Meson Theory Research Articles

Quantum gate sets for lattice QCD in the strong-coupling limit: Nf=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$N_{f}=1$\\end{document}

We derive the primitive quantum gate sets to simulate lattice quantum chromodynamics (LQCD) in the strong-coupling limit with one flavor of massless staggered quarks. This theory is of interest for studies at non-zero density as the sign problem can be overcome using Monte Carlo methods. In this work, we use it as a testing ground for quantum simulations. The key point is that no truncation of the bosonic Hilbert space is necessary as the theory is formulated in terms of color-singlet degrees of freedom (“baryons” and “mesons”). The baryons become static in the limit of continuous time and decouple, whereas the dynamics of the mesonic theory involves two qubits per lattice site. Lending dynamics also to the “baryons” simply requires to use the derived gate set in its controlled version.

Scattering theory of mesons in doped antiferromagnetic Mott insulators: Multichannel perspective and Feshbach resonance

Scattering theory of mesons in doped antiferromagnetic Mott insulators: Multichannel perspective and Feshbach resonance

BCF anomaly and higher-group structure in the low energy effective theories of mesons

We discuss the BCF anomaly of massless QCD-like theories, first obtained by Anber and Poppitz, from the viewpoint of the low energy effective theories. We assume that the QCD-like theories exhibit spontaneous chiral symmetry breaking due to a quark bilinear condensate. Using the ’t Hooft anomaly matching condition for the BCF anomaly, we find that the low energy effective action is composed of a chiral Lagrangian and a Wess-Zumino-Witten term together with an interaction term of the η′ meson with the background gauge field for a discrete one-form symmetry. It is shown that the low energy effective action cancels the quantum inconsistencies associated with η′ due to an ambiguity of how to uplift the action to a five-dimensional spacetime with a boundary. The η′ term plays a substantial role in exploring the emergent higher-group structure at low energies.

COMPARATIVE STUDY ON CHARGED AND NEUTRAL PION-NUCLEON COUPLING CONSTANTS USING YUKAWA POTENTIAL MODEL

The meson field theory based on the Yukawa model for nuclear forces is estimated using a simple relationship between the charged and neutral pion- nucleon coupling constant. This signifies that the charged coupling constant is larger compared to the value obtains for neutral pions. Therefore since np interaction is stronger than the pp interaction, we look at the value obtained for charged pion – nucleon constant which gives good agreement with one of the recent experimental values, and then the splitting between the charged and neutral pion – nucleon coupling constants is practically the same as that between charged and neutral pion mass. In this case, the mass difference between the charged and neutral pion is also calculated to assess the amount of charge dependence of the Neutron – Neutron scattering length

Chiral theory of ρ -meson gravitational form factors

The low-energy chiral effective field theory of vector mesons and Goldstone bosons in external gravitational field is considered. The energy-momentum tensor is obtained and the gravitational form factors of the $\rho$-meson are calculated up to next-to-leading order in the chiral expansion. This amounts to considering tree-level and one-loop order diagrams. The chiral expansion of the form factors at zero momentum transfer as well as of the slope parameters is worked out. Also, the long-range behaviour of the energy and internal force distributions is obtained and analysed.

Strongly Interacting Dark Matter from Sp(4) Gauge Theory

The stable hadronic bound states in a hidden new non-Abelian gauge sector provide interesting candidates for strongly-interacting Dark Matter (DM). A particular example are theories in which DM is made up of dark pions which set the DM relic abundance through self-annihilation. One of the simplest realizations is Sp(4)c gauge theory with two Dirac fermions. We discuss its mesonic multiplets for degenerate and non-degenerate fermions, construct a low-energy effective theory and present lattice results for the pseudoscalar mesons and vector mesons.

Theoretical study on η′ → π+π−π+(0)π−(0)

The η′ meson is associated with the U(1) anomaly. In this paper, a successful effective chiral theory of mesons has been applied to study the anomalous decays of η′→π+π−π+(0)π−(0). Contribution of triangle and box diagrams is calculated, which indicates that the box anomaly has a significant contribution to the decay amplitudes. We predict branching ratios of Br(η′→π+π−π+π−)=12Br(η′→π+π−π0π0)=(8.3±1.2)×10−5, which is in good agreement with BESIII measurement.

