Leading Order Chiral Perturbation Theory Research Articles

Steady electric currents in magnetized QCD and their use for the equation of state

In this paper we study the emergence of steady electric currents in QCD as a response to a non-uniform magnetic background using lattice simulations with 2 + 1 quark flavors at the physical point, as well as leading-order chiral perturbation theory. Using these currents, we develop a novel method to determine the leading-order coefficient of the equation of state in a magnetic field expansion: the magnetic susceptibility of the QCD medium. We decompose the current expectation value into valence- and sea-quark contributions and demonstrate that the dominant contribution to the electric current is captured by the valence term alone, allowing for a comparably cheap determination of the susceptibility. Our continuum extrapolated lattice results for the equation of state confirm the findings of some of the existing studies in the literature, namely that the QCD medium behaves diamagnetically at low and paramagnetically at high temperatures.

Thermal QCD in a non-uniform magnetic background

Off-central heavy-ion collisions are known to feature magnetic fields with magnitudes and characteristic gradients corresponding to the scale of the strong interactions. In this work, we employ equilibrium lattice simulations of the underlying theory, QCD, involving similar inhomogeneous magnetic field profiles to achieve a better understanding of this system. We simulate three flavors of dynamical staggered quarks with physical masses at a range of magnetic fields and temperatures, and extrapolate the results to the continuum limit. Analyzing the impact of the field on the quark condensate and the Polyakov loop, we find non-trivial spatial features that render the QCD medium qualitatively different as in the homogeneous setup, especially at temperatures around the transition. In addition, we construct leading-order chiral perturbation theory for the inhomogeneous background and compare its prediction to our lattice results at low temperature. Our findings will be useful to benchmark effective theories and low-energy models of QCD for a better description of peripheral heavy-ion collisions.

Scattering of two and three physical pions at maximal isospin from lattice QCD

We present the first direct N_f=2 lattice QCD computation of two- and three-pi ^+ scattering quantities that includes an ensemble at the physical point. We study the quark mass dependence of the two-pion phase shift, and the three-particle interaction parameters. We also compare to phenomenology and chiral perturbation theory (ChPT). In the two-particle sector, we observe good agreement to the phenomenological fits in s- and d-wave, and obtain M_pi a_0 = -0.0481(86) at the physical point from a direct computation. In the three-particle sector, we observe reasonable agreement at threshold to the leading order chiral expansion, i.e. a mildly attractive three-particle contact term. In contrast, we observe that the energy-dependent part of the three-particle quasilocal scattering quantity is not well described by leading order ChPT.

I=3 Three-Pion Scattering Amplitude from Lattice QCD.

We analyze the spectrum of two- and three-pion states of maximal isospin obtained recently for isosymmetric QCD with pion mass M≈200 MeV in Hörz and Hanlon, [Phys. Rev. Lett. 123, 142002 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.142002]. Using the relativistic three-particle quantization condition, we find ∼2σ evidence for a nonzero value for the contact part of the 3π^{+} (I=3) scattering amplitude. We also compare our results to leading-order chiral perturbation theory. We find good agreement at threshold and some tension in the energy dependent part of the 3π^{+} scattering amplitude. We also find that the 2π^{+} (I=2) spectrum is fit well by an s-wave phase shift that incorporates the expected Adler zero.

Pion scattering in the isospin I=2 channel from elongated lattices

Pion-pion elastic scattering in the isospin I=2 channel is investigated in two-flavor dynamical lattice QCD. Six ensembles are used with lattices elongated in one of the spatial dimensions at two quark masses corresponding to a pion mass of 315 MeV and 226 MeV. The energy of the low-lying states below the inelastic threshold are extracted in each case using the standard variational method.The extracted finite-volume spectrum is fitted by the inverse amplitude method simultaneously for both quark masses and extrapolated thereafter to the physical point. The resulting phase-shifts and scattering length are compared with those from experiment, leading-order chiral perturbation theory and other lattice studies. Our calculations match the experimental results.

Light-Neutrino Exchange and Long-Distance Contributions to 0ν2β Decays: An Exploratory Study on ππ→ee.

We present an exploratory lattice QCD calculation of the neutrinoless double beta decay ππ→ee. Under the mechanism of light-neutrino exchange, the decay amplitude involves significant long-distance contributions. The calculation reported here, with pion masses m_{π}=420 and 140MeV, demonstrates that the decay amplitude can be computed from first principles using lattice methods. At unphysical and physical pion masses, we obtain that amplitudes are 24% and 9% smaller than the predication from leading order chiral perturbation theory. Our findings provide the lattice QCD inputs and constraints for effective field theory. A follow-on calculation with fully controlled systematic errors will be possible with adequate computational resources.

