[Paper Review] Space anisotropy search at colliders

I. S. Karpikov, D. Kirpichnikov+1 more|arXiv (Cornell University)|Dec 7, 2016

Noncommutative and Quantum Gravity Theories3 references3 citations

TL;DR

This paper investigates Lorentz violation in the quark sector using $e^+e^-$ collider data within the Standard Model Extension (SME) framework. It derives time-dependent $q\bar{q}$ production cross-sections sensitive to SME coefficients and sets conservative limits on dimensionless Lorentz-violating couplings using ALEPH and OPAL data from LEP, finding $|c_{ZZ}^{q}| < 0.027$ (ALEPH) and $< 0.036$ (OPAL) under symmetric assumptions, with looser bounds for individual quarks. The study also predicts time-modulated signals for future lepton colliders.

ABSTRACT

In the framework of model with Lorentz violation (LV) we discuss a physical observables for $q\bar{q}$ pair production at lepton-lepton colliders and describe the experimental signal to be detected. We obtain a conservative limits on Lorentz-violating dimensionless coupling for quark sector from LEP data. We also make a phenomenological prediction for LV model at the future lepton collider.

Motivation & Objective

• To probe Lorentz violation in the quark sector using $e^+e^-$ collider data within the SME framework.
• To derive time-dependent $q\bar{q}$ production cross-sections sensitive to SME coefficients due to Earth's rotation.
• To set conservative experimental limits on dimensionless Lorentz-violating couplings $c_{ZZ}^{q}$ using ALEPH and OPAL data from LEP.
• To provide phenomenological predictions for future lepton colliders based on SME-induced time-modulated signals.
• To assess the sensitivity of collider experiments to $CPT$-even Lorentz-violating couplings in the quark sector, particularly $c_{ZZ}^{q}$.

Proposed method

• Constructs a SME Lagrangian with $CPT$-even Lorentz-violating terms for quarks, focusing on $c_{Q\mu\nu}$, $c_{U\mu\nu}$, and $c_{D\mu\nu}$ couplings.
• Calculates the matrix element squared for $e^+e^-\to q\bar{q}$, including interference terms between SM and SME amplitudes.
• Transforms the SME coefficients from the Sun-centered inertial frame to the Earth-based laboratory frame using sidereal time dependence.
• Derives a time-modulated cross-section expression $\sigma^{SME} = \sigma^{SM} \cdot (1 + \epsilon(t))$, where $\epsilon(t)$ depends on $c_{XX}^q$ and Earth's orientation.
• Applies experimental uncertainties from ALEPH and OPAL to derive conservative bounds on $|c_{ZZ}^{q}|$, accounting for $b\bar{b}$ and $c\bar{c}$ branching fractions.
• Proposes a benchmark SME matrix with $c_{XX}^q$ and $-c_{XX}^q$ components to model time-dependent signals for future collider studies.

Experimental results

Research questions

• RQ1 Can $e^+e^-$ colliders like LEP probe Lorentz-violating couplings in the quark sector through $q\bar{q}$ production?
• RQ2 How does the time-dependent orientation of the Earth affect the $q\bar{q}$ production cross-section in the SME framework?
• RQ3 What are the conservative experimental limits on $c_{ZZ}^{q}$ for $u,d,s,c,b$ quarks derived from ALEPH and OPAL data?
• RQ4 How do uncertainties in $R_b$ and $R_c$ affect the bounds on $|c_{ZZ}^{b}|$ and $|c_{ZZ}^{c}|$?
• RQ5 What is the expected time-modulated signal for $q\bar{q}$ production at future lepton colliders due to SME-induced Lorentz violation?

Key findings

• Conservative bounds on the dimensionless Lorentz-violating coupling $|c_{ZZ}^{q}|$ are set at $< 0.027$ (ALEPH) and $< 0.036$ (OPAL) under the assumption that all quark flavors have equal $c_{ZZ}^{q}$ values.
• For individual quarks, the bounds are looser: $|c_{ZZ}^{b}| < 0.35$ (ALEPH) and $< 0.46$ (OPAL), with $|c_{ZZ}^{c}| < 0.4$ (ALEPH), due to large uncertainties in $R_b$ and $R_c$.
• The time-dependent cross-section for $e^+e^-\to q\bar{q}$ is modulated by a function $\epsilon(t)$ that varies with sidereal time, with a period of one sidereal day.
• The signal modulation arises from the Earth's rotation, which changes the orientation of the laboratory frame relative to the Sun-centered frame, affecting the SME coefficients.
• The study identifies that only the $ZZ$ component of the SME coupling matrix is constrained by the data, as $XY$, $XZ$, and $YZ$ components average out over time.
• The paper provides a phenomenological prediction for future lepton colliders, showing that time-modulated $q\bar{q}$ signals could be detectable if SME couplings are non-zero.