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In this work, we study the weak decay between two heavy baryons $ \mathcal{B}_i(\frac{1}{2}^+)\to \mathcal{B}_f(\frac{3}{2}^+)$ in the light-front quark model where three-quark picture is employed for baryon. We derive general form of transition amplitude of $ \mathcal{B}_i(\frac{1}{2}^+)\to \mathcal{B}_f(\frac{3}{2}^+)$, and analyze two specific cases of transitions: the weak decays of single heavy baryon $\Sigma_{b} \to \Sigma_{c}^*$ and the decays of double-charmed baryon $\Xi_{cc}\to \Sigma_{c}^*(\Xi_{c}^*)$. We compute the hadronic form factors for the transitions and apply them to study the decay widths of the semi-leptonic $\mathcal B_i(\frac{1}{2}^+)\to\mathcal B_f(\frac{3}{2}^+) l\bar{\nu}_l$ and non-leptonic $\mathcal B_i(\frac{1}{2}^+)\to\mathcal B_f(\frac{3}{2}^+)M$. Previously we studied the transition $\Sigma_{b} \to \Sigma_{c}^*$ with the quark-diquark picture of baryon in the light-front quark model. Here we revisit this transition with three-quark picture of baryon. At the quark level, the transition $\Sigma_{b} \to \Sigma_{c}^*$ is induced by the $b\rightarrow c$ transition.The subsystem of the two unchanged light quarks which possesses definite and same spin in initial and final state can be viewed as a spectator, so the spectator approximation can be applied directly. For the weak decay of doubly charmed baryon $\Xi_{cc}$, a $c$ quark decays to a light quark $q_1$, so both the initial state $cc$ and final state $q_1q_2$ ($q_1$ and the original $q_2$ in initial state may be the same flavor quarks) which possess definite spin are no longer spectators. A rearrangement of quarks for initial and final states is adopted to isolate the unchanged subsystem $cq_2$ which can be viewed as the spectator approximately. Future measurements on these channels will constrain the nonperturbative parameter in the wavefunctions and test the model predictions., Comment: 20 pages, 6 figures and 10 tables

Correlated fluctuations in the activity of neural populations reflect the network's dynamics and connectivity. The temporal and spatial dimensions of neural correlations are interdependent. However, prior theoretical work mainly analyzed correlations in either spatial or temporal domains, oblivious to their interplay. We show that the network dynamics and connectivity jointly define the spatiotemporal profile of neural correlations. We derive analytical expressions for pairwise correlations in networks of binary units with spatially arranged connectivity in one and two dimensions. We find that spatial interactions among units generate multiple timescales in auto- and cross-correlations. Each timescale is associated with fluctuations at a particular spatial frequency, making a hierarchical contribution to the correlations. External inputs can modulate the correlation timescales when spatial interactions are nonlinear, and the modulation effect depends on the operating regime of network dynamics. These theoretical results open new ways to relate connectivity and dynamics in cortical networks via measurements of spatiotemporal neural correlations., Comment: 25 pages, 20 figures

Correlated activity fluctuations in the neocortex influence sensory responses and behavior. Neural correlations reflect anatomical connectivity but also change dynamically with cognitive states such as attention. Yet, the network mechanisms defining the population structure of correlations remain unknown. We measured correlations within columns in the visual cortex. We show that the magnitude of correlations, their attentional modulation, and dependence on lateral distance are explained by columnar On-Off dynamics, which are synchronous activity fluctuations reflecting cortical state. We developed a network model in which the On-Off dynamics propagate across nearby columns generating spatial correlations with the extent controlled by attentional inputs. This mechanism, unlike previous proposals, predicts spatially non-uniform changes in correlations during attention. We confirm this prediction in our columnar recordings by showing that in superficial layers the largest changes in correlations occur at intermediate lateral distances. Our results reveal how spatially structured patterns of correlated variability emerge through interactions of cortical state dynamics, anatomical connectivity, and attention., Noise correlations in the neocortex change dynamically with cognitive states. Here the authors show how heterogeneous spatial patterns of noise correlations emerge through interactions of cortical On-Off dynamics, connectivity, and attention.

Recently LHCb declared a new structure $X(6900)$ in the final state di-$J/\psi$ which is popularly regarded as a $cc$-$\bar c\bar c$ tetraquark state. %popularly. Within the Bethe-Salpeter (B-S) frame we study the possible $cc$-$\bar c\bar c$ bound states and the interaction between diquark ($cc$) and antidiquark ($\bar c\bar c$). In this work $cc$ ($\bar c\bar c$) is treated as a color anti-triplet (triplet) axial-vector so the quantum numbers of $cc$-$\bar c\bar c$ bound state are $0^+$, $1^+$ and $2^+$. Learning from the interaction in meson case and using the effective coupling we suggest the interaction kernel for diquark and antidiquark system. Then we deduce the B-S equations for different quantum numbers. Solving these equations numerically we find the spectra of some excited states can be close to the mass of $X(6900)$ when we assign appropriate values for parameter $\kappa$ introduced in the interaction (kernel).We also briefly calculate the spectra of $bb$-$\bar b\bar b$ bound states. Future measurement of $bb$-$\bar b\bar b$ state will help us to determine the exact form of effective interaction., Comment: 14 pages, two figures

Correlated activity fluctuations in neocortex influence sensory responses and behavior. Neural correlations reflect anatomical connectivity and change dynamically with cognitive states, such as attention. Yet, how anatomical connectivity and cognitive states define the population structure of correlations is not known. We measured correlations in single cortical columns and found that the magnitude of correlations, their attentional modulation and dependence on lateral distance are predicted by On-Off dynamics, synchronous fluctuations in population activity across cortical layers. We developed a network model, in which spatial connectivity correlates the On-Off dynamics across nearby columns. We show that attentional inputs modulate the spatial extent of On-Off dynamics, resulting in spatially non-uniform changes in correlations. We confirm this prediction in our columnar recordings by showing that attentional modulation of correlations depends on lateral distance. Our results reveal how heterogeneous spatial patterns of correlations arise from the connectivity and network dynamics during attention.

