Margarita García Pérez, Antonio González-Arroyo, Masanori Okawa
We present our preliminary results on the determination of the low lying meson spectrum for pure gauge theory in the large $N$ limit. Some results are also shown for the theory with two flavours of quarks in the adjoint representation.
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The lattice formulation of gauge theories in a renormalizable gauge is discussed. The formulation invokes a new phase diagram, and it may allow for a lattice definition of Chiral Gauge Theories.
$B$ Meson Matrix Elements from Various Heavy Quark Effective Theories
确定了重轻介子的各种性质，包括衰变常数、$B_{B}$参数和Isgur-Wise函数。重（底）夸克模拟静态，NRQCD和/或（固定速度）格点HQET有效理论，使用最佳涂抹源的“最大算子涂抹技术”。
The magnetic dipole polarizabilities of the vector $ρ^0$ and $ρ^{\pm}$ mesons in $SU(3)$ pure gauge theory are calculated in the article. Based on this the authors explore the contribution of the dipole magnetic polarizabilities to the tensor polarization of the vector mesons in external abelian magnetic field. The tensor polarization leads to the dilepton asymmetry observed in non-central heavy ion collisions and can be also estimated in lattice gauge theory.
We review recent progress in studying mesons within gauge/gravity duality, in the context of adding flavour degrees of freedom to generalizations of the AdS/CFT correspondence. Our main focus is on the `top-down approach' of considering models constructed within string theory. We explain the string-theoretical constructions in detail, aiming at non-specialists. These give rise to a new way of describing strongly coupled confining large N gauge gauge theories similar to large N QCD. In particular, we consider gravity dual descriptions of spontaneous chiral symmetry breaking, and compare with la…
Gauge theories with gauge group $SU(N)$ and quarks belonging to arbitrary representations of $SU(N)$ form a rich landscape of QCD-like theories, whose study can shed new light on the properties of confinement. Four cases are particularly worth of interest: quarks in the fundamental representation, quarks in the 2-indice (anti)symmetric representation and quarks in the adjoint representation. The last three corresponding QCD-like theories are equivalent at large-$N$ for bosonic observables: It is the orientifold equivalence. The behavior of the lightest vector meson mass versus $N$ has been stu…
We present a method for implementing gauge theories of chiral fermions on the lattice.
This paper has been withdrawn by the author.
In this thesis we study some non perturbative aspects of gauge theories. We give particular emphasis on the understanding of dual confinement of magnetic monopoles by using flux tube configurations.
We investigate the masses (ground state energies) of neutral pseudoscalar and vector meson in $SU(3)$ lattice gauge theory in strong abelian magnetic field. The energy of $ρ^0$ meson with zero spin projection $s_z=0$ on the axis of the external magnetic field decreases, while the energies with non-zero spins $s_z=-1$ and $+1$ increase with the field. The energy of $π^0$ meson decrease as a function of the magnetic field. We calculated the magnetic polarizabilities of pseudoscalar and vector mesons for lattice volume $18^4$. For $ρ^0$ with spin $|s_z|=1$ and $π^0$ meson the extrapolations to ze…
We calculate the relativistic six-meson scattering amplitude at low energy within the framework of QCD-like theories with $n$ degenerate quark flavors at next-to-leading order in the chiral counting. We discuss the cases of complex, real and pseudo-real representations, i.e. with global symmetry and breaking patterns $\text{SU}(n)\times\text{SU}(n)/\text{SU}(n)$ (extending the QCD case), $\text{SU}(2n)/\text{SO}(2n)$, and $\text{SU}(2n)/\text{Sp}(2n)$. In case of the one-particle-irreducible part, we obtain analytical expressions in terms of 10 six-meson subamplitudes based on the flavor and g…
Two-index SU(N) theories: QCD, Orientifolds, Super Yang-Mills, Lattice and Steven Weinberg's $ππ$ scattering legacy
本文回顾并改进了双指标 SU(N) 规范-费米子理论在获取 QCD、超杨-米尔斯大 N 真空与谱及介子散射信息中的应用，结合格点模拟推导 1/N^2 修正，并以此纪念 Weinberg，展示该理论自然容纳四夸克态以实现低能介子散射幺正化。
We calculated correlators of vector, axial and pseudoscalar currents in external strong abelian magnetic field according to SU(2) gluodynamics. The masses of neutral $ρ$ and $A$ mesons with various spin projections to the axis parallel to the external magnetic field B have been calculated. We found that the masses of neutral mesons with zero spin $s=0$ decrease in increasing magnetic field, while the masses of the $ρ$ and $A$ mesons with spin $s=\pm 1$ increase in the mentioned field. Also we performed extrapolation and renormalization of masses on the lattice.
