The Higgs boson couples to particles that constitute matter around us, such as electrons, protons, and neutrons. Its virtual quanta are constantly being exchanged between these particles. In other words, it gives rise to a force - the Higgs force. I'm surprised why this PR-cool aspect is not explored in our outreach efforts. Higgs bosons mediate the Higgs force in the same fashion as gravitons, gluons, photons, W and Z bosons mediate the gravity, strong, electromagnetic, and weak forces. Just like gravity, the Higgs force is always attractive and its strength is proportional, in the first approximation, to particle's mass. It is a force in a common sense; for example, if we bombarded long enough a detector with a beam of particles interacting only via the Higgs force, they would eventually knock off atoms in the detector.
There is of course a reason why the Higgs force is less discussed: it has never been detected directly. Indeed, in the absence of midi-chlorians it is extremely weak. First, it shares the feature of the weak interactions of being short-ranged: since the mediator is massive, the interaction strength is exponentially suppressed at distances larger than an attometer (10^-18 m), about 0.1% of the diameter of a proton. Moreover, for ordinary matter, the weak force is more important because of the tiny Higgs couplings to light quarks and electrons. For example, for the proton the Higgs force is thousand times weaker than the weak force, and for the electron it is hundred thousand times weaker. Finally, there are no known particles interacting only via the Higgs force and gravity (though dark matter in some hypothetical models has this property), so in practice the Higgs force is always a tiny correction to more powerful forces that shape the structure of atoms and nuclei. This is again in contrast to the weak force, which is particularly relevant for neutrinos who are immune to strong and electromagnetic forces.
Nevertheless, this new paper argues that the situation is not hopeless, and that the current experimental sensitivity is good enough to start probing the Higgs force. The authors propose to do it by means of atom spectroscopy. Frequency measurements of atomic transitions have reached the stunning accuracy of order 10^-18. The Higgs force creates a Yukawa type potential between the nucleus and orbiting electrons, which leads to a shift of the atomic levels. The effect is tiny, in particular it is always smaller than the analogous shift due to the weak force. This is a serious problem, because calculations of the leading effects may not be accurate enough to extract the subleading Higgs contribution. Fortunately, there may be tricks to reduce the uncertainties. One is to measure how the isotope shift of transition frequencies for several isotope pairs. The theory says that the leading atomic interactions should give rise to a universal linear relation (the so-called King's relation) between isotope shifts for different transitions. The Higgs and weak interactions should lead to a violation of King's relation. Given many uncertainties plaguing calculations of atomic levels, it may still be difficult to ever claim a detection of the Higgs force. More realistically, one can try to set limits on the Higgs couplings to light fermions which will be better than the current collider limits.
Atomic spectroscopy is way above my head, so I cannot judge if the proposal is realistic. There are a few practical issues to resolve before the Higgs force is mastered into a lightsaber. However, it is possible that a new front to study the Higgs boson will be opened in the near future. These studies will provide information about the Higgs couplings to light Standard Model fermions, which is complementary to the information obtained from collider searches.