arXiv subjects

Stephen P. Martin

Publications and source records attributed to Stephen P. Martin.

At least 37 records · Page 2Linked to original sources

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.

hep-ph↗

arXiv2020

Criteria for projected discovery and exclusion sensitivities of counting experiments

The projected discovery and exclusion capabilities of particle physics and astrophysics/cosmology experiments are often quantified using the median expected $p$-value or its corresponding significance. We argue that this criterion leads to flawed results, which for example can counterintuitively project lessened sensitivities if the experiment takes more data or reduces its background. We discuss the merits of several alternatives to the median expected significance, both when the background is known and when it is subject to some uncertainty. We advocate for standard use of the "exact Asimov significance" $Z^{\rm A}$ detailed in this paper.

physics.data-an↗

arXiv2020

Signal-background interference for digluon resonances at the Large Hadron Collider

We study the interference between the amplitudes for $gg \rightarrow X \rightarrow gg$, where $X$ is a new heavy digluon resonance, and the QCD background $gg \rightarrow gg$, at the Large Hadron Collider. The interference produces a large low-mass tail and a deficit of events above the resonance mass, compared to the naive pure resonance peak. For a variety of different resonance quantum numbers and masses, we evaluate the signal-background interference contribution at leading order, including showering, hadronization, and detector effects. The resulting new physics dijet mass distribution may have a shape that appears, after QCD background fitting and subtraction, to resemble an enhanced peak, a shelf, a peak/dip, or even a pure dip. We argue that the true limits on new digluon resonances are likely to differ significantly from the limits obtained when interference is neglected, especially if the branching ratio to $gg$ is less than 1.

hep-ph↗

arXiv2019

Mixed gluinos and sgluons from a new SU(3) gauge group

I study supersymmetric models in which the QCD gauge group is the remnant diagonal subgroup from the spontaneous breaking of an $SU(3) \times SU(3)$ gauge group at a multi-TeV scale. In renormalizable models with soft supersymmetry breaking, the scalar potential is shown to have global minima with the required gauge symmetry breaking pattern. In addition to a massive color octet vector boson, this framework predicts 3 color octet spin-0 sgluons, and 4 color octet gluinos with both Dirac and Majorana mass terms. One of the gluino mass eigenstates typically has a coupling to quark-squark pairs that is at least as large as the prediction of minimal supersymmetry, but it need not be the lightest one.

hep-ph↗

arXiv2019

Signal-background interference for a singlet spin-0 digluon resonance at the LHC

Dijet mass distributions can be used to search for spin-0 resonances that couple to two gluons. I show that there is a substantial impact on such searches from the interference between the resonant signal and the continuum QCD background amplitudes. The signal dijet mass distribution is qualitatively modified by this interference, compared to the naive expectation from considering only the pure resonant contribution, even if the total width of the resonance is minimal and very small compared to the experimental dijet mass resolution. The impact becomes more drastic as the total width of the resonance increases. These considerations are illustrated using examples relevant to the 750 GeV diphoton excess recently observed at the LHC.

hep-ph↗

arXiv2019

Prospects for vectorlike leptons at future proton-proton colliders

Vectorlike leptons are an intriguing possibility for physics beyond the Standard Model. We study the reach for discovering (at 5$σ$ significance) or excluding (at 95 per cent confidence) models of charged vectorlike leptons that mix predominantly with the tau, using multi-lepton signatures at various future proton-proton collider options: a high-luminosity LHC with $\sqrt{s} =$ 14 TeV, a high-energy LHC with $\sqrt{s} =$ 27 TeV, and possible new longer-tunnel colliders with $\sqrt{s} =$ 70 or 100 TeV. For weak isodoublet vectorlike leptons, we estimate that a 27 TeV high-energy LHC with 15 ab$^{-1}$ could exclude masses up to about 2300 GeV, or discover them if the mass is less than about 1700 GeV, while a 100 TeV collider with 30 ab$^{-1}$ could exclude masses up to about 5750 GeV, or make a discovery if the mass is less than about 4000 GeV. However, we find that weak isosinglet vectorlike leptons present a much more difficult challenge, with some reach for exclusion, but not for discovery at any of the collider options considered.

