Pion Theory Research Articles

Bootstrapping pions at large N. Part II. Background gauge fields and the chiral anomaly

We continue the program [1] of carving out the space of large N confining gauge theories by modern S-matrix bootstrap methods, with the ultimate goal of cornering large N QCD. In this paper, we focus on the effective field theory of massless pions coupled to background electromagnetic fields. We derive the full set of positivity constraints encoded in the system of 2 → 2 scattering amplitudes of pions and photons. This system probes a larger set of intermediate meson states, and is thus sensitive to intricate large N selection rules, especially when supplemented with expectations from Regge theory. It also has access to the coefficient of the chiral anomaly. We find novel numerical bounds on several ratios of Wilson coefficients, in units of the rho mass. By matching the chiral anomaly with the microscopic theory, we also derive bounds that contain an explicit N dependence.

All-loop soft theorem for pions

In this paper we discuss a generalization of the Adler zero to loop integrands in the planar limit of the SU(N) nonlinear sigma model (NLSM). The Adler zero for integrands is violated starting at the two-loop order and is only recovered after integration. Here we propose a soft theorem satisfied by loop integrands with any number of loops and legs. This requires a generalization of NLSM integrands to an off shell framework with certain deformed kinematics. Defining an , we identify a simple nonvanishing soft behavior of integrands, which we call the . We find that the proposed soft theorem is satisfied by the “surface” integrand of Arkani-Hamed and Figueiredo [], which is obtained from the shifted Trφ3 surfacehedron integrand. Finally, we derive an on shell version of the algebraic soft theorem that takes an interesting form in terms of self-energy factors and lower-loop integrands in a mixed theory of pions and scalars. Published by the American Physical Society 2024

QCD with an infrared fixed point: The pion sector

The possibility that gauge theories with chiral symmetry breaking below the conformal window exhibit an infrared fixed point is explored. With this assumption three aspects of pion physics are reproduced if the quark mass anomalous dimension at the infrared fixed point is γ*=1. First, by matching the long-distance scalar adjoint correlation function. Second, by perturbing the fixed point by a small quark mass, the mq-dependence of the pion mass is reproduced by renormalization group arguments. Third, consistency of the trace anomaly and the Feynman-Hellmann theorem, for small mq, imply the same result once more. This suggests the following picture for the conformal window; close to its upper boundary γ* is zero and grows as the number of fermions is reduced until its lower boundary γ*=1 is reached, where chiral symmetry breaking sets in. Below, the strongly coupled gauge theory with γ*=1 is infrared dual to the free theory of pions. A possible dilaton sector of the scenario will be addressed in a companion paper. Published by the American Physical Society 2024

Gravitational form factors of the nucleon and one pion graviproduction in chiral EFT

In the framework of chiral effective field theory of delta resonances, nucleons, and pions interacting with background gravitational field we calculate the gravitational form factors of the nucleon up to fourth order in the small scale expansion and obtain the long-range behavior of the corresponding contributions to the energy, spin, pressure, and shear force distributions. By comparing nucleon gravitational form factors with and without delta contributions we conclude that explicit inclusion of deltas plays an important role. Next we explore the Lorentz structure of the N↦Nπ transition matrix element of the conserved symmetric energy-momentum tensor and introduce its parametrization in terms of twelve transition form factors. We use the chiral effective field theory to calculate the tree-order contributions to the gravitational transition form factors of the pion graviproduction off the nucleon up to third order. Published by the American Physical Society 2024

Bootstrapping pions at large N

We revisit from a modern bootstrap perspective the longstanding problem of solving QCD in the large N limit. We derive universal bounds on the effective field theory of massless pions by imposing the full set of positivity constraints that follow from 2 → 2 scattering. Some features of our exclusion plots have intriguing connections with hadronic phenomenology. The exclusion boundary exhibits a sharp kink, raising the tantalizing scenario that large N QCD may sit at this kink. We critically examine this possibility, developing in the process a partial analytic understanding of the geometry of the bounds.

