arXiv subjects

Jiang-Hao Yu

Publications and source records attributed to Jiang-Hao Yu.

At least 19 recordsLinked to original sources

arXiv2026

Massless-Massive Amplitude Correspondence III: Massive Amplitude Bases in the SMEFT

We develop a systematic correspondence between massless contact amplitudes in an unbroken theory and massive contact amplitudes after spontaneous symmetry breaking. Our construction employs the spin-transversality (ST) massive amplitude basis, with the systematic high energy expansion through minimal-helicity-chirality (MHC) amplitudes. The resulting $U(2)=SU(2)\times U(1)_t$ description of a massive particle makes the semi-standard Young-tableau construction of massless Lorentz structures directly applicable to massive amplitudes. When the leading-order MHC component has a massless contact limit, it is one-to-one matched directly to its UV amplitude. Otherwise, five exceptional classes of ST amplitudes are identified, their first non-zero descendant components are matched through conserved current couplings to the massless contact amplitude. We apply the framework to the one-flavor electroweak sector of the Standard Model Effective Field Theory (SMEFT) through dimension eight, obtaining explicit relations between unbroken-phase Wilson coefficients and broken-phase ST amplitude coefficients for amplitudes with three to eight external particles.

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arXiv2026

Massive On-shell Splitting Functions in Spinor-Helicity Formalism

Collinear splitting functions govern parton evolution, parton showers, and resummation at high-energy colliders. While on-shell spinor-helicity methods have successfully yielded massless QCD splitting functions, a complete on-shell construction for massive particles, systematically incorporating finite-mass effects, is less developed. We present an on-shell constructive formalism for massive collinear splitting functions based on Soper-Weinberg collinear spinors, whose transformation properties follow from a light-front Galilean subgroup of the Poincar\'e group. Decomposing massive momenta and spinors with respect to fixed lightlike vectors $n$ and $\bar n$ makes the expansion in the alignment regime $m<p_T\ll p_+$ manifest. The leading-order structures are matched to massless three-point amplitudes, while an additional Higgs momentum along $\bar n$ probes the subleading spinor components and relates them to massless four-point amplitudes. We derive the complete set of leading and subleading massive splitting functions for all Standard Model particles and establish a systematic matching dictionary between massless and massive coupling coefficients at both the three- and four-point levels. Higher-point splitting functions are obtained through the recursive bootstrap relation with a universal substitution rule as a consequence of the Galilean symmetry. This constructive framework extends naturally to effective field theory operators and higher perturbative orders, providing a flexible computational tool for precision collider physics and parton shower development.

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arXiv2026

Covariant Spinor Formalism for Multipole Expanded Form Factor

We present a systematic technique for constructing Lorentz covariant orbital-spin ($LS$) bases for matrix elements of local operators and the associated form factors, thereby extending the traditional multipole expansion to a Lorentz covariant formalism. In the spinor-helicity formalism, matrix elements of local operators for spin-$j$ particles can be treated as several massive 3-point scattering amplitudes, each of which can be further decomposed into different $LS$ partial wave amplitudes. We obtain explicit complete and linearly independent $LS$ amplitude bases for scalar, vector, and rank 2 tensor form factor of particles with spin-$\frac{1}{2}$, $1$, and $\frac{3}{2}$. In the Breit frame, it recovers the traditional multipole expansion expression, and we show the explicit equivalence among the traditional multipole expansion, canonical $LS$ expansion, and the $\mathrm{SO}(3)$ Zemach tensor expansion. Finally noting covariant structures built from the relativistic external wave functions and momenta of the initial and final state particles, we give a universal construction formula for form factor of arbitrary Lorentz tensor operators for arbitrary external spin particles.

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arXiv2026

Covariant Construction of Generalized Form Factors

We present a systematic technique for constructing the Lorentz-covariant structures of hadronic matrix elements of local operators. The spinor Young tableaux of the Lorentz group is employed to construct all possible structures for the matrix elements of arbitrary operators, using the relativistic wave functions and momenta of the initial and final state particles of arbitrary spin as building blocks. We obtain the form factor bases for the scalar, vector, and rank-2 tensor operators for particles with spin-$\frac{1}{2}$, $1$, $\frac{3}{2}$, and $2$, among which the general $P$ and $T$ form factors for spin-$\frac{3}{2}$ and spin-$2$ particles are presented for the first time. The independent form factor structures are also cross-checked by the non-relativistic counting and Hilbert Series method and we find there is redundant $P$ and $T$ conserved structure for spin-$2$ particles in literature. As an application, the matrix elements of general nonlocal operators can be expanded by towers of the matrix elements of local operators, and thus can be decomposed by the constructed form factor bases above.

