Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory

We review some recent progress in our understanding of the lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments （MMs） in terms of Chiral Perturbation Theory （ChPT）.In particular,we show that at next-to-leading-order ChPT can describe the MMs of the octet baryons quite well.We also make predictions for the decuplet MMs at the same chiral order.Among them,the MMs of the Δ＋＋ and Δ ＋ are found to agree well with data within the experimental uncertainties.

Ratio of a strange quark mass m_s to up or down quark mass m_(u,d) predicted by a quark propagator in the framework of the chiral perturbation theory

Based on the fully dressed quark propagator and chiral perturbation theory, we study the ratio of the strange quark mass ms to up or down quark mass mu,d . The ratio is related to the determination of quark masses which are fundamental input parameters of QCD Lagrangian in the Standard Model of particle physics and can not be directly measured since the quark is confined within a hadron. An accurate determination of these QCD free parameters is extremely important for both phenomenological and theoretical applications. We begin with a brief introduction to the non-perturbation QCD theory, and then study the mass ratio in the framework of the chiral perturbation theory （χPT） with a parameterized fully dressed quark propagator which describes confining fully dressed quark propagation and is analytic everywhere in the finite complex p2-plane and has no Lehmann representation so there are no quark production thresholds in any theoretical calculations of observable data. Our prediction for the ratio ms/mu,d is consistent with other model predictions such as Lattice QCD, instanton model, QCD sum rules and the empirical values used widely in the literature. As a by-product of this study, our theoretical results, together with other predictions of physical quantities that used this quark propagator in our previous publications, clearly show that the parameterized form of the fully dressed quark propagator is an applicable and reliable approximation to the solution of the Dyson-Schwinger Equation of quark propagator in the QCD.

The Pionic Deuterium and the Pion Tetrahedron Vacuum Polarization

A double-well potential model is proposed for the pionic deuterium that enables to calculate the energy split, the potential barrier height and estimate the pion tetrahedron edge length. We propose that pion tetrahedrons, πTd = ud~dũ, play a central role in the Yukawa interaction by enabling quark exchange reactions between protons and neutrons by tunneling through a potential barrier. A vacuum polarization Feynman diagram is proposed for the πTd having chains of fermion loops for the two valence quarks and anti-quarks connected by gluons. With a higher order vacuum polarization diagram, the d and u quark loops are interleaved and the chiral symmetry is broken dynamically. The proposed πTd vacuum polarization integral does not diverge in both the IR and UV limits and vanishes in the limit of an infinite pion tetrahedron condensate. We propose a new Delbruck scattering Feynman diagram that includes d and u quark and anti-quark interleaved loops. We further propose that conversion of gravitons to photons may occur via quark and anti-quark loops that describe the pion tetrahedrons dynamics in the vacuum and may also transfer gravitational waves.

Leading order relativistic chiral nucleon-nucleon interaction

Motivated by the successes of relativistic theories in studies of atomic/molecular and nuclear systems and the need for a relativistic chiral force in relativistic nuclear structure studies, we explore a new relativistic scheme to construct the nucleon-nucleon interaction in the framework of covariant chiral effective field theory. The chiral interaction is formulated up to leading order with covariant power counting and a Lorentz invariant chiral Lagrangian.We find that the relativistic scheme induces all six spin operators needed to describe the nuclear force. A detailed investigation of the partial wave potentials shows a better description of the;S——0 and;P;phase shifts than the leading order Weinberg approach, and similar to that of the next-to-leading order Weinberg approach. For the other partial waves with angular momenta J≥1, the relativistic results are almost the same as their leading order non-relativistic counterparts.

Effective field theory approach to lepton number violatingτdecays

We continue our endeavor to investigate lepton number violating(LNV)processes at low energies in the framework of effective field theory(EFT).In this work we study the LNV tau decaysτ^(+)→lP_(i)^(+)P_(J)^(+),where L=e.μand P_(i,j)^(+)denote the lowest-lying charged pseudoscalarsπ^(+),K^(+).We analyze the dominant contributions in a series of EFTs from high to low energy scales,namely the standard model EFT(SMEFT),the low-energy EFT(LEFT),and the chiral perturbation theory(χPT).The decay branching ratios are expressed in terms of the Wilson coefficients of dimension-five and-seven operators in SMEFT and the hadronic low-energy constants.These Wilson coefficients involve the first and second generations of quarks and all generations of leptons;thus,they cannot be explored in low-energy processes such as nuclear neutrinoless double beta decay or LNV kaon decays.Unfortunately,the current experimental upper bounds on the branching ratios are too weak to set useful constraints on these coefficients.Alternatively,if we assume the new physics scale is larger than 1 TeV,the branching ratios are well below the current experimental bounds.We also estimate the hadronic uncertainties incurred in applyingχPT toτdecays by computing one-loop chiral logarithms and attempt to improve the convergence of chiral perturbation by employing dispersion relations in the short-distance part of the decay amplitudes.

