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The Higgs Boson

Physics and Arts Summer Institute 2009

Derek Robins

July 28, 2009

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Table of Contents

IntroductionStandard Model Summary

Standard Model Interactions (Illustration & Table)

Standard ModelFermions, Bosons, Quarks, Leptons, Force Carriers , and

the Higgs Boson (Illustration)

Summary of Standard Model Particles and Force Interactions (Illustration)

The Higgs Boson in ContextHow the Higgs Mechanism WorksEinstein 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 BangBig 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)

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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 alongwith Robert Brout and Franois Englert theorized its existence in 1964. Thesearch for the Higgs remains one of the most important objective of research inelementary 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 worlds newest and mostpowerful particle accelerator, the Large Hadron Collider (LHC) at CERN on theFranco-Swiss Border, is to detect the Higgs particle.

Experiments also continue at the Tevatron at the Fermi National AcceleratorLaboratory (Fermilab) in Batavia, Illinois, the worlds second most powerful

collider.

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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 thefundamental particles and how they interact via three of the fourfundamental forces of naturestrong nuclear, weak nuclear, andelectromagneticgravity 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 andquantum mechanics which spurred on other theories over the last fewdecades leading to the SM of todaythe heart of particle physics theory.

The Standard Model has successfully predicted the existence of the topquark, the W Boson, and the Z Boson. It is strongly backed by experimentaldata 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.

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Summary of Standard Model Particlesand Force Interactions

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The Higgs Boson in Context

The Higgs boson is the last missing

piece of the Standard Model and the 5thmember of the boson family (but not aforce carrier).

The Higgs is a hypothetical particle thatgives mass to all other particles thatnormally have mass.

The Higgs particle creates a Higgs fieldthat permeates spacetime.

The Higgs particle and its correspondingfield are critical to the understanding andvalidation of the SM, since the Higgs isdeemed responsible for giving particlestheir mass.

The elusive Higgs is so central to the SMand the theory on which the wholeunderstanding of matter is based, if theHiggs does not exist (is not detected), wewill not be able to explain the origin ofmass.

From: The Remote Sensing Tutorial,Nicholas Short

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How the Higgs Mechanism

WorksEinstein Analogy

1. Numerous physicists chatquietly in a fairly crowded

room.

2. Einstein enters the room

causing a disturbance in the

field.

3. Followers cluster and

surround Einstein as this

group of people forms a

massive object.

1.

2.

3.

Source: David Miller

(University College London)

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How the Higgs Mechanism Works (continued)The Higgs Mechanism operates in a way

similar to the case of Einstein in the crowdedroom.

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 artists depiction of a bottom quark field

interacting with the HiggsSource: Sized Matter-Perception of the Extreme Unseen, Jan-Henrik Andersen

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Why Do We Need the Higgs?

In order for the Standard Model to retainits symmetry, all particles would have to

be massless. This is not possible sincethrough experiments we know the weakforce carriers have mass.

Yukawas formula states that force carriermass is inversely proportional to force

range. In this way, we can also deducethat weak force carriers have mass.(Because of the nature of the strong force,it is an exception to this rule).

The Higgs mechanism was originally

introduced to allow the W and Z bosonsto have mass. Physicists found to theirdelight that this was a way to givefermions mass as well.

The current Standard Model provides no

explanation of how some particles cometo have mass.

Source: CERN

Source: CDF, Fermilab

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Spontaneous Symmetry Breaking The SM (based on the Lagrangian)

must be symmetric under gauge

transformations.

Without the Higgs mechanism, theSM remains symmetric only ifmediators remain massless and

produces nonsense results if weakforce mediators have mass.

Developers of the Higgsmechanism used spontaneous

symmetry breaking to introducemass while retaining the SMsoverall symmetry.

The SMs symmetry is broken only

at a single point.

