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A Universe without Weak Interactions

One of the biggest problems facing theoretical particle physics since the discovery of the Standard Model is the hierarchy problem. The Standard Model explains why the weak interactions are so weak relative to electromagnetism. But in the Standard Model, it is hard to understand why the weak interactions are so strong relative to gravity. An idea that has recently become popular among theorists is that the weak interactions must be so strong because, through their role in setting the masses of known particles and also in the formation of chemical elements and stellar burning, they are essential to life. Recently, Graham Kribs of the University of Oregon, Gilad Perez of SUNY, Stony Brook, and I put forward a significant challenge to this idea by constructing an imaginary universe, suitable for life, in which the weak interactions play no role.

The strength of the weak force is determined by the mass of the W boson, which in turn is given by the expectation value or condensate of the Higgs field. If this value is much larger than the proton mass, the weak interactions will be weak. But we would naturally expect that value to be even larger and the weak interactions would be weaker. Most of the particles in the Standard Model—quarks, leptons, and W and Z bosons—interact with the Higgs field to receive their masses. Through quantum effects, those interactions feed back on the Higgs condensate and can push it to extremely high values. If the Standard Model is valid all the way up to the Planck mass, the mass scale that determines the strength of gravity, the Higgs condensate would naturally be of a size comparable to the Planck mass. This would make the weak force so weak that it would play essentially no role in physics. The weak interaction could still have the strength we actually observe, but only if two numbers in the theory that affect the Higgs condensate are arranged to cancel accurately in the first 32 decimal places.

This is a serious conceptual problem for the Standard Model that has challenged theorists for the last 30 years. One way to solve the problem is to introduce new particles that can generate the Higgs condensate without this fine-tuning of parameters. Supersymmetry gives a popular way to do this, and there are many other possibilities, including models with other extended symmetries, new strong forces, large extra dimensions and warped extra dimensions. Today, the particle physics community is excited that one or another of these models might be proved correct by the discovery of new particles at the upcoming Large Hadron Collider.

A completely different approach to the problem invokes the "anthropic principle." In this approach, the solution is to show that, if the weak force were weaker, it would not be possible to evolve creatures that could observe it. About 10 years ago, Agrawal, Barr, Donoghue and Seckel pointed out that, if the Higgs condensate became larger, and the other Higgs interactions remained the same, the mass splitting between the neutron and the proton would grow. Quickly one would reach the point at which neutrons would decay to protons inside nuclei, making the nuclei unstable and destroying all elements heavier than hydrogen. Without chemistry, it would very hard to have observers.

To complete an anthropic argument, one more step is needed. It is not enough to find a hypothetical tragedy, such as the instability of atoms, at some particular value of a parameter of Nature. It is also necessary to show that all possibilities for this parameter are realized somewhere in the universe. That is, it is necessary to construct a "multiverse" in which different regions realize the Standard Model many different sets of parameters. Stanford's Andrei Linde introduced this way of thinking about the universe in the 1980's. Two new developments have recently given an impetus to the idea. First, theorists discovered huge families of solutions to string theory, containing up to 10500 vacuum states. (See a related SLAC Today article here.) These would be predicted to coexist at different places in the universe. Second, after astronomers measured the value of the cosmological constant from supernova data, theorists have not succeeded in providing a dynamical reason for the cosmological constant to be so small, yet nonzero. On the other hand, Weinberg and others have pointed out that the value of the cosmological constant plays an important role. If it were somewhat higher, it would prevent galaxies from forming, which is an unfortunate outcome for observers of our kind.

The specific argument of Agrawal and collaborators was based on the idea that, in different places in the multiverse, the Higgs condensate would vary in size while all other Higgs interactions remained fixed. However, the multiverse or landscape of string theory is far more diverse. It contains theories that do not resemble the Standard Model at all, and it contains models with very different systems of Higgs interactions. Kribs, Perez and I decided to explore a different direction, in which the Higgs condensate is allowed to be very large but the interactions of quarks and leptons with the Higgs field are correspondingly reduced. In this universe, electrons, protons, and neutrons have masses identical to those in our universe, but the weak interactions are turned off. We call this the "Weakless Universe."

The Weakless Universe is similar to ours in many ways. The laws of chemistry and strong-interaction nuclear physics are the same as in our universe. It may seem difficult to produce burning stars in this universe, since, for example, the first reaction in our Sun's nuclear burning cycle is a weak interaction process (p + p -> deuterium + electron + antineutrino). However, we have shown that, by small adjustment of the cosmological initial conditions, it is possible to arrange for a large amount of deuterium to be produced primordially in the early universe. Then stars can skip directly to reactions that burn deuterium into Helium. Though these stars are different from our Sun, simulations done by the University of Arizona's Adam Burrows show that they are capable of burning for billions of years. In a similar way, we have shown that other bottlenecks for which the weak interactions seem to be needed to create the chemical elements can be evaded by small adjustments of early cosmology. The Weakless Universe is thus a sharp challenge to the idea that the value of the Higgs condensate is set by the anthropic principle.

The Weakless Universe seems to provide a perfectly natural setting for the formation of planets, life, and even physicists. However, in my view, the life of these physicists will not be as exciting as ours. They will not have a Higgs condensate hierarchy problem to solve. Thus, they will not have the pleasure of finding out its solution as the LHC turns on!

óRoni Harnik, February 15, 2007