arXiv subjects
Publications and source records attributed to C. B. Lang.
I discuss how masses and widths of hadron resonances are extracted from lattice QCD. Recent lattice results on the light, strange and charm meson resonances are reviewed. Their properties are revealed by simulating the corresponding scattering channels pi-pi, K-pi and D-pi on the lattice and extracting the scattering phase shifts. In particular we address the resonances rho, D0*(2400), D1(2430), K*, kappa and K0*(1430).
Results for the excited meson and baryon spectrum with two flavors of Chirally Improved sea quarks are presented. We simulate several ensembles with pion masses ranging from 250 to 600 MeV and extrapolate to the physical pion mass. Strange quarks are treated within the partially quenched approximation. Using the variational method, we investigate the content of the states. Among others, we discuss the flavor singlet/octet content of Lambda states. In general, our results compare well with experiment, in particular we get very good agreement with the Lambda(1405) and confirm its flavor singlet nature.
We study the coupled pion-nucleon system (negative parity, isospin 1/2) based on a lattice QCD simulation for nf=2 mass degenerate light quarks. Both, standard 3-quarks baryon operators as well as meson-baryon (4+1)-quark operators are included. This is an exploratory study for just one lattice size and lattice spacing and at a pion mass of 266 MeV. Using the distillation method and variational analysis we determine energy levels of the lowest eigenstates. Comparison with the results of simple 3-quark correlation studies exhibits drastic differences and a new level appears. A clearer picture of the negative parity nucleon spectrum emerges. For the parameters of the simulation we may assume elastic s-wave scattering and can derive values of the phase shift.
In a lattice QCD calculation with two light dynamical Chirally Improved (CI) quarks we determine ground state and some excited state masses in all four Lambda baryon channels 1/2^\pm and 3/2^\pm. We perform an infinite volume extrapolation and confirm the widely discussed Lambda(1405). We also analyze the amount of octet-singlet mixing, which is helpful in comparing states with the quark model.
We simulate K pi scattering in s-wave and p-wave for both isospins I=1/2, 3/2 using quark-antiquark and meson-meson interpolating fields. We extract the elastic phase shifts delta at several values of the K-pi relative momenta. The resulting phases exhibit qualitative agreement with the experimental phases in all four channels. We express the s-wave phase shifts near threshold in terms of the scattering length and the effective range. Our K pi system has zero total momentum and is simulated on a single ensemble with two dynamical quarks, so results apply for mpi=266 MeV and mK=552 MeV in our simulation. The backtracking contractions in both I=1/2 channels are handled by the use of Laplacian-Heavyside smeared quarks within the distillation method. Elastic phases are extracted from the energy levels using Luscher's relations. In all four channels we observe the expected K(n)pi(-n) scattering states, which are shifted due to the interaction. In both attractive I=1/2 channels we observe additional states that are related to resonances; we attribute them to K_0^*(1430) in s-wave and K*(892), K*(1410) and K*(1680) in p-wave.
Chiral symmetry breaking in Quantum Chromodynamics is associated with the low lying spectral modes of the Dirac operator according to the Banks-Casher relation. Here we study how removal of a variable number of low lying modes from the valence quark sector affects the masses of the ground states and first excited states of baryons and mesons in two flavor lattice QCD.
We study hadron correlators upon artificial restoration of the spontaneously broken chiral symmetry. In a dynamical lattice simulation we remove the lowest lying eigenmodes of the Dirac operator from the valence quark propagators and study evolution of the hadron masses obtained. All mesons and baryons in our study, except for a pion, survive unbreaking the chiral symmetry and their exponential decay signals become essentially better. From the analysis of the observed spectroscopic patterns we conclude that confinement still persists while the chiral symmetry is restored. All hadrons fall into different chiral multiplets. The broken U(1)_A symmetry does not get restored upon unbreaking the chiral symmetry. We also observe signals of some higher symmetry that includes chiral symmetry as a subgroup. Finally, from comparison of the Δ- N splitting before and after unbreaking of the chiral symmetry we conclude that both the color-magnetic and the flavor-spin quark-quark interactions are of equal importance.
We present results for the spectrum of light and strange mesons on configurations with two flavors of mass-degenerate Chirally Improved sea quarks. The calculations are performed on seven ensembles of lattice size 16^3x32 at three different gauge couplings and with pion masses ranging from 250 to 600 MeV. To reliably extract excited states, we use the variational method with an interpolator basis containing both gaussian and derivative quark sources. Both conventional and exotic channels up to spin 2 are considered. Strange quarks are treated within the partially quenched approximation. For kaons we investigate the mixing of interpolating fields corresponding to definite C-parity in the SU(3) limit. This enlarged basis allows for an improved determination of the low-lying kaon spectrum. In addition to masses we also extract the ratio of the pseudoscalar decay constants of the kaon and pion and obtain F_K/F_π=1.215(41). The results presented here include some ensembles from previous publications and the corresponding results supersede the previously published values.
We report lattice QCD results on the axial charges of ground and excited nucleon states of both parities. This is the first study of these quantities with approximately chiral (CI) fermions. Two energy levels in the range of the negative parity resonances N*(1535) and N*(1650) are observed and we determine the axial charge for both. We obtain a small axial charge for one of them, which is consistent with the chiral symmetry restoration in this state as well as with the small axial charge of the N*(1535) predicted within the quark model. This result agrees with the findings of Takahashi et al. obtained with Wilson quarks which violate chiral symmetry for finite lattice spacing. At the same time for the other observed negative parity state we obtain a large axial charge, that is close to the axial charge of the nucleon. This is in disagreement both with the quark model prediction as well as with the chiral restoration but allows for an interpretation as an s-wave π N state.