Higgs field exhibits gauge and rotational symmetry

Source: Time Travel Research Center-Turkey/Denizli

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Spontaneous Symmetry Breaking AnalogiesDinner table analogy

Glasses of water are placed between each plate ata 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 Hatthe ball

decides spontaneously where to fall. There is no

influence on the balls 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

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The Higgs and the Big Bang At the instant of the Big Bang, the

universe was comprised of particlesof pure energy.

Milliseconds after the event, theuniverse cooled and the Higgs fielddeveloped.

Particles began to acquire mass asthey cooled, slowed down and movedthrough the newly created Higgs

field. Particles lost kinetic energy andgained mass (E=mc2).

Elementary particles developed andthe Higgs field continued to permeatespacetime.

In unification theory, physicists look

to the big bang for evidence of asingle superforce. Each of the fourfundamental forces is thought of as amanifestation of a single force at lowenergies.

Particle accelerators attempt to

recreate the original conditions of theBig Bang.

Source: Williams College Astronomy Department

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Source: CERN

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Predicted Mass of the Higgs Boson

The SM predicts a Higgs mass ofless than 1 TeV.

Fermilab searches for a light Higgs(115-180 GeV).

The LHC will search for a heavierHiggs (180+ GeV).

Fermilab has acquired enough datato rule out a Higgs mass of 160-170GeV.

With more data, Fermilab may beable to eventually rule out entireregions of theoretically possibleHiggs masses.

Source: CDF, Fermilab

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Will the Higgs Boson be Detected?

The cost to build the Large Hadron Collider was up to $10billion.

There are thousands of scientists working at CERN and aroundthe world, and the ongoing costs of the project are

significantit uses as much electricity as the City of Geneva.

Because of the historical success of the Standard Model in itspredictions thus far and the power of the LHC, many particlephysicists 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 theHiggs will not be found.

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Will the Higgs Boson be Detected? (continued)

The LHC can accelerate hadrons to a

maximum energy of 14 TeV (7 times greaterthan Fermilabs Tevatron).

If the Higgs mass is less than about 800 GeV,it is likely that it would be detected at theLHC.

However, no experimental data to date hintsat the existence of the Higgs and finding theHiggs at the LHC (or Tevatron) is extremelydifficult.

If the Higgs is not found, physicists will haveto develop new models to explain thefundamentals of our universe.

Whatever the outcome, the probability ofdiscovering something new is extremelyhigh.

Either the Higgs will be found or newphysics (e.g. extra dimensions orsupersymmetry) should come out of the LHC

experiments.

Source: CERN

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The Search for the Higgs Particle

at Hadron Colliders

An Independent Research Study

Physics and Arts Summer Institute 2009

Derek Robins

July 29, 2009

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Table of Contents

Introduction

Particle AcceleratorsCross 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+mu-

The Higgs Search

Higgs Modeling with MadGraphResults: 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

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Introduction

An Independent Research Study was undertaken with Professor DoreenWackeroth, Department of Physics, University at Buffalo over a ninemonth period, September 2008 - May 2009.

The majority of time on the project was spent learning key particle physicsconcepts at the advanced undergraduate and graduate school levels,

modeling particle collisions at particle accelerators, and comparingtheoretical data to real collision data from the Fermi National AcceleratorLaboratory in Batavia, Illinois (Fermilab).

Key sources of information were articles from physics journals, particlephysics 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 particleaccelerators was the core focus of the research.

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Particle Accelerators Accelerate particles to near light speed and then collide them together. The

Tevatron collides protons and antiprotons whereas the LHC collides protonsand protons.

Attempt to recreate the conditions of the universe fractions of a second afterthe big bang.

Use supercooled magnets (near absolute zero) to steer and accelerate particlesaround a tunnel

Particles collide, annihilate into energy, and create new particles (E=mc2).

Particle detectors detect different particles created in a collision by detectingwhere particles travel after emerging from the collision site.

The two largest and most powerful accelerators in the world are: the Tevatronat the Fermi National Laboratory (Fermilab) in Batavia, Illinois and the LargeHadron Collider (LHC) at CERN on the Franco-Swiss border, the worldsmost powerful collider.

