Warped Passages - Lisa Randall [105]
Weak gauge bosons interact with this weak charge of the vacuum, just as they do with all weak charge. And the charge that pervades the vacuum blocks the weak gauge bosons as they try to communicate forces over long distances. The further they try to travel, the more “paint” they encounter. (Because the charge actually spreads throughout three dimensions, you might prefer to imagine a fog of paint.)
The Higgs field plays a role very similar to that of the traffic cop in the story, restricting the weak force’s influence to very short distances. When attempting to communicate the weak force to distant particles, the force-carrying weak gauge bosons bump into the Higgs field, which gets in their way and cuts them off. Like Ike, who could travel freely only within a half-mile radius of his starting point, weak gauge bosons move unimpeded only for a very short distance, about one ten thousand trillionth of a centimeter. Both weak gauge bosons and Ike are free to travel short distances, but are intercepted at longer distances.
The weak charge in the vacuum is spread out so thinly that at short distance there is very little sign of the nonzero Higgs field and the associated charge. Quarks, leptons, and the weak gauge bosons travel freely over short distances, almost as if the charge in the vacuum didn’t exist. The weak gauge bosons can therefore communicate forces over short distances, almost as if the two Higgs fields were both zero.
However, at longer distances, particles travel further and therefore encounter a more significant amount of weak charge. How much they encounter depends on the charge density, which depends in turn on the value of the nonzero Higgs field. Long-distance travel (and communication of the weak force) is not an option for low-energy weak gauge bosons, for on long-distance excursions the weak charge in the vacuum gets in the way.
This is exactly what we needed to make sense of weak gauge bosons. Quantum field theory says that particles that travel freely over short distances, but only extremely rarely travel over longer distances, have nonzero masses. The weak gauge bosons’ interrupted travel tells us that they act as if they have mass, since massive gauge bosons just don’t get very far. The weak charge that permeates space hinders the weak gauge bosons’ travel, making them behave exactly as they should in order to agree with experiments.
The weak charges in the vacuum have a density that corresponds roughly to charges that are separated by one ten thousand trillionth of a centimeter. With this weak charge density, the masses of the weak gauge bosons—the charged Ws and the neutral Z—take their measured values of approximately 100 GeV.
And that’s not all that the Higgs mechanism accomplishes. It is also responsible for the masses of quarks and leptons, the elementary particles constituting the matter of the Standard Model. Quarks and leptons acquire mass in a very similar fashion to the weak gauge bosons. Quarks and leptons interact with the Higgs field distributed throughout space and are therefore also hindered by the universe’s weak charge. Like weak gauge bosons, quarks and leptons acquire mass by bouncing off the Higgs charge distributed everywhere throughout spacetime. Without the Higgs field, these particles would also have zero mass. But once again, the nonzero Higgs field and the vacuum’s weak charge interfere with motion and make the particles have mass. The Higgs mechanism is also necessary for quarks and leptons to acquire their masses.
Although the Higgs mechanism is a more elaborate origin of mass than you might think necessary, it is the only sensible way for the weak gauge bosons to acquire mass according to quantum field theory. The beauty of the Higgs mechanism is that it gives the weak gauge bosons mass while accomplishing precisely the task I laid out at the beginning of this chapter. The Higgs mechanism makes it look as though the weak force symmetry is preserved at short distances (which, according to quantum mechanics and special