arXiv subjects

Matthias R. Schindler

Publications and source records attributed to Matthias R. Schindler.

At least 19 recordsLinked to original sources

arXiv2026

Symmetries of QCD and their relevance for low-energy nuclear physics

QCD, the theory of the strong interactions, is formulated in terms of quarks and gluons, while low-energy nuclear physics deals with hadrons such as protons, neutrons, and pions. Symmetries establish a systematic connection between these two descriptions of strongly-interacting systems. The objective of this article is to review the symmetries of QCD and to explain how they constrain hadronic interactions. Chiral symmetry, which emerges in QCD in the limit of massless quarks, is of particular importance for low-energy nuclear physics. Together with its explicit and spontaneous breaking, chiral symmetry provides the basis for chiral perturbation theory, the effective field theory describing pions and nucleons at low energies.

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arXiv2026

Hadronic Lorentz violation in chiral perturbation theory

Lorentz violation in hadronic systems is related to Lorentz-violating operators of quarks and gluons. Due to the nonperturbative nature of quantum chromodynamics (QCD) at low energies, establishing these relationships is complex. Chiral perturbation theory (ChPT) is an effective theory that provides one method of connecting quark- and gluon-level operators to those at the hadronic level, which can be used to calculate hadronic observables.

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arXiv2025

Inferring the breakdown scales of the chiral expansions for $g_A$ and $m_N$

We apply Bayesian inference to the order-by-order chiral perturbation theory ($χ$PT) expansions for the axial-vector coupling constant $g_A$ and the nucleon mass m_N, and thereby infer the scales at which $χ$PT breaks down for these two observables. Using a pointwise Bayesian analysis, we find that the inferred breakdown scales are notably different for the two observables. For the chiral expansion of $g_A$, we obtain $251^{+20}_{-50}$ MeV and $211^{+20}_{-30}$ MeV using two distinct sets of low-energy constants, while for the chiral expansion of $m_N$ we infer a significantly larger breakdown scale of $491^{+60}_{-90}$ MeV.

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arXiv2025

The role of intermediate $ΔΔ$ states in nucleon-nucleon scattering in the large-$N_c$ and unitary limits, and $ΔΔ$ and $ΩΩ$ scattering

We explore potential explanations for why using large-$N_c$ ($N_c$ is the number of colors) scaling to determine the relative size of few-nucleon low-energy operators agrees with experiment even when dynamical $Δ$'s are not explicitly included. Given that the large-$N_c$ analysis is predicated on the nucleons and $Δ$'s being degenerate, this is a curious result. We show that for purely $S$-wave interactions the relationships dictated by large-$N_c$ scaling are unaffected whether the $Δ$ is included or not. In the case of higher partial waves that do not mix with $S$-waves, the impact of the $Δ$ is perturbative, which makes the agreement with naive ($Δ$-less) large-$N_c$ ordering unsurprising. For higher partial waves that mix with $S$-waves, the nucleon and $Δ$ would need to decouple to get agreement with naive large-$N_c$ ordering. We find all $NN$, $ΔN$, and $ΔΔ$ low energy coefficients for leading-order baryon-baryon scattering in $Δ$-full pionless effective field theory in terms of the two independent parameters dictated by the SU($2F$) spin-flavor symmetry that arises in the $N_c \rightarrow \infty$ limit. Because of recent lattice QCD results and experimental interest, we extend our analysis to the three-flavor case to study $ΩΩ$ scattering. We show that in the unitary limit (where scattering lengths become infinite) one of the two SU($2F$) parameters is driven to zero, resulting in enhanced symmetries, which agree with those found in spin-1/2 entanglement studies.

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arXiv2022

Implications of Large-$N_c$ QCD for the NN Interaction

We present a method for ordering two-nucleon interactions based upon their scaling with the number of QCD colors, $N_c$, in the limit that $N_c$ becomes large. Available data in the two-nucleon sector shows general agreement with this ordering, indicating that the method may be useful in other contexts where data is less readily available. However, several caveats and potential pitfalls can make the large-$N_c$ ordering fragile and/or vulnerable to misinterpretation. We discuss the application of the large-$N_c$ analysis to two- and three-nucleon interactions, including those originating from weak and beyond-the-standard-model interactions, as well as two-nucleon external currents. Finally, we discuss some open questions in the field.

