Chiral Power Counting Research Articles

Effect of chiral nuclear forces on the neutrino mean free path in hot neutron matter

We study the role of chiral nuclear forces on the propagation of neutrinos in hot neutron matter. In particular, we analyze the convergence of the dynamical structure factor and the neutrino mean free path with the order of the power counting of the chiral forces, as well as the role of the regulator cut-off of these forces in the determination of these quantities. Single-particle energies and chemical potentials needed to calculate the dynamical structure factor are obtained within the Brueckner--Hartree--Fock approximation extended to finite temperature. Our results show that the dynamical structure factor and the neutrino mean free path depend on the cut-off only when the chiral potential is considered at leading order (LO) and next-to leading order (NLO), becoming this dependence strongly reduced at higher orders in the chiral power counting due to the role of three-nucleon forces that start to contribute at next-to-next-to leading order (N$^2$LO) being, in particular, almost negligible at next-to-next-to-next-to leading order (N$^3$LO). The neutrino mean free path is found to converge up to densities slightly below $\sim 0.15$ fm$^{-3}$ when increasing the order of the chiral power counting, although no signal of convergence is found for densities above this value. The uncertainty associated with our order-by-order nuclear many-body calculation of the neutrino mean free path is roughly estimated from the difference between the results obtained at N$^2$LO and N$^3$LO, finding that it varies from about a few centimeters at low densities up to a bit less than $2$ meters at the largest one considered in this work, $0.3$ fm$^{-3}$.

Axial-vector form factors of the baryon octet and chiral symmetry

We consider the axial-vector form factors of the baryon octet in flavor-SU(3) chiral perturbation theory. The baryon octet and decuplet and the pseudoscalar-meson octet are included as explicit degrees of freedom. We explore the use of on-shell meson and baryon masses in the one-loop contributions to the axial-vector form factors and focus on a consistent treatment in terms of chiral power counting. The convergence properties of such an approach are scrutinized. We discuss the potential for comparison to upcoming QCD lattice data.

Patterns of C- and CP-violation in hadronic η and η′ three-body decays

We construct hadronic amplitudes for the three-body decays η(′) → π+π−π0 and η′ → ηπ+π− in a non-perturbative fashion, allowing for C- and CP-violating asymmetries in the π+π− distributions. These amplitudes are consistent with the constraints of analyticity and unitarity. We find that the currently most accurate Dalitz-plot distributions taken by the KLOE-2 and BESIII collaborations confine the patterns of these asymmetries to a relative per mille and per cent level, respectively. Our dispersive representation allows us to extract the individual coupling strengths of the C- and CP-violating contributions arising from effective isoscalar and isotensor operators in η(′) → π+π−π0 and an effective isovector operator in η′ → ηπ+π−, while the strongly different sensitivities to these operators can be understood from chiral power counting arguments.

The axion-baryon coupling in SU(3) heavy baryon chiral perturbation theory

In the past, the axion-nucleon coupling has been calculated in the framework of SU(2) heavy baryon chiral perturbation theory up to third order in the chiral power counting. Here, we extend these earlier studies to the case of heavy baryon chiral perturbation theory with SU(3) flavor symmetry and derive the axion coupling to the full SU(3) baryon octet, showing that the axion also significantly couples to hyperons. As studies on dense nuclear matter suggest the possible existence of hyperons in stellar objects such as neutron stars, our results should have phenomenological implications related to the so-called axion window.

Covariant propagator and chiral power counting

Some one-loop diagrams with one and two external baryons/nucleons are revisited using covariant baryon propagators in chiral effective theory. We showed that it is enough to separate and subtract all the local terms that violate chiral power counting to recover chiral power counting, no need to introduce extra operations. The structures of leading chiral corrections and IR enhancement or threshold effects are ‘stable’ or persist as long as covariant propagators are employed for all particles.

Implication of K→πνν¯ for generic neutrino interactions in effective field theories

