Chiral Extrapolation Of Lattice Data Research Articles

Chiral Extrapolation of Lattice Data of Λb →Λc Form Factors

An extrapolation to the physical limit for the lattice data of Λb →Λc form factors computed in the nonphysical region is made in this work through a class of fitting functions proposed by us with nonlinear dependence on derived in the chiral perturbative theory (ChPT) and the heavy quark effective theory (HQET) framework. Then the results are applied to calculate the differential and integrated Λb →Λc semileptonic decay rates. Meanwhile, a comparison between our results and those obtained through the extrapolation functions with naive linear dependence on is made. It is shown that the difference between the extrapolated central values of these two cases is about 5%. The total uncertainties (depending on the momentum transfer q2) in the linear case are about 5% ∼ 10% (caused by the uncertainties of lattice data) and those in the nonlinear case are about 10% ∼ 20% (caused by the uncertainties of both lattice data and input parameters in ChPT and HQET). More accurate lattice data and parameters in ChPT and HQET are needed to reduce the uncertainties of the extrapolated results.

Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?

In recent years, many investigations of confining Yang Mills gauge theories near the edge of the conformal window have been carried out using lattice techniques. These studies have revealed that the spectrum of hadrons in nearly conformal ("walking") gauge theories differs significantly from the QCD spectrum. In particular, a light singlet scalar appears in the spectrum which is nearly degenerate with the PNGBs at the lightest currently accessible quark masses. This state is a viable candidate for a composite Higgs boson. Presently, an acceptable effective field theory (EFT) description of the light states in walking theories has not been established. Such an EFT would be useful for performing chiral extrapolations of lattice data and for serving as a bridge between lattice calculations and phenomenology. It has been shown that the chiral Lagrangian fails to describe the IR dynamics of a theory near the edge of the conformal window. Here we assess a linear sigma model as an alternate EFT description by performing explicit chiral fits to lattice data. In a combined fit to the Goldstone (pion) mass and decay constant, a tree level linear sigma model has a Χ2/d.o.f. = 0.5 compared to Χ2/d.o.f. = 29.6 from fitting nextto-leading order chiral perturbation theory. When the 0++ (σ) mass is included in the fit, Χ2/d.o.f. = 4.9. We remark on future directions for providing better fits to the σ mass.

Chiral corrections to the 1−+ exotic meson mass**Supported by National Natural Science Foundation of China (11222547, 11175073, 11575008) and 973 Program. XL is also supported by the National Youth Top-Level Talent Support Program (“Thousand Talents Scheme”).

We first construct the effective chiral Lagrangians for the 1−+ exotic mesons. With the infrared regularization scheme, we derive the one-loop infrared singular chiral corrections to the π1(1600) mass explicitly. We investigate the variation of the different chiral corrections with the pion mass under two schemes. Hopefully, the explicit non-analytical chiral structures will be helpful for the chiral extrapolation of lattice data from the dynamical lattice QCD simulation of either the exotic light hybrid meson or the tetraquark state.

Strange Quarks and Lattice QCD

The last few years have seen a dramatic improvement in our knowledge of the strange form factors of the nucleon. With regard to the vector from factors the level of agreement between theory and experiment gives us considerable confidence in our ability to calculate with non-perturbative QCD. The calculation of the strange scalar form factor has moved significantly in the last two years, with the application of new techniques which yield values considerably smaller than believed for the past 20 years. These new values turn out to have important consequences for the detection of neutralinos, a favourite dark matter candidate. Finally, very recent lattice studies have resurrected interest in the famed H-dibaryon, with modern chiral extrapolation of lattice data suggesting that it may be only slightly unbound. We review some of the major sources of uncertainty in that chiral extrapolation.

Chiral extrapolation of the strangeness changing scalar Kπ form factor

We perform a chiral extrapolation of lattice data on the scalar Kπ form factor and the ratio of the kaon and pion decay constants within Chiral Perturbation Theory to two loops. We determine the value of the scalar form factor at zero momentum transfer, at the Callan-Treiman point and at its soft kaon analog as well as its slope. Results are in good agreement with their determination from experiment using the standard couplings of quarks to the W boson. The slope is however rather large. A study of the convergence of the chiral expansion is also performed.

1/Nccorrections to the magnetic susceptibility of the QCD vacuum

We investigate the magnetic susceptibility of the QCD vacuum with the $1/{N}_{c}$ corrections taken into account, based on the instanton vacuum. Starting from the instanton liquid model, we derive the gauged light-quark partition function in the presence of the current quark mass as well as of external Abelian vector and tensor fields. We consider the $1/{N}_{c}$ meson-loop corrections which are shown to contribute to the magnetic susceptibility by around 15% for the up (and down) quarks. We also take into account the tensor terms of the quark-quark interaction from the instanton vacuum as well as the finite-width effects, both of which are of order $\mathcal{O}(1/{N}_{c})$. The effects of the tensor terms and finite width turn out to be negligibly small. The final results for the up-quarks are given as: $\ensuremath{\chi}⟨i{\ensuremath{\psi}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\psi}{⟩}_{0}\ensuremath{\simeq}35--40\text{ }\text{ }\mathrm{MeV}$ with the quark condensate $⟨i{\ensuremath{\psi}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\psi}{⟩}_{0}$. We also discuss the pion mass dependence of the magnetic susceptibility in order to give a qualitative guideline for the chiral extrapolation of lattice data.

