Contact Terms Research Articles

On-shell Higgsing for EFTs

We study the on-shell version of the Higgs mechanism in effective theories (EFTs) containing particles of different spins, focusing on contact terms as a simple starting point. We derive the massive contact terms and their coefficients from the massless amplitudes of the EFT above the symmetry breaking scale, by covariantizing the massless contact terms under the massive little group. In the little-group-covariant massive-spinor formalism, this notationally amounts to bolding spinor labels. Mass-suppressed contributions to the contact-term coefficients arise from higher-point contact terms with additional soft Higgs legs. We apply this procedure to obtain massive four-point amplitudes featuring scalars, spin 1/2 fermions and vectors, in the standard-model EFT. The subleading helicity-flipped components of each massive contact term, which are dictated by little-group covariance, are associated with the residues of factorizable massless amplitudes. Extra “frozen” Higgses emitted from each leg of a massless contact term supply the additional light-like momentum component, needed to form a massive leg of the same polarization. As another application, we derive various components of massive three-point amplitudes from massless amplitudes with up to three additional Higgses, in a standard-model-like toy model.

Lessons from [formula omitted] models in one dimension

Various topics related to the O(N) model in one spacetime dimension (i.e. ordinary quantum mechanics) are considered. The focus is on a pedagogical presentation of quantum field theory methods in a simpler context where many exact results are available, but certain subtleties are discussed which may be of interest to active researchers in higher dimensional field theories as well.Large N methods are introduced in the context of the zero-dimensional path integral and the connection to Stirling’s series is shown. The entire spectrum of the O(N) model, which includes the familiar l(l+1) eigenvalues of the quantum rotor as a special case, is found both diagrammatically through large N methods and by using Ward identities. The large N methods are already exact at ON−1 and the ON−2 corrections are explicitly shown to vanish. Peculiarities of gauge theories in d=1 are discussed in the context of the CPN−1 sigma model, and the spectrum of a more general squashed sphere sigma model is found. The precise connection between the O(N) model and the linear sigma model with a ϕ4 interaction is discussed. A valid form of the self-consistent screening approximation (SCSA) applicable to O(N) models with a hard constraint is presented. The point is made that at least in d=1 the SCSA may do worse than simply truncating the large N expansion to ON−1 even for small N. In both the supersymmetric and non-supersymmetric versions of the O(N) model, naive equations of motion relating vacuum expectation values are shown to be corrected by regularization-dependent finite corrections arising from contact terms associated to the equation of constraint.

3d [formula omitted] dualities for SU(Nc)×U(1) Chern-Simons gauge theories

We systematically study 3d N=2 dualities for U(Nc) gauge theories with different CS levels for the abelian and the non-abelian factors. We derive such dualities by a gauging/ungauging procedure on other known dualities and by adding an opportune CS contact term for the baryonic symmetry. This allows us to follow the various steps on the three sphere partition function, obtaining exact identities among the new dual phases proposed here. We apply the procedure to various cases, namely SQCD without and with adjoint, chiral dualities and some sporadic cases arising from the real mass flow of models with an E7×U(1) enhancement of the global symmetry.