Using holography, we study the low-lying mesonic spectrum of a range of asymptotically free gauge theories. First we revisit a simple top-down holographic model of QCD-like dynamics with predictions in the M_rho-M_pi plane. The meson masses in this model are in very good agreement with lattice gauge theory calculations in the quenched approximation. We show that the key ingredient for the meson mass predictions is the running of the anomalous dimension of the quark condensate, gamma. This provides an explanation for the agreement of holographic and quenched lattice gauge theory calculations. W…
Correlators of vector, axial and pseudoscalar currents have been calculated in external strong magnetic field in SU(2) gluodynamics on the lattice. Neutral $ρ$ and $A$ meson masses with a zero spin projection to the axis parallel to the external magnetic field $B$ are calculated. The mass of the neutral $ρ$ meson with zero spin decreases with increasing of the magnetic field for available values of the magnetic field $eB\lesssim 2-2.5\, \Gev^2$, such behavior is necessary for a condensation of $ρ$ mesons in a strong magnetic field.
Residual meson-meson interaction from lattice gauge simulation in a simple QED model
介子-介子系统的剩余相互作用是利用动量-时空关联矩阵的累积量展开计算的。累积展开用来定义渐近的或自由的介子-介子算符。有效相互作用的定义则基于完整（相互作用）和自由（非相互作用）时间相关矩阵的比较。本文将所提出的方法应用于一个简单的2+1维U（1）格点规范模型，使其具有约束性。费米子处理的交错计划。有效的相互作用表现出一个排斥的核心和吸引力在中间的相对距离。这些发现是一致的早期研究相同的模型，利用Lüscher的方法，散射相移直接获得。
We study hybrid mesons from the clover and improved gauge actions at $β=2.6$ on the anisotropic $12^3\times36$ lattice using our PC cluster. We estimate the mass of $1^{-+}$ light quark hybrid as well as the mass of the charmonium hybrid. The improvement of both quark and gluonic actions, first applied to the hybrid mesons, is shown to be more efficient in reducing the lattice spacing and finite volume errors.
We explore the masses of neutral and charged $ρ$ mesons in strong abelian magnetic field in $SU(3)$ gluodynamics. The behaviour of the ground state energy of these particles in the external magnetic field depends on its spin projection $s_z$ on the axis of external magnetic field. The masses of $ρ^0$ meson with $s_z=\pm 1$ increase with the field. The masses of $ρ^{\pm}$ mesons with zero spin also grow with the magnetic field. The ground state energies of $ρ^{-}$ meson with $s_z=-1$ and $ρ^{+}$ meson with $s_z=+1$ diminish as a function of the field, while the energies of $ρ^{+}$ meson with $s…
We report meson spectra obtained by using valence overlap fermion propagators generated on a background of 2+1 flavor domain wall fermion gauge configurations on 16^3 X 32, 24^3 X 64 and 32^3 X 64 lattices. We use many-to-all correlators with Z3 grid source and low eigenmode substitution which is efficient in reducing errors for the hadron correlators. The preliminary results on meson spectrum, a0 correlators, and charmonium hyperfine splitting for three sea quark masses are reported here.