The emergence of electroweak Skyrmions through Higgs bosons

Skyrmions are extended field configurations, initially proposed to describe baryons as topological solitons in an effective field theory of mesons. We investigate and confirm the existence of skyrmions within the electroweak sector of the Standard Model and study their properties. We find that the interplay of the electroweak sector with a dynamical Higgs field and the Skyrme term leads to a non-trivial vacuum structure with the skyrmion and perturbative vacuum sectors separated by a finite energy barrier. We identify dimension-8 operators that stabilise the electroweak skyrmion as a spatially localised soliton field configuration with finite size. Such operators are induced generically by a wide class of UV models. To calculate the skyrmion energy and radius we use a neural network method. Electroweak skyrmions are non-topological solitons but are exponentially long lived, and we find that the electroweak skyrmion is a viable dark matter candidate. While the skyrmion production cross section at collider experiments is suppressed, measuring the size of the Skyrme term in multi-Higgs-production processes at high-energy colliders is a promising avenue to probe the existence of electroweak skyrmions.

Galilean-invariant effective field theory for the X(3872) at next-to-leading order

XEFT is a low-energy effective field theory for charm mesons and pions that provides a systematically improvable description of the $X(3872)$ resonance. To simplify calculations beyond leading order, we introduce a new formulation of XEFT with a dynamical field for a pair of charm mesons in the resonant channel. We simplify the renormalization of XEFT by introducing a new renormalization scheme that involves the subtraction of amplitudes at the complex $D^{*0} \bar D^0$ threshold. The new formulation and the new renormalization scheme are illustrated by calculating the complex pole energy of $X$ and the $D^{*0} \bar D^0$ scattering amplitude to next-to-leading order using Galilean-invariant XEFT.

Conventional nuclear forces as a consequence of the quark-gluonic hadronization into mesons

The conventional nuclear forces at low energies are described by NN-potentials that arise within the framework of the classical mesonic theory as a consequence of the interchange of mesons. Under the situation the mentioned NN-potentials depend on the mesonic masses as parameters. From the point of view of quantum chromodynamics (QCD), however, the mesons and nucleons are composed of quark-gluon configurations and are the result of a confinement mechanism, i.e., the quark-gluonic hadronization into mesons (nucleons). Hence the above mesonic masses should be some functions of quark-gluonic degrees of freedom. When using the confinement mechanism proposed earlier by one of the authors in QCD we adduce the sought functions in an explicit form which enables us to conclude that the NN-potentials only correspond to some residual interactions while the latter are the direct result of the quark-gluonic hadronization into mesons when approching two nucleons.

Effective field theory approach to lepton number violating decays K\xb1\u2192 \u03c0\u2213l\xb1l\xb1: short-distance contribution

This is the first paper of our systematic efforts on lepton number violating (LNV) hadronic decays in the effective field theory approach. These decays provide information complementary to popular nuclear neutrinoless double-β (0νββ) decay in that they can probe LNV interactions involving heavier quarks and charged leptons. We may call them hadronic 0νββ decays in short, though β refers to all charged leptons. In this work we investigate the decays K±→ π∓l±l± that arise from short-distance or contact interactions involving four quark fields and two charged lepton fields, which have canonical dimension nine (dim-9) at leading order in low energy effective field theory (LEFT). We make a complete analysis on the basis of all dim-9 operators that violate lepton number by two units, and compute their one-loop QCD renormalization effects. We match these effective interactions in LEFT to those in chiral perturbation theory (χPT) for pseudoscalar mesons, and determine the resulting hadronic low energy constants (LECs) by chiral symmetry and lattice results in the literature. The obtained decay rate is general in that all physics at and above the electroweak scale is completely parameterized by the relevant Wilson coefficients in LEFT and hadronic LECs in χPT. Assuming the standard model effective field theory (SMEFT) is the appropriate effective field theory between some new physics scale and the electroweak scale, we match our LEFT results to SMEFT whose leading effective interactions arise from LNV dim-7 operators. This connection to SMEFT simplifies significantly the interaction structures entering in the kaon decays, and we employ the current experimental bounds to set constraints on the relevant Wilson coefficients in SMEFT.

