Effective Field Theory Calculations Research Articles

Symmetry energy and neutron star properties constrained by chiral effective field theory calculations

Symmetry energy and neutron star properties constrained by chiral effective field theory calculations

Chiral effective field theory calculation of neutrino reactions in warm neutron-rich matter

Chiral effective field theory calculation of neutrino reactions in warm neutron-rich matter

Constraints on Strong Phase Transitions in Neutron Stars

We study current bounds on strong first-order phase transitions (PTs) along the equation of state (EOS) of dense strongly interacting matter in neutron stars, under the simplifying assumption that on either side of the PT, the EOS can be approximated by a simple polytropic form. We construct a large ensemble of possible EOSs of this form, anchor them to chiral effective field theory calculations at nuclear density and perturbative Quantum Chromodynamics at high densities, and subject them to astrophysical constraints from high-mass pulsars and gravitational-wave observations. Within this setup, we find that a PT permits neutron-star solutions with larger radii, but only if the transition begins below twice nuclear saturation density. We also identify a large parameter space of allowed PTs currently unexplored by numerical-relativity studies. Additionally, we locate a small region of parameter space allowing twin-star solutions, though we find them to only marginally pass the current astrophysical constraints. Finally, we find that sizeable cores of high-density matter beyond the PT may be located in the centers of some stable neutron stars, primarily those with larger masses.

Electroweak input schemes and universal corrections in SMEFT

The choice of an electroweak (EW) input scheme is an important component of perturbative calculations in Standard Model Effective Field Theory (SMEFT). In this paper we perform a systematic study of three different EW input schemes in SMEFT, in particular those using the parameter sets {MW, MZ, GF}, {MW, MZ, α}, or {α, MZ, GF}. We discuss general features and calculate decay rates of Z and W bosons to leptons and Higgs decays to bottom quarks in these three schemes up to next-to-leading order (NLO) in dimension-six SMEFT. We explore the sensitivity to Wilson coefficients and perturbative convergence in the different schemes, and show that while the latter point is more involved than in the Standard Model, the dominant scheme-dependent NLO corrections are universal and can be taken into account by a simple set of substitutions on the leading-order results. Residual NLO corrections are then of similar size between the different input schemes, and performing calculations in multiple schemes can give a useful handle on theory uncertainties in SMEFT predictions and fits to data.

Revisiting the matching of black hole tidal responses: A systematic study of relativistic and logarithmic corrections

The worldline effective field theory (EFT) gives a gauge-invariant definition of black hole conservative tidal responses (Love numbers), dissipation numbers, and their spin-0 and spin-1 analogs. In the first part of this paper we show how the EFT allows us to circumvent the source/response ambiguity without having to use the analytic continuation prescription. The source/response ambiguity appears if relativistic corrections to external sources overlap with the response. However, these corrections can be clearly identified and isolated using the EFT. We illustrate that by explicitly computing static one-point functions of various external fields perturbing the four-dimensional Schwarzschild geometry. Upon resumming all relevant Feynman diagrams, we find that the relativistic terms that may mimic the response actually vanish for static black holes. Thus, the extraction of Love numbers from matching the EFT and general relativity (GR) calculations is completely unambiguous, and it confirms previous results that the Love numbers vanish identically for all types of perturbations. We also study in detail another type of fine-tuning in the EFT, the absence of Love numbers' running. We show that logarithmic corrections to Love numbers do stem from individual loop diagrams in generic gauges, but cancel after all diagrams are summed over. In the particular cases of spin-0 and spin-2 fields the logarithms are completely absent if one uses the Kaluza-Klein metric decomposition. In the second part of the paper we compute frequency-dependent dissipative response contributions to the one-point functions using the Schwinger-Keldysh formalism. We extract black hole dissipation numbers by comparing the one-point functions in the EFT and GR. Our results are in perfect agreement with those obtained from a manifestly gauge-invariant matching of absorption cross sections.

