arXiv subjects

Stephen P. Martin

Publications and source records attributed to Stephen P. Martin.

At least 19 recordsLinked to original sources

arXiv2026

Bare effective potential and Goldstone boson anti-resummation

I discuss the evaluation of the effective potential and related quantities starting from bare perturbation theory followed by $\overline{\rm{MS}}$ renormalization. The advantages of this method include a simple new way of avoiding infrared problems associated with Goldstone bosons, by treating their bare masses as two-point interaction vertices instead of incorporating them into the propagators. Thus, only positive integer powers of the Goldstone-boson masses appear at every stage of calculation, completely avoiding the imaginary parts and singularities encountered in intermediate steps of previous resummation methods. This Goldstone boson anti-resummation approach is implemented using simple rules provided through three-loop order in terms of the master vacuum integrals. Explicit results are given for the Standard Model at three-loop order. The method is shown to give effective potential minimization conditions that are consistent with previous resummation methods, but in a form more directly useful for related future multi-loop calculations of observables in the tadpole-free scheme.

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arXiv2025

Chasing higgsino dark matter at colliders in the neutrino fog era

Higgsinos can be the lightest supersymmetric particles, allowing for either a full or partial dark matter interpretation, with the correct thermal freeze-out abundance obtained for masses near 1.1 TeV. Dark matter direct detection experimental results, now rapidly approaching the neutrino fog, imposes increasingly stringent requirements on higgsino purity. We begin by summarizing the purity constraints implied by the current strong limits from the LUX-ZEPLIN experiment in 2024, presenting them as lower bounds on gaugino masses in scenarios with decoupled sfermions and heavy Higgs bosons. We further quantify how these constraints will evolve as direct detection approaches various neutrino fog discovery and exclusion definitions and future exclusion projections. Finally, given that nearly pure higgsinos remain notoriously challenging to probe directly at colliders, we explore complementary signatures in which higgsinos are produced from the decays of heavier superpartners, where additional leptons and jets can be used for triggering. In particular, we advocate for searches of stop and wino pairs decaying directly to higgsinos as a promising means to probe higgsino dark matter well into the neutrino fog era.

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arXiv2025

Three-loop corrections to the Fermi decay constant in the $\overline{\rm{MS}}$ scheme

I present the leading 3-loop contributions to the Fermi decay constant in the Standard Model, using the tadpole-free pure $\overline{\rm{MS}}$ scheme. The calculation is exact in the limit in which the QCD coupling, the top-quark Yukawa coupling, and the square root of the Higgs self-coupling are all treated as large compared to the electroweak gauge couplings. The effect of the 3-loop contribution is to decrease the estimate of the Higgs VEV, for fixed on-shell inputs, by about 3.5 MeV. The renormalization scale dependence of the computed Fermi constant is greatly reduced compared to the previously known complete 2-loop order result, and as a fraction is now less than $\pm 2 \times 10^{-6}$ for renormalization scales between 90 and 250 GeV. This corresponds to a theoretical uncertainty in the VEV that is well under 1 MeV, and much smaller than the current parametric uncertainties coming mostly from the top-quark mass. I also comment on the impact on the precise prediction of the $W$-boson mass.

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arXiv2024

The curtain lowers on directly detectable higgsino dark matter

A higgsino could be some or all of the dark matter, with a mass bounded from above by about 1.1 TeV assuming a thermal freezeout density, and from below by collider searches. Direct detection experiments imply purity constraints on a dark matter higgsino, limiting the mixing with the electroweak gauginos. Using the new strong limits available as of the end of 2024 from the LUX-ZEPLIN experiment, I quantify the resulting lower bounds on gaugino masses and upper bounds on higgsino mass splittings, assuming that the scalar superpartners and Higgs bosons of minimal supersymmetry are in the decoupling limit. Similar bounds are projected for the critical future scenario that direct detection experiments reach the neutrino fog that hampers discovery prospects.

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arXiv2024

Effective K\"ahler and auxiliary field potentials for chiral superfield models at three loops

I obtain the effective K\"ahler potential at three-loop order for a general renormalizable supersymmetric theory containing only chiral supermultiplets. The three-loop contribution is remarkably simple, consisting of only four terms involving three distinct renormalized master integrals. In the case of the Wess-Zumino model with a single chiral superfield, I also obtain the effective auxiliary field potential at three-loop order, extending previous results at one-loop order. The method used is inferential, relying on existing knowledge of the ordinary scalar effective potential.

