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DOE OSTI2022

A lattice study of ππ scattering at large N c

We present the first lattice study of pion-pion scattering with varying number of colors, N c . We use lattice simulations with four degenerate quark flavors, N f = 4, and N c = 3 – 6. We focus on two scattering channels that do not involve vacuum diagrams. These correspond to two irreducible representations of the SU(4) flavor group: the fully symmetric one, SS, and the fully antisymmetric one, AA. The former is a repulsive channel equivalent to the isospin-2 channel of SU(2). By contrast, the latter is attractive and only exists for N f ≥ 4. A representative state is (|D$^{+}_{s}$π + > – | D + K + >)/√2. Using Lüscher’s formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large N c . For this, we compute the analytical U(N f ) ChPT prediction for two-pion scattering, and use the lattice results to constrain the N c scaling of the relevant low-energy couplings.

1/N Expansion↗

DOE OSTI2025

Off-shell vertices in heavy particle effective theories and B → Dπℓν

We study the modifications to decay amplitudes in heavy to heavy semileptonic decays with multiple hadrons in the final state due to intermediate heavy hadrons being off-shell or having a finite width. Combining Heavy Hadron Chiral Perturbation Theory (HHχPT) with a BCFW on-shell factorization formula, we show that these effects induce O (1/M) corrections to the standard results computed in the narrow-width approximation and therefore are important in extracting form factors from data. A combination of perturbative unitarity, analyticity, and reparameterization invariance fully determine these corrections in terms of known Isgur-Wise functions without the need to introduce new form factors. In doing so, we develop a novel technique to compute the boundary term at complex infinity in the BCFW formula for theories with derivatively coupled scalars. While we have used the $\overline{B}$ → Dπℓν decay as an example, these techniques can generally be applied to effective field theories with (multiple) distinct reference vectors. Article PDF

Chiral Lagrangian↗

DOE OSTI2024

Final state rescattering effects in axio-hadronic η and η′ decays

It has been long-understood that final state rescattering effects provide (1) corrections to hadronic meson decays rates, such as η → πππ and η' → ηππ. Hence, one would expect that such effects would be just as important in axio-hadronic η and η' decays, such as η(') → ππa, where a is an axion or axion-like particle (ALP). And indeed they are, as we show in this paper by using the treatment of dispersion relations to include the effects of strong final state interactions in several axio-hadronic processes, namely, η(') → π 0 π 0 a, η(') → π+π-a, and η' → ηπ 0 a. We also compute the perturbative, leading order decay rates for multiple ALP emission, such as in η(') → π 0 aa, η' → ηaa and η(') → aaa, and briefly discuss the expected corrections from strong interactions and the processes that must be considered for an accurate rate estimation of these multi-ALP decay channels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization

Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the e + e - → π + π - channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for e + e - → 3π by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and ρ–ω mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor η3π that generalizes the analog treatment of virtual and final-state photons in the 2π case. The global fit to the e+e- → 3π data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives for the total 3π contribution to the anomalous magnetic moment of the muon, of which ${a}^{FSR}_\mu [3\pi]$ = 0.51(1) x 10 -10 and ${a}^{\rho - \omega}_\mu [3\pi]$ = -2.68(70) x 10 -10 can be ascribed to IB. We argue that the resulting cancellation with ρ–ω mixing in e + e - → 2π can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters M ω = 782.70(3) MeV, M Φ = 1019.21(2) MeV, Γ ω = 8.71(3) MeV, and Γ Φ = 4.27(1) MeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Real-time chiral dynamics at finite temperature from quantum simulation

In this study, we explore the real-time dynamics of the chiral magnetic effect (CME) at a finite temperature in the (1+1)-dimensional QED, the massive Schwinger model. By introducing a chiral chemical potential μ 5 through a quench process, we drive the system out of equilibrium and analyze the induced vector currents and their evolution over time. The Hamiltonian is modified to include the time-dependent chiral chemical potential, thus allowing the investigation of the CME within a quantum computing framework. We employ the quantum imaginary time evolution (QITE) algorithm to study the thermal states, and utilize the Suzuki-Trotter decomposition for the real-time evolution. This study provides insights into the quantum simulation capabilities for modeling the CME and offers a pathway for studying chiral dynamics in low-dimensional quantum field theories.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Light quark loops in ${K}^{\pm}\to {\pi}^{\pm}\nu \overline{\nu}$ from vector meson dominance and update on the Kaon Unitarity Triangle

