[Paper Review] Constraints on R-parity Violation from Precision Electroweak Measurements

Tatsu Takeuchi, Oleg Lebedev+1 more|ArXiv.org|Sep 15, 2000

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper constrains R-parity violating couplings in the MSSM using precision electroweak data from LEP and SLD. By analyzing radiative corrections to Zf̄f vertices mediated by top-quark-sfermion loops, it derives bounds on λ′ijk and λ′′ijk couplings, finding 1σ limits of |λ′i3k| ≤ 0.40 and |λ′′3jk| ≤ 0.28, with stronger constraints from hadronic observables and Bayesian analysis.

ABSTRACT

We constrain the size of R-parity violating couplings using precision electroweak data.

Motivation & Objective

• To constrain R-parity violating couplings in the MSSM using precision electroweak measurements from LEP and SLD.
• To assess the impact of R-parity violating interactions on Zf̄f couplings, particularly those involving top-quark-sfermion loops.
• To isolate and quantify corrections to Z-boson couplings from λ′ijk and λ′′ijk terms, neglecting bilinear and soft-breaking terms.
• To derive model-independent bounds on the magnitudes of R-parity violating couplings using global fits to Z-pole observables.
• To compare frequentist and Bayesian approaches in setting confidence limits on the couplings, accounting for theoretical and experimental uncertainties.

Proposed method

• Model the R-parity violating interactions via the superpotential terms λ′ijkLiQjDk and λ′′ijkUiDjDk, focusing on couplings involving third-generation fermions.
• Compute radiative corrections to Zf̄f vertices using one-loop diagrams with sfermions in the internal lines, with top quarks as dominant contributors.
• Use the approximation of degenerate sfermion masses (100 GeV) to simplify the calculation of coupling shifts δhf̄f.
• Express shifts in Zf̄f couplings as δh ∝ |λ|², with coefficients derived from loop integrals: δhμL̄ = +0.00038 for μL, δhdR̄ = +0.081 for dR.
• Perform global fits to Z-pole observables (e.g., partial widths, forward-backward asymmetries) using ZFITTER predictions and experimental data.
• Apply both frequentist and Bayesian statistical frameworks to derive confidence limits, with the latter incorporating prior assumptions on the underlying theory.

Experimental results

Research questions

• RQ1 What are the constraints on λ′ijk and λ′′ijk R-parity violating couplings from precision electroweak data at the Z-pole?
• RQ2 How do R-parity violating interactions affect Zf̄f couplings, and which fermion generations contribute most significantly to the corrections?
• RQ3 To what extent do lepton universality and hadronic Z-decay observables constrain the magnitudes of λ′ and λ′′ couplings?
• RQ4 How do frequentist and Bayesian approaches differ in setting confidence limits on the R-parity violating couplings?
• RQ5 How do the bounds scale with the sfermion mass, and what is the functional dependence of the corrections on m̃f?

Key findings

• The 1σ (2σ) frequentist bounds on |λ′i3k| are 0.40 (0.50) for μL and 0.28 (0.42) for τL, derived from lepton universality tests.
• Hadronic Z-decay observables yield stronger constraints: δhdR̄ = 0.081 ± 0.077 (1σ), with |λ′i31| ≤ 5.8 (8.4) and |λ′i32| ≤ 3.8 (5.9) at 1σ (2σ).
• The coupling |λ′′321| is bounded at 2.7 (4.1) at 1σ (2σ), and |λ′′33i| at 1.0 (1.5), based on right-handed down-quark couplings.
• Bayesian analysis yields weaker but consistent bounds: |λ′i31| ≤ 5.2 (7.6), |λ′i32| ≤ 3.8 (5.6), and |λ′′321| ≤ 2.7 (3.9), with higher χ² values indicating less compatibility.
• The negative sign of the observed δhdR̄, δhsR̄, and δhbR̄ shifts rules out the R-parity violating contributions from λ′ and λ′′ terms at 1σ, as they predict negative shifts.
• Bounds scale with sfermion mass as √[F(x₀)/F(x)], where F(x) = (x/(1−x))(1 + (1/(1−x))ln x), with x = mₜ²/m̃f².