We consider a class of models in even spacetime dimensions 2n which share many similarities with Chern-Simons theories in odd spacetime dimensions 2n + 1. The independent dynamical variables of these models are a GL(2n)-connection and a metric in internal space. The action is a polynomial of degree n in the curvature of the connection, with indices saturated by means of the metric and the Levi-Civita tensor. We show that the theory has no local degree of freedom in 2 spacetime dimensions (n = 1), where it can be reformulated as a constrained BF model, but that its dynamics is more intrincate in higher dimensions (n > 1), where local degrees of freedom are present. We treat in detail the cases of 2 and 4 spacetime dimensions.
{"title":"Palatini Gauss-Bonnet theory","authors":"Máximo Bañados, Marc Henneaux","doi":"10.1007/JHEP03(2026)064","DOIUrl":"10.1007/JHEP03(2026)064","url":null,"abstract":"<p>We consider a class of models in even spacetime dimensions 2<i>n</i> which share many similarities with Chern-Simons theories in odd spacetime dimensions 2<i>n</i> + 1. The independent dynamical variables of these models are a GL(2<i>n</i>)-connection and a metric in internal space. The action is a polynomial of degree <i>n</i> in the curvature of the connection, with indices saturated by means of the metric and the Levi-Civita tensor. We show that the theory has no local degree of freedom in 2 spacetime dimensions (<i>n</i> = 1), where it can be reformulated as a constrained <i>BF</i> model, but that its dynamics is more intrincate in higher dimensions (<i>n ></i> 1), where local degrees of freedom are present. We treat in detail the cases of 2 and 4 spacetime dimensions.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)064.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Following a proposal for an experiment with sensitivity to an electric dipole moment (EDM) of the muon dμ of order 6 × 10−23e cm, three to four orders of magnitude below the current bound, but still seven orders of magnitude above the current bound on the EDM of the electron de, we explore the discovery potential of such an experiment. Within the dimension-six CP violating operators of the Standard Model effective field theory (SMEFT), we identify two dipole operators where dμ has the strongest sensitivity, and four classes of four-fermion operators where it has the best sensitivity for regions of parameter space that are far from minimal flavor violation. We further consider three UV completions: vector-like leptons (VLLs), heavy vector boson with off-diagonal leptonic couplings, and two Higgs doublet model. For each, we identify the region in parameter space that will be uniquely explored by the proposed dμ experiment. In case of VLLs, we also find measurements of Γ(h → μμ) offer competitive sensitivity, highlighting the complementary role of collider observables. Generically, the potential reach is to ( mathcal{O} )(10 TeV) scale of new physics.
我们提出了一个对μ介子的电偶极矩(EDM)敏感的实验,该实验的灵敏度为6 × 10−23 e cm,比电流界低3到4个数量级,但仍然比电流界高7个数量级,我们探索了这种实验的发现潜力。在标准模型有效场论(SMEFT)的六维CP违背算子中,我们确定了两种偶极子算子,其中dμ具有最强的灵敏度,以及四类四费米子算子,在参数空间的区域中,它对最小味违背具有最佳的灵敏度。我们进一步考虑了三种UV补全:类矢量轻子(VLLs)、具有非对角轻子耦合的重矢量玻色子和两个希格斯双重态模型。对于每一个,我们在参数空间中确定将由所提出的dμ实验唯一探索的区域。在VLLs的情况下,我们还发现Γ(h→μμ)的测量值具有竞争性灵敏度,突出了对撞机观测值的互补作用。一般来说,潜在的范围是( mathcal{O} ) (10 TeV)规模的新物理。
{"title":"Chasing the muon EDM to constrain the SMEFT and UV models","authors":"Kuldeep Deka, Marta Losada, Yosef Nir","doi":"10.1007/JHEP03(2026)065","DOIUrl":"10.1007/JHEP03(2026)065","url":null,"abstract":"<p>Following a proposal for an experiment with sensitivity to an electric dipole moment (EDM) of the muon <i>d</i><sub><i>μ</i></sub> of order 6 × 10<sup><i>−</i>23</sup> <i>e</i> cm, three to four orders of magnitude below the current bound, but still seven orders of magnitude above the current bound on the EDM of the electron <i>d</i><sub><i>e</i></sub>, we explore the discovery potential of such an experiment. Within the dimension-six CP violating operators of the Standard Model effective field theory (SMEFT), we identify two dipole operators where <i>d</i><sub><i>μ</i></sub> has the strongest sensitivity, and four classes of four-fermion operators where it has the best sensitivity for regions of parameter space that are far from minimal flavor violation. We further consider three UV completions: vector-like leptons (VLLs), heavy vector boson with off-diagonal leptonic couplings, and two Higgs doublet model. For each, we identify the region in parameter space that will be uniquely explored by the proposed <i>d</i><sub><i>μ</i></sub> experiment. In case of VLLs, we also find measurements of Γ(<i>h</i> → <i>μμ</i>) offer competitive sensitivity, highlighting the complementary role of collider observables. Generically, the potential reach is to <span>( mathcal{O} )</span>(10 TeV) scale of new physics.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)065.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The 11D pure spinor worldline has been proved to successfully describe the physical states of 11D supergravity in a manifestly super-Poincaré covariant fashion. Within this framework, the computation of scattering amplitudes requires the existence of vertex operators carrying different ghost numbers. A recent no-go theorem demonstrated the impossibility of constructing a ghost number zero vertex operator consistent with 11D supergravity in the minimal pure spinor formalism. In this letter, we overcome this obstruction by working in the non-minimal formulation of the 11D pure spinor superparticle. We construct, for the first time, a ghost number zero vertex operator with a remarkably compact structure when expressed in terms of physical operators. We further verify that it satisfies the expected descent relation with the ghost number one vertex operator, and that its commutator with the ghost number three single-particle vertex reproduces the two-particle superfield recently introduced in the literature.
