Two-loop Threshold Corrections Research Articles

Full two-loop QCD corrections to the Higgs mass in the MSSM with heavy superpartners

We improve the determination of the Higgs-boson mass in the MSSM with heavy superpartners, by computing the two-loop threshold corrections to the quartic Higgs coupling that involve both the strong and the electroweak gauge couplings. Combined with earlier results, this completes the calculation of the two-loop QCD corrections to the quartic coupling at the SUSY scale. We also compare different computations of the relation between the quartic coupling and the pole mass of the Higgs boson at the EW scale. We find that the numerical impact of the new corrections on the prediction for the Higgs mass is modest, but comparable to the accuracy of the Higgs-mass measurement at the LHC.

Supersymmetric models in light of improved Higgs mass calculations

We discuss the parameter spaces of supersymmetry (SUSY) scenarios taking into account the improved Higgs-mass prediction provided by FeynHiggs 2.14.1. Among other improvements, this prediction incorporates three-loop renormalization-group effects and two-loop threshold corrections, and can accommodate three separate mass scales: m_{{{tilde{q}}}} (for squarks), m_{tilde{g,}!} (for gluinos) and m_{{{tilde{chi }}}} (for electroweakinos). Furthermore, it contains an improved treatment of the overline{mathrm {DR}} scalar top parameters avoiding problems with the conversion to on-shell parameters, that yields more accurate results for large SUSY-breaking scales. We first consider the CMSSM, in which the soft SUSY-breaking parameters m_0 and m_{1/2} are universal at the GUT scale, and then sub-GUT models in which universality is imposed at some lower scale. In both cases, we consider the constraints from the Higgs-boson mass M_h in the bulk of the (m_0, m_{1/2}) plane and also along stop coannihilation strips where sparticle masses may extend into the multi-TeV range. We then consider the minimal anomaly-mediated SUSY-breaking scenario, in which large sparticle masses are generic. In all these scenarios the substantial improvements between the calculations of M_h in FeynHiggs 2.14.1 and FeynHiggs 2.10.0, which was used in an earlier study, change significantly the preferred portions of the models’ parameter spaces. Finally, we consider the pMSSM11, in which sparticle masses may be significantly smaller and we find only small changes in the preferred regions of parameter space.

Improved determination of the Higgs mass in the MSSM with heavy superpartners

We present several advances in the effective field theory calculation of the Higgs mass in MSSM scenarios with heavy superparticles. In particular, we compute the dominant two-loop threshold corrections to the quartic Higgs coupling for generic values of the relevant SUSY-breaking parameters, including all contributions controlled by the strong gauge coupling and by the third-family Yukawa couplings. We also study the effects of a representative subset of dimension-six operators in the effective theory valid below the SUSY scale. Our results will allow for an improved determination of the Higgs mass and of the associated theoretical uncertainty.

Mr: A C++ library for the matching and running of the Standard Model parameters

We present the C++ program library mr that allows us to reliably calculate the values of the running parameters in the Standard Model at high energy scales. The initial conditions are obtained by relating the running parameters in the MS¯ renormalization scheme to observables at lower energies with full two-loop precision. The evolution is then performed in accordance with the renormalization group equations with full three-loop precision. Pure QCD corrections to the matching and running are included through four loops. We also provide a Mathematica interface for this program library. Program summaryProgram title:mrCatalogue identifier: AFAI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFAI_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 517613No. of bytes in distributed program, including test data, etc.: 2358729Distribution format: tar.gzProgramming language: C++.Computer: IBM PC.Operating system: Linux, Mac OS X.RAM: 1 GBClassification: 11.1.External routines: TSIL [1], OdeInt [2], boost [3]Nature of problem: The running parameters of the Standard Model renormalized in the MS¯ scheme at some high renormalization scale, which is chosen by the user, are evaluated in perturbation theory as precisely as possible in two steps. First, the initial conditions at the electroweak energy scale are evaluated from the Fermi constant GF and the pole masses of the W, Z, and Higgs bosons and the bottom and top quarks including the full two-loop threshold corrections. Second, the evolution to the high energy scale is performed by numerically solving the renormalization group evolution equations through three loops. Pure QCD corrections to the matching and running are included through four loops.Solution method: Numerical integration of analytic expressionsAdditional comments: Available for download from URL: http://apik.github.io/mr/. The MathLink interface is tested to work with Mathematica 7–9 and, with an additional flag, also with Mathematica 10 under Linux and with Mathematica 10 under Mac OS X.Running time: less than 1 second

Symmetry-improved 2PI approach to the Goldstone-boson IR problem of the SM effective potential

The effective potential of the Standard Model (SM), from three loop order and higher, suffers from infrared (IR) divergences arising from quantum effects due to massless would-be Goldstone bosons associated with the longitudinal polarizations of the W± and Z bosons. Such IR pathologies also hinder accurate evaluation of the two-loop threshold corrections to electroweak quantities, such as the vacuum expectation value of the Higgs field. However, these divergences are an artifact of perturbation theory, and therefore need to be consistently resummed in order to obtain an IR-safe effective potential. The so-called Two-Particle-Irreducible (2PI) effective action provides a rigorous framework to consistently perform such resummations, without the need to resort to ad hoc subtractions or running into the risk of over-counting contributions. By considering the recently proposed symmetry-improved 2PI formalism, we address the problem of the Goldstone-boson IR divergences of the SM effective potential in the gaugeless limit of the theory. In the same limit, we evaluate the IR-safe symmetry-improved 2PI effective potential, after taking into account quantum loops of chiral fermions, as well as the renormalization of spurious custodially breaking effects triggered by fermionic Yukawa interactions. Finally, we compare our results with those obtained with other methods presented in the literature.