Nuclear structure is governed by the fundamental laws of electromagnetism

Contradicting interpretations of the nuclear force as given by two contrasted approaches like the meson theory and the quantum chromodynamics, are overcome here by reviving the basic electromagnetic laws which are applicable on the existing charged subconstituents in nucléons. On this basis, considerable charge distributions in nucleons are determined after a careful analysis of the magnetic moments and the results of the deep inelastic scattering. Basic equations derived from the distributed charges of oriented spins of nucléons give strong and short ranged forces leading exactly to the binding energies of the deuteron and other nuclei. According to these interactions, p-p and n-n systems repel and only the p-n bonds form rectangles and closely packed parallelepipeds. Such contrary forces create structures of saturation and of finite number of nucléons. They also invalidate the charge independence hypothesis and differ fundamentally from the central potential and the effects of the Pauli principle of the electronic configurations responsible for the development of the models of the Fermi gas and nuclear shell. There are two kinds of p-n bonds, which imply anisotropy, leading often to elongated shapes of vibrational and rotational modes of excitation, while the surface tension contributes to the creation of non elongated shapes of stable arrangements. Finally, for A>40 a type of shell structure provides new rules for understanding the structure of magic nuclei for N>Z and the increasing ratio N/Z with A.

On the Breakdown of Charge Independence and Charge Symmetry of the Pion—Nucleon Coupling Constant

A simple, physically validated, model of charge-independence and charge-symmetry breaking is proposed for the pion-nucleon coupling constant. Within this model, the pion-nucleon coupling constants are assumed to be in direct proportion to the masses of nucleons and pions involved in the interaction. The charge dependence of the pion-nucleon coupling constants and low-energy parameters of nucleon-nucleon scattering in the 1S0 spin-singlet state is studied on the basis of Yukawa’s meson theory. By using the value of $$f_{pp\pi^0}^2=0.0749(7)$$ established reliably for the pseudovector pion-nucleon coupling constant, which characterizes the strength of the nuclear proton-proton interaction, the values of $$f_c^2=0.0802(7)$$ and $$f_0^2=0.0750(7)$$ were calculated for, respectively, the charged and neutral pion-nucleon coupling constants, along with the value of $$f_{nn\pi^0}^2=0.0751(7)$$, which characterizes the strength of the nuclear neutron-neutron interaction. The values calculated for the low-energy parameters of neutron-proton and neutron-neutron scattering with the aid of the above constants agree well with experimental data.

Production of X(3872) accompanied by a pion in B meson decay

If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced by the creation of $D^{*0} \bar{D}^0$ or $D^{0} \bar{D}^{*0}$ at short distances followed by the formation of the bound state from the charm-meson pairs. It can also be produced by the creation of $D^{*} \bar{D}^*$ at short distances followed by the rescattering of the charm mesons into $X \pi$. We use results of a previous isospin analysis of $B$ meson decays into $K D^{(*)} \bar D^{(*)}$ to estimate the short-distance amplitudes for creating $D^* \bar D^*$. We use an effective field theory for charm mesons and pions called XEFT to calculate the amplitudes for rescattering of $D^{*} \bar{D}^*$ into $X \pi$ with small relative momentum. The $X\pi$ invariant mass distribution is predicted to have a narrow peak near the $D^{*} \bar{D}^*$ threshold from a charm-meson triangle singularity. We estimate the branching fractions into the peak from the triangle singularity for the decays $B^0 \to K^+ X \pi^-$ and $B^+ \to K^0 X \pi^+$.

O(4) ϕ4 model as an effective light meson theory: A lattice-continuum comparison

We investigate the possibility of using the 4 dimensional $O(4)$ symmetric $\phi^4$ model as an effective theory for the sigma-pion system. We carry out lattice Monte Carlo simulations to establish the triviality bound in the case of explicitly broken symmetry and to compare it with results from continuum functional methods. In case of a physical parametrization we find that triviality restricts the possible lattice spacings to a narrow range, therefore cutoff independence in the effective theory sense is practically impossible for thermal quantities. We match the critical line in the space of bare couplings in the different approaches and compare vacuum physical quantities along the line of constant physics (LCP).