{"title":"The 11D pure spinor ghost number zero vertex operator","authors":"Max Guillen, Marcelo dos Santos, Eggon Viana","doi":"10.1007/JHEP03(2026)053","DOIUrl":"10.1007/JHEP03(2026)053","url":null,"abstract":"<p>The 11D pure spinor worldline has been proved to successfully describe the physical states of 11D supergravity in a manifestly super-Poincaré covariant fashion. Within this framework, the computation of scattering amplitudes requires the existence of vertex operators carrying different ghost numbers. A recent no-go theorem demonstrated the impossibility of constructing a ghost number zero vertex operator consistent with 11D supergravity in the minimal pure spinor formalism. In this letter, we overcome this obstruction by working in the non-minimal formulation of the 11D pure spinor superparticle. We construct, for the first time, a ghost number zero vertex operator with a remarkably compact structure when expressed in terms of physical operators. We further verify that it satisfies the expected descent relation with the ghost number one vertex operator, and that its commutator with the ghost number three single-particle vertex reproduces the two-particle superfield recently introduced in the literature.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)053.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Orbifold CFTs contain twist operators that can join and split copies of the CFT. In this paper, we study the effects of four twist-2 operators on two copies of a single free boson. A recent study analyzed their effects on the vacuum, finding a nontrivial left-right mixing that arises from the fact that the covering surface is a torus, while the effects of one or two twist-2 operators do not produce such mixing. Here, we extend this analysis to excited states and find a similar left-right mixing. Furthermore, we explore the continuum, or high-energy, limit and show that the left-right mixing becomes negligible in this limit.
{"title":"Four-twist effects on excitations in orbifold CFTs","authors":"Bin Guo, Shaun D. Hampton","doi":"10.1007/JHEP03(2026)048","DOIUrl":"10.1007/JHEP03(2026)048","url":null,"abstract":"<p>Orbifold CFTs contain twist operators that can join and split copies of the CFT. In this paper, we study the effects of four twist-2 operators on two copies of a single free boson. A recent study analyzed their effects on the vacuum, finding a nontrivial left-right mixing that arises from the fact that the covering surface is a torus, while the effects of one or two twist-2 operators do not produce such mixing. Here, we extend this analysis to excited states and find a similar left-right mixing. Furthermore, we explore the continuum, or high-energy, limit and show that the left-right mixing becomes negligible in this limit.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)048.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We discuss a basis for the nonperturbative Hilbert space of quantum gravity with one asymptotic boundary. We use this basis to show that the Hilbert space for gravity with two disconnected boundaries factorizes into a product of two copies of the single boundary Hilbert space.
{"title":"The nonperturbative Hilbert space of quantum gravity with one boundary","authors":"Vijay Balasubramanian, Tom Yildirim","doi":"10.1007/JHEP03(2026)040","DOIUrl":"10.1007/JHEP03(2026)040","url":null,"abstract":"<p>We discuss a basis for the nonperturbative Hilbert space of quantum gravity with one asymptotic boundary. We use this basis to show that the Hilbert space for gravity with two disconnected boundaries factorizes into a product of two copies of the single boundary Hilbert space.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)040.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147363004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the problem of bulk metric reconstruction in holography by leveraging the inverse scattering framework applied to boundary two-point correlation functions. We generalize our previous work of scalar field and show that reconstruction can be achieved using a single operator rather than a pair. We also apply this method into reconstruction of static homogeneous anisotropic black holes and the reconstruction using correlation function of gauge field. In addition, we analyze the method’s robustness under measurement noise and propose filtering strategies to improve reconstruction accuracy. This work advances data-driven bulk reconstruction by providing a concrete, experimentally viable pathway to recover spacetime geometry from field-theoretic observables.
