arXiv subjects

Aneesh V. Manohar

Publications and source records attributed to Aneesh V. Manohar.

At least 19 recordsLinked to original sources

arXiv2026

Darkly Charged ALPs

The established $d=5$ ALP effective Lagrangian describes the interaction of scalars with approximate shift-symmetry which carry no Standard Model (SM) charges with SM fields. It implicitly assumes that ALPs are not charged under any symmetries of the dark sector. In this paper, we remove this assumption. For ALPs carrying conserved dark charges, no $d=5$ ALP effective interaction to SM particles is possible. We build the effective Lagrangian for these darkly charged ALPs stemming from a general breaking pattern, and we show that the lowest-order shift-symmetric effective Lagrangian contains just two $d=6$ operators coupling ALPs to SM particles. We explore the model-independent phenomenological implications of these interactions, as well as the question of whether the dark matter observed in the Universe may consist of darkly charged ALPs. We identify higher order operators of the effective field theory, and determine which types of dark symmetry groups can seed darkly charged ALPs. Illustrative examples of ultraviolet completions which result in darkly charged ALPs at low-energies are provided as well. The darkly-charged ALP scenario can be generalized by including dark gauge interactions. In this paper, we have considered only the case with no such interactions.

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arXiv2026

Polarized Deep Inelastic Scattering as $x \to 1$ using Soft Collinear Effective Theory

We use Soft Collinear Effective Theory (SCET) to factorize the polarized Deep Inelastic Scattering (DIS) structure functions $g_1(x)$ and $g_2(x)$, and to sum Sudakov double logarithms of $1-x$. The analysis is done both in terms of lightcone parton distributions and their moments. Computing $g_2$ requires subleading SCET operators which contain gluons. We calculate the one-loop matching coefficients from QCD onto these subleading SCET operators, and the one-loop matching from SCET onto the parton distribution function (PDF). The PDF in SCET is given by a bilocal operator, rather than the trilocal operator used in the QCD analysis of $g_2$ for generic $x$. We compute the one-loop anomalous dimension of the PDF operator for any $x$, and show that as $x \to 1$, it factors into a single-variable evolution. We comment on the QCD anomalous dimensions of twist-three operators, their equation-of-motion relation, and connection to the SCET analysis. We briefly discuss the definition of axial operators in the BMHV scheme. As a side result, we derive the $1/N$ dependence of the QCD coefficient functions for $F_1$, $F_L$ and $g_1$ in the $N \to \infty$ limit, where $N$ is the moment, which is expected to hold to all orders in $α_s$.

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arXiv2024

Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology

We calculate the gauge terms of the one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory (SM EFT). Combining these results with our previous results for the $λ$ and Yukawa coupling terms completes the calculation of the one-loop anomalous dimension matrix for the dimension-six operators. There are 1350 $CP$-even and $1149$ $CP$-odd parameters in the dimension-six Lagrangian for 3 generations, and our results give the entire $2499 \times 2499$ anomalous dimension matrix. We discuss how the renormalization of the dimension-six operators, and the additional renormalization of the dimension $d \le 4$ terms of the SM Lagrangian due to dimension-six operators, lays the groundwork for future precision studies of the SM EFT aimed at constraining the effects of new physics through precision measurements at the electroweak scale. As some sample applications, we discuss some aspects of the full RGE improved result for essential processes such as $gg \to h$, $h \to γγ$ and $h \to Z γ$, for Higgs couplings to fermions, for the precision electroweak parameters $S$ and $T$, and for the operators that modify important processes in precision electroweak phenomenology, such as the three-body Higgs boson decay $h \rightarrow Z \, \ell^+ \, \ell^-$ and triple gauge boson couplings. We discuss how the renormalization group improved results can be used to study the flavor problem in the SM EFT, and to test the minimal flavor violation (MFV) hypothesis. We briefly discuss the renormalization effects on the dipole coefficient $C_{eγ}$ which contributes to $μ\to e γ$ and to the muon and electron magnetic and electric dipole moments.

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arXiv2024

Low-Energy Effective Field Theory below the Electroweak Scale: Anomalous Dimensions

We compute the one-loop anomalous dimensions of the low-energy effective Lagrangian below the electroweak scale, up to terms of dimension six. The theory has 70 dimension-five and 3631 dimension-six Hermitian operators that preserve baryon and lepton number, as well as additional operators that violate baryon number and lepton number. The renormalization group equations for the quark and lepton masses and the QCD and QED gauge couplings are modified by dimension-five and dimension-six operator contributions. We compute the renormalization group equations from one insertion of dimension-five and dimension-six operators, as well as two insertions of dimension-five operators, to all terms of dimension less than or equal to six. The use of the equations of motion to eliminate operators can be ambiguous, and we show how to resolve this ambiguity by a careful use of field redefinitions.