SU(2) gauge theories with two quark flavours in the fundamental representation are among the most promising theories of composite dynamics describing the electroweak sector. Three out of five Goldstone bosons in these models become the longitudinal components of the W and Z bosons giving them mass. Like in QCD, we expect a spectrum of excitations which appear as resonances in vector boson scattering, in particular the vector resonance corresponding to the rho-meson in QCD. In this talk I will present the preliminary results of the first calculation of the rho-meson decay width in this theory, …
Some physical results in four dimensional large N gauge theories on a periodic torus are summarized.
A brief overview is given of recent progress in understanding the dynamics of hot gauge theories.
Contents: 1. Introduction, 2. Chiral gauge theories & the gauge anomaly, 3. The regularization problem, 4. Weyl fermions from 4+1 dimensions, 5. The Ginsparg-Wilson relation, 6. Gauge-invariant lattice regularization of anomaly-free theories.
Smeared Abelian and center gauges are introduced in pure non-Abelian lattice gauge theories. Popular Abelian and center gauges are limits of smeared gauges. Smeared gauges are also shown to be equivalent to Higgs theories. As a result, distributions and interactions of monopoles and vortices, which are objects responsible for confinement in pure gauge theories, can be studied by investigating classical solutions of Higgs theories.
A recently proposed formulation of chiral lattice gauge theories is reviewed, in which the locality and gauge invariance of the theory can be preserved if the fermion representation of the gauge group is anomaly-free.
Some general considerations on the problem of non-perturbative definition of Chiral Gauge Theories are presented.
Scalable Quantum Algorithm for Meson Scattering in a Lattice Gauge Theory
本研究针对(1+1)维Z2格点规范理论中介子散射的实时动力学模拟，开发了量子子空间展开技术构建高保真介子产生算符，并利用Givens旋转设计高效量子电路，为近期的量子器件提供了非变分且可扩展的模拟框架。
After an introduction in which we review the fundamental difficulty in constructing lattice chiral gauge theories, we summarize the analytic and numerical evidence that abelian lattice chiral gauge theories can be nonperturbatively constructed through the gauge-fixing approach. In addition, we indicate how we believe that the method may be extended to nonabelian chiral gauge theories.
We reconsider gauge-transformation properties in chiral gauge theories on the lattice observing all pertinent information and show that these properties are actually determined in a general way for any gauge group and for any value of the index. In our investigations we also clarify several related issues.
We show that gauge-transformation properties of correlation functions in chiral gauge theories on the finite lattice are determined in a general way.
Since the pioneering work of Eichten and Lane it has been known that the scale of the interactions responsible for the generation of the strange-quark mass in extended technicolor theories must, absent any "GIM-like" mechanism for suppressing flavor-changing neutral currents, be greater than of order 1000 TeV. In this note we point out that the constraint from the neutral D-meson system is now equally strong, implying that the charm quark mass must also arise from flavor dynamics at a scale this high. We then quantify the degree to which the technicolor condensate must be enhanced in order to …
Meson dynamics from locally exciting a particle-conserving $Z_2$ lattice gauge theory
该研究在一维粒子守恒$Z_2$格点规范理论中，通过局域高能激发表征禁闭介子的动力学特性，揭示线性禁闭下介子尺寸振荡、尺寸与速度的关联等规律，且该规律在强弱禁闭极限下均成立。
Light Scalar Meson and Decay Constant in SU(3) Gauge Theory with Eight Dynamical Flavors
本研究针对含8个近无质量狄拉克费米子的SU(3)近共形规范理论，通过分析格点计算的σ介子关联函数的有限体积效应，外推得到无限体积下σ及a0标量介子的质量与衰变常数。
Bethe-Salpeter Amplitudes and Density Correlations for Mesons with Wilson Fermions
研究了格点量子色动力学中介子的$q\bar q$ Bethe-Salpeter（BS）振幅的各种规范不变量定义，并与库仑和朗道规范BS振幅进行了比较.我们表明，规范不变BS振幅是相当广泛的使用“胖”规范链接（通过涂抹原晶格的链接）。给出了π介子波函数在非零动量下的洛伦兹收缩的定性证明。我们还计算了密度-密度相关，并讨论了从这些观测值中提取π介子电荷半径的局限性。最后，我们给出了$ρ$介子的BS振幅的偏振依赖性，并提取了$l=0$和$l=2$态的相对混合态，表明简单的类氢波函数提供了很好的拟合。
After an introduction in which we review the fundamental difficulty in constructing lattice chiral gauge theories, we discuss the analytic and numerical evidence that abelian lattice chiral gauge theories can be non-perturbatively constructed through the gauge-fixing approach. While a complete non-abelian extension is still under construction, we also show how fermion-number violating processes are realized in this approach.
