The Higgs Boson

1. The Higgs Boson Physics and Arts Summer Institute 2009 Derek Robins July 28, 2009

2. 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)

3. 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.

4. 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.

7. Summary of Standard Model Particles and Force Interactions

8. 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

9. How the Higgs Mechanism Works—Einstein Analogy  Numerous physicists chat quietly in a fairly crowded room. 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)

10. 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

11. 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). 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: CERN Source: CDF, Fermilab

12. 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. The SM’s symmetry is broken only at a single point. Higgs field exhibits gauge and rotational symmetry Source: Time Travel Research Center-Turkey/Denizli 

13. 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

14. 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

15. Big Bang Timeline Source: CERN

16. 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

17. 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.

18. 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

19. The Search for the Higgs Particle at Hadron Colliders An Independent Research Study Physics and Arts Summer Institute 2009 Derek Robins July 29, 2009

20. 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+mu- The 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

21. 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.

22. 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.

23. Cross Section of a Particle Detector Particle Data Group, Lawrence Berkeley National Laboratory

24. 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.

25. 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

26. The Atlas Detector at the LHC LHC Alive! Pheno 2009 Symposium, WI, USA

27. 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).

28. 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.

29. 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.

30. Graphical and Numerical Output from MadGraphfor Process e+e-  mu+mu- Cross section=28.703 pb =29 GeV

31. 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.

32. 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.

33. Results: MH=115 GeV, 1.96 TeV

34. Results: MH=150 GeV, 1.96 TeV

35. Results: MH=200 GeV, 1.96 TeV, 14 TeV F-H F-NH LHC

36. 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.

37. 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!