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arXiv2024

Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching

The gauge-invariant operators up to dimension six in the low-energy effective field theory below the electroweak scale are classified. There are 70 Hermitian dimension-five and 3631 Hermitian dimension-six operators that conserve baryon and lepton number, as well as $ΔB= \pm ΔL = \pm 1$, $ΔL=\pm 2$, and $ΔL=\pm 4$ operators. The matching onto these operators from the Standard Model Effective Field Theory (SMEFT) up to order $1/Λ^2$ is computed at tree level. SMEFT imposes constraints on the coefficients of the low-energy effective theory, which can be checked experimentally to determine whether the electroweak gauge symmetry is broken by a single fundamental scalar doublet as in SMEFT. Our results, when combined with the one-loop anomalous dimensions of the low-energy theory and the one-loop anomalous dimensions of SMEFT, allow one to compute the low-energy implications of new physics to leading-log accuracy, and combine them consistently with high-energy LHC constraints.

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arXiv2024

Geometry in Scattering Amplitudes

We formulate the field-space geometry for an effective field theory of scalars and gauge bosons. Geometric invariants such as the field-space curvature enter in both scattering amplitudes and the renormalization group equations, with the scalar and gauge results unified in a single expression.

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arXiv2024

Field Redefinitions and Infinite Field Anomalous Dimensions

Field redefinitions are commonly used to reduce the number of operators in the Lagrangian by removing redundant operators and transforming to a minimal operator basis. We give a general argument that such field redefinitions, while leaving the $S$-matrix invariant and consequently finite, lead not only to infinite Green's functions, but also to infinite field anomalous dimensions $γ_ϕ$. These divergences cannot be removed by counterterms without reintroducing redundant operators.

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arXiv2023

Two Loop Renormalization of Scalar Theories using a Geometric Approach

We derive a general formula for two-loop counterterms in Effective Field Theories (EFTs) using a geometric approach. This formula allows the two-loop results of our previous paper to be applied to a wide range of theories. The two-loop results hold for loop graphs in EFTs where the interaction vertices contain operators of arbitrarily high dimension, but at most two derivatives. We also extend our previous one-loop result to include operators with an arbitrary number of derivatives, as long as there is at most one derivative acting on each field. The final result for the two-loop counterterms is written in terms of geometric quantities such as the Riemann curvature tensor of the scalar manifold and its covariant derivatives. As applications of our results, we give the two-loop counterterms and renormalization group equations for the O(n) EFT to dimension six, the scalar sector of the Standard Model Effective Field Theory (SMEFT) to dimension six, and chiral perturbation theory to order $p^6$.

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arXiv2023

An Algebraic Formula for Two Loop Renormalization of Scalar Quantum Field Theory

We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending 't~Hooft's one-loop result. The method can also be used for theories with higher derivative interactions, as long as the terms in the Lagrangian have at most one derivative acting on each field. We show that diagrams with factorizable topologies do not contribute to the renormalization group equations. The results in this paper will be combined with the geometric method in a subsequent paper to obtain the counterterms and renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order.

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arXiv2023

Fermion Geometry and the Renormalization of the Standard Model Effective Field Theory

The geometry of field space governs on-shell scattering amplitudes. We formulate a geometric description of effective field theories which extends previous results for scalars and gauge fields to fermions. The field-space geometry reorganizes and simplifies the computation of quantum loop corrections. Using this geometric framework, we calculate the fermion loop contributions to the renormalization group equations for bosonic operators in the Standard Model Effective Field Theory up to mass dimension eight.

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arXiv2022

Renormalization of the Standard Model Effective Field Theory from Geometry

$S$-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and gauge fields are treated together, with a metric on the combined space of both types of fields. Scalar and gauge scattering amplitudes are given by the Riemann curvature $R_{ijkl}$ of this combined space, with indices $i,j,k,l$ chosen to be scalar or gauge indices depending on the type of external particle. One-loop divergences can also be computed in terms of geometric invariants of the combined space, which greatly simplifies the computation of renormalization group equations. We apply our formalism to the Standard Model Effective Field Theory (SMEFT), and compute the renormalization group equations for even-parity bosonic operators to mass dimension eight.

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arXiv2022

Dark Matter Effective Field Theory and an Application to Vector Dark Matter

The Standard Model Effective Field Theory (SMEFT) and the Low Energy Effective Field Theory (LEFT) can be extended by adding additional spin 0, 1/2 and 1 dark matter particles which are singlets under the Standard Model (SM) gauge group. We classify all gauge invariant interactions in the Lagrangian up to terms of dimension six, and present the tree-level matching conditions between the two theories at the electroweak scale. The most widely studied dark matter models, such as those based on the Higgs portal or on kinetic mixing between the photon and a dark photon, are based on dimension-four interactions with the SM sector. We consider a model with dark vector particles with a $\mathbb{Z}_2$ symmetry, so that the lightest dark matter particle is stable. The leading interaction with the SM is through dimension-six operators involving two dark vector field-strength tensors and the electromagnetic field-strength tensor. This model is a viable dark matter model in the freeze-in scenario for a wide range of parameters.

