Search

This review is devoted to summarizing recent developments of the linear sigma model (LSM) in cold and dense two-color QCD (QC2D), in which lattice simulations are straightforwardly applicable thanks to the disappearance of the sign problem. In QC2D, both theoretical and numerical studies derive the presence of the so-called baryon superfluid phase at a sufficiently large chemical potential ( μ q ), where diquark condensates govern the ground state. The hadron mass spectrum simulated in this phase shows that the mass of an iso-singlet ( I = 0 ) and 0 − state is remarkably reduced, but such a mode cannot be described by the chiral perturbation theory. Motivated by this fact, I have invented a LSM constructed upon the linear representation of chiral symmetry, more precisely Pauli–Gürsey symmetry. It is shown that my LSM successfully reproduces the low-lying hadron mass spectrum in a broad range of μ q simulated on the lattice. As applications of the LSM, topological susceptibility and sound velocity in cold and dense QC2D are evaluated to compare with the lattice results. Additionally, the generalized Gell–Mann–Oakes–Renner relation and hardon mass spectrum in the presence of a diquark source are analyzed. I also introduce an extended version of the LSM incorporating spin-1 hadrons. [ABSTRACT FROM AUTHOR]

In their seminal work, Lellouch and Lüscher derived a conversion factor relating a finite-volume matrix element, calculable using numerical lattice QCD, with the infinite-volume decay amplitude for K → ππ. The conversion factor depends on the ππ → ππ scattering amplitude with the same total isospin as the decay channel (either zero or two). Although an infinite tower of ππ → ππ partial-wave components affect the conversion factor, the S-wave (ℓ = 0) component is expected to dominate, and only this contribution is included in the well-known Lellouch-Lüscher factor, with other ππ → ππ partial-wave amplitudes formally set to zero. However, as the precision of lattice calculations increases, it may become important to assess the systematic uncertainty arising from this approximation. With this motivation, we compare the S-wave-only results with those truncated at the next contaminating partial wave: the G-wave (ℓ = 4) for zero total momentum in the finite-volume frame and the D-wave (ℓ = 2) otherwise. Using the general framework for 1 → J 2 transitions derived in ref. [1], we quantify the effect of higher partial waves for systems with zero and non-zero total momentum as well as with anti-periodic boundary conditions, presenting both generic numerical examples and results for realistic ππ amplitudes taken from chiral perturbation theory and dispersive analysis. We also consider the accidental degeneracy occurring in the 8th excited state of the zero-momentum system. This exhibits qualitatively new features at ℓ = 4, not seen in the ℓ = 0 truncation. [ABSTRACT FROM AUTHOR]

The article "DO ΛCC AND G RUN?" by John F. Donoghue examines the concept of running coupling constants in gravitational interactions, specifically focusing on the cosmological constant (ΛCC) and Newton's constant (G). The author discusses various theoretical frameworks and research papers related to quantum gravity, exploring topics such as unimodular relativity, cosmological constants, and asymptotic safety scenarios. The text provides a critical analysis of the Asymptotic Safety program and highlights the limitations of defining running parameters based on cutoffs, ultimately concluding that ΛCC and G do not exhibit running behavior in physical amplitudes. [Extracted from the article]

The values of the low-energy constants (LECs) are very important in the chiral perturbation theory. This paper adopts a Bayesian method with the truncation errors to globally fit eight next-to-leading order (NLO) LECs Lir and next-to-next-leading order (NNLO) LECs Cir. With the estimation of the truncation errors, the fitting results of Lir in the NLO and NNLO are very close. The posterior distributions of Cir indicate the boundary-dependent relations of these Cir. Ten Cir are weakly dependent on the boundaries and their values are reliable. The other Cir are required more experimental data to constrain their boundaries. Some linear combinations of Cir are also fitted with more reliable posterior distributions. If one knows some more precise values of Cir, some other Cir can be obtained by these values. With these fitting LECs, most observables provide a good convergence, except for the πK scattering lengths a03/2 and a01/2. An example is also introduced to test the improvement of the method. All the computations indicate that considering the truncation errors can improve the global fit greatly, and more prior information can obtain better fitting results. This fitting method can be extended to the other effective field theories and the perturbation theory. [ABSTRACT FROM AUTHOR]

The low-energy antineutrino- and neutrino–nucleon neutral current elastic scattering is studied within the framework of the relativistic SU(2) baryon chiral perturbation theory up to the order of O (p 3 ) . We have derived the model-independent hadronic amplitudes and extracted the form factors from them. It is found that differential cross sections dσ/dQ2 for the processes of (anti)neutrino–proton scattering are in good agreement with the existing MiniBooNE data in the Q2 region [0.13, 0.20] GeV2, where nuclear effects are expected to be negligible. For Q2 ≤ 0.13 GeV2, large deviation is observed, which is mainly owing to the sizeable Pauli blocking effect. Comparisons with the simulation data produced by the NuWro and GENIE Mento Carlo events generators are also discussed. The chiral results obtained in this work can be utilized as inputs in various nuclear models to achieve the goal of precise determination of the strangeness axial vector form factor, in particular when the low-energy MicroBooNE data are available in the near future. [ABSTRACT FROM AUTHOR]

