Bosonic quantum field theories, even when regularized using a finite lattice, possess an infinite dimensional Hilbert space and, therefore, cannot be simulated in quantum computers with a finite number of qubits. A truncation of the Hilbert space is
then needed and the physical results are obtained after a double limit: one to remove the truncation and another to remove the regulator (the continuum limit). A simpler alternative is to find a model with a finite dimensional Hilbert space belonging to the same universality class as the continuum model (a qubitization), so only the space continuum limit is required. A qubitization of the $1+1$ dimensional asymptotically free $O(3)$ nonlinear $sigma$-model based on ideas of non-commutative geometry was previously proposed arXiv:1903.06577 and, in this paper, we provide evidence that it reproduces the physics of the $sigma$-model both in the infrared and the ultraviolet regimes.
We compute the overlap Dirac spectrum on three ensembles generated using 2+1 flavor domain wall fermions. The spectral density is determined up to $lambdasim$100 MeV with sub-percentage statistical uncertainty. The three ensembles have different latt
ice spacings and two of them have quark masses tuned to the physical point. We show that we can resolve the flavor content of the sea quarks and constrain their masses using the Dirac spectral density. We find that the density is close to a constant below $lambdale$ 20 MeV (but 10% higher than that in the 2-flavor chiral limit) as predicted by chiral perturbative theory ($chi$PT), and then increases linearly due to the strange quark mass. Using the next to leading order $chi$PT, one can extract the light and strange quark masses with $sim$20% uncertainties. Using the non-perturbative RI/MOM renormalization, we obtain the chiral condensates at $overline{textrm{MS}}$ 2 GeV as $Sigma=(260.3(0.7)(1.3)(0.7)(0.8) textrm{MeV})^3$ in the $N_f=2$ (keeping the strange quark mass at the physical point) chiral limit and $Sigma_0=(232.6(0.9)(1.2)(0.7)(0.8) textrm{MeV})^3$ in the $N_f=3$ chiral limit, where the four uncertainties come from the statistical fluctuation, renormalization constant, continuum extrapolation and lattice spacing determination. Note that {$Sigma/Sigma_0=1.40(2)(2)$ is much larger than 1} due to the strange quark mass effect.
We present the first lattice QCD calculation of the charm quark contribution to the nucleon electromagnetic form factors $G^c_{E,M}(Q^2)$ in the momentum transfer range $0leq Q^2 leq 1.4$ $rm GeV^2$. The quark mass dependence, finite lattice spacing
and volume corrections are taken into account simultaneously based on the calculation on three gauge ensembles including one at the physical pion mass. The nonzero value of the charm magnetic moment $mu^c_M=-0.00127(38)_{rm stat}(5)_{rm sys}$, as well as the Pauli form factor, reflects a nontrivial role of the charm sea in the nucleon spin structure. The nonzero $G^c_{E}(Q^2)$ indicates the existence of a nonvanishing asymmetric charm-anticharm sea in the nucleon. Performing a nonperturbative analysis based on holographic QCD and the generalized Veneziano model, we study the constraints on the $[c(x)-bar{c}(x)]$ distribution from the lattice QCD results presented here. Our results provide complementary information and motivation for more detailed studies of physical observables that are sensitive to intrinsic charm and for future global analyses of parton distributions including asymmetric charm-anticharm distribution.
The theory of finitely supported algebraic structures represents a reformulation of Zermelo-Fraenkel set theory in which every construction is finitely supported according to the action of a group of permutations of some basic elements named atoms. I
n this paper we study the properties of finitely supported sets that contain infinite uniformly supported subsets, as well as the properties of finitely supported sets that do not contain infinite uniformly supported subsets. For classical atomic sets, we study whether they contain or not infinite uniformly supported subsets.
A new algorithm is developed allowing the Monte Carlo study of a 1 + 1 dimensional theory in real time. The main algorithmic development is to avoid the explicit calculation of the Jacobian matrix and its determinant in the update process. This impro
vement has a wide applicability and reduces the cost of the update in thimble-inspired calculations from O(N^3) to less than O(N^2). As an additional feature, the algorithm leads to improved Monte Carlo proposals. We exemplify the use of the algorithm to the real time dynamics of a scalar {phi}^4 theory with weak and strong couplings.
