● 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”)
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 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
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
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.
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 Interacting with the Higgs Boson (Make it, or break it) e l c i t
The Higgs interaction is proportional to the r a P
a mass of particles with which it interacts, so h t i w we want to first make heavy particles so we n o i t c
can hope to make Higgs particles from a r e t n I those. s g g i H
e h t
Luckily, we have the ability to collide f o
particles with plenty of chance of making g n e r t
very heavy objects! S
for scale, m = 0.939 GeV ~ 1 GeV proton Stephen J. Sekula - SMU 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.
Stephen J. Sekula - SMU 31/44 WHEN PROTONS COLLIDE
P(BOTH PROTONS SHATTER) = P(MAKE A HIGGS) + P(DON'T MAKE A HIGGS) What fraction of all double-proton “shatters” do we expect to contain at least 1 Higgs boson at the Large Hadron Collider (LHC)? LHC COLLISION ENERGY P(MAKE A HIGGS) (TeV) P(BOTH PROTONS SHATTER)
7 1.8 8 2.2 ⨯ 10-10 13 3.8 14 4.1 Stephen J. Sekula - SMU 32/44 The LHC: A Gluon Collider and Higgs Factory
This cartoon and the underlying Feynman Diagram demonstrate the prevalent way of making single Higgs particles at the LHC: ● Gluons are abundant (they are most of the proton) ● Gluons love to make quarks (strong coupling constant) ● The Higgs is most likely to interact with heavy things like top and bottom quarks. Every 25ns, the LHC collides two groups (“bunches”) each of 1011 protons, wherein about 60 proton-proton collisions happen. It takes about 10 billion proton-proton collisions to get 1 Higgs boson. LHC makes about 1 Higgs every 4 seconds. Stephen J. Sekula - SMU 33/44 HOW MANY HIGGS?
The LHC has two major parameters that can be tuned to produce more Higgs Bosons: ● Energy: more energy means more ability to make Higgs bosons ● Intensity: more proton-proton collisions per second per unit area, even at low energy, means more chances to make Higgs Bosons
LHC COLLISION ENERGY HIGGS BOSONS (TeV) PRODUCED 7 88,000 8 471,000 13 7,300,000
Stephen J. Sekula - SMU 34/44 How to See a Higgs Particle (without fooling yourself too much) Seeing a Higgs... the “easy” way
There are a few decay channels that were used to discover the Higgs boson, prized because they are “clean”; there are many others that have been used to measure the Higgs Bosons properties and even more yet to be observed. Decay Mode What it looks like...
Stephen J. Sekula - SMU 36/44 Using your particle detector worksheet and the image (left) as guidance, try to draw one of the following Higgs final states interacting with the ATLAS detector:
● γ γ ● e+e- e+e- ● e+e- μ+μ- ● μ+μ- μ+μ-
Stephen J. Sekula - SMU 37/44 GUESS THE HIGGS DECAY! H → γγ
Stephen J. Sekula - SMU 38/44 GUESS THE HIGGS DECAY!
H → Z1Z2 + - Z1 → e e + - Z2 → μ μ
Stephen J. Sekula - SMU 39/44 GUESS THE HIGGS DECAY!
Not all things that resemble Higgs decays will actually be Higgs decays Stephen J. Sekula - SMU 40/44 Spying a Higgs Boson: Data Analysis and Frequency of Candidates
Recipe for finding a Higgs Relativistic Invariant decaying to two photons: Mass M 2 =(E +E )2−(⃗p +⃗p )2 1)Select proton-proton γ γ 1 2 1 2 collisions with two good- quality photon candidates What is a “resonance”? 2)Use special relativity to Δ E Δ t≥ℏ/2 combine the energy and momentum of the
photons into a single P( M γ γ | M H , τ H )= parent particle k
3)Look at the invariant mass 2 2 2 2 2 (M γ γ−M H ) +M H (ℏ/ τ H ) of the parent for evidence Density of candidates per unit mass (N/m ) of a “resonance” γγ Stephen J. Sekula - SMU 41/44 THE HIGGS AND ITS IMITATORS: An Exercise with H → γγ
Photons get made all the time by lots of processes in the LHC. They needn’t (and most often do not) come from the Higgs Boson. V V e e G G / / s s t t n n e e v v E E
Higgs Boson Candidate Mass [GeV] Higgs Boson Candidate Mass [GeV]
Each of the above plots contains two numbers, representing the rest mass (invariant mass) of a pair of photons. Which plot, if any, do you think contains real H→γγ ? Stephen J. Sekula - SMU 42/44 THE HIGGS AND ITS IMITATORS V V V V e e e e G G / / G G / / s s t t s s t t n n n n e e v v e e v v E E E E
Higgs Boson CandidateCandidate Mass Mass [GeV] [GeV] HiggsHiggs Boson Boson Candidate Candidate Mass Mass [GeV] [GeV]
We see that from any single (or even very few) proton-proton collisions that otherwise meet our selection criteria, it's very hard to know on a case-by-case basis whether we have observed a Higgs Boson. Only the sum total of lots of data (tens or thousands of events) gives us the complete picture.
Stephen J. Sekula - SMU 43/44 Do You See Any New Particles?
V These are statistical artifacts - e
G “fakes” - the true distribution used /
s -ax t to make these “data” was e n e v E
Higgs Candidate Mass [GeV] You might think you've spotted some “bumps” - but are they real? It's easy to fool ourselves – the mind perceives connections that are not really there. We must employ rigorous and detailed statistical methods to sort fake and real signatures of new particles. Stephen J. Sekula - SMU 44/44 A View from the Shadows: What are the New Questions? (An Epilogue) The Higgs Boson and Fundamental Mass
● We have discovered the Higgs boson predicted in the Standard Model of Particle Physics.
● its properties are so-far consistent with the predictions of this model ● But what have we learned about the origin of mass?
● We've traded one question - “why is there mass?” - for another - “why are the Higgs interactions set as they are?”
Stephen J. Sekula - SMU 46/44 The Questions We Face Now
● Like the electric field, the Higgs field has an associated potential. What is the structure of this potential? Is it as described by the Standard Model of Particle Physics?
● Neutrinos appear to have mass (I have ignored neutrinos for nearly all of this talk). The Higgs boson is an unlikely explanation of this mass. Where does neutrino mass come from?
● Why, though there is a relative balance of matter and antimatter in the Standard Model, is the universe dominated by matter? Stephen J. Sekula - SMU 47/44 The “stuff” in the Standard Model appears to account for only 4.9% of the total energy density of the Universe. ● A non-luminous form of matter appears to dominate the dynamics of galaxies and larger cosmic structures; it seems to have left its imprint on the light left over from the beginning of the universe. What explains this matter? [“Dark Matter”] ● The expansion of the universe appears to be accelerating. What explains this? [“Dark Energy”] ● Will explanations for the above naturally include and expand upon the Standard Model? Stephen J. Sekula - SMU 48/44 A Young Physicist’s Guide to the Higgs Boson