In this work we investigate the implication of $K\to \pi \nu \bar{\nu}$ from the recent KOTO and NA62 measurements for generic neutrino interactions and the new physics scale in effective field theories. The interactions between quarks and left-handed Standard Model (SM) neutrinos are first described by the low energy effective field theory (LEFT) below the electroweak scale. We match them to the chiral perturbation theory ($\chi$PT) at the chiral symmetry breaking scale to calculate the branching fractions of Kaon semi-invisible decays and match them up to the SM effective field theory (SMEFT) to constrain new physics above the electroweak scale. In the framework of effective field theories, we prove that the Grossman-Nir bound is valid for both dim-6 and dim-7 LEFT operators, and the dim-6 vector and scalar operators dominantly contribute to Kaon semi-invisible decays based on LEFT and chiral power counting rules. They are induced by multiple dim-6 lepton-number-conserving operators and one dim-7 lepton-number-violating operator in the SMEFT, respectively. In the lepton-number-conserving $s\to d$ transition, the $K\to \pi \nu \bar{\nu}$ decays provide the most sensitive probe for the operators with $\tau\tau$ component and point to a corresponding new physics scale of $\Lambda_{\rm NP} \in[47~\text{TeV},~72~\text{TeV}]$ associated with a single effective coefficient. The lepton-number-violating operator can also explain the observed $K\to\pi\nu\bar{\nu}$ discrepancy with the SM prediction within a narrow range $\Lambda_{\rm NP}\in [19.4~\text{TeV},~21.5~\text{TeV}]$, which is consistent with constraints from Kaon invisible decays.

A neutrinoless double beta decay master formula from effective field theory

We present a master formula describing the neutrinoless-double-beta decay (0νββ) rate induced by lepton-number-violating (LNV) operators up to dimension nine in the Standard Model Effective Field Theory. We provide an end-to-end framework connecting the possibly very high LNV scale to the nuclear scale, through a chain of effective field theories. Starting at the electroweak scale, we integrate out the heavy Standard Model degrees of freedom and we match to an SU(3)c ⊗ U(1)em effective theory. After evolving the resulting effective Lagrangian to the QCD scale, we use chiral perturbation theory to derive the lepton-number-violating chiral Lagrangian. The chiral Lagrangian is used to derive the two-nucleon 0νββ transition operators to leading order in the chiral power counting. Based on renormalization arguments we show that in various cases short-range two-nucleon operators need to be enhanced to leading order. We show that all required nuclear matrix elements can be taken from existing calculations. Our final result is a master formula that describes the 0νββ rate in terms of phase-space factors, nuclear matrix elements, hadronic low-energy constants, QCD evolution factors, and high-energy LNV Wilson coefficients, including all the interference terms. Our master formula can be easily matched to any model where LNV originates at energy scales above the electroweak scale. As an explicit example, we match our formula to the minimal left-right-symmetric model in which contributions of operators of different dimension compete, and we discuss the resulting phenomenology.

Low-energy lepton-proton bremsstrahlung via effective field theory

We present a systematic calculation of the cross section for the lepton-proton bremsstrahlung process l + p --> l' + p + gamma in chiral perturbation theory at next-to-leading order. This process corresponds to an undetected background signal for the proposed MUSE experiment at PSI. MUSE is designed to measure elastic scattering of low-energy electrons and muons off a proton target in order to extract a precise value of the proton's r.m.s. radius. We show that the commonly used peaking approximation, which is used to evaluate the radiative tail for the elastic cross section, is not applicable for muon-proton scattering at the low-energy MUSE kinematics. Furthermore, we point out a certain pathology with the standard chiral power counting scheme associated with electron scattering, whereby the next-to-next-to-leading order contribution from the pion loop diagrams is kinematically enhanced and numerically of the same magnitude as the next-to-leading order corrections. We correct a misprint in a commonly cited review article.

Neutrinoless double- β decay in effective field theory: The light-Majorana neutrino-exchange mechanism

We present the first chiral effective theory derivation of the neutrinoless double beta-decay $nn\rightarrow pp$ potential induced by light Majorana neutrino exchange. The effective-field-theory framework has allowed us to identify and parameterize short- and long-range contributions previously missed in the literature. These contributions can not be absorbed into parameterizations of the single nucleon form factors. Starting from the quark and gluon level, we perform the matching onto chiral effective field theory and subsequently onto the nuclear potential. To derive the nuclear potential mediating neutrinoless double beta-decay, the hard, soft and potential neutrino modes must be integrated out. This is performed through next-to-next-to-leading order in the chiral power counting, in both the Weinberg and pionless schemes. At next-to-next-to-leading order, the amplitude receives additional contributions from the exchange of ultrasoft neutrinos, which can be expressed in terms of nuclear matrix elements of the weak current and excitation energies of the intermediate nucleus. These quantities also control the two-neutrino double beta-decay amplitude. Finally, we outline strategies to determine the low-energy constants that appear in the potentials, by relating them to electromagnetic couplings and/or by matching to lattice QCD calculations.

