Finding The Higgs Boson

1. FindingThe Higgs Boson A (hopefully) slightly better explained version of the events around July 4, 2012 Dr. B. Todd Huffman, Oxford UniversityDr. A. Weidberg, Oxford University

2. Explanation in two parts • Finding the Higgs (part 1) • Standard Model Higgs properties • How to Find the Boson • Bump Hunting • Special Relativity • July 4th: the data • Detector performance • CMS and ATLAS results • Stat. Confidence of Discovery

3. Explanation in two parts • Why Higgs? (part 2)(Explain why it is needed.) • Conclude

4. Standard Model Higgs(part 1) • Start with Higgs boson as a given. • Standard Model is a quantitative theory. • Predicts Probability of a Higgs boson at the LHC • Prediction is the cross-section (sh) in “barns” • What does this mean for us? Standard Model does not predictthe Higgs Mass though. B. Todd Huffman, Oxford University

5. Cross Section is an area. 10 pb = 10-35 cm2. Brightness = Lum. # Particles per cm2 per second = 1034n/(cm2s)

6. Reason for Radiation Hard Electronics Mh = 125 GeV/c2SM Higgs Production Rate = 10-35 cm2 x 1034 cm-2s-1 = 0.1 Hz or one every 10 seconds. But Hang on! spp~ 100 mbthat’s “millibarns” With L = 1034 cm-2s-1random interactions a billion times a second. (not Higgs)Beam bunches cross once every 50 ns. 50 interactions/crossing B. Todd Huffman, Oxford University

7. The LHC Once the Energy is fixed (ring size) Then the only thing we can tweak is Luminosity. This is a hard problem.

8. More Predictions:Higgs Decays gg

9. Irreducible photon processes time Photon (g) Standard Model shape:Number of photon pairs vs. energy quark B. Todd Huffman, Oxford University

10. Irreducible ZZ* processes l+ l- l- l+ Zo Zo quark Standard Model shape:Number of 4-lepton pairs vs. energy Anti-quark B. Todd Huffman, Oxford University

11. Why did we find it in the decays that are so rare? Higgs to gg → 100 per year Higgs to ZZ* → 1000 per year (but Z to ee, mm means ~5 per year)

12. One Step back: Special Relativity But what if we were moving really fast to the left? Two things happen! Decay B Explosion A At time t0 and location x0 At time t1 and location x1 B. Todd Huffman, Oxford University

13. V The order and distance depends on the speed you travel! Two things happen! Decay B Explosion A At time t1’ and location x1’ At time t0’ and location x0’ B. Todd Huffman, Oxford University

14. Special Relativity But this quantity is the same in ALL frames of reference. Time t0 ; location x0 Invariant Scalar t1 ; x1

15. Special Relativity • Momentum and Energy do this too! E2 - p2c2 = m2c4 • No momentum, P = 0, then you get E = MC2 • Throw in this fact of nature: • Energy and momentum are conserved. ALWAYS g1 g0 Mhiggs

16. Invariant Mass E2-p2c2=m2c4 (E0 + E1)2 – (P0 + P1)2c2 = M2higgsc4 e- Works for any number of particles.Works no matter how fast or slow the Higgs is moving in the lab. Does not work if they did not come from a Higgs m- m+ e+ Mhiggs B. Todd Huffman, Oxford University

17. Irreducible ZZ* processes time l+ l- l- l+ Zo Zo quark Standard Model shape:Number of 4-lepton pairs vs. energy Anti-quark B. Todd Huffman, Oxford University

18. Higgs Bump Hunting 6 months Many events have 4 lepton or two photon candidates. So just plug E and p of eachone into the formula to find their scalar invariant mass. Mostly not Higgs.The scalarformula then puts a pip randomly on this histogram If there really is a parent  ALL combinations land at Mhiggs; every time.

19. 2 years B. Todd Huffman, Oxford University

20. 15 years Glad I did not book a flight to Stockholm. Last Paper for TheoristPrior to Managing a Hedge Fund B. Todd Huffman, Oxford University

21. ATLAS • Features: • Standalone muon spectrometer (air-core toroid). • Conventional EM calorimeter (Pb/LAr). B. Todd Huffman, Oxford University

22. CMS • Some Powerful detectors (e.g. tracker). • Less demanding on muon chamber technology. B. Todd Huffman, Oxford University

23. Why The Pain is Worth It • Backgrounds • H  g g • Protons have quarks with electric charge. Two photons can result when q-qbar’s annihilate • Neutral pions decay to photons po  g g • Bad News; Quark jet could fake a photon • CMS and ATLAS detectors built to ID pions this way. • H  Z Z* then Z  e+ e- or m+ m- • Proton-Proton  Z Z* happens too • No Higgs involved • “Irreducible Background” • We must deal with Backgrounds • Careful Detector design. B. Todd Huffman, Oxford University

24. Geometric exploitspo g g Fine strip segmentation Very Useful! B. Todd Huffman, Oxford University

26. B. Todd Huffman, Oxford University

27. The Data – gg CMS ATLAS B. Todd Huffman, Oxford University

28. The Data - ZZ* Next: Detector Resolution ATLAS CMS B. Todd Huffman, Oxford University

29. Accurate Measurement Much Pain: to obtain track resolutions less than ten microns. To measure mand eenergy as accuratelyas possible B. Todd Huffman, Oxford University

