In this work, we use the Born-Oppenheimer approximation where the potential between atoms can be approximated as a function of distance between the two nuclei to study the four-quark bound states. By the approximation, Heitler and London calculated t
he spectrum of hydrogen molecule which includes two protons (heavy) and two electrons (light). Generally, the observed exotic mesons $Z_b(10610)$, $Z_b(10650)$, $Z_c(3900)$ and $Z_c(4020)$($Z_c(4025)$) may be molecular states made of two physical mesons and/or in diquark-anti-diquark structures. In analog to the Heitler-London method for calculating the mass of hydrogen molecule, we investigate whether there exist energy minima for these two structures. By contrary to the hydrogen molecule case where only the spin-triplet possesses an energy minimum, there exist minima for both of them. It implies that both molecule and tetraquark states can be stable objects. But since they have the same quantum numbers, the two states may mix to result in the physical states. A consequence would be that partner exotic states co-existing with $Z_b(10610)$, $Z_b(10650)$, $Z_c(3900)$ and $Z_c(4020)$($Z_c(4025)$) are predicted and should be experimentally observed.
Assuming the newly observed $Z_c(3900)$ to be a molecular state of $Dbar D^*(D^{*} bar D)$, we calculate the partial widths of $Z_c(3900)to J/psi+pi;; psi+pi;; eta_c+rho$ and $Dbar D^*$ within the light front model (LFM). $Z_c(3900)to J/psi+pi$ is th
e channel by which $Z_c(3900)$ was observed, our calculation indicates that it is indeed one of the dominant modes whose width can be in the range of a few MeV depending on the model parameters. Similar to $Z_b$ and $Z_b$, Voloshin suggested that there should be a resonance $Z_c$ at 4030 MeV which can be a molecular state of $D^*bar D^*$. Then we go on calculating its decay rates to all the aforementioned final states and as well the $D^*bar D^*$. It is found that if $Z_c(3900)$ is a molecular state of ${1oversqrt 2}(Dbar D^*+D^*bar D)$, the partial width of $Z_c(3900)to Dbar D^*$ is rather small, but the rate of $Z_c(3900)topsi(2s)pi$ is even larger than $Z_c(3900)to J/psipi$. The implications are discussed and it is indicated that with the luminosity of BES and BELLE, the experiments may finally determine if $Z_c(3900)$ is a molecular state or a tetraquark.
The successful operation of LHC provides a great opportunity to study the processes where heavy baryons are involved. {In this work we mainly study} the weak transitions of $Sigma_bto Sigma_c$. Assuming the reasonable quark-diquark structure where th
e two light quarks constitute an axial vector, we calculate the widths of semi-leptonic decay $Sigma_{b}toSigma_c e u_e$ and non-leptonic decay modes $Sigma_{b}toSigma_c +M$ (light mesons) in terms of the light front quark model. We first construct the vertex function for the concerned baryons and then deduce the form factors which are related to two Isgur-Wise functions for the $Sigma_{b}toSigma_c$ transition under the heavy quark limit. Our numerical results indicate that $Gamma(Sigma_{b}toSigma_c e u_e)$ is about $1.38times10^{10}{rm s}^{-1}$ and $Gamma(Sigma_{b}toSigma_c +M)$ is slightly below $1times10^{10}{rm s}^{-1}$ which may be accessed at the LHCb detector. By the flavor SU(3) symmetry we estimate the rates of $Omega_btoOmega_c$. We suggest to measure weak decays of $Omega_btoOmega_c$, because $Omega_b$ does not decay via strong interaction, the advantage is obvious.
We indicated in our previous work that for QED the role of the scalar potential which appears at the loop level is much smaller than that of the vector potential and in fact negligible. But the situation is different for QCD, one reason is that the l
oop effects are more significant because $alpha_s$ is much larger than $alpha$, and secondly the non-perturbative QCD effects may induce a sizable scalar potential. In this work, we phenomenologically study the contribution of the scalar potential to the spectra of charmonia, bottomonia and $bbar c(bar b c)$ family. Taking into account both vector and scalar potentials, by fitting the well measured charmonia and bottomonia spectra, we re-fix the relevant parameters and test them by calculating other states of not only the charmonia, bottomonia, but also further the $bbar c$ family. We also consider the Lamb shift of the spectra.
The Light-front quark model (LFQM) has been applied to calculate the transition matrix elements of heavy hadron decays. However, it is noted that using the traditional wave functions of the LFQM given in literature, the theoretically determined decay
constants of the $Upsilon(nS)$ obviously contradict to the data. It implies that the wave functions must be modified. Keeping the orthogonality among the $nS$ states and fitting their decay constants we obtain a series of the wave functions for $Upsilon(nS)$. Based on these wave functions and by analogy to the hydrogen atom, we suggest a modified analytical form for the $Upsilon(nS)$ wave functions. By use of the modified wave functions, the obtained decay constants are close to the experimental data. Then we calculate the rates of radiative decays of $Upsilon(nS)to eta_b+gamma$. Our predictions are consistent with the experimental data on decays $Upsilon(3S)to eta_b+gamma$ within the theoretical and experimental errors.
