arXiv subjects

Chuan Liu

Publications and source records attributed to Chuan Liu.

At least 91 records · Page 5Linked to original sources

arXiv2018

Glueball spectrum from $N_f=2$ lattice QCD study on anisotropic lattices

The lowest-lying glueballs are investigated in lattice QCD using $N_f=2$ clover Wilson fermion on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion mass of $m_π\sim 938$ MeV and $650$ MeV. The quark mass dependence of the glueball masses have not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363(39) GeV and 2.384(67) GeV at $m_π\sim 938$ MeV and $650$ MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of $ε_{ijk}TrB_iD_jB_k$, we obtain the ground state mass to be 2.573(55) GeV and 2.585(65) GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter (around 1GeV) and compatible with the expected masses of the flavor singlet $q\bar{q}$ meson. This indicates that the operator $ε_{ijk}TrB_iD_jB_k$ and the topological charge density couple rather differently to the glueball states and $q\bar{q}$ mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which is close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be further clarified in the future.

hep-lat↗

arXiv2018

Three-particle bound states in a finite volume: unequal masses and higher partial waves

An explicit expression for the finite-volume energy shift of shallow three-body bound states for non-identical particles is obtained in the unitary limit. The inclusion of the higher partial waves is considered. To this end, the method of arXiv:1412.4969 (Meißner et al.) is generalized for the case of unequal masses and arbitrary angular momenta. It is shown that in the S-wave and in the equal mass limit, the result from arXiv:1412.4969 is reproduced.

hep-lat↗

arXiv2017

The $k_{R}$-property of free Abelian topological groups and products of sequential fans

A space $X$ is called a $k_{R}$-space, if $X$ is Tychonoff and the necessary and sufficient condition for a real-valued function $f$ on $X$ to be continuous is that the restriction of $f$ to each compact subset is continuous. In this paper, we discuss the $k_{R}$-property of products of sequential fans and free Abelian topological groups by applying the $κ$-fan introduced by Banakh. In particular, we prove the following two results: (1) The space $S_{ω_{1}}\times S_{ω_{1}}$ is not a $k_{R}$-space. (2) The space $S_ω\times S_{ω_{1}}$ is a $k_{R}$-space if and only if $S_ω\times S_{ω_{1}}$ is a $k$-space if and only if $\mathfrak b>ω_1$. These results generalize some well-known results on sequential fans. Furthermore, we generalize some results of Yamada on the free Abelian topological groups by applying the above results. Finally, we pose some open questions about the $k_{R}$-spaces.

math.GN↗

arXiv2017

The $k$-property and countable tightness of free topological vector spaces

The free topological vector space $V(X)$ over a Tychonoff space $X$ is a pair consisting of a topological vector space $V(X)$ and a continuous map $i=i_{X}: X\rightarrow V(X)$ such that every continuous mapping $f$ from $X$ to a topological vector space $E$ gives rise to a unique continuous linear operator $\overline{f}: V(X)\rightarrow E$ with $f=\overline{f}\circ i$. In this paper the $k$-property and countable tightness of free topological vector space over some generalized metric spaces are studied. The characterization of a space $X$ is given such that the free topological vector space $V(X)$ is a $k$-space or the tightness of $V(X)$ is countable. Furthermore, the characterization of a space $X$ is also provided such that if the fourth level of $V(X)$ has the $k$-property or is of the countable tightness then $V(X)$ is too.

math.GN↗

arXiv2017

The $k_{R}$-property on free topological groups

math.GR↗

arXiv2017

Investigating the topological structure of quenched lattice QCD with overlap fermions by using multi-probing approximation

The topological charge density and topological susceptibility are determined by multi-probing approximation using overlap fermions in quenched SU(3) gauge theory. Then we investigate the topological structure of the quenched QCD vacuum, and compare it with results from the all-scale topological density, the results are consistent. Random permuted topological charge density is used to check whether these structures represent underlying ordered properties. Pseudoscalar glueball mass is extracted from the two-point correlation function of the topological charge density. We study $3$ ensembles of different lattice spacing $a$ with the same lattice volume $16^{3}\times32$, the results are compatible with the results of all-scale topological charge density, and the topological structures revealed by multi-probing are much closer to all-scale topological charge density than that by eigenmode expansion.

hep-lat↗

arXiv2016

Review on Hadron Spectroscopy

I review some of the lattice results on spectroscopy and resonances in the past years. For the conventional hadron spectrum computations, focus has been put on the isospin breaking effects, QED effects, and simulations near the physical pion mass point. I then go through several single-channel scattering studies within Lüscher formalism, a method that has matured over the past few years. The topics cover light mesons and also the charmed mesons, with the latter case intimately related to the recently discovered exotic $XYZ$ particles. Other possible related formalisms that are available on the market are also discussed.