In this study, we analyze the strong decays of singly charmed baryons into another singly charmed baryon and a light pseudo scalar meson by means of Heavy Hadron Chiral Perturbation Theory (HHChPT) which combines heavy quark symmetry with chiral symmetry. HHChPT worked excellently for describing the strong decays of 1 S -wave charmed baryons. The strong decay widths of well-established singly charmed baryons are well reproduced. Further, the strong decay width of 1 P states is calculated in this approach by using the calculated masses in the Relativistic Flux Tube (RFT) model. By analyzing the mass spectra from the RFT model with strong decays in HHChPT, we investigate the spin-parity assignments. We identify Σ c (2 8 0 0) and Ξ c (2 9 3 9) as 1 P -wave states having J P = 3 2 − . [ABSTRACT FROM AUTHOR]

In this work, we make a study of the τ− → ωπ−ντ decay in the framework of low-energy effective field theory. The J P G decompositions of the quark currents and the ωπ final state show that, besides the Standard Model vector interaction, only the non-standard tensor interaction can have a non-zero contribution to the decay. To discuss its effect, a reliable calculation of the ωπ tensor form factors is necessary. After constructing the Lagrangian of resonance chiral theory with external tensor sources, we calculate both the vector and tensor form factors with the relevant resonance couplings determined by combining the QCD short-distance constraints, the fit to the spectral function of τ− → ωπ−ντ decay, as well as the matching between the O p 4 odd-intrinsic-parity operators after integrating out the vector resonances and the O p 6 operators of chiral perturbation theory. The new physics effect is then investigated in the distributions of the spectral function and the forward-backward asymmetry of τ− → ωπ−ντ decay. We find that the spectral function is dominated by the Standard Model, and the non-standard tensor contribution is negligible. However, since the forward-backward asymmetry can be only generated with a non-zero tensor interaction, the observable is quite sensitive to this kind of new physics. A future measurement of the observable at the Belle II experiment as well as at the proposed Tera-Z and STCF facilities is, therefore, strongly called for to check the existence of such a non-standard tensor interaction. [ABSTRACT FROM AUTHOR]

We revisit the low-energy K + N elastic scatterings in the context of the in-medium quark condensate with strange quarks. The chiral ward identity connects the in-medium quark condensate to the soft limit value of the pseudoscalar correlation function evaluated in nuclear matter. The in-medium correlation function of the pseudoscalar fields with strangeness describes in-medium kaon propagation and is obtained by kaon–nucleon scattering amplitudes in the low-density approximation. We construct the kaon–nucleon scattering amplitudes in chiral perturbation theory up to the next-to-leading order and add some terms of the next-to-next-to-leading order with the strange quark mass to improve expansion of the strange quark sector. We also consider the effect of a possible broad resonance state around P lab = 600 MeV/ c for I = 0 reported in the previous study. The low-energy constants are determined by existing K + N scattering data. We obtain good reproduction of the K + p scattering amplitude by chiral perturbation theory, while the description of the KN amplitude with I = 0 is not so satisfactory due to the lack of low-energy data. Performing analytic continuation of the scattering amplitudes obtained by chiral perturbation theory to the soft limit, we estimate the in-medium strange quark condensate. [ABSTRACT FROM AUTHOR]

This study focuses on the interaction of the pseudoscalar meson octet and the baryon decuplet. In the continuum, it is observed that several J P = 3 2 - baryon resonances can be produced by the Weinberg-Tomozawa interaction in unitarized chiral perturbation theory, including the N(1875), Σ (1670) , Σ (1910) , Ξ (1820) and Ω (2012) . Among them, the Ξ (1820) and Σ (1670) may exhibit a potential two-pole structures. The unitarized chiral perturbation approach is then applied as the underlying theory to predict the energy levels of these systems in a finite volume. These energy levels are well described by the K-matrix parameterization constrained by flavor SU(3) symmetry. With the parameters from the best fits, the poles extracted from the K-matrix parameterization closely correspond to those derived from the underlying chiral effective field theory, as long as they are close to physical region and not significantly higher than the lowest relevant threshold. [ABSTRACT FROM AUTHOR]

The NA48/2 experiment at CERN reports the first observation of the K± → π0π0μ±ν decay based on a sample of 2437 candidates with 15% background contamination collected in 2003–2004. The decay branching ratio in the kinematic region of the squared dilepton mass above 0.03 GeV2/c4 is measured to be (0.65 ± 0.03) × 10−6. The extrapolation to the full kinematic space, using a specific model, is found to be (3.45 ± 0.16) × 10−6, in agreement with chiral perturbation theory predictions. [ABSTRACT FROM AUTHOR]

The three-particle K-matrix, K df,3, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions in all isospin channels through next-to-leading order in Chiral Perturbation Theory, generalizing previous work done at maximum isospin. We obtain analytic expressions through quadratic order (or cubic order, in the case of zero isospin) in the expansion about the three-pion threshold. [ABSTRACT FROM AUTHOR]

