Collective oscillation modes of a superfluid Bose-Fermi mixture

In this work, we present a theoretical study for the collective oscillation modes, i.e. quadrupole, radial and axial mode, of a mixture of Bose and Fermi superfluids in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a molecular Bose-Einstein condensate (BEC) in harmonic trapping potentials with cylindrical symmetry of experimental interest. To this end, we start from the coupled superfluid hydrodynamic equations for the dynamics of Bose-Fermi superfluid mixtures and use the scaling theory that has been developed for a coupled system. The collective oscillation modes of Bose-Fermi superfluid mixtures are found to crucially depend on the overlap integrals of the spatial derivations of density profiles of the Bose and Fermi superfluids at equilibrium. We not only present the explicit expressions for the overlap density integrals, as well as the frequencies of the collective modes provided that the effective Bose-Fermi coupling is weak, but also test the valid regimes of the analytical approximations by numerical calculations in realistic experimental conditions. In the presence of a repulsive Bose-Fermi interaction, we find that the frequencies of the three collective modes of the Bose and Fermi superfluids are all upshifted, and the change speeds of the frequency shifts in the BCS-BEC crossover can characterize the different groundstate phases of the Bose-Fermi superfluid mixtures for different trap geometries.Comment: 26 pages,6 figure

Study of Bˉs0→(Ds+,Ds∗+)l−νˉl\bar{B}_s^0 \to (D_s^+,D_s^{*+}) l^-\bar{\nu}_l decays in the pQCD factorization approach

The $\bar{B}_s^0 \to D_s^{(*)+} l^- \bar{\nu}_l$ semileptonic decays were calculated in the framework of the standard model (SM) by employing the perturbative QCD (pQCD) factorization approach. We defined four ratios of the branching ratios of the considered decays $R(D_s^{(*)})$ and $R_{D_s}^{l,\tau}$. From the numerical results and phenomenological analysis we found that: (a) The pQCD predictions for the branching ratios $Br(\bar{B}_s^0 \to D_s^{(*)+} l^-\bar{\nu}_l)$ generally agree well with the previous theoretical predictions; (b) For the four ratios, the pQCD predictions are $R(D_s)= 0.392 \pm 0.022$, $R(D_s^{*})= 0.302\pm 0.011$, $R_{D_{s}}^l=0.448^{+0.058}_{-0.041}$ and $R_{D_{s}}^\tau=0.582^{+0.071}_{-0.045}$, which show a very good $SU(3)_F$ flavor symmetry with the corresponding ratios for $B\to D^{(*)} l^- \bar{\nu}_l$ decays; and (c) we strongly suggest the measurements of the new ratios $R(D_s^{(*)})$ and $R_{D_{s}}^{l,\tau}$ in the forthcoming Super-B experiments.Comment: 14pages, 4 ps figure

Semileptonic decays Bc→(ηc,J/Ψ)lνB_c\to(\eta_c,J/\Psi)l\nu in the perturbative QCD approach

In this paper we study the semileptonic decays of $B_c^- \to (\eta_c,J/\psi)l^-\bar\nu_l$. We firstly evaluate the $B_c \to (\eta_c,J/\Psi)$ transition form factors $F_0(q^2)$, $F_+(q^2)$, $V(q^2)$ and $A_{0,1,2}(q^2)$ by employing the pQCD factorization approach, and then we calculate the branching ratios for all considered semileptonic decays. Based on the numerical results and the phenomenological analysis, we find that: (a) the pQCD predictions for the values of the $B_c \to \eta_c$ and $B_c \to J/\Psi$ transition form factors agree well with those obtained by using other methods; (b) the pQCD predictions for the branching ratios of the considered decays are $Br\left(B_c^- \to\eta_c e^-\bar\nu_e(\mu^-\bar\nu_\mu)\right) =(4.41^{+1.22}_{-1.09})\times10^{-3}$, $Br\left(B_c^- \to\eta_c\tau^-\bar\nu_\tau\right) =(1.37^{+0.37}_{-0.34})\times10^{-3}$, $Br(B_c^- \to J/\Psi e^-\bar\nu_e(\mu^-\bar\nu_\mu)) =(10.03^{+1.33}_{-1.18})\times10^{-3}$, and $Br\left(B_c^- \to J/\Psi\tau^-\bar\nu_\tau\right) =(2.92^{+0.40}_{-0.34})\times10^{-3}$; and (c) we also define and calculate two ratios of the branching ratios $R_{\eta_c}$ and $R_{J/\Psi}$, which will be tested by LHCb and the forthcoming Super-B experiments.Comment: 12 pages, 2 figures, typos removed, some modifications in content and the numerical results. To be published in Chinese Physics

Dichotomy in underdoped high TcT_c superconductors and spinon-dopon approach to tt-t′t'-t′′t''-JJ model