Analysis of the γn→K+Σ−(1385) photoproduction

In our previous work [Phys. Rev. D 101, 074025 (2020)], the photoproduction $\ensuremath{\gamma}p\ensuremath{\rightarrow}{K}^{+}{\mathrm{\ensuremath{\Sigma}}}^{0}(1385)$ has been investigated within an effective Lagrangian approach. There, the reaction amplitudes were constructed by considering the $t$-channel $K$ and ${K}^{*}(892)$ exchanges, $s$-channel $N$ contribution, $u$-channel $\mathrm{\ensuremath{\Lambda}}$ exchange, generalized contact term, and a minimum number of $s$-channel $N$ and $\mathrm{\ensuremath{\Delta}}$ resonance diagrams. It was found that the inclusion of one of the $N(1895){1/2}^{\ensuremath{-}}$, $\mathrm{\ensuremath{\Delta}}(1900){1/2}^{\ensuremath{-}}$, and $\mathrm{\ensuremath{\Delta}}(1930){5/2}^{\ensuremath{-}}$ resonances is essential to reproduce the available differential and total cross-section data for $\ensuremath{\gamma}p\ensuremath{\rightarrow}{K}^{+}{\mathrm{\ensuremath{\Sigma}}}^{0}(1385)$. In the present work, we employ the same model to study the photoproduction $\ensuremath{\gamma}n\ensuremath{\rightarrow}{K}^{+}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}(1385)$, with the purpose being to understand the reaction mechanism and, in particular, to figure out which one of the $N(1895){1/2}^{\ensuremath{-}}$, $\mathrm{\ensuremath{\Delta}}(1900){1/2}^{\ensuremath{-}}$, and $\mathrm{\ensuremath{\Delta}}(1930){5/2}^{\ensuremath{-}}$ resonances is really capable for a simultaneous description of the data for both ${K}^{+}{\mathrm{\ensuremath{\Sigma}}}^{0}(1385)$ and ${K}^{+}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}(1385)$ photoproduction reactions. The results show that the available data on differential and total cross sections and photobeam asymmetries for $\ensuremath{\gamma}n\ensuremath{\rightarrow}{K}^{+}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}(1385)$ can be reproduced only with the inclusion of the $\mathrm{\ensuremath{\Delta}}(1930){5/2}^{\ensuremath{-}}$ resonance rather than the other two. The generalized contact term and the $t$-channel $K$ exchange are found to dominate the background contributions. The resonance $\mathrm{\ensuremath{\Delta}}(1930){5/2}^{\ensuremath{-}}$ provides the most important contributions in the whole energy region considered, and it is responsible for the bump structure exhibited in the total cross sections.

ABJM at strong coupling from M-theory, localization, and Lorentzian inversion

We study the stress tensor multiplet four-point function in the 3d maximally supersymmetric ABJ(M) theory with Chern-Simons level k = 2, which in the large N limit is holographically dual to weakly coupled M-theory on AdS4 × S7/ℤ2. We use the Lorentzian inversion to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity R and the first higher derivative correction R4 vertices, up to a finite number of contact terms that contribute to low spins where the inversion formula does not converge. We find a precise match with the corresponding terms in the 11d M-theory S-matrix by taking the flat space limit, which is not sensitive to these contact terms. We then conjecturally fix these contact terms by analytically continuing the inversion formula below its expected range of convergence, and verify this conjecture using supersymmetric localization. Finally, we compare some of the 1-loop CFT data to non-perturbative in N bounds from the numerical conformal bootstrap, which we compute at unprecedently high accuracy, and find that the 1-loop corrections saturate the bounds in the large N regime, which extends the previously observed match at tree level.

Nonlinear collision shifts of the 0-0 hyperfine transition due to van der Waals molecule formation.

We consider the origin of nonlinear collision shifts for the 0-0 hyperfine transition in alkali/noble-gas systems due to van der Waals molecule formation. Developing a semi-empirical model, we describe the shift as arising from three fundamental interactions: (1) a fractional change in the alkali's valence electron density at the alkali nucleus, η, which affects the hyperfine contact term; (2) a mixing of p-wavefunction character into the alkali ground state (characterized by the probability for p-state character appearing in the perturbed wavefunction ξ1 2), which gives rise to an electric quadrupole term in the ground-state hyperfine splitting; and (3) an interaction of the alkali's valence electron with the magnetic field produced by molecular rotation, characterized by a magnetic field strength BvdW. In addition to these molecular parameters, the model also depends on the formation rate of van der Waals molecules, kfP2, and the breakup rate of the molecules, kbP, where P is the noble-gas pressure. Fitting the model to the 85Rb/Xe and 87Rb/Xe experimental data of McGuyer and co-workers (and taking previously measured values for kf and BvdW), we find that η = 9 × 10-3, ξ1 2 = 5 × 10-3, and kb = 2.9×107s-1/Torr.