Based on the chiral perturbation theory at the leading order, we show a signal of the presence of a new phase in rapidly rotating QCD matter with two flavors, that is a domain-wall Skyrmion phase. Based on the chiral Lagrangian with a Wess-Zumino-Witten (WZW) term responsible for the chiral anomaly and chiral vortical effect, it was shown that the ground state is a chiral soliton lattice (CSL) consisting of a stack of η-solitons in a high density region under rapid rotation. In a large parameter region, a single η-soliton decays into a pair of non-Abelian solitons, each of which carries SU(2)V/U(1) ≃ ℂP1 ≃ S2 moduli as a consequence of the spontaneously broken vector symmetry SU(2)V. In such a non-Abelian CSL, we construct the effective world-volume theory of a single non-Abelian soliton to obtain a d = 2 + 1 dimensional ℂP1 model with a topological term originated from the WZW term. We show that when the chemical potential is larger than a critical value, a topological lump supported by the second homotopy group π2(S2) ≃ ℤ has negative energy and is spontaneously created, implying the domain-wall Skyrmion phase. This lump corresponds in the bulk to a Skyrmion supported by the third homotopy group π3[SU(2)] ≃ ℤ carrying a baryon number. This composite state is called a domain-wall Skyrmion, and is stable even in the absence of the Skyrme term. An analytic formula for the effective nucleon mass in this medium can be written only in terms of the meson's constants as 4 2 π f π f η / m π ~ 1.21 GeV with the decay constants fπ and fη of the pions and η meson, respectively, and the pion mass mπ. This is reasonably heavier than the nucleon mass in the QCD vacuum. [ABSTRACT FROM AUTHOR]

The gravitational form factors of the transition from the proton to the ∆+ resonance are calculated to leading one-loop order using a manifestly Lorentz-invariant formulation of chiral perturbation theory. We take into account the leading electromagnetic and strong isospin-violating effects. The loop contributions to the transition form factors are found to be free of power-counting violating pieces, which is consistent with the absence of tree-level diagrams at the considered order. In this sense, our results can be regarded as predictions of chiral perturbation theory. [ABSTRACT FROM AUTHOR]

We present an exact evaluation of the two-photon exchange contribution to the elastic lepton-proton scattering process at low-energies using heavy baryon chiral perturbation theory. The evaluation is performed including next-to-leading order accuracy. This exact analytical evaluation contains all soft and hard two-photon exchanges and we identify the contributions missing in a soft-photon approximation approach. We evaluate the infrared divergent four-point box diagrams analytically using dimensional regularization. We also emphasize the differences between muon-proton and electron-proton scatterings relevant to the MUSE kinematics due to lepton mass differences. [ABSTRACT FROM AUTHOR]

The anomalous dimension γ m = 1 in the infrared region near the conformal edge in the broken phase of the large N f QCD has been shown by the ladder Schwinger–Dyson equation and also by the lattice simulation for N f = 8 and for N c = 3 . Recently, Zwicky made another independent argument (without referring to explicit dynamics) for the same result, γ m = 1 , by comparing the pion matrix element of the trace of the energy-momentum tensor π (p 2) | (1 + γ m) · ∑ i = 1 N f m f ψ ¯ i ψ i | π (p 1) = π (p 2) | θ μ μ | π (p 1) = 2 M π 2 (up to trace anomaly) with the estimate of π (p 2) | 2 · ∑ i = 1 N f m f ψ ¯ i ψ i | π (p 1) = 2 M π 2 through the Feynman–Hellmann theorem combined with an assumption M π 2 ∼ m f characteristic of the broken phase. We show that this is not justified by the explicit evaluation of each matrix element based on the dilaton chiral perturbation theory (dChPT): π (p 2) | 2 · ∑ i = 1 N f m f ψ ¯ i ψ i | π (p 1) = 2 M π 2 + [ (1 − γ m) M π 2 · 2 / (1 + γ m) ] = 2 M π 2 · 2 / (1 + γ m) ≠ 2 M π 2 in contradiction with his estimate, which is compared with π (p 2) | (1 + γ m) · ∑ i = 1 N f m f ψ ¯ i ψ i | π (p 1) = (1 + γ m) M π 2 + [ (1 − γ m) M π 2 ] = 2 M π 2 (both up to trace anomaly), where the terms in [ ] are from the σ (pseudo-dilaton) pole contribution. Thus, there is no constraint on γ m when the σ pole contribution is treated consistently for both. We further show that the Feynman–Hellmann theorem is applied to the inside of the conformal window where dChPT is invalid and the σ pole contribution is absent, and with M π 2 ∼ m f 2 / (1 + γ m) instead of M π 2 ∼ m f , we have the same result as ours in the broken phase. A further comment related to dChPT is made on the decay width of f 0 (500) to π π for N f = 2 . It is shown to be consistent with the reality, when f 0 (500) is regarded as a pseudo-NG boson with the non-perturbative trace anomaly dominance. [ABSTRACT FROM AUTHOR]

The long-range, parity-odd nucleon interaction generated by single-pion exchange is captured in the parity-odd pion–nucleon coupling h π 1 . Its calculation in lattice QCD requires the evaluation of four-quark operator nucleon three-point functions. We investigate a new numerical approach to compute h π 1 based on nucleon matrix elements of parity-even four-quark operators and related to the parity-violating electroweak theory by partial conservation of axial current (PCAC) and chiral perturbation theory. This study is performed with 2+1+1 dynamical flavors of twisted mass fermions at pion mass m π ≈ 260 MeV in a lattice box of L ≈ 3 fm and with lattice spacing of a ≈ 0.091 fm . From a calculation excluding fermion loop diagrams we find a bare coupling of h π 1 = 8.08 (98) · 10 - 7 . [ABSTRACT FROM AUTHOR]

