Proton Pressure : How do Quarks Tackle Stress?

Proton Pressure : How do Quarks Tackle Stress?

Reading Time: 9 minutes

Proton pressure, theoretically estimated to be higher than even neutron stars, has been notoriously difficult to measure experimentally. Recently, however, particle physicists have used a nice trick to measure proton pressure. The Nerd Druid delves deeper.


Subnucleonic particles

Quarks

Particle physics is the study of extremely small particles. In the nineteenth century, atoms were thought to be indivisible and fundamental. Then, in 1897, J.J. Thompson discovered the electron. Following the Geiger-Marsden experiment in 1909, Ernest Rutherford in 1911 postulated the existence of the proton. The now-familiar subatomic trio was completed when James Chadwick discovered the neutron in 1932.

Image of a comparison of various physical properties of the three most familiar subatomic particles.
Comparison of various physical properties of the three most familiar subatomic particles.

In the three decades following 1932, the use of higher and higher energies in particle accelerators led to the discovery of a veritable particle zoo. In 1964, Murray Gell-Mann and George Zweig attempted to simplify matters. They proposed that protons, neutrons and all the other hadrons were not as fundamental as once thought. Instead, they suggested that smaller particles called quarks are the true fundamental particles that make up hadrons.

Image of Murray Gell-Mann (left) and George Zweig (right) were the first to propose the existence of quarks. 10 years after their proposal, the discovery of the charm quark in 1974 definitively proved Gell-Mann and Zweig to be correct. Gell-Mann received the Nobel Prize in physics in 1969.
Murray Gell-Mann (left) and George Zweig (right) were the first to propose the existence of quarks. 10 years after their proposal, the discovery of the charm quark in 1974 definitively proved Gell-Mann and Zweig to be correct. Gell-Mann received the Nobel Prize in physics in 1969.

The naming of quarks

Quarks are possibly one of the first particles named without reference to a Greek or Latin dictionary. Murray Gell-Mann, the man responsible for the name, had borrowed the word from the novel Finnegan’s Wake by James Joyce. At one point in the novel, a character, presumably drunk, exclaims

Three quarks for Muster Mark!

the words quarks and Muster possibly drunk modifications of quarts and Mister.

The Nerd Druid has once attempted to read Finnegan’s Wake. In his opinion, had Joyce not written Ulysses, Finnegan’s Wake would have been, without doubt, one of the most difficult books to read in the English language.

The discovery of the quarks

According to Gell-Mann and Zweig, there were three types or flavours of quarks. These were the up, down and the strange quarks. In 1970, Glashow, Iliopoulus and Maiani (GIM) proposed that a fourth flavour, the charm quark, should also exist. Three years later, Kobayashi and Maskawa’s proposal of top and bottom quarks increased the number of quark flavours to six.

Despite such stunning theoretical success, particle physicists were initially unwilling to accept the quark model. Richard Feynman proposed an alternative and called them partons. However, increasingly complex and beautiful experiments in the decade since Gell-Mann and Zweig seemed to weigh evidence in favour of quarks. Deep inelastic scattering experiments at the Stanford Linear Accelerator Centre (SLAC) found particles that would later be identified with the up and the down quark. The SLAC experiment also indirectly suggested that strange quarks should exist.

The November Revolution

The final breakthrough came in the November of 1974. Unlike its more illustrious and political Russian cousin, the particle physics November Revolution took place at SLAC and at Brookhaven National Laboratory, both in the USA. The two teams almost simultaneously discovered the charm quark and its antiparticle, bound together to form a meson. Burton Richter, who led the SLAC team, named it the ψ (psi) meson. Samuel Ting, who led the Brookhaven team, preferred to call it the J meson. Due to the joint announcement of their discovery, the J/ψ meson is the only particle with a two letter name.

Images of Samuel Ting (left) and Burton Richter (right), discoverers of the J/psi meson. They received the 1976 Nobel Prize in Physics for their work.
Samuel Ting (left) and Burton Richter (right), discoverers of the J/ψ meson. They received the 1976 Nobel Prize in Physics for their work.

The J/ψ discovery validated the quark model and led to rapid changes in high-energy particle physics. One of the major innovations to come out of this incredible time is what is known as the Standard Model of particle physics. To put it in a nutshell, the Standard Model puts the entire workings of the universe–sans gravity–in a nutshell. Thus, the name November Revolution.

