## Prospects for the International Linear Collider

Title: “Physics Case for the International Linear Collider”
Author: Linear Collider Collaboration (LCC) Physics Working Group
Published: arXiV hep-ex 1506:05992

For several years, rumors have been flying around the particle physics community about an entirely new accelerator facility, one that can take over for the LHC during its more extensive upgrades and can give physicists a different window into the complex world of the Standard Model and beyond. Through a few setbacks and moments of indecision, the project seems to have more momentum now than ever, so let’s go ahead and talk about the International Linear Collider: what it is, why we want it, and whether or not it will ever actually get off the ground.

The ILC is a proposed linear accelerator that will collide electrons and positrons, in comparison to the circular Large Hadron Collider ring that collides protons. So why make these design differences? Hasn’t the LHC done a lot for us? In two words: precision measurements!

Of course, the LHC got us the Higgs, and that’s great. But there are certain processes that physicists really want to look at now that occupy much higher fractions of the electron-positron cross section. In addition, the messiness associated with strong interactions is entirely gone with a lepton collider, leaving only a very well-defined initial state and easily calculable backgrounds. Let’s look specifically at what particular physical processes are motivating this design.

1. The Higgs. Everything always comes back to the Higgs, doesn’t it? We know that it’s out there, but beyond that, there are still many questions left unanswered. Physicists still want to determine whether the Higgs is composite, or whether it perhaps fits into a supersymmetric model of some kind. Additionally, we’re still uncertain about the couplings of the Higgs, both to the massive fermions and to itself. Figure 1 shows the current best estimate of Higgs couplings, which we expect to be proportional to the fermion mass, in comparison to how the precision of these measurements should improve with the ILC.

2.The Top Quark. Another thing that we’ve already discovered, but still want to know more about its characteristics and behaviors. We know that the Higgs field takes on a symmetry breaking value in all of space, due to the observed split of the electromagnetic and weak forces. As it turns out, it is the coupling of the Higgs to the top that provides this value, making it a key player in the Standard Model game.

3.New Physics. And of course there’s always the discovery potential. Since electron and positron beams can be polarized, we would be able to measure backgrounds with a whole new level of precision, providing a better image of possible decay chains that include dark matter or other beyond the SM particles.

Let’s move on to the actual design prospects for the ILC. Figure 2 shows the most recent blueprint of what such an accelerator would look like.  The ILC would have 2 separate detectors, and would be able to accelerate electrons/positrons to an energy of 500 GeV, with an option to upgrade to 1 TeV at a later point. The entire tunnel would be 31km long with two damping rings shown at the center. When accelerating electrons to extremely high energies, a linear collider is needed to offset extremely relativistic effects. For example, the Large Electron-Positron Collider synchrotron at CERN accelerates electrons to 50 GeV, giving them a relativistic gamma factor of 98,000. Compare that to a proton of 50 GeV in the same ring, which has a gamma of 54. That high gamma means that an electron requires an insane amount of energy to offset its synchrotron radiation, making a linear collider a more reasonable and cost effective choice.

In any large (read: expensive) experiment such as this, a lot of politics are going to come into play. The current highest bidder for the accelerator seems to be Japan, with possible construction sites in the mountain ranges (see Figure 3). The Japanese government is pretty eager to contribute a lot of funding to the project, something that other contenders have been reluctant to do (but such funding promises can very easily go awry, as the poor SSC shows us.) The Reference Design Reports report the estimated cost to be $6.7 billion, though U.S. Department of Energy officials have placed the cost closer to$20 billion. But the benefits of such a collaboration are immense. The infrastructure of such an accelerator could lead to the creation of a “new CERN”, one that could have as far-reaching influence in the future as CERN has enjoyed in the past few decades. Bringing together about 1000 scientists from more than 20 countries, the ILC truly has the potential to do great things for future international scientific collaboration, making it one of the most exciting prospects on the horizon of particle physics.

1. The International Linear Collider site: all things ILC
2. ILC Reference Design Reports (RDR), for the very ambitious reader

## A New Solution to the Hierarchy Problem?

Hello particle Chompers,

Today I want to discuss a slightly more advanced topic which I will not be able to explain in much detail, but goes by the name of the gauge Hierarchy problem or just the the Hierarchy Problem‘. My main motivation is to simply make you curious enough that you will feel inspired to investigate it further for yourself since it is one of the outstanding problems in particle physics and one of the main motivations for the construction of the LHC. A second motivation is to bring to your attention a recent and exciting paper which proposes a potentially new solution to the hierarchy problem.

The hierarchy problem can roughly be stated as the problem of why the vacuum expectation value (VEV) of the Higgs boson, which determines the masses of the electroweak W and Z bosons, is so small compared to the highest energy scales thought to exist in the Universe. More specifically, the masses of the W and Z bosons (which define the weak scale) are roughly $\sim 10^{2}$ GeV (see Figure 1) in particle physics units (remember in these units mass = energy!).

On the other hand the highest energy scale thought to exist in the Universe is the planck scale at $\sim 10^{19}$ GeV which is associated with the physics of gravity. Quantum field theory tells us that the Higgs VEV should get contributions from all energy scales (see Figure 2) so the question is why is the Higgs VEV, and thus the W and Z boson masses, a factor of roughly $\sim 10^{17}$ smaller than it should be?

In the Standard Model (SM) there is no solution to this problem. Instead one must rely on a spectacularly miraculous numerical cancellation among the parameters of the SM Lagrangian. Miraculous numerical coincidences’ like this make us physicists feel uncomfortable to the point that we give it the special name of fine tuning’. The hierarchy problem is thus also known as the fine tuning problem.

A search for a solution to this problem has been at the forefront of particle physics for close to 40 years. It is the aversion to fine tuning which leads most physicist to believe there must be new physics beyond the SM whose dynamics are responsible for keeping the Higgs VEV small. Proposals include supersymmetrycomposite Higgs models, extra dimensions, as well as invoking the anthropic principle in the context of a multiverse. In many cases, these solutions require a variety of new particles at energies close to the weak scale ($\sim 100-1000$ GeV) and thus should be observable at the LHC. However the lack of evidence at the LHC for any physics beyond the SM is already bringing tension to many of these solutions. A solution which does not require new particles at the weak scale would thus be very attractive.

Recently a novel mechanism, which goes by the name of $\emph{cosmological relaxation of the electroweak scale}$, has been proposed which potentially offers such a solution. The details (which physicists are currently still digesting) are well beyond the scope of this blog. I will just mention that the mechanism incorporates two previously proposed mechanisms known as inflation$^1$ and the QCD axion$^2$ which solve other known problems. These are combined with the SM in a novel way such that the weak scale can arise naturally in our universe without any fine tuning and without new particles at the weak scale (or multiple universes)! And as a bonus, the axion in this mechanism (referred to as the relaxion’) makes a good dark matter candidate!

Whether or not this mechanism turns out to be a solution to the hierarchy problem will of course require experimental tests and further theoretical scrutiny, but its a fascinating idea which combines aspects of quantum field theory and general relativity so I hope it will serve as motivation for you to begin learning more about these subjects!

$\bf{Footnotes:}$

1. Inflation is a theorized period of exponential accelerated expansion of our Universe in the moments just after the big bang. It was proposed as a solution to the problems of why our Universe is so flat and (mostly) homogenous while also explaining the structure we see throughout the Universe and in the cosmic microwave background.

2. Axions are particles proposed to explain why the amount of CP violation in the QCD sector in the SM is so small, which is known as the `strong CP problem‘.