[Paper Review] Flux-Induced Baryon Asymmetry

Luis E. Ibáñez|ArXiv.org|Feb 27, 2006

Black Holes and Theoretical Physics19 references3 citations

TL;DR

This paper proposes a novel mechanism for generating the primordial baryon asymmetry via a constant background flux $ H_{\mu\nu\rho} $ of an antisymmetric tensor field in a universe with a gauged $ U(1)_{B-L} $ symmetry. The flux induces a net $ B-L $ charge density through a Stuckelberg-type mass generation for the $ U(1)_{B-L} $ gauge boson, producing a baryon asymmetry without requiring any of the Sakharov conditions.

ABSTRACT

I propose that the primordial baryon asymmetry of the universe was induced by the presence of a non-vanishing antisymmetric field background H_ijk across the three space dimensions. This background creates a dilute (B-L)-number density in the universe cancelling the contribution from baryons and leptons. This situation naturally appears if the U(1)_{B-L} symmetry is gauged and the corresponding gauge boson gets a Stuckelberg mass by combining with an antisymmetric field B_ij. All these ingredients are present in D-brane models of particle physics. None of the Sakharov conditions are required.

Motivation & Objective

• To resolve the unnaturalness of the initial $ n_B/n_\gamma \sim 10^{-10} $ baryon asymmetry in the standard Sakharov framework.
• To propose a mechanism that generates a primordial baryon asymmetry without relying on baryon number violation, CP violation, or thermal non-equilibrium.
• To show that a non-vanishing $ H_{\mu\nu\rho} $ background can induce a $ B-L $ charge density while preserving vacuum quantum numbers.
• To connect this mechanism to string compactifications, particularly D-brane models with Stuckelberg masses and fluxes.
• To explore the possibility that baryon asymmetry and dark matter are correlated through a common origin in SUSY-breaking scale.

Proposed method

• Introduce a constant background flux $ H_{\mu\nu\rho} $ in three spatial dimensions, coupling to a $ U(1)_{B-L} $ gauge field via a $ B \wedge F $ interaction.
• Utilize the Stuckelberg mechanism where the $ U(1)_{B-L} $ gauge boson acquires mass by mixing with an antisymmetric tensor field $ B_{\mu\nu} $, preserving global $ U(1)_{B-L} $ symmetry.
• Derive the induced $ B-L $ charge density as proportional to the flux $ H_{\mu\nu\rho} $, with the density given by $ n_{B-L} \propto H_{\mu\nu\rho} $.
• Ensure anomaly freedom via the generalized Green-Schwarz mechanism involving $ B \wedge F $ and $ \eta \wedge F \wedge F $ couplings.
• Analyze the thermal history, assuming the flux is generated at reheating, and estimate the resulting $ n_B/n_\gamma $ from $ n_{B-L} \sim M H / T^{*3} $.
• Explore the possibility that the flux $ H $ is dynamically fixed by moduli stabilization in string compactifications, with $ H \sim G \sim M_{\text{sb}} M_p $ at high temperature.

Experimental results

Research questions

• RQ1 Can a primordial baryon asymmetry arise without satisfying any of the three Sakharov conditions?
• RQ2 How can a non-zero $ B-L $ asymmetry be generated in a vacuum that otherwise has zero net quantum numbers?
• RQ3 What role does a constant $ H_{\mu\nu\rho} $ background play in generating a $ U(1)_{B-L} $ charge density?
• RQ4 Can the observed $ n_B/n_\gamma \sim 10^{-10} $ be naturally reproduced via flux-induced $ B-L $ density in a Stuckelberg-type $ U(1)_{B-L} $ model?
• RQ5 Is there a dynamical mechanism in string compactifications that can naturally produce the required flux scale for the observed asymmetry?

Key findings

• A non-vanishing $ H_{\mu\nu\rho} $ background induces a $ B-L $ charge density proportional to the flux, leading to a primordial baryon asymmetry without requiring baryon number violation or CP violation.
• The mechanism works because the $ U(1)_{B-L} $ gauge boson acquires a Stuckelberg mass via coupling to $ B_{\mu\nu} $, leaving the global $ U(1)_{B-L} $ symmetry intact and allowing a net charge density to be generated.
• The resulting baryon asymmetry is estimated as $ n_B/n_\gamma \simeq M H / T^{*3} $, and for $ M \sim 10^{16} \text{ GeV} $, $ T^* \sim 10^9 \text{ GeV} $, a flux $ H \sim (300 \text{ MeV})^2 $ reproduces the observed $ 10^{-10} $ asymmetry.
• If the reheating temperature is close to the string scale $ M \sim 10^{16} \text{ GeV} $, the flux $ H \sim M_{\text{sb}} M_p / M $ can naturally yield $ n_B/n_\gamma \sim 10^{-10} $, linking baryon asymmetry to SUSY-breaking scale.
• The mechanism generalizes to other $ U(1) $ symmetries (e.g., hidden sector $ U(1) $), potentially generating dark matter particle densities correlated with baryon asymmetry.
• The model correlates baryon asymmetry and dark matter if both arise from similar flux scales and SUSY-breaking soft masses, offering a unified origin for visible and dark matter.