The influence of the nuclear matter incompressibility on heavy-ion fusion reactions at near- and above-barrier energies

Based on simulating the saturation property of cold nuclear matter for complete fusion channel of two approaching nuclei, we systematically investigate the role of nuclear incompressibility in the nucleus-nucleus potential and fusion-evaporation cross section of 69 medium-heavy and heavy mass systems with 208≤Z1Z2≤1520. Our observations based on the uncoupled single-barrier potential model and the M3Y double-folding potential which is corrected with a repulsive core term reveal that the incompressibility of cold nuclear matter can be responsible for the discrepancy between the measured and calculated values of the fusion cross sections at energies around and above the Coulomb barrier. In other words, one can find that the high energy fusion cross sections can not be reproduced using the standard form of the M3Y-DF potential model without considering the repulsive core effects. We show that the strength of the repulsive contact term and also the incompressibility of the compound nuclei exhibit systematic behaviors with respect to the atomic and mass numbers of reacting nuclei. It is shown that the hardness level of nuclear matter reduces when one passes from lighter to heavier systems.

High precision calculations of Fermi contact term for lithium-like ions

The Fermi contact term is closely related to the atomic hyperfine constants. It often dominates the hyperfine splittings. The quality of the wave function near the origin and the correlation effect between electrons are two main factors which affect the numerical accuracy of the Fermi contact term. It is not an easy task to compute the Fermi contact term with high precision for a general atom. In the present paper, the Schrödinger equations of the <inline-formula><tex-math id="M4">\begin{document}$ {\text{1s2s3s}}{\;^{\text{4}}}{\text{S}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220923_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220923_M4.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ {\text{1s2s4s}}{\;^{\text{4}}}{\text{S}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220923_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220923_M5.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ {\text{1s2s2p}}{\;^{\text{4}}}{\text{P}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220923_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220923_M6.png"/></alternatives></inline-formula>states of lithium atom and lithium-like ions (<i>Z</i> = 4–10) are solved by using Rayleigh-Ritz variational method in Hylleraas coordinates. The variational energiesenergy converges to an accuracy of 10<sup>–13</sup>. Then the Fermi contact terms for these states are calculated based on the high precision variation wave functions. In particular, the Drachman global method are adopted in order to improve the convergence of the Fermi contact term. The effect of finite nuclear mass on Fermi contact term, i.e. the first-order mass polarization coefficient is also calculated. The Fermi contact term converges to an accuracy of 10<sup>–10</sup>, which is the most accurate result at present. Our results can be used as a reference for other theoretical methods or relevant experimental studies.

AbInitio Calculation of the Contact Operator Contribution in the Standard Mechanism for Neutrinoless Double Beta Decay.

Starting from chiral nuclear interactions, we evaluate the contribution of the leading-order contact transition operator to the nuclear matrix element (NME) of neutrinoless double-beta decay, assuming a light Majorana neutrino-exchange mechanism. The corresponding low-energy constant (LEC) is determined by fitting the transition amplitude of the nn→ppe^{-}e^{-} process to a recently proposed synthetic datum. We examine the dependence of the amplitude on similarity renormalization group scale and chiral expansion order of the nuclear interaction, finding that both dependences can be compensated to a large extent by readjusting the LEC. We evaluate the contribution of both the leading-order contact operator and standard long-range operator to the neutrinoless double-beta decays in the light nuclei ^{6,8}He and the candidate nucleus ^{48}Ca. Our results provide the first clear demonstration that the contact term enhances the NME in calculations with commonly used chiral two- plus three-nucleon interactions. In the case of ^{48}Ca, for example, the NME obtained with the EM(1.8/2.0) interaction is enhanced from 0.61 to 0.87(4), where the uncertainty is propagated from the synthetic datum.

