Kinetic Mixing of the Photon with Hidden U(1)s in String Phenomenology

TL;DR

The paper investigates kinetic mixing between the Standard Model hypercharge and hidden U(1)s in Type II string compactifications. It develops and compares two complementary approaches—the conformal field theory computation in supersymmetric toroidal orientifolds and a low-energy supergravity framework that includes fluxes and warping—to derive the kinetic-mixing parameter $χ_{ab}$ and related Stückelberg masses $m_{ab}^2$. It demonstrates that kinetic mixing can occur between anomaly-free, massless U(1)s, with its magnitude highly model-dependent and potentially enhanced in warped backgrounds such as Randall-Sundrum or Klebanov-Tseytlin throats, while mediator masses can induce suppression. The work connects string-theoretic constructions to near-future experimental probes of hidden photons and minicharged particles, offering concrete predictions and a framework for testing string vacua through low-energy phenomenology. Overall, it provides a rigorous link between string compactifications and observable hidden-sector phenomena.

Abstract

Embeddings of the standard model in type II string theory typically contain a variety of U(1) gauge factors arising from D-branes in the bulk. In general, there is no reason why only one of these - the one corresponding to weak hypercharge - should be massless. Observations require that standard model particles must be neutral (or have an extremely small charge) under additional massless U(1)s, i.e. the latter have to belong to a so called hidden sector. The exchange of heavy messengers, however, can lead to a kinetic mixing between the hypercharge and the hidden-sector U(1)s, that is testable with near future experiments. This provides a powerful probe of the hidden sectors and, as a consequence, of the string theory realisation itself. In the present paper, we show, using a variety of methods, how the kinetic mixing can be derived from the underlying type II string compactification, involving supersymmetric and nonsupersymmetric configurations of D-branes, both in large volumes and in warped backgrounds with fluxes. We first demonstrate by explicit example that kinetic mixing occurs in a completely supersymmetric set-up where we can use conformal field theory techniques. We then develop a supergravity approach which allows us to examine the phenomenon in more general backgrounds, where we find that kinetic mixing is natural in the context of flux compactifications. We discuss the phenomenological consequences for experiments at the low-energy frontier, searching for signatures of light, sub-electronvolt or even massless hidden-sector U(1) gauge bosons and minicharged particles.

Figures (5)

• Figure 1: Upper limits on the kinetic mixing parameter $\chi$ versus the hidden-sector $U(1)$ gauge boson mass $m_{\gamma^\prime}$, from electroweak precision tests (EWPT) at LEP and future experiments at LHC and ILC Chang:2006fpKumar:2006gmFeldman:2007wj, from searches for deviations of the Coulomb law Williams:1971msBartlett:1988yy, and from searches for signatures of $\gamma\leftrightarrow \gamma^\prime$ oscillations, exploiting, as a photon source, current and future laboratory lasers (light-shining-through-a-wall (LSW) experiments) Ahlers:2007qf, future microwave cavities Jaeckel:2007ch, or the sun Popov:1991Redondo:2008aa.
• Figure 2: Upper limits on the fractional charge $\epsilon = Q_\epsilon/e$ of a hidden-sector fermion with mass $m_\epsilon$. Some of the limits only apply if there is also an ultralight hidden-sector $U(1)$ gauge boson which gives rise to the minicharge $\epsilon \sim \chi$ by gauge kinetic mixing with the photon. Laboratory limits arise from laser polarization and light-shining-through-a-wall (LSW) experiments Ahlers:2007qf, from energy loss considerations of RF cavities Gies:2006hv, from searches for the invisible decay of orthopositronium Gninenko:2006fi, from Lamb shift measurements Gluck:2007ia and from searches at accelerators Goldberg:1986nkDavidson:1991si. Limits from cosmology are due the non-observation of a significant distortion of the spectrum of the cosmic microwave background (CMB) radiation Melchiorri:2007sq (for a limit exploiting the CMB anisotropy, see Ref. Dubovsky:2003yn), due to the apparent successfullness of standard big bang nucleosynthesis (BBN) Davidson:2000hf, and due to the observational requirement that the contribution of MCPs to the energy density should not overclose the universe, $\Omega = \rho/\rho_{\rm crit}<1$Davidson:1993sj. Finally, an astrophysical limit can be placed by energy loss considerations of red giants Davidson:2000hf.
• Figure 3: Schematic illustration of the reason why kinetic mixing need not cancel between anomaly-free $U(1)$s. We show contributions to photon mixing with hidden $U(1)$s in the presence of an orientifold plane: Stückelberg mass-terms cancel, whereas kinetic mixing terms do not.
• Figure 4: Supersymmetric configuration corresponding to the model in Table 1. Solid lines denote $A$ stacks and dashed-dotted lines represent $B$ stacks. Each of these stacks is separated into $A_1$, $A_2$, and $B_1$, $B_2$ in the first torus only. The orientifold planes are represented by the dashed lines with arrows. In the first torus, the two sets of orientifold planes are coincident. Finally the dots on each of the last two tori show the orbifold fixed points (or more precisely planes).
• Figure 5: Mixing on the conifold varying with distance of the hidden brane, $y_1=\log(r_1/r_s)$, up to the mouth of the throat at $y_1=16$. ($M$ is the number of fractional D5 branes wrapped on a compact $S^3 \subset T^{1,1}$ at the tip of the throat.)