[Paper Review] How Can We Go From Hadron Collider Data Toward the Underlying Theory That Extends the Standard Model? After the Champagne

Gordon Kane|arXiv (Cornell University)|Apr 27, 2005

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper addresses the challenge of extracting fundamental physics from LHC data after the discovery of supersymmetry, proposing advanced techniques to infer supersymmetry-breaking parameters and underlying string-theory structures from inclusive signatures and kinematic distributions, despite the lack of a linear collider and the inherent ambiguity in mapping experimental observables to Lagrangian parameters.

ABSTRACT

This is a composite based on talks at Physics at LHC, Vienna, July 2004, TeV4LHC, Fermilab, Sept. 2004, and the String Phenomenology meeting, Perimeter Institute, March 2005.

Motivation & Objective

• To develop methods for inferring supersymmetry-breaking parameters (e.g., gaugino masses, trilinear couplings, μ, tanβ) from LHC data, despite the lack of direct access to these parameters.
• To overcome the fundamental obstacle that hadron colliders produce more Lagrangian parameters than measurable observables, making unique parameter reconstruction impossible in general.
• To propose strategies—particularly using inclusive signatures and CP-odd observables—to extract information about the underlying theory, such as string-theory-motivated structures, when direct measurements are not possible.
• To prepare for the LHC era by designing analysis techniques in advance, ensuring that non-obvious phenomena like CP violation and correlations between observables can be detected.
• To demonstrate that theoretical input is essential for interpreting LHC data beyond the Standard Model, especially in the absence of a linear collider for precision measurements.

Proposed method

• Use inclusive signatures (e.g., multi-jet, multi-lepton final states) to increase statistical power and reduce reliance on exclusive decay chain reconstruction.
• Apply kinematic distributions and event topology analysis to extract information about mass eigenstates and their mixing, even when direct access to soft-breaking parameters is unavailable.
• Utilize CP-odd observables and angular correlations to probe complex phases in the Lagrangian, such as those in gaugino and Higgsino mass parameters (M₂, μ), which are not directly measurable.
• Model the chargino mass matrix in the wino–higgsino basis using complex soft-breaking parameters, with the eigenvalues of the matrix determining the physical chargino masses.
• Leverage indirect constraints from rare processes (e.g., Bs → μ⁺μ⁻) and precision measurements to narrow down viable parameter spaces and guide analysis strategies.
• Develop theoretical frameworks that connect 10D string theories to low-energy effective Lagrangians with specific soft-breaking structures, enabling testable phenomenological predictions.

Experimental results

Research questions

• RQ1 How can we infer the complex soft-breaking parameters (e.g., M₂, μ, tanβ) from LHC data when they are not directly measurable?
• RQ2 What inclusive signatures can replace direct measurement of supersymmetry-breaking parameters in the absence of a linear collider?
• RQ3 How can CP-odd observables and angular correlations be used to detect complex phases in the supersymmetry-breaking sector?
• RQ4 What theoretical assumptions are necessary to connect string-theory models to observable LHC signatures, and how can these be tested?
• RQ5 How can analysis strategies be designed in advance to ensure detection of non-obvious effects like CP violation and non-trivial correlations between observables?

Key findings

• The number of Lagrangian parameters in the supersymmetry-breaking sector exceeds the number of measurable observables at hadron colliders, making unique parameter determination impossible without additional theoretical input.
• Inclusive signatures and kinematic distributions can serve as proxies for missing information about soft-breaking parameters, especially when exclusive decay chains are not reconstructible.
• CP-odd observables—such as those derived from angular correlations in multi-lepton or multi-jet final states—can probe complex phases in gaugino and Higgsino masses, even when the phases are not directly measurable.
• The chargino mass matrix, derived from soft-breaking parameters M₂, μ, and tanβ, determines the physical mass eigenstates, but these eigenvalues are not directly related to the underlying Lagrangian parameters without diagonalization.
• Backgrounds from SM processes are calculable and can be used as benchmarks, enabling the detection of deviations that signal new physics, including CP violation.
• Proactive theoretical and experimental planning—especially for trigger and analysis selection—is essential to preserve the ability to detect subtle effects like CP violation and non-trivial correlations.