hep-ph↗

arXiv2019

Matching relations for decoupling in the Standard Model at two loops and beyond

I discuss the matching relations for the running renormalizable parameters when the heavy particles (top quark, Higgs scalar, Z and W vector bosons) are simultaneously decoupled from the Standard Model. The complete two-loop order matching for the electromagnetic coupling and all light fermion masses are obtained, augmenting existing results at 4-loop order in pure QCD and complete two-loop order for the strong coupling. I also review the further sequential decouplings of the lighter fermions (bottom quark, tau lepton, and charm quark) from the low-energy effective theory.

hep-ph↗

arXiv2018

Refined gluino and squark pole masses beyond leading order

The physical pole and running masses of squarks and gluinos have recently been related at two-loop order in a mass-independent renormalization scheme. I propose a general method for improvement of such formulas, and argue that better accuracy results. The improved version gives an imaginary part of the pole mass that agrees exactly with the direct calculation of the physical width at next-to-leading order. I also find the leading three-loop contributions to the gluino pole mass in the case that squarks are heavier, using effective field theory and renormalization group methods. The efficacy of these improvements for the gluino and squarks is illustrated with numerical examples. Some necessary three-loop results for gauge coupling and fermion mass beta functions and pole masses in theories with more than one type of fermion representation, which are not directly accessible from the published literature, are presented in an Appendix.

hep-ph↗

arXiv2018

Two-loop effective potential for generalized gauge fixing

We obtain the two-loop effective potential for general renormalizable theories, using a generalized gauge-fixing scheme that includes as special cases the background-field $R_ξ$ gauges, the Fermi gauges, and the familiar Landau gauge, and using dimensional regularization in the bare and \MSbar renormalization schemes. As examples, the results are then specialized to the Abelian Higgs model and to the Standard Model. In the case of the Standard Model, we study how the vacuum expectation value and the minimum vacuum energy depend numerically on the gauge-fixing parameters. The results at fixed two-loop order exhibit non-convergent behavior for sufficiently large gauge-fixing parameters; this can presumably be addressed by a resummation of higher-order contributions.

hep-ph↗

arXiv2017

Quasi-fixed points from scalar sequestering and the little hierarchy problem in supersymmetry

In supersymmetric models with scalar sequestering, superconformal strong dynamics in the hidden sector suppresses the low-energy couplings of mass dimension two, compared to the squares of the dimension one parameters. Taking into account restrictions on the anomalous dimensions in superconformal theories, I point out that the interplay between the hidden and visible sector renormalizations gives rise to quasi-fixed point running for the supersymmetric Standard Model squared mass parameters, rather than driving them to 0. The extent to which this dynamics can ameliorate the little hierarchy problem in supersymmetry is studied. Models of this type in which the gaugino masses do not unify are arguably more natural, and are certainly more likely to be accessible, eventually, to the Large Hadron Collider.

hep-ph↗

arXiv2017

Effective potential at three loops

I present the effective potential at three-loop order for a general renormalizable theory, using the \MSbar renormalization scheme and Landau gauge fixing. As applications and illustrative points of reference, the results are specialized to the supersymmetric Wess-Zumino model and to the Standard Model. In each case, renormalization group scale invariance provides a consistency check. In the Wess-Zumino model, the required vanishing of the minimum vacuum energy yields an additional check. For the Standard Model, I carry out the resummation of Goldstone boson contributions, which provides yet more opportunities for non-trivial checks, and obtain the minimization condition for the Higgs vacuum expectation value at full three-loop order. An infrared divergence due to doubled photon propagators appears in the three-loop Standard Model effective potential, but it does not affect the minimization condition or physical observables and can be eliminated by resummation.

hep-ph↗

arXiv2016

TSIL: a program for the calculation of two-loop self-energy integrals

TSIL is a library of utilities for the numerical calculation of dimensionally regularized two-loop self-energy integrals. A convenient basis for these functions is given by the integrals obtained at the end of O.V. Tarasov's recurrence relation algorithm. The program computes the values of all of these basis functions, for arbitrary input masses and external momentum. When analytical expressions in terms of polylogarithms are available, they are used. Otherwise, the evaluation proceeds by a Runge-Kutta integration of the coupled first-order differential equations for the basis integrals, using the external momentum invariant as the independent variable. The starting point of the integration is provided by known analytic expressions at (or near) zero external momentum. The code is written in C, and may be linked from C, C++, or Fortran. A Fortran interface is provided. We describe the structure and usage of the program, and provide a simple example application. We also compute two new cases analytically, and compare all of our notations and conventions for the two-loop self-energy integrals to those used by several other groups.