We report a lattice QCD calculation of the strange quark contribution to the nucleons magnetic moment and charge radius. This analysis presents the first direct determination of strange electromagnetic form factors including at the physical pion mass
. We perform a model-independent extraction of the strange magnetic moment and the strange charge radius from the electromagnetic form factors in the momentum transfer range of $0.051 ,text{GeV}^2 lesssim Q^2 lesssim 1.31 ,text{GeV}^2 $. The finite lattice spacing and finite volume corrections are included in a global fit with $24$ valence quark masses on four lattices with different lattice spacings, different volumes, and four sea quark masses including one at the physical pion mass. We obtain the strange magnetic moment $G^s_M(0) = - 0.064(14)(09), mu_N$. The four-sigma precision in statistics is achieved partly due to low-mode averaging of the quark loop and low-mode substitution to improve the statistics of the nucleon propagator. We also obtain the strange charge radius $langle r_s^2rangle_E = -0.0043 (16)(14),$ $text{fm}^2$.
We introduce a stochastic sandwich method with low-mode substitution to evaluate the connected three-point functions. The isovector matrix elements of the nucleon for the axial-vector coupling $g_A^3$, scalar couplings $g_S^3$ and the quark momentum
fraction $langle xrangle_{u -d}$ are calculated with overlap fermion on 2+1 flavor domain-wall configurations on a $24^3 times 64$ lattice at $m_{pi} = 330$ MeV with lattice spacing $a = 0.114$ fm.
We use overlap fermions as valence quarks to calculate meson masses in a wide quark mass range on the $2+1$-flavor domain-wall fermion gauge configurations generated by the RBC and UKQCD Collaborations. The well-defined quark masses in the overlap fe
rmion formalism and the clear valence quark mass dependence of meson masses observed from the calculation facilitate a direct derivation of physical current quark masses through a global fit to the lattice data, which incorporates $O(a^2)$ and $O(m_c^4a^4)$ corrections, chiral extrapolation, and quark mass interpolation. Using the physical masses of $D_s$, $D_s^*$ and $J/psi$ as inputs, Sommers scale parameter $r_0$ and the masses of charm quark and strange quark in the $overline{rm MS}$ scheme are determined to be $r_0=0.465(4)(9)$ fm, $m_c^{overline{rm MS}}(2,{rm GeV})=1.118(6)(24)$ GeV (or $m_c^{overline{rm MS}}(m_c)=1.304(5)(20)$ GeV), and $m_s^{overline{rm MS}}(2,{rm GeV})=0.101(3)(6),{rm GeV}$, respectively. Furthermore, we observe that the mass difference of the vector meson and the pseudoscalar meson with the same valence quark content is proportional to the reciprocal of the square root of the valence quark masses. The hyperfine splitting of charmonium, $M_{J/psi}-M_{eta_c}$, is determined to be 119(2)(7) MeV, which is in good agreement with the experimental value. We also predict the decay constant of $D_s$ to be $f_{D_s}=254(2)(4)$ MeV. The masses of charmonium $P$-wave states $chi_{c0}, chi_{c1}$ and $h_c$ are also in good agreement with experiments.
We present a valence calculation of the electric polarizability of the neutron, neutral pion, and neutral kaon on two dynamically generated nHYP-clover ensembles. The pion masses for these ensembles are 227(2) MeV and 306(1) MeV, which are the lowest
ones used in polarizability studies. This is part of a program geared towards determining these parameters at the physical point. We carry out a high statistics calculation that allows us to: (1) perform an extrapolation of the kaon polarizability to the physical point; we find $alpha_K =0.269(43)times10^{-4}$fm$^{3}$, (2) quantitatively compare our neutron polarizability results with predictions from $chi$PT, and (3) analyze the dependence on both the valence and sea quark masses. The kaon polarizability varies slowly with the light quark mass and the extrapolation can be done with high confidence.