QCD matter in strong magnetic field exhibits a rich phase structure. In the presence of an external magnetic field, the chiral Lagrangian for two flavors is accompanied by the Wess-Zumino-Witten (WZW) term containing an anomalous coupling of the neutral pion π0 to the magnetic field via the chiral anomaly. Due to this term, the ground state is inhomogeneous in the form of either chiral soliton lattice (CSL), an array of solitons in the direction of magnetic field, or domain-wall Skyrmion (DWSk) phase in which Skyrmions supported by π3[SU(2)] ≃ ℤ appear inside the solitons as topological lumps supported by π2(S2) ≃ ℤ in the effective worldvolume theory of the soliton. In this paper, we determine the phase boundary between the CSL and DWSk phases beyond the single-soliton approximation, within the leading order of chiral perturbation theory. To this end, we explore a domain-wall Skyrmion chain in multiple soliton configurations. First, we construct the effective theory of the CSL by the moduli approximation, and obtain the ℂP1 model or O(3) model, gauged by a background electromagnetic gauge field, with two kinds of topological terms coming from the WZW term: one is the topological lump charge in 2+1 dimensional worldvolume and the other is a topological term counting the soliton number. Topological lumps in the 2+1 dimensional worldvolume theory are superconducting rings and their sizes are constrained by the flux quantization condition. The negative energy condition of the lumps yields the phase boundary between the CSL and DWSk phases. We find that a large region inside the CSL is occupied by the DWSk phase, and that the CSL remains metastable in the DWSk phase in the vicinity of the phase boundary. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In light of the contribution of the states with isospin in the difference of the amplitudes of the processes and being very small, the dispersion sum rules for the difference between the dipole polarizabilities of the charged and neutral pions are analyzed as a function of the meson's parameters. Using the value of the chiral theory of perturbations for , is found for the meson parameter within the region MeV, MeV, keV. Estimated optimum value of decay width yields keV. [ABSTRACT FROM AUTHOR]

The pseudoscalar particles pions, kaons and the η -particle are considerably lighter than the other hadrons such as protons or neutrons. Their lightness was understood as a consequence of approximate chiral symmetry breaking. This led to current algebra, a way to express the relations imposed by the symmetry breaking. It was realized by Weinberg that because of their low mass, it is possible to formulate a purely pionic (effective) field theory at experimental energies, which carries all information on the (non-perturbative) dynamics, symmetries, and their spontaneous breaking of quantum chromodynamics (QCD) and allows for systematic calculations of observables. In this review, we trace these developments and present recent activities in this field. We make the connection to other effective theories, more generally introduced by Wilson, as approximate field theories at low energies. Indeed, principles and paradigms introduced first for pions have become ubiquitous in particle physics and the standard model. Lastly, we turn to the latest development where the present (fundamental) standard model itself is considered as an effective field theory of a—yet to be formulated—even more fundamental theory. We also discuss important techniques that were developed in order to turn chiral perturbation theory into a predictive framework and briefly review some connections between lattice QCD and chiral perturbation theory (ChPT). [ABSTRACT FROM AUTHOR]

It was demonstrated in a series of papers employing unitarized chiral perturbation theory that the phenomenology of the scalar open-charm state, the D 0 ∗ (2300) , can be understood as the interplay of two poles, corresponding to two scalar-isospin doublet states with different SU(3) flavor content. Within this formalism the lightest open charm positive parity states emerge as being dynamically generated from the scattering of the Goldstone-boson octet off D mesons, a picture that at the same time solves various problems that the experimental observations posed. However, in recent lattice studies of D π scattering at different pion masses only one pole was reported in the D 0 ∗ channel, while it was not possible to extract reliable parameters of a second pole from the lattice data. In this paper we demonstrate how this seeming contradiction can be understood and that imposing SU(3) constraints on the fitting amplitudes allows one to extract information on the second pole from the lattice data with minimal bias. The results may also be regarded as a showcase how approximate symmetries can be imposed in the K-matrix formalism to reduce the number of parameters. [ABSTRACT FROM AUTHOR]

Multi-particle states with additional pions are expected to result in a difficult-to-control excited-state contamination in lattice simulations. We show that heavy meson chiral perturbation theory can be employed to estimate the contamination due to two-particle B π states in various B-meson observables, like the B-meson decay constant and the B ∗ B π coupling. We work in the static limit and to next-to-leading order in the chiral expansion, i.e. including O (p). The B π states are found to typically lead to an overestimation of the observables at the few percent level. We determine two of the LECs from B → π form factor computations of the KEK group (Colquhoun et al. in Phys. Rev. D 106:054502, 2022) and discuss ways to determine the others. In particular, one LEC which is associated with smeared interpolating fields seems to be easily accessible and thus opens up a way to systematically study the effect of smearing on excited-state effects. [ABSTRACT FROM AUTHOR]