Plausible presence of new state in neutron stars with masses above [formula omitted

We investigate the neutron star (NS) equation of state (EOS) by incorporating multi-messenger data of GW170817, PSR J0030 + 0451, PSR J0740 + 6620, and state-of-the-art theoretical progresses, including the information from chiral effective field theory (χEFT) and perturbative quantum chromodynamics (pQCD) calculation. Taking advantage of the various structures sampling by a single-layer feed-forward neural network model embedded in the Bayesian nonparametric inference, the structure of NS matter’s sound speed cs is explored in a model-agnostic way. It is found that a peak structure is common in the cs2 posterior, locating at (2.4-4.8)ρsat (nuclear saturation density) and cs2 exceeds c2/3 at 90% credibility. The non-monotonic behavior suggests evidence of the state deviating from the hadronic matter inside the very massive NSs. Assuming the new/exotic state is featured as it is softer than typical hadronic models or even with hyperons, we find that a sizable (⩾10-3M⊙) exotic core, likely made of quark matter, is plausible for the NS with a gravitational mass above about 0.98MTOV, where MTOV represents the maximum gravitational mass of a non-rotating cold NS. The inferred MTOV=(2.18-0.13+0.27)M⊙ (90% credibility) is well consistent with the value of (2.17-0.12+0.15)M⊙ estimated independently with GW170817/GRB 170817A/AT2017gfo assuming a temporary supramassive NS remnant formed after the merger. PSR J0740 + 6620, the most massive NS detected so far, may host a sizable exotic core with a probability of ≈0.36.

Evanescent operators in one-loop matching computations

Effective Field Theory calculations used in countless phenomenological analyses employ dimensional regularization, and at intermediate stages of computations, the operator bases extend beyond the four-dimensional ones. The extra pieces — the evanescent operators — can ultimately be removed with a suitable renormalization scheme, resulting in a finite shift of the physical operators. Modern Effective Field Theory matching techniques relying on the method of expansion by regions have to be extended to account for this. After illustrating the importance of these shifts in two specific examples, we compute the finite shifts required to remove all evanescent operators appearing in the one-loop matching of generic ultraviolet theories to the Standard Model Effective Field Theory and elucidate the formalism for generic Effective Field Theory calculations.

Understanding the systematic differences in extractions of the proton electric form factors at low Q2

Systematic differences exist between values of the proton's electric form factors in the low-$Q^2$ region extracted by different experimental and theoretical groups, though they are all making use of basically the same electron-proton scattering data. To try understand the source of these differences, we make use of the analytically well-behaved rational (N=1, M=1) function, a predictive function that can be reasonably used for extrapolations at $Q^{2} \rightarrow 0$. First, we test how well this deceptively simple two-parameter function describes the extremely complex and state-of-the-art dispersively improved chiral effective field theory calculations. Second, we carry out a complete re-analysis of the 34 sets of eletron-proton elastic scattering cross-section data of the Mainz A1 Collaboration with its unconstrained 31 normalization parameters up to $Q^{2} = 0.5~{\rm (GeV/c)^{2}}$. We find that subtle shifts in the normalization parameters can result in relatively large changes in the extracted physical qualities. In conclusion, we show that by simply using a well-behaved analytic function, the apparent discrepancy between recent form-factor extractions can be resolved.

Coupled-channels treatment of Be7(p,γ)B8 in effective field theory

The $E1$ and $M1$ contributions to $^{7}\mathrm{Be}(p,\ensuremath{\gamma})^{8}\mathrm{B}$ at low energies are calculated in halo effective field theory. The excited $^{7}\mathrm{Be}^{★}$ core is included as an explicit degree of freedom in a coupled-channels calculation. The $E1$ transition is calculated up to next-to-next-to-leading order. The leading contribution from $M1$ transition that gives significant contribution in a narrow energy region around the ${1}^{+}$ resonance state of $^{8}\mathrm{B}$ is included. We compare our results with previous halo effective field theory calculations that also included the $^{7}\mathrm{Be}^{★}$ as an explicit degree of freedom. We disagree with these previous calculations in both the formal expressions and also in the analysis. Bayesian inference of the data gives ${S}_{17}(0)=21.0(7)$ eV b when combined with the expected theory error.