Chiral power counting of one- and two-body currents in direct detection of dark matter

We present a common chiral power-counting scheme for vector, axial-vector, scalar, and pseudoscalar WIMP–nucleon interactions, and derive all one- and two-body currents up to third order in the chiral expansion. Matching our amplitudes to non-relativistic effective field theory, we find that chiral symmetry predicts a hierarchy amongst the non-relativistic operators. Moreover, we identify interaction channels where two-body currents that previously have not been accounted for become relevant.

Erratum to: Nuclear electric dipole moments in chiral effective field theory

We provide a consistent and complete calculation of the electric dipole moments of the deuteron, helion, and triton in the framework of chiral effective field theory. The CP-conserving and CP-violating interactions are treated on equal footing and we consider CP-violating one-, two-, and three-nucleon operators up to next-to-leading-order in the chiral power counting. In particular, we calculate for the first time EDM contributions induced by the CP-violating three-pion operator. We find that effects of CP-violating nucleon-nucleon contact interactions are larger than those found in previous studies based on phenomenological models for the CP-conserving nucleon-nucleon interactions. Our results which apply to any model of CP violation in the hadronic sector can be used to test various scenarios of CP violation. As examples, we study the implications of our results on the QCD $\theta$-term and the minimal left-right symmetric model.

Nuclear electric dipole moments in chiral effective field theory

We provide a consistent and complete calculation of the electric dipole moments of the deuteron, helion, and triton in the framework of chiral effective field theory. The CP-conserving and CP-violating interactions are treated on equal footing and we consider CP-violating one-, two-, and three-nucleon operators up to next-to-leading-order in the chiral power counting. In particular, we calculate for the first time EDM contributions induced by the CP-violating three-pion operator. We find that effects of CP-violating nucleon-nucleon contact interactions are larger than those found in previous studies based on phenomenological models for the CP-conserving nucleon-nucleon interactions. Our results which apply to any model of CP violation in the hadronic sector can be used to test various scenarios of CP violation. As examples, we study the implications of our results on the QCD θ-term and the minimal left-right symmetric model.

Reexamination of the standard model nucleon electric dipole moment

The Cabibbo-Kobayashi-Maskawa matrix in the Standard Model is currently the only experimentally-confirmed source of CP-violation. The intrinsic electric dipole moment of the nucleon induced by this CP-phase via hadronic loop and pole diagrams has been studied more than two decades ago, but the existing calculation is subject to various theoretical issues such as the breakdown of chiral power counting and uncertainties in the determination of low energy constants. We carry out an up-to-date re-analysis on both one-loop and pole diagram contributions to the nucleon electric dipole moment based on Heavy Baryon Chiral Perturbation Theory in a way that preserves power counting, and redo the determination of the low energy constants following the results of more recent articles. Combined with an estimation of higher-order contributions, we expect the long-distance contribution to the Standard Model nucleon electric dipole moment to be approximately $(1\times10^{-32}-6\times10^{-32})e\,\mathrm{cm}$.

Scattering lengths of Nambu-Goldstone bosons offDmesons and dynamically generated heavy-light mesons

Recent lattice QCD simulations of the scattering lengths of Nambu-Goldstone bosons off the $D$ mesons are studied using unitary chiral perturbation theory. We show that the lattice QCD data are better described in the covariant formulation than in the heavy-meson formulation. The ${D}_{s0}^{*}(2317)$ can be dynamically generated from the coupled-channels $DK$ interaction without a priori assumption of its existence. A new renormalization scheme is proposed which manifestly satisfies chiral power counting rules and has well-defined behavior in the infinite heavy-quark mass limit. Using this scheme we predict the heavy-quark spin and flavor symmetry counterparts of the ${D}_{s0}^{*}(2317)$.

WIMP-nucleus scattering in chiral effective theory

We discuss long-distance QCD corrections to the WIMP-nucleon(s) interactions in the framework of chiral effective theory. For scalar-mediated WIMP-quark interactions, we calculate all the next-to-leading-order corrections to the WIMP-nucleus elastic cross-section, including two-nucleon amplitudes and recoil-energy dependent shifts to the single-nucleon scalar form factors. As a consequence, the scalar-mediated WIMP-nucleus cross-section cannot be parameterized in terms of just two quantities, namely the neutron and proton scalar form factors at zero momentum transfer, but additional parameters appear, depending on the short-distance WIMP-quark interaction. Moreover, multiplicative factorization of the cross-section into particle, nuclear and astro-particle parts is violated. In practice, while the new effects are of the natural size expected by chiral power counting, they become very important in those regions of parameter space where the leading order WIMP-nucleus amplitude is suppressed, including the so-called "isospin-violating dark matter" regime. In these regions of parameter space we find order-of-magnitude corrections to the total scattering rates and qualitative changes to the shape of recoil spectra.