We studied underdoped high $T_c$ superconductors using a spinon-dopon approach (or doped-carrier approach) to $t$-$t'$-$t''$-$J$ model, where spinon carries spin and dopon carries both spin and charge. In this approach, the mixing of spinon and dopon describes superconductivity. We found that a nonuniform mixing in $k$-space is most effective in lowering the $t'$ and $t''$ hopping energy. We showed that at mean-field level, the mixing is proportional to quasiparticle spectral weight $Z_-$. We also found a simple monte-carlo algorithm to calculate $Z_{-}$ from the projected spinon-dopon wavefunction, which confirms the mean-field result. Thus the non-uniform mixing caused by $t'$ and $t"$ explains the different electron spectral weights near the nodal and anti-nodal points ({\it i.e.} the dichotomy) observed in underdoped high $T_c$ superconductors. For hole-doped sample, we found that $Z$ is enhanced in the nodal region and suppressed in the anti-nodal region. For electron doped sample, the same approach leads to a suppressed $Z$ in the nodal region and enhanced in the anti-nodal region, in agreement with experimental observations.Comment: 19 pages, 18 figure

Detecting topological orders through continuous quantum phase transition

We study a continuous quantum phase transition that breaks a $Z_2$ symmetry. We show that the transition is described by a new critical point which does not belong to the Ising universality class, despite the presence of well defined symmetry breaking order parameter. The new critical point arises since the transition not only break the $Z_2$ symmetry, it also changes the topological/quantum order in the two phases across the transition. We show that the new critical point can be identified in experiments by measuring critical exponents. So measuring critical exponents and identifying new critical points is a way to detect new topological phases and a way to measure topological/quantum orders in those phases.Comment: 4 pages, 7 figures, homepage http://dao.mit.edu/~we

Continuous quantum phase transitions beyond Landau's paradigm in a large-N spin model

We study a large-N generalization of $J_1$-$J_2$ Heisenberg model on square lattice -- an $Sp(2N)$ spin model. The possible quantum spin liquid phases of the $Sp(2N)$ model are studied using the SU(2) projective construction. We find several spin liquid states at least in large $N$ limit, which include SU(2) $\pi$-flux state, SU(2) chiral spin state and $Z_2$ spin liquid states. All those spin liquid states have non-trivial quantum orders. We show how projective symmetry group, which characterizes quantum order, protects the stability of even gapless spin liquids. We also study the continuous quantum phase transition from the SU(2) $\pi$-flux state to the SU(2) chiral spin liquid state, and from the SU(2) $\pi$-flux state to the $Z_2$ spin liquid state. We show that those phase transitions are beyond the paradigm of Landau symmetry-breaking theory. The first phase transition, although a $Z_2$ symmetry breaking transition, contains critical exponents that are different from those obtained from the Ginzburg-Landau theory of Ising universality class. The second transition does not even involve a change of symmetry and has no symmetry breaking order parameter.Comment: added citations, corrected minor typo

The semileptonic decays of B/BsB/B_s meson in the perturbative QCD approach: A short review

In this short review, we present the current status about the theoretical and experimental studies for some important semileptonic decays of $B/B_s$ mesons. We firstly gave a brief introduction for the experimental measurements for $B/B_s \to P (l^+l^-, l^-\bar{\nu}_l, \nu \bar{\nu})$ decays, the BaBar's $R(D)$ and $R(D^*)$ anomaly, the $P_5^\prime$ deviation for $B^0 \to K^{*0} \mu^+ \mu^-$ decay. We then made a careful discussion about the evaluations for the relevant form factors in the light-cone QCD sum rule (LCSRs), the heavy quark effective theory, and the perturbative QCD factorization approach. By using the form factors calculated in the perturbative (pQCD) approach, we then calculate and show the pQCD predictions for the decay rates of many semileptonic decays of $B/B_s$ mesons. We also made careful phenomenological analysis for these pQCD predictions and found, in general, the following points: (a) For all the considered $B/B_s$ semileptonic decays, the next-to-leading order (NLO) pQCD predictions for their decay rates agree well with the data and those from other different theoretical methods; (b) For $R(D)$ and $R(D^*)$, the pQCD predictions agree very well with the data, the BaBar's anomaly of $R(D^{(*)})$ are therefore explained successfully in the standard model by employing the pQCD approach; and (c) We defined several new ratios $R_D^{l,\tau}$ and $R_{D_s}^{l,\tau}$, they may be more sensitive to the QCD dynamics which controls the $B/B_s \to (D^{(*)},D_s^{(*)})$ transitions than the old ratios, we therefore strongly suggest LHCb and the forthcoming Super-B experiments to measure these new ratios.Comment: 23 pages, 3 figures and 7 tables. Some references are updated. Final version being published in Chinese Science Bulleti