Exploring the NΛ–NΣ coupled system with high precision correlation techniques at the LHC

The interaction of Λ and Σ hyperons (Y) with nucleons (N) is strongly influenced by the coupled-channel dynamics. Due to the small mass difference of the NΛ and NΣ systems, the sizable coupling strength of the NΣ↔NΛ processes constitutes a crucial element in the determination of the NΛ interaction. In this letter we present the most precise measurements on the interaction of pΛ pairs, from zero relative momentum up to the opening of the NΣ channel. The correlation function in the relative momentum space for pΛ⊕p‾Λ‾ pairs measured in high-multiplicity triggered pp collisions at s=13 TeV at the LHC is reported. The opening of the inelastic NΣ channels is visible in the extracted correlation function as a cusp-like structure occurring at relative momentum k⁎=289MeV/c. This represents the first direct experimental observation of the NΣ↔NΛ coupled channel in the pΛ system. The correlation function is compared with recent chiral effective field theory calculations, based on different strengths of the NΣ↔NΛ transition potential. A weaker coupling, as possibly supported by the present measurement, would require a more repulsive three-body NNΛ interaction for a proper description of the Λ in-medium properties, which has implications on the nuclear equation of state and for the presence of hyperons inside neutron stars.

Finite-volume pionless effective field theory for few-nucleon systems with differentiable programming

Finite-volume pionless effective field theory provides an efficient framework for the extrapolation of nuclear spectra and matrix elements calculated at finite volume in lattice QCD to infinite volume, and to nuclei with larger atomic number. In this work, it is demonstrated how this framework may be implemented via a set of correlated Gaussian wave functions optimized using differentiable programming and via solution of a generalized eigenvalue problem. This approach is shown to be significantly more efficient than a stochastic implementation of the variational method based on the same form of correlated Gaussian wave functions, yielding comparably accurate representations of the ground-state wave functions with an order of magnitude fewer terms. The efficiency of representation allows such calculations to be extended to larger systems than in previous work. The method is demonstrated through calculations of the binding energies of nuclei with atomic number $A\ensuremath{\in}{2,3,4}$ in finite volume, matched to lattice QCD calculations at quark masses corresponding to ${m}_{\ensuremath{\pi}}=806\text{ }\text{ }\mathrm{MeV}$, and infinite-volume effective field theory calculations of $A\ensuremath{\in}{2,3,4,5,6}$ systems based on this matching.

Large and massive neutron stars: Implications for the sound speed within QCD of dense matter

The NASA telescope NICER has recently measured x-ray emissions from the heaviest of the precisely known two-solar mass neutron stars, PSR J0740+6620. Analysis of the data [Miller et al., Astrophys. J. Lett. 918, L28 (2021); Riley et al., Astrophys. J. Lett. 918, L27 (2021)] suggests that PSR J0740+6620 has a radius in the range of $R_{2.0} \approx (11.4-16.1)$ km at the $68\%$ credibility level. In this article, we study the implications of this analysis for the sound speed in the high-density inner cores by using recent chiral effective field theory ($\chi$EFT) calculations of the equation of state at next-to-next-to-next-to-leading order to describe outer regions of the star at modest density. We find that the lower bound on the maximum speed of sound in the inner core, $\textbf{min}\{c^2_{s, {\rm max}}\}$, increases rapidly with the radius of massive neutron stars. If $\chi$EFT remains an efficient expansion for nuclear interactions up to about twice the nuclear saturation density, $R_{2.0}\geqslant 13$ km requires $\textbf{min}\{c^2_{s, {\rm max}}\} \geqslant 0.562$ and $0.442$ at the $68\%$ and $95\%$ credibility level, respectively.