30. Meaning: What if the momentum we measure is further away from the true momentum? What would happen if tracking resolution was worse? LHC 2 years B. Todd Huffman, Oxford University

31. B. Todd Huffman, Oxford University

32. Would have published earlier. B. Todd Huffman, Oxford University

33. How do we know this is real? “The Data were inconclusive, so we applied Statistics” (A quote taken from Louis Lyons’ book) B. Todd Huffman, Oxford University

34. 15 years Basic Question: What is the probability, if it IS just random, that this “signal” is just a fake? Random events can, occasionally,fake a signal. B. Todd Huffman, Oxford University

35. Discovery!And Limits ATLAS CMS

36. Why bother with a Higgs at all?(Part 2) Warning! There will be a lot more math(s). Bigger Warning! If I do this right, your brain will hurt. (But in a good way) But Fortune Favours us! Reception just down the road afterward(s) and alcohol really does help.

37. Maxwell’s Equations(review) • Note: setting speed of light and Plank’s constant equal to unity (c = = 1) • (Gauss’s law) • (Faraday – Lenz laws) • (no Magnetic mono-poles) • (Ampere’s law) B. Todd Huffman, Oxford University

38. Quantum Physics acts on Potentials • We re-cast Maxwells equations in terms of the electric potential (V) and the vector potential () • Put these into and • Result After much tedious vector algebra: Wave Equations with sources.Free-space the right sides both zero.

39. Important thing • Substitutions: • “q” = constant • E and B fields stay the same! • Reasons: • The curl of a gradient is always zero. • B-field unaltered by the vector potential-plus-gradient • “x” and “t” are independent so B. Todd Huffman, Oxford University

40. Quantum Physics(another review) • Start with Energy equation of a free particle: • Turn “E” and “p” into operators • and (or just think of it as px -id/dx) • they operate on the wave function y • the probability of finding the particle between x and x+dx is given by:

41. Time Dependent SDE • Non-relativistic Schrödinger Equation (SDE) • E = p2/2m  • the probability of finding the particle between x and x+dx is given by: • Again, what we measure, P(x,t), has a symmetry. • Y Y’ = exp(ib)Y and BOTH P(x,t) and SDE are unchanged if b = constant. B. Todd Huffman, Oxford University

42. Invariant and symmetry • Substitutions: • “q” = constant • E and B fields stay the same! • We make a change to something. • e.g. Substitute in the gradient of a function in addition to the potential • If the quantity remains unchanged we call this a “symmetry”. • And the physics is “invariant” B. Todd Huffman, Oxford University

43. Summary of things to remember! • There are hidden symmetries in these equations • Leaves E and B AND therefore Maxwell’s equations unchanged, while • Y Y’ = e(ib)Y (b=constant) • Leaves SDE, P(x,t) and Physics unchanged. B. Todd Huffman, Oxford University

44. Going from “global” to “local” invariance • Y Y’ = e(ib)Y (b=constant) • What if we make “b  b(x,t)” but try to demand the SDE “looks” the same anyway? • Why do this? • With the standard Schrodinger equation, we have no interactions! • This is really really boring. • So let’s play a theorists game • Dink around by doing the next easiest thing we might do. • b=constant  b = b(x,t) B. Todd Huffman, Oxford University

45. Going from “global” to “local” invariance • Y Y’ = e(ib)Y (b=constant) • If b  b’=b(x,t) … and after MUCH tedious algebra These do not look the same to me. Clearly NOT “locally” invariant.  Reminder:E and B and their dynamics the same B. Todd Huffman, Oxford University

46. We Can Fix this! • Replace • Replace +iqV • Then: • Looks like the free SDE but EM is built into it. • Non-relativistic equation for a charged particle in an EM field. • Invariant when: • b  b’ = b(x,t) B. Todd Huffman, Oxford University

47. Explain the whole theoretical game. • So the modified SDE • And the equations of the EM wave in free space • Are all invariant under these transformations • Non-Rel. QM theory. Idea is to seek out all kinds of these possible symmetries. Look at implications if we make the symmetry “local”, allowing it to be different at every space-time point. Does this then hang together with what is observed? What does this predict? B. Todd Huffman, Oxford University

48. “Photons” with Mass • But we have some massive “photons” like the Z0 or the W±. These would need “vector” equations too. • What do equations of “photons with mass” look like? Wave Equations in free spaceMassless photons, Relativity included

49. Proca’s EquationsPhotons with mass Oh NO!! Still leaves E and B unchanged. The equations of motion of the fields are now affected. “Massive Photons lack our symmetry” B. Todd Huffman, Oxford University

50. This is the problem! • Problem for ANY type of symmetry you want to make “local” with a massive force carrier. • I’ve shown “U(1)” • But it is true in “SU(2)” as well (and others)… • Unfortunate because SU(2) requires two charged and one neutral boson! • Weak interactions! • How to solve it? You hire Prof. Peter Higgs B. Todd Huffman, Oxford University