[Paper Review] Phenomenology of Non-Commutative Field Theories

Stephen Godfrey, M. A. Doncheski|ArXiv.org|Nov 15, 2002

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper investigates non-commutative quantum electrodynamics (NCQED) at high-energy $e^+e^-$ colliders, focusing on fermion pair production ($\gamma\gamma\to f\bar{f}$) and Compton scattering ($e\gamma\to e\gamma$). It shows that NCQED introduces momentum-dependent phase factors and new 3- and 4-point photon vertices, leading to azimuthally dependent cross sections that break Lorentz invariance. The key result is that Compton scattering can probe non-commutative scales $\Lambda_{\text{NC}}$ roughly twice as large as those accessible via pair production, with limits exceeding the center-of-mass energy for $\sqrt{s} = 500$ GeV and $\Lambda_{\text{NC}} \gtrsim 1-2\sqrt{s}$.

ABSTRACT

We study the effects of non-commutative QED (NCQED) in fermion pair production, gamma + gamma to f + \bar{f} and Compton scattering, e + gamma to e + gamma. Non-commutative geometries give rise to 3- and 4-point photon vertices and to momentum dependent phase factors in QED vertices which will have observable effects in high energy collisions. We consider e^+ e^- colliders with energies appropriate to the TeV Linear Collider proposals and the multi-TeV CLIC project operating in gamma gamma and e gamma modes. Non-commutative scales roughly equal to the center of mass energy of the e^+e^- collider can be probed, with the exact value depending on the model parameters and experimental factors. The Compton process is sensitive to Lambda_{NC} values roughly twice as large as those accessible to the pair production process.

Motivation & Objective

• To explore the phenomenological signatures of non-commutative quantum field theories (NCQFT) in high-energy $e^+e^-$ collider experiments.
• To assess the sensitivity of $\gamma\gamma\to f\bar{f}$ and $e\gamma\to e\gamma$ processes to non-commutative scales $\Lambda_{\text{NC}}$.
• To determine whether $\Lambda_{\text{NC}}$ values near the TeV scale can be probed at future linear colliders such as the TeV Linear Collider and CLIC.
• To compare the relative sensitivity of pair production and Compton scattering to space-time and space-space non-commutativity parameters.

Proposed method

• The paper employs the Moyal-Weyl approach to map non-commutative field theories into conventional QFTs, introducing momentum-dependent phase factors in fermion-photon vertices.
• It incorporates new 3- and 4-point photon vertices arising from non-commutative geometry, which break Lorentz invariance.
• The analysis uses the Hewett-Petriello-Rizzo parametrization with $\theta_{\mu\nu} = i\theta_{\mu\nu}/\Lambda_{\text{NC}}^2$, where $\Lambda_{\text{NC}}$ sets the scale of non-commutativity.
• The $C_{\mu\nu}$ matrix is parameterized using angles $\alpha$ (E-field direction) and $\gamma$ (B-field direction), allowing separation of space-time and space-space NC effects.
• Cross sections for $\gamma\gamma\to e^+e^-$ and $e\gamma\to e\gamma$ are calculated with and without NCQED contributions, including statistical uncertainties from 500 fb$^{-1}$ luminosity.
• Azimuthal angular distributions ($d\sigma/d\phi$) are analyzed to detect NC-induced modulations, which serve as the primary experimental signature.

Experimental results

Research questions

• RQ1 Can $\gamma\gamma\to f\bar{f}$ and $e\gamma\to e\gamma$ processes at $e^+e^-$ colliders probe non-commutative scales $\Lambda_{\text{NC}}$ near the TeV scale?
• RQ2 How do momentum-dependent phase factors and new photon vertices in NCQED modify cross sections and angular distributions in $2\to2$ processes?
• RQ3 What is the relative sensitivity of Compton scattering versus pair production to the space-time and space-space components of non-commutativity?
• RQ4 To what extent do azimuthal modulations in the cross sections serve as a unique signature of Lorentz violation in NCQED?
• RQ5 Can collider experiments exclude $\Lambda_{\text{NC}}$ values significantly larger than the center-of-mass energy?

Key findings

• The Compton scattering process ($e\gamma\to e\gamma$) is more sensitive to non-commutative scales than fermion pair production, with exclusion limits for $\Lambda_{\text{NC}}$ roughly twice as large.
• For $\sqrt{s} = 500$ GeV and $500$ fb$^{-1}$ luminosity, $\Lambda_{\text{NC}} > (1-2)\sqrt{s}$ can be probed, indicating limits exceeding the center-of-mass energy.
• Azimuthal angular distributions in $d\sigma/d\phi$ exhibit strong modulations due to the preferred direction from the $C_{\mu\nu}$ tensor, especially when $\alpha = \pi/2$ (E-field perpendicular to beam).
• The pair production process is only sensitive to space-time non-commutativity ($\alpha$) and shows reduced deviations from the Standard Model as $\alpha \to \pi/2$, where it recovers SM behavior.
• Compton scattering is sensitive to both space-time ($\alpha$) and space-space ($\gamma$) non-commutativity, enabling complementary probing of the full $C_{\mu\nu}$ parameter space.
• Despite lower statistics, the large modification of angular distributions in Compton scattering leads to higher exclusion power than pair production, making it a superior probe for NCQED.