Chapter 2 Motion Along a Straight Line Position, Displacement ...
Topic 7: Atomic, nuclear and particle physics 7.3 The structure of matter Description and classification of particles An elementary particle has no internal structure. PRACTICE: At one time it was thought that atoms were elementary particles. Explain why they are not. SOLUTION: They have an internal structure: Namely protons, neutrons and electrons. EXAMPLE: At one time it was thought that protons and neutrons were elementary particles. Explain why they are not. SOLUTION: Protons and neutrons are each built from three elementary particles called quarks. Description and classification of particles To date there are three major divisions in
the elementary particles. The force carriers/gauge bosons are the particles that allow compatible particles to sense and react to each others presence through exchange of these carriers. The quarks are the heavier, tightly bound particles that make up particles like protons and neutrons. The leptons are the lighter, more loosely bound particles like electrons. Fundamental forces and their properties STRONG ELECTRO-WEAK ELECTROMAGNETIC WEAK
GRAVITY + + nuclear light, heat and force charge STRONGEST Range: Extremely Short Force Carrier: Gluon Range: radioactivity
Range: Short Force Carrier: Photon freefall WEAKEST Range: Force Carrier: Graviton The nature and range of the force carriers There are four force carriers INTERACTION 1: STRONG: 1.0
Strongest of all the interactions between particles. We can give it an arbitrary value of 1.0 for comparison. INTERACTION 2: ELECTROMAGNETIC 0.01 This is the NEXT strongest. In comparison to the strong interaction, it has a relative strength of 10 -2. INTERACTION 3: WEAK 0.000001 This interaction has a relative strength of 10 -6. INTERACTION 4: GRAVITATIONAL This interaction has a relative strength of 10 -39 0.000000000000000000000000000000000000001 The nature and range of the force carriers
In 1933 Hideki Yukawa developed the theory of exchange forces. The basic idea is that all forces are due to the exchange of particles between like elementary particles. Consider two protons in space. Yukawa postulated that the protons exchange photons and repel each other because of this exchange. This photon exchange is the electromagnetic force. The nature and range of the force carriers Yukawa explained that the electromagnetic force was long range (in fact infinite in range) because photons "live forever" until they are absorbed. Yukawa explained that the strong force was short range (in fact only in the
nuclear range) because the strong force exchange particle (the gluon) has a very short life. LONG RANGE EXCHANGE PARTICLE SHORT RANGE EXCHANGE (VIRTUAL) PARTICLE The nature and range of the force carriers Exchange particles whose range of influence is limited are called virtual particles. The four fundamental forces have different ranges and a different gauge boson is responsible for each force. The mass of the boson establishes the range of the force. The bosons carry the force between particles. Virtual particles can only exist within their range of influence. Quarks and their antiparticles Although you have heard of protons and neutrons,
both of which react to the strong force exchange particle (the gluon), you have probably not heard of most of the following particles: Particle Symbol Particle Symbol Particle Symbol proton p
delta 0 sigma + neutron n delta - sigma
0 lambda 0 delta ++ sigma - omega - delta
+ xi 0 With the advent of particle research the list of new particles became endless! Quarks and their antiparticles In 1964 the particle model was looking quite complex and unsatisfying. Murray Gell-Mann proposed a model where all the strong-force particles were made up of three fundamental particles called quarks. proton is uud neutron is udd proton
u d u Quarks and their antiparticles Every particle has an antiparticle which has the same mass but all of its quantum numbers are the opposite. Angels and Demons Thus an antiproton (p) has the same mass as a proton (p), but the opposite charge (-1). Thus an antielectron (e+ or e-) has the same mass as an electron but the opposite charge (+1). When matter meets antimatter both annihilate each other to become energy!
Paul Dirac After giving a lecture in 1929, Dirac agreed to take questions from the audience. One guy got up and said, "Professor Dirac wonderful lecture. I didn't understand the equation at the top right hand on the blackboard." Then there was total awkward silence, for almost a minute. The chairman turns to Dirac and says, "Would you like to answer the question?" And Dirac said "It wasn't a question. It was a comment". Quarks Quarksand andtheir theirantiparticles antiparticles Each quark has an antiquark, which has the opposite charge as the corresponding quark.