hep-lat↗

arXiv2016

The countable type properties in free paratopological groups

A space $X$ is of countable type (resp. subcountable type) if every compact subspace $F$ of $X$ is contained in a compact subspace $K$ that is of countable character (resp. countable pseudocharacter) in $X$. In this paper, we mainly show that: (1) For a functionally Hausdorff space $X$, the free paratopological group $FP(X)$ and the free abelian paratopological group $AP(X)$ are of countable type if and only if $X$ is discrete; (2) For a functionally Hausdorff space $X$, if the free abelian paratopological group $AP(X)$ is of subcountable type then $X$ has countable pseudocharacter. Moreover, we also show that, for an arbitrary Hausdorff $μ$-space $X$, if $AP_{2}(X)$ or $FP_{2}(X)$ is locally compact, then $X$ is homeomorphic to the topological sum of a compact space and a discrete space.

math.GR↗

arXiv2016

A Lattice Study of $(\bar{D}_1 D^{*})^\pm$ Near-threshold Scattering

In this exploratory lattice study, low-energy near threshold scattering of the $(\bar{D}_1 D^{*})^\pm$ meson system is analyzed using lattice QCD with $N_f=2$ twisted mass fermion configurations. Both s-wave ($J^P=0^-$) and p-wave ($J^P=1^+$) channels are investigated. It is found that the interaction between the two charmed mesons is attractive near the threshold in both channels. This calculation provides some hints in the searching of resonances or bound states around the threshold of $(\bar{D}_1 D^{*})^\pm$ system.

hep-lat↗

arXiv2016

Two Photon Decays of $η_c$ from Lattice QCD

We present an exploratory lattice study for the two-photon decay of $η_c$ using $N_f=2$ twisted mass lattice QCD gauge configurations generated by the European Twisted Mass Collaboration. Two different lattice spacings of $a=0.067$fm and $a=0.085$fm are used in the study, both of which are of physical size of 2$fm$. The decay widths are found to be $1.025(5)$KeV for the coarser lattice and $1.062(5)$KeV for the finer lattice respectively where the errors are purely statistical. A naive extrapolation towards the continuum limit yields $Γ\simeq 1.122(14)$KeV which is smaller than the previous quenched result and most of the current experimental results. Possible reasons are discussed.

hep-lat↗

arXiv2016

Two Weak Forms of Countability Axioms in Free Topological Groups

Given a Tychonoff space $X$, let $F(X)$ and $A(X)$ be respectively the free topological group and the free Abelian topological group over $X$ in the sense of Markov. For every $n\in\mathbb{N}$, let $F_{n}(X)$ (resp. $A_n(X)$) denote the subspace of $F(X)$ (resp. $A(X)$) that consists of words of reduced length at most $n$ with respect to the free basis $X$. In this paper, we discuss two weak forms of countability axioms in $F(X)$ or $A(X)$, namely the $csf$-countability and $snf$-countability. We provide some characterizations of the $csf$-countability and $snf$-countability of $F(X)$ and $A(X)$ for various classes of spaces $X$. In addition, we also study the $csf$-countability and $snf$-countability of $F_n(X)$ or $A_n(X)$, for $n=2, 3, 4$. Some results of Arhangel'ski\vı in \cite{A1980} and Yamada in \cite{Y1998} are generalized. An affirmative answer to an open question posed by Li et al. in \cite{LLL} is provided.

math.GR↗

arXiv2016

The $k$-spaces property of free Abelian topological groups over non-metrizable Lašnev spaces

Given a Tychonoff space $X$, let $A(X)$ be the free Abelian topological group over $X$ in the sense of Markov. For every $n\in\mathbb{N}$, let $A_n(X)$ denote the subspace of $A(X)$ that consists of words of reduced length at most $n$ with respect to the free basis $X$. In this paper, we show that $A_4(X)$ is a $k$-space if and only if $A(X)$ is a $k$-space for the non-metrizable Lašnev space $X$, which gives a complementary for one result of K. Yamada's. In addition, we also show that, under the assumption of $\flat=ω_1$, the subspace $A_3(X)$ is a $k$-space if and only if $A(X)$ is a $k$-space for the non-metrizable Lašnev space $X$. However, under the assumption of $\flat>ω_1$, we provide a non-metrizable Lašnev space $X$ such that $A_3(X)$ is a $k$-space but $A(X)$ is not a $k$-space.

