Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Phys. Lett. B702, 139 (2011) Charged charmonium-like states as rescattering effects in B  D sJ D (*) P. Pakhlov

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Z(4430) + Belle’s observation vs BaBar non-observation two spectra are in a good agreement: almost all (even minor) features matches! Why so different conclusions?

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Real state or some other effect?  Molecular state  two loosely bound charm mesons  quark/color exchange at short distances  pion exchange at large distance  Tetraquark  tightly bound four-quark state  Hadro-charmonium  specific charmonium state “coated” by excited light- hadron matter u – c u c – c c – π π π c c – u u –  Threshold effects: peak influenced by nearby D (*(*)) D (*(*)) threshold  J. Rosner (PRD, 76, , 2007) paid attention to proximity of M(Z) to M(D * (2010)) + M(D 1 (2420)) B  D * D 1 (2420) K rescattering to B  'π K Mass of the peak M=M(D * )+M(D 1 (2420)) Width of the peak  ~  (D 1 (2420))

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Rescattering B D D*D* ’’ π K Consider decay B  D sJ D (*)  D sJ decays to D (*) K at time scale << D * lifetime  velocity of c-quark in D (*) and  -mesons is ~ ( ) c; comparable with D-meson velocities in DD * rest frame at mass ~ 4.4GeV (0.5 c)  Overlapping of wave functions of (DD * ) and (  'π) should not be negligible, although it is color suppressed.

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Assumptions  Assume factorization of the decay B  D sJ D and (DD * )  (  'π) rescattering  Assume the rescattering amplitude independent on M(DD * ) ( = M(  'π))  Calculate only angular part of triangle graph N. N. Achasov & A.A. Kozhevnikov, Z.Phys. C48, 121 (1990) ON THE NATURE OF C(1480) RESONANCE  considered triangle graph to explain anomalous cross-section pπ  nφπ 0 found at Serpukhov (has never confirmed by any other experiment)

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Spin-parity constraints DD *   (2S) π allowed with both sides of the reaction in s-wave  =>  (2S) π system has J P =1 + ; B  – (K) the final state with positive parity, therefore only B  D (*) D sJ (  DD * K) decays with positive parity can contribute! orbital excitations j=3/2 radial excitations P-wave (j=1/2) are below D (*) K threshold; Two body B-decays to P-wave (j=3/2) are suppressed; Radial excitations are expected to be large Br(B  DD * K) ~ 1%

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Search for D sJ candidates new D sJ  (4160)  (3770) J=0  2 /ndf = 185/5 J=1  2 /ndf = 7/5 J=2  2 /ndf = 250/5 N=182±30 ■ B + →D 0 D sJ (2700) ■ B + →ψ(3770)K + ■ B + →ψ(4160)K + ■ B + →D 0 D 0 K + NR ■ threshold comp M=2715  11  14 GeV  =115  20  14 GeV Angular analysis – D sJ (2700) polarization: The first radial excitation of D s should be MeV lighter; two-body B decay into D s ' are also expected to be large. New D s vector state produced with a huge rate (>0.1%) in two-body B decay; this state is a good candidate for the first radial excitation of D s *. Belle observation of D s * radial exct.

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Calculate B  DD s '  DD * K  ZK D DsDs K D*D* θ D Z K D*D* θ '' Angular part for B  DD s '  DD * K  Z K D s ' decay (0 –  1 – 0 – ): A Ds ~ 1; D * helicity (in D s ' frame)= 0 Z formation (1 – 0 –  1 + ): A Z ~ d 1 00 (θ'') = cos(θ''); D * helicity (in Z frame)= 0 D * spin rotation between different frames A D* ~ d 1 00 (θ') = cos(θ'); θ' – angle between D s 'and Z in D * rest frame Full amplitude: A BW (M D*K ) × A Ds × A D* × A Z

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Why rescattering results in a peak? M(DD * ) distribution from B  Scalar Scalar is flat cos(angle rotation D * spin ) correlates with M(DD * ) M(DD * ) ~ 4.6 GeV suppressed M(DD * ) ~ 4.8 GeV suppressed

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Comments on D s ' mass toy MC with M =2610 MeV  = 50MeV D s ' is not observed yet, expected mass MeV (2S 1 -2S 3 splitting MeV) tune mass and width to agree with Belle Z parameters dependence on D s ' width dependence on D s ' mass 10 MeV 50 MeV 100 MeV 2.60 GeV 2.61 GeV 2.62 GeV 2.63 GeV

