[Paper Review] Renormalization of Newton's constant and Particle Physics

Xavier Calmet|arXiv (Cornell University)|Feb 2, 2010

Black Holes and Theoretical Physics10 references3 citations

TL;DR

This paper investigates the renormalization group running of Newton's constant in quantum field theory coupled to gravity, showing that the Planck mass decreases with energy due to quantum corrections from matter fields. The key result is a scale-dependent Planck mass $ M(\mu)^2 = M(0)^2 - \frac{1\mu^2}{12\pi}N $, where $ N = N_0 + N_{1/2} - 4N_1 $, implying that quantum gravity effects become strong at a dynamically generated scale $ \mu_* \sim M(\mu_*) $, potentially solving the hierarchy problem and affecting grand unification.

ABSTRACT

We report on particle physics applications of the renormalization group equation of Newton's constant.

Motivation & Objective

• To understand how quantum corrections from matter fields affect the running of Newton's constant in curved spacetime.
• To determine whether the Planck scale is fundamental or dynamically generated via renormalization group evolution.
• To explore implications of scale-dependent gravity for the hierarchy problem and grand unification of forces.
• To assess the viability of models with large hidden sectors that lower the scale of strong gravity to the TeV region.

Proposed method

• Uses the heat kernel method to compute quantum corrections to the Planck mass in curved spacetime, preserving gauge and diffeomorphism symmetries.
• Derives the renormalization group equation $ M(\mu)^2 = M(0)^2 - \frac{\mu^2}{12\pi}N $, where $ N = N_0 + N_{1/2} - 4N_1 $, from one-loop contributions of spin-0, 1/2, and spin-1 particles.
• Considers the graviton contribution to the running, showing it enhances the Planck mass at high energy, similar in sign to vector fields.
• Applies the result to estimate higher-loop corrections, finding they are suppressed by powers of $ \Lambda/M(0) \sim 10^{-15} $, justifying perturbative control.
• Uses the running Planck mass to analyze the scale $ \mu_* $ at which gravity becomes strong, defined by $ M(\mu_*) \sim \mu_* $.
• Applies the framework to model-building scenarios, including large hidden sectors and grand unified theories, to assess phenomenological consequences.

Experimental results

Research questions

• RQ1 How does the effective Planck mass evolve with energy scale in quantum field theory coupled to gravity?
• RQ2 What is the physical significance of the scale $ \mu_* $ where $ M(\mu_*) \sim \mu_* $, and how does it relate to the onset of strong quantum gravity?
• RQ3 Can a large number of light matter fields dynamically lower the scale of strong gravity to the TeV region, resolving the hierarchy problem?
• RQ4 How do quantum gravitational corrections affect the unification of gauge couplings in SUSY and non-SUSY grand unified theories?
• RQ5 What constraints do unitarity bounds in gravitational scattering impose on the particle content of models coupled to linearized gravity?

Key findings

• The Planck mass exhibits running with energy scale, following $ M(\mu)^2 = M(0)^2 - \frac{\mu^2}{12\pi}N $, where $ N = N_0 + N_{1/2} - 4N_1 $, indicating a decrease in effective Planck mass at high energy.
• The scale $ \mu_* $ at which quantum gravity effects become strong is dynamically determined by $ M(\mu_*) \sim \mu_* $, not fixed at the naive Planck scale.
• A hidden sector with $ \sim 10^{33} $ scalar or fermionic fields can reduce $ \mu_* $ to the TeV scale, enabling production of microscopic black holes at the LHC.
• Graviton contributions to the running of $ M(\mu) $ have the same sign as vector fields, increasing the Planck mass at high energy.
• Higher-loop diagrams involving multiple graviton propagators are suppressed by powers of $ \Lambda/M(0) \sim 10^{-15} $, justifying perturbative treatment.
• In grand unified theories with $ N \sim 1000 $ particles near the unification scale, the scale of strong gravity shifts from $ \sim 10^{18} $ GeV to $ \sim 10^{17} $ GeV, altering unification conditions.