The chirally rotated Schroedinger functional provides a test bed for universality and automatic O(a) improvement. We here report on extensive quenched simulations of lattice QCD with Wilson quarks in the massless limit. We demonstrate that, after proper tuning of a dimension 3 boundary counterterm, the expected chirally rotated boundary conditions are indeed obtained. This implies automatic O(a) improvement which we then verify in a few examples. Universality of properly renormalized correlation functions is confirmed by comparing to the standard set-up of the Schroedinger functional. As a by-product of this study the non-singlet current renormalisation constants Z_A and Z_V are obtained from ratios of 2-point functions.
We study the curvature of the chiral transition/crossover line between the low-temperature hadronic phase and the high-temperature quark-gluon-plasma phase at low densities, performing simulations of two-flavor QCD with improved Wilson quarks. After confirming that the chiral order parameter defined by a Ward-Takahashi identity is consistent with the scaling of the O(4) universality class at zero chemical potential, we extend the scaling analysis to finite chemical potential to determine the curvature of the chiral transition/crossover line at low densities assuming the O(4) universality. To c…
Results on the thermal transition of QCD with 3 degenerate flavors, in the lower-left corner of the Columbia plot, are puzzling. The transition is expected to be first-order for massless quarks, and to remain so for a range of quark masses until it turns second-order at a critical quark mass. But this critical quark mass and resulting "pion" mass disagree violently between Wilson and staggered fermions at finite lattice spacing, and decrease sharply with the lattice spacing, for staggered fermions at least. To clarify this puzzle and eliminate potential systematic effects from rooting, we stud…
研究了规范固定到最大阿贝尔规范（MAG）后的阿贝尔投影SU（2）格点规范理论.为了检查阿贝尔优势的普遍性，我们采用蝌蚪改进树级（TI）的行动。我们表明，在最大的集群（IR组件）的单极子的密度是有限的连续极限，这是近似已经在相对较大的晶格间距。其值本身小于威尔逊作用的情况。我们目前的阿贝尔弦张力的比率的威尔逊和TI行动的晶格间距在0.06 fm < a < 0.35 fm的范围内的一些结果。这些结果表明，该比率是在0.9和0.95之间的所有考虑的值的晶格耦合和两个行动。我们比较了两种规范-在MAG和Laplacian阿贝尔规范（LAG）中的Oscillator集群的属性。而在MAG中的红外分量的电子密度表现出良好的收敛到连续极限，我们发现，在LAG中，它甚至不清楚是否存在一个有限的限制。
In this talk we determine the phase diagram and pion spectrum for Wilson and twisted-mass fermions in the presence of non-degeneracy between the up and down quark and discretization errors. We find that the CP-violating phase of the continuum theory, which occurs for sufficiently large non-degeneracy, is continuously connected to the Aoki phase found in the lattice theory with degenerate quarks. Both for the Aoki and first-order scenarios, this results in a critical surface along which at least one of the pions is massless. In the pion spectrum, we focus mainly on the untwisted case, where the…
We report on a two-flavour lattice QCD determination of the $B_s\to D_s$ and $B_s\to D_s^*$ transitions, which in the heavy quark limit can be parameterised by the form factors $\mathcal{G}$, and $h_{\text A_1}$, $h_{\text A_2}$ and $h_{\text A_3}$. In the search of New Physics through tests of lepton-flavour universality, $B_s$ decay channels are complementary to $B$ decays and widely studied at $B$ factories and LHCb. The purpose of our study is to explore a suitable method to extract form factors associated with $b\to c$ currents from lattice QCD. In particular, we present numerical results…
We determine non-perturbatively the normalisation constant Z_m*Z_P/Z_A as well as the Symanzik coefficients b_m and b_A-b_P, required in O(a) improved quark mass renormalisation with Wilson fermions. The strategy underlying their computation involves simulations in N_f=3 QCD with O(a) improved massless sea and non-degenerate valence quarks in the finite-volume Schroedinger functional scheme. Our results, which cover the typical gauge coupling range of large-volume N_f=2+1 QCD simulations with Wilson fermions at lattice spacings below 0.1 fm, are of particular use for the non-perturbative calcu…
Scaling behaviour at the $N_t=6$ chiral phase transition for 2-flavour lattice QCD with massless staggered quarks, and an irrelevant 4-fermion interaction