The Standard Model

The standard model did to high-energy particle physics what Dmitry Mendeleev’s periodic table had done for chemistry almost exactly a hundred years earlier. It cut through all the noise and gave a beautiful tabular representation of all the fundamental particles that interact among each other via the four fundamental forces 1.

Image of a schematic depiction of the Standard Model of elementary particles. Shown are the six quark flavours, the three leptons and their corresponding neutrinos, the four force-carrying vector gauge bosons, and the solitary mass-carrying scalar gauge boson, the Higgs.
A schematic depiction of the Standard Model of elementary particles. Shown are the six quark flavours, the three leptons and their corresponding neutrinos, the four force-carrying vector gauge bosons, and the solitary mass-carrying scalar gauge boson, the Higgs. (Image Credit : Wikipedia).

The Fermions

In the image above, the six purple boxes represent the six flavours of quarks, while the six green boxes represents the three leptons and their neutrino counterparts. These twelve particles are fermions : particles that follow Fermi-Dirac statistics and have half-integer spins.

The Bosons

The particles on the right half of the image are bosons. These follow Bose-Einstein statistics and have integer spins. The four red boxes represent vector gauge bosons. These carry and mediate three of the four fundamental forces of nature; the fourth, gravity and its mediating gravitons, are still out of the standard model’s grasp. The yellow box on the very right represents the solitary scalar gauge boson, the Higgs, which carries and mediates mass.

Thus, all in all, 17 particles (and their antiparticles) are involved in almost everything that happens in the universe. The Nerd Druid will, hopefully, expand on the standard model in a later post.

Proton Constituents

Quarks are the building blocks of protons, neutrons, and a host of other particles. Together, these quark-based particles are called hadrons. For instance, the J/ψ meson is a hadron. There are two types of hadrons:

  1. Baryons : Composed of three quarks. These can be any flavour.
  2. Mesons : Composed of a quark and its antiquark.

The J/ψ is a meson because it comprises the charm (c) quark and its antiquark. Protons are composed to two up quarks and a down quark (uud), while neutrons have two down and one up quark.

Image of the quark composition of protons and neutrons. On the left, two up and one down quark make up a proton. On the right, two down and one up quark make up a neutron. The quarks have different "colour charges" that add up to "white", and are joined by gluon flux tubes.
On the left, two up and one down quark make up a proton. On the right, two down and one up quark make up a neutron. The quarks have different “colour charges” that add up to “white”, and are joined by gluon flux tubes. Do note that the flux tubes as shown here are wrong. They do not act along the sides of the triangle making up the quarks, but rather form a Y-shape, much like the flux capacitor in the movie Back to the Future.

Why does a proton not break up?

An up quark has charge +2/3, a down quark has charge -1/3. This makes the interior of nucleons a very interesting place. Take the proton, for instance. It has two positively charged up quarks within it, each of which is attracted towards, and attracts, the third negatively charged down quark. However, since they are both positive, they repel each other. How in the world does the proton not break up?

{Atomic nuclei have a similar problem. Going by common sense, the positive protons should never be confined to such a small region.}

If conditions are energetically favourable, bound protons transmute into neutrons. Free protons, one of the stablest objects in the universe, only do so if bombarded with high energy particles. The quarks within them never fly apart on their own, although, electromagnetically speaking, they should be flying apart. What the proton needs is an attractive force that keeps the various quarks together. One candidate is gravitation. However, that is approximately 1040 times weaker than the EM force. So that’s no help.

The Strong Force

Luckily, there is a force stronger than even the EM force. This is the imaginatively named strong force. While the EM force is mediated by photons, the strong force is mediated via gluons.

Take a quick peek at the standard model diagram. The topmost red box on the right half is the gluon. It is a vector gauge boson, and functions as a force-carrier. The strong force holding the quarks together manifests as constant exchanges of gluons between the quarks. From a quantum field theoretic viewpoint, the three quarks within the proton live in a sea of frothing bubbling gluon field.

{The strong force is, of course, also responsible for holding the nucleus together, and manifests itself via constant exchange of gluons between protons and neutrons.}

Proton Mass

The mass of an atom is approximately the same as the mass of its nucleus, since electrons are 1839 times lighter than neutrons, and 1836 times lighter than protons. Adding the masses (the rest masses) of the nucleons is the mass of the atom minus the binding energy needed to keep the nucleus together. However, this is still a small percentage of the nucleonic rest masses.

