The masses of fundamental particles such as the Z and W bosons could have arisen from the twisted geometry of hidden dimensions, new theoretical work has shown.
The work highlighted a way to bypass the Higgs field as a source of particle masses, providing a new tool for understanding how the Higgs field itself might have arisen, as well as a possible means of addressing some of the lingering gaps in the Standard Model of particle physics.
“In our picture,” says theoretical physicist Richard Pinčák of the Slovak Academy of Sciences, “matter emerges from the resistance of the geometry itself, not from an external field.”
Related: The Higgs boson may not be the portal to new physics after all
The Higgs field was first proposed in the 1960s as a way to explain why fundamental particles have mass—a huge problem that has hampered efforts to build a consistent model of particle physics. Thanks in part to the Higgs field, physicists were able to build the standard model we rely on today.
Here’s how it works. Imagine that the Universe is filled with an invisible goo. Any particles moving through the Universe are also moving through this substance, and each particle interacts with it slightly differently.
Particles that interact strongly with the soft matter as if through mud behave as “heavy,” like W and Z bosons. Particles that barely interact are “light,” like electrons. Photons do not interact with it at all. This interaction is known as the Higgs mechanism and it explains very clearly the masses of the particles.
We know the Higgs field is real because its quantum ripple, the Higgs boson, was finally and with great confidence discovered at the Large Hadron Collider in 2012. However, that doesn’t mean the Higgs mechanism is the whole story.
We still don’t know, for example, why the Higgs field has the properties it does. Nor does the Higgs solution explain dark matter, or dark energy, or why the Higgs field even exists in the first place.
We’re missing some information somewhere—and Pinčák and his colleagues think some clues may lie in hidden geometry, according to their study of a seven-dimensional space called G.2 variety.
Varieties can describe the curvature of apparently flat spaces at different scales. (yuanyuan yan/Moment/Getty Images)
A manifold is a kind of mathematical space—a general term used for any “shape” that can have curves, folds, or twists. Physicists often use manifolds to describe the geometry of spacetime or the hidden extra dimensions proposed in theories such as string theory.
These spaces can have more directions than the familiar up-down, left-right, and back-and-forth of everyday life. Some manifolds require seven independent directions. A manifold with a specific seven-dimensional structure, arranged in a highly constrained fashion, is known as a G2 manifold.
The researchers developed a new equation called G2– Ricci flow which allowed them to model how a G2 multiple changes over time.
“As in organic systems, such as the twisting of DNA or the manipulation of amino acids, these extra-dimensional structures can have torsion, a kind of intrinsic twisting,” explains Pinčák.
“When we let them evolve over time, we find that they can settle into stable configurations called solitons. These solitons could provide a purely geometric explanation for phenomena like spontaneous symmetry breaking.”
A soliton is like a single, self-sustaining wave that can keep its shape forever. The researchers found that G2 the manifold relaxed into such a stable configuration—and that configuration had a twist, or torsion, that imprinted itself on the W and Z bosons, producing exactly the same mass-donating effect as the Higgs mechanism.
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The results also suggest that the accelerated expansion of the Universe may be related to the curvature imparted by the torsion type of a G.2 variety could give. And if this torsion behaves like a field, it should manifest particles, just as the Higgs field gives rise to the Higgs boson.
The researchers named this hypothetical particle Torstone and described how such a particle should behave.
If present, Torstone may be detectable in particle collider anomalies, strange glitches in the cosmic microwave background, and even gravitational wave glitches. Its existence is far from proven, but if the torsion field does exist, we now know where to start looking.
It’s pretty wild and heady stuff, but so was the Higgs field in its day—and it took almost 50 years to prove itself. Hopefully we won’t have to wait that long for answers about the possible G2 many, but so far, this approach promises a path to solutions to some burning questions.
“Nature often prefers simple solutions,” says Pinčák.
“Maybe the W and Z boson masses come not from the famous Higgs field, but directly from the geometry of seven-dimensional space.”
The research was published in Nuclear physics B.