math.GR↗

arXiv2016

Spectrum and Bethe-Salpeter amplitudes of $Ω$ baryons from lattice QCD

The $Ω$ baryons with $J^P=3/2^\pm, 1/2^\pm$ are studied on the lattice in the quenched approximation. Their mass levels are ordered as $M_{3/2^+}<M_{3/2^-}\approx M_{1/2^-}<M_{1/2^+}$, as is expected from the constituent quark model. The mass values are also close to those of the four $Ω$ states observed in experiments, respectively. We calculate the Bethe-Salpeter amplitudes of $Ω(3/2^+)$ and $Ω(1/2^+)$ and find there is a radial node for the $Ω(1/2^+)$ Bethe-Salpeter amplitude, which may imply that $Ω(1/2^+)$ is an orbital excitation of $Ω$ baryons as a member of the $(D,L_N^P)=(70,0_2^+)$ supermultiplet in the $SU(6)\bigotimes O(3)$ quark model description. Our results are helpful for identifying the quantum number of experimentally observed $Ω$ states.

hep-lat↗

arXiv2016

Twist-3 Contributions in Semi-Inclusive DIS with Transversely Polarized Target

We study semi-inclusive DIS with a transversely polarized target in the approach of collinear factorization. The effects related with the transverse polarization are at twist-3. We derive the complete result of twist-3 contributions to the relevant hadronic tensor at leading order of $α_s$, and construct correspondingly experimental observables. Measuring these observables will help to extract the twist-2 transversity distribution, twist-3 distributions and twist-3 fragmentation functions of the produced unpolarized hadron. A detailed comparison with the approach of transverse-momentum-dependent factorization is made.

hep-ph↗

arXiv2015

The topological properties of $q$-spaces in free topological groups

Given a Tychonoff space $X$, let $F(X)$ and $A(X)$ be respectively the free topological group and the free Abelian topological group over $X$ in the sense of Markov. In this paper, we provide some topological properties of $X$ whenever one of $F(X)$, $A(X)$, some finite level of $F(X)$ and some finite level of $A(X)$ is $q$-space (in particular, locally $ω$-bounded spaces and $r$-spaces), which give some partial answers to a problem posed in [11].

math.GR↗

arXiv2015

The mapping $i_{2}$ on the free paratopological groups

Let $FP(X)$ be the free paratopological group over a topological space $X$. For each non-negative integer $n\in\mathbb{N}$, denote by $FP_{n}(X)$ the subset of $FP(X)$ consisting of all words of reduced length at most $n$, and $i_{n}$ by the natural mapping from $(X\bigoplus X^{-1}\bigoplus\{e\})^{n}$ to $FP_{n}(X)$. In this paper, we mainly improve some results of A.S. Elfard and P. Nickolas's [On the topology of free paratopological groups. II, Topology Appl., 160(2013), 220--229.]. The main result is that the natural mapping $i_{2}: (X\bigoplus X_{d}^{-1}\bigoplus\{e\})^{2}\longrightarrow FP_{2}(X)$ is a closed mapping if and only if every neighborhood $U$ of the diagonal $Δ_{1}$ in $X_{d}\times X$ is a member of the finest quasi-uniformity on $X$, where $X$ is a $T_{1}$-space and $X_{d}$ denotes $X$ when equipped with the discrete topology in place of its given topology.

math.GR↗

arXiv2015

Phase transition in finite density and temperature lattice QCD

We investigate the behavior of the chiral condensate in lattice QCD at finite temperature and finite chemical potential. The study was done using two flavors of light quarks and with a series of $β$ and $ma$ at the lattice size $24\times12^{2}\times6$. The calculation was done in the Taylar expansion formalism. We are able to calculate the first and second order derivatives of $\langle\barψψ\rangle$ in both isoscalar and isovector channels. With the first derivatives being small, we find that the second derivatives are sizable close to the phase transition and the magnitude of $\barψψ$ decreases under the influence of finite chemical potential in both channels.

hep-lat↗

arXiv2015

Low-energy Scattering of $(D^{}\bar{D}^{})^\pm$ System and the Resonance-like Structure $Z_c(4025)$

In this paper, low-energy scattering of the $(D^{*}\bar{D}^{*})^\pm$ meson system is studied within Lüscher's finite-size formalism using $N_{f}=2$ twisted mass gauge field configurations. With three different pion mass values, the $s$-wave threshold scattering parameters, namely the scattering length $a_0$ and the effective range $r_0$, are extracted in $J^P=1^+$ channel. Our results indicate that, in this particular channel, the interaction between the two vector charmed mesons is weakly repulsive in nature hence do not support the possibility of a shallow bound state for the two mesons, at least for the pion mass values being studied. This study provides some useful information on the nature of the newly discovered resonance-like structure $Z_c(4025)$ observed in various experiments.

hep-lat↗