To decay or not to decay

Vasudevan Mukunth

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Belle experiment A typical B- → τ-ν candidate event at the Belle experiment. This candidate decays to an electron and missing energy/momentum.

Why do physicists study decay processes? Because they give us the pieces of a puzzle we can't fully reconstruct.

In particle physics, every particle dreams of losing weight and turning into a bunch of lighter particles. There are no exceptions. This process is called decaying.

Even the Higgs boson, that elusive goddamned residual particle of the Higgs field, decays into W bosons, Z bosons, leptons, and photons. In fact, each Z boson then decays to two leptons.

These processes are important because they allow physicists to reconstruct objects that exist for too short a period for them to be captured and studied. Instead, physicists study what the results of the decay process are and then piece together what must have come before.

Going by observations: The heavier the particle, the stronger the desire to decay into lighter particles. This is evinced by the particle’s lifetime.

The most massive elementary particle is the top quark, one of six kinds, or flavours, of quarks. It weighs a whopping 172.9 ± 1.5 GeV/c², which is almost as heavy as an atom of tungsten! Its lifetime, however, is a pitiful five trillion-trillionths of one second. (Here, GeV/c² is a unit of mass: Einstein's famous equation states mass and energy are related as E = mc², 'c' being the speed of light. So, m = E/c².)

One of the least massive elementary particles, on the other hand, is the electron. It weighs a decent 0.511 MeV/c², is perfectly stable, and never decays.

Decay to what and when

Because of their propensity for decaying, heavier particles will not only decay faster but also in more combinations of lighter particles. This is because the heavier you are, the more options there are of particles lighter than you to choose from. Of course, there are limits to how often one combination of particles is chosen to decay through over another.

Moreover, heavier particles seldom come together to make up even heavier particles. The top quark, for example, doesn’t even last long enough to pair up with other quarks to form hadrons like protons and neutrons.

However, in the off-chance that two heavy particles have come together, the composite particle is going to have a far shorter lifetime than either of the constituents, and is going to decay through literally an abundance of combinations. One example of such a particle that’s been in the news is the B_c meson, first discovered by the Tevatron in 1995.

Mesons are particles that contain one quark and one antiquark. Unfortunately, the B_c meson contains two of the heaviest flavours of quarks (after the top quark) known – bottom and charm – and so its lifetime is abysmal…

But not abysmal enough for the Large Hadron Collider (LHC).

The B_c meson decays

The LHCb detector on the LHC is specialised to study the bottom quark, which weighs around 4.2 GeV/c². The other particle in the B_c meson, the charm antiquark, weighs 1.3 GeV/c².

Note that these masses are approximates; a strange quantum mechanical principle called colour confinement has kept us from accurately measuring their masses.

Anyway, the B_c meson has access to a whopping 66 decay modes (PDF). However, only a few have been observed experimentally, such as the following:

1. B_c^± → J/ψ (meson) + l^± (lepton) + ν (neutrino) (link)

2. B_c^± → J/ψ + π^± (pion) (link)

3. B_c^± → J/ψ + K^± (kaon)

The B_c’s decay to a J/ψ (pronounced “jay psi”) meson is favoured by experimental physicists because this particle consequently decays into two µ-mesons, i.e. muons, which are easy to detect and measure.

And via a paper submitted to the arXiv pre-print server on March 7, 2013, the LHCb collaboration announced another decay mode that it had spotted: B_c⁺ → ψ(2S) + π⁺. Here, ψ(2S), also known as ψ(3686), is an excited state of the J/ψ meson.

The paper also revealed that a B_c’s decay to an excited J/ψ meson instead of a “normal” J/ψ meson happened fully one-fourth of the time. It also noted the emergence of another decay mode: B_c⁺ → J/ψ + π⁺ + π⁺ + π^-.

LHCb data showing spikes for two decay processes of the B_c meson. The height of each spike denotes the strength of the signal while its narrowness brackets off the B_c meson's mass-range.

The mechanism of these decays is through what’s called the weak interaction because it transpires through the exchange of W^± and Z bosons. What happens is one quark decays while the other remains spectator.

Why are these measurements important? As I stated earlier, the colour confinement principle, which prevents quarks from being spotted in isolation, keeps physicists from measuring their masses accurately. By extension, the B_c meson’s mass also eludes capture.

But when they decay, physicists can zero in on those elusive masses by noting how the decay process progresses. They use their knowledge of the properties of lighter particles to piece together the properties of the heavier particles.

For example, the decay mode B_c^± → J/ψ + l^± + ν was used in 1998 by scientists at Fermilab to determine the B_c⁺ meson’s mass to be 6.40 ± 0.39 (stat. error) ± 0.13 (sys. error) GeV/c² and its lifetime to be around 0.46 picoseconds (i.e., 0.46 of one trillionth of one second).

These are important numbers because 1) they validate some hypotheses and invalidate some others, 2) they indicate by how much our calculations were off, and 3) they let us give values to things and find a way to accommodate them in our formulae.

In fact, this is what most of experimental physics has to give theoretical particle physics, and side by side, keep our curiosity well-equipped to keep moving.

The world is not enough.

Vasudevan Mukunth

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Are we to accelerate through space-time? Image: markhenspeter

If a Soviet astronomer named Nikolai Kardashev and an American physicist named Michio Kaku are correct, then interstellar travel, 400 yottawatts of energy, and a terrible space-crunch lie in humanity's next millennium.

I just came across an interesting concept called the Kardashev scale. Using a simple formula, it defines how advanced a civilization is based on its energy consumption on a scale of three possible values. These values are demarcated as Types I, II and III.