The ongoing experimental efforts to measure the hyperfine transition in muonic hydrogen prompt an accurate evaluation of the proton-structure effects. At the leading order in α , which is O (α 5) in the hyperfine splitting (hfs), these effects are usually evaluated in a data-driven fashion, using the empirical information on the proton electromagnetic form factors and spin structure functions. Here we perform a first calculation based on the baryon chiral perturbation theory (B χ PT). At leading orders it provides a prediction for the proton polarizability effects in hydrogen (H) and muonic hydrogen (μ H). We find large cancellations among the various contributions leading to, within the uncertainties, a zero polarizability effect at leading order in the B χ PT expansion. This result is in significant disagreement with the current data-driven evaluations. The small polarizability effect implies a smaller Zemach radius R Z , if one uses the well-known experimental 1S hfs in H or the 2S hfs in μ H. We, respectively, obtain R Z (H) = 1.010 (9) fm, R Z (μ H) = 1.040 (33) fm. The total proton-structure effect to the hfs at O (α 5) is then consistent with previous evaluations; the discrepancy in the polarizability is compensated by the smaller Zemach radius. Our recommended value for the 1S hfs in μ H is 182.640 (18) meV. [ABSTRACT FROM AUTHOR]

We perform a complete calculation of the pion-kaon scattering amplitude in Chiral Perturbation Theory at finite temperature, paying particular attention to the analytic structure of the amplitude and the main differences with respect to the zero temperature case. We also extend the Inverse Amplitude Method at finite temperature for unequal-mass scattering processes, which allows us to unitarize the amplitude and obtain the thermal evolution of the K 0 ∗ 700 and K∗(892) pole parameters. As a direct application of our analysis, we show that the thermal evolution of the K 0 ∗ 700 resonance is crucial to explain the behavior of the scalar susceptibility for isospin I = 1/2, which in turn, is directly connected with chiral and U(1)A restoration properties of the QCD phase diagram. [ABSTRACT FROM AUTHOR]

This review is devoted to the modern understanding of the two-color QCD phase diagram at finite baryon density and low temperatures. First, we consider the theoretical picture of this phase diagram. It is believed that at low baryon density, two-color QCD can be described by chiral perturbation theory (ChPT), which predicts a second-order phase transition with Bose-Einstein condensation of diquarks at μ = m π / 2 . At larger baryon chemical potentials, the interactions between baryons become important, and ChPT is not applicable anymore. At sufficiently large baryon chemical potential, the Fermi sphere composed of quarks is formed, and diquarks are condensed on the surface of this sphere. In this region, two-color baryon matter reveals properties similar to those of the Quarkyonic phase. Particular attention in this review is paid to lattice studies of dense two-color QCD phase diagram. In the low-density region, the results of lattice studies are in agreement with ChPT predictions. At sufficiently large baryon densities, lattice studies observe a Fermi sphere composed of quarks and condensation of diquarks on its surface. Thus, available lattice studies support most of the theoretical predictions. Finally, we discuss the status of the deconfinement in cold dense two-color matter, which was observed in lattice simulation with staggered fermions. [ABSTRACT FROM AUTHOR]

We compute the free energy of the chiral soliton lattice state in quantum chromodynamics (QCD) at nonzero baryon chemical potential, temperature and external magnetic field at the next-to-leading order of chiral perturbation theory. This extends previous work where only a special limit of the chiral soliton lattice, the domain wall, was considered. Our results therefore serve as a consistency check of the previously established phase diagram of QCD at moderate magnetic fields and temperature and sub-nuclear baryon chemical potentials. Moreover, we use the result for the free energy to determine the magnetization carried by the domain wall and the chiral soliton lattice, both at the next-to-leading order. [ABSTRACT FROM AUTHOR]

The interactions between the spin-1/2 doubly charmed baryons and Nambu-Goldstone bosons are analyzed within a manifestly relativistic baryon chiral perturbation theory up to next-to-next-to leading order, by using the so-called extended-on-mass-shell scheme. We utilize heavy diquark-antiquark symmetry to estimate the low-energy constants in the chiral effective Lagrangians. The S- and P-wave scattering lengths are predicted. We find that those diagrams, vanishing exactly in the heavy-quark limit, do contribute slightly to the S-wave scattering lengths in reality. The influence of the spin-3/2 doubly charmed baryons, as heavy-quark spin partners of the spin-1/2 ones, on the scattering lengths is discussed as well. Finally, S-wave phase shifts for elastic scattering processes are presented in the energy region near threshold. Our results in this work will not only be very useful for performing chiral extrapolations of future lattice QCD data, but also provide us chiral inputs for the investigation of the spectroscopy of doubly heavy baryons. [ABSTRACT FROM AUTHOR]

It is well known that the gluon anomaly is responsible for the mass of the U(1) Goldstone boson. It is also manifested in the properties of pseudo-Goldstone states: the gluon anomaly in the next order of the 1/Nc expansion induces interactions violating the Zweig rule. A necessary condition for this is the explicit breaking of the chiral symmetry by the masses of light quarks. One of the physical consequences is that the η–η' mixing does not affect the amplitude. Another consequence is the suppression of the first 1/Nc correction to the η–η' mixing angle. The mechanism of such suppression is discussed in detail. The conclusions are based on the 1/Nc expansion and the effective meson Lagrangian of the Nambu–Jona-Lasinio model and are compared with the results of the 1/Nc chiral perturbation theory. [ABSTRACT FROM AUTHOR]