Implications of PREX-2 data on the electron-neutrino opacity in dense matter

Motivated by the recent measurement of the neutron distribution radius of ${}^{208}$Pb from the PREX--2 data, I study the effects of the new G3(M) parameter set constrained by PREX--2 data on the electron--neutrino scattering in dense matter using the extended relativistic mean field (E--RMF) model. I employ the G3(M) parameter set to describe the nuclear matter. The obtained equation of state for the G3(M) parameter set has an excellent agreement with experimental data and the chiral effective field theory calculation with N$^3$LO 3N forces. I analyze both differential cross section of electron--neutrino and electron--neutrino mean free path to observe their sensitivity to the G3(M) parameter set. One finds that the differential cross sections of electron--neutrino for different baryon densities have higher values compared with that obtained for the TM1e and FSU Garnet parameter sets. The higher cross section decreases the electron--neutrino mean free path.

Constraints on the Dense Matter Equation of State and Neutron Star Properties from NICER’s Mass–Radius Estimate of PSR J0740+6620 and Multimessenger Observations

Abstract In recent years our understanding of the dense matter equation of state (EOS) of neutron stars has significantly improved by analyzing multimessenger data from radio/X-ray pulsars, gravitational wave events, and from nuclear physics constraints. Here we study the additional impact on the EOS from the jointly estimated mass and radius of PSR J0740+6620, presented in Riley et al. by analyzing a combined data set from X-ray telescopes NICER and XMM-Newton. We employ two different high-density EOS parameterizations: a piecewise-polytropic (PP) model and a model based on the speed of sound in a neutron star (CS). At nuclear densities these are connected to microscopic calculations of neutron matter based on chiral effective field theory (EFT) interactions. In addition to the new NICER data for this heavy neutron star, we separately study constraints from the radio timing mass measurement of PSR J0740+6620, the gravitational wave events of binary neutron stars GW190425 and GW170817, and for the latter the associated kilonova AT2017gfo. By combining all these, and the NICER mass–radius estimate of PSR J0030+0451, we find the radius of a 1.4 M ⊙ neutron star to be constrained to the 95% credible ranges 12.33 − 0.81 + 0.76 km (PP model) and 12.18 − 0.79 + 0.56 km (CS model). In addition, we explore different chiral EFT calculations and show that the new NICER results provide tight constraints for the pressure of neutron star matter at around twice saturation density, which shows the power of these observations to constrain dense matter interactions at intermediate densities.

Coupled-channel treatment of $${\varvec{^7}}$$Li$${\varvec{(n,\gamma )^8}}$$Li in effective field theory

The E1 contribution to the capture reaction $^7\mathrm{Li}(n,\gamma)^8\mathrm{Li}$ is calculated at low energies. We employ a coupled-channel formalism to account for the $^7\mathrm{Li}^\star$ excited core contribution. The halo effective field theory calculations show that the contribution of the $^7\mathrm{Li}^\star$ degree of freedom is negligible at momenta below 1 MeV and significant only beyond the $3^+$ resonance energy, though still compatible with a next-to-next-to-leading order correction. A power counting that accounts for the size of this correction is proposed. We compare our formalism with a previous halo effective field theory [Zhang, Nollett, and Phillips, Phys. Rev. C {\bf 89}, 024613 (2014)] that also treated the $^7\mathrm{Li}^\star$ core as an explicit degree of freedom. Our formal expressions and analysis disagree with this earlier work in several aspects.

