Collider Physics

Prerequisites: Particle Physics. Full path (33 pages)

Best explanations

Concrete Collider Physics for Theory Students

Intuitive
Concrete
Abstract
Why is it interesting?

Intuitive

A collider accelerates two beams of particles to high energy and makes them hit each other head on. Physicists then study what comes out of the collision. The reason to do this is that the smaller the structure we want to see, the shorter the wavelength of the probe has to be, and in quantum mechanics a short wavelength means a large momentum. High energy also lets the collision create heavy particles that do not exist in ordinary matter, because energy can turn into mass. The W and Z bosons, the top quark and the Higgs boson were all found this way.

Colliding two beams head on wastes much less energy than shooting one beam at a fixed target. When a fast particle hits a target at rest, most of the energy goes into moving the debris forward. When two equal beams meet head on, the total momentum is zero and all of the energy is available to make new particles.

The collision itself is invisible. What the experiment records is the debris: tracks of charged particles bending in a magnetic field, showers of energy in calorimeters, muons that pass through everything else. Most collisions are uninteresting, so the detector has to decide in real time which events to keep. Collider physics is the craft of connecting these recorded signals back to the short-distance process that produced them, and of telling a rare signal from a huge background of ordinary events.

Recommended Books:

Anomaly! Collider Physics and the Quest for New Phenomena by Dorigo

Concrete

The basic numbers of a collider are its energy and its luminosity.

Energy. For two incoming particles with four-momenta $p_1$ and $p_2$ , the invariant that controls what can be produced is the Mandelstam variable $s = (p_1 + p_2)^2 ,$ with $c = 1$ and metric signature $(+,-,-,-)$ , so that $s > 0$ . For two beams of energy $E$ colliding head on, with masses negligible, $s = 4E^2$ and the center-of-mass energy is $\sqrt{s} = 2E$ . For a beam of energy $E$ on a fixed target of mass $m$ , $s = m_1^2 + m^2 + 2Em \approx 2Em$ when $E \gg m, m_1$ , so $\sqrt{s}$ grows only like $\sqrt{E}$ . This is why modern high-energy machines are colliders.

Luminosity and cross section. The rate of events of a given type is $\frac{dN}{dt} = \mathcal{L}\, \sigma ,$ where $\sigma$ is the cross section of the process (an area, measured in barn, $1\,\text{b} = 10^{-24}\,\text{cm}^2$ ) and $\mathcal{L}$ is the instantaneous luminosity (units $\text{cm}^{-2}\text{s}^{-1}$ ), which depends only on the beams: number of particles per bunch, bunch crossing frequency and beam size. The expected number of events in a data set is $N = \sigma \int \mathcal{L}\, dt$ . The integrated luminosity $\int \mathcal{L}\,dt$ is quoted in inverse femtobarn: a process with $\sigma = 1\,\text{fb}$ gives on average one event per $\text{fb}^{-1}$ .

Hadron colliders and parton distributions. In a proton-proton collider the hard collision happens between partons (quarks and gluons) that carry fractions $x_1, x_2$ of the proton momenta. The partonic center-of-mass energy squared is $\hat s = x_1 x_2 s$ . The cross section is computed with the factorization formula $\sigma = \sum_{i,j} \int_0^1 dx_1 \int_0^1 dx_2 \; f_i(x_1, \mu_F)\, f_j(x_2, \mu_F)\; \hat\sigma_{ij}(\hat s, \mu_F, \mu_R) ,$ where $f_i(x,\mu_F)$ are the parton distribution functions, measured in experiments and evolved in the factorization scale $\mu_F$ with the DGLAP equations, and $\hat\sigma_{ij}$ is the partonic cross section computed in perturbation theory at renormalization scale $\mu_R$ . Because $x_1 \neq x_2$ in general, the partonic system moves along the beam axis with an unknown longitudinal boost.

Kinematic variables. This unknown boost is the reason collider analyses use variables that behave simply under boosts along the beam axis $z$ : - the transverse momentum $p_T = \sqrt{p_x^2 + p_y^2}$ , which is invariant under such boosts; - the rapidity $y = \frac{1}{2}\ln\frac{E + p_z}{E - p_z}$ , which shifts by a constant under a $z$ boost, so that rapidity differences $\Delta y$ are invariant; - the pseudorapidity $\eta = -\ln\tan(\theta/2)$ , with $\theta$ the polar angle to the beam, which equals $y$ for massless particles and only needs the angle; - the azimuthal angle $\phi$ , and the distance $\Delta R = \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2}$ used to define cones and jets.

Since the initial transverse momentum is close to zero, the vector sum of all transverse momenta in the final state should vanish. An imbalance, the missing transverse momentum, signals particles that escape detection, such as neutrinos or hypothetical new neutral particles.

Jets. Quarks and gluons are not observed directly. They radiate and hadronize into collimated sprays of hadrons called jets. Jet algorithms (for example the anti- $k_t$ algorithm) group the measured particles into jets in a way that is insensitive to soft and collinear emissions, so that jet cross sections can be computed in perturbative QCD.

Collider Physics for Theory Students by Flip Tanedo
CRASH COURSE IN THE LHC by Nima Arkani-Hamed

Abstract

http://www.slac.stanford.edu/econf/C010630/papers/MT1001.PDF

Is Mr. Lindley right? He concludes: "We are already at the point where experiments are becoming impossible for technological reasons and unthinkable for social and political reasons. An accelerator bigger than the supercollider would be a vast technical challenge. . . . Experiments to test fundamental physics are at the point of impossibility." Physicists, he says, seem to be returning to the days of the ancient Greeks, who did physics "by means of thought alone." Maybe he doesn't know about the Livingston curve. Mr. Lindley, I'm sure, would hate the Livingston curve. It's one of those mathematical curiosities that are probably meaningless. In the 1950's, a physicist named Stanley Livingston drew a line on a graph that plotted the energy available in laboratories from the time of J. J. Thomson (circa 1897) to his own era, then extended it into the future. He found a logarithmic relationship: the energy increased by roughly a factor of 10 every 10 years. The Livingston curve has accurately predicted accelerator energies in the 1960's, 70's, 80's and 90's. Extrapolated to the future, it predicts that we'll have what is called Planck-scale energy in the lab by the year 2150. A Planck-scale accelerator would be powerful enough to prove one of the most popular unified theories, superstring theory.

http://www.nytimes.com/1993/09/05/books/perhaps-this-universe-is-only-a-test.html?pagewanted=all

Why is it interesting?

A particle collider is essentially a large microscope. It doesn’t use light, it uses fast particles, and it doesn’t probe a target plate, it probes other particles, but the idea is the same: It lets us look at matter very closely. A larger collider would let us look closer than we have so far, and that’s the most obvious way to learn more about the structure of matter.https://backreaction.blogspot.de/2018/03/the-multiworse-is-coming.html

Richard P. Feynman once said that doing elementary particle physics is a lot like banging two fine Swiss watches against each other and trying to figure out their workings by examining the debris. That was the challenge.

From My Life As A Quant by Emanuel Derman

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Leads to: LHC.