The quest for new sources of the simultaneous violation of C and CP symmetry was popular in the 1960s and has since been mostly neglected for more than half a century. In this work we revisit fundamental quark-level operators that break C and CP up to and including mass dimension 8 for flavor-conserving transitions, relying on the complete operator sets of the so-called Standard Model effective field theory and the low-energy effective field theory. With the formalism of chiral perturbation theory, we match these quark operators to light-meson physics, derive C- and CP -odd Lagrangians for several processes in the η, η', and pion sectors, and furthermore, as a proof of principle, give estimates for the respective observables in explicit dependence of the underlying high-energy scale for new physics. [ABSTRACT FROM AUTHOR]

We study radiative corrections to neutron beta decay and low-energy (anti)neutrino-nucleon scattering within a top-down effective field theory approach. As it was recently shown, a few electromagnetic and electroweak low-energy coupling constants in heavy-baryon chiral perturbation theory are yet to be determined. Performing matching to the four-fermion effective field theory, we relate these low-energy constants to correlation functions of vector and axial-vector currents. Such relations allow us to explicitly clarify scheme dependence for radiative corrections to neutron decay and low-energy charged-current (anti)neutrino scattering, provide a robust prediction of leading in the electromagnetic coupling constant contributions, and achieve a clear separation between short-distance and long-distance contributions. [ABSTRACT FROM AUTHOR]

Chiral symmetry and its spontaneous breaking play an important role both in the light hadron and heavy hadron systems. The chiral perturbation theory (χ PT) is the low energy effective field theory of the Quantum Chromodynamics. In this work, we shall review the investigations on the chiral corrections to the properties of the heavy mesons and baryons within the framework of χ PT. We will also review the scatterings of the light pseudoscalar mesons and heavy hadrons, through which many new resonances such as the D s 0 ∗ (2317) could be understood. Moreover, many new hadron states were observed experimentally in the past decades. A large group of these states is near-threshold resonances, such as the charged charmoniumlike Z c and Z c s states, bottomoniumlike Z b states, hidden-charm pentaquark P c and P c s states and the doubly charmed T c c state, etc. They are very good candidates of the loosely bound molecular states composed of a pair of charmed (bottom) hadrons, which are very similar to the loosely bound deuteron. The modern nuclear force was built upon the chiral effective field theory (χ EFT), which is the extension of the χ PT to the systems with two matter fields. The long-range and medium-long-range interactions between two nucleons arise from the single- and double-pion exchange respectively, which are well constrained by the chiral symmetry and its spontaneous breaking. The short-distance interactions can be described by the low energy constants. Such a framework works very well for the nucleon–nucleon scattering and nuclei. In this work, we will perform an extensive review of the progress on the heavy hadronic molecular states within the framework of χ EFT. We shall emphasize that the same chiral dynamics not only govern the nuclei and forms the deuteron, but also dictates the shallow bound states or resonances composed of two heavy hadrons. [ABSTRACT FROM AUTHOR]

We study phonon modes associated with magnetic vortex lattices of finite isospin chiral perturbation theory near the upper critical point by introducing quasimomentum fluctuations to the lattice and calculate dispersion relations associated with the optical and acoustic modes. We find that one of the acoustic modes is massless and that its energy for small transverse quasimomentum is quartic (due the presence of an isospin chemical potential), which is significantly softer than the "supersoft" (quadratic) massless mode of the Abelian Higgs Model (AHM). Due to the presence of derivative interactions, which is absent in the AHM, the speed of the longitudinal mode depends on both the isospin chemical potential and the external magnetic field. Our results suggest that the standard assumption of an ordered lattice in finite isospin QCD should be revisited and the existence of a disordered spaghetti phase of a vortex liquid or gas, should be considered. [ABSTRACT FROM AUTHOR]

We study the ground state of the low energy dense QCD with the assumption of chiral condensates of quarks. Under an external magnetic field, mesons could form soliton lattices via the chiral anomaly. For such scenarios, we present a unified description of pions and η meson with a U(2) field in the framework of the chiral perturbation theory. Our result shows the ground state is a mixture of the magnetized domain walls formed by neutral pion π0 and η meson when they coexist. The winding number of the ground state would alter according to the strength of the magnetic field. When the magnetic field is strong or the chemical potential is large, the proportion of the mixture is determined by the decay constants and the contributions to the anomalous action of π0 and η meson. The resulting configuration is either a mixed soliton lattice or a quasicrystal which could be dubbed a "chiral soliton quasicrystal". [ABSTRACT FROM AUTHOR]

The three-particle K-matrix, K df , 3 , is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions at maximal isospin through next-to-leading order (NLO) in Chiral Perturbation Theory (ChPT). We compare the values to existing lattice QCD results and find that the agreement between lattice QCD data and ChPT in the first two coefficients of the threshold expansion of K df , 3 is significantly improved with respect to leading order once NLO effects are incorporated. [ABSTRACT FROM AUTHOR]