We use vector meson dominance to calculate non-perturbative contributions to the branching ratio of the rare decay $K$ ± → π ± $v\overline{v}$ stemming from matrix elements involving up-quark loops. The importance of this observable as well as of K 0 → π 0 l + l - and of the direct CP violation parameter ϵ' K is then discussed in the context of a Unitarity Triangle sqtudy based on Kaon sector observables only.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Towards a theory of hadron resonances

In this review, we present the current state of the art of our understanding of the spectrum of excited strongly interacting particles and discuss methods that allow for a systematic and model-independent calculation of the hadron spectrum. These are lattice QCD and effective field theories. Synergies between both approaches can be exploited allowing for a deeper understanding of the hadron spectrum. Results based on effective field theories and hadron–hadron scattering in lattice QCD or combinations thereof are presented and discussed. We also show that the often used Breit–Wigner parametrization is at odds with chiral symmetry and should not be used in case of strongly coupled channels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Pion Nucleon Scattering in BCHPT Combined with 1/Nc Expansion

Pion nucleon scattering has played a crucial role in advancing our understanding of the low-energy regime of strong interactions. This dissertation presents the development of a new theoretical framework that combines Baryon Chiral Perturbation Theory (BChPT) with the 1/Nc Expansion to analyze pion nucleon scattering. The resulting effective Lagrangian incorporates both chiral and spin-flavor symmetries. Scattering amplitudes are calculated up to the one-loop level (NNLO), which includes four tree-level Feynman diagrams and 45 non-zero loop diagrams. The effective Lagrangian is renormalized at the one-loop level. With spin-3/2 baryons naturally included, the framework demonstrates strong convergence at higher energies. The NNLO pion nucleon scattering amplitude shows good agreement with experimental data from the SAID database. This novel approach, BChPT combined with 1/Nc Expansion, demonstrates substantial predictive power at higher energies where other low-energy theories fall short, achieving the goals of this combined framework. The contribution from loop diagrams is essential for achieving good agreement with the data, highlighting the importance of conducting the calculation up to NNLO. Extracted values for physically measurable quantities agree reasonably well with independently extracted values, underscoring the robustness of the theory.

Jayakodige, Dulitha [Hampton Univ., Hampton, VA (U↗

DOE OSTI2026

Coupled-channel approach to isotensor π π π scattering from lattice QCD

The quest to understand three-body dynamics from first-principle QCD includes the study of nonresonant and resonant systems. The isospin I = 2 system is of particular interest having no three-body resonance but featuring a resonance in a subchannel, while also being a coupled-channel problem. In this study, we calculate the finite-volume spectrum from lattice QCD at two different pion masses, map the amplitude to the infinite volume through a generalized Finite-Volume Unitarity three-body quantization condition, investigate the limit of a narrow ρ , and compare with an effective Lagrangian prediction at leading order. Chiral extrapolations between different pion masses are performed.

Feng, Yuchuan [The George Washington University] (↗

DOE OSTI2025

New insights into the doubly charmed exotic mesons

Abstract Using effective Lagrangians constrained by the heavy quark spin symmetry and chiral symmetry, for the light quarks, we analyze the $$D^0 D^0\pi ^+,$$ D 0 D 0 π + , $$\bar{D}^0D^0\pi ^0$$ D ¯ 0 D 0 π 0 and $$D^0\bar{D}^{*0}$$ D 0 D ¯ ∗ 0 invariant mass spectra. Performing a simultaneous analysis of the doubly charmed and charm-anti-charm states gives further insights into the nature of the $$T^+_{cc}$$ T cc + and $$\chi ^0_{c1}(3872),$$ χ c 1 0 ( 3872 ) , exotic hadrons. It is confirmed that both states should lie below their respective $$DD^*$$ D D ∗ / $$D\bar{D}^*$$ D D ¯ ∗ thresholds. Also, the contributions of the triangle and box diagrams are negligible.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Large $$N_c$$ QCD phase diagram at $$\mu _B=0$$

