We present a more efficient method for constructing the complete EFT operator basis for particles of any mass and spin, based on on-shell method and Young tableaux. By classifying the amplitude bases according to the polarization configurations of massive particles and using their high-energy limit, our approach can construct EFT basis in a straightforward way, without need of auxiliary fields and tedious basis decomposition. Based on this improved method, we develop a $\textit{Mathematica}$ code that can automatically construct the EFT basis for particles of any spin. As applications, the EFT bases up to $\textit{d}$ = 8 are explicitly constructed for dark photons and, for the first time, for spin-3/2 particles.

Spain

Ziyu Dong

China

Teng Ma

Chengjie Yang

Zizheng Zhou

Dark photons and high spin particles: complete EFT operator basis

The Electron-Ion Collider in China (EicC), a proposed high-luminosity facility with advanced charged particle and photon detection capabilities, provides unique opportunities to uncover new physics beyond the Standard Model. We analyze its sensitivity to dark photons produced through electron bremsstrahlung in coherent scattering. Thanks to its beam energy settings, it has the potential to comprehensively probe the previously unexplored parameter space between the constraints from meson decays and beam dumps below $$ \mathcal{O}(1) $$ GeV with displaced-vertex search. Additionally, the EicC has the potential to probe axion-like particles (ALPs) in the mass range 0$\textit{.}$1 GeV ≲ $\textit{m}$ ≲ 5 GeV, with a coupling reach of Λ ≲ 10 GeV, by combining the prompt-decay and displaced-vertex searches. The projected sensitivities to ALPs exceed the current bounds.

Qiyuan Gao

Dan Lin

Israel

United States

Hongkai Liu

Dark photons and axion-like particles at the electron-ion collider in China

We analyze causality and unitarity constraints in graviton scattering amplitudes, aiming to establish new bounds on theories with U(1)-gravitational anomalies, such as axion models or strongly-coupled gauge theories. For this purpose, we show the necessity of coupling these theories to gravity. We obtain a universal scale Λ at which states with $\textit{J}$ ≥ 4 must appear in the theory. We show that this scale can lie below the quantum gravity scale. For axion models, we get Λ ∼ $$\sqrt{{M}_{P}{f}_{a}}$$ where $\textit{f}$ is the axion decay constant. In strongly-coupled gauge theories in the large-$\textit{N}$ limit, the presence of glueballs allows to evade these bounds, provided the number of fermions $\textit{N}$ ≪ $\textit{N}$ and the ’tHooft coupling is not large. Nevertheless, for models that have a holographic 5D dual (large ’tHooft coupling), Λ emerges as a new cutoff scale, unless certain conditions on the parameters of the 5D models are satisfied.

Zi-Yu Dong

Alex Pomarol

Francesco Sciotti

Bootstrapping the chiral-gravitational anomaly

The Electron-Ion Collider (EIC), a forthcoming powerful high-luminosity facility, represents an exciting opportunity to explore new physics. In this article, we study the potential of the EIC to probe the coupling between axion-like particles (ALPs) and photons in coherent scattering. The ALPs can be produced via photon fusion and decay back to two photons inside the EIC detector. In a prompt-decay search, we find that the EIC can set the most stringent bound for m  a  ≲ 20 GeV and probe the effective scales Λ ≲ 105 GeV. In a displaced-vertex search, which requires adopting an EM calorimeter technology that provides directionality, the EIC could probe ALPs with m  a  ≲ 1 GeV at effective scales Λ ≲ 107 GeV. Combining the two search strategies, the EIC can probe a significant portion of unexplored parameter space in the 0.2 &lt; m  a  &lt; 20 GeV mass range.

Reuven Balkin

Or Hen

Wenliang Li

Yotam Soreq

Mike Williams

Probing axion-like particles at the Electron-Ion Collider

The bootstrap approach (demanding consistency conditions to scattering amplitudes) has shown to be quite powerful to tightly constrain gauge theories at large N  c . We extend previous analysis to scattering amplitudes involving pions and external gauge bosons. These amplitudes allow us to access the chiral anomaly and connect low-energy physical quantities to UV properties of the theory. In particular, we are able to obtain an analytic bound on the chiral anomaly coefficient as a function of the pion dipole polarizabilities. This bound can be useful for holographic models whose dual UV completions are not known, and provide a consistency condition to lattice simulations.