We study the interactions of systems of two and three nondegenerate mesons composed of pions and kaons at maximal isospin using lattice QCD, specifically π+K+, π+π+K+ and K+K+π+. Utilizing the stochastic LapH method, we determine the spectrum of these systems on two CLS Nf = 2 + 1 ensembles with pion masses of 200 MeV and 340 MeV, and include many levels in different momentum frames. We constrain the K matrices describing two- and three-particle interactions by fitting the spectrum to the results predicted by the finite-volume formalism, including up to p waves. This requires also results for the π+π+ and K+K+ spectrum, which have been obtained previously on the same configurations. We explore different fitting strategies, comparing fits to energy shifts with fits to energies boosted to the rest frame, and also comparing simultaneous global fits to all relevant two- and three-particle channels to those where we first fit two-particle channels and then add in the three-particle information. We provide the first determination of the three-particle K matrix in π+π+K+ and K+K+π+ systems, finding statistically significant nonzero results in most cases. We include s and p waves in the K matrix for π+K+ scattering, finding evidence for an attractive p-wave scattering length. We compare our results to Chiral Perturbation Theory, including an investigation of the impact of discretization errors, for which we provide the leading order predictions obtained using Wilson Chiral Perturbation Theory. [ABSTRACT FROM AUTHOR]

We determine the light baryon spectrum on ensembles generated by the Coordinated Lattice Simulations (CLS) effort, employing Nf = 2 + 1 flavours of non-perturbatively improved Wilson fermions. The hadron masses are interpolated and extrapolated within the quark mass plane, utilizing three distinct trajectories, two of which intersect close to the physical quark mass point and the third one approaching the SU(3) chiral limit. The results are extrapolated to the continuum limit, utilizing six different lattice spacings ranging from a ≈ 0.10 fm down to below 0.04 fm. The light pion mass varies from Mπ ≈ 429 MeV down to 127 MeV. In general, the spatial extent is kept larger than four times the inverse pion mass and larger than 2.3 fm, with additional small and large volume ensembles to investigate finite size effects. We determine the Wilson flow scales t 0 , ph = 0.1449 9 7 fm [1] and t 0 ∗ ≈ t 0 , ph [2] from the octet cascade (Ξ baryon). Determining the light baryon spectrum in the continuum limit, we find the nucleon mass m N = 941.7 7.6 6.5 MeV and the other stable baryon masses to agree with their experimental values within sub-percent level uncertainties. Moreover, we determine SU(3) and SU(2) chiral perturbation theory low energy constants, including the octet and the Ω baryon sigma terms σπN = 43.9(4.7) MeV, σ π Λ = 28.2 5.4 4.3 MeV, σ π Σ = 25.9 6.1 3.8 MeV, σ π Ξ = 11.2 6.4 4.5 and σ π Ω = 6.9 4.3 5.3 MeV, as well as various parameters, renormalization factors and improvement coefficients that are relevant for simulations with our lattice action. [ABSTRACT FROM AUTHOR]

We find that the phase appearing in the unitarity relation between B K L → μ + μ − and B K L → γγ is equal to the phase shift in the interference term of the time- dependent K → μ+μ− decay. A probe of this relation at future kaon facilities constitutes a Standard Model test with a theory precision of about 2%. The phase has further importance for sensitivity studies regarding the measurement of the time-dependent K → μ+μ− decay rate to extract the CKM matrix element combination ∣ V ts V td sin β + β s ∣ ≈ A 2 λ 5 η ¯ . We find a model-independent theoretically clean prediction, cos2φ0 = 0.96 ± 0.03. The quoted error is a combination of the theoretical and experimental errors, and both of them are expected to shrink in the future. Using input from the large-NC limit within chiral perturbation theory, we find a theory preference towards solutions with negative cos φ0, reducing a four-fold ambiguity in the angle φ0 to a two-fold one. [ABSTRACT FROM AUTHOR]

Using dispersion theory, the electromagnetic Sigma-to-Lambda transition form factors are expressed as the product of the pion electromagnetic form factor and the Σ Λ ¯ → π π scattering amplitudes with the latter estimated from SU(3) chiral perturbation theory including the baryon decuplet as explicit degrees of freedom. The contribution of the K K ¯ channel is also taken into account and the π π – K K ¯ coupled-channel effect is included by means of a two-channel Muskhelishvili–Omnès representation. It is found that the electric transition form factor shows a significant shift after the inclusion of the K K ¯ channel, while the magnetic transition form factor is only weakly affected. However, the K K ¯ effect on the electric form factor is obscured by the undetermined coupling h A in the three-flavor chiral Lagrangian. The error bands of the Sigma-to-Lambda transition form factors from the uncertainties of the couplings and low-energy constant in three-flavor chiral perturbation theory are estimated by a bootstrap sampling method. [ABSTRACT FROM AUTHOR]