The nucleon-nucleon potential beyond the static approximation

We point out that, due to the use of static nucleon propagators in Heavy-Baryon Chiral Perturbation Theory (HBχPT), the current calculations of the nucleon-nucleon potential miss certain contributions starting at two loops. These contributions give rise to contact interactions, which are both parametrically and numerically more important than the so-called NNLO potentials. They show a peculiar dependence on the light-quark masses, which should be taken into account when performing chiral extrapolations of lattice data. However, they do not appear to have an impact on phenomenology since they can be absorbed into redefinitions of unknown parameters which are usually fitted to data.

Chiral extrapolation of lattice data for B-meson decay constant

The B-meson decay constant fB has been calculated from unquenched lattice QCD in the unphysical region. For extrapolating the lattice data to the physical region, we propose a phenomenological functional form based on the effective chiral perturbation theory for heavy mesons, which respects both the heavy quark symmetry and the chiral symmetry, and the non-relativistic constituent quark model which is valid at large pion masses. The inclusion of pion loop corrections leads to non-analytic contributions to fB when the pion mass is small. The finite-range regularization technique is employed for the re-summation of higher-order terms of the chiral expansion. We also take into account the finite volume effects in lattice simulations. The dependence on the parameters and other uncertainties in our model are discussed.

Chiral corrections to the Roper mass☆☆This research is part of the EU Integrated Infrastructure Initiative Hadron Physics Project under contract number RII3-CT-2004-506078. Work supported in part by DFG (SFB/TR 16, “Subnuclear Structure of Matter”, and BO 1481/6-1) and by Canada's NSERC and CRC programs.

We analyze the quark mass dependence of the Roper mass to one-loop order in relativistic baryon chiral perturbation theory. The loop integrals are evaluated using infrared regularization which preserves chiral symmetry and establishes a chiral counting scheme. The derived chiral expansion of the Roper mass may prove useful for chiral extrapolations of lattice data. For couplings of natural size the quark mass dependence of the Roper mass is similar to the one of the nucleon.

Pion mass dependence of the nucleon mass in the chiral quark soliton model

The dependence of the nucleon mass on the mass of the pion is studied in the framework of the chiral quark-soliton model. A remarkable agreement is observed with lattice data from recent full dynamical simulations. The possibility and limitations to use the results from the chiral quark soliton model as a guideline for the chiral extrapolation of lattice data are discussed.

Chiral Extrapolation of Lattice Data for Heavy Meson Hyperfine Splittings

We investigate the chiral extrapolation of the lattice data for the light-heavy meson hyperfine splittings D^*-D and B^*-B to the physical region for the light quark mass. The chiral loop corrections providing non-analytic behavior in m_\pi are consistent with chiral perturbation theory for heavy mesons. Since chiral loop corrections tend to decrease the already too low splittings obtained from linear extrapolation, we investigate two models to guide the form of the analytic background behavior: the constituent quark potential model, and the covariant model of QCD based on the ladder-rainbow truncation of the Dyson-Schwinger equations. The extrapolated hyperfine splittings remain clearly below the experimental values even allowing for the model dependence in the description of the analytic background.

Chiral extrapolation of lattice data for heavy baryons

The masses of heavy baryons containing a b quark have been calculated numerically in lattice QCD with pion masses which are much larger than its physical value. In the present work we extrapolate these lattice data to the physical mass of the pion by applying the effective chiral Lagrangian for heavy baryons, which is invariant under chiral symmetry when the light quark masses go to zero and heavy quark symmetry when the heavy quark masses go to infinity. A phenomenological functional form with three parameters, which has the correct behavior in the chiral limit and appropriate behavior when the pion mass is large, is proposed to extrapolate the lattice data. It is found that the extrapolation deviates noticably from the naive linear extrapolation when the pion mass is smaller than about 500MeV. The mass differences between Sigma_b and Sigma_b^* and between Sigma_b^{(*)} and Lambda_b are also presented. Uncertainties arising from both lattice data and our model parameters are discussed in detail. We also give a comparision of the results in our model with those obtained in the naive linear extrapolations.

B0 — [formula omitted]0 mixing in two-flavor dynamical lattice QCD

We report on a calculation of the B meson decay constant and B parameters in two-flavor dynamical QCD. Sea quark effect on both quantities is examined by comparing with previous quenched results. The effect of chiral logarithms in the chiral extrapolation of lattice data is also investigated.

Chiral extrapolation of lattice data for the hyperfine splittings of heavy mesons

Hyperfine splittings between the heavy vector ${(D}^{*}{,B}^{*})$ and pseudoscalar $(D,B)$ mesons have been calculated numerically in lattice QCD, where the pion mass (which is related to the light quark mass) is much larger than its physical value. Naive linear chiral extrapolations of the lattice data to the physical mass of the pion lead to hyperfine splittings which are smaller than experimental data. In order to extrapolate these lattice data to the physical mass of the pion more reasonably, we apply the effective chiral perturbation theory for heavy mesons, which is invariant under chiral symmetry when the light quark masses go to zero and heavy quark symmetry when the heavy quark masses go to infinity. This leads to a phenomenological functional form with three parameters to extrapolate the lattice data. It is found that the extrapolated hyperfine splittings are even smaller than those obtained using linear extrapolation. We conclude that the source of the discrepancy between lattice data for hyperfine splittings and experiment must lie in non-chiral physics.