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arXiv2026

Complete UV Resonances of SMEFT Dim-9 Operators for Short-range Neutrinoless Double Beta Decay

We present a systematic classification of tree-level ultraviolet (UV) completions for dimension-nine SMEFT operators relevant to short-range neutrinoless double beta decay. Using the SMEFT J-basis framework, we categorize distinct UV completions, including both all-boson and boson-fermion-boson topologies. A primary objective is the identification of minimal UV realizations, defined as the smallest set of genuine heavy degrees of freedom required to generate each operator. Out of the 505 unique mediator combinations identified, 440 are found to be minimal, with 12 cases necessitating only two distinct heavy species. While our findings reproduce the scalar- and fermion-mediated results of Ref.[1], we significantly extend the classification by providing the first comprehensive compilation of 324 minimal UV completions featuring vector resonances -- a category previously unexplored in this context.

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arXiv2026

Comprehensive Effective Field Theory Analysis for Baryon Number Violating Processes

Baryon number-violating processes arise generically in many extensions of the Standard Model, with Grand Unified Theories providing the most compelling realizations. Ongoing experimental searches at JUNO, Hyper-K, and DUNE motivate a more precise and model-independent analysis utilizing the effective field theory (EFT) framework capable of connecting ultraviolet dynamics to low-energy hadronic observables. In this work, we perform a pipeline analysis that connects baryon number-violating (BNV) new physics to its low-energy description through the Standard Model EFT (SMEFT) up to dimension nine and the Low-Energy EFT (LEFT) up to dimension eight, and subsequently matches onto chiral perturbation theory using a systematic spurion method. We show that the complete set of dimension-eight LEFT operators enables the inclusion of the full set of chiral representations for three-quark operators with derivatives, which are also embedded in the chiral Lagrangian after quark-hadron matching. By contrast, the conventional dimension-six operators generate only the $(\bar{\mathbf{3}},\mathbf{3})$ and $(\mathbf{8},\mathbf{1})$ representations. The higher dimensional LEFT operators should be matched from higher order SMEFT operators, and thus a wider class of UV completions are allowed. We consider the complete tree-level UV resonances for dimension 6 and 7 SMEFT operators, and representative UVs for higher dimension operators.

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arXiv2026

Covariant canonical-spinor amplitudes for partial wave analysis

We propose a covariant orbital-spin ($LS$) decomposed amplitude for the partial wave analysis using the massive spinor-helicity formalism. First we review the traditional-$LS$ method in the little group space and the Zemach tensor method in the double cover of the $\mathrm{SO}(3)$ space. To recover the $\mathrm{SO}(3,1)$ Lorentz covariance, several Lorentz covariant $LS$ tensors have been constructed in several different methods: covariant tensor, covariant projection tensor in pure-spin and general-spin schemes, but performing a intrinsic separation between $LS$ coupling while maintaining covariance is not obvious. We utilize the massive canonical-spinor variables to determine general three-point amplitudes, in which the spin-orbital decomposition is realized in single little group space by projecting little group indices of each particles into one, while the Lorentz covariance is ensured by the spinor form naturally. This covariant spinor method allows direct evaluation in any frame and a streamlined treatment of cascade decays within a single frame without additional alignment rotations in non-covariant treatment. As a benchmark, we implement the method in TF-PWA and analyze $\Lambda_c^+\to\Lambda\pi^+\pi^0$, finding consistent fit results across the helicity, traditional-$LS$, and canonical-spinor amplitudes. This validates the canonical-spinor amplitude as a practical tool for modern partial wave analyses of complex decay chains.

