The Higgs Boson
Physics and Arts Summer Institute 2009
Derek Robins
July 28, 2009
Table of Contents
Introduction
Standard Model Summary
Standard Model Interactions (Illustration & Table)
Standard Model—Fermions, Bosons, Quarks, Leptons, Force Carriers , and
the Higgs Boson (Illustration)
Summary of Standard Model Particles and Force Interactions (Illustration)
The Higgs Boson in Context
How the Higgs Mechanism Works—Einstein Analogy
How the Higgs Mechanism Works (continued)
Why Do We Need the Higgs?
Spontaneous Symmetry Breaking
Spontaneous Symmetry Breaking Analogies
The Higgs and the Big Bang
Big Bang Timeline, “History of the Universe” (Illustration)
Predicted Mass of the Higgs Boson
Will the Higgs Boson be Detected?
Will the Higgs Boson be Detected? (continued)
Introduction
• The Higgs Boson is a theoretical elementary, subatomic particle predicted to
exist by the Standard Model of particle physics. It is the only Standard Model
(SM) particle that has not yet been observed.
• Dubbed “the God” particle by Nobel Prize winning physicist Leon Lederman,
the Higgs is thought to impart mass to all other particles in the universe.
• The Higgs particle is named after the British theorist Peter Higgs who along
with Robert Brout and François Englert theorized its existence in 1964. The
search for the Higgs remains one of the most important objective of research in
elementary particle physics today.
• Since the current way to test particle physics theories is experiments in particle
accelerators (colliders), one of the main goals of the world’s newest and most
powerful particle accelerator, the Large Hadron Collider (LHC) at CERN on the
Franco-Swiss Border, is to detect the Higgs particle.
• Experiments also continue at the Tevatron at the Fermi National Accelerator
Laboratory (Fermilab) in Batavia, Illinois, the world’s second most powerful
collider.
Standard Model Summary
• The Standard Model (SM) of particle physics describes our universe at the
most fundamental level. It is an elegant model that describes the
fundamental particles and how they interact via three of the four
fundamental forces of nature—strong nuclear, weak nuclear, and
electromagnetic—gravity is not included.
• The SM is a theory of how the universe works at the subatomic level and is
the basis for physicists’ understanding of matter.
• The Standard Model (SM) grew out of combining special relativity and
quantum mechanics which spurred on other theories over the last few
decades leading to the SM of today—the heart of particle physics theory.
• The Standard Model has successfully predicted the existence of the top
quark, the W Boson, and the Z Boson. It is strongly backed by experimental
data and has been never made false predictions.
• The only SM particle predicted but not yet detected is the Higgs Boson.
If the Higgs is found, the SM will be considered to be complete.
Summary of Standard Model Particles
and Force Interactions
The Higgs Boson in Context
• The Higgs boson is the last “missing
piece” of the Standard Model and the 5th
member of the boson family (but not a
force carrier).
• The Higgs is a hypothetical particle that
gives mass to all other particles that
normally have mass.
• The Higgs particle creates a Higgs field
that permeates spacetime.
• The Higgs particle and its corresponding
field are critical to the understanding and
validation of the SM, since the Higgs is
deemed responsible for giving particles
their mass.
• The elusive Higgs is so central to the SM
and the theory on which the whole
understanding of matter is based, if the
Higgs does not exist (is not detected), we
will not be able to explain the origin of
mass.
From: The Remote Sensing Tutorial,
Nicholas Short
How the Higgs Mechanism
Works—Einstein Analogy 
1.
1. Numerous physicists chat
quietly in a fairly crowded
room.
2. Einstein enters the room
causing a disturbance in the
field.
↓
2.
↓
3.
Followers cluster and
3.
surround Einstein as this
group of people forms a
Source: David Miller
“massive object”.
(University College London)
How the Higgs Mechanism Works (continued)
•The Higgs Mechanism operates in a way
similar to the case of Einstein in the crowded
room.
•Particles that normally would have mass
(e.g. Fermions, weak force carriers) move
through the Higgs field interacting with
Higgs particles.
•Through this interaction or disturbance
particles may acquire mass. Heavier particles
interact more with the Higgs field taking on
more mass.
•Those particles that normally do not have
mass, do not interact with the Higgs field,
and therefore do not acquire it.
An artist’s depiction of a bottom quark field
interacting with the Higgs
Source: Sized Matter-Perception of the Extreme Unseen, Jan-Henrik Andersen
Why Do We Need the Higgs?