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arXiv2022

Chiral perturbation theory

Chiral perturbation theory (ChPT) is an effective field theory that describes the properties of strongly-interacting systems at energies far below typical hadron masses. The degrees of freedom are hadrons instead of the underlying quarks and gluons. ChPT is a systematic and model-independent approximation method based on an expansion of amplitudes in terms of light-quark masses and momenta. The following is a brief overview of ChPT that is largely based on Scherer, Schindler, Lect. Notes Phys. 830 (2012), which can be referred to for a more detailed introduction.

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arXiv2022

Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives

This is a collection of perspective pieces contributed by the participants of the Institute of Nuclear Theory's Program on Nuclear Physics for Precision Nuclear Physics which was held virtually from April 19 to May 7, 2021. The collection represents the reflections of a vibrant and engaged community of researchers on the status of theoretical research in low-energy nuclear physics, the challenges ahead, and new ideas and strategies to make progress in nuclear structure and reaction physics, effective field theory, lattice QCD, quantum information, and quantum computing. The contributed pieces solely reflect the perspectives of the respective authors and do not represent the viewpoints of the Institute for Nuclear theory or the organizers of the program.

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arXiv2021

Large-$N_c$ analysis of two-nucleon neutrinoless double beta decay and charge-independence-breaking contact terms

The interpretation of experiments that search for neutrinoless double beta decay relies on input from nuclear theory. Cirigliano et al. recently showed that, for the light Majorana exchange formalism, effective field theory calculations require a $nn\to pp e^- e^-$ contact term at leading order. They estimated the size of this contribution by relating it to measured charge-independence-breaking (CIB) nucleon-nucleon interactions and making an assumption about the relative sizes of CIB operators. We show that the assumptions underlying this approximation are justified in the limit of the number of colors $N_c$ being large. We also obtain a large-$N_c$ hierarchy among CIB nucleon-nucleon interactions that is in agreement with phenomenological results.

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arXiv2020

Large-$N_c$ and renormalization group constraints on parity-violating low-energy coefficients for three-derivative operators in pionless effective field theory

We extend from operators with one derivative to operators with three derivatives the analysis of two-body hadronic parity violation in a combined pionless effective field theory (EFT$_{π\!/}$) and large-$N_c$ expansion, where $N_c$ is the number of colors in quantum chromodynamics (QCD). In elastic scattering, these operators contribute to $S$-$P$ and $P$-$D$ wave transitions, with five operators and their accompanying low energy coefficients (LECs) characterizing the $S$-$P$ transitions and six operators and LECs those in $P$-$D$ transitions. We show that the large-$N_c$ analysis separates them into leading order in $N_c$, next-to-leading order in $N_c$, etc. Relationships among EFT$_{π\!/}$ LECs emerge in the large-$N_c$ expansion. We also discuss the renormalization scale dependence of these LECs. Our analysis can complement lattice QCD calculations and help prioritize future parity-violating experiments.

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arXiv2020

Electric dipole moments of three-nucleon systems in the pionless effective field theory

We calculate the electric dipole moments (EDMs) of three-nucleon systems at leading order in pionless effective field theory. The one-body contributions that arise from permanent proton and neutron EDMs and the two-body contributions that arise from CP-odd nucleon-nucleon interactions are taken into account. Neglecting the Coulomb interaction, we consider the triton and ${}^3$He, and also investigate them in the Wigner-SU(4) symmetric limit. We also calculate the electric dipole form factor and find numerically that the momentum dependence of the electric dipole form factor in the Wigner limit is, up to an overall constant (and numerical accuracy), the same as the momentum dependence of the charge form factor.

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arXiv2020

Large-$N_c$ analysis of magnetic and axial two-nucleon currents in pionless effective field theory

We analyze magnetic and axial two-nucleon contact terms in a combined large-$N_c$ and pionless effective field theory expansion. These terms play important roles in correctly describing, e.g., the low-energy cross section of radiative neutron capture and the deuteron magnetic moment. We show that the large-$N_c$ expansion hints towards a hierarchy between the two leading-order magnetic terms that matches that found in phenomenological fits. We also comment on the issue of naturalness in different Lagrangian bases.