Conceived by Soviet astronomer Nikolai Kardashev in 1964, and given a formula by Carl Sagan in 1973, the scale places the human civilization as in 2008 at 0.717, and about 100-200 years away from attaining Type I status according to an extrapolation by physicist Michio Kaku.

According to Kardashev, and later, Guillermo Lemarchand, a Type I civilization consumes between 10E16 and 10E17 watts, a Type II, about 4E26 watts, and a Type III, about 4E37 watts. Ergo, successive stages involve a hike in 10 orders of magnitude and then 11 orders of magnitude, respectively.

These are exponentially massive jumps, as Kaku's estimation of few thousand years and a million years as the consecutive attainment periods evince.

What's really interesting about these definitions is that, on Earth, humans are hardly the civilization to keep an eye out for. In 2008, humans consumed about 15 terawatts while photosynthesis, the primary biotic source of energy on the planet, produced about 1,800 terawatts of energy, with single-celled microalgae being the most efficient among the producers.

That places nature at 0.9 on the Kardashev scale.

Not that this comes as any kind of a surprise, but we are underdeveloped in our own environment. Forget extra-terrestrial intelligentsia: Diseases should be the stuff of Asimov-esque or Clarke-esque science fiction! That we imagine we are ready to confront alien military technology and so scream high-energy radio signals into space in the hope of pinging another civilization is laughable.

Another interesting aspect comes to light if we addressed the human biosphere as one system - conserving energy and momentum all the time and everywhere - then a Type 0.717 civilization like ours must consume and expel 15 terawatts. All that power cannot accumulate and then disappear from our ergonomic accounts. All units must have a contraentry. So, as a formula:

Consumed energy = Expelled energy

There are different ways of expelling this energy. As a simple example, consider the running of a car: every second, some amount of petrol and electrical energy from the battery goes into keep the car moving at some speed. This energy is lost in transmission, combustion, air-conditioning, overcoming friction, etc.

Similarly, at the moment, a planet of 7 billion humans consumes and expels 15 terawatts.

Consider if we were a Type III civilization, however. We'd have to consume and expel about 4E37 watts, which is about the entire luminosity of the Milky Way galaxy (100-400 billion stars). This means that, if each human body consumed and expelled about 100 watts, i.e. the basal metabolic rate, then Earth would have to harbor... 400 million trillion quadrillion humans.

Obviously, the world is not enough.

One would imagine that as we progressed, we'd consume and expel energy at higher efficiencies. As a result, fewer machines would be needed to convert energy into useful energy. So, with the same quantity of resources, we'd be able to produce more machines as time passes. Consequently, the rate at which we consume energy will grow exponentially, i.e. accelerate.

In fact, even as a Type II civilization, we'd need space for more than a quadrillion humans. Thus, somewhere between the Type I and Type II statuses, we'd have to figure out interstellar travel or simply go the Douglas Adams way and ship off all our telephone sanitizers into a random direction in space.

Footnote: If you're able to track down a reliable ballpark of how much of the Earth's surface area is occupied by humans, then you'll be able to calculate the Kardashev-scale's counterpart in occupation-space scaling.

Earth Was Blasted With A Gamma Ray Burst During The Eighth Century

January 21, 2013

Image Caption: An artist's impression of the merger of two neutron stars. Short duration gamma-ray bursts are thought to be caused by the merger of some combination of white dwarfs, neutron stars or black holes. Theory suggests that they are short lived as there is little dust and gas to fuel an 'afterglow'. Credit: NASA/Dana Berry

Lee Rannals for redOrbit.com – Your Universe Online
According to a new study, black hole cosmic radiation blasted into the Earth back in the 8th century.
Japanese astrophysicist Fusa Miyake discovered last year clues for the strange event located in the rings of ancient cedar trees that dated back to either 774 or 775 AD.
Researchers teamed together to determine what had caused the surge in carbon-14 in the rings and found no evidence of a supernova, as they had expected.
The Anglo-Saxon Chronicle references the appearance of a “red crucifix” seen in the skies after sunset, but that took place in 776 AD, which was too late for when the tree rings show the event took place.
Scientists were also able to rule out a CME burst from the Sun, during which solar flares shoot out cosmic rays, sometimes towards Earth.
They wrote in the Monthly Notices of the Royal Astronomical Society, instead, black holes may be the culprit behind the carbon-14 isotope surge in the rings. These isotopes are created when intense radiation hits the atoms in the upper atmosphere, which suggests a blast of energy had once hit Earth.
German-based scientists Valeri Hambaryan and Ralph Neuhauser say two black holes collided and then merged, releasing an intense, but extremely brief, burst of gamma rays during the time period. The same kind of bursts could have also taken place if two neutron stars, or white dwarf stars, collided.
“Gamma-ray bursts are very, very explosive and energetic events, and so we considered from the energy what would be the distance given the energy observed,” Neuhauser wrote in the journal.
They said the event could only have taken place at least 3,000 light years away from here, otherwise the planet would have been fried.
Also, if their theory is right, then it would help explain why there is no record of some brilliant event taking place in the sky, or evidence of any extinction event in Earth’s biodiversity during the time.
The authors suggest astronomers should look up to the sky for any evidence that may still exist today from the astronomical event in 774 or 775 AD.
Neuhauser said if a gamma-ray burst had been much closer to earth, then it would have caused significant harm to the biosphere.
“But even thousands of light years away, a similar event today could cause havoc with the sensitive electronic systems that advanced societies have come to depend on,” he wrote in the journal. “The challenge now is to establish how rare such carbon-14 spikes are, i.e. how often such radiation bursts hit the Earth.”
He said in the last 3,000 years, the maximum age of trees alive today, only one of these events has taken place. He added it was unlikely Earth would be seeing another one of these cosmic events soon.