Here are the names of the 6 quarks: An antiquark has the quark symbol, with a bar over it. Thus an anti-up quark looks like this: u (u-bar). Hadrons, baryons, and mesons A hadron is a particle made up of quarks and participates in the strong force. A baryon is made of three quarks (qqq). An antibaryon is made of three antiquarks (qqq). A meson is made up of a quark and an antiquark (qq): Since quarks participate in the strong force, and since baryons and mesons are made of quarks, baryons and mesons are hadrons. A single quark cannot be isolated. We will talk about quark confinement later. Basically, confinement states that you cannot separate a single quark from a hadron.
Protons and neutrons in terms of quarks A proton is a baryon made out of two up quarks and a down quark. p = (uud). A proton is a hadron. Why? A neutron is a baryon made out of one up quark and two down quarks. n = (udd). A neutron is also a hadron. EXAMPLE: Show that the charge of a proton is +1, and that the charge of a neutron is 0. The charge of an up quark is +2/3. The charge of a down quark is -1/3. Proton = uud : +2/3 + +2/3 + -1/3 = +1. u d u Neutron = udd : +2/3 + -1/3 + -1/3 = 0. proton
Conservation of baryon number In order to explain which particles can exist and to explain the outcome of observed interactions between particles, the quarks are assigned properties described by a numerical value. The quark is given a baryon number B of 1/3. The antiquark is given a baryon number B of -1/3 PRACTICE: What is the baryon number of a proton and an antiproton? What is the baryon number of a meson? +1 +1 +( +( =+1 ( +1 ) ) 3 3 3 )
Like charge, baryon number is conserved in all reactions. Conservation of strangeness The strangeness number S of a baryon is related to the number of strange quarks the particle has. S = # antistrange quarks # strange quarks EXAMPLE: The lambda zero particle (0) is a baryon having the quark combo of (uds). What is its charge? What is its strangeness? From the table the charges are u = +2/3, d = -1/3 and s = -1/3 so that the total charge is 0. S = # antistrange quarks # strange quarks = 0 1 = -1. https://en.wikipedia.org/wiki/Strangeness Strangeness ("S") is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions which occur in a short period of time. The terms strange and strangeness predate the discovery of the quark, and were adopted
after its discovery in order to preserve the continuity of the phrase; strangeness of antiparticles being referred to as +1, and particles as 1 as per the original definition. For all the quark flavor quantum numbers (strangeness, charm, topness and bottomness) the convention is that the flavor charge and the electric charge of a quark have the same sign. With this, any flavor carried by a charged meson has the same sign as its charge. Strangeness was introduced by Murray Gell-Mann and Kazuhiko Nishijima to explain the fact that certain particles, such as the kaons or certain hyperons[which?], were created easily in particle collisions, yet decayed much more slowly than expected for their large masses and large production cross sections. Noting that collisions seemed to always produce pairs of these particles, it was postulated that a new conserved quantity, dubbed "strangeness", was preserved during their creation, but not conserved in their decay. In our modern understanding, strangeness is conserved during the strong and the electromagnetic interactions, but not during the weak interactions. Consequently, the lightest particles containing a strange quark cannot decay by the strong interaction, and must instead decay via the much slower weak interaction. In most cases these decays change the value of the strangeness by one unit. However, this doesn't necessarily hold in second-order weak reactions, where there are mixes of K0 and K0 mesons. All in all, the amount of strangeness can change in a weak interaction reaction by +1, 0 or -1 (depending on the reaction). Conservation of strangeness
The is a hadron because it is composed of quarks. The proton is composed of uud If X is sss, then the reaction can be written su + uud ds + us + sss. The left has an s, u, and d left. The right also has an s, u, and d left. The quarks are balanced on each side. Quark confinement Quark confinement means that we cannot ever separate a single quark from a baryon or a meson. Because of the nature of the strong force holding the quarks together we need to provide an energy that is proportional to the separation. Eventually, that energy is so vast that a new quarkantiquark pair forms and all we have is a meson, instead of an isolated quark!