The excited isovector meson spectrum is explored using two chirally improved dynamical quarks. Seven ensembles, with pion masses down to \approx 250 MeV are discussed and used for extrapolations to the physical point. Strange mesons are investigated using partially quenched s-quarks. Using the variational method, we extract excited states in several channels and most of the results are in good agreement with experiment.
From the parton distributions in the infinite momentum frame one finds that only about 30% of the nucleon spin is carried by spins of the valence quarks, which gave rise to the term "spin crisis". Similar results hold for the lowest mesons, as it follows from the lattice simulations. We define the spin content of a meson in the rest frame and use a complete and orthogonal $\bar q q$ chiral basis and a unitary transformation from the chiral basis to the (2S+1)LJ basis. Then, given a mixture of different allowed chiral representations in the meson wave function at a given resolution scale, one can obtain its spin content at this scale. To obtain the mixture of the chiral representations in the meson we measure in dynamical lattice simulations a ratio of couplings of interpolarors with different chiral structure. For the rho meson we obtain practically the 3S1 state with no trace of the spin crisis. Then a natural question arises: which definition does reflect the spin content of a hadron?
We extract the P-wave pi-pi phase shift for five values of pion relative momenta, which gives information on the rho resonance. The Breit-Wigner formula describes the pi-pi phase shift dependence nicely and we extract m(rho)=792(7)(8) MeV and the coupling g_{ρππ}=5.13(20) at our mpi=266 MeV. We extract the P-wave scattering length a_{l=1}^{ππ}=0.082(10)(3) fm^3 from the state with the lowest pion relative momenta. We also determine the S-wave rho-pi phase shift for two values of relative momenta, which provides parameters of the lowest axial resonance a1(1260). Using the Breit-Wigner fit we extract m(a1)=1.44(4) GeV and the coupling g_{a_1ρπ}=1.1(3) GeV. From the lowest state we also extract the rho-pi scattering length a_{l=0}^{ρπ}=0.23(12) fm for our mpi. The simulation is performed using one Nf=2 ensemble of gauge configurations with clover-improved Wilson quarks. The phase shifts are determined from the lowest two energy-levels, which are obtained by the variational analysis with a number of quark-antiquark and meson-meson interpolators. The correlation functions are calculated using the distillation method with the Laplacian Heaviside (LapH) smearing of quarks.
The lowest eigenmodes of the Dirac operator are related to the dynamical breaking of the chiral symmetry in Quantum Chromodynamics (QCD). In our work we construct quark propagators which exclude a varying number of the lowest Dirac eigenmodes and study the influence thereof on meson correlators and the meson spectrum. That procedure partially restores the chiral symmetry (in the valence sector) and we observe degeneracies in the spectrum while confinement seems not to be affected.
We describe the method for extracting the elastic scattering phase shift from a lattice simulation at an introductory level, for non-lattice practitioners. We consider the scattering in a resonant channel, where the resulting phase shift delta(s) allows the lattice determination of the mass and the width of the resonance from a Breit-Wigner type fit. We present the method for the example of P-wave pi-pi scattering in the rho meson channel.
In Quantum Chromodynamics (QCD) the eigenmodes of the Dirac operator with small absolute eigenvalues have a close relationship to the dynamical breaking of the chiral symmetry. In a simulation with two dynamical quarks, we study the behavior of meson propagators when removing increasingly more of those modes in the valence sector, thus partially removing effects of chiral symmetry breaking. We find that some of the symmetry aspects are restored (e.g., the masses of $ρ$ and $a_1$ approach each other) while confining properties persist.
Using interpolators with different SU(2)_L \times SU(2)_R transformation properties we study the chiral symmetry and spin contents of the rho- and rho'-mesons in lattice simulations with dynamical quarks. A ratio of couplings of the $\qbarγ^iτq$ and $\qbarσ^{0i}τq$ interpolators to a given meson state at different resolution scales tells one about the degree of chiral symmetry breaking in the meson wave function at these scales. Using a Gaussian gauge invariant smearing of the quark fields in the interpolators, we are able to extract the chiral content of mesons up to the infrared resolution of ~1 fm. In the ground state rho meson the chiral symmetry is strongly broken with comparable contributions of both the (0,1) + (1,0) and (1/2,1/2)_b chiral representations with the former being the leading contribution. In contrast, in the rho' meson the degree of chiral symmetry breaking is manifestly smaller and the leading representation is (1/2,1/2)_b. Using a unitary transformation from the chiral basis to the {2S +1}L_J basis, we are able to define and measure the angular momentum content of mesons in the rest frame. This definition is different from the traditional one which uses parton distributions in the infinite momentum frame. The rho meson is practically a 3S_1 state with no obvious trace of a "spin crisis". The rho' meson has a sizeable contribution of the 3D_1 wave, which implies that the rho' meson cannot be considered as a pure radial excitation of the rho meson.
Gauge link smearing is widely used in lattice QCD computations. The idea is to remove the local (UV) fluctuations of the gauge field configurations while keeping the longer-range (IR) properties intact. Important applications are in the definitions of interpolating hadron operators as well as in updating the gauge field configurations with dynamical quarks in the so-called Hybrid Monte Carlo (HMC) algorithm. Here we study the effectiveness of various smearing methods and try to quantify these with tools known from Monte Carlo Renormalization Group (MCRG).
Results of hadron spectroscopy with two dynamical mass-degenerate chirally improved quarks are presented. Three ensembles with pion masses of 322(5), 470(4) and 525(7) MeV, lattices of size 16^3 \times 32, and lattice spacings close to 0.15 fm are investigated. We discuss the possible appearance of scattering states, considering masses and eigenvectors. Partially quenched results in the scalar channel suggest the presence of a 2-particle state, however, in most channels we cannot identify them. Where available, we compare to results from quenched simulations using the same action.