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arXiv2019

Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions

A relation is presented between single-hadron long-range matrix elements defined in a finite Euclidean spacetime, and the corresponding infinite-volume Minkowski amplitudes. This relation is valid in the kinematic region where any number of two-hadron states can simultaneously go on shell, so that the effects of strongly-coupled intermediate channels are included. These channels can consist of non-identical particles with arbitrary intrinsic spins. The result accommodates general Lorentz structures as well as non-zero momentum transfer for the two external currents inserted between the single-hadron states. The formalism, therefore, generalizes the work by Christ et al.~[Phys.Rev. D91 114510 (2015)], and extends the reach of lattice quantum chromodynamics (QCD) to a wide class of new observables beyond meson mixing and rare decays. Applications include Compton scattering of the pion ($πγ^\star \to [ππ, K \overline K] \to πγ^\star$), kaon ($K γ^\star \to [πK, ηK] \to K γ^\star$) and nucleon ($N γ^\star \to N π\to N γ^\star$), as well as double-$β$ decays, and radiative corrections to the single-$β$ decay, of QCD-stable hadrons. The framework presented will further facilitate generalization of the result to studies of nuclear amplitudes involving two currents from lattice QCD.

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arXiv2019

The Lorentz- and CPT-Violating Standard Model Extension in Chiral Perturbation Theory

Lorentz and CPT violation in hadronic physics must be tied to symmetry violations at the underlying quark and gluon level. Chiral perturbation theory provides a method for translating novel operators that may appear in the Lagrange density for color-charged parton fields into equivalent forms for effective theories at the meson and baryon levels. We extend the application of this technique to the study of Lorentz-violating and potentially CPT-violating operators from the minimal standard model extension. For dimension-4 operators, there are nontrivial relations between the coefficients of baryon-level operators related to underlying quark and gluon operators with the same Lorentz structures. Moreover, in the mapping of the dimension-3 operators from the quark and gluon level to the hadron level (considered here for the first time), many of the hadronic observables contain no new low-energy coupling constants at all, which makes it possible to make direct translations of bounds derived using experiments on one kind of hadron into bounds in a completely different corner of the hadronic sector. A notable consequence of this is bounds (at $10^{-15}$-$10^{-20}$ GeV levels) on differences $a^μ_{B}-a^μ_{B'}$ of Lorentz and CPT violation coefficients for $SU(3)_{f}$ octet baryons that differ in their structure by the replacement of a single valance $d$ quark by a $s$ quark. Never before has there been any proposal for how these kinds of differences could be constrained.

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arXiv2018

Large-$N_c$ Relationships Among Two-Derivative Pionless Effective Field Theory Couplings

We analyze two-derivative two-nucleon interactions in a combined pionless effective field theory and large-$N_c$ expansion. At leading order in the large-$N_c$ expansion, relationships among low-energy constants emerge. We find these to be consistent with experiment. However, it is critical to correctly address the subtraction-point dependence of the low-energy constants. These results provide additional confidence that the dual-expansion procedure is useful for analyzing low-energy few-body observables.

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arXiv2018

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.

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arXiv2018

Large-N(c) limit reduces the number of independent few-body parity-violating low-energy constants in pionless effective field theory

The symmetries of the Standard Model dictate that for very low energies, where nucleon dynamics can be described in terms of a pionless effective field theory, the leading-order parity-violating nucleon-nucleon Lagrangian contains five independent unknown low-energy constants (LECs). We find that imposing the approximate symmetry of QCD that appears when the number of colors N(c) becomes large reduces the number of independent LECs to two at leading order in the combined pionless effective field theory and large-N(c) expansions. We also find a relation between the two isoscalar LECs in the large-N(c) limit. This has important implications for the number of experiments and/or lattice calculations necessary to confirm this description of physics.

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arXiv2016

Hadronic Lorentz Violation in Chiral Perturbation Theory

Any possible Lorentz violation in the hadron sector must be tied to Lorentz violation at the underlying quark level. The relationships between the theories at these two levels are studied using chiral perturbation theory. Starting from a two-flavor quark theory that includes dimension-four Lorentz-violation operators, the effective Lagrangians are derived for both pions and nucleons, with novel terms appearing in both sectors. Since the Lorentz violation coefficients for nucleons and pions are all related to a single set of underlying quark coefficients, it is possible to place approximate bounds on pion Lorentz violation using only proton and neutron observations. The resulting bounds on four pion parameters are at the $10^{-23}$ level, representing improvements of ten orders of magnitude.

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arXiv2016

Screening of Nucleon Electric Dipole Moments in Nuclei

A partial screening of nucleon electric dipole moments (EDMs) in nuclear systems, which is related to the Schiff mechanism known for neutral atomic systems, is discussed. It is shown that the direct contribution from the neutron EDM to the deuteron EDM is partially screened by about 1% in a zero-range approximation calculation.

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