In this contribution, we report on our study of the properties of the Wilson flow and on the calculation of the topological susceptibility of $Sp(N_c)$ gauge theories for $N_c=2,\,4,\,6,\,8$. The Wilson flow is shown to scale according to the quadratic Casimir operator of the gauge group, as was already observed for $SU(N_c)$, and the commonly used scales $t_0$ and $w_0$ are obtained for a large interval of the inverse coupling for each probed value of $N_c$. The continuum limit of the topological susceptibility is computed and we conjecture that it scales with the dimension of the group. The …
We study the scaling properties of the finite temperature QCD phase transition, for light quark masses ranging from the heavy quark regime to their physical values. The lattice results are obtained in the fixed scale approach from simulations of $N_f=2+1+1$ flavours of Wilson fermions at maximal twist. We identify an order parameter free from the the linear contributions in mass due to additive renormalization and regular terms in the Equation of State, which proves useful for the assessment of the hypothesized universal behaviour. We find compatibility with the 3D $O(4)$ universality class fo…
We develop the $(1+1)$d lattice $U(1)$ gauge theory in order to define $2$-flavor massless Schwinger model, and discuss its connection with Haldane conjecture. We propose to use the central-branch Wilson fermion, which is defined by relating the mass, $m$, and the Wilson parameter, $r$, as $m+2r=0$. This setup gives two massless Dirac fermions in the continuum limit, and it turns out that no fine-tuning of $m$ is required because the extra $U(1)$ symmetry at the central branch, $U(1)_{\bar{V}}$, prohibits the additive mass renormalization. Moreover, we show that Dirac determinant is positive s…
A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for renormalizing the energy-momentum tensor on the lattice. In this paper, we utilize the Wilson flow to define a procedure to renormalize the energy-momentum tensor for a three-dimensional massless scalar field in the adjoint of $SU(N)$ with a $φ^4$ interaction on the lattice. In this theory the energy-momentum tensor can mix with $φ^2$ and we present numerical resu…
This is the second paper on hadronic wave functions in the light front formulation. We first consider only confinement effects, using the classical Nambu-Gotto string with massive end points in the light cone gauge. We derive the light-front Hamiltonian and show how to solve it, using an expansion in suitable basis functions. We next discuss the correlators of Wilson lines on the light front, leading to an effective Hamiltonian that includes spin effects. At the end, we consider a separate problem of instanton-induced interactions, at the origin of the pion as a massless Goldstone mode on the …
In the holographic approach to cosmology, cosmological observables are described in terms of correlators of a three-dimensional boundary quantum field theory. As a concrete model, we study the $3D$ massless $SU(N)$ scalar matrix field theory with a $ϕ^4$ interaction. On the lattice, the energy-momentum tensor (EMT) in this theory can mix with the operator $ϕ^2$. We utilize the Wilson Flow to renormalize the EMT on the lattice, and present numerical results for the mixing coefficient for $N = 2$. Obtaining the renormalized EMT will allow us to make predictions for the CMB power spectra in the r…
We critically analyze the body of results that hints to the existence of New Physics from possible violations of lepton universality observed by the LHCb experiment in the $μ/e$ ratios $R_{K}$ and $R_{K^*}$ to the $g-2$ lepton anomalies. The analysis begins with a theoretical, in depth, study of the $μ/e$ ratios $R_{K}$ and $R_{K^*}$ as well as the process $B_s \rightarrow μ^+ μ^-$. Here we consider the impact of complex Wilson coefficients and derive constraints on their imaginary and real parts. We then move to a comprehensive comparison with experimental results. We show that, by fitting a …
Universality of k-string Tensions from Holography and the Lattice
本文考虑SU（N）Yang-Mills理论中含有高阶表示夸克的大威尔逊圈。我们考虑具有共同N-度的表示，并检查威尔逊圈的期望值是否取决于特定表示或仅取决于N-度。在AdS/CFT的框架下，我们证明了：<W_R>= dim R exp -sigma_k A，即弦张力只依赖于N阶数k，而预指数因子依赖于表象.晶格强耦合展开在无限N下产生相同的结果，但在有限N下显示弦张力的表示依赖性，我们将此结果解释为人工制品。为了证实弦张力的表象独立性，我们重新分析了纯SU（N）Yang-Mills理论中涉及公共N度算子的晶格模拟结果。我们发现弦的张力与表象无关的图像被弦区的激发态谱所证实，而最低激发态似乎依赖于表象。我们认为，这一意外的结果是由于静态源的渐近行为是可见的距离不足，并给出了一个估计的距离以上，一个真正的代表独立的频谱应观察到。
