1 + (1 + )= 1 p 2 0 bb 1 lt +1 bb 0 lt Z 0 b =1 + (1 + )= 1 p 2 0 bb 1 lt 1 bb 0 lt 2 1 bb 1 lt J=0 & %,h b, b W 0 0 = 1 (0 + )= p bb 0 lt bb 1 lt! b, b, J=0 Molecule treatment predicts decay ratios among them (Mehen/Powell) L eff = + H a = P a + V ~ ~ now B ( ) multiplet rather than D ( ) multiplet

34 Summary Many new exotic unexpected particles discovered at B factories X(3872) may be a molecular bound state of the D 0 and D 0 mesons. If so, it must have J PC =1 ++ Measurements needed to check molecular hypothesis: a. D 0( ), D 0( ) scattering enhancement b. polarization of (2S) indecay c. polarization of X(3872) in creation Possible analogues seen in bottomonium-like system Again, additional data needed to prove or disprove character LHC, BESIII,... exciting times ahead for heavy quark spectroscopy and our ability to understand bound states of QCD Will this cleaner system shed light on nuclear bound states?

35 Additional Slides

36 Baru et al

37 Amplitudes M 2 = g F 1 (, E ) + g 2 c 1 F 2 (, E ) + c 2 1F 3 (E ) M( ) 2 = 2g A 2 E 4 + 4g 2 c 1 ACE 2 + 2c 2 1C 2 ˆk 2 + g B 2 E 4 2g 2 c 1 BCE 2 + c 2 1C 2 ˆk MeV; E 181 MeV

38 Hadrocharmonium J/, (2S),...even? a nity for light hadronic matter small QQ light (excited) hadronic matter Y 0 s are 1 Z 1 (4050) +! + c1(1p ) Z 2 (4250) +! + c1(1p ) Y (4260)! J/ Y (4360)! + (2S) Z(4430) +! + (2S) Y (4660)! + (2S) widths (MeV) ± ± ± 15 look for J/ with baryons; b analogs

39 Strong Interaction Terms L = N (i M )N 1 8 C(1 S 0 ) 0 (N T 2 a 2 N) (N 2 a 2 N) 1 S 1 ) 8 C(3 (N 0 T 2 2 i N) (N 2 2 i N) +..., P a ( 1 S 0 ) = a 2 ; P i ( 3 S 1 ) = i L = N dibaryon treatment i M g (3 S 1 ) s a g (1 S 0 ) N t i i M t i N T P i ( 3 S 1 )N + h.c. i M ( 1 S 0 ) s a s a N T P a ( 1 S 0 )N + h.c. ( 3 S 1 ) t i