Higher order corrections and unification in the minimal supersymmetric standard model: SOFTSUSY3.5

We explore the effects of three-loop minimal supersymmetric standard model renormalisation group equation terms and some leading two-loop threshold corrections on gauge and Yukawa unification: each being one loop higher order than current public spectrum calculators. We also explore the effect of the higher order terms (often 2–3 GeV) on the lightest CP even Higgs mass prediction. We illustrate our results in the constrained minimal supersymmetric standard model. Neglecting threshold corrections at the grand unified scale, the discrepancy between the unification scale αs and the other two unified gauge couplings changes by 0.1% due to the higher order corrections and the difference between unification scale bottom-tau Yukawa couplings neglecting unification scale threshold corrections changes by up to 1%. The difference between unification scale bottom and top Yukawa couplings changes by a few percent. Differences due to the higher order corrections also give an estimate of the size of theoretical uncertainties in the minimal supersymmetric standard model spectrum. We use these to provide estimates of theoretical uncertainties in predictions of the dark matter relic density (which can be of order one due to its strong dependence on sparticle masses) and the LHC sparticle production cross-section (often around 30%). The additional higher order corrections have been incorporated into SOFTSUSY, and we provide details on how to compile and use the program. We also provide a summary of the approximations used in the higher order corrections. Program SummaryNature of problem: Calculating supersymmetric particle spectrum and mixing parameters in the minimal supersymmetric standard model. The solution to the renormalisation group equations must be consistent with boundary conditions on supersymmetry breaking parameters, as well as the weak-scale boundary condition on gauge couplings, Yukawa couplings and the Higgs potential parameters.Program title:SOFTSUSYCatalogue identifier: ADPM_v5_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADPM_v5_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 240528No. of bytes in distributed program, including test data, etc.: 2597933Distribution format: tar.gzProgramming language: C++, Fortran.Computer: Personal computer.Operating system: Tested on Linux 3.4.6.Word size: 64 bits.Classification: 11.1, 11.6.External routines: At least GiNaC1.3.5 [1] and CLN1.3.1 (both freely obtainable from http://www.ginac.de).Does the new version supersede the previous version?: YesCatalogue identifier of previous version: ADPM_v4_0Journal reference of previous version: Comput. Phys. Comm. 185 (2014) 2322Solution method: Nested iterative algorithm.Reasons for new version: Extension to include additional two and three-loop terms.Summary of revisions: All quantities in the minimal supersymmetric standard model are extended to have three-loop renormalisation group equations (including 3-family mixing) in the limit of real parameters and some leading two-loop threshold corrections are incorporated to the third family Yukawa couplings and the strong gauge coupling.Restrictions:SOFTSUSY will provide a solution only in the perturbative regime and it assumes that all couplings of the model are real (i.e. CP-conserving). If the parameter point under investigation is non-physical for some reason (for example because the electroweak potential does not have an acceptable minimum), SOFTSUSY returns an error message. The higher order corrections included are for the real R-parity conserving minimal supersymmetric standard model (MSSM) only.Running time: A minute per parameter point. The tests provided with the package only take a few seconds to run.

Large, negative threshold contributions to light soft masses in models with effective supersymmetry

Threshold contributions to light scalar soft masses due to heavy sparticles (possibly including a heavy Higgs mostly aligned with H_d) in Effective SUSY scenarios are dominated by two-loop diagrams involving gauge couplings. This is due to the fact that in the limit in which the heavy states are degenerate, their one-loop contributions to the light soft masses only depend on small Yukawas and the hypercharge coupling. The two-loop threshold corrections involving only gauge couplings are calculated accounting for nonzero gaugino and light squark masses and shown to be negative, and rather large (\delta m^2_{t,L}\sim-480^2 GeV^2 for heavy sparticles with masses around 10 TeV). The effect on tachyon bounds is revisited with calculations implementing decoupling. It is pointed out that models yielding Effective SUSY spectra using gaugino mediation require in general very heavy gluinos or a very low SUSY breaking scale in order to avoid tachyons (e.g. for heavy squarks at 10 TeV and a SUSY breaking scale of 125 TeV, minimal scenarios require \tilde m_3 >=2 TeV at 500 GeV, while nonminimal ones demand \tilde m_3 >= 8 TeV).

Inclusive jet production at the tevatron using the d0 experiment

A preliminary measurement is presented of the inclusive jet production cross section in pp collisions at a center-of-mass energy of s√ = 1960GeV. The data was taken with the D0 detector and represents an integrated luminosity of ~ 900pb-1 of Tevatron RunII data. The cross section is studied as a function of jet transverse momentum (pt) and rapidity (y) and compared to perturbative QCD predictions in next-to-leading order including two-loop threshold corrections.

Jet production in the D0 experiment: measurements and data-to-Monte Carlo comparisons

A preliminary measurement is presented of the inclusive jet production cross section in pp collisions with the D0 detector using an integrated luminosity of 800 pb-1 of Tevatron RunII data. The cross section is studied as a function of jet pT and rapidity and compared to perturbative QCD predictions in next-to-leading order including two-loop threshold corrections. Also presented is a preliminary measurement of Z/γ∗+jet production based on 950 pb-1. A comparison to the sherpa event generator shows excellent agreement for jet multiplicities and good agreement for the pT spectra of the jets and the Z boson and for the inter-jet angular correlations.