• In order for the Standard Model to retain
its symmetry, all particles would have to
be massless. This is not possible since
through experiments we know the weak
force carriers have mass.
• Yukawa’s formula states that force carrier
mass is inversely proportional to force
range. In this way, we can also deduce
that weak force carriers have mass.
(Because of the nature of the strong force,
it is an exception to this rule).
Source: CERN
• The Higgs mechanism was originally
introduced to allow the W and Z bosons
to have mass. Physicists found to their
delight that this was a way to give
fermions mass as well.
• The current Standard Model provides no
explanation of how some particles come
to have mass.
Source: CDF, Fermilab
Spontaneous Symmetry Breaking
• The SM (based on the Lagrangian)
must be symmetric under gauge
transformations.
• Without the Higgs mechanism, the
SM remains symmetric only if
mediators remain massless and
produces nonsense results if weak
force mediators have mass.
• Developers of the Higgs
mechanism used spontaneous
symmetry breaking to introduce
mass while retaining the SM’s
overall symmetry.
Higgs field exhibits gauge and rotational symmetry
Source: Time Travel Research Center-Turkey/Denizli
• The SM’s symmetry is broken only
at a single point.
Spontaneous Symmetry Breaking Analogies
Dinner table analogy—
•Glasses of water are placed between each plate at
a circular dinner table. The arrangement is
considered symmetric.
• The first person chooses a glass to take on their
right or left. When that glass is chosen
spontaneously, symmetry is broken, and everyone
else at the table is forced to choose that side.
Mexican hat analogy—
•Set a ball on the tip of a Mexican Hat— the ball
decides “spontaneously” where to fall. There is no
influence on the ball’s path of choice.
•Here the trough of the sombrero represents Higgs
field lowest energy states. The chosen field is
spontaneously chosen, breaking the symmetry.
•In the SM, the Higgs is introduced so that the
physics and symmetry of the Standard model is
retained.
Source: Madras College
Mathematics Department
The Higgs and the Big Bang
• At the instant of the Big Bang, the
universe was comprised of particles
of pure energy.
• Milliseconds after the event, the
universe cooled and the Higgs field
developed.
• Particles began to acquire mass as
they cooled, slowed down and moved
through the newly created Higgs
field. Particles lost kinetic energy and
gained mass (E=mc2).
• Elementary particles developed and
the Higgs field continued to permeate
spacetime.
• In unification theory, physicists look
to the big bang for evidence of a
single superforce. Each of the four
fundamental forces is thought of as a
manifestation of a single force at low
energies.
• Particle accelerators attempt to
recreate the original conditions of the
Big Bang.
Source: Williams College Astronomy Department
Source: CERN
Predicted Mass of the Higgs Boson
• The SM predicts a Higgs mass of
less than 1 TeV.
• Fermilab searches for a light Higgs
(115-180 GeV).
• The LHC will search for a heavier
Higgs (180+ GeV).
• Fermilab has acquired enough data
to rule out a Higgs mass of 160-170
GeV.
• With more data, Fermilab may be
able to eventually rule out entire
regions of theoretically possible
Higgs masses.
Source: CDF, Fermilab
Will the Higgs Boson be Detected?
• The cost to build the Large Hadron Collider was up to $10
billion.
• There are thousands of scientists working at CERN and around
the world, and the ongoing costs of the project are
significant—it uses as much electricity as the City of Geneva.
• Because of the historical success of the Standard Model in its
predictions thus far and the power of the LHC, many particle
physicists think the Higgs will be detected at the LHC.
• Yet there is no guarantee the Higgs will be found.
• Some physicists, Stephen Hawking among them, think the
Higgs will not be found.
Will the Higgs Boson be Detected? (continued)
• The LHC can accelerate hadrons to a
maximum energy of 14 TeV (7 times greater
than Fermilab’s Tevatron).
• If the Higgs mass is less than about 800 GeV,
it is likely that it would be detected at the
LHC.
• However, no experimental data to date hints
at the existence of the Higgs and finding the
Higgs at the LHC (or Tevatron) is extremely
difficult.
• If the Higgs is not found, physicists will have
to develop new models to explain the
fundamentals of our universe.
• Whatever the outcome, the probability of
discovering something new is extremely
high.
• Either the Higgs will be found or new
physics (e.g. extra dimensions or
supersymmetry) should come out of the LHC
experiments.