{"title":"Application of solving inverse scattering problem in holographic bulk reconstruction","authors":"Bo-Wen Fan, Run-Qiu Yang","doi":"10.1007/JHEP03(2026)044","DOIUrl":"10.1007/JHEP03(2026)044","url":null,"abstract":"<p>We investigate the problem of bulk metric reconstruction in holography by leveraging the inverse scattering framework applied to boundary two-point correlation functions. We generalize our previous work of scalar field and show that reconstruction can be achieved using a single operator rather than a pair. We also apply this method into reconstruction of static homogeneous anisotropic black holes and the reconstruction using correlation function of gauge field. In addition, we analyze the method’s robustness under measurement noise and propose filtering strategies to improve reconstruction accuracy. This work advances data-driven bulk reconstruction by providing a concrete, experimentally viable pathway to recover spacetime geometry from field-theoretic observables.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)044.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147363118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Instanton contributions in 2d string theory are known to include subtle numerical factors ζn closely related to a contour prescription in multi-instanton string amplitudes. Both ingredients appear to be ambiguous due to a degeneracy between (1, n)-ZZ instantons and n (1,1)-ZZ instantons in the linear dilaton background. We resolve this ambiguity using insights from the dual matrix quantum mechanics where the multipliers ζn can be derived from an integral representation of the scattering phase and follow from the median resummation prescribed by resurgence theory. We evaluate multi-instanton string amplitudes in the theory compactified on a circle of finite radius for arbitrary number of instantons and show that they reproduce the matrix model predictions provided the Lorentzian contour prescription is used for their evaluation. We also show that the non-perturbative free energy matches the structure of the D-instanton induced string field theory effective action, which suggests the vanishing of contributions from worldsheet topologies of negative Euler number.
{"title":"Multi-instantons in 2d string theory","authors":"Sergei Alexandrov, Rishabh Kaushik","doi":"10.1007/JHEP03(2026)052","DOIUrl":"10.1007/JHEP03(2026)052","url":null,"abstract":"<p>Instanton contributions in 2d string theory are known to include subtle numerical factors <i>ζ</i><sub><i>n</i></sub> closely related to a contour prescription in multi-instanton string amplitudes. Both ingredients appear to be ambiguous due to a degeneracy between (1<i>, n</i>)-ZZ instantons and <i>n</i> (1,1)-ZZ instantons in the linear dilaton background. We resolve this ambiguity using insights from the dual matrix quantum mechanics where the multipliers <i>ζ</i><sub><i>n</i></sub> can be derived from an integral representation of the scattering phase and follow from the median resummation prescribed by resurgence theory. We evaluate multi-instanton string amplitudes in the theory compactified on a circle of finite radius for arbitrary number of instantons and show that they reproduce the matrix model predictions provided the Lorentzian contour prescription is used for their evaluation. We also show that the non-perturbative free energy matches the structure of the D-instanton induced string field theory effective action, which suggests the vanishing of contributions from worldsheet topologies of negative Euler number.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)052.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The current work involves augmenting the ∆(54) discrete flavor model by incorporating two Standard Model Higgs particles into the Inverse Seesaw mechanism. We introduced Weyl fermions and Vector like fermions, which are gauge singlets in the Standard Model and produces Majorana mass terms in our Lagrangian. The resulting mass matrix produces a non-zero reactor angle (θ13). We have determined the effective Majorana neutrino mass, which is the parameter of relevance in neutrinoless double beta decay investigations. We additionally investigate the possibility of baryogenesis in the proposed framework via resonant leptogenesis. We have the non-zero value for resonantly enhanced CP asymmetry originating from the decay of right-handed neutrinos at the TeV scale, accounting for flavor effects. The evolution of lepton asymmetry is systematically analyzed by numerically solving a set of Boltzmann equations, leading to the determination of the baryon asymmetry with a magnitude of |ηB| ≈ 6 × 10−10. This outcome is achieved by selecting specific values for the right-handed neutrino mass M1 = 10 TeV and mass splitting, d ≈ 10−8.
