The $D \bar{D}^*$ interaction via a $ρ$ or $ω$ exchange is constructed within an extended hidden gauge symmetry approach, where the strange quark is replaced by the charm quark in the $SU(3)$ flavor space. With this $D \bar{D}^*$ interaction, a bound state slightly lower than the $D \bar{D}^*$ threshold is generated dynamically in the isospin zero sector by solving the Bethe-Salpeter equation in the coupled-channel approximation, which might correspond to the $X(3872)$ particle announced by many collaborations. This formulism is also used to study the $B \bar{B}^*$ interaction, and a $B \bar{B}^*$ bound state with isospin zero is generated dynamically, which has no counterpart listed in the review of the Particle Data Group. Furthermore, the one-pion exchange between the $D$ meson and the $\bar{D}^*$ is analyzed precisely, and we do not think the one-pion exchange potential need be considered when the Bethe-Salpeter equation is solved.
The pentaquark $P_c^+(4450)$ recently discovered by LHCb has been interpreted as a bound state of $Ψ(2S)$ and nucleon. The charmonium-nucleon interaction which provides the binding mechanism is given, in the heavy quark limit, in terms of charmonium chromoelectric polarizabilities and densities of the nucleon energy-momentum tensor (EMT). In this work we show in model-independent way, by exploring general properties of the effective interaction, that $Ψ(2S)$ can form bound states with nucleon and $Δ$. Using the Skyrme model to evaluate the effective interaction in the large-$N_c$ limit and est…
In the paper, we construct eight color singlet-singlet type five-quark currents with distinguished isospins to study the $\bar{D}Ξ^{\prime}$, $\bar{D}Ξ_c^{*}$, $\bar{D}^{*}Ξ_c^{\prime}$ and $\bar{D}^{*}Ξ_c^{*}$ molecular states with strangeness via the QCD sum rules. Numerical results show that the central values of the pentaquark masses with higher (lower) isospin are slightly above (below) the thresholds of the corresponding meson-baryon pairs, and support assigning the $P_{cs}(4459)$ as the $\bar{D}Ξ_c^{*}$ molecular state with the quantum numbers $IJ^P=0{\frac{3}{2}}^-$. The other predicti…
We study the isospin amplitudes in the exclusive $B$ to $D^*\bar{D}K$ decay process and fit the available $D^{*0}\bar{D}^0$ invariant mass distributions near threshold. The analysis demonstrates that the production of the isospin triplet $D^*\bar{D}$ state is highly suppressed compared to the isospin singlet one. That explains why the $Z_c(3900)$ has not been found in $B$ decays. In addition, the production of the negative charge-parity state might be further suppressed in the heavy quark limit. These two reasons which are based on the molecular assumption offer the first explanation why the $…
In this article, we construct the color singlet-singlet type five-quark currents with the isospins $(I,I_3)=(\frac{1}{2},\frac{1}{2})$ and $(\frac{3}{2},\frac{1}{2})$ unambiguously to explore the $\bar{D}Σ_c$, $\bar{D}Σ_c^*$, $\bar{D}^*Σ_c$ and $\bar{D}^*Σ_c^*$ pentaquark states via the QCD sum rules for the first time, where the $\bar{D}$, $Σ_c$, $\cdots$ represent the color-singlet clusters having the same quantum numbers as the corresponding physical mesons or baryons. The numerical results support assigning the $P_c(4312)$, $P_c(4380)$, $P_c(4440)$ and $P_c(4457)$ as the $\bar{D}Σ_c$, $\ba…
The strong interactions among nucleons have an approximate spin-isospin exchange symmetry that arises from the properties of quantum chromodynamics in the limit of many colors, $N_c$. However this large-$N_c$ symmetry is well hidden and reveals itself only when averaging over intrinsic spin orientations. Furthermore, the symmetry is obscured unless the momentum resolution scale is close to an optimal scale that we call $Λ_{{\rm large-}N_c}$. We show that the large-$N_c$ derivation requires a momentum resolution scale of $Λ_{{\rm large-}N_c} \sim 500$ MeV. We derive a set of spin-isospin exchan…