Source: CERN
The Search for the Higgs Particle
at Hadron Colliders
An Independent Research Study
Physics and Arts Summer Institute 2009
Derek Robins
July 29, 2009
Table of Contents
Introduction
Particle Accelerators
Cross Section of a Particle Detector
The Tevatron at Fermilab
Large Hadron Collider (LHC) From Above
The Atlas Detector at the LHC
Feynman Rules and Feynman Diagrams
Feynman Rules and Feynman Diagrams (continued)
MadGraph/MadEvent
Graphical and Numerical Output from MadGraph
for Process e+e-  mu+muThe Higgs Search
Higgs Modeling with MadGraph
Results: MH=115 GeV, 1.96 TeV
Results: MH=150 GeV, 1.96 TeV
Results: MH=200 GeV, 1.96 TeV, 14 TeV
About the Results
Final Thoughts and Next Steps
Introduction
• An Independent Research Study was undertaken with Professor Doreen
Wackeroth, Department of Physics, University at Buffalo over a nine
month period, September 2008 - May 2009.
• The majority of time on the project was spent learning key particle physics
concepts at the advanced undergraduate and graduate school levels,
modeling particle collisions at particle accelerators, and comparing
theoretical data to real collision data from the Fermi National Accelerator
Laboratory in Batavia, Illinois (Fermilab).
• Key sources of information were articles from physics journals, particle
physics textbooks and presentations, one on one tutorials with Dr.
Wackeroth, and data from Fermilab.
• Modeling ways in which the Higgs Boson can be produced at particle
accelerators was the core focus of the research.
Particle Accelerators
• Accelerate particles to near light speed and then collide them together. The
Tevatron collides protons and antiprotons whereas the LHC collides protons
and protons.
• Attempt to recreate the conditions of the universe fractions of a second after
the big bang.
• Use supercooled magnets (near absolute zero) to steer and accelerate particles
around a tunnel
• Particles collide, annihilate into energy, and create new particles (E=mc2).
• Particle detectors detect different particles created in a collision by detecting
where particles travel after emerging from the collision site.
• The two largest and most powerful accelerators in the world are: the Tevatron
at the Fermi National Laboratory (Fermilab) in Batavia, Illinois and the Large
Hadron Collider (LHC) at CERN on the Franco-Swiss border, the world’s
most powerful collider.
Cross Section of a Particle Detector
Particle Data Group, Lawrence Berkeley National Laboratory
The Tevatron at Fermilab
• The Tevatron at Fermi National Accelerator Laboratory (Fermilab), located
in Batavia, Illinois near Chicago, began operation in 1983. It is the second
most powerful particle accelerator in the world (1.96 TeV) behind the
Large Hadron Collider (14 TeV).
• The bottom quark (1977) and top quark (1995) were found at Fermilab.
• Since the Tevatron began running 26 years ago, physicists at Fermilab have
been searching for the Higgs Boson.
• The Tevatron recently began to acquire enough data to start closing in on
the mass of the Higgs particle.
• The Tevatron will likely be running through 2010 and has a chance at
finding the Higgs or narrowing down its likely mass range before the LHC.
Large Hadron Collider (LHC) From Above
•Cost: up to $10 Billion
•17 Miles in circumference
•Proton-proton collider
•Biggest science project
ever constructed
•14 TeV of Energy
(7x that of the Tevatron)
•40 million collisions per
second
•Most complex machine
ever built
The Atlas Detector at the LHC
LHC Alive! Pheno 2009 Symposium, WI, USA
Feynman Rules and Feynman Diagrams
• A set of mathematical rules developed by the eminent physicist and Nobel
Prize winner Richard Feynman that describe and determine the results of a
particle collision
• The rules are derived from the Lagrangian of a particle system and are a
way of expressing movements and interactions of a particle in the language
of mathematics.
• Feynman Diagrams are pictorial representations of particle collisions and
can be constructed from the Feynman rules.
1) The above
expression
describes how a
particle with
mass m
propagates in
space-time.
2) This part describes
the interaction of a
particle with the
electromagnetic force.
The strength of the
force is determined by
the electric charge (q).
Feynman Rules and Feynman Diagrams (continued)
•
An example of a collision event that
could take place in an accelerator can
be written as: e+ e-  μ+ μ-
•
This interaction is mediated by the
electromagnetic or weak nuclear force
(Z).
