  The bispectrum of primordial curvature perturbations in the squeezed
configuration, in which one wavenumber, $k_3$, is much smaller than the other
two, $k_3\ll k_1\approx k_2$, plays a special role in constraining the physics
of inflation. In this paper we study a new phenomenological signature in the
squeezed-limit bispectrum: namely, the amplitude of the squeezed-limit
bispectrum depends on an angle between ${\bf k}_1$ and ${\bf k}_3$ such that
$B_\zeta(k_1, k_2, k_3) \to 2 \sum_L c_L P_L(\hat{\bf k}_1 \cdot \hat{\bf k}_3)
P_\zeta(k_1)P_\zeta(k_3)$, where $P_L$ are the Legendre polynomials. While
$c_0$ is related to the usual local-form $f_{\rm NL}$ parameter as $c_0=6f_{\rm
NL}/5$, the higher-multipole coefficients, $c_1$, $c_2$, etc., have not been
constrained by the data. Primordial curvature perturbations sourced by
large-scale magnetic fields generate non-vanishing $c_0$, $c_1$, and $c_2$.
Inflation models whose action contains a term like $I(\phi)^2 F^2$ generate
$c_2=c_0/2$. A recently proposed "solid inflation" model generates $c_2\gg
c_0$. A cosmic-variance-limited experiment measuring temperature anisotropy of
the cosmic microwave background up to $\ell_{\rm max}=2000$ is able to measure
these coefficients down to $\delta c_0=4.4$, $\delta c_1=61$, and $\delta
c_2=13$ (68% CL). We also find that $c_0$ and $c_1$, and $c_0$ and $c_2$, are
nearly uncorrelated. Measurements of these coefficients will open up a new
window into the physics of inflation such as the existence of vector fields
during inflation or non-trivial symmetry structure of inflaton fields. Finally,
we show that the original form of the Suyama-Yamaguchi inequality does not
apply to the case involving higher-spin fields, but a generalized form does.