Constraints on the varLambda -Neutron Interaction from Charge Symmetry Breaking in the mathbf {^4_Lambda mathrm{He}} - mathbf {^4_Lambda mathrm{H}} Hypernuclei

We utilize the experimentally known difference of the varLambda separation energies of the mirror hypernuclei {^4_varLambda mathrm{He}} and {^4_varLambda mathrm{H}} to constrain the varLambda -neutron interaction. We include the leading charge-symmetry breaking (CSB) interaction into our hyperon-nucleon interaction derived within chiral effective field theory at next-to-leading order. In particular, we determine the strength of the two arising CSB contact terms by a fit to the differences of the separation energies of these hypernuclei in the 0^+ and 1^+ states, respectively. By construction, the resulting interaction describes all low energy hyperon-nucleon scattering data, the hypertriton and the CSB in {^4_varLambda mathrm{He}}-{^4_varLambda mathrm{H}} accurately. This allows us to provide first predictions for the varLambda n scattering lengths, based solely on available hypernuclear data.

Photoproduction of possible pentaquark states Λb0(5912) and Λb0(5920) in the γp→Λb0(*)B+ reactions

In this work, we report on a theoretical study of possible pentaquark states $\Lambda^0_b(5912)$ and $\Lambda^0_b(5920)$ in the $\gamma{}p\to{}\Lambda_b^{0(*)}B^+$ reactions within an effective Lagrangian approach. In addition to the contributions from the $s$-channel nucleon pole and $t$-channel $\bar{B}^{{*}-}$ exchange, the contact term contribution are also included. Our theoretical approach is based on the chiral unitary theory where the $\Lambda^0_b(5912)$ and $\Lambda^0_b(5920)$ resonances are dynamically generated. Within the coupling constants of the $\Lambda^0_b(5912)$ and $\Lambda^0_b(5920)$ to $\bar{B}p$ and $\bar{B}^{*}p$ channels obtained from chiral unitary theory, the total and differential cross sections of the $\gamma{}p\to{}\Lambda_b^{0(*)}B^+$ are evaluated. Our calculation indicates that the cross section for $\gamma{}p\to{}\Lambda_b^{0}(5912)B^{+}$ and $\gamma{}p\to{}\Lambda_b^{0}(5920)B^{+}$ reactions are of the order of 0.0164 nb and 0.00527 nb,respectively. If measured in future experiments, such as Electron-Ion Collider in China (EicC) or US(US-EIC), the predicted total cross sections and specific features of the angular distributions can be used to test the (molecular) nature of the $\Lambda^0_b(5912)$ and $\Lambda^0_b(5920)$ that they may be pentaquark states.

Higher spin 3-point functions in 3d CFT using spinor-helicity variables

In this paper we use the spinor-helicity formalism to calculate 3-point functions involving scalar operators and spin-s conserved currents in general 3d CFTs. In spinor-helicity variables we notice that the parity-even and the parity-odd parts of a correlator are related. Upon converting spinor-helicity answers to momentum space, we show that correlators involving spin-s currents can be expressed in terms of some simple conformally invariant conserved structures. This in particular allows us to understand and separate out contact terms systematically, especially for the parity-odd case. We also reproduce some of the correlators using weight-shifting operators.

Heavy-ion fusion cross sections in the barrier and high-energy regions: Signature of energy dependence in the repulsive core potential

The effect of incompressibility of cold nuclear matter (CNM) on the high-energy fusion data of the 26Mg+248Cm, 36S+238U, 48Ca+208Pb, 50Ti+209Bi and 40,48Ca+238U colliding systems with 1152≤Z1Z2≤1840 has been analyzed using coupled-channels (CC) calculations. To apply the effect of saturation property of nuclear matter, we use the M3Y double-folding model which is corrected with a repulsive term. The repulsive parameters are adjusted to provide an optimum fit to the available experimental fusion cross sections. For each of the 26Mg+248Cm, 36S+238U, 48Ca+208Pb colliding systems, the best fit to the measured fusion cross sections at high energies is achieved using the CC calculations based on the M3Y+Repulsion potential with a constant value for the strength of the repulsive contact term. While focusing on the heavy-ion fusion reactions existing in the mass range Z1Z2>1800 reveals that it is necessary to consider an energy-dependent behavior for the repulsive parameters. When these conditions are imposed on entrance channel potential, it is possible to obtain an excellent description of the fusion data for 50Ti+209Bi, 40Ca+238U, and 48Ca+238U reactions. Our findings indicate that the extracted values of the strength Vrep of the repulsive contact term increase with increasing incident energy Ec.m.. In addition, we conclude that the repulsive part of the density distribution becomes more diffused with an increase in bombarding energy.