Unnuclear physics: Conformal symmetry in nuclear reactions

We investigate a nonrelativistic version of Georgi's "unparticle physics." We define the unnucleus as a field in a nonrelativistic conformal field theory. Such a field is characterized by a mass and a conformal dimension. We then consider the formal problem of scatterings to a final state consisting of a particle and an unnucleus and show that the differential cross-section, as a function of the recoil energy received by the particle, has a power-law singularity near the maximal recoil energy, where the power is determined by the conformal dimension of the unnucleus. We argue that unlike the relativistic unparticle, which remains a hypothetical object, the unnucleus is realized, to a good approximation, in nuclear reactions involving emission of a few neutrons, when the energy of the final-state neutrons in their center-of-mass frame lies in the range between about 0.1 MeV and 5 MeV. Combining this observation with the known universal properties of fermions at unitarity in a harmonic trap, we predict a power-law behavior of an inclusive cross-section in this kinematic regime. We verify our predictions with previous effective field theory and model calculations of the 6He[Formula: see text], 3H[Formula: see text], and 3H[Formula: see text] reactions and discuss opportunities to measure unnuclei at radioactive beam facilities.

Symmetry-protected topological phases and competing orders in a spin- 12 XXZ ladder with a four-spin interaction

We study a spin-$\frac{1}{2}$ XXZ model with a four-spin interaction on a two-leg ladder. By means of effective field theory and matrix product state calculations, we obtain rich ground-state phase diagrams that consist of eight distinct gapped phases. Four of them exhibit spontaneous symmetry breaking with either a magnetic or valence-bond-solid (VBS) long-range order. The other four are featureless, i.e., the bulk ground state is unique and does not break any symmetry. The featureless phases include the rung singlet (RS) and Haldane phases as well as their variants, the RS* and Haldane* phases, in which twisted singlet pairs $(|\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\rangle}+|\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\rangle})/\sqrt{2}$ are formed between the two legs. We argue and demonstrate that Gaussian transitions with the central charge $c=1$ occur between the featureless phases and between the ordered phases while Ising transitions with $c=1/2$ occur between the featureless and ordered phases. The two types of transition lines cross at the $\mathrm{SU}(2)$-symmetric point, where the criticality is described by the $\mathrm{SU}{(2)}_{2}$ Wess-Zumino-Witten theory with $c=3/2$. The RS-Haldane* and RS*-Haldane transitions give examples of topological phase transitions. Interestingly, the RS* and Haldane* phases, which have highly anisotropic nature, appear even in the vicinity of the isotropic case. We demonstrate that all the four featureless phases are distinguished by topological indices in the presence of certain symmetries.

Effective field theory for dilute Fermi systems at fourth order

We discuss high-order calculations in perturbative effective field theory for fermions at low energy scales. The Fermi-momentum or $k_{\rm F} a_s$ expansion for the ground-state energy of the dilute Fermi gas is calculated to fourth order, both in cutoff regularization and in dimensional regularization. For the case of spin one-half fermions we find from a Bayesian analysis that the expansion is well-converged at this order for ${| k_{\rm F} a_s | \lesssim 0.5}$. Further, we show that Pad{\'e}-Borel resummations can improve the convergence for ${| k_{\rm F} a_s | \lesssim 1}$. Our results provide important constraints for nonperturbative calculations of ultracold atoms and dilute neutron matter.

Leading logs in QCD axion effective field theory

The axion is much lighter than all other degrees of freedom introduced by the Peccei-Quinn mechanism to solve the strong CP problem. It is therefore natural to use an effective field theory (EFT) to describe its interactions. Loop processes calculated in the EFT may however explicitly depend on the ultraviolet cutoff. In general, the UV cutoff is not uniquely defined, but the dimensionful couplings suggest to identify it with the Peccei-Quinn symmetry-breaking scale. An example are K+ → π+ + a decays that will soon be tested to improved precision in NA62 and KOTO and whose amplitude is dominated by the term logarithmically dependent on the cutoff. In this paper, we critically examine the adequacy of using such a naive EFT approach to study loop processes by comparing EFT calculations with ones performed in complete QCD axion models. In DFSZ models, for example, the cutoff is found to be set by additional Higgs degrees of freedom and to therefore be much closer to the electroweak scale than to the Peccei-Quinn scale. In fact, there are non-trivial requirements on axion models where the cutoff scale of loop processes is close to the Peccei-Quinn scale, such that the naive EFT result is reproduced. This suggests that the existence of a suitable UV embedding may impose restrictions on axion EFTs. We provide an explicit construction of a model with suitable fermion couplings and find promising prospects for NA62 and IAXO.

