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Register a new userFirst direct lattice calculation of the chiral perturbation theory low-energy constant $ell_7$
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We evaluate by means of lattice QCD calculations the low-energy constant $ell_{7}$ which parametrizes strong isospin effects at NLO in $rm{SU}(2)$ chiral perturbation theory. Among all low-energy constants at NLO, $ell_{7}$ is the one known less precisely, and its uncertainty is currently larger than $50%$. Our strategy is based on the RM123 approach in which the lattice path-integral is expanded in powers of the isospin breaking parameter $Delta m= (m_{d}-m_{u})/2$. In order to evaluate the relevant lattice correlators we make use of the recently proposed rotated twisted-mass (RTM) scheme. Within the RM123 approach, it is possible to cleanly extract the value of $ell_{7}$ from either the pion mass splitting $M_{pi^{+}}-M_{pi^{0}}$ induced by strong isospin breaking at order $mathcal{O}left((Delta m)^{2}right)$ (mass method), or from the coupling of the neutral pion $pi^{0}$ to the isoscalar operator $left(bar{u}gamma_{5}u + bar{d}gamma_{5} dright)/sqrt{2}$ at order $mathcal{O}(Delta m)$ (matrix element method). In this pilot study we limit the analysis to a single ensemble generated by the Extended Twisted Mass Collaboration (ETMC) with $N_{f}=2+1+1$ dynamical quark flavours, which corresponds to a lattice spacing $asimeq 0.095~{rm fm}$ and to a pion mass $M_{pi}simeq 260~{rm MeV}$. We find that the matrix element method outperforms the mass method in terms of resulting statistical accuracy. Our determination, $ell_{7} = 2.5(1.4)times 10^{-3}$, is in agreement and improves previous calculations.
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We measure the pion mass and decay constant on ensembles generated by the Wuppertal-Budapest Collaboration, and extract the NLO low-energy constants l_3 and l_4 of SU(2) chiral perturbation theory. The data are generated in 2+1 flavor simulations with Symanzik glue and 2-fold stout-smeared staggered fermions, with pion masses varying from 135 MeV to 400 MeV, lattice scales between 0.7 GeV and 2.0 GeV, and m_s kept at its physical value. Furthermore, by excluding the lightest mass points, we are able to test the reliability of SU(2) chPT as a tool to extrapolate towards the physical point from higher pion masses.
We perform a detailed, fully-correlated study of the chiral behavior of the pion mass and decay constant, based on 2+1 flavor lattice QCD simulations. These calculations are implemented using tree-level, O(a)-improved Wilson fermions, at four values of the lattice spacing down to 0.054 fm and all the way down to below the physical value of the pion mass. They allow a sharp comparison with the predictions of SU(2) chiral perturbation theory (chi PT) and a determination of some of its low energy constants. In particular, we systematically explore the range of applicability of NLO SU(2) chi PT in two different expansions: the first in quark mass (x-expansion), and the second in pion mass (xi-expansion). We find that these expansions begin showing signs of failure around M_pi=300 MeV for the typical percent-level precision of our N_f=2+1 lattice results. We further determine the LO low energy constants (LECs), F=88.0 pm 1.3pm 0.3 and B^msbar(2 GeV)=2.58 pm 0.07 pm 0.02 GeV, and the related quark condensate, Sigma^msbar(2 GeV)=(271pm 4pm 1 MeV)^3, as well as the NLO ones, l_3=2.5 pm 0.5 pm 0.4 and l_4=3.8 pm 0.4 pm 0.2, with fully controlled uncertainties. We also explore the NNLO expansions and the values of NNLO LECs. In addition, we show that the lattice results favor the presence of chiral logarithms. We further demonstrate how the absence of lattice results with pion masses below 200 MeV can lead to misleading results and conclusions. Our calculations allow a fully controlled, ab initio determination of the pion decay constant with a total 1% error, which is in excellent agreement with experiment.
We present a comprehensive study of the electromagnetic form factor, the decay constant and the mass of the pion computed in lattice QCD with two degenerate O(a)-improved Wilson quarks at three different lattice spacings in the range 0.05-0.08fm and pion masses between 280 and 630MeV at m_pi L >~ 4. Using partially twisted boundary conditions and stochastic estimators, we obtain a dense set of precise data points for the form factor at very small momentum transfers, allowing for a model-independent extraction of the charge radius. Chiral Perturbation Theory (ChPT) augmented by terms which model lattice artefacts is then compared to the data. At next-to-leading order the effective theory fails to produce a consistent description of the full set of pion observables but describes the data well when only the decay constant and mass are considered. By contrast, using the next-to-next-to-leading order expressions to perform global fits result in a consistent description of all data. We obtain <r^2_pi>=0.481(33)(13)fm^2 as our final result for the charge radius at the physical point. Our calculation also yields estimates for the pion decay constant in the chiral limit, F_pi/F=1.080(16)(6), the quark condensate, Sigma^{1/3}_MSbar(2GeV)=261(13)(1)MeV and several low-energy constants of SU(2) ChPT.
We have performed fits of the pseudoscalar masses and decay constants, from a variety of RBC-UKQCD domain wall fermion ensembles, to $SU(2)$ partially quenched chiral perturbation theory at next-to leading order (NLO) and next-to-next-to leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to other lattice and phenomenological determinations. We discuss the size of successive terms in the chiral expansion and use our large set of low energy constants to make predictions for mass splittings due to QCD isospin breaking effects and the S-wave $pi pi$ scattering lengths. We conclude that, for the range of pseudoscalar masses explored in this work, $115~mathrm{MeV} lesssim m_{rm PS} lesssim 430~mathrm{MeV}$, the NNLO $SU(2)$ expansion is quite robust and can fit lattice data with percent-scale accuracy.
We study the scattering lengths of charmonia (J/psi and eta_c) with light hadrons (pi, rho and N) by the quenched lattice QCD simulations on 24x24x24x48, 32x32x32x48 and 48x48x48x48 lattices with the lattice spacing a = 0.068 fm. The scattering length is extracted by using the Luschers phase-shift formula together with the measurement of the energy shift Delta E of two hadrons on the lattice. We find that there exist attractive interactions in all channels, J/psi(eta_c)-pi, J/psi(eta_c)-rho and J/psi(eta_c)-N: The s-wave J/psi-pi (eta_c-pi) scattering length is determined as 0.0119+-0.0039 fm (0.0113+-0.0035 fm) and the corresponding elastic cross section at the threshold becomes 0.018+0.013-0.010 mb (0.016+0.011-0.008 mb). Also, the J/psi-N (eta_c-N) spin-averaged scattering length is 0.71+-0.48 fm (0.70+-0.66 fm), which is at least an order of magnitude larger than the charmonium-pion scattering length. The volume dependence of the energy shifts is also investigated to check the expected 1/L^3 behavior of Delta E at a large spatial size L.
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