Effective theories of dark mesons with custodial symmetry

Dark mesons are bosonic composites of a new, strongly-coupled sector beyond the Standard Model. We consider several dark sectors with fermions that transform under the electroweak group, as arise from a variety of models including strongly-coupled theories of dark matter (e.g., stealth dark matter), bosonic technicolor (strongly-coupled indcued electroweak symmetry breaking), vector-like confinement, etc. We consider theories with two and four flavors under an SU(N) strong group that acquire variously chiral, vector-like, and mixed contributions to their masses. We construct the non-linear sigma model describing the dark pions and match the ultraviolet theory onto a low energy effective theory that provides the leading interactions of the lightest dark pions with the Standard Model. We uncover two distinct classes of effective theories that are distinguishable by how the lightest dark pions decay: “Gaugephilic”: where π0 → Zh, π± → W h dominate once kinematically open, and “Gaugephobic”: where {pi}^0to overline{f}f , {pi}^{pm}to overline{f}^{prime }f dominate. Custodial SU(2) plays a critical role in determining the “philic” or “phobic” nature of a model. In dark sectors that preserve custodial SU(2), there is no axial anomaly, and so the decay π0 → γγ is highly suppressed. In a companion paper, we study dark pion production and decay at colliders, obtaining the constraints and sensitsivity at the LHC.

Effective mesonic theory for the ’t Hooft model on the lattice

We apply to a lattice version of the ’t Hooft model, QCD in two space–time dimensions for large number of colours, a method recently proposed to obtain an effective mesonic action starting from the fundamental, fermionic one. The idea is to pass from a canonical, operatorial representation, where the low-energy states have a direct physical interpretation in terms of a Bogoliubov vacuum and its corresponding quasiparticle excitations, to a functional, path integral representation, via the formalism of the transfer matrix. In this way we obtain a lattice effective theory for mesons in a self-consistent setting. We also verify that well-known results from other different approaches are reproduced in the continuum limit.

Antiproton-proton annihilation into light neutral meson pairs within an effective meson theory

Antiproton--proton annihilation into light neutral mesons in the few GeV energy domain is investigated in view of a global description of the existing data and predictions for future experiments at PANDA, FAIR. An effective meson model earlier developed, with mesonic and baryonic degrees of freedom in $s$, $t$, and $u$ channels, is applied here to $\pi^0\pi^0$ production. Form factors with logarithmic $s$ and $t(u)$ dependencies are applied. A fair agreement with the existing angular distributions is obtained. Applying SU(3) symmetry, it is straightforward to recover the angular distributions for $ \pi^0\eta$, and $\eta\eta$ production in the same energy range. A good agreement is generally obtained with all existing data.

Chern-Simons five-form and holographic baryons

In the top-down holographic model of QCD based on D4/D8-branes in type IIA string theory and some of the bottom up models, the low energy effective theory of mesons is described by a 5 dimensional Yang-Mills-Chern-Simons theory in a certain curved background with two boundaries. The 5 dimensional Chern-Simons term plays a crucial role to reproduce the correct chiral anomaly in 4 dimensional massless QCD. However, there are some subtle ambiguities in the definition of the Chern-Simons term for the cases with topologically non-trivial gauge bundles, which include the configurations with baryons. In particular, for the cases with three flavors, it was pointed out by Hata and Murata that the naive Chern-Simons term does not lead to an important constraint on the baryon spectrum, which is needed to pick out the correct baryon spectrum observed in nature. In this paper, we propose a formulation of well-defined Chern-Simons term which can be used for the cases with baryons, and show that it recovers the correct baryon constraint as well as the chiral anomaly in QCD.

Antiproton-proton annihilation into charged light meson pairs within effective meson theory

Antiproton--proton annihilation into light mesons is revisited in the few GeV energy domain, in view of a global description of the existing data. An effective meson model is developed, with mesonic and baryonic degrees od freedom in $s$, $t$, and $u$ channels. Regge factors are added to reproduce the proper energy behavior and the forward and backward peaked behavior. A comparison with existing data and predictions for angular distributions and energy dependence are done for charged and neutral pion pair production.