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arXiv2026

Systematic Operator Construction for Non-relativistic Effective Field Theories: Hilbert Series versus Young Tensor

This work establishes a systematic framework for operator construction in the non-relativistic effective field theory, incorporating both the three dimensional Euclidean symmetry and the internal symmetries. By employing double cover of the rotation group, we extend the Hilbert series to the non-relativistic systems, and eliminates redundancies introduced by the spin operator. We also generalize the Young tensor method to the non-relativistic cases through the $SU(2)$ semi-standard Young tableaux, which allows for the construction of operator bases with repeated fields at any given mass dimension. Utilizing the Young tensor technique and Hibert series as cross-check, we obtain the complete operator bases for the following cases: heavy particle (and also heavy quark) effective theory operators up to mass dimension 9; pion-less effective theory operators, including nucleon-nucleon contact interactions up to $\mathcal{O}(Q^4)$ and three-nucleon interactions at $\mathcal{O}(Q^2)$; and finally the spin-1/2 dark matter-nucleon operators up to $\mathcal{O}(v^4)$.

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arXiv2026

An introduction to gauge theories and group theory in particle physics

In this review, the fundamental concepts of group theory and representation theory are introduced. Special emphasis is placed on the unitary irreducible representations of the $SU(N)$ Lie group, the Poincare group, Little Group, discrete group, and their applications in particle physics. Based on the principle of local gauge symmetry, the construction of gauge-invariant Lagrangians and their quantization procedure are discussed. To address gauge redundancy, the modern on-shell amplitude approach is applied to gauge theories, demonstrating both conceptual and computational advantages. From the perspective of symmetry, the Standard Model is presented through the identification of its gauge symmetry, its anomaly-free matter content, and its global symmetries, including flavor symmetry, custodial symmetry, and baryon and lepton number conservation, etc.

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arXiv2026

Complete Operator Basis for the modular invariant SMEFT

We implement modular flavor symmetries within the Standard Model Effective Field Theory (SMEFT) framework, using the flavor group $A_4^{(q)} \times A_4^{(e)}$ with distinct moduli $\tau_q$ and $\tau_e$, and assigning different modular weights to right-handed quarks using simplest weight assignment. By treating the moduli as non-dynamical spurions, adopting the MFV-like assumption, and neglecting effects associated with $\mathrm{Im}\,\tau$, we systematically construct a finite set of independent modular-invariant higher-dimensional operators via the Hilbert-series techniques. In the holomorphic $A_4$ scenario, where all modular forms derive from the weight-2 triplet $Y^{(2)}_{\mathbf{3}}$, we present two equivalent Hilbert-series bases. This establishes that higher-dimensional operators can be formally organized as $[Y_{\mathbf{r}}^{(k_Y)},{Y_{\mathbf{r}'}^{(k_Y')}}^{*},\mathcal{O}]_{\mathbf{1}}$ singlets. We subsequently enumerate all independent operators up to dimension 7 under this assumption and provide explicit constructions for all dimension-5 operators as well as baryon- and lepton-number conserving dimension-6 operators. Relaxing holomorphicity to the non-holomorphic case of polyharmonic Maas forms, considering that non-holomorphic modular forms are not closed under multiplication, adopting the holomorphic organizing idea would generically lead to an infinite proliferation of modular-invariant structures. To retain a finite and complete operator basis, we therefore impose the same minimal formal organizing principle, which reproduces the benchmark Weinberg operator and the corresponding dimension-$6$ operators.

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arXiv2026

A Comprehensive Effective Field Theory Framework for Coherent Elastic Neutrino-Nucleus Scattering

Coherent elastic neutrino-nucleus scattering (CE$\nu$NS) stands out as a pivotal process for precision tests of the Standard Model electroweak sector, investigations of neutrino properties, and searches for new physics (NP). Recent experimental measurements by COHERENT, CONUS+, and ton-scale xenon detectors--including PandaX-4T and XENONnT--underscore the need for a systematic theoretical framework to bridge high-energy physics scenarios with low-energy observational data. In this work, we develop a comprehensive end-to-end effective field theory (EFT) framework for CE$\nu$NS, encompassing the complete energy scale hierarchy spanning the ultraviolet (UV) regime down to the nuclear sector. We consider the low-energy EFT (LEFT) operators up to dimension 8, incorporating their QCD renormalization group running effects, and employ the systematic spurion method to achieve the matching between these operators and the chiral Lagrangian. A full power counting analysis is performed, extending to nuclear response functions, which evaluates contributions from LEFT operators up to dimension 8 while accounting for the nucleon number enhancement effect intrinsic to CE$\nu$NS. Moreover, we match the relevant LEFT operators for CE$\nu$NS onto operators up to dimension 8 within the Standard Model EFT. By also providing their complete tree-level ultraviolet completions, this procedure establishes a consistent top-down theoretical workflow. Leveraging a broad suite of CE$\nu$NS experimental data, this framework enables a combined analysis to extract constraints on the scales of EFT operators and neutrino non-standard interaction parameters.