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arXiv2024

Implications of purity constraints on light higgsinos

The lightest supersymmetric particles could be higgsinos that have a small mixing with gauginos. If the lightest higgsino-like state makes up some or all of the dark matter with a thermal freezeout density, then its mass must be between about 100 and 1150 GeV, and dark matter searches put bounds on the amount of gaugino contamination that it can have. Motivated by the generally good agreement of flavor- and CP-violating observables with Standard Model predictions, I consider models in which the scalar particles of minimal supersymmetry are heavy enough to be essentially decoupled, except for the 125 GeV Higgs boson. I survey the resulting purity constraints as lower bounds on the gaugino masses and upper bounds on the higgsino mass splittings. I also discuss the mild excesses in recent soft lepton searches for charginos and neutralinos at the LHC, and show that they can be accommodated in these models if $\tanβ$ is small and $μ$ is negative.

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arXiv2024

Isosinglet vectorlike leptons at $e^+e^-$ colliders

We study weak isosinglet vectorlike leptons that decay through a small mixing with the tau lepton, for which the discovery and exclusion reaches of the Large Hadron Collider and future proposed hadron colliders are limited. We show how an $e^+ e^-$ collider may act as a discovery machine for these $τ^{\prime}$ particles, demonstrate that the $τ^{\prime}$ mass peak can be reconstructed in a variety of distinct signal regions, and explain how the $τ^{\prime}$ branching ratios may be measured.

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arXiv2023

Three-loop effective potential for softly broken supersymmetry

The effective potential has been previously calculated through three-loop order, in Landau gauge, for a general renormalizable theory using dimensional regularization. However, dimensional regularization is not appropriate for softly broken supersymmetric gauge theories, because it explicitly violates supersymmetry. In this paper, I obtain the three-loop effective potential using a supersymmetric regulator based on dimensional reduction. Checks follow from the vanishing of the effective potential in examples with supersymmetric vacua, and from renormalization scale invariance in examples for which supersymmetry is broken, either spontaneously or explicitly by soft terms. As byproducts, I obtain the three-loop Landau gauge anomalous dimension for the scalar component of a chiral supermultiplet, and the beta function for the field-independent vacuum energy.

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arXiv2023

Statistical significances and projections for proton decay experiments

We study the statistical significances for exclusion and discovery of proton decay at current and future neutrino detectors. Various counterintuitive flaws associated with frequentist and modified frequentist statistical measures of significance for multi-channel counting experiments are discussed in a general context and illustrated with examples. We argue in favor of conservative Bayesian-motivated statistical measures, and as an application we employ these measures to obtain the current lower limits on proton partial lifetime at various confidence levels, based on Super-Kamiokande's data, generalizing the 90\% CL published limits. Finally, we present projections for exclusion and discovery reaches for proton partial lifetimes in $p \rightarrow \overline νK^+$ and $p \rightarrow e^+ π^0$ decay channels at Hyper-Kamiokande, DUNE, JUNO, and THEIA.

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arXiv2023

Evaluation of three-loop self-energy master integrals with four or five propagators

I obtain identities satisfied by the 3-loop self-energy master integrals with four or five propagators with generic masses, including the derivatives with respect to each of the squared masses and the external momentum invariant. These identities are then recast in terms of the corresponding renormalized master integrals, enabling straightforward numerical evaluation of them by the differential equations approach. Some benchmark examples are provided. The method used to obtain the derivative identities relies only on the general form implied by integration by parts relations, without actually following the usual integration by parts reduction procedure. As a byproduct, I find a simple formula giving the expansion of the master integrals to arbitrary order in the external momentum invariant, in terms of known derivatives of the corresponding vacuum integrals.

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arXiv2022

The Standard Model at 200 GeV

The Standard Model can be defined quantitatively by running parameters in a mass-independent renormalization scheme at a fixed reference scale. We provide a set of simple interpolation formulas that give the fundamental Lagrangian parameters in the $\bar{\rm MS}$ scheme at a renormalization scale of 200 GeV, safely above the top-quark mass and suitable for matching to candidate new physics models at very high mass scales using renormalization group equations. These interpolation formulas take as inputs the on-shell experimental quantities, and use the best available calculations in the pure $\bar{\rm MS}$ scheme. They also serve as an accounting of the parametric uncertainties for the short-distance Standard Model Lagrangian. We also include an interpolating formula for the W boson mass.