We calculate the meson spectrum of the Sp(4) lattice gauge theory coupled to two fundamental flavours of dynamical Dirac fermions. We focus on some of the lightest (flavoured) spin-0 and spin-1 states. This theory provides an ultraviolet completion for composite Higgs models based upon the SU(4)/Sp(4) coset. We analyse the strongly coupled dynamics in isolation, without explicit coupling to the standard model. We carry out continuum extrapolations using dynamical ensembles generated at five different values of bare lattice coupling, and for several values of the bare fermion mass. We fit the r…
We address the problem of the gauge fixing versus Gribov copies in lattice gauge theories. For the Landau gauge, results show that a suitable combination of evolutionary algorithms with traditional steepest descent methods identifies the global maximum of the optimisation function. We discuss the performance of the combined algorithm on small cubic lattices for SU(2) and SU(3).
Using quenched chiral perturbation theory we compute meson correlation functions at finite volume and fixed gauge field topology. We also present the corresponding analytical predictions for the unquenched theory at fixed gauge field topology. These results can be used to measure the low-energy parameters of the chiral Langrangian from lattice simulations in volumes much smaller than one pion Compton wavelength.
We study the meson spectrum of the SU(2) gauge theory with two Wilson fermions in the fundamental representation. The theory unifies both Technicolor and composite Goldstone Boson Higgs models of electroweak symmetry breaking. We have calculated the masses of the lightest spin one vector and axial vector mesons. In addition, we have also obtained preliminary results for the mass of the lightest scalar (singlet) meson state. The simulations have been done with multiple masses and two different lattice spacings for chiral and continuum extrapolations. The spin one meson masses set lower limits f…
Chiral gauge theories on the lattice without gauge fixing?
本文讨论了格点上手征规范理论的非微扰表述的两种方案。在这两种情况下，规范化都破坏了规范对称性。我们的目标是对称性的动态恢复。如果规范对称性破缺不太严重，这个过程可能导致在连续极限中得到所需的手征规范理论。
We study Abelian monopole and vortex condensation in lattice pure gauge theories. Condensation is detected by means of a disorder parameter defined in terms of a gauge-invariant effective action introduced using the lattice Schrödinger functional. Dirac monopoles condense in the confined phase of U(1) lattice gauge theory. Abelian monopoles and Abelian vortices condense in the confined phase of SU(2) and SU(3) lattice gauge theories.
We have calculated the running coupling in SU(2), SU(3), and SU(4) gauge theories to see whether they have infrared fixed points. An infrared fixed point means no confinement: It means that the long-distance physics is conformal, without a mass scale and indeed without a particle spectrum. All these theories run slowly in perturbation theory, so a nonperturbative determination is interesting.
We give a completely general derivation revealing the precise origin and the quantitative effects of CP and T violations in chiral gauge theories on the lattice.