The decay of $Λ_c^+$ into $π^+π^0Λ(1405)$ with the $Λ(1405)$ decay into $π^0Σ^0$ through a triangle diagram is studied. This process is initiated by $ Λ_c^+ \to π^+ \bar{K}^*N $, then the $\bar{K}^*$ decays into $\bar{K} π$ and $\bar{K} N$ produce the $Λ(1405)$ through a triangle loop containing $\bar{K}^*N\bar{K}$ which develops a singularity around $1890$ MeV. This process is prohibited by the isospin symmetry, but the decay into this channel is enhanced by the contribution of the triangle diagram, which is sensitive to the mass of the internal particles. We find a narrow peak in the $π^0Σ^0…
We present a study of the isospin-violating one-pion strong decays of single heavy tetraquarks $X_Q = X(s q \bar q \bar Q)$, $Q=c, b$, and $q=u, d$ with spin-parity $J^P = 0^+$. We assume that the tetraquarks have the configuration of a color diquark and a antidiquark. Three mechanisms of isospin violation can contribute to the decay rate: (1) mixing of the $X(s u \bar u \bar Q)$ and $X(s d \bar d \bar Q)$ tetraquark currents, (2) an explicit $m_d-m_u$ quark mass difference in the quark diagrams describing the corresponding decay transitions and (3) $π^0-η$ mixing in the final state. Our main …
In this paper, the electromagnetic mass differences of heavy hadrons are discussed, while ignoring the relevant hyperfine interactions. The effects of one-photon exchange interaction and up-down quark mass difference are parameterized. Two mass difference equations 2Σ_c^+ - (Σ_c^{++} + Σ_c^0) = 2Σ_b^0 - (Σ_b^+ + Σ_b^-) and (Ξ_{cc}^+ - Ξ_{cc}^{++}) + (Ξ_{bb}^- - Ξ_{bb}^{0}) =2(Ξ_{bc}^0 - Ξ_{bc}^{+}) for the heavy baryons are obtained. In addition, the masses of Σ_b^0, Ξ_b^0, and Ξ_{cc}^{++} are predicted based on the known experimental data.
我们分析了夸克凝聚和手征（标量）包括在有限温度$T$的同位旋破缺效应的兼容性。这些包括$m_u\neq m_d$的贡献以及电磁（$e\neq 0$）的修正，都在一个一致的手征拉格朗日框架中处理的SU（2）和SU（3）手征微扰理论的领先秩序，使我们的预测是模型无关的。从$<\bar q q>= <\bar u u + \bar d d >$中提取的手性恢复温度几乎不受影响，而对于三味情形SU（3），同位旋断裂序参量$<\bar u u - \bar d d >$随$T$增长。我们推导出一个求和规则的凝聚比$<\bar q q>(e\neq 0)/<\bar q q>(e=0)$与标量磁化率差$χ(T)-χ(0)$，直接测量的晶格。这种求和规则也适用于交错格点分析中凝聚态误差的估计。保持$m_u\neq m_d$允许获得的连接和断开的贡献的磁化率，即使在同位旋极限，其温度，质量和同位旋断裂的依赖性，我们详细分析。断开的部分线性增长，在手征（红外）极限为$T/M_π$发散，而连接的部分显示二次行为，红外规则为$T^2/M_η^2$和来自$π^0η$混合条款。这种光滑的连接行为表明，在转变温度附近的同位旋破缺关联弱于临界手征关联。我们探讨了一些后果与晶格数据和它们的标度特性，我们目前的分析物理质量，即超出手征极限，提供了一个有用的模型独立的描述低和中等温度。
A study of the meson-baryon interaction in the $S=-1$ sector is performed, employing a chiral SU(3) lagrangian up to next-to-leading order (NLO) and implementing unitarization in coupled channels. The model is constrained by a large set of experimental data, paying a especial attention to processes that are sensitive to the NLO contributions, such as the $K^- p\to K^+Ξ^-, K^0Ξ^0$ reactions. The consideration of additional cross sections in single isospin channels, $K^-p\to ηΛ, ηΣ$, has been found to provide more homogeneous and reliable values of the low-energy constants, the stability of whic…
In this paper we investigate the phase structure of a (1+1)-dimensional schematic quark model with four-quark interaction and in the presence of baryon ($μ_B$), isospin ($μ_I$) and chiral isospin ($μ_{I5}$) chemical potentials. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation (PC) one. The role and influence of this property on the phase structure of the model are studied. Moreover, it is shown that the chemical potential $μ_{I5}$ promotes th…
We have chosen the reactions $D_s^+ \to π^+ π^0 a_0(980) (f_0(980))$ investigating the isospin violating channel $D_s^+ \to π^+ π^0 f_0(980)$. The reaction was chosen because by varying the $π^0 a_0(980) (f_0(980))$ invariant mass one goes through the peak of a triangle singularity emerging from $D_s^+ \to π^+\bar K^* K$, followed by $\bar K^* \to \bar K π^0$ and the further merging of $K \bar K$ to produce the $a_0(980)$ or $f_0(980)$. We found that the amount of isospin violation had its peak precisely at the value of the $π^0 a_0(980) (f_0(980))$ invariant mass where the singularity has its…
In this work we extend our formalism to study meson-baryon interactions by including $s$- and $u$-channel diagrams for pseudoscalar-baryon systems. We study the coupled systems with strangeness $-1$ and focus on studying the isospin-1 resonance(s), especially in the energy region around 1400 MeV. By constraining the model parameters to fit the cross section data available on several processes involving relevant channels, we find resonances in the isoscalar as well as the isovector sector in the energy region around 1400 MeV.
