A Young Physicist’s Guide to the Higgs Boson Tel Aviv University Future Scientists – CERN Tour Presented by Stephen Sekula Associate Professor of Experimental Particle Physics SMU, Dallas, TX Programme ● You have a problem in your theory: (why do you need the Higgs Particle?) ● How to Make a Higgs Particle (One-at-a-Time) ● How to See a Higgs Particle (Without fooling yourself too much) ● A View from the Shadows: What are the New Questions? (An Epilogue) Stephen J. Sekula - SMU 2/44 You Have a Problem in Your Theory Credit for the ideas/example in this section goes to Prof. Daniel Stolarski (Carleton University) The Usual Explanation Usual Statement: “You need the Higgs Particle to explain mass.” 2 F=ma F=G m1 m2 /r Most of the mass of matter lies in the nucleus of the atom, and most of the mass of the nucleus arises from “binding energy” - the strength of the force that holds particles together to form nuclei imparts mass-energy to the nucleus (ala E = mc2). Corrected Statement: “You need the Higgs Particle to explain fundamental mass.” (e.g. the electron’s mass) E2=m2 c4+ p2 c2→( p=0)→ E=mc2 Stephen J. Sekula - SMU 4/44 Yes, the Higgs is important for mass, but let’s try this... ● No doubt, the Higgs particle plays a role in fundamental mass (I will come back to this point) ● But, as students who’ve been exposed to introductory physics (mechanics, electricity and magnetism) and some modern physics topics (quantum mechanics and special relativity) you are more familiar with... ● inverse-square laws for forces, e.g. Newton’s Law of Gravitation and Coulomb’s Law ● You have been working with models of nature that actually have fundamental problems in them, just like the Standard Model of Particle Physics would have if there was no Higgs Particle ● Let’s explore this idea: your theory has a flaw... what does it look like, and what does it imply? Stephen J. Sekula - SMU 5/44 Coulomb’s Force Law ⃗ F12 Model electric + - Two kinds of charges as points electric charge 1 2 Force that 2 exerts on 1 described by Coulomb’s Law: 1 q q F = 1 2 12 π ϵ 2 4 0 r12 Stephen J. Sekula - SMU 6/44 Electric Potential and Coulomb’s Law ⃗ F12 Model electric + - Two kinds of charges as points electric charge 1 2 Fundamental Concept: the Electric Potential of charge 2 1 q2 dV 2 V 2=− F12=q1 4 π ϵ0 r dr Stephen J. Sekula - SMU 7/44 Picturing Forces (“Interactions”) Electron (e) Electron - Deflected by Electric Field + anti-Muon - (μ+) μ “Classical Picture” “Quantum Picture” Feynman Diagram Stephen J. Sekula - SMU 10/44 From Early Physics to Advanced Physics: Coulomb’s Law as an Example of Theoretical Problems 1 q q 1 q Electric F = 1 2 V =− 2 Electric Force 12 π ϵ 2 2 π ϵ Potential 4 0 r12 4 0 r Discussion: how does the potential (energy per unit charge) of charge 2 change with your distance from it? Discussion: can we identified any problems in this classical description of electric potential/force? Stephen J. Sekula - SMU 11/44 From Early Physics to Advanced Physics: Coulomb’s Law as an Example of Theoretical Problems ● The Coulomb Potential “blows up” to infinity as the charge separation distance goes to zero ● Not very “physical” ● In other words, Coulomb’s Law doesn’t give us a clear picture of what happens right at the charge. ● An infinity in a physical theory is typically considered a sign of where the theory breaks down. Stephen J. Sekula - SMU 12/44 From Early Physics to Advanced Physics: Coulomb’s Law as an Example of Theoretical Problems 1 q1 q2 ● Perhaps classical U 1=q1 V = 4 π ϵ0 r electromagnetism is incomplete ● ... if some new rules take over at Maybe a broader theory of short distances, but in the limit of nature takes over at short large distances converges to the classical result... distances and modifies the law 1 q1 q2 U 1= ×( 1+f (r /rcutoff)) 4 π ϵ0 r Stephen J. Sekula - SMU 13/44 Uniting Quantum Mechanics and Relativity: the very small and the very fast When one successfully unites the theory of F⃗ =q⃗v×B⃗ the very fast (special relativity) with the theory of the very small (quantum mechanics), something new emerges... X Non-Relativistic Schroedinger Wave Magnetic Equation Field into ⃗v Page You have matter and forces, but you “twin” Fully Relativistic Dirac all matter: for every particle, you find there Equation must be an antiparticle with the same mass and opposite electric charge. Stephen J. Sekula - SMU 17/44 The Heisenberg Uncertainty Principle and Virtual Particles – A look back at an “electric field” As a consequence of the fundamental wave nature of matter and forces (quantum mechanics), one finds this principle applies: