World Science Scholars
2.2 Quantum Mixing
summary
Significant advances in technology have pushed particle physics forward over the last century.

• In order to arrive to this point experimentally, particle physicists have utilized particle accelerators to discover all sorts of phenomena.
• A particle accelerator uses electromagnetic fields to impart charged particles like protons and electrons with massive amounts of energy. Once contained in well-defined beams, these high-energy particles are spun along a circular path and collided, producing new elementary particles that can be seen by large detectors.
• In the last hundred years, we have gone from tabletop-sized accelerators to the Large Hadron Collider in Geneva, Switzerland. The next goal is to recreate the energies achievable at the LHC back on the tabletop-scale.
• Elementary particles do not naturally have mass, but they can acquire mass through dynamics. For gauge bosons, this is through the Higgs mechanism.
• Quarks and charged leptons also acquire mass from different interactions with the Higgs field. However, the mass generation for the diverse “flavors” of fermions is still a big mystery.

A particle like a quark or a lepton can be 'mixed.'

• When we talk about particles, we describe them as being in states that are interacting through a particular kind of symmetry and force.
• Additionally, we have what are called mass eigenstates, in other words, the physical realizations.
• In nature, quarks and leptons are allowed to have mixed quantum states—for instance a little bit of each of the “flavors” of a quark are included in one mass realization of the quark and thus it is not “pure” in that sense.
• How much they mix is important, because behind the mixing of the particles, one can explore big questions of the universe, namely why the universe is dominated by matter and not antimatter.

For over fifty years, the quark sector of the Standard Model has been studied.

• Understanding how quarks mix and measuring the mixing angles and the CP-violating phase angle are crucial to understanding our universe.
• CP stands for “charge” and “parity,” and CP-symmetry states that the laws of physics should be the same if a particle were to be interchanged with its antiparticle. Studying the violation of CP-symmetry can help physicists understand the matter-antimatter asymmetry in our universe.
• The Cabibbo-Kobayashi-Maskawa matrix (CKM matrix) describes the strength of quark mixing, and is important to understanding CP-violation.
$V_{ud}$ $V_{us}$ $V_{ub}$
$V_{cd}$ $V_{cs}$ $V_{cb}$
$V_{td}$ $V_{ts}$ $V_{tb}$
• The values of the CKM matrix have been calculated experimentally. Similarly, the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix describes the mismatch of quantum states of leptons.

Many questions about mass, mixing, and CP-violation still remain.

• What are the dynamical origins of fermion masses, mixings, and CP-violation?
• What are the energy scales associated with these dynamics?
• What are the symmetries and symmetry-breakings?
• How are quark and lepton flavors related?
• What other flavor sectors are accessible? (e.g. superpartners, dark matter)

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