Nuclear symmetry energy from neutron skins and pure neutron matter in a Bayesian framework

We present an inference of the nuclear symmetry energy magnitude $J$, the slope $L$, and the curvature ${K}_{\mathrm{sym}}$ from combining neutron skin data on calcium, lead and tin isotopes, and our best theoretical information about pure neutron matter. A Bayesian framework is used to consistently incorporate prior knowledge of the pure neutron matter equation of state from chiral effective field theory calculations. Neutron skins are modeled in a fully quantum Skyrme-Hartree-Fock approach using an extended Skyrme energy-density functional which allows for independent variation of $J$, $L$, and ${K}_{\mathrm{sym}}$ without affecting the symmetric nuclear matter equation of state. The effect of using neutron skin data obtained with different physical probes is quantified. We argue that, given the existing data, combining the errors in quadrature is the more appropriate way to obtain unified errors for each nuclide, and in doing so we obtain 95% credible values of $J=31.3\begin{array}{c}+4.2\\ \ensuremath{-}5.9\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, $L=40\begin{array}{c}+34\\ \ensuremath{-}26\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, and ${K}_{\ensuremath{\tau}}=L\ensuremath{-}6{K}_{\mathrm{sym}}=\ensuremath{-}444\begin{array}{c}+100\\ \ensuremath{-}84\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ using uninformative priors in $J$, $L$, and ${K}_{\mathrm{sym}}$, and $J=31.9\begin{array}{c}+1.3\\ \ensuremath{-}1.3\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, $L=37\begin{array}{c}+9\\ \ensuremath{-}8\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, and ${K}_{\ensuremath{\tau}}=\ensuremath{-}480\begin{array}{c}+25\\ \ensuremath{-}26\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ using pure neutron matter (PNM) priors. We also show that the nonpositive correlation between $J$ and $L$ induced by neutron skin data is consistent with the nuclear droplet model. Neutron skin data alone are shown to place limits on the symmetry energy parameters as stringent as those obtained from chiral effective field theory alone, and when combined the 95% credible intervals are reduced by a factor of 4--5. It is also shown that the majority of nuclear interactions used in the literature have subsaturation density dependencies that are inconsistent with the combination of PNM priors and neutron skin data. We show measurements of lead and calcium neutron skins from upcoming parity-violating electron scattering experiments at Jefferson Lab and Mainz Superconducting Accelerator should obtain total error ranges $\mathrm{\ensuremath{\Delta}}L\ensuremath{\approx}50\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and $\mathrm{\ensuremath{\Delta}}{K}_{\ensuremath{\tau}}\ensuremath{\approx}240\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ for uninformative priors and $\mathrm{\ensuremath{\Delta}}L\ensuremath{\approx}30\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and $\mathrm{\ensuremath{\Delta}}{K}_{\ensuremath{\tau}}\ensuremath{\approx}100\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ for PNM priors at 67% credible bounds. Ahead of those experiments, we make predictions based on existing data on neutron skins of tin alone for the neutron skins of calcium and lead of $0.166\ifmmode\pm\else\textpm\fi{}0.008$ fm and $0.169\ifmmode\pm\else\textpm\fi{}0.014$ fm, respectively, using uninformative priors and $0.167\ifmmode\pm\else\textpm\fi{}0.008$ fm and $0.172\ifmmode\pm\else\textpm\fi{}0.015$ fm, respectively, using PNM priors.