Bootstrapping the chiral anomaly at large N  c

We present the explicit construction of the effective field theory (EFT) of standard model mass eigenstates. The EFT, which is invariant under U(1)e.m. × SU(3) c , is constructed based on the on-shell method and Young Tableau technique. This EFT serves as a new formulation of the Higgs EFT (HEFT), which can describe the infrared effects of new physics at the electroweak symmetry-breaking phase with greater conciseness. The current HEFT operator basis has a clear physical interpretation, making it more accessible for research in phenomenology. A complete list of HEFT operator bases for any-point vertices up to any dimension could be provided, and three- and four-point bases are provided as examples. Additionally, this framework realized as Mathematica program can be used to construct the EFT of any type of dark matter or particles with any spin.

Jing Shu

Zi-Zheng Zhou

The new formulation of higgs effective field Theory

We propose a theory to systematically construct a complete set of on-shell effective operator bases involving massive particles with any spins. The amplitude bases involving massive fields can be factorized into two charged and neutral parts under the little groups of massive particles, respectively. The complete bases of these two parts can be constructed by the Young diagrams of Lorentz subgroup <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>r</mi></msub></math> and global symmetry <math><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> (<math><mi>N</mi></math> is the number of external particles), respectively, without any redundancies. The corresponding effective field theory bases with the lowest dimension can be obtained by eliminating the linear correlation bases from a complete but redundant set of bases with all possible polarization tensors. Based on this theory, the amplitude bases involving identical particles can be constructed by a matrix projection method. A generic massive effective field theory can thus be constructed automatically by computer programs.

Constructing on-shell operator basis for all masses and spins

We derive the contact terms contributing to the four-point amplitudes of the standard model particles, keeping terms with up to quartic energy growth. Imposing just the unbroken low-energy symmetry, and treating the electroweak gauge bosons and the Higgs as independent degrees of freedom, we obtain the most general four-point contact-term amplitudes, corresponding to the Higgs Effective Field Theory (HEFT) framework. The contact terms are spanned by a basis of Stripped Contact Terms, which carry the polarization information, multiplied by polynomials in the Mandelstam invariants. For terms with quadratic energy growth, we also derive the low-energy Standard Model Effective Field Theory (SMEFT) predictions, via on-shell Higgsing of the massless SMEFT contact terms. We discuss several aspects of bottom-up versus top-down on-shell derivations of the HEFT and SMEFT amplitudes, highlighting in particular the simple counting of HEFT dimensions in the on-shell approach and the transparent relation between perturbative unitarity and gauge-invariance in the little-group covariant massive spinor formalism. Our results provide a formulation of Effective Field Theory analyses directly in terms of observable quantities. For terms with quadratic energy growth, we also provide the mapping to the Warsaw basis.

Yael Shadmi

Michael Waterbury

An EFT hunter’s guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes

We present a general method of constructing unfactorizable on-shell amplitudes (amplitude basis) and build up their one-to-one correspondence to the independent and complete operator basis in effective field theory (EFT). We apply our method to the Standard Model EFT and identify the amplitude basis in dimensions 5 and 6, which correspond to the Weinberg operator and operators in the Warsaw basis, except for some linear combinations.

Ming-Lei Xiao

Standard model effective field theory from on-shell amplitudes  

We propose a novel way to search for feebly interacting massive particles, exploiting two properties of systems involving collisions between high energy electrons and intense laser pulses. The first property is that the electron-laser collision results in a large flux of hard photons, as the laser behaves effectively as a thick medium. The second property is that the emitted photons free-stream inside the laser and thus for them the laser behaves effectively as a very thin medium. Combining these two features implies that the electron-intense-laser collision is an apparatus, which can efficiently convert <math><mrow><mi>O</mi><mo>(</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>)</mo></mrow></math> electrons to a large flux of hard, collinear photons. The photons are directed onto a solid dump in which feebly interacting massive particles may be produced. With the much smaller backgrounds induced by the photon beam compared to those expected in electron- or proton-beam dump experiments and combined with a relatively shorter dump used here, the sensitivity to short lifetimes is unparalleled. We denote this novel apparatus as “optical dump” or NPOD (new physics search with optical dump). The proposed LUXE experiment at the European XFEL has all the basic required ingredients to realize this experimental concept for the first time. Moreover, the NPOD extension of LUXE is essentially parasitic to the main experiment and thus, practically it does not have any bearing on its main program. We discuss how the NPOD concept can be realized in practice by adding a detector after the last physical dump of the experiment to reconstruct the two-photon decay of a new spin-0 particle. We show that even with a relatively short dump, the search can still be background-free. Remarkably, even with a few days of data taking with a 40 TW laser corresponding to its initial run, LUXE-NPOD will be able to probe an uncharted territory of models with pseudoscalars and scalars. Furthermore, with a 350 TW laser of the main run, LUXE-NPOD will have a unique reach for these models. In particular it can probe natural scalar theories for masses above 100 MeV. We note that the new NPOD concept may be ported to other existing or future facilities worldwide, including, e.g., future lepton colliders.