Abstract Lattice studies suggest that at zero baryon chemical potential and increasing temperature there are three characteristic regimes in QCD that are connected by smooth analytical crossovers: a hadron gas regime at$$T < T_{ch}\sim 155$$ T < T ch ∼ 155 MeV, an intermediate regime, called stringy fluid, at$$T_{ch}< T < \sim 3 T_{ch}$$ T ch < T < ∼ 3 T ch , and a quark-gluon plasma regime at higher temperatures. These regimes have been interpreted to reflect different approximate symmetries and effective degrees of freedom. In the hadron gas the effective degrees of freedom are hadrons and the approximate chiral symmetry of QCD is spontaneously broken. The intermediate regime has been interpreted as lacking spontaneous chiral symmetry breaking along with the emergence of new approximate symmetry, chiral spin symmetry, that is not a symmetry of the Dirac Lagrangian, but is a symmetry of the confining part of the QCD Lagrangian. While the high temperature regime is the usual quark-gluon plasma which is often considered to reflect “deconfinement” in some way. This paper explores the behavior of these regimes of QCD as the number of colors in the theory,$$N_c$$ N c , gets large. In the large$$N_c$$ N c limit the theory is center-symmetric and notions of confinement and deconfinement are unambiguous. The energy density is$$\mathcal{O}(N_c^0)$$ O ( N c 0 ) in the meson gas,$${{\mathcal {O}}}(N_c^1)$$ O ( N c 1 ) in the intermediate regime and$${{\mathcal {O}}}(N_c^2)$$ O ( N c 2 ) in the quark-gluon plasma regime. In the large$$N_c$$ N c limit these regimes may become distinct phases separated by first order phase transitions. The intermediate phase has the peculiar feature that glueballs should exist and have properties that are unchanged from what is seen in the vacuum (up to$$1/N_c $$ 1 / N c corrections), while the ordinary dilute gas of mesons with broken chiral symmetry disappears and approximate chiral spin symmetry should emerge.

Physics↗

DOE OSTI2025

Interacting mesons as degrees of freedom in a chiral model

Here, we study the equation of state of hot and dense hadronic matter using an extended chiral mean field (CMF) model framework where the addition is the inclusion of interactions of thermally excited mesons. This is implemented by calculating the in-medium masses of pseudoscalar and vector mesons, obtained through the explicit chiral symmetry-breaking and vector-interaction terms in the Lagrangian, respectively, prior to applying the mean-field approximation. As a result, the in-medium meson contributions generate a feedback term to the CMF’s equations of motion, which then modifies the equation of state. With this improvement, we quantify the effect on the equation of state of strongly interacting matter through comparisons with state-of-the-art lattice QCD results and other hadronic models like the hadron resonance gas model. We find that the results of the updated hadronic CMF model with an improved meson description (mCMF) provide a better agreement with lattice-QCD data for thermodynamic state variables across a wide range of temperatures and baryon chemical potentials.

phenomenology↗

DOE OSTI2022

Instanton Effects in Euclidean vacuum, Real Time Production, and in the Light-front Wave Functions

Nontrivial topological structures of non-Abelian gauge fields were discovered in the 1970s. Instanton solutions, describing vacuum tunneling through topological barriers, have fermionic zero modes which are at the origin of ‘t Hooft effective Lagrangian. In the 1980s, instanton ensembles have been used to explain chiral symmetry breaking. In the 1990s, a large set of numerical simulations were performed deriving Euclidean correlation functions. The special role of scalar diquarks in nucleons and color superconductivity in dense quark matter has been elucidated. In these lectures, we discuss further developments of physics related to gauge topology. We show that the instanton–anti-instanton “streamline” configurations describe “sphaleron transitions” in high-energy collisions, which result in production of hadronic clusters with nontrivial topological/chiral charges. (They are not yet observed, but discussions of dedicated experiments at the LHC and RHIC are ongoing.) Another new direction is instanton effects in hadronic spectroscopy, both in the rest frame and on the light front. We will discuss their role in central and spin-dependent potentials, form factors and antiquark nuclear “sea”. Finally, we summarize the advances in the semiclassical theory of deconfinement, and chiral phase transitions at finite temperature, in QCD, and in some of its “deformed” versions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Nonlocal chiral contributions to generalized parton distributions of the proton at nonzero skewness

