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PARTICLE PHYSICS: Deep Inelastic Scattering, Time dilation and The Higgs Boson. by emperorhassy

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PARTICLE PHYSICS: Deep Inelastic Scattering, Time dilation and The Higgs Boson.
<p class="MsoNormal"><span style="font-size: 1rem;">Deep inelastic scattering (DIS) is an
extension of the scattering experiments like that of Geiger and Marsden that
led to the discovery of the atomic nucleus. If the alpha particles used had had
more energy they could have broken up the target nucleus, with results that
might have been too confusing to evaluate at that time. The scattering would
have been inelastic as the alpha particles lost energy in breaking up the
nucleus, rather than the elastic scattering that Rutherford was able to assume.</span><br></p><p class="MsoNormal"><span lang="">But in 1968 high-speed electrons were used to
probe the proton (hydrogen nucleus), contained in a tank of liquid hydrogen at
the Stanford Linear Accelerator Center in California. This was about the time
that theory was predicting that even such fundamental particles as the proton
had internal structure, and should contain smaller objects with fractional
charge and baryon number. These were named as quarks by the theoretical physicist
Murray Gell-Mann. The pattern of scattering of the electrons confirmed the
existence of small scattering centres inside the proton. These were identified
as quarks.</span></p><p class="MsoNormal"><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1577807680/iegziusvaub5o272dqum.png" data-filename="iegziusvaub5o272dqum" style="width: 480px; float: left;" class="note-float-left"><div style="text-align: center;"><a href="https://commons.wikimedia.org/wiki/File:DIS.svg" target="_blank"><a href="https://commons.wikimedia.org/wiki/File:DIS.svg" target="_blank" style="background-color: rgb(255, 255, 255); font-size: 1rem;"><sup>Deep inelastic scattering of a lepton (l) on a hadron (h), at leading order in perturbative expansion. The virtual photon (γ*) knocks a quark (q) out of the hadron. E2m, Public Domai</sup>n</a><br></a></div></p><p class="MsoNormal"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal"><span lang="">The interaction between particles is mediated
by exchange particles, in this case by virtual photons between the incoming
electron and the proton. When the electron kinetic energy is low these photons
also have low energy, meaning an associated wavelength too large to ‘see’ the
quarks. The electrons are scattered elastically through small angles. To
resolve quarks, high-energy, short-wavelength photons are needed. When such a
photon is emitted by a high-speed electron the electron recoils at a large
angle. The photon also has enough energy to knock a quark out of the proton.
But when quarks separate, new quarks are formed and the proton remains a
three-quark object. The ejected quark breaks up into one or more quark-antiquark
pairs observed as a jet of mesons. <o:p></o:p></span></p><p class="MsoNormal"><span lang="">This process of deep inelastic scattering is
now one of the main tools of investigation in particle physics, with ever more
massive and higher energy particle colliding with each other. The overall aim
now is to find new more massive particles that can only be created with the
‘spare’ energy from inelastic collisions. I will discuss such collisions
next.<o:p></o:p></span></p><h2><span lang="">Quarks and the weak interaction<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">In a collision, any new particles carry away
kinetic energy and their rest mass-energy. Both energies are provided by the
total energy of the colliding particles. I shall consider two situations
involving a proton and an antiproton. In the first, the moving antiproton hits
the proton which is a stationary target. In the second, both particles collide
while moving with equal energies towards each other (as in a collider). The
total energy of each moving particle is 2 GeV. Suppose that in each case a single
particle is produced as a result of the collision. What total energy will this
particle have?</span></p><p class="MsoNormal"><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1577807444/umpcowvokxdzl5vmrlgt.png" data-filename="umpcowvokxdzl5vmrlgt" style="width: 527.5px;"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Quark_weak_interactions.svg" target="_blank"><sup>The strengths of the weak interactions between the six quarks. The "intensities" of the lines are determined by the elements of the CKM matrix. TimothyRias, Public Domain</sup></a><span lang=""><o:p><br></o:p></span></p><h2><span lang="">A COLLISION WITH A STATIONARY TARGET<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">The total energy is 2 GeV for the moving
antiproton plus the rest-mass energy of 1 GeV of the target proton, total 3 GeV.
