D-branes and the Standard Model

TL;DR

This paper studies an embedding of the Standard Model within a TeV-scale type I string theory realized by D-brane configurations. It identifies a minimal four-stack setup with a bulk U(1) that, via anomaly cancellation, yields baryon and lepton number as global symmetries, enabling proton stability and controlled neutrino masses. The authors analyze gauge coupling unification, propose four viable models with two Higgs doublets and calculable Yukawas that reproduce heavy-generation masses, and explore a bulk right-handed neutrino to generate small Dirac masses and neutrino oscillations. Their neutrino-physics scenario relies on a two-dimensional bulk with a non-trivial angle, producing two oscillation frequencies that can fit solar and atmospheric data while highlighting potential tension with sterile-neutrino constraints, thereby outlining a promising yet intricate path for TeV-scale string phenomenology.

Abstract

We perform a systematic study of the Standard Model embedding in a D-brane configuration of type I string theory at the TeV scale. We end up with an attractive model and we study several phenomenological questions, such as gauge coupling unification, proton stability, fermion masses and neutrino oscillations. At the string scale, the gauge group is U(3)_color x U(2)_weak x U(1)_1 x U(1)_bulk. The corresponding gauge bosons are localized on three collections of branes; two of them describe the strong and weak interactions, while the last abelian factor lives on a brane which is extended in two large extra dimensions with a size of afew microns. The hypercharge is a linear combination of the first three U(1)s. All remaining U(1)s get masses at the TeV scale due to anomalies, leaving the baryon and lepton numbers as (perturbatively) unbroken global symmetries at low energies. The conservation of baryon number assures proton stability, while lepton number symmetry guarantees light neutrino masses that involve a right-handed neutrino in the bulk. The model predicts the value of the weak angle which is compatible with the experiment when the string scale is in the TeV region. It also contains two Higgs doublets that provide tree-level masses to all fermions of the heaviest generation, with calculable Yukawa couplings; one obtains a naturally heavy top and the correct ratio m_b/m_tau. We also study neutrino masses and mixings in relation to recent solar and atmospheric neutrino data.

Figures (4)

• Figure 1: Pictorial representation of models$A, A'$.
• Figure 2: Pictorial representation of models $B$ and $B'$.
• Figure 3: Evolution of the ratio $m_b/m_\tau$ as a function of the energy $\mu$ for $\tan \beta=2$ and $\tan \beta=80$. We have used as low energy parameters $m_b=4$GeV, $m_{top}=174$GeV$a_3(M_z)=0.12$, $\sin^2\theta_W=0.23113$.
• Figure 4: Plot of the infinite two-dimensional sum $\sum_{\vec{n}\in\mathbb{Z}^2}\frac{\delta^{-\frac{2h_{\vec{n}}}{M^2 R^2}}}{h_{\vec{n}}} \sin^2\left(\frac{L}{4 E}\frac{h_{\vec{n}}}{R^2} \right)$ with $h_{\vec{n}}=\cos^{-2}\theta(n_1^2+n_2^2-2 n_1 n_2 \sin\theta)$ in the case $M^2 R^2=10^6$, $\delta=16$ and $\sin\theta=\frac{119}{120}$. The gray line represents the dominant frequency mode $\rho \sin^2\left(\frac{L}{4 E}\frac{240}{239 R^2}\right)$ with amplitude $\rho={0.8 \pi}\cos\theta\log (M^2 R^2\cos\theta\log\delta^2)$.