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arXiv2026

Effective Field Theory Description of Light Dilaton

Dilatons, the CP-even pseudo-Nambu-Goldstone bosons arising from spontaneous scale symmetry breaking, offer a compelling alternative to axion-like particles (ALPs) yet lack a comprehensive low-energy framework. We address this by constructing a systematic effective field theory (EFT) for the dilaton based on a manifestly scale-invariant regularization scheme. This approach derives universal linear couplings to the trace anomaly while preserving consistent renormalization group evolution. We establish a hierarchical EFT tower connecting the ultraviolet conformal sector to the infrared, encompassing the dilaton-extended SMEFT, low-energy EFT up to dimension-7, and a chiral Lagrangian describing meson and baryon interactions. We perform a comprehensive phenomenological analysis across two distinct mass regimes, where dilaton manifests as either conventional particle or wave-like particle. For MeV-scale dilatons behaving as conventional particles, we obtain constraints from LHC production, semi-invisible $B$- and $K$-meson decays, and supernova cooling. For ultralight dilatons acting as dark matter, we project sensitivities for atomic clocks and atom interferometers. This unified EFT framework would pave the way for extended phenomenological studies across the full mass spectrum of the light dilaton.

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arXiv2026

Massless-Massive Amplitude Correspondence I: Helicity-chirality Matching and On-shell Higgsing

In this work, the massless-massive correspondence for the on-shell scattering amplitudes is constructed so the massive amplitudes could inherit advantageous techniques developed in the massless calculation. This correspondence is established by matching massless amplitudes to Minimal Helicity-Chirality (MHC) amplitudes, which arise from an expansion of massive spin-spinor amplitudes in terms of the chirality-flip $m\eta$ order by order. The primary MHC amplitude deforms into a massless amplitude of the same helicity; if a vector boson is involved, it may instead vanish due to the associated conserved current. In cases where the primary amplitude vanishes, the leading contributions originate from descendant MHC amplitudes, each corresponding to a distinct massless amplitude in the ultraviolet theory containing either a transverse gauge boson or a Goldstone boson. We propose a systematic amplitude deformation procedure for three-point massless-massive matching based on helicity-chirality unification and the scaling properties of $m\eta$. Sub-leading MHC amplitudes are matched to massless amplitudes with additional on-shell Higgs splitting, a process known as on-shell Higgsing. In this work, we extend and reinterpret on-shell Higgsing as a transversality flip between different MHC states, and obtain all the 3-point massless-massive matching results in the spontaneous broken standard model.

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arXiv2026

Massless-Massive Amplitude Correspondence II: Constructive Massive Amplitudes in Standard Model

In the minimal helicity-chirality formalism, we systematically construct higher-point massive amplitudes from the fundamental building blocks: the contact three-point and four-point massive amplitudes. The inclusion of four-point contact amplitudes is essential to maintain gauge invariance in the spontaneously broken Standard Model. We construct all the standard model massive contact amplitudes and identify the physical light-cone gauge nature of massive amplitudes. Then only using the contact minimal helicity-chirality amplitudes at the leading order, we show both bootstrap techniques and on-shell recursion relations can be utilized to compute higher-point massive amplitudes. This provides a systematic framework for constructing various higher-point electroweak amplitudes, analogous to established on-shell methods for massless theories. Finally by deforming the gauge-invariant $n$-point amplitudes, we extend the massless-massive correspondence from three-and-four point contact amplitudes to general $n$-point factorized amplitudes.