Chiral corrections to the masses of the doubly heavy baryons

We study the masses of the doubly bottom baryons and the charmed-bottom baryons up to O(p^(3))in heavy baryon chiral perturbation theory.We determine the unknown low energy constants in the quark model and lattice QCD.We show the numerical results for the masses of the doubly bottom baryons and the charmed-bottom baryons up to O(p^(3)).

Molecular states in D_(s)^(*)+=^_(c)^(′,*)systems^(*)

The possible hadronic molecules in D_(S)^(∗)+Ξ_(c)(′,∗)systems with J^(P)=1/2−,3/2−,and 5/2−are investigated with interactions described by light meson exchanges.By varying the cutoff in a phenomenologically reasonable range of 1−2.5 GeV,we find ten near-threshold(bound or virtual)states in the single-channel case.After introducing the coupled-channel dynamics of D_(+)^(s)Ξ_(c)-D_(s)^(+)Ξ′c-D_(s)^(∗+)Ξ_(c-)D_(s)^(+)Ξ_(c)^(*)-D_(s)^(∗)+sΞ′_(c)-D_(s)^(∗)Ξ_(c)^(∗)systems,these states,except those below the lowest channels in each JP sector,move into the complex energy plane and become resonances in the mass range 4.43−4.76 GeV.Their spin-parities and nearby thresholds are 1/2−(D_(s)^(+)Ξ′_(c)),1/2^(−)(D_(s)^(++)Ξ_(c)^(*)),1/2−(D_(s)^(∗+)Ξ_(c)),1/2−(D_(s)^(∗+)Ξ_(c)^(′)),1/2−(D_(s)^(∗+)Ξ_(c)^(∗)),3/2−(D_(s)^(∗+)(Ξc),3/2−(D_(s)^(+)Ξ_(c)),3/2−(D_(s)^(∗+)Ξ′c),3/2−(D_(+s)^(∗)Ξ_(c)^(∗)),and 5/2−(D_(s)^(∗+)Ξ_(c)^(∗)).The impact of theδ(r)-term in the one-boson-exchange model on these states is presented.SettingΛ=1.5 GeV as an illustrative value,it is found that 1/2−(D_(s)^(*+)Ξ_(c))is a stable bound state(becoming unstable if the coupling to lower channels is turned on),1/2−(D∗+sΞc)and 3/2−(D_(s)^(∗+)Ξ_(c))are physical resonances in cases where theδ(r)-term is included or excluded,and the other seven states are physical resonances or"virtual-state-like"poles near thresholds,depending on whether theδ(r)-term is included.In addition,the partial decay widths of the physical resonances are provided.These double-charm hidden-strangeness pentaquark states,as the partners of the experimentally observed Pc and Pcs states,can be searched for in the D(∗)Λ_(c)final states in the future.

Phase diagram of two-color QCD matter at finite baryon and axial isospin densities

We study the two-color QCD matter with two fundamental quark flavors using the chiral perturbation theory and the Nambu-Jona-Lasinio(NJL)model.The effective Lagrangian is derived in terms of mesons and baryons,i.e.diquarks.The low lying excitations lie in the extended SU(4)flavor symmetry space.We compute the leading order terms of the Lagrangian as a function of the baryon and axial isospin densities.After numerically solving the gap equations in the two-color NJL model,the phase diagram is obtained in the μ−ν5 plane.

Transport coefficients of a massive pion gas

We review our main results concerning the transport coefficients of a light meson gas,in particular we focus on the case of a massive pion gas.Leading order results according to the chiral power-counting are presented for the DC electrical conductivity,thermal conductivity,shear viscosity,and bulk viscosity.We also comment on the possible correlation between the bulk viscosity and the trace anomaly in QCD,as well as the relation between unitarity and a minimum of the quotient η/s near the phase transition.

Extracting the low-energy constant L_(0)^(r)at three flavors from pion-kaon scattering

based on our analysis of the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude,we provide the first determination of the only free low-energy constant at O(p^(4)),known as L_(0)^(r),in SU(4|1)Partially-Quenched Chiral Perturbation theory using the data from the Extended Twisted Mass collaboration,L_(0)^(r)(μ=M_(ρ))=0.77(20)(25)(7)(7)(2)·10^(-3).The theory uncertainties originate from the unphysical scattering length,the physical low-energy constants,the higher-order chiral corrections,the(lattice)meson masses and the pion decay constant,respectively.