Semileptonic Decays of Heavy Mesons: A Status Report
我们目前的中间结果，我们正在进行的调查有关的半轻子衰变的重赝标介子的赝标和矢量介子。相应的形状因子进行评估，在几个动量和适当的组合，四个轻和四个重夸克，这是选择允许外推到B介子区域。为了获得清晰的基态信号，我们对夸克应用规范不变量“Wuppertal”涂抹。分析是基于32淬火规范配置的大小$24^3 \times 64$在$β=6.3$，威尔逊费米子。
We present our preliminary results of SO(2N) gauge theories, approaching the large-N limit. SO(2N) theories may help us to understand QCD at finite chemical potential since there is an orbifold equivalence between SO(2N) and SU(N) gauge theories at large-N and SO(2N) theories do not have the sign problem present in QCD. We consider the string tensions, mass spectra, and deconfinement temperatures in the SO(2N) pure gauge theories in 2+1 dimensions, comparing them to their corresponding SU(N) theories.
We investigate the dynamics of lattice gauge theories in an Abelian monopole background field. By means of the gauge-invariant lattice Schrodinger functional we study the Abelian monopole condensation in U(1) lattice gauge theory at zero temperature and in SU(3) lattice gauge theory at finite temperature.
We discuss the possible form of gluon and ghost propagators in the infrared region of Yang-Mills theory in the covariant gauge from the viewpoint of general principles of quantized gauge field theories.
Quenched Chiral Perturbation Theory for Heavy-light Mesons
建立了与π介子耦合的重轻介子的猝灭手征微扰理论，计算了对$f_B$，$f_{B_{s}}$，$B_B$和$B_{B_{s}}$的单圈手征对数修正.我们还计算了这些修正的“部分淬火”的理论。在这两种理论中，手征谱在手征极限上是发散的，这表明（部分）猝灭理论不应该被用来研究这个极限。将手征谱与QCD中的手征谱进行了比较，估计了（部分）猝灭引起的误差。通过形成合适的比率，我们可以减少估计中的不确定性。
The Bethe-Salpeter equation in QCD connects the gauge-dependent gluon and quark degrees of freedom with the gauge-invariant properties of mesons. We study the rho meson mass and decay constant for various versions of the gauge-dependent input functions discussed in the literature, which start to differ generically below the hadronic scale, and show qualitative different infrared behavior. We find that, once the gauge-dependent quark-gluon vertex is permitted to vary as well, the rho mass and decay constant is reproduced equally well for all forms investigated. A possible conclusion from this i…
We explore some aspects of $Sp(4)$ gauge theory with two fundamental fermions in the context of composite Goldstone Dark Matter. We present preliminary lattice results for the mass of the pseudoscalar iso-singlet meson $η'$ using unimproved Wilson fermions and the standard plaquette action. We find that the $η'$ is slightly heavier than the pseudoscalar non-singlets $π$ and lighter than the vector mesons $ρ$ for multiple ensembles with $m_π/m_ρ\geq 0.77$. This pattern is potentially relevant for Beyond the Standard Model physics model building. Furthermore, we show that for $N_f=1+1$ flavours …
In this talk I present the formalism we have used to analyze Lattice data on two meson systems by means of effective field theories. In particular I present the results obtained from a reanalysis of the lattice data on the $KD^{(*)}$ systems, where the states $D^*_{s0}(2317)$ and $D^*_{s1}(2460)$ are found as bound states of $KD$ and $KD^*$, respectively. We confirm the presence of such states in the lattice data and determine the contribution of the $KD$ channel in the wave function of $D^*_{s0}(2317)$ and that of $KD^*$ in the wave function of $D^*_{s1}(2460)$. Our findings indicate a large …
The stable hadronic bound states in a hidden new non-Abelian gauge sector provide interesting candidates for strongly-interacting Dark Matter (DM). A particular example are theories in which DM is made up of dark pions which set the DM relic abundance through self-annihilation. One of the simplest realizations is $Sp(4)_c$ gauge theory with two Dirac fermions. We discuss its mesonic multiplets for degenerate and non-degenerate fermions, construct a low-energy effective theory and present lattice results for the pseudoscalar mesons and vector mesons.
Thermal modifications of mesons and energy-energy correlators from real-time simulations of a $U(1)$ lattice gauge theory
本文通过实时模拟研究了 $U(1)$ 晶格规范理论中介子的热修改及能量流相关性，揭示了量子态中非平凡相关性的存在。
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