Dynamics of the O(4) critical point in QCD

We perform a Langevin simulation of the $O(4)$ critical point, which lies in the dynamic universality class of ``model G.'' This is the dynamic universality class of the chiral phase transition in QCD with two massless flavors. The axial charge and the order parameter ${\ensuremath{\phi}}_{a}=(\ensuremath{\sigma},\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\pi}})$ exhibit a rich dynamical interplay, which reflects the qualitative differences in the hydrodynamic effective theories above and below ${T}_{c}$. From the axial charge correlators on the critical line we extract a dynamical critical exponent of $\ensuremath{\zeta}=1.47\ifmmode\pm\else\textpm\fi{}0.01(\text{stat.})$, which is compatible with the theoretical expectation of $\ensuremath{\zeta}=d/2$ (with $d=3$) when systematic errors are taken into account. At low temperatures, we quantitatively match the $O(4)$ simulations to the superfluid effective theory of soft pions.

A theory of dark pions

We present a complete model of a dark QCD sector with light dark pions, broadly motivated by hidden naturalness arguments. The dark quarks couple to the Standard Model via irrelevant Z- and Higgs-portal operators, which encode the low-energy effects of TeV-scale fermions interacting through Yukawa couplings with the Higgs field. The dark pions, depending on their CP properties, behave as either composite axion-like particles (ALPs) mixing with the Z or scalars mixing with the Higgs. The dark pion lifetimes fall naturally in the most interesting region for present and proposed searches for long-lived particles, at the LHC and beyond. This is demonstrated by studying in detail three benchmark scenarios for the symmetries and structure of the theory. Within a coherent framework, we analyze and compare the GeV-scale signatures of flavor-changing meson decays to dark pions, the weak-scale decays of Z and Higgs bosons to hidden hadrons, and the TeV-scale signals of the ultraviolet theory. New constraints are derived from B decays at CMS and from Z-initiated dark showers at LHCb, focusing on the displaced dimuon signature. We also emphasize the strong potential sensitivity of ATLAS and CMS to dark shower signals with large multiplicities and long lifetimes of the dark pions. As a key part of our phenomenological study, we perform a new data-driven calculation of the decays of a light ALP to exclusive hadronic Standard Model final states. The results are provided in a general form, applicable to any model with arbitrary flavor-diagonal couplings of the ALP to fermions.

Chiral theory of nucleons and pions in the presence of an external gravitational field

We extend the standard second order effective chiral Lagrangian of pions and nucleons by considering the coupling to an external gravitational field. As an application we calculate one-loop corrections to the one-nucleon matrix element of the energy-momentum tensor to fourth order in chiral counting, and next-to-leading order tree-level amplitude of the pion-production in an external gravitational field. We discuss the relation of the obtained results to experimentally measurable observables. Our expressions for the chiral corrections to the nucleon gravitational form factors differ from those in the literature. That might require to revisit the chiral extrapolation of the lattice data on the nucleon gravitational form factors obtained in the past.

Finite-volume and thermal effects in the leading-HVP contribution to muonic (g \u2212 2)

The leading finite-volume and thermal effects, arising in numerical lattice QCD calculations of {a}_{mu}^{mathrm{HVP},mathrm{LO}}equiv {left(g-2right)}_{mu}^{mathrm{HVP},mathrm{LO}}/2 , are determined to all orders with respect to the interactions of a generic, relativistic effective field theory of pions. In contrast to earlier work [1] based in the finite-volume Hamiltonian, the results presented here are derived by formally summing all Feynman diagrams contributing to the Euclidean electromagnetic-current two-point function, with any number of internal pion loops and interaction vertices. As was already found in ref. [1], the leading finite-volume corrections to {a}_{mu}^{mathrm{HVP},mathrm{LO}} scale as exp[−mL] where m is the pion mass and L is the length of the three periodic spatial directions. In this work we additionally control the two sub-leading exponentials, scaling as exp[− sqrt{2} mL] and exp[− sqrt{3} mL]. As with the leading term, the coefficient of these is given by the forward Compton amplitude of the pion, meaning that all details of the effective theory drop out of the final result. Thermal effects are additionally considered, and found to be sub-percent-level for typical lattice calculations. All finite-volume corrections are presented both for {a}_{mu}^{mathrm{HVP},mathrm{LO}} and for each time slice of the two-point function, with the latter expected to be particularly useful in correcting small to intermediate current separations, for which the series of exponentials exhibits good convergence.

