arXiv subjects

Frank X. Lee

Publications and source records attributed to Frank X. Lee.

At least 37 records · Page 2Linked to original sources

arXiv2021

Higher order quantization conditions for two spinless particles

Lattice QCD calculations of scattering phaseshifts and resonance parameters in the two-body sector are becoming precision studies. Early calculations employed Lüscher's formula for extracting these quantities at lowest order. As the calculations become more ambitious, higher-order relations are required. In this study we derive higher-order quantization conditions and introduce a method to transparently cross-check our results. This is an important step given the involved derivations of these formulae. We derive quantization conditions up to $\ell=5$ partial waves in both cubic and elongated geometries, and for states with zero and non-zero total momentum. All 45 quantization conditions we include here (22 in cubic box, 23 in elongated box) pass our cross-check test.

hep-lat↗

arXiv2021

Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD

Resonant hadronic systems often exhibit a complicated decay pattern in which three-body dynamics play a relevant or even dominant role. In this work we focus on the $a_1(1260)$ resonance. For the first time, the pole position and branching ratios of a three-body resonance are calculated from lattice QCD using one-, two-, and three-meson interpolators and a three-body finite-volume formalism extended to spin and coupled channels. This marks a new milestone for ab-initio studies of ordinary resonances along with hybrid and exotic hadrons involving three-body dynamics.

hep-lat↗

arXiv2021

Three-body interactions from the finite-volume QCD spectrum

We perform a fit of the finite-volume QCD spectrum of three pions at maximal isospin to constrain the three-body force. We use the unitarity-based relativistic three-particle quantization condition, with the GWUQCD spectrum obtained at 315 MeV and 220 MeV pion mass in two-flavor QCD. For the heavier pion mass we find that the data is consistent with a constant contact term close to zero, whereas for the lighter mass we see a statistically significant energy dependence in tension with the prediction of leading order ChPT. Our results also suggest that with enough three-body energy levels, the two-body amplitude could be constrained.

hep-lat↗

arXiv2021

Charged pion electric polarizability from lattice QCD

We present a calculation of the charged pion electric polarizability using the background field method. To extract the mass-shift induced by the electric field for the accelerated charged particle we fit the lattice QCD correlators using correlators derived from an effective model. The methodology outlined in this study (boundary conditions, fitting procedure, etc.) is designed to ensure that the results are invariant under gauge transformations of the background field. We apply the method to four $N_f=2$ dynamical ensembles to extract $α_{π^\pm}$ at pion mass of $315$ MeV.

hep-lat↗

arXiv2020

Finite-volume energy spectrum of the $K^-K^-K^-$ system

The dynamics of multi-kaon systems are of relevance for several areas of nuclear physics. However, even the simplest systems, two and three kaons, are hard to prepare and study experimentally. Here we show how to extract this information using first-principle lattice QCD results. We (1) extend the relativistic three-body quantization condition to the strangeness sector, predicting for the first time the excited level finite-volume spectrum of three kaon systems at maximal isospin, and (2) present a first lattice QCD calculation of the excited levels of this system in a finite box. We compare our predictions with the lattice results reported here and with previous ground state calculations and find very good agreement.

hep-lat↗

arXiv2020

Setting the scale for nHYP fermions with the Lüscher-Weisz gauge action

Lattice QCD calculations using gauge smearing for fermion kernels are computationally efficient. Hypercubic blocking (nHYP smearing) has been shown to reduce scaling errors. In this work we use an improved action for $N_f=2$ QCD, based on the Lüscher-Weisz gauge action and clover-improved Wilson fermions with nHYP smeared gauge links. We perform a parameter scan in the region with lattice spacing between $0.066 \mathop{\hbox{fm}}$ and $0.115 \mathop{\hbox{fm}}$ and pion mass between $207 \mathop{\hbox{MeV}}$ and $834 \mathop{\hbox{MeV}}$. We determine the lattice spacing and pion mass as a function of the bare coupling parameters ($β$ and $κ$). The results are obtained from twenty-two ensembles on a $24^3\times 48$ lattice to percent level in statistical accuracy. The finite-volume effects for these ensemble are at the sub-percent level. From these measurements we produce easy-to-use parameterizations to help tune simulations with this action. The lattice spacing is fixed using a mass-independent procedure, by matching observables in the chiral limit. We also provide a parameterization for the chiral extrapolation which is universal and should hold for all discretizations of $N_f=2$ QCD.