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Cross Section of a Particle Detector

Particle Data Group, Lawrence Berkeley National Laboratory

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The Tevatron at Fermilab

The Tevatron at Fermi National Accelerator Laboratory (Fermilab), locatedin Batavia, Illinois near Chicago, began operation in 1983. It is the secondmost powerful particle accelerator in the world (1.96 TeV) behind theLarge 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 havebeen 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 atfinding the Higgs or narrowing down its likely mass range before the LHC.

L H d C llid (LHC) F Ab

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Large Hadron Collider (LHC) From Above

Cost: up to $10 Billion

Proton-proton collider

14 TeV of Energy

(7x that of the Tevatron)

40 million collisions per

second

17 Miles in circumference

Biggest science project

ever constructed

Most complex machine

ever built

Th Atl D t t t th LHC

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The Atlas Detector at the LHC

LHC Alive! Pheno 2009 Symposium, WI, USA

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Feynman Rules and Feynman Diagrams

A set of mathematical rules developed by the eminent physicist and NobelPrize 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 away of expressing movements and interactions of a particle in the languageof mathematics.

Feynman Diagrams are pictorial representations of particle collisions andcan be constructed from the Feynman rules.

1) The above

expression

describes how a

particle with

mass m

propagates inspace-time.

2) This part describes

the interaction of a

particle with the

electromagnetic force.

The strength of the

force is determined bythe electric charge (q).

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Feynman Rules and Feynman Diagrams (continued)

An example of a collision event that

could take place in an accelerator canbe written as: e+ e-+ -

This interaction is mediated by theelectromagnetic or weak nuclear force(Z).

Using the mathematical Feynmanrules, the cross section of a particularprocess can be calculatedtheprobability that it will occur.

N=L relates the number of events

produced to the luminosity and crosssection for a given event.

N= number of events, L=luminosityintensity and narrowness of a particlebeam in an accelerator, =crosssection 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.

M dG h/M dE t

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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 ofdistributions 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.

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Graphical and Numerical Output from MadGraph

for Process e+e- mu+mu-

=29 GeVs Cross section=28.703 pb

The Higgs Search

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The Higgs Search The production of a Higgs particle, if it exists,

is an extremely rare event. We estimate aHiggs is produced every few trillion collisions.

Using the equation N=L , a luminosity of 2.4fb-1 and an average cross section (probability)of .0828 fb, we are left with less than 1 event.

Higgs background noise (process where finalstate particles are identical but no Higgs

mediator is involved) is problematic inattempting to detect a Higgs.

Background noise is greater at the LHC than atthe Tevatronmore energy and gluoninteractions. The LHC is best suited to find aheavier Higgs (MH>180 GeV).

Fermilab is better suited for finding a lightHiggs (MH=115-180 GeV)backgroundnoise, PDFs.

The LHC has enough energy to find theHiggs. If the Higgs exists, it should bedetected there.

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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 morecommon Higgs processes that might appear at Fermilabs 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: M =115 GeV 1 96 TeV

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HiggsNo Higgs 115

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

80 100 120 140 160

Invariant Mass (GeV)

CrossSection(femtobarn)

Series1

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Results: M =200 GeV 1 96 TeV 14 TeV

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Results: MH=200 GeV, 1.96 TeV, 14 TeV

LHC

F-H

F-NH

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About the Results

At Fermilab, an increase in the Higgs mass produces a Higgs signal that isincreasingly difficult to see. The Higgs peak is very pronounced at 115GeV but very difficult to see at 200 GeV.

With a weaker or flatter Higgs signal, subtraction of background noise isnecessary 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 signalat the Tevatron compared to that of the LHC, especially for lower Higgsmasses.

Final Thoughts and Next Steps

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Final Thoughts and Next StepsExplore 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 andStandard Model is complete. If not, there is more to discover about the physical laws

of the universe!

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Higgs Pasi2009