ed t a -cre y l w Ne son me ark u q nti from r a k ar eated ed fo u Q r cr
eed i n a p rgy n ene aratio sep al n i g Ori son me Leptons and their antiparticles You are already familiar with two of the six leptons: the electron and the electron neutrino ( decay). Leptons, unlike hadrons (baryons and mesons),
do NOT participate in the strong interaction The leptons interact only via the electromagnetic force carrier, the photon Leptons, unlike quarks, do not react to the gluon Quarks react to both the gluon and the photon. Leptons and quarks also react to gravitons. Of course the leptons also have their antiparticles. Standard model of elementary particles The following graphic shows part of an organizational structure for particles called the standard model. These are the quarks from which mesons and hadrons are formed. Particles are divided into generations or families of increasing mass. (none of IB interest -) These are the leptons, the most common of which is the electron.
Muons are created in upper atmosphere by cosmic rays. Tau particles are created in the laboratory. You may be asked to decide whether an interaction or decay is feasible on the basis of the conservation rules. Applying conservation laws in particle reactions PRACTICE: Find the lepton number of an electron, a positron, an antielectron neutrino, an antimuon neutrino, a tau particle, and a proton: SOLUTION: An electron has a lepton number of L = +1. A positron is an antiparticle and so has L = -1. An antielectron neutrino has L = -1. An antimuon neutrino has L = -1. An tau particle has L = +1. A proton is not a lepton and so has L = 0.
Applying conservation laws in particle reactions EXAMPLE: Consider the following reactions. Assign charge, lepton numbers and baryon numbers to each particle to determine the feasibility of each reaction. Baryon number: Lepton number: Charge: Baryon number: Lepton number: Charge: Baryon number: Lepton number: Charge: p n + e + + e 1 =1+ 0+ 0 0 0 + -1I + +1I
L must be conserved by family. NOT FEASIBLE B must be conserved. Applying conservation laws in particle reactions L must be conserved by family. Thus LII and LI are not conserved. A pion is a meson and has B = 0. p and n each have B = 1. Baryon number not conserved. Baryon number not conserved. Charge not conserved. Applying conservation laws in particle reactions Gluons.
Conservation of charge. Conservation of baryon number. Conservation of lepton number (by family no IB). Also strangeness, parity, isotopic spin, angular momentum. Applying conservation laws in particle reactions Family I lepton number is not conserved. Equation needs Family I lepton with no charge and L = -1. e fits the bill. n p + e- + e. The Higgs boson an analogy Higgs boson is another particle that physicists IfThe the particle found in July of 2012 is the Higgs think exists and were in search of.
boson, it definitely brings with it a very puzzling This particleAs is the one that gives quarks leptons that the problem. physicists begin toand accept their mass. Higgs boson has likely been found, they are turning their attention to this most unnatural quandary. The On 4 July 2012, the discovery of a new particle with a main focus of LHCGeV/c is now
2 mass between 125the and 127 was becoming announced; a search for aphysicists naturalsuspected solution thisthedifficult question: thatto it was Higgs boson. Discovered: Hadron Why is theLarge Higgs
so Collider light?(2011-2013) Mean lifetime: 1.561022 s (predicted) Mass: 125.090.21 (stat.)0.11 (syst.) GeV/c2 ... Electric charge: 0 e CERN and the Large Hadron Collider were developed with the Higgs boson in mind. The Large Hadron Collider at CERN. The Higgs boson an analogy Imagine a room full of physicists. The Higgs field. Suddenly Einstein enters and attempts to cross the room, but the star-struck physicists cluster around him and impede his movements, effectively increasing his mass. High-mass particle. Now imagine that I enter the room. Nobody wants to interact with me, so I pass through the physicists relatively unimpededno effective mass for me! Low-mass (or
massless) particle. Lastly, imagine that somebody whispers a rumor, causing the physicists to cluster together excitedly on their own. Field disturbance Higgs boson. -Burton DeWilde The Higgs boson an analogy Higgs field Big mass Einstein Small mass Me The Higgs boson We call the process whereby mass is not the property of the particle, but part of space itself, the Higgs mechanism.