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arXiv2025

On-Shell Renormalization of Dim-8 SMEFT from Complete Amplitude Basis: I. Four-Fermion Operators

We compute the complete one-loop renormalization group equations (RGEs) for all the four-fermion operators at dimension-8 Standard Model Effective Field Theory (SMEFT). We adopt the on-shell framework, where the RGEs are obtained from the unitarity cuts of the bubble integrals. To construct a consistent set of RGEs without redundancy, we utilize the Young Tensor amplitude/operator basis as the building blocks of the tree-level amplitudes that constitute the unitarity cuts, which incorporates the full flavor structures of the effective operators. Due to the large number of effective operators for a dimension-8 type, it is crucial to reduce the integrated cuts to the same RGE amplitude basis, which is also made possible by the algorithm in the Young Tensor method. With the Mathematica package ABC4EFT that implements the method, we obtain the full result of the dimension-8 four-fermion RGEs with the output file attached as the supplementary material.

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arXiv2025

Constructive Heavy Particle Effective Theory with Nonlinear Poincar\'{e} Symmetry

We develop a constructive heavy particle effective theory (HPET) through the nonlinear realization of the spontaneously broken Poincar\'{e} symmetry $R^{3,1} \rtimes SO(3,1) \rightarrow R^{3,1} \rtimes SO(3)$. Starting from the heavy one-particle state, we find the nonlinear boost transformation indicates the shift symmetry in the coset construction, corresponding to the reparameterization invariance. Using the little group Wigner rotation, we obtain the nonlinear boost transformation for corresponding heavy field, recovering the Foldy-Wouthuysen transformation. At the operator level, since interaction terms would modify the nonlinear transformation, we propose a most general parametrization on the boost transformation only based on symmetry. The nonlinear boost transformation relates different Wilson coefficients of the HPET operators, providing a bottom-up approach of constructing the independent HPET operators, and generalizing the top-down HPET operators beyond the tree-level integrating out. Utilizing the HPET as example, we obtain additional constraints for the boost transformation as well as the additional variation $\delta \mathcal{L}$ at the $1/m^3$.

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arXiv2025

Matching from quark to hadronic operators: external source vs spurion methods

Various weak processes at the hadronic scale have been utilized to search for new physics at high energy scale, which can be described by the QCD chiral Lagrangian matched from the low-energy effective theory (LEFT). Utilizing the chiral symmetry $SU(2)_L\times SU(2)_R \to SU(2)_V$ at the quark and hadronic levels, we make a comprehensive comparison of various matching methods, including the external source method, conventional spurion method, and our systematic spurion method. Although different methods show agreements for dimension-6 LEFT operator matching, we find that for higher-dimensional operators, the external source method is quite limited or inapplicable, the conventional spurion methods needs to introduce more and more spurions, while our spurion method does not need to introduce any new spurions than the ones in the dimension-6 matching. Using minimal set of spurions, we thus establish an one-to-one correspondence between the LEFT and chiral operators, with several examples, such as derivative operators at dimensions 7 and 8 with a single bilinear, four-quark operators at the dimension-9 level with two quark bilinears, which can be applied to the study of neutrino/electron scatterings and neutrinoless double beta decay.

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arXiv2025

Gravitational wave cosmology

Gravitational waves (GWs) originating from cosmological sources offer direct insights into the physics of the primordial Universe, the fundamental nature of gravity, and the cosmic expansion of the Universe. In this review paper, we present a comprehensive overview of our recent advances in GW cosmology, supported by the national key research and development program of China, focusing on cosmological GW sources and their implications for fundamental physics and cosmology. We first discuss the generation mechanisms and characteristics of stochastic gravitational wave backgrounds generated by physical processes occurred in the early Universe, including those from inflation, phase transitions, and topological defects, and summarize current and possible future constraints from pulsar timing array and space-based detectors. Next, we explore the formation and observational prospects of primordial black holes as GW sources and their potential connection to dark matter. We then analyze how GWs are affected by large-scale structure, cosmological perturbations, and possible modifications of gravity on GW propagation, and how these effects can be used to test fundamental symmetry of gravity. Finally, we discuss the application of GW standard sirens in measuring the Hubble constant, the expansion history, and dark energy parameters, including their combination with electromagnetic observations. These topics together show how GW observations, especially with upcoming space-based detectors, such as LISA, Taiji, and Tianqin, can provide new information about the physics of the early Universe, cosmological evolution, and the nature of gravity.

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