Semileptonic decays B→D(∗)lνB \to D^{(*)} l\nu in the perturbative QCD factorization approach

In this paper, we study the $B \to D^{(*)} l^- \bar{\nu}_{\rm l}$ semileptonic decays and calculate the branching ratios ${\cal B}(B \to D^{(*)} l^- \bar{\nu}_{\rm l})$ and the ratios $R(D^{(*)})$ and $R_{\rm D}^{\rm l,\tau}$ by employing the perturbative QCD (pQCD) factorization approach. We find that (a) for $R(D)$ and $R(D^*)$ ratios, the pQCD predictions are $R(D)=0.430^{+0.021}_{-0.026}$, $R(D^*)=0.301 \pm 0.013$ and agree well with BaBar's measurements of $R(D^{(*)})$; (b) for the newly defined $R_{\rm D}^{\rm l}$ and $R_{\rm D}^{\rm \tau}$ ratios, the pQCD predictions are $R_{\rm D}^{\rm l} = 0.450^{+0.064}_{-0.051}$ and $R_{\rm D}^{\rm \tau} =0.642^{+0.081}_{-0.070}$, which may be more sensitive to the QCD dynamics of the considered semileptonic decays than $R(D^{(*)})$ and should be tested by experimental measurements.Comment: 13 pages, 2 ps figures, 3 tables. Final version published in Chinese Science Bulleti

Semileptonic decays B/B_s \to (\eta,\etar, G)(l^+l^-,l\bar{\nu},\nu\bar{\nu}) in the perturbative QCD approach beyond the leading order

In this paper we make a systematic study of the semileptonic decays B/B_s \to (\eta,\etar, G)(l^+l^-,l\bar{\nu},\nu\bar{\nu}) by employing the perturbative QCD (pQCD) factorization approach. The next-to-leading-order (NLO) contributions to the relevant form factors are included, and the ordinary $\eta$-\etar mixing scheme and the $\eta$-\etar-$G$ mixing scheme are considered separately, where $G$ denotes a pseudoscalar glueball. The numerical results and the phenomenological analysis indicate that (a) the NLO contributions to the relevant form factors provide 25% enhancement to the leading-order pQCD predictions for the branching ratios $Br(B^-\to \eta^{(')} l^-\bar{\nu}_l)$, leading to a good agreement between the predictions and the data; (b) for all considered decays, the pQCD results are basically consistent with those from other different theoretical models; (c) the pQCD predictions in the two considered mixing schemes agree well with each other within theoretical errors. The outcomes presented here can be tested by LHCb and forthcoming Super-$B$ experiments.Comment: 8 pages, 1 figure. Published in Phys.Rev. D87, 097501 (2013

Anatomy of B→Kη(′)B \to K \eta^{(\prime)} decays in different mixing schemes and effects of next-to-leading order contributions in the perturbative QCD approach

In this paper we perform a comprehensive study of the four B \to K \etap decays in the pQCD factorization approach. We calculate the CP-averaged branching ratios and CP-violating asymmetries of B \to K\etap decays in the ordinary $\eta$-\etar, the $\eta$-\etar-$G$, and the $\eta$-\etar-$G$-$\eta_c$ mixing schemes. Besides the full LO contributions, all currently known NLO contributions to B \to K \etap decays in the pQCD approach are taken into account. From our calculations and phenomenological analysis, we find the following. (a) The NLO contributions in general can provide significant enhancements to the LO pQCD predictions for the decay rates of the two B \to K \etar decays, around $70$ in magnitude, but result in relatively small changes to $Br(B \to K \eta)$. (b) Although the NLO pQCD predictions in all three considered mixing schemes agree well with the data within one standard deviation, those pQCD predictions in the $\eta$-\etar-$G$ mixing scheme provide the best interpretation for the measured pattern of Br(B \to K \etap): $Br(B^0 \to K^0 \eta) \approx 1.13\times 10^{-6}$, Br(B^0 \to K^0 \etar) \approx 66.5 \times 10^{-6}, $Br(B^\pm \to K^\pm \eta) \approx 2.36\times 10^{-6}$, and Br(B^\pm \to K^\pm \etar) \approx 67.3 \times 10^{-6}, which agree perfectly with the measured values. (c) The NLO pQCD predictions for the CP-violating asymmetries for the four considered decays are also in good consistent with the data. (d) The newly known NLO contribution to the relevant form factors \calm_{FF} can produce about a 20% enhancement to the branching ratios Br(B \to K \etar), which plays an important role in closing the gap between the pQCD predictions and the relevant data. (e) The general expectations about the relative strength of the LO and NLO contributions from different sources are examined and confirmed by explicit numerical calculations.Comment: 42 pages, 5 ps figure