Calculation #1: The Top Quark's Lifetime

Sheldon's whiteboard features a straightforward Feynman diagram illustrating a calculation related to the lifetime of the top quark, often referred to as the 'truth' quark. He was working on the decay process ( t rightarrow W + b ).

In scientific circles, we typically refer to this particle as the top quark, a name favored by more traditional academics, though I still hold fondness for the original names like strange and charm quarks. The lifetime of a particle inversely correlates with the number of decay channels available. Sheldon specifically calculated the branching ratio, which determines the likelihood of the top quark decaying into a W boson and a bottom quark compared to all possible decay pathways.

Interestingly, the depiction of the W boson with a dashed line is inaccurate; as a spin-1 boson, it should be represented with a squiggly line, while dashed lines are designated for spin-0 particles like the Higgs boson.

The calculations yield a result that approaches nearly 100%, serving as a baseline. If Sheldon were computing the 'width' due solely to the b-channel decay, the calculated lifetime would be approximately ( 5 times 10^{-25} ) seconds, aligning closely with experimental findings. The top quark is incredibly elusive, existing for less than a quadrillionth of a second due to its substantial mass and strong coupling to the b quark.

Quick Aside: Understanding Quarks

Quarks are not fundamental particles but rather intriguing entities with fractional charges. They reside within hadrons and cannot exist freely due to the strong nuclear force, which intensifies with distance.

A baryon, such as a proton, consists of three quarks, while a meson, like a pion, contains two. We can infer their presence through deep inelastic scattering experiments, though direct observation remains elusive. There are six known quarks categorized in pairs: down/up, strange/charm, and bottom/top.

Calculation #2: Exploring Rare Decays

The second set of calculations depicted on the whiteboard is more engaging. Sheldon explores processes that contribute minimally to the top quark's lifetime but represent intriguing ultra-rare decays. These occur at the loop level, involving virtual particles that emerge and annihilate before the decay happens.

This leads to flavor-changing neutral currents (FCNCs), where a charged particle transitions to another charged particle without a change in overall charge, contrasting with the first calculation. The rarity of these decays can provide insights into potential new physics beyond the Standard Model.

FCNCs do not occur at tree level in the Standard Model; they only manifest through loop processes, as the necessary interactions cannot occur otherwise. If experimental data shows a higher rate of such decays than predicted, it could imply the existence of new theoretical particles, possibly in the TeV mass range.

These anomalies could lead to breakthroughs in our understanding of particle physics. I engaged in similar calculations during my doctoral studies, proposing various experiments related to CP violation and meson mixing.

Next Steps for Sheldon

Looking ahead, it seems Sheldon may intend to evaluate hypothetical contributions from non-Standard Model physics related to these rare decay modes. If you have any questions about the content or seek further clarification, feel free to ask!

The first video titled "Leslie Fixes Sheldon's Equation | The Big Bang Theory" humorously illustrates the complexities of Sheldon's calculations, shedding light on the intricacies of particle physics.

The second video, "TBBT S02E02. Loop Quantum Gravity Vs String Theory," further delves into the debates surrounding different theoretical frameworks in physics, complementing our discussion on Sheldon's work.