hep-ph↗

arXiv2016

Resummation of Goldstone boson contributions to the MSSM effective potential

We discuss the resummation of the Goldstone boson contributions to the effective potential of the Minimal Supersymmetric Standard Model (MSSM). This eliminates the formal problems of spurious imaginary parts and logarithmic singularities in the minimization conditions when the tree-level Goldstone boson squared masses are negative or approach zero. The numerical impact of the resummation is shown to be almost always very small. We also show how to write the two-loop minimization conditions so that Goldstone boson squared masses do not appear at all, and so that they can be solved without iteration.

hep-ph↗

arXiv2016

Top-quark pole mass in the tadpole-free MS-bar scheme

The complex pole mass of the top quark is presented at full two-loop order in the Standard Model, augmenting the known four-loop QCD contributions. The input parameters are the MS-bar Yukawa and gauge couplings, the Higgs self-coupling, and the Higgs vacuum expectation value (VEV). Here, the VEV is defined as the minimum of the full effective potential in Landau gauge, so that tadpoles vanish. This is an alternative to earlier results that instead minimize the tree-level potential, resulting in a VEV that is gauge-fixing independent but accompanied by negative powers of the Higgs self-coupling in perturbative expansions. The effects of non-zero Goldstone boson mass are eliminated by resummation. I also study the renormalization scale dependence of the calculated pole mass.

hep-ph↗

arXiv2016

A Supersymmetry Primer

I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry. Topics covered include: motivations for supersymmetry, the construction of supersymmetric Lagrangians, superspace and superfields, soft supersymmetry-breaking interactions, the Minimal Supersymmetric Standard Model (MSSM), R-parity and its consequences, the origins of supersymmetry breaking, the mass spectrum of the MSSM, decays of supersymmetric particles, experimental signals for supersymmetry, and some extensions of the minimal framework.

hep-ph↗

arXiv2016

The Inclusion of Two-Loop SUSYQCD Corrections to Gluino and Squark Pole Masses in the Minimal and Next-to-Minimal Supersymmetric Standard Model: SOFTSUSY3.7

We describe an extension of the SOFTSUSY spectrum calculator to include two-loop supersymmetric QCD (SUSYQCD) corrections of order $\mathcal{O}(α_s^2)$ to gluino and squark pole masses, either in the minimal supersymmetric standard model (MSSM) or the next-to-minimal supersymmetric standard model (NMSSM). This document provides an overview of the program and acts as a manual for the new version of SOFTSUSY, which includes the increase in accuracy in squark and gluino pole mass predictions.

hep-ph↗

arXiv2015

Vectorlike leptons at the Large Hadron Collider

We study the prospects for excluding or discovering vectorlike leptons using multilepton events at the LHC. We consider models in which the vectorlike leptons decay to tau leptons. If the vectorlike leptons are weak isosinglets, then discovery in multilepton states is found to be extremely challenging. For the case that the vectorlike leptons are weak isodoublet, we argue that there may be an opportunity for exclusion for masses up to about 275 GeV by direct searches with existing LHC data at sqrt{s}=8 TeV. We also discuss prospects for exclusion or discovery at the LHC with future sqrt{s}=13 TeV data.

hep-ph↗

arXiv2015

Non-standard supersymmetry breaking and Dirac gaugino masses without supersoftness

I consider models in which non-standard supersymmetry breaking terms, including Dirac gaugino masses, arise from F-term breaking mediated by operators with a $1/M^3$ suppression. In these models, the supersoft properties found in the case of D-term breaking are absent in general, but can be obtained as a special case that is a fixed point of the renormalization group equations. The $μ$ term is replaced by three distinct supersymmetry-breaking parameters, decoupling the Higgs scalar potential from the Higgsino masses. Both holomorphic and non-holomorphic scalar cubic interactions with minimal flavor violation are induced in the supersymmetric Standard Model Lagrangian.

hep-ph↗