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arXiv2022

Three-loop QCD corrections to the electroweak boson masses

I find the three-loop corrections at leading order in QCD to the physical masses of the Higgs, W, and Z bosons in the Standard Model. The results are obtained as functions of the $\overline{\rm{MS}}$ Lagrangian parameters only, using the tadpole-free scheme for the vacuum expectation value. The dependences of the computed masses on the renormalization scale are found to be smaller than present experimental uncertainties in each case. In the case of the Higgs boson mass, the new result is the state-of-the-art, while the results for $W$ and $Z$ are in good numerical agreement with corresponding results in the on-shell and hybrid schemes. These results are now included in the SMDR (Standard Model in Dimensional Regularization) computer code.

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arXiv2022

TASI 2011 lectures notes: two-component fermion notation and supersymmetry

These notes, based on work with Herbi Dreiner and Howie Haber, discuss how to do practical calculations of cross sections and decay rates using two-component fermion notation, as appropriate for supersymmetry and other beyond-the-Standard-Model theories. Included are a list of two-component fermion Feynman rules for the Minimal Supersymmetric Standard Model, and some example calculations.

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arXiv2022

Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry

Two-component spinors are the basic ingredients for describing fermions in quantum field theory in four space-time dimensions. We develop and review the techniques of the two-component spinor formalism and provide a complete set of Feynman rules for fermions using two-component spinor notation. These rules are suitable for practical calculations of cross-sections, decay rates, and radiative corrections in the Standard Model and its extensions, including supersymmetry, and many explicit examples are provided. The unified treatment presented in this review applies to massless Weyl fermions and massive Dirac and Majorana fermions. We exhibit the relation between the two-component spinor formalism and the more traditional four-component spinor formalism, and indicate their connections to the spinor helicity method and techniques for the computation of helicity amplitudes.

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arXiv2022

Renormalized $ε$-finite master integrals and their virtues: the three-loop self energy case

Loop diagram calculations typically rely on reduction to a finite set of master integrals in $4 - 2ε$ dimensions. It has been shown that for any problem, the masters can be chosen so that their coefficients are finite as $ε\rightarrow 0$. I propose a definition of renormalized $ε$-finite master integrals, which incorporate ultraviolet divergence subtractions in a specific way. A key advantage of this choice is that in expressions for physical observables, expansions to positive powers in $ε$ are never needed. As an example, I provide the subtractions for general three-loop self-energy integrals. The differential equations method is used to compute numerically the renormalized $ε$-finite master integrals for arbitrary external momentum invariant, in special cases with internal masses equal to a single scale or zero. These include the ones necessary for the three-loop QCD corrections to the self-energies of the W, Z, and Higgs bosons. In principle, the same method should provide for numerical computation of general three-loop self energies with any masses.

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arXiv2022

Higgs boson mass in the Standard Model at two-loop order and beyond

We calculate the mass of the Higgs boson in the Standard Model in terms of the underlying Lagrangian parameters at complete 2-loop order with leading 3-loop corrections. A computer program implementing the results is provided. The program also computes and minimizes the Standard Model effective potential in Landau gauge at 2-loop order with leading 3-loop corrections.

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arXiv2021

High-quality axions in solutions to the $μ$ problem

Solutions to the $μ$ problem in supersymmetry based on the Kim-Nilles mechanism naturally feature a Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) axion with decay constant of order the geometric mean of the Planck and TeV scales, consistent with astrophysical limits. We investigate minimal models of this type with two gauge-singlet fields that break a Peccei-Quinn symmetry, and extensions with extra vectorlike quark and lepton supermultiplets consistent with gauge coupling unification. We show that there are many anomaly-free discrete symmetries, depending on the vectorlike matter content, that protect the Peccei-Quinn symmetry to sufficiently high order to solve the strong CP problem. We study the axion couplings in this class of models. Models of this type that are automatically free of the domain wall problem require at least one pair of strongly interacting vectorlike multiplets with mass at the intermediate scale, and predict axion couplings that are greatly enhanced compared to the minimal supersymmetric DFSZ models, putting them within reach of proposed axion searches.

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arXiv2021

Evaluation of the general 3-loop vacuum Feynman integral

We discuss the systematic evaluation of 3-loop vacuum integrals with arbitrary masses. Using integration by parts, the general integral of this type can be reduced algebraically to a few basis integrals. We define a set of modified finite basis integrals that are particularly convenient for expressing renormalized quantities. The basis integrals can be computed numerically by solving coupled first-order differential equations, using as boundary conditions the analytically known special cases that depend on only one mass scale. We provide the results necessary to carry this out, and introduce an implementation in the form of a public software package called 3VIL (3-loop Vacuum Integral Library), which efficiently computes the numerical values of the basis integrals for any specified masses. 3VIL is written in C, and can be linked from C, C++, or FORTRAN code.

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