For the Higgs mechanism to work, all of space has to be covered by some sort of field called the Higgs field. Just as the electromagnetic field has a particle associated with it (a photon) so too does the Higgs field in this case the particle associated with the Higgs field is the Higgs boson. One of the design criteria for CERN was the capability of discovering the Higgs boson (sometimes called the god particle). The Higgs boson Discovery of the Higgs particle would be evidence that the standard model is correct. Without the Higgs particle, the standard model will not extend into the realm of general relativity. String theory could be an alternative to the standard model. NEW STANDARD MODEL of ELEMENTARY PARTICLES By MissMJ - Own work by uploader, PBS NOVA , Fermilab, Office of
Science, United States Department of Energy, Particle Data Group, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=4286964 Feynman diagrams Richard Feynman developed a graphic representation of particle interactions that could be used to predict the probabilities of the outcomes of particle collisions. SPACE A typical Feynman diagram consists of two axes: Space and Time: TIME Some books switch the space and time axis. The IB presentation is as shown above. Feynman diagrams
The bubble of ignorance SPACE Consider two electrons approaching oneanother from the top and the bottom of the page A purely spatial sketch of this interaction would look like this: But if we also apply a time axis, the sketch would look like this: The Time axis allows us to draw the reaction in a spread-out way to make it clearer. e- e- e-
e- eTIME e- The bubble of ignorance is the actual place in the plot that exchange particles do their thing. Ingoing and outgoing particles are labeled. Feynman diagrams Particles are represented with straight arrows, as were the two electrons in the previous electron-electron interaction. Exchange (force) particles are represented with either wavy lines (photons, W+, W- and Z0), or curly lines (gluons).
Particle Electromagnetic and weak exchange Strong exchange You may have noticed that the electromagnetic exchange particle and the weak exchange particles all have the same wavy symbol. Indeed, it has been found that the two forces are manifestations of a single ELECTRO-WEAK force. Feynman diagrams SPACE EXAMPLE: The complete Feynman diagram showing the repulsion of two
electrons looks like this: e e e- - TIME SPACE EXAMPLE: Here is a diagram for one electron emitting a photon: e- e-
e- TIME Feynman diagrams EXAMPLE: Here is a diagram for one positron emitting a photon: SPACE SPACE EXAMPLE: In a Feynman diagram, antimatter points backward in time. This diagram
represents two positrons repelling each other: e+ e+ e+ e+ TIME e+ e+ TIME EXAMPLE:
Here is a photon producing an electron-positron pair. SPACE Feynman diagrams e e+ EXAMPLE: Here is an electron-positron pair annihilating to become a photon: SPACE TIME e+
e - TIME Feynman diagrams d SPACE EXAMPLE: Here is a diagram of a down quark emitting a W- particle that decays into an electron and an antineutrino:
u e W - eTIME One can use Feynman diagrams to map out complete processes including the bubble of ignorance. Using the conservation rules and the exchange particles, you can predict what kind of processes can occur. Feynman diagrams EXAMPLE: Explain what has happened in this Feynman diagram. SPACE
SOLUTION: The up quark of a proton (uud) emits a gluon. The gluon decays into a down quark and an antidown quark. d u u d u u g d d
TIME Quarks cannot exist by themselves. Thus the two quarks produced above will quickly annihilate. Feynman diagrams EXAMPLE: Explain what has happened in this Feynman diagram. SPACE SOLUTION: It is a diagram of a down quark emitting a W- particle that decays into an electron and an antineutrino: Recall that a neutron consists of an up-down-down quark combo. Recall that a proton consists of an up-up-down quark combo.
This is non other than the beta decay (- ) we talked about a long time ago. u d d n p W - u d u e
eTIME + + Feynman diagrams EXAMPLE: Write the reaction (including the neutrino) for beta (+) decay. SOLUTION: p n + e+ + e SPACE EXAMPLE: Now draw the Feynman diagram for the above + decay: u d u
p nu W+ e+ TIME Why is the neutrino not an anti-neutrino as in the - decay? To conserve lepton number. d d e Feynman diagrams +2 / 3
-1/3 -1 e st b u -1 M 0 A virtual particle is a particle that has a very short range of influence. Look at charge The particle must be a W-.
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