Inside a proton, the situation is rather different. The total rest mass of the three quarks (2u+1d) is only about 10% of the total mass of the proton. The rest 90% of the mass is provided by the highly energetic gluon field. Since it has energy, and by Einstein’s Mass-Energy equivalence, E = mc2, the gluon field has relativistic mass.

Image of a schematic of the masses of the six different quark flavours. The larger the balls, the higher the mass. The mass of the proton (grey) and electron (red) are shown in the southwest corner. Note that the total mass of 2u+1d would be quite a bit lesser than that of the proton.
A schematic of the masses of the six different quark flavours. The larger the balls, the higher the mass. The mass of the proton (grey) and electron (red) are shown in the southwest corner. Note that the total mass of 2u+1d would be quite a bit lesser than that of the proton.

Proton Pressure

Probing the inside of a proton is not easy. While it is possible to build up a three-dimensional image of the proton using the EM force, probing the mechanical properties of the proton is another matter entirely.

The Energy-Momentum Tensor

The energy-momentum tensor provides a complete classical dynamical description of a particle. It encodes information such as its mass and its momentum, and the shear stresses and pressures on it. Einstein’s Field Equations, which form the backbone of general relativity, relates this tensor with the curvature of spacetime. In the image, the E-M tensor is represented as a 4-by-4 matrix. The energy density, shown in the red box on the top left corner, is equivalent to the mass. The rest of the diagonal, the green band, represents pressure.

Image of the energy-momentum tensor, represented as a 4-by-4 matrix. The northwest corner (red) is mass. The northern and western walls (yellow-orange) are momentum. The elements along the diagonal (green) are pressure acting along the three space axes.
The energy-momentum tensor, represented as a 4-by-4 matrix. The northwest corner (red) is mass. The northern and western walls (yellow-orange) are momentum. The elements along the diagonal (green) are pressure acting along the three space axes.

Gravitational Form Factors

To obtain information about the mechanical structure of a proton, you’d need to prod it with a gravity probe. However, a gravity probe will not directly measure the matrix elements of the E-M tensor. Instead, what it can do it measure what are called gravitational form factors. In 1966, Heinz Pagels developed the concept of these GFFs and also analytically calculated them. Pagels, however, was not very confident that it would ever be possible to measure the detailed structure of a particle using the GFFs, since there was

…very little hope of learning anything about the detailed mechanical structure of a particle, because of the extreme weakness of the gravitational interaction.

And therein lies the rub. Gravity is just too weak a force at the scale of subnucleonic particles.

Image of Heinz Pagels, who constructed the gravitation form factors for nucleons in 1966, at the age of 27. He was extremely capable of explaining science in a simple way. Pagel's work in chaos theory provided the inspiration for the character of Ian Malcolm in Michael Crichton's Jurassic Park.
Heinz Pagels constructed the gravitation form factors for nucleons in 1966, at the age of 27. He was extremely capable of explaining science in a simple way. Pagel’s work in chaos theory provided the inspiration for the character of Ian Malcolm in Michael Crichton’s Jurassic Park.

Generalised Parton Distributions

If restricted to EM probes, then, using something called generalised parton distributions, researches can build up a 3D model of the proton. The word parton here is not quite used in the sense Feynman envisioned it; the term parton nowadays collectively refer to quarks, antiquarks, and gluons. GPDs were introduced around the year 1994. In the quarter century till then, they have emerged as an extremely valuable tool for probing hadrons.

However, the puzzle was still incomplete. GPDs are electromagnetic objects, while GFFs are gravitational. Proton investigations required a bridge between these two.

Measuring Proton Pressure

Deeply Virtual Compton Scattering

The bridge was finally proposed in 1997, when the Xiandong Ji suggested that a method called deep virtual compton scattering (DVCS) could be used to map GFFs onto GPDs. In this process, a beam of electrons is fired into atomic nuclei. Some of these electrons shoot through protons. In doing so, they transfer some of their energy to one of the quarks inside the proton. This is mediated by a virtual photon. The proton, thus energised, doesn’t hold on to this excess energy for long. It soon emits another photon and drops down to its original state.

Magnitude of Proton Pressure

By analysing these photons, Jefferson Lab scientists Volker Burkert, Latifa Elouadrhiri, and Francois-Xavier Girod (BEG) have built up a mechanical picture of the interior of the proton. In particular, they have calculated proton pressure for the very first time. BEG have found that quarks near the centre of the proton feel pressures of the order of 1035 pascal.