The total momentum is due to the incoming particle only, and is calculated from:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">P<sup>2</sup> = E<sup>2</sup>/c<sup>2</sup>
– m<sub>0</sub><sup>2</sup>c<sup>2</sup><o:p></o:p></span></h4><h4 align="center" style="text-align:center"><span lang="">which gives: p<sup>2</sup>
= 3(GeV/c)<sup>2</sup><o:p></o:p></span></h4><h4 align="center" style="text-align:center"><span lang="">and: p = 1.7 GeV/c<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">The new particle must carry away exactly this
quantity of momentum. Its rest mass m<sub>new</sub> must be given by:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">m<sup>2</sup><sub>new</sub>
= E<sup>2</sup>/c<sup>4</sup> – p<sup>2</sup>/c<sup>2</sup> = 3<sup>2</sup>(GeV/c<sup>2</sup>)
– 1.7<sup>2</sup>(GeV/c<sup>2</sup>)<o:p></o:p></span></h4><h4 align="center" style="text-align:center"><span lang="">So that: m<sub>new</sub>
= 2.5 GeV/c<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">This is in fact a Z particle.<o:p></o:p></span></p><h2><span lang="">COLLISIONS IN A COLLIDER<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">As explained above, the energy for each
colliding particle is 2 GeV, totalling 4 GeV. The total momentum before collision
is zero, since each particle is moving with the same speed but in opposite
directions. The momentum of the new particle must also be zero. This means that
its kinetic energy is zero, so all the energy must appear as the rest mass of
the new particle: which is thus 4 GeV/c<sup>2</sup>.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">This shows that the collider system is able to
create particles of greater rest mass than the stationary target system is able
to.<o:p></o:p></span></p><h2><span lang="">TIME DILATION: PARTICLES LIVE LONGER AT SPEED<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">Many of the new particles produced in
accelerators decay with very short half-lives, and even at high speeds they
would have decayed before reaching a detector except for the relativistic
effect of time dilation. This effect has been explained before, (<a href="https://www.steemstem.io/#!/@emperorhassy/what-does-moving-through-space-and-time-mean" target="_blank">check here</a>&nbsp;and <a href="https://www.steemstem.io/#!/@emperorhassy/an-insight-into-einstein-s-general-relativity" target="_blank">here</a>),
in connection with the detection of muons produced in the upper atmosphere by
cosmic-ray collisions. </span></p><p class="MsoNormal" style="text-align: center; "><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1577807935/vv5v63lpv46ltii8rjd8.jpg" data-filename="vv5v63lpv46ltii8rjd8" style="width: 527.5px;"><span lang=""><br></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:2mv_accelerator-MJC01.jpg" target="_blank"><sup>A 1960s single stage 2 MeV linear Van de Graaff accelerator, here opened for maintenance. Martin Conway, CC BY-SA 3.0</sup></a><span lang=""><br></span></p><p class="MsoNormal"><span lang="">A particle that would decay in 10<sup>-8</sup> seconds
should travel just 3 m in this time at speeds close to light speed. In fact
they travel 66 m and can be observed in detectors that are so large that they
have to be several metres from the collision point where the particle was
created. This is because to a stationary observer the particle’s lifetime
increases as a consequence of the special theory of relativity. To a fixed
observer, the observed time </span><span lang="">Δ</span><span lang="">t’ of a process
occurring in a time </span><span lang="">Δ</span><span lang="">t in a moving system is
longer:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">Δt’ = Δt/(1-v<sup>2</sup>/c<sup>2</sup>)<sup>½</sup>
&nbsp;= γt<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">A particle travelling at 0.999c would actually
have a mean lifetime as observed increased from 10<sup>-8</sup> s to 2.2 </span><span lang="">× </span><span lang="">10<sup>-7</sup> s, over 20 times longer, so that it can travel that
much further on average.<o:p></o:p></span></p><h2><span lang="">MATTER AS WE KNOW IT<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">In the families of the quarks and the leptons,
there are three generations. Each particle has its antiparticle. They make up
all the matter and antimatter that has so far been discovered. But most of the
Universe may consist of dark matter, which has not yet been identified.<o:p></o:p></span></p><h2><span lang="">AND FINALLY…<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">Atoms and nuclei exist because they are made
of particles which cannot have the same set of quantum numbers while part of
the same system. The reason why is outside the scope of Advanced level physics.