Revisiting the nature of the Pc pentaquarks

The nature of the three narrow hidden-charm pentaquark Pc states, i.e., Pc(4312), Pc(4440) and Pc(4457), is under intense discussion since their discovery from the updated analysis of the process {Lambda}_b^0to J/psi {pK}^{-} by LHCb. In this work we extend our previous coupled-channel approach [Phys. Rev. Lett. 124, 072001 (2020)], in which the Pc states are treated as {Sigma}_c^{left(ast right)}{overline{D}}^{left(ast right)} molecules, by including the {Lambda}_c{overline{D}}^{left(ast right)} and ηcp as explicit inelastic channels in addition to the J/ψp, as required by unitarity and heavy quark spin symmetry (HQSS), respectively. Since inelastic parameters are very badly constrained by the current data, three calculation schemes are considered: (a) scheme I with pure contact interactions between the elastic, i.e., {Sigma}_c^{left(ast right)}{overline{D}}^{left(ast right)} , and inelastic channels and without the {Lambda}_c{overline{D}}^{left(ast right)} interactions, (b) scheme II, where the one-pion exchange (OPE) is added to scheme I, and (c) scheme III, where the {Lambda}_c{overline{D}}^{left(ast right)} interactions are included in addition. It is shown that to obtain cutoff independent results, OPE in the multichannel system is to be supplemented with S-wave-to-D-wave mixing contact terms. As a result, in line with our previous analysis, we demonstrate that the experimental data for the J/ψp invariant mass distribution are consistent with the interpretation of the Pc(4312) and Pc(4440)/Pc(4457) as {Lambda}_coverline{D} and {Sigma}_c{overline{D}}^{ast } hadronic molecules, respectively, and that the data show clear evidence for a new narrow state, Pc(4380), identified as a {Sigma}_c^{ast}overline{D} molecule, which should exist as a consequence of HQSS. While two statistically equally good solutions are found in scheme I, only one of these solutions with the quantum numbers of the Pc(4440) and Pc(4457) being JP = 3/2− and 1/2−, respectively, survives the requirement of regulator independence once the OPE is included. Moreover, we predict the line shapes in the elastic and inelastic channels and demonstrate that those related to the Pc(4440) and the Pc(4457) in the {Sigma}_c^{left(ast right)}overline{D} and ηcp mass distributions from {Lambda}_b^0to {Sigma}_c^{left(ast right)}overline{D}{K}^{-} and {Lambda}_b^0to {eta}_c{pK}^{-} will shed light on the quantum numbers of those states, once the data are available. We also investigate possible pentaquark signals in the {Lambda}_c{overline{D}}^{left(ast right)} final states.

Three-body interactions from the finite-volume QCD spectrum

We perform a fit of the finite-volume QCD spectrum of three pions at maximal isospin to constrain the three-body force. We use the unitarity-based relativistic three-particle quantization condition, with the GWUQCD spectrum obtained at 315 MeV and 220 MeV pion mass in two-flavor QCD. For the heavier pion mass we find that the data is consistent with a constant contact term close to zero, whereas for the lighter mass we see a statistically significant energy dependence in tension with the prediction of leading order ChPT. Our results also suggest that with enough three-body energy levels, the two-body amplitude could be constrained.