We compute the one-loop contributions to spin-averaged generalized parton distributions (GPDs) in the proton from pseudoscalar mesons with intermediate octet and decuplet baryon states at nonzero skewness. Our framework is based on nonlocal covariant chiral effective theory, with ultraviolet divergences regularized by introducing a relativistic regulator derived consistently from the nonlocal Lagrangian. Using the splitting functions calculated from the nonlocal Lagrangian, we find the nonzero skewness GPDs from meson loops by convoluting with the phenomenological pion GPD and the generalized distribution amplitude, and verify that these satisfy the correct polynomiality properties. We also compute the lowest two moments of GPDs to quantify the meson loop effects on the Dirac, Pauli, and gravitational form factors of the proton.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Propagator Zeros and Lattice Chiral Gauge Theories

Symmetric mass generation (SMG) has been advocated as a mechanism to render mirror fermions massive without symmetry breaking, ultimately aiming for the construction of lattice chiral gauge theories. It has been argued that in an SMG phase, the poles in the mirror fermion propagators are replaced by zeros. Using an effective Lagrangian approach, we investigate the role of propagator zeros when the gauge field is turned on, finding that they act as coupled ghost states. In four dimensions, a propagator zero makes an opposite-sign contribution to the one-loop beta function as compared to a normal fermion. In two dimensional Abelian theories, a propagator zero makes a negative contribution to the photon mass squared. In addition, propagator zeros generate the same anomaly as propagator poles. Thus, gauge invariance will always be maintained in an SMG phase, in fact, even if the target chiral gauge theory is anomalous, but unitarity of the gauge theory is lost. Published by the American Physical Society 2024

Physics↗

DOE OSTI2025

Nonlocal Effective Field Theory and Its Applications

We review recent applications of nonlocal effective field theory, particularly focusing on nonlocal chiral effective theory and nonlocal quantum electrodynamics (QED), as well as an extension of nonlocal effective theory to curved spacetime. For the chiral effective theory, we discuss the calculation of generalized parton distributions (GPDs) of the nucleon at nonzero skewness, along with the corresponding gravitational (or mechanical) form factors, within the convolution framework. In the QED application, we extend the nonlocal formulation to construct the most general nonlocal QED interaction, in which both the propagator and fundamental QED vertex are modified due to the nonlocal Lagrangian, while preserving the Ward–Green–Takahashi identities. For consistency with the modified propagator, a solid quantization is proposed, and the nonlocal QED is applied to explain the lepton g−2 anomalies without the introduction of new particles beyond the standard model. Finally, with an extension of the chiral effective action to curved spacetime, we investigate the nonlocal energy–momentum tensor and gravitational form factors of the nucleon with a nonlocal pion–nucleon interaction.

chiral effective field theory↗

DOE OSTI2024

Flows in the space of interacting chiral boson theories

We study interacting theories of N left-moving and N ¯ right-moving Floreanini-Jackiw bosons in two dimensions. A parametrized family of such theories is shown to enjoy (nonmanifest) Lorentz invariance if and only if its Lagrangian obeys a flow equation driven by a function of the energy-momentum tensor. We discuss the canonical quantization of such theories along classical stress tensor flows, focusing on the case of the root- T T ¯ deformation, where we obtain perturbative results for the deformed spectrum in a certain large-momentum limit. In the special case N = N ¯ , we consider the quantum effective action for the root- T T ¯ -deformed theory by expanding around a general classical background, and we find that the one-loop contribution vanishes for backgrounds with constant scalar gradients. Our analysis can also be interpreted via dual U ( 1 ) Chern-Simons theories in three dimensions, which might be used to describe deformations of charged AdS 3 black holes or quantum Hall systems. Published by the American Physical Society 2024

Ebert, Stephen (ORCID:0000000154670155)↗

DOE OSTI2024

Interacting chiral form field theories and $$ T\overline{T} $$-like flows in six and higher dimensions

Abstract In this paper we initiate the study of six-dimensional non-linear chiral two-form gauge theories as deformations of free chiral two-form gauge theories driven by stress-tensor$$ T\overline{T} $$ T T ¯ -like flows. To lay the background for this study, we elaborate on the relationship between different Lagrangian formulations of duality-invariantp-form theories and corresponding$$ T\overline{T} $$ T T ¯ -like flows in various dimensions. To this end we propose a new formulation which (i) is a generalization of the four-dimensional construction by Ivanov, Nurmagambetov and Zupnik (INZ) and (ii) turns into the PST formulation upon integrating out an auxiliary self-dual field. We elucidate space-time covariant properties of the PST formulation by clarifying and making use of its relation to the INZ-type formulation and to a so-called “clone” construction.

Physics↗