Hadronic Lorentz violation in chiral perturbation theory including the coupling to external fields

If any violation of Lorentz symmetry exists in the hadron sector, its ultimate origins must lie at the quark level. We continue the analysis of how the theories at these two levels are connected, using chiral perturbation theory. Considering a two-flavor quark theory, with dimension-4 operators that break Lorentz symmetry, we derive a low-energy theory of pions and nucleons that is invariant under local chiral transformations and includes the coupling to external fields. The pure meson and baryon sectors, as well as the couplings between them and the couplings to external electromagnetic and weak gauge fields, contain forms of Lorentz violation which depend on linear combinations of quark-level coefficients. In particular, at leading order the electromagnetic couplings depend on the very same combinations as appear in the free particle propagators. This means that observations of electromagnetic processes involving hadrons--such as vacuum Cerenkov radiation, which may be allowed in Lorentz-violating theories--can only reliably constrain certain particular combinations of quark coefficients.

Electromagnetic transition form factors of the Roper resonance in baryon chiral perturbation theory

We consider the electromagnetic transition form factors of the Roper resonance in the framework of an effective field theory of pions, nucleons and delta and Roper resonances as explicit degrees of freedom. Due to the lack experimental data in the region of applicability of low energy effective field theory we fit available free coupling constants and compare obtained results compare to the predictions of a theoretical model.

Effective pion mass term and the trace anomaly

Recently, we developed an effective theory of pions and a light dilatonic meson for gauge theories with spontaneously broken chiral symmetry that are close to the conformal window. The pion mass term in this effective theory depends on an exponent $y$. We derive the transformation properties under dilatations of the renormalized fermion mass, and use this to rederive $y=3-\gamma_m^*$, where $\gamma_m^*$ is fixed-point value of the mass anomalous dimension at the sill of the conformal window. This value for $y$ is consistent with the trace anomaly of the underlying near-conformal gauge theory.

Holographic Skyrmions

Skyrmions are topological solitons that describe baryons within a nonlinear theory of pions. In holographic QCD, baryons correspond to topological solitons in a bulk theory with an extra spatial dimension. Thus, the three-dimensional Skyrmion lifts to a four-dimensional holographic Skyrmion in the bulk. We begin this review with a description of the simplest example of this correspondence, where the holographic Skyrmion is exactly the self-dual Yang–Mills instanton in flat space. This places an old result of Atiyah and Manton within a holographic framework and reveals that the associated Skyrme model extends the nonlinear pion theory to include an infinite tower of vector mesons, with specific couplings for a BPS theory. We then describe the more complicated curved space version that arises from the string theory construction of Sakai and Sugimoto. The basic concepts remain the same but the technical difficulty increases as the holographic Skyrmion is a curved space version of the Yang–Mills instanton, so self-duality and integrability are lost. Finally, we turn to a low-dimensional analog of holographic Skyrmions, where aspects such as multi-baryons and finite baryon density are amenable to both numerical computation and an approximate analytic treatment.

Regularization methods for Nuclear Lattice Effective Field Theory

We investigate Nuclear Lattice Effective Field Theory for the two-body system for several lattice spacings at lowest order in the pionless as well as in the pionful theory. We discuss issues of regularizations and predictions for the effective range expansion. In the pionless case, a simple Gaussian smearing allows to demonstrate lattice spacing independence over a wide range of lattice spacings. We show that regularization methods known from the continuum formulation are necessary as well as feasible for the pionful approach.

Scalar Form Factor of the Pion in the Kroll-Lee-Zumino Field Theory

The renormalizable Kroll-Lee-Zumino field theory of pions and a neutral rho-meson is used to determine the scalar form factor of the pion in the space-like region at next-to-leading order. Perturbative calculations in this framework are parameter-free, as the masses and the rho-pion-pion coupling are known from experiment. Results compare favorably with lattice QCD calculations.