We calculate the complete T matrices of the elastic light pseudoscalar meson and heavy meson scattering to the third order in heavy meson chiral perturbation theory. We determine the low-energy constants by fitting the phase shifts and scattering lengths from lattice QCD simulations simultaneously and predict the phase shifts at the physical meson masses. The phase shifts in the D π (I = 1 / 2) , D K (I = 0) , D K ¯ (I = 0) , D s K ¯ , D η and D s η S waves are so strong that bound states or resonances may be generated dynamically in all these channels. The D K (I = 0) channel corresponds to the well-known exotic state D s 0 ∗ (2317) . The D K (I = 0) channel corresponds to the well-known exotic state D s 0 ∗ (2317) . The coupled-channel D π , D η and D s K ¯ scattering corresponds to D 0 ∗ (2400) . The coupled-channel D π , D η and D s K ¯ scattering corresponds to D 0 ∗ (2400) . We also predict the scattering lengths and scattering volumes and observe good convergence in the scattering volumes. Our calculations provide a possibility to accurately investigate the exotic state in the light pseudoscalar meson and heavy meson interactions. [ABSTRACT FROM AUTHOR]

The electromagnetic form factors of the Λ hyperon in the time-like region are determined precisely through a dispersion-theoretical analysis of the world data for the cross section of the annihilation process e + e - → Λ ¯ Λ . The spectral function is represented by a superposition of narrow and broad vector meson poles. We test different scenarios for the spectral function and obtain a good description of the world data in the time-like region. The uncertainties in the extracted form factors are estimated by means of the bootstrap sampling method. The analytical continuation of the form factors to the space-like region introduces large errors due to the lack of data. When the electric Λ radius from chiral perturbation theory is taken as a constraint, the magnetic radius is predicted as r M = 0.681 ± 0.002 fm. We also extract various vector meson to baryon coupling constants. [ABSTRACT FROM AUTHOR]

We present the first unquenched lattice-QCD calculation of the form factors for the decay B → D ∗ ℓ ν at nonzero recoil. Our analysis includes 15 MILC ensembles with N f = 2 + 1 flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from a ≈ 0.15 fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valence b and c quarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element | V cb | . We obtain V cb = (38.40 ± 0. 68 th ± 0. 34 exp ± 0. 18 EM) × 10 - 3 . The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall χ 2 /dof = 126 / 84 , which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is in agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict R (D ∗) = 0.265 ± 0.013 , which confirms the current tension between theory and experiment. [ABSTRACT FROM AUTHOR]

[Display omitted] Weak radiative hyperon decays, important to test the strong interaction and relevant in searches for beyond the standard model physics, have remained puzzling both experimentally and theoretically for a long time. The recently updated branching fraction and first measurement of the asymmetry parameter of Λ → n γ by the BESIII Collaboration further exacerbate the issue, as none of the existing predictions can describe the data. We show in this work that the covariant baryon chiral perturbation theory, with constraints from the latest measurements of hyperon non-leptonic decays, can well describe the BESIII data. The predicted branching fraction and asymmetry parameter for Ξ - → Σ - γ are also in agreement with the experimental data. We note that a more precise measurement of the asymmetry parameter, which is strongly constrained by chiral symmetry and related with that of Σ + → p γ , is crucial to test Hara's theorem. We further predict the branching fraction and asymmetry parameter of Σ 0 → n γ , whose future measurement can serve as a highly nontrivial check on our understanding of weak radiative hyperon decays and on the covariant baryon chiral perturbation theory. [ABSTRACT FROM AUTHOR]

Advances in scattering amplitudes have exposed previously-hidden color-kinematics and double-copy structures in theories ranging from gauge and gravity theories to effective field theories such as chiral perturbation theory and the Born–Infeld model. These novel structures both simplify higher-order calculations and pose tantalizing questions related to a unified framework underlying relativistic quantum theories. This introductory mini-review article invites further exploration of these topics. After a brief introduction to color-kinematics duality and the double copy as they emerge at tree and loop-level in gauge and gravity theories, we present two distinct examples: (1) an introduction to the web of double-copy-constructible theories, and (2) a discussion of the application of the double copy to calculation relevant to gravitational-wave physics. [ABSTRACT FROM AUTHOR]

We review some recent progress in the theory of electroweak radiative corrections in semileptonic decay processes. The resurrection of the so-called Sirlin’s representation based on current algebra relations permits a clear separation between the perturbatively-calculable and incalculable pieces in the O(GFα) radiative corrections. The latter are expressed as compact hadronic matrix elements that allow systematic non-perturbative analysis such as dispersion relation and lattice QCD. This brings substantial improvements to the precision of the electroweak radiative corrections in semileptonic decays of pion, kaon, free neutron and JP=0+ nuclei that are important theory inputs in precision tests of the Standard Model. Unresolved issues and future prospects are discussed.

We show that the recent MIT lattice QCD data for the pion's gravitational form factors are, in the covered momentum transfer range, fully consistent with the meson dominance principle. In particular, the 2 + + component can be accurately saturated with the f 2 (1270) meson, whereas the 0 + + component with the σ meson. To incorporate the large width of the σ , we use the dispersion relation with the spectral density obtained from analyses of the physical pion scattering data. Effects of the pion mass are estimated within Chiral Perturbation Theory and are found to be small between the lattice and the physical point. We also discuss the implications of the perturbative QCD constraints at high momentum transfers, leading to specific sum rules for the spectral densities of the gravitational form factors, and argue that these densities cannot be of definite sign. [ABSTRACT FROM AUTHOR]