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Calculate B  D * D s * '  DD * K  ZK D DsDs K D*D* θ D Z K D*D* θ '' Angular part for B  D * D s * '  DD * K  Z K Three amplitudes (D * helicity (in B frame) = ±1, 0) D s * ' decay (1 –  0 – 0 – ): A Ds ~ d 1 0λ (θ) = cos(θ) or ±sin(θ)/√2 Z formation (1 – 0 –  1 + ): A Z ~ d 1 00 (θ'') = cos(θ''); D * helicity (in Z frame)= 0 D * spin rotation between different frames A D* ~ d 1 λ0 (θ') = cos(θ') or ±sin(θ') /√2; θ' – angle between B and Z in D * rest frames Full amplitude:  a λ A BW (M DK ) × A Ds × A D* × A Z, assuming only s-wave a 0 =1/√3, a ±1 = –1 /√3

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Only two amplitudes match parity constraint (S and D-waves) assuming S-wave dominates a 0 = –1/√3, a ±1 = 1 /√3 λ=1 λ=0 S-wave (1/√3 a 1 –1/√3 a 0 ) Calculate B  D * D s * '  DD * K  ZK

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Compare with Belle/BaBar data Sum B  DD s '  DD * K and B  D * D s * '  DD * K (S-wave). Not a perfect description. should sum complex amplitudes (interference). also need to take into account interference with remaining (after veto) K *(*) background efficiency is also important issue: sharp drop around high mass limit due to soft kaon. This is just very naive illustration: correct procedure is fit! + soft kaon – low efficieny

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Peaks in χ c1 π mass spectrum Any D (*) D (*)  χ c1 π requires at least one p-wave to conserve parity.  Only B  D (*) D sJ  D (*) D (*) K chains with negative parity is allowed for rescattering (D (*) D (*) ) P  (χ c1 π) S  Note χ c1 is a p-wave orbital excitation, therefore p-wave D (*) D (*) rescattering can be not suppressed (and even favored)!  The simplest one is (DD) P  (χ c1 π) S : J P (Z)= 1 –  Other are also possible. Can be useful to describe the double peak structure in M(χ c1 π)). D s * ' decay (1 –  0 – 0 – ): A Ds ~ d 1 00 (θ) = cos(θ) Z formation (0 – 0 –  1 – ): A Z ~ d 1 00 (θ'') = cos(θ'') No spin rotation A D* ~ d 0 00 (θ') = 1 Known decay chain B  DD s * '  D DK (  Z K) Full amplitude: A BW (M DK ) × A Ds × A D* × A Z

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Calculate B  DD s * '  DDK  ZK B  DD s * '  DD K roughly reproduces the broad bump near 4.2GeV; the second peak at high mass limit expected from this chain is hidden in the data by sharp drop of reconstruction efficiency. Other D sJ D (*) (only with negative parity!) can contribute e.g. B  D * D s * '  D * D * K (P-wave only)

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Summary  A peak (and nearby structure) in M(  ' π) in B   ' π K decay can be explained by B  DD s ' and B  D * D s * ' decays followed by rescattering DD *   ' π  both decays are not observed so far, but both are expected to be large  even D s ' is not observed so far, but its mass/width are in agreement with expectations  A chain with opposite parity is required to explain peak(s) in χ c1 π. The simplest (and probably the largest) one is the known B  DD s * '  DDK can describe the general features of the data spectrum. While within the proposed explanation the peaks in charmonium-π system are results of the kinematics, these peaks reveal a very interesting effect: large rescattering, not expected by theory

Φ→Ψ, BINP, Novosibirsk.2011P. Pakhlov Summary If the proposed explanation is true there are many ways to check it with the BaBar/Belle data. Direct search for D s ' in two body B decays: M ~ 2610 GeV;  ~ 50 MeV; Br(B  D s ' D) × Br(D s '  D * K) ≥ 10 –3 Dalitz (Dalitz+polarization fit) of B   ' π K: check Z + vs rescattering hypothesis If rescattering D * D   ' π is large in B decays it should also reveal itself in all process where DD * (J P =1 + ) are produced at one point T H A N K Y O U !