We perform a systematic study of the possible molecular states composed of a pair of heavy mesons such as $D\bar{D}$
 
, $D^{\ast}\bar{D}$
 
, $D^{\ast}\bar{D}^{\ast}$
 
in the framework of the meson exchange model. The exchanged mesons include the pseudoscalar, scalar and vector mesons. Through our investigation, we find the following results. (1) The structure X(3764) is not a molecular state. (2) There exists strong attraction in the range r<1 fm for the $D^{*}\bar{D}^{*}$
 
system with J=0,1. If future experiments confirm Z
 +(4051) as a loosely bound molecular state, its quantum number is probably J
 P
 =0+. Its partner state Φ
 **0 may be searched for in the π
 0
 χ
 c1 channel. (3) Vector meson exchange provides strong attraction in the $D^{\ast}\bar{D}$
 
channel together with pion exchange. A bound state solution may exist with a reasonable cutoff parameter Λ∼1.4 GeV. X(3872) may be accommodated as a molecular state dynamically although drawing a very definite conclusion needs further investigation. (4) The $B^{\ast}\bar{B}$
 
molecular state may exist.

X(3872) and Other Possible Heavy Molecular States

There exist many experimental indications that final-state interactions (FSIs) may play a prominent role not only in charmful $B$ decays but also in charmless $B$ ones. We examine the final-state rescattering effects on the hadronic $B$ decay rates and their impact on direct CP violation. The color-suppressed neutral modes such as ${B}^{0}\ensuremath{\rightarrow}{D}^{0}{\ensuremath{\pi}}^{0},{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0},{\ensuremath{\rho}}^{0}{\ensuremath{\pi}}^{0},{K}^{0}{\ensuremath{\pi}}^{0}$ can be substantially enhanced by long-distance rescattering effects. The direct CP-violating partial rate asymmetries in charmless $B$ decays to $\ensuremath{\pi}\ensuremath{\pi}/\ensuremath{\pi}K$ and $\ensuremath{\rho}\ensuremath{\pi}$ are significantly affected by final-state rescattering, and their signs are generally different from that predicted by the short-distance (SD) approach. For example, direct CP asymmetry in ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{\ensuremath{\pi}}^{0}$ is increased to around 60% due to final-state rescattering effects whereas the short-distance picture gives about 1%. Evidence of direct CP violation in the decay ${\overline{B}}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ is now established, while the combined BABAR and Belle measurements of ${\overline{B}}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}$ imply a $3.6\ensuremath{\sigma}$ direct CP asymmetry in the ${\ensuremath{\rho}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ mode. Our predictions for CP violation agree with experiment in both magnitude and sign, whereas the QCD factorization predictions (especially for ${\ensuremath{\rho}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$) seem to have some difficulty with the data. Direct CP violation in the decay ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ is very small ($\ensuremath{\lesssim}1%$) in the standard model even after the inclusion of FSIs. Its measurement will provide a nice way to search for new physics as in the standard model QCD penguins cannot contribute (except by isospin violation). Current data on $\ensuremath{\pi}K$ modes seem to violate the isospin sum-rule relation, suggesting the presence of electroweak penguin contributions. We have also investigated whether a large transverse polarization in $B\ensuremath{\rightarrow}\ensuremath{\phi}{K}^{*}$ can arise from the final-state rescattering of ${D}^{(*)}{\overline{D}}_{s}^{(*)}$ into $\ensuremath{\phi}{K}^{*}$. While the longitudinal polarization fraction can be reduced significantly from short-distance predictions due to such FSI effects, no sizable perpendicular polarization is found owing mainly to the large cancellations occurring in the processes $\overline{B}\ensuremath{\rightarrow}{D}_{s}^{*}\overline{D}\ensuremath{\rightarrow}\ensuremath{\phi}{\overline{K}}^{*}$ and $\overline{B}\ensuremath{\rightarrow}{D}_{s}{\overline{D}}^{*}\ensuremath{\rightarrow}\ensuremath{\phi}{\overline{K}}^{*}$, and this can be understood as a consequence of CP and SU(3) [CPS] symmetry. To fully account for the polarization anomaly (especially the perpendicular polarization) observed in $B\ensuremath{\rightarrow}\ensuremath{\phi}{K}^{*}$, FSI from other states or other mechanism, e.g., the penguin-induced annihilation, may have to be invoked. Our conclusion is that the small value of the longitudinal polarization in $VV$ modes cannot be regarded as a clean signal for new physics.

Final state interactions in hadronic B decays

Probing the nature of Z c (′) states via the η c ρ decay

Using a coupled channel unitary approach, combining the heavy quark spin symmetry and the dynamics of the local hidden gauge, we investigate the meson-baryon interaction with hidden beauty and obtain several new states of N ∗ around 11 GeV. We consider the basis of states ηbN, �N, Bb, Bb, B ∗ �b, B ∗ �b, B ∗ � ∗ and find four basic bound states which correspond to Bb, B� ∗ , B ∗ �b and B ∗ � ∗ , decaying mostly into ηbN andN and with a binding energy about 50−130 MeV with respect to the thresholds of the corresponding channel. All of them have isospin I = 1/2, and there are no bound states or resonances in I = 3/2. The Bb state appears in J = 1/2, the B� ∗ in J = 3/2, the B ∗ �b appears nearly degenerate in J = 1/2, 3/2 and the B ∗ � ∗ appears nearly degenerate in J = 1/2, 3/2, 5/2. These states have a width from 6 ∼ 45 MeV except for the one in J = 5/2 which has zero width since it cannot decay into any of the states of the basis chosen.

/pdf/hidden-beauty-baryon-states-in-the-local-hidden-gauge-26axjs1632.pdf

Hidden beauty baryon states in the local hidden gauge approach with heavy quark spin symmetry

We perform a systematic study of the possible molecular states composed of a pair of heavy mesons such as $D\bar D$, $D^\ast\bar D$, $D^\ast \bar D^\ast$ in the framework of the meson exchange model. The exchanged mesons include the pseudoscalar, scalar and vector mesons. Through our investigation, we find that (1) the structure X(3764) is not a molecular state; (2) There exists strong attraction in the range $r < 1$ fm for the $D^*\bar D^*$ system with $J=0, 1$. If future experiments confirm $Z^+(4051)$ as a loosely bound molecular state, its quantum number is probably $J^{P}=0^+$. Its partner state $\Phi^{**0}$ may be searched for in the $\pi^0\chi_{c1}$ channel; (3) The vector meson exchange provides strong attraction in the $D^\ast \bar D$ channel together with the pion exchange. A bound state solution exists with a reasonable cutoff parameter $\Lambda\sim 1.4$ GeV. X(3872) may be accommodated as a molecular state dynamically although drawing a very definite conclusion needs further investigation; (4) The $B^\ast \bar B$ molecular state exists.

Wei Liu

Papers

Systematic study on QCD interactions of heavy mesons with ρ meson