The lifetimes of doubly charmed hadrons are analyzed within the framework of the heavy quark expansion (HQE). Lifetime differences arise from spectator effects such as $W$-exchange and Pauli interference. The $\Xi_{cc}^{++}$ baryon is longest-lived in the doubly charmed baryon system owing to the destructive Pauli interference absent in the $\Xi_{cc}^+$ and $\Omega_{cc}^+$. In the presence of dimension-7 contributions, its lifetime is reduced from $\sim5.2\times 10^{-13}s$ to $\sim3.0\times 10^{-13}s$. The $\Xi_{cc}^{+}$ baryon has the shortest lifetime of order $0.45\times 10^{-13}s$ due to a large contribution from the $W$-exchange box diagram. It is difficult to make a precise quantitative statement on the lifetime of $\Omega_{cc}^+$. Contrary to $\Xi_{cc}$ baryons, $\tau(\Omega_{cc}^+)$ becomes longer in the presence of dimension-7 effects and the Pauli interference $\Gamma^{\rm int}_+$ even becomes negative. This implies that the subleading corrections are too large to justify the validity of the HQE. Demanding the rate $\Gamma^{\rm int}_+$ to be positive for a sensible HQE, we conjecture that the $\Omega_c^0$ lifetime lies in the range of $(0.75\sim 1.80)\times 10^{-13}s$. The lifetime hierarchy pattern is $\tau(\Xi_{cc}^{++})>\tau(\Omega_{cc}^+)>\tau(\Xi_{cc}^+)$ and the lifetime ratio $\tau(\Xi_{cc}^{++})/\tau(\Xi_{cc}^+)$ is predicted to be of order 6.7., Comment: 17 pages, 1 figure, version to appear in PRD. arXiv admin note: text overlap with arXiv:1807.00916

We analyze patterns of dynamical symmetry breaking in strongly coupled chiral gauge theories with direct-product gauge groups $G$. If the gauge coupling for a factor group $G_i \subset G$ becomes sufficiently strong, it can produce bilinear fermion condensates that break the $G_i$ symmetry itself and/or break other gauge symmetries $G_j \subset G$. Our comparative study of a number of strongly coupled direct-product chiral gauge theories elucidates how the patterns of symmetry breaking depend on the structure of $G$ and on the relative sizes of the gauge couplings corresponding to factor groups in the direct product., Comment: 25 pages, latex

We study asymptotically free chiral gauge theories with an $\mathrm{SU}(N)$ gauge group and chiral fermions transforming according to the antisymmetric rank-$k$ tensor representation, ${A}_{k}\ensuremath{\equiv}[k{]}_{N}$, and the requisite number, ${n}_{\overline{F}}$, of copies of fermions in the conjugate fundamental representation, $\overline{F}\ensuremath{\equiv}{\overline{[1]}}_{N}$, to render the theories anomaly-free. We denote these as ${A}_{k}\overline{F}$ theories. We take $N\ensuremath{\ge}2k+1$ so that ${n}_{\overline{F}}\ensuremath{\ge}1$. The ${A}_{2}\overline{F}$ theories form an infinite family with $N\ensuremath{\ge}5$, but we show that the ${A}_{3}\overline{F}$ and ${A}_{4}\overline{F}$ theories are only asymptotically free for $N$ in the respective ranges $7\ensuremath{\le}N\ensuremath{\le}17$ and $9\ensuremath{\le}N\ensuremath{\le}11$, and that there are no asymptotically free ${A}_{k}\overline{F}$ theories with $k\ensuremath{\ge}5$. We investigate the types of ultraviolet to infrared evolution for these ${A}_{k}\overline{F}$ theories and find that, depending on $k$ and $N$, they may lead to a non-Abelian Coulomb phase, or may involve confinement with massless gauge-singlet composite fermions, bilinear fermion condensation with dynamical gauge and global symmetry breaking, or formation of multifermion condensates that preserve the gauge symmetry. We also show that there are no asymptotically free, anomaly-free $\mathrm{SU}(N)$ ${S}_{k}\overline{F}$ chiral gauge theories with $k\ensuremath{\ge}3$, where ${S}_{k}$ denotes the rank-$k$ symmetric representation.

Whether molecular states indeed exist in nature has been disputed for a long time. Several new resonances have been observed in the recent experiments and they seem to be of exotic structures and some of them have been proposed to be molecular states. The very recent observation of $Z_b(10610)[(10608.4\pm 2.0)$ MeV] and $Z_b(10650)[(10653.2\pm 1.5)$ MeV] encourages the interpretation of multi-quark states. In the Beter-Salpeter (BS) approach, we study the possibility if two heavy mesons can form a molecular state by exchanging light mesons. Our results indicate that two heavy mesons can form an isospin singlet (I=0) bound state but cannot form an isospin triplet (I=1) when the contribution of $\sigma-$ exchange is reasonably small, i.e. as the coupling of $\sigma$ with mesons $g_{\sigma}$ takes the value given in previous literatures. Thus we conclude that the newly observed $Z_b(10610)$ should not be a molecular state, but a tetraquark state instead, at most, the fraction of the molecular state in the physical resonance $Z_b(10610)$ is tiny., Comment: 15 pages, 2 figures, an important reference added; Accepted by JHEP