•
Using the mathematical Feynman
rules, the cross section of a particular
process can be calculated—the
probability that it will occur.
•
•
N=Lσ relates the number of events
produced to the luminosity and cross
section for a given event.
N= number of events, L=luminosity—
intensity and narrowness of a particle
beam in an accelerator, σ =cross
section measured in barns.
•Theoretical particle physicists use the
Feynman rules and the Standard Model to
predict what an experimentalist might see
at an actual particle accelerator.
•Scientists look for deviations between
theory predictions and observations at
accelerators. Deviations indicate possible
“new physics”. To this day, the Standard
Model has never made an incorrect
prediction.
MadGraph/MadEvent
• MadGraph/MadEvent models particle collisions that take place in particle
accelerators. It is a professional research software tool that generates
collision data based on the Standard Model. It calculates cross sections and
produces a number of histograms of collisions.
•
An example of input of a common process is: e+e-mu+mu
• All possible Feynman diagrams are produced as well a number of
distributions including invariant mass, momentum, and angular
distributions.
• Cross section (probability that the event occurs) calculations are displayed.
• Feynman diagrams show that e+e-mu+mu can be either mediated by a Z
boson (Z) or a photon (A).
• Angular distributions show that when e+ and e- collide, most muons
emerge at a low angle relative to the beam line.
Graphical and Numerical Output from MadGraph
for Process e+e-  mu+mu-
s =29 GeV
Cross section=28.703 pb
The Higgs Search
•
The production of a Higgs particle, if it exists,
is an extremely rare event. We estimate a
Higgs is produced every few trillion collisions.
•
Using the equation N=L σ, a luminosity of 2.4
fb-1 and an average cross section (probability)
of .0828 fb, we are left with less than 1 event.
•
Higgs “background noise” (process where final
state particles are identical but no Higgs
mediator is involved) is problematic in
attempting to detect a Higgs.
•
Background noise is greater at the LHC than at
the Tevatron—more energy and gluon
interactions. The LHC is best suited to find a
heavier Higgs (MH>180 GeV).
•
Fermilab is better suited for finding a light
Higgs (MH=115-180 GeV)—background
noise, PDFs.
•
The LHC has enough energy to find the
Higgs. If the Higgs exists, it should be
detected there.
Higgs Modeling with MadGraph
• In the exploration of the process: pp>mu+mu- b bbar using MadGraph, the
Z boson and Higgs are mediators for this process. This is one of the more
common Higgs processes that might appear at Fermilab’s Tevatron.
• The objective is to compare the Higgs signals by adjusting the mass of the
Higgs (evidenced in cross sections and histograms produced by
MadEvent).
• The results focused on Higgs production at Tevatron and some results for
the LHC as well.
Results: MH=115 GeV, 1.96 TeV
Higgs—No Higgs 115
Cross Section (femtobarn)
0.8
0.7
0.6
0.5
0.4
Series1
0.3
0.2
0.1
0
-0.1 80
100
120
Invariant Mass (GeV)
140
160
Results: MH=150 GeV, 1.96 TeV
Results: MH=200 GeV, 1.96 TeV, 14 TeV
F-H
F-NH
LHC
About the Results
• At Fermilab, an increase in the Higgs mass produces a Higgs signal that is
increasingly difficult to see. The Higgs peak is very pronounced at 115
GeV but very difficult to see at 200 GeV.
• With a weaker or flatter Higgs signal, subtraction of background noise is
necessary to determine if a Higgs is being produced.
•
The LHC results show more background noise due to gluon interactions
(addition of the strong force), W interactions, and higher energy.
• The Z Higgs process (used in this study) appears to have a greater signal
at the Tevatron compared to that of the LHC, especially for lower Higgs
masses.
Final Thoughts and Next Steps
•Explore other Higgs processes such as W decays and gluon interactions at LHC
•Combine results of multiple Higgs processes and extract Higgs signal
•Finding the Higgs at Fermilab is unlikely, but there is a chance. There is a possibility
of ruling out the “light” range predicted by the Standard Model (110-180 GeV).
•In March, Fermilab excluded the160-170 GeV Higgs mass range.
•The appearance of the Higgs would be an extremely rare event. If it exists, it should
be seen at the LHC once it acquires enough data.
•If the Higgs exists, our understanding of the fundamental forces of nature and
Standard Model is complete. If not, there is more to discover about the physical laws
of the universe!