New spectrum of negative-parity doubly charmed baryons: Possibility of two quasistable states

The discovery of $\Xi_{cc}^{++}$ by the LHCb Collaboration triggers predictions of more doubly charmed baryons. By taking into account both the $P$-wave excitations between the two charm quarks and the scattering of light pseudoscalar mesons off the ground state doubly charmed baryons, a set of negative-parity spin-1/2 doubly charmed baryons are predicted already from a unitarized version of leading order chiral perturbation theory. Moreover, employing heavy antiquark-diquark symmetry the relevant low-energy constants in the next-to-leading order are connected with those describing light pseudoscalar mesons scattering off charmed mesons, which have been well determined from lattice calculations and experimental data. Our calculations result in a spectrum richer than that of heavy mesons. We find two very narrow $J^P=1/2^-$ $\Omega_{cc}^P$, which very likely decay into $\Omega_{cc}\pi^0$ breaking isospin symmetry. In the isospin-1/2 $\Xi_{cc}^P$ sector, three states are predicted to exist below 4.2~GeV with the lowest one being narrow and the other two rather broad. We suggest to search for the $\Xi_{cc}^{P}$ states in the $\Xi_{cc}^{++}\pi^-$ mode. Searching for them and their analogues are helpful to establish the hadron spectrum.

Casimir squared correction to the standard rotator Hamiltonian for the O(n) sigma-model in the delta-regime

In a previous paper we found that the isospin susceptibility of the O(n) sigma-model calculated in the standard rotator approximation differs from the next-to-next-to leading order chiral perturbation theory result in terms vanishing like 1/ℓ, for ℓ = Lt/L → ∞ and further showed that this deviation could be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant. Here we confront this expectation with analytic nonperturbative results on the spectrum in 2 dimensions, by Balog and Hegedüs for n = 3, 4 and by Gromov, Kazakov and Vieira for n = 4, and find good agreement in both cases. We also consider the case of 3 dimensions.

On the effect of excited states in lattice calculations of the nucleon axial charge

Excited-state contamination is one of the dominant uncertainties in lattice calculations of the nucleon axial-charge, gA. Recently published results in leading-order chiral perturbation theory (ChPT) predict the excited-state contamination to be independent of the nucleon interpolator and positive [1–3]. We reproduce these results using ChPT in infinite volume along with the Lellouch–Lüscher formalism to relate finite- and infinite-volume matrix elements. We then go beyond ChPT by using the experimentally determined Nπ scattering phase to estimate the correction due to the final-state interactions, both on the discrete energy levels and on the Lellouch–Lüscher factors. We find that, while individual Lellouch–Lüscher factors differ significantly, the overall effect on the excited-state contamination is small. However, empirical results from numerical lattice calculations show negative contamination (downward curvature), indicating that present-day calculations are not in the regime where the leading-order ChPT predictions apply. We show that, under plausible assumptions, one can reproduce the behavior of lattice correlators by postulating a sign change in the infinite-volume N→Nπ axial-vector transition amplitude roughly in the region of the Roper resonance. Improved data, either from experiment or from a lattice QCD calculation, would allow for a direct test of this postulate.

Equation of state of imbalanced cold matter from chiral perturbation theory

We study the thermodynamic properties of matter at vanishing temperature for non-extreme values of the isospin chemical potential and of the strange quark chemical potential. From the leading order pressure obtained by maximizing the static chiral Lagrangian density we derive a simple expression for the equation of state in the pion condensed phase and in the kaon condensed phase. We find an analytical expression for the maximum of the ratio between the energy density and the Stefan-Boltzmann energy density as well as for the isospin chemical potential at the peak both in good agreement with lattice simulations of quantum chromodynamics. We speculate on the location of the crossover from the Bose-Einstein condensate state to the Bardeen-Cooper-Schrieffer state by a simple analysis of the thermodynamic properties of the system. For $\mu_I \gtrsim 2 m_\pi$ the leading order chiral perturbation theory breaks down; as an example it underestimates the energy density of the system and leads to a wrong asymptotic behavior.

Finite-volume effects in the muon anomalous magnetic moment on the lattice

We investigate finite-volume effects in the hadronic vacuum polarization, with an eye toward the corresponding systematic error in the muon anomalous magnetic moment. We consider both recent lattice data as well as lowest-order, finite-volume chiral perturbation theory, in order to get a quantitative understanding. Even though leading-order chiral perturbation theory does not provide a good description of the hadronic vacuum polarization, it turns out that it gives a good representation of finite-volume effects. We find that finite-volume effects cannot be ignored when the aim is a few percent level accuracy for the leading-order hadronic contribution to the muon anomalous magnetic moment, even when using ensembles with $m_\pi L> 4$ and $m_\pi \sim 200$ MeV.

Non-perturbative test of the Witten-Veneziano formula from lattice QCD

We compute both sides of the Witten-Veneziano formula using lattice techniques. For the one side we perform dedicated quenched simulations and use the spectral projector method to determine the topological susceptibility in the pure Yang-Mills theory. The other side we determine in lattice QCD with $N_f=2+1+1$ dynamical Wilson twisted mass fermions including for the first time also the flavour singlet decay constant. The Witten-Veneziano formula represents a leading order expression in the framework of chiral perturbation theory and we also employ leading order chiral perturbation theory to relate the flavor singlet decay constant to the relevant decay constant parameters in the quark flavor basis and flavor non-singlet decay constants. After taking the continuum and the SU$(2)$ chiral limits we compare both sides and find good agreement within uncertainties.