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arXiv2022

Radiated Angular Momentum and Dissipative Effects in Classical Scattering

We present a new formula for the angular momentum $J^{μν}$ carried away by gravitational radiation in classical scattering. This formula, combined with the known expression for the radiated linear momentum $P^μ$, completes the set of radiated Poincare charges due to scattering. We parametrize $P^μ$ and $J^{μν}$ by non-perturbative form factors and derive exact relations using the Poincare algebra. There is a contribution to $J^{μν}$ due to static (zero-frequency) modes, which can be derived from Weinberg's soft theorem. Using tools from scattering amplitudes and effective field theory, we calculate the radiated $J^{μν}$ due to the scattering of two spinless particles to third order in Newton's constant $G$, but to all orders in velocity. Our form-factor analysis elucidates a novel relation found by Bini, Damour, and Geralico between energy and angular momentum loss at $\mathcal{O}(G^3)$. Our new results have several nontrivial implications for binary scattering at $\mathcal{O}(G^4)$. We give a procedure to bootstrap an effective radiation reaction force from the loss of Poincare charges due to scattering.

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arXiv2021

Effective field theory interpretation of lepton magnetic and electric dipole moments

We perform a model-independent analysis of the magnetic and electric dipole moments of the muon and electron. We give expressions for the dipole moments in terms of operator coefficients of the low-energy effective field theory (LEFT) and the Standard Model effective field theory (SMEFT). We use one-loop renormalization group improved perturbation theory, including the one-loop matching from SMEFT onto LEFT, and one-loop lepton matrix elements of the effective-theory operators. Semileptonic four-fermion operators involving light quarks give sizable non-perturbative contributions to the dipole moments, which are included in our analysis. We find that only a very limited set of the SMEFT operators is able to generate the current deviation of the magnetic moment of the muon from its Standard Model expectation.

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arXiv2021

Quark-Gluon Backscattering in the Regge Limit at One-Loop

At small momentum transfer, the quark-gluon scattering cross section dσ/dt has a power-law divergence in the backward scattering region where the outgoing quark is nearly collinear to the incoming gluon. In this Regge limit |t|<< s, the leading behavior of the 2 2 amplitude can be described by the exchange of Glauber quarks. In Soft-Collinear Effective Theory (SCET) at leading power, Glauber quark exchange is given by five non-local Glauber quark operators, of which only one is generated at tree-level. We show that at leading power the QCD amplitude for quark-gluon backscattering at one-loop can be exactly reproduced by SCET using the tree-level Glauber operator. The agreement between QCD and SCET of the ultraviolet, infrared, and rapidity divergences as well as all logarithms, Glauber phases and finite parts for all polarizations of the external gluons is a strong check on the effective theory. We find that the entire one-loop matching vanishes -- there is no correction to the operator generated at tree-level, and the coefficients of the other four operators remain zero at one-loop. This suggests that SCET with Glauber operators may be useful for uncovering new aspects of Regge physics in a systematically improveable way.

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arXiv2021

Axion strings are superconducting

We explore the cosmological consequences of the superconductivity of QCD axion strings. Axion strings can support a sizeable chiral electric current and charge, which alters their early universe dynamics. Shrinking axion string loops can become effectively stable remnants called vortons, supported by the electromagnetic force of the string current. Generically, vortons produced by axion strings overclose the universe, unless there are efficient current leakage processes. Furthermore, if a primordial magnetic field (PMF) exists in the early universe, a large current is induced on axion strings, creating a significant drag force from interactions with the surrounding plasma. As a result, the strings are slowed down, which leads to an orders of magnitude enhancement in the number of strings per Hubble volume. Finally, we study the implications for the QCD axion relic abundance. The QCD axion window is shifted by orders of magnitude in some parts of our parameter space.

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arXiv2021

Renormalization Group Improvement of the Effective Potential: an EFT Approach

We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the $O(N)$ model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop $β$-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem.

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arXiv2020

Disentangling observable dependence in SCETI and SCETII anomalous dimensions: angularities at two loops

The resummation of radiative corrections to collider jet observables using soft collinear effective theory is encoded in differential renormalization group equations (RGEs), with anomalous dimensions depending on the observable under consideration. This observable dependence arises from the ultraviolet (UV) singular structure of real phase space integrals in the effective field theory. We show that the observable dependence of anomalous dimensions in SCETI problems can be disentangled by introducing a suitable UV regulator in real radiation integrals. Resummation in the presence of the new regulator can be performed by solving a two-dimensional system of RGEs in the collinear and soft sectors, and resembles many features of resummation in SCETII theories by means of the rapidity renormalization group. We study the properties of SCETI with the additional regulator and explore the connection with the system of RGEs in SCETII theories, highlighting some universal patterns that can be exploited in perturbative calculations. As an application, we compute the two-loop soft and jet anomalous dimensions for a family of recoil-free angularities and give new analytic results. This allows us to study the relations between the SCETI and SCETII limits for these observables. We also discuss how the extra UV regulator can be exploited to calculate anomalous dimensions numerically, and the prospects for numerical resummation.

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