Skyrmions in a truncated BPS theory

Recently, it has been shown that (4 + 1)-dimensional Yang-Mills theory may be written as a (3 + 1)-dimensional BPS Skyrme model, in which the Skyrme field is coupled toan infinite tower of vector mesons. Truncating this tower to a single vector meson yields an extension of the standard Skyrme model to a theory of pions coupled to the ρ meson, with the significant simplification that no additional free parameters are introduced. The present paper is concerned with this truncated theory and results are presented for Skyrmions with baryon numbers one to four. The approach involves the use of an extended version of the Atiyah-Manton construction, in which the Skyrme field is approximated by the holonomy of a Yang-Mills instanton. It is found that the coupling to the ρ meson significantly reduces Skyrmion binding energies, to produce an improved comparison with the experimental data on nuclei. A truncation that includes both a vector and an axial vector meson is also investigated, providing a model of pions, the ρ meson and the a 1 meson. Binding energies are further reduced by the inclusion of this additional meson, shifting the Skyrmion energies a little closer to those of nuclei. Fixing the energy unit by equating the energy of the baryon number four Skyrmion to the He4 mass, yields masses for all lower baryon numbers that are within 20MeV of the experimental values, which is an error that is four times smaller than in the standard Skyrme model.

Pions in LargeNQuantum Chromodynamics

An effective field theory of quarks, gluons, and pions, with the number N of colors treated as large, is proposed as a basis for calculations of hadronic phenomena at moderate energies. The qualitative consequences of the large N limit are similar though not identical to those in pure quantum chromodynamics, but because constituent quark masses appear in the effective Lagrangian, the 't Hooft coupling in the effective theory need not be strong at moderate energies. To leading order in 1/N the effective theory is renormalizable, with only a finite number of terms in the Lagrangian.

Scalar radius of the pion in the Kroll-Lee-Zumino renormalizable theory

The Kroll-Lee-Zumino renormalizable Abelian quantum field theory of pions and a massive $\ensuremath{\rho}$-meson is used to calculate the scalar radius of the pion at next-to-leading (one-loop) order in perturbation theory. Because of renormalizability, this determination involves no free parameters. The result is $⟨{r}_{\ensuremath{\pi}}^{2}{⟩}_{s}=0.40\text{ }\text{ }{\mathrm{fm}}^{2}$. This value gives for ${\overline{\ensuremath{\ell}}}_{4}$, the low energy constant of chiral perturbation theory, ${\overline{\ensuremath{\ell}}}_{4}=3.4$, and ${F}_{\ensuremath{\pi}}/F=1.05$, where $F$ is the pion decay constant in the chiral limit. Given the level of accuracy in the masses and the $\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}$ coupling, the only sizable uncertainty in this result is due to the (uncalculated) next-to-next-to-leading order contribution.

Low-Energy Inelastic Neutrino Reactions onHe4

The inelastic scattering of neutrino off 4He is calculated microscopically at energies typical for core-collapse supernova environment. The calculation is carried out with the Argonne V18 nucleon-nucleon potential and the Urbana IX three-nucleon force. Full final state interaction is included via the Lorentz integral transform method. The contribution of axial meson exchange currents to the cross sections is taken into account from effective field theory of nucleons and pions to order O(Q3).

Dual interpretations of pion clouds in relativistic heavy ion collisions

A gauge theory of pions interacting with \ensuremath{\rho}-mesons at elevated temperatures is used to calculate the pressure in a hot pion gas. No reference is made to the pion's status as a QCD Goldstone boson. The role of the pion is merely that of a carrier of an SU(2) symmetry, gauged to create a vector-meson interaction, the \ensuremath{\rho} playing the role of the interacting vector particle. The results are in rough agreement with much more elaborate calculations, both of the purely hadronic variety, and those that invoke quark-gluon degrees of freedom. The quark-gluon and purely hadronic calculations seemingly lead to very similar predictions which are in accord with recent data from the BNL Relativistic Heavy Ion Collider (RHIC). The results motivate the question as to whether the two descriptions are dual to each other in the sense of being alternate models, each sufficient to explain the observed data.