Starobinksy inflation, gravitational contact terms, and the induced Brout-Englert-Higgs boson mass

The Starobinsky model of inflation remains consistent with observation, forty years after its introduction. It provides a well motivated origin for the scalar inflaton, the "scaleron" with a mass of $O(10^{13})$ GeV, emerging as a graviton degree of freedom from $R^2$ corrections to Einstein-Hilbert gravity. However the coupling of such a heavy state to the BEH ("Higgs") scalar is problematic as its quantum loop corrections can induce an unacceptably large contribution to the radiatively induced BEH scalar mass. The calculation of these corrections is normally done by Weyl transforming to the Einstein frame, yet at the quantum level Weyl transformations are fraught with ambiguities. However the recent realization that there exist "gravitational contact interactions" largely sidesteps these ambiguities. Such contact terms are necessarily present, coming from t-channel graviton exchange interactions, and they show that the theory defined in the "Jordan Frame" is identical to the theory in the Einstein frame, with additional Planck-scale suppressed interactions that take on the form of a Weyl transformation. This avoids ambiguous nonlinear field redefinitions, and reliable loop calculations are possible leading to a consistent low energy theory in an expansion in $1/M^2$. Taking account of the contact terms we study the radiative corrections to the BEH mass in the mixed Higgs/$R^2$ model with explicit scale breaking, and in an extension of the model in which exact scale symmetry is spontaneously broken.

Efficient emulator for solving three-nucleon continuum Faddeev equations with chiral three-nucleon force comprising any number of contact terms

We demonstrate a computational scheme which drastically decreases the required time to get theoretical predictions based on chiral two- and three-nucleon forces for observables in three-nucleon continuum. For a three-nucleon force containing N short-range terms all workload is reduced to solving N+1 Faddeev-type integral equations. That done, computation of observables for any combination of strengths of the contact terms is done in a flash. We demonstrate on example of the elastic nucleon-deuteron scattering observables the high precision of the proposed emulator and its capability to reproduce exact results.

Exploration of the doubly charmed molecular pentaquarks

We perform a systematic study on the interactions of the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$ systems within the framework of chiral effective field theory. We introduce the contact term, one-pion-exchange and two-pion-exchange contributions to describe the short-, long-, and intermediate-range interactions. The low energy constants of the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$ systems are estimated from the $N\overline{N}$ scattering data by introducing a quark level Lagrangian. With three solutions of LECs, all the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$ systems with isospin $I=1/2$ can form bound states, in which different inputs of LECs may lead to distinguishable mass spectra. In addition, we also investigate the interactions of the charmed-bottom ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{\overline{B}}^{(*)}$, ${\mathrm{\ensuremath{\Sigma}}}_{b}^{(*)}{D}^{(*)}$, and ${\mathrm{\ensuremath{\Sigma}}}_{b}^{(*)}{\overline{B}}^{(*)}$ systems. Among the obtained bound states, the bindings become deeper when the reduced masses of the corresponding systems are heavier.

Renormalization of the energy-momentum tensor in three-dimensional scalar SU(N) theories using the Wilson flow

A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for renormalizing the energy-momentum tensor on the lattice. In this paper, we utilize the Wilson flow to define a procedure to renormalize the energy-momentum tensor for a three-dimensional massless scalar field in the adjoint of $SU(N)$ with a $\varphi^4$ interaction on the lattice. In this theory the energy-momentum tensor can mix with $\varphi^2$ and we present numerical results for the mixing coefficient for the $N=2$ theory.

Crossing Symmetric Dispersion Relations for Mellin Amplitudes.

We consider manifestly crossing symmetric dispersion relations for Mellin amplitudes of scalar four point correlators in conformal field theories. This allows us to set up the nonperturbative Polyakov bootstrap for the conformal field theories in Mellin space on a firm foundation, thereby fixing the contact term ambiguities in the crossing symmetric blocks. Our new approach employs certain "locality" constraints replacing the requirement of crossing symmetry in the usual fixed-t dispersion relation. Using these constraints, we show that the sum rules based on the two channel dispersion relations and the present dispersion relations are identical. Our framework allows us to connect with the conceptually rich picture of the Polyakov blocks being identified with Witten diagrams in anti-de Sitter space. We also give two sided bounds for Wilson coefficients for effective field theories in anti-de Sitter space.