Topological susceptibility and the sampling of field space in N f = 2 lattice QCD simulations

We present a measurement of the topological susceptibility in two flavor QCD. In this observable, large autocorrelations are present and also sizable cutoff effects have to be faced in the continuum extrapolation. Within the statistical accuracy of the computation, the result agrees with the expectation from leading order chiral perturbation theory.

Pion masses in two-flavor QCD with η condensation.

We investigate some aspects of two-flavor QCD with mu≠md at low energy, using the leading order chiral perturbation theory including anomaly effects. While nothing special happens at mu=0 for the fixed md≠0, the neutral pion mass becomes zero at two critical values of mu, between which the neutral pion field condenses, leading to a spontaneously CP broken phase, the so-called Dashen phase. We also show that the "topological susceptibility" in the chiral perturbation theory diverges at these two critical points. We briefly discuss a possibility that mu=0 can be defined by the vanishing the "topological susceptibility. We finally analyze the case of mu=md=m with θ=π, which is equivalent to mu=-md=-m with θ=0 by the chiral rotation. In this case, the η condensation occurs at small m, violating the CP symmetry spontaneously. Deep in the η condensation phase, three pions become Nambu-Goldstone bosons, but they show unorthodox behavior at small m that mπ2=O(m2), which, however, is shown to be consistent with the chiral Ward-Takahashi identities.

Decay of kaonium in a chiral approach

The decay of the K+K− hadronic atom kaonium is investigated non-perturbatively using meson–meson interaction amplitudes taken from leading order chiral perturbation theory in an approach adapted from that proposed by Oller and Oset (1997) [18]. The Kudryavtsev–Popov eigenvalue equation is solved numerically for the energy shift and decay width due to strong interactions in the 1s state. These calculations introduce a cutoff ∼1.4 GeV in O(4) momentum space that is necessary to regulate divergent loop contributions to the meson–meson scattering amplitudes in the strong-interaction sector. One finds lifetimes of (2.2±0.9)×10−18 s for the ground state of kaonium.

Fluctuations of the quark number and of the chiral condensate

The distributions of the quark number and chiral condensate over the gauge fields are computed for QCD in Euclidean space at nonzero quark chemical potential. As both operators are non-Hermitian the distributions are in the complex plane. Moreover, because of the sign problem, the distributions are not real and positive. The computations are carried out within leading order chiral perturbation theory and give a direct insight into the delicate cancellations that take place in contributions to the total baryon number and the chiral condensate.

Kaon condensation with lattice QCD

Kaon condensation may play an important role in the structure of hadronic matter at densities greater than that of nuclear matter, as exist in the interior of neutron stars. We present the results of the first lattice QCD investigation of kaon condensation obtained by studying systems containing up to 12 negatively charged kaons. Surprisingly, the properties of the condensate that we calculate are remarkably well reproduced by leading order chiral perturbation theory. In our analysis, we also determine the three-kaon interaction from the multi-kaon systems and update our results for pion condensates.

Proton lifetime bounds from chirally symmetric lattice QCD

We present results for the matrix elements relevant for proton decay in grand unified theories (GUTs). The calculation is performed at a fixed lattice spacing α -1 = 1.73(3) GeV using 2 + 1 flavors of domain-wall fermions on lattices of size 16 3 X 32 and 24 3 X 64 with a fifth dimension of length 16. We use the indirect method which relies on an effective field theory description of proton decay, where we need to estimate the low-energy constants, a = -0.0112(25) GeV 3 and β = 0.0120(26) GeV 3 . We relate these low-energy constants to the proton decay matrix elements using leading order chiral perturbation theory. These can then be combined with experimental bounds on the proton lifetime to bound parameters of individual GUTs.

Scalar form-factors fππ(Q2) and fKK(Q2) with light-cone QCD sum rules

In this paper, we calculate the scalar form-factors fππ(Q2) and fKK(Q2) in the framework of the light-cone QCD sum rules approach. The numerical value of fππ(Q2) changes quickly with the variation of Q2 near zero momentum transfer, while fKK(Q2) has a rather good behavior at small momentum transfer. The value fKK(0) = 2.21+0.35−0.19 GeV is compatible with the result from the leading order chiral perturbation theory. At large momentum transfer with Q2 > 6 GeV2, the form-factor fππ(Q2) takes up the asymptotic behavior approximately, while fKK(Q2) decreases more quickly than .

First Observation ofKL→π±e∓νe+e−

This Letter is the first report of the K L → π ± e ∓ ve + e - decay. Based on 19208 ± 144 events, we determine the branching fraction, B(K L → π ± e ∓ ve + e - ; M e + e - > 5MeV/c 2 , E * e + e - > 30 MeV) = (1.285 ± 0.041) X 10 -5 , and Γ(K e3ee ; M e + e - > 5 MeV/c 2 )/Γ(K e3 ) = [4.57 ± 0.04(stat) ± 0.14(syst)] X 10 -5 . This ratio agrees with a theoretical prediction based on chiral perturbation theory (ChPT) calculated to O(p 4 ). The measured kinematical distributions agree with those predicted by just ChPT O(p 4 ), but show significant disagreement with ones predicted by leading-order ChPT.