Light Neutrinos without Heavy Mass Scales: A Higher-Dimensional Seesaw Mechanism

TL;DR

The paper investigates how light or massless neutrinos can arise without a large right-handed Majorana mass by invoking extra spatial dimensions. It develops several higher-dimensional mechanisms in which a bulk right-handed neutrino with a KK tower couples to the brane-localized left-handed neutrino, leading to light masses through KK-induced seesaws, power-law running of Yukawa couplings, and brane dynamics, including Scherk-Schwarz twists. A key finding is that the heavy mass scale can be effectively replaced by the radius of the extra dimensions ($1/R$), with the dominant mass scale often scaling as $m^2 R$; in some setups, neutrino oscillations can occur even when the light neutrinos are massless. The work also proposes lepton-number-violation mechanisms via brane positioning and highlights substantial theoretical and phenomenological challenges in embedding these ideas into realistic string or brane-world models, along with directions for future study.

Abstract

Recent theoretical developments have shown that extra spacetime dimensions can lower the fundamental GUT, Planck, and string scales. However, recent evidence for neutrino oscillations suggests the existence of light non-zero neutrino masses, which in turn suggests the need for a heavy mass scale via the seesaw mechanism. In this paper, we make several observations in this regard. First, we point out that allowing the right-handed neutrino to experience extra spacetime dimensions naturally permits the left-handed neutrino mass to be power-law suppressed relative to the masses of the other fermions. This occurs due to the power-law running of the neutrino Yukawa couplings, and therefore does not require a heavy scale for the right-handed neutrino. Second, we show that a higher-dimensional analogue of the seesaw mechanism may also be capable of generating naturally light neutrino masses without the introduction of a heavy mass scale. Third, we show that such a higher-dimensional seesaw mechanism may even be able to explain neutrino oscillations without neutrino masses, with oscillations induced indirectly via the masses of the Kaluza-Klein states. Fourth, we point out that even when higher-dimensional right-handed neutrinos are given a bare Majorana mass, the higher-dimensional seesaw mechanism surprisingly replaces this mass scale with the radius scale of the extra dimensions. Finally, we also discuss a possible new mechanism for inducing lepton-number violation by shifting the positions of D-branes in Type I string theory.

Figures (6)

• Figure 1: Typical one-loop diagram that can induce power-law running of the neutrino Yukawa coupling as a result of Kaluza-Klein states for the right-handed neutrino field $N$. If only the right-handed neutrino $N$ experiences the extra dimensions, then the Yukawa coupling for the neutrino can be power-law suppressed relative to the Yukawa couplings for all other matter fields.
• Figure 2: Tree-level diagram showing the generation of an effective neutrino mass term through a mixing with the right-handed Kaluza-Klein states $N^{(k)}$.
• Figure 3: (a) Eigenvalue solutions to (\ref{['trans1']}), represented as those values of $\lambda$ for which $\cot(\pi \lambda R)$ intersects $\lambda R/ [\pi (mR)^2]$. We have taken the fixed value $mR=0.4$ for this plot. The behavior of the eigenvalues as functions of $mR$ can be determined graphically by changing the slope of the intersecting diagonal line. (b) The lightest eigenvalue (neutrino mass) $\lambda_+$ as a function of $mR$. For $mR\ll 1$, we see that the curve is approximately linear, corresponding to $\lambda_+ \approx m$. However, as $mR$ increases, the neutrino mass increases non-linearly, ultimately reaching an asymptote at $\lambda_+ R =1/2$ at which point the volume factor becomes irrelevant.
• Figure 4: Higher-dimensional neutrino oscillations in the orbifold scenario discussed in Sect. 2.4. (a) The evolution of the probability sum in (\ref{['deficit2']}) as more and more Kaluza-Klein states are included in the sum. We have taken $mR=0.4$. The flat line shows the contribution when only the degenerate zero-mode $\lambda_\pm$ eigenvalues are included (no oscillations); the cosine shows the probability when the first excited Kaluza-Klein states are also included; and the irregular curve shows the interference that results when the second excited Kaluza-Klein states are also included. Note that the initial probability $P(t=0)$ approaches $1$ as the full spectrum of Kaluza-Klein states is included. (b) The final result: the total probability that the gauge neutrino $\nu_L$ is preserved as a function of time when all Kaluza-Klein states are included. The multi-component nature of the neutrino oscillation is reflected in the jagged shape of the oscillations, as well as in the fact that the resulting neutrino deficits and regenerations, though sizable, are never total.
• Figure 5: Eigenvalue solutions to (\ref{['trans2']}), represented as those values of $\lambda$ for which $-\tan(\pi \lambda R)$ intersects $\lambda R/ [\pi (mR)^2]$. We have taken the fixed value $mR=0.4$ for this plot. The behavior of the eigenvalues as functions of $mR$ can be determined graphically by changing the slope of the intersecting diagonal line. Regardless of the value of $mR$, we see that the zero eigenvalue is fixed and unique.