{"title":"Neutrino mixing and resonant leptogenesis in inverse seesaw and ∆(54) flavor symmetry","authors":"Hrishi Bora, Ng. K. Francis, Shawan Kumar Jha","doi":"10.1007/JHEP03(2026)047","DOIUrl":"10.1007/JHEP03(2026)047","url":null,"abstract":"<p>The current work involves augmenting the ∆(54) discrete flavor model by incorporating two Standard Model Higgs particles into the Inverse Seesaw mechanism. We introduced Weyl fermions and Vector like fermions, which are gauge singlets in the Standard Model and produces Majorana mass terms in our Lagrangian. The resulting mass matrix produces a non-zero reactor angle (<i>θ</i><sub>13</sub>). We have determined the effective Majorana neutrino mass, which is the parameter of relevance in neutrinoless double beta decay investigations. We additionally investigate the possibility of baryogenesis in the proposed framework via resonant leptogenesis. We have the non-zero value for resonantly enhanced CP asymmetry originating from the decay of right-handed neutrinos at the TeV scale, accounting for flavor effects. The evolution of lepton asymmetry is systematically analyzed by numerically solving a set of Boltzmann equations, leading to the determination of the baryon asymmetry with a magnitude of |<i>η</i><sub><i>B</i></sub>| ≈ 6 × 10<sup>−10</sup>. This outcome is achieved by selecting specific values for the right-handed neutrino mass <i>M</i><sub>1</sub> = 10 TeV and mass splitting, <i>d</i> ≈ 10<sup>−8</sup>.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)047.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147363121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Prateek Agrawal, Anson Hook, Vazha Loladze, Mario Reig
Axion models generically suffer from a severe quality problem when coupled to gravity. In this article we provide a very simple model with a high quality axion. The axion is a pseudo-Nambu-Goldstone boson of the baryon number symmetry, U(1)B, of a new composite sector that breaks U(1)B spontaneously when it confines. A controlled example is a supersymmetric QCD (SQCD) with Nc = Nf. The axion shift symmetry is automatically protected due to the high dimension of the gauge-invariant baryon operator, with the Peccei-Quinn breaking operators arising at dimension Nc + 2. The standard model gauge group is embedded as a subgroup of the flavor symmetry group of SQCD that has an anomaly with U(1)B, generating the standard coupling with gluons.
{"title":"Axion quality problem: keep calm and baryon","authors":"Prateek Agrawal, Anson Hook, Vazha Loladze, Mario Reig","doi":"10.1007/JHEP03(2026)041","DOIUrl":"10.1007/JHEP03(2026)041","url":null,"abstract":"<p>Axion models generically suffer from a severe quality problem when coupled to gravity. In this article we provide a very simple model with a high quality axion. The axion is a pseudo-Nambu-Goldstone boson of the baryon number symmetry, U(1)<sub><i>B</i></sub>, of a new composite sector that breaks U(1)<sub><i>B</i></sub> spontaneously when it confines. A controlled example is a supersymmetric QCD (SQCD) with <i>N</i><sub><i>c</i></sub> = <i>N</i><sub><i>f</i></sub>. The axion shift symmetry is automatically protected due to the high dimension of the gauge-invariant baryon operator, with the Peccei-Quinn breaking operators arising at dimension <i>N</i><sub><i>c</i></sub> + 2. The standard model gauge group is embedded as a subgroup of the flavor symmetry group of SQCD that has an anomaly with U(1)<sub><i>B</i></sub>, generating the standard coupling with gluons.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)041.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147363119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The free energy, or equivalently the ground state energy in finite volume, may be calculated from forward scattering amplitudes using a formula due to Dashen, Ma, and Bernstein [1]. However a naive treatment leads to singularities when considering the scattering of three or more particles. It is shown in detail how the approach can be applied to multi-particle scattering in various massive scalar theories in 1+1d, with or without integrability. The results for the sinh-Gordon, Lieb-Liniger, and O(N) non-linear sigma models are compared to exact results. It is shown how bound states can be considered in this approach by considering the attractive Lieb-Liniger model.
{"title":"Free energy from forward scattering in 1+1d","authors":"Daniel Schubring","doi":"10.1007/JHEP03(2026)030","DOIUrl":"10.1007/JHEP03(2026)030","url":null,"abstract":"<p>The free energy, or equivalently the ground state energy in finite volume, may be calculated from forward scattering amplitudes using a formula due to Dashen, Ma, and Bernstein [1]. However a naive treatment leads to singularities when considering the scattering of three or more particles. It is shown in detail how the approach can be applied to multi-particle scattering in various massive scalar theories in 1+1d, with or without integrability. The results for the sinh-Gordon, Lieb-Liniger, and <i>O</i>(<i>N</i>) non-linear sigma models are compared to exact results. It is shown how bound states can be considered in this approach by considering the attractive Lieb-Liniger model.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)030.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147363046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}