Δ E Δ t≥ℏ/2 Δ p Δ x≥ℏ/2 So long as it obeys these rules, a photon can emit and be reabsorbed... μ μ μ A charged particle isn’t just “sitting ... and this is allowed, too. there” with nothing happening Stephen J. Sekula - SMU 18/44 How the Cutoff Manifests μ μ Quantum Mechanics + Relativity: Scattering “shielded” by virtual particles The closer the photon gets to the charge, the more “virtual” particles it encounters Stephen J. Sekula - SMU 19/44 Some Practice with Feynman Diagrams and Physics EXERCISE: Draw a Feynman Diagram that represents one electron scattering off of another electron (e-e- → e-e-) using as few lines as possible (minimum possible drawing). HINT: conservation laws hold, so conserve electric charge, energy, and momentum. Stephen J. Sekula - SMU 20/44 The Standard Model Picture Matter Particles ● Quarks: down, up, strange, charm, bottom, top ● Leptons: (electron, muon, tau neutrinos), electron, muon, tau Force-Carrying Particles ● Electromagnetism: photon ● Weak Interaction: W±,Z0 ● Strong Interaction: gluons Stephen J. Sekula - SMU 21/44 Let’s Scatter Something Else: W Bosons! (in a universe without the Higgs Particle) W W W W Here are some Feynman Diagrams of γ,Z ways, in the Standard Model picture, to scatter W bosons off one another. W W W W As long as electric charge, momentum, W W and other fundamental quantities are γ,Z conserved at each vertex, these are allowed. W W Stephen J. Sekula - SMU 22/44 An Aside: A Theory that Predicts the Probability of an Event Let’s say I have a mathematical theory that predicts the probability of a rainy day in Geneva, Switzerland: N 2 P(rain|Geneva)= 7 where N is the number of the day of the week (Sunday = 1). Any problems? Stephen J. Sekula - SMU 23/44 Let’s Scatter Something Else: W Bosons! (in a universe without the Higgs Particle) The W boson has a mass of MW=86⨯ mp. If one tries to predict the probability at which it scatters off of another W boson (proportional to a ), as a function of its energy (E), one finds: 0 g is a number that 2 2 : g E characterizes the degree a0= 2 of the weak interaction, 16 π M W g ~ 0.654 Discussion: thinking back to the problem with the classical Coulomb Potential, what problems arise here? Stephen J. Sekula - SMU 24/44 The Higgs Particle to the Rescue W W W W W W Now: γ,Z H 2 2 g M H a0= 2 W W W W W W 16 π M W W W W W a0 remains within its physical boundaries (corresponding to a γ,Z H total probability of not more than W W W W 100%) so long as MH < 1300mp. Stephen J. Sekula - SMU 25/44 Left-to-right: Tom Kibble, Gerald Guralnik, Carl Hagen, Francois Englert, Philip Warren Anderson Robert Brout, and Peter Higgs. 1962: Anderson noted, based on an argument from Julian Schwinger, that a classical field theory does not necessarily require zero-mass bosons. He was considering charged plasmas at the time, and speculated that a quantum field theory extension might be possible. 1964: three separate groups - Brout and Englert; Higgs; Guralnik, Hagen, and Kibble - propose mechanisms for quantum field theories in which force-carrying particles (“gauge bosons”) can acquire mass and thus allow for short- ranged forces, as inside the nucleus of the atom. Stephen J. Sekula - SMU 26/44 The Standard Model Higgs Particle The Standard Model of MASS Particle Physics (unpredicted) incorporates a Higgs CHARGE Boson whose (predicted) interactions with other SPIN particles yields their (predicted) inertial mass. Its mass is unpredicted and must be measured. Stephen J. Sekula - SMU 27/44 (Make it, or break it) it, or break (Make Boson Interactingthe Higgs with very heavy objects! particles with plenty of chanceLuckily, of makingwe have the ability to collide those. can hope to make Higgs particleswe from want to first make heavy particlesmass of so particles we with which itThe interacts, Higgs interaction so is proportional to the for scale, m scale, for proton = 0.939 GeV GeV 1 GeV ~ 0.939 = Stephen SekulaJ. - SMU Strength of the Higgs Interaction with a Particle 28 / 44 How to Make a Higgs Particle (One-at-a-Time) WHAT IS A PROTON? This picture gives you the idea: ● Three primary quarks – two up- quarks and one down-quark ● They are bound together by the “strong force,” carried by “gluons” This picture is utterly wrong otherwise. Stephen J. Sekula - SMU 30/44 WHAT IS A PROTON? This is a more honest picture, though still fairly inaccurate. At least we see now that most of the structure of the proton arises from the activity of the gluons, and the fact that virtual quark- antiquark pairs are popping into and out of existence constantly in this strong energy field.