This post has shown that the rules which define the behaviour of particles are
due to the fundamental properties of quarks. But no one knows why quarks have these
properties.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">The rich variety of particles exists – and
just for very short times – only in conditions of high energy such as during
collisions in accelerators, in the interiors of stars and also at the time of
the Big Bang. Most of the Universe makes do with protons, neutrons and
electrons.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">The next main goal of particle physicists is
to find a particle called the <b>Higgs</b> <b>boson</b> which is important
because its interaction with other particles is believed to be the source of
their mass. Like all bosons, it is a ‘field particle’, which means that it
carries a force of some kind.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">We observe mass as something that makes it
hard to accelerate something. The harder it is to accelerate, the greater the
mass of the object. But imagine trying to push a sheet of aluminium in a strong
magnetic field. You feel a force opposing your efforts, which we explain as
being due to eddy currents excited in the aluminium by its motion through the
magnetic field. If you didn’t know about magnetism and electricity, you might
confuse this effect with the ‘inertial force’ that seems to stop you giving
instantaneous velocity to a mass. In a similar way, the Higgs field opposes
motion by exchanging virtual bosons – just as the exchange of photons mediates
electromagnetic forces. The effect is to produce an interaction of some kind
that appears as inertial resistance to motion. You can think of the Higgs boson
as somehow making space ‘sticky’.</span></p><p class="MsoNormal"><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1577808360/l3ltp6ehydv8um7an55p.png" data-filename="l3ltp6ehydv8um7an55p" style="width: 369px; float: left;" class="note-float-left"><div style="text-align: center;"><a href="https://commons.wikimedia.org/wiki/File:Candidate_Higgs_Events_in_ATLAS_and_CMS.png" target="_blank"><a href="https://commons.wikimedia.org/wiki/File:Candidate_Higgs_Events_in_ATLAS_and_CMS.png" target="_blank" style="background-color: rgb(255, 255, 255); font-size: 1rem;"><sup>Candidate Higgs boson events from collisions between protons in the LHC. CERN for the ATLAS and CMS Collaborations, https://cds.cern.ch/record/1630222, CC BY-SA 3.</sup>0</a><br></a></div></p><p class="MsoNormal"><br></p><p class="MsoNormal"><span lang="">The theory put forward by Peter Higgs of
Edinburgh University as long ago as 1964 is now seen to be very useful, as it
links with the ‘theories of everything’ – superstring theory, supersymmetry and
supergravity – now being explored by the ‘super-theorists. The mass of the
Higgs boson is predicted to be between 0.1 and 1 TeV, so should be within the
scope of the ATLAS experiment in the Large Hadron Collider at CERN.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Physics would quite like to know what causes
mass – and be able to link quantum physics with Einstein’s gravity theories.<o:p></o:p></span></p><h2><span lang="">SUMMARY<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">After reading through all the series of my
post on particle physics, starting with <a href="https://www.steemstem.io/#!/@emperorhassy/particle-physics-dis-1575234766" target="_blank">1</a>, <a href="https://www.steemstem.io/#!/@emperorhassy/particle-physics-the-1575818004" target="_blank">2</a>, <a href="https://www.steemstem.io/#!/@emperorhassy/particle-physics-qua-1576255763" target="_blank">3</a>, <a href="https://www.steemstem.io/#!/@emperorhassy/particle-physics-wha-1577109749" target="_blank">4</a>, <a href="https://www.steemstem.io/#!/@emperorhassy/particle-physics-det-1577360146" target="_blank">5</a>, and this final one, you should know and understand the
following:<o:p></o:p></span></p><ul><li><span lang="">Three particles – the neutron, proton and electron
– are able to explain the main behaviours of stable atoms.</span></li><li>The four types of interaction between
particles require additional exchange particles – bosons – which mediate the
interactions (they ‘carry the forces’).</li><li>Many new particles have been discovered,
initially from the collisions of cosmic rays (high-speed protons, electrons and
atomic nuclei) and later from accelerator experiments.</li><li>Each particle has an antiparticle, described
as matter and antimatter.</li><li>Particles and their antiparticles – hadrons