To put that into perspective, standard atmospheric pressure at sea level on Earth is slightly more than a million pascal. That is 106.

The centres of neutron stars used to be the undisputed champions of the universe when it came to ultrahigh pressures. They’ve been dethroned, for proton pressure is about 10 times the pressure found within neutron stars.

Distribution of Proton Pressure

Image of the proton pressure distribution. The y-axis is in units of force (positive outward), while the x-axis shows distance from proton centre (in femtometer, 10^-15 m). The repulsive proton pressure near the centre, directed outwards, is balanced by the confining proton pressure from the outer edges of the proton, directed inwards.
Pressure distribution within a proton. The y-axis is in units of force (positive outward), while the x-axis shows the distance from proton centre (in femtometer, 10^-15 m). The repulsive pressure near the centre, directed outwards, is balanced by the confining pressure from the outer edges of the proton, directed inwards.

According the BEG analysis, the proton pressure at the centre of the proton is highest. It is also repulsive, threatening to push the three quarks apart. However, proton pressure near its edge, though less in magnitude, is compressive in nature. This confines the quarks to within the interior of the proton, within a diameter of about 2 fm (1 fm = 10-15 m).

BEG are not done yet, though. They are waiting for better and precise data that they hope to obtain soon. This will help them polish some of their current results on the distribution of proton pressure. BEG are confident that their method of DVCS-GPD-GFF will reveal more about the interior of the proton, such as internal shear forces and the its mechanical radius.


References

Original Paper

Burkert, V. and Elouadrhiri, L. and Girod, F-X. : The pressure distribution inside the proton, Nature (2018).

Reference papers

  1. Pagels, Heinz : Energy-Momentum Structure Form Factors of Particles, Physical Review (1966)
  2. Maxim V. Polyakov, Maxim V. and Schweitzer, Peter : Forces inside hadrons: pressure, surface tension, mechanical radius, and all that, arXiv (2018)
  3. Ji, Xiangdong : Gauge-Invariant Decomposition of Nucleon Spin, Physical Review Letters (1997)
  4. Ji, Xiangdong : Deeply virtual Compton scattering, Physical Review D (1997)
  5. Rutherford, Ernest : The scattering of α and β particles by matter and the structure of the atom (2011)
  6. Chadwick, James : Possible Existence of a Neutron, Nature (1932)
  7. Belitsky, A.V. and Radyushkin, A.V. : Unraveling hadron structure with generalized parton distributions, Physics Reports (2005)

Other resources

  1. Perdrisat, Charles and Punjabi, Vina : Nucleon Form Factors, Scholarpedia (2010)
  2. Wikipedia
    1. Atoms#Subatomic Particles
    2. Proton#History
    3. Neutron#Discovery

Articles

  1. Press Release : First measurement of subatomic particle’s mechanical property reveals distribution of pressure inside proton
  2. Press Release : Quarks feel the pressure in the proton
    1. EurekaAlert (2018)
    2. Jefferson Lab (2018)
  3. Mandelbaum, Ryan F. : Scientists Calculate the Pressure Inside a Proton and It’s Higher Than in a Neutron Star, Gizmodo.com (2018)
  4. Micu, Alexandru : Pressure in protons’ cores is over ten times greater that that in neutron stars
  5. News Staff : Physicists Measure Pressure Distribution inside Proton, Sci-News.com (2018)
  6. Yirka, Bob : Best of Last Week – Measuring pressure inside a proton, flying wireless robot insects and yogurt may treat inflammation, ScienceX.com (2018)
  7. McRae, Mike : Protons Contain 10 Times More Pressure Than a Neutron Star, According to First-Ever Measurement, Science Alert (2018)
  8. Grossman, David : Pressures Inside a Proton Are More Extreme Than Inside a Neutron Star, Popular Mechanics (2018).
  9. Williams, Matt : The Pressure Inside Every Photon is 10x That Inside Neutron Stars, Universe Today (2018)
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Footnotes

  1. Gravitation, Electromagnetic, Strong, and Weak. In the seventies, Glashow (him of GIM), Weinberg and Salam combined the electromagnetic and weak forces into the electroweak theory. Quantum field theory representations exist for each of the three forces. Should an enterprising physicist manage to find one for gravitation too, she would have the so-called Grand Unified Theory in her hands.

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