The mixing of $eta-eta$ or $eta-eta-G$ is of a great theoretical interest, because it concerns many aspects of the underlying dynamics and hadronic structure of pseudoscalar mesons and glueball. Determining the mixing parameters by fitting data is by
no means trivial. In order to extract the mixing parameters from the available processes where hadrons are involved, theoretical evaluation of hadronic matrix elements is necessary. Therefore model-dependence is somehow unavoidable. In fact, it is impossible to extract the mixing angle from a unique experiment because the model parameters must be obtained by fitting other experiments. Recently $BR(Dtoeta+bar l+ u_l)$ and $BR(D_stoeta(eta)+bar l+ u_l)$ have been measured, thus we are able to determine the $eta-eta$ mixing solely from the semileptonic decays of D-mesons where contamination from the final state interactions is absent. Thus we hope that the model-dependence of the extraction can be somehow alleviated. Once $BR(Dtoeta+bar l+ u_l)$ is measured, we can further determine all the mixing parameters for $eta-eta-G$. As more data are accumulated, the determination will be more accurate. In this work, we obtain the transition matrix elements of $D_{(s)}to eta^{(prime)}$ using the light-front quark model whose feasibility and reasonability for such processes have been tested.
In this work we calculate the branching ratios of semi-leptonic and non-leptonic decays of $Lambda_b$ into light baryons ($p$ and $Lambda$), as well as the measurable asymmetries which appear in the processes, in the light front quark model (LFQM). I
n the calculation, we adopt the diquark picture and discuss the justifiability of applying the picture in our case. Our result on the branching ratio of $Lambda_btoLambda+J/psi$ is in good agreement with data. More predictions are made in the same model and the results will be tested in the future experiments which will be conducted at LHCb and even ILC.
Only two isospin-singlet scalar mesons $f_0(600)$ ($sigma$) and $f_0(980)$ exist below 1 GeV, so that it is natural to suppose that they are two energy eigenstates which are mixtures of ${1oversqrt 2}(ubar u+dbar d)$ and $sbar s$. Is this picture rig
ht? Generally, it is considered that $f_0(600)$ mainly consists of ${1oversqrt 2}(ubar u+dbar d)$, if so, the dominant component of $f_0(980)$ should be $sbar s$. The recent measurement of the CLEO collaboration on the branching ratio of $D_sto f_0(980) e^+ u_e$ provides an excellent opportunity to testify the structure of $f_0(980)$, namely whether the data can be understood as long as it consists of mainly the conventional $qbar q$ structure. We calculate the form factors of $D_sto f_0(980)$ in the light-front quark model (LFQM) and the corresponding branching ratio of the semileptonic decay. By fitting the data, we obtain the mixing angle $phi$. The obtained mixing angle shows that the $sbar s$ component in $f_0(980)$ may not be dominant.
It has been suggested that the high symmetries in the Schrodinger equation with the Coulomb or harmonic oscillator potentials may remain in the corresponding relativistic Dirac equation. If the principle is correct, in the Dirac equation the potentia
l should have a form as ${(1+beta)over 2}V(r)$ where $V(r)$ is ${-e^2over r}$ for hydrogen atom and $kappa r^2$ for harmonic oscillator. However, in the case of hydrogen atom, by this combination the spin-orbit coupling term would not exist and it is inconsistent with the observational spectra of hydrogen atom, so that the symmetry of SO(4) must reduce into SU(2). The governing mechanisms QED and QCD which induce potential are vector-like theories, so at the leading order only vector potential exists. However, the higher order effects may cause a scalar fraction. In this work, we show that for QED, the symmetry restoration is very small and some discussions on the symmetry breaking are made. At the end, we briefly discuss the QCD case and indicate that the situation for QCD is much more complicated and interesting.
The recent measurement on the decay constant of $D_s$ shows a discrepancy between theory and experiment. We study the leptonic and semileptonic decays of $D$ and $D_s$ simultaneously within the standard model by employing a lightfront quark model. Th
ere is space by tuning phenomenological parameters which can explain the $f_{D_s}$ puzzle and do not contradict other experiments on the semileptonic decays. We also investigate the leptonic decays of D and $D_{s}$ with a new physics scenario, unparticle physics. The unparticle effects induce a constructive interference with the standard model contribution. The nontrivial phase in unparticle physics could produce direct CP violation which may distinguish it from other new physics scenarios.