(baryons, mesons) and leptons – are classified by rest mass and by other
properties (baryon number, strangeness) and their response to forces.</li><li>These properties were discovered by applying
conservation rules in reactions.</li><li>The behaviour, interactions and nature of hadrons
may be explained more simply using the quark model.</li><li>There are three lepton families and three
quark families, arranged in successive generations.</li><li>There are several types of accelerator, each
based on a physical principle. Accelerators give particles high energies at
which they interact.</li><li>Many investigations involve deep inelastic
scattering.</li><li>There are several types of particle detector,
each design based on a particular underlying physical principle but usually
relying on the ability of a particle to cause ionisation.</li><li>For simple reactions there are calculations
and decays involving the masses, energies and momenta of high-speed,
relativistic particles.</li><li>Conservation rules enable particle
interactions to be analysed.</li><li>Feynman diagrams can be used to illustrate what
happens in interactions and decays involving particles.</li></ul><h2><span lang="">REFERENCES<o:p></o:p></span></h2><p class="MsoNormal"><a href="https://www.worldscientific.com/worldscibooks/10.1142/4814" target="_blank">https://www.worldscientific.com/worldscibooks/10.1142/4814</a><span lang="">&nbsp;</span></p><p class="MsoNormal"><a href="https://www.worldscientific.com/worldscibooks/10.1142/4586" target="_blank">https://www.worldscientific.com/worldscibooks/10.1142/4586</a><span lang="">&nbsp;</span></p><p class="MsoNormal"><a href="http://www.tunl.duke.edu/nnpss/lectures/11/NNPSS11-2-nobuilds.pdf" target="_blank">http://www.tunl.duke.edu/nnpss/lectures/11/NNPSS11-2-nobuilds.pdf</a><span lang="">&nbsp;</span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Deep_inelastic_scattering" target="_blank">https://en.wikipedia.org/wiki/Deep_inelastic_scattering</a><span lang="">&nbsp;</span></p><p class="MsoNormal"><a href="http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/funfor.html" target="_blank">http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/funfor.html</a><span lang="">&nbsp;</span></p><p class="MsoNormal"><a href="https://www.britannica.com/science/weak-force" target="_blank">https://www.britannica.com/science/weak-force</a><span lang="">&nbsp;</span></p><p>













































































































</p><p class="MsoNormal"><a href="https://www.livescience.com/49254-weak-force.html" target="_blank">https://www.livescience.com/49254-weak-force.html</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Weak_interaction" target="_blank">https://en.wikipedia.org/wiki/Weak_interaction</a><span lang=""><br></span></p><p class="MsoNormal"><a href="http://hyperphysics.phy-astr.gsu.edu/hbase/colsta.html" target="_blank">http://hyperphysics.phy-astr.gsu.edu/hbase/colsta.html</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://www.open.edu/openlearn/science-maths-technology/collisions-and-conservation-laws/content-section-3.1" target="_blank">https://www.open.edu/openlearn/science-maths-technology/collisions-and-conservation-laws/content-section-3.1</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://www.symmetrymagazine.org/article/whats-really-happening-during-an-lhc-collision" target="_blank">https://www.symmetrymagazine.org/article/whats-really-happening-during-an-lhc-collision</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Collider" target="_blank">https://en.wikipedia.org/wiki/Collider</a><span lang=""><br></span></p><p class="MsoNormal"><a href="http://www.schoolphysics.co.uk/age16-19/Relativity/text/Muons_time_dilation/index.html" target="_blank">http://www.schoolphysics.co.uk/age16-19/Relativity/text/Muons_time_dilation/index.html</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Experimental_testing_of_time_dilation" target="_blank">https://en.wikipedia.org/wiki/Experimental_testing_of_time_dilation</a><span lang="">&nbsp;</span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Time_dilation" target="_blank">https://en.wikipedia.org/wiki/Time_dilation</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://home.cern/science/physics/higgs-boson" target="_blank">https://home.cern/science/physics/higgs-boson</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Higgs_boson" target="_blank">https://en.wikipedia.org/wiki/Higgs_boson</a><span lang=""><br></span></p><p class="MsoNormal"><span lang=""><br></span></p>
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