hep-lat↗

arXiv2020

Roper State from Overlap Fermions

The Roper state is extracted with valence overlap fermions on a $2+1$-flavor domain-wall fermion lattice (spacing $a = 0.114$ fm and $m_π = 330$ MeV) using both the Sequential Empirical Bayes (SEB) method and the variational method. The results are consistent, provided that a large smearing-size interpolation operator is included in the variational calculation to have better overlap with the lowest radial excitation. Similar calculations carried out for an anisotropic clover lattice with similar parameters find the Roper $\approx 280$ MeV higher than that of the overlap fermion. The fact that the prediction of the Roper state by overlap fermions is consistently lower than those of clover fermions, chirally improved fermions, and twisted-mass fermions over a wide range of pion masses has been dubbed a "Roper puzzle." To understand the origin of this difference, we study the hairpin $Z$-diagram in the isovector scalar meson ($a_0$) correlator in the quenched approximation. Comparing the $a_0$ correlators for clover and overlap fermions, at a pion mass of 290 MeV, we find that the spectral weight of the ghost state with clover fermions is smaller than that of the overlap at $a = 0.12$ fm and $0.09$ fm, whereas the whole $a_0$ correlators of clover and overlap at $a = 0.06$ fm coincide within errors. This suggests that chiral symmetry is restored for clover at $a \le 0.06$ fm and that the Roper should come down at and below this $a$. We conclude that this work supports a resolution of the "Roper puzzle" due to $Z$-graph type chiral dynamics. This entails coupling to higher components in the Fock space (e.g. $Nπ$, $Nππ$ states) to induce the effective flavor-spin interaction between quarks as prescribed in the chiral quark model, resulting in the parity-reversal pattern as observed in the experimental excited states of $N, Δ$ and $Λ$.

hep-ph↗

arXiv2019

A cross-channel study of pion scattering from lattice QCD

We use a chiral model for pion interactions, in the inverse amplitude formalism, to perform a simultaneous analysis of lattice QCD results for pion-pion scattering in all three isospin channels. The input is the finite-volume two-pion spectrum computed using lattice QCD from six ensembles on lattices elongated in one of the spatial dimensions. A two-flavor dynamical lattice QCD action is used with two quark masses corresponding to a pion mass of 315 MeV and 224 MeV. The spectrum in the elastic region is subjected to a global fit which takes into account full correlations across isospin, pion mass and decay constant. The parameters from the fit are used to perform a chiral extrapolation to the physical point. The cross-channel fit results in a more precise determination of the parameters of the model when compared with single channel fits. We obtain $m_πa_0^{I=0}=0.2132(9)$, and $m_πa_0^{I=2}=0.0433(2)$ as well as $m_σ=443(3)-i221(6)$ MeV and $m_ρ=724(4)-i67(1)$ MeV. Several aspects of scale setting and consistency with previous analyses of lattice QCD results are discussed as well.

hep-lat↗

arXiv2017

Scattering phaseshift formulas for mesons and baryons in elongated boxes

We derive Lüscher phaseshift formulas for two-particle states in boxes elongated in one of the dimensions. Such boxes offer a cost-effective way of varying the relative momentum of the particles. Boosted states in the elongated direction, which allow wider access to energies, are also considered. The formulas for the various scenarios (moving and zero-momentum states in cubic and elongated boxes) are compared and relations between them are clarified. The results are applicable to a wide set of meson-meson and meson-baryon elastic scattering processes, with the two-particle system having equal or unequal masses.

hep-lat↗

arXiv2015

Charm and strange quark masses and $f_{D_s}$ from overlap fermions

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 fermion 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 $J/ψ$ as inputs, Sommer's 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, $M_{J/ψ}-M_{η_c}$, 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 $χ_{c0}, χ_{c1}$ and $h_c$ are also in good agreement with experiments.

hep-lat↗

arXiv2014

Update on the sea contributions to hadron polarizabilities via reweighting

We have made significant progress on extending lattice QCD calculation of the polarizability of the neutron and other hadrons to include the effects of charged dynamical quarks. This is done by perturbatively reweighting the charges of the sea quarks to couple them to the background field. The dominant challenge in such a calculation is stochastic estimation of the weight factors, and we discuss the difficulties in this estimation. Here we use an extremely aggressive dilution scheme with N = 124,416 sources per configuration to reduce the stochastic noise to a manageable level. We find that α_E = 2.70(55) * 10^-4 fm^3 for the neutron on one ensemble. We show that low-mode substitution can be used in tandem with dilution to construct an even better estimator, and introduce the offdiagonal matrix element mapping technique for predicting estimator quality.

hep-lat↗

arXiv2014

Sea contributions to the electric polarizability of the hadrons

We present a lattice QCD calculation of the polarizability of the neutron and other neutral hadrons that includes the effects of the background field on the sea quarks. This is done by perturbatively reweighting the charges of the sea quarks to couple them to the background field. The main challenge in such a calculation is stochastic estimation of the weight factors, and we discuss the difficulties in this estimation. Here we use an extremely aggressive dilution scheme to reduce the stochastic noise to a manageable level. The pion mass in our calculation is 306 MeV and the lattice size is 3 fm. For neutron, we find that $α_E = 2.70(55) * 10^{-4}fm^3$, which is the most precise lattice QCD determination of the polarizability to date that includes sea effects.