Nucleon-nucleon interactions from dispersion relations: Elastic partial waves

We consider nucleon-nucleon (NN) interactions from chiral effective field theory. In this work we restrict ourselves to the elastic NN scattering. We apply the N/D method to calculate the NN partial waves taking as input the one-pion exchange discontinuity along the left-hand cut. This discontinuity is amenable to a chiral power counting as discussed by Lacour, Oller and Meissner [Ann. Phys. (NY) 326, 241 (2011)], with one-pion exchange as its leading order contribution. The resulting linear integral equation for a partial wave with orbital angular momentum L>=2 is solved in the presence of L-1 constraints, so as to guarantee the right behavior of the D and higher partial waves near threshold. The calculated NN partial waves are based on dispersion relations and are independent of regulator. This method can also be applied to higher orders in the calculation of the discontinuity along the left-hand cut and extended to triplet coupled partial waves.

The chiral quark condensate and pion decay constant in nuclear matter at next-to-leading order

Making use of the recently developed chiral power counting for the physics of nuclear matter (Oller et al 2010 J. Phys. G: Nucl. Part. Phys. 37 015106, Lacour et al Ann. Phys. at press), we evaluate the in-medium chiral quark condensate up to next-to-leading order for both symmetric nuclear matter and neutron matter. Our calculation includes the full in-medium iteration of the leading order local and one-pion exchange nucleon–nucleon interactions. Interestingly, we find a cancellation between the contributions stemming from the quark mass dependence of the nucleon mass appearing in the in-medium nucleon–nucleon interactions. Only the contributions originating from the explicit quark mass dependence of the pion mass survive. This cancellation is the reason of previous observations concerning the dominant role of the long-range pion contributions and the suppression of short-range nucleon–nucleon interactions. We find that the linear density contribution to the in-medium chiral quark condensate is only slightly modified for pure neutron matter by the nucleon–nucleon interactions. For symmetric nuclear matter, the in-medium corrections are larger, although smaller compared to other approaches due to the full iteration of the lowest order nucleon–nucleon tree-level amplitudes. Our calculation satisfies the Hellmann–Feynman theorem to the order worked out. Also we address the problem of calculating the leading in-medium corrections to the pion decay constant. We find that there are no extra in-medium corrections that violate the Gell-Mann–Oakes–Renner relation up to next-to-leading order.

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.

Non-perturbative methods for a chiral effective field theory of finite density nuclear systems

Recently we have developed a novel chiral power counting scheme for an effective field theory of nuclear matter with nucleons and pions as degrees of freedom [1]. It allows for a systematic expansion taking into account both local as well as pion-mediated multi-nucleon interactions. We apply this power counting in the present study to the evaluation of the pion self-energy and the energy density in nuclear and neutron matter at next-to-leading order. To implement this power counting in actual calculations we develop here a non-perturbative method based on Unitary Chiral Perturbation Theory for performing the required resummations. We show explicitly that the contributions to the pion self-energy with in-medium nucleon–nucleon interactions to this order cancel. The main trends for the energy density of symmetric nuclear and neutron matter are already reproduced at next-to-leading order. In addition, an accurate description of the neutron matter equation of state, as compared with sophisticated many-body calculations, is obtained by varying only slightly a subtraction constant around its expected value. The case of symmetric nuclear matter requires the introduction of an additional fine-tuned subtraction constant, parameterizing the effects from higher order contributions. With that, the empirical saturation point and the nuclear matter compressibility are well reproduced while the energy per nucleon as a function of density closely agrees with sophisticated calculations in the literature.

Chiral effective field theory for nuclear matter including long- and short-range multi-nucleon interactions

We review on a novel chiral power counting scheme for in-medium chiral perturbation theory with nucleons and pions as degrees of freedom. It allows for a systematic expansion taking into account local as well as pion-mediated inter-nucleon interactions. Based on this power counting, one can identify classes of nonperturbative diagrams that require a resummation. As a method for performing those resummations we review on the techniques of Unitary Chiral Pertubation Theory for nucleon-nucleon interactions. We then apply both power counting and non-perturbative methods to the example of calculating the pion self-energy in asymmetric nuclear matter up-to-and-including next-to-leading order. It is shown that the leading corrections involving in-medium nucleon-nucleon interactions cancel between each other at given chiral orders.