We study the Kondo effect for a $Σ_{c}$ ($Σ_{c}^{\ast}$) baryon in nuclear matter. In terms of the spin and isospin ($\mathrm{SU}(2)_{\mathrm{spin}} \times \mathrm{SU}(2)_{\mathrm{isospin}}$) symmetry, the heavy-quark spin symmetry and the S-wave interaction, we provide the general form of the Lagrangian for a $Σ_{c}$ ($Σ_{c}^{\ast}$) baryon and a nucleon. We analyze the renormalization equation at the one-loop level, and find that the coexistence of spin exchange and isospin exchange magnifies the Kondo effect in comparison with the case where the spin-exchange interaction and the isospin-exc…
A hidden strongly-interacting sector is a possible candidate for dark matter. One scenario consistent with astrophysical constraints is a QCD-like theory with gauge group Sp(4) and two fundamental non-degenerate fermions. We report exploratory investigations of the light spectrum and decay constants for this theory using lattice calculations.
In this work, we tentatively identify the $P_{cs}(4338)$ as the $\bar{D}Ξ_c$ molecular state, and distinguish the isospins of the current operators to explore the $\bar{D}Ξ_c$, $\bar{D}Λ_c$, $\bar{D}_sΞ_c$, $\bar{D}_sΛ_c$, $\bar{D}^*Ξ_c$, $\bar{D}^*Λ_c$, $\bar{D}^*_sΞ_c$ and $\bar{D}^*_sΛ_c$ molecular states without strange, with strange and with double strange in the framework of the QCD sum rules in details. The present explorations favor identifying the $P_{cs}(4338)$ ($P_{cs}(4459)$) as the $\bar{D}Ξ_c$ ($\bar{D}^*Ξ_c$) molecular state with the spin-parity $J^P={\frac{1}{2}}^-$ (${\frac{3}…
Isospin splittings in baryons with two heavy quarks and a $u$ or $d$ quark are calculated using simple methods proposed previously by the authors. The results are $M(Ξ_{cc}^{++})-M(Ξ_{cc}^+) = 1.41 \pm 0.12^{+0.76}$ MeV, $M(Ξ_{bb}^0) - M(Ξ_{bb}^-) = - 4.78 \pm 0.06^{+0.03}$ MeV, and $M(Ξ_{bc}^+)-M(Ξ_{bc}^0)=-1.69 \pm0.07 ^{+0.39}$ MeV, where the statistical errors reflect uncertainties in input mass splittings, and the systematic errors are associated with the choice of constituent-quark masses.
We investigate the direct $CP$ violation for the decay process of $\bar{B}_{s}\rightarrow P(V)π^{0}$ (P,V refer to the pseudoscalar meson and vector meson, respectively) via isospin symmetry breaking effects from the $π^{0}-η-η'$ mixing mechanism in PQCD factorization approach. Isospin symmetry breaking arises from the electroweak interaction and the u-d quark mass difference by the strong interaction which are known to be tiny. However, we find that isospin symmetry breaking at the leading order shifts the $CP$ violation due to the new strong phases.