hep-lat↗

arXiv2013

Update on the Sea Contributions to Hadron Electric Polarizabilities through Reweighting

We present the results of a reweighting calculation to compute the contribution of the charged quark sea to the neutron electric polarizability. The chief difficulty is the stochastic estimation of weight factors, and we present a hopping parameter expansion-based technique for reducing the stochastic noise, along with a discussion of why this particular reweighting is so difficult. We used this technique to estimate weight factors for 300 configurations of nHYP-clover fermions and compute the neutron polarizability, but the reweighting greatly inflates the overall statistical error, driven by the stochastic noise in the weight factors.

hep-lat↗

arXiv2012

A Problem in Particle Physics and Its Bayesian Analysis

There is a class of statistical problems that arises in several contexts, the Lattice QCD problem of particle physics being one that has attracted the most attention. In essence, the problem boils down to the estimation of an infinite number of parameters from a finite number of equations, each equation being an infinite sum of exponential functions. By introducing a latent parameter into the QCD system, we are able to identify a pattern which tantamounts to reducing the system to a telescopic series. A statistical model is then endowed on the series, and inference about the unknown parameters done via a Bayesian approach. A computationally intensive Markov Chain Monte Carlo (MCMC) algorithm is invoked to implement the approach. The algorithm shares some parallels with that used in the particle Kalman filter. The approach is validated against simulated as well as data generated by a physics code pertaining to the quark masses of protons. The value of our approach is that we are now able to answer questions that could not be readily answered using some standard approaches in particle physics. The structure of the Lattice QCD equations is not unique to physics. Such architectures also appear in mathematical biology, nuclear magnetic imaging, network analysis, ultracentrifuge, and a host of other relaxation and time decay phenomena. Thus, the methodology of this paper should have an appeal that transcends the Lattice QCD scenario which motivated us.

stat.ME↗

arXiv2011

Spin Polarizabilities on the Lattice

Spin polarizabilities provide information on the internal structure of hadrons in the presence of weak external electromagnetic fields, and are actively studied by Compton scattering experiments. They provide finer detail than the regular polarizabilities since they require space and time-varying fields. Using an effective action in the weak field limit, we have identified methods to isolate each of the physical quantities ($μ, α, β, γ_{E1}, γ_{M1}, γ_{E2}, γ_{M2}$) for spin-1/2 hadrons, both neutral and charged. We also perform a lattice QCD simulation to investigate the feasibility of the effective action approach.

hep-lat↗

arXiv2011

$ρ$ meson decay on asymmetrical lattices

We present a lattice QCD calculation of the characteristics of the $ρ$ meson decay. The study is carried out on spatially asymmetric boxes using nHYP-smeared clover fermions in the quenched approximation. The resonance mass and coupling constant are calculate using the P-wave scattering phaseshifts, of the isospin I=1 two-pion system. We use pion masses m_π= 418 MeV and m_π=312 MeV. In both cases, the $ρ$ decay is kinematically feasible. We work on lattice sizes N_z X 24^2 X 48 with lattice spacing a=0.1 fm and N_z=24,30,34,48.

hep-lat↗

arXiv2011

Efficient implementation of the overlap operator on multi-GPUs

Lattice QCD calculations were one of the first applications to show the potential of GPUs in the area of high performance computing. Our interest is to find ways to effectively use GPUs for lattice calculations using the overlap operator. The large memory footprint of these codes requires the use of multiple GPUs in parallel. In this paper we show the methods we used to implement this operator efficiently. We run our codes both on a GPU cluster and a CPU cluster with similar interconnects. We find that to match performance the CPU cluster requires 20-30 times more CPU cores than GPUs.

hep-lat↗

arXiv2011

Transition magnetic moment of $Λ$ $\to$ $Σ^0$ in QCD sum rules

The $Λ$ $\to$ $Σ^0$ transition magnetic moment is computed in the QCD sum rules approach. Three independent tensor structures are derived in the external field method using generalized interpolating fields. They are analyzed together with the $Λ$ and $Σ^0$ mass sum rules using a Monte-Carlo-based analysis, with attention to OPE convergence, ground-state dominance, and the role of the transitions in the intermediate states. Relations between sum rules for magnetic moments of $Λ$ and $Σ^0$ and sum rules for transition magnetic moment of $Λ$ $\to$ $Σ^0$ are also examined. Our best prediction for the transition magnetic moment is $μ_{Σ^0Λ}= 1.60\pm 0.07\; μ_N$. A comparison is made with other calculations in the literature.

hep-ph↗