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Effective Field Theory and Collider Physics

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Howard Georgi Lisa Randall and Matthew Schwartz Center for the Fundamental Laws of Nature Harvard University quarks leptons u d e n c s m n b t t n gravity strong g force g h electromagnetism W/Z weak force That’s it! Perturbation theory fails for the weak force Quantum Corrections W/Z W/Z W/Z W/Z + = + W/Z W/Z W/Z Tiny correction at atomic energies E ~10-6 TeV … …but as big as leading order a LHC energies E~1 TeV Perturbation theory is restored if there is a Higgs W/Z = + Higgs - ~ 0.01 Large correction cancels The Higgs Boson restores our ability to calculate Must there be a Higgs? No. • But then quantum field theory fails above 1 TeV • We would need a new framework for particle physics •Very exciting possibility! Indirect Exclusion (95%) Combine many observables to constrain Higgs mass 45 80 144 Direct Exclusion Indirect Exclusion (95%) Combine many observables to constrain Higgs mass 114 144 RecentTevatron exclusion (160-170 GeV) Combined bound (95%) Combined bound (95%) Combine many observables to constrain Higgs mass 114 182 Geneva Two experiments can find the Higgs ATLAS CMS Boston New York 25 kilometers in diameter The LHC is being built to find the Higgs If there is no Higgs The LHC will find something better Quantum Field •supersymmetry Theory •technicolor FAILS •extra-dimensions • … no Higgs (m = 1) most exciting possibility! The LHC is a win-win situation Yes. But we hope not. Clues to new physics 1. Dark Matter 2. Unification 3. The Higgs is weird 4. Quantum Gravity Yes. But we hope not. Clues to new physics 1. Dark Matter 2. Unification 3. The Higgs is weird 4. Quantum Gravity When two seemingly different things turn out to be the same Chemistry Electromagnetism Gravity n = = p+ = = e- Quark model u + d Electroweak p u unification n d = u d p u d s u L d … H. Georgi and S. Glashow g strong force g Unified g force electromagnetism g W/Z W/Z weak force XY U(2) electroweak force • Explains why proton and electron have the same charge • Coupling constants should be the same proton decay + •astrong = 0.15 New force! p •ae = 0.04 hmm… New effects! XY •aweak = 0.02 unification at 1015 GeV e+ p predicts: proton lifetime = 1031 years limit (1974) ~ 1029 years limit (2009) ~ 5x1033 years hmm… but they are energy dependent! quarks leptons Particles and Forces higgs u d e n c s m n • What if every matter particle is unified with a force particle? b t t n • Matter and force particles must have strong g g the same charges! force g gravity • No pairings work… h electromagnetism hmm… W/Z weak force H. Georgi and S. Dimopoulos quarks leptons Particles and Forces higgs u d e n c s m n • What if every matter particle is unified 2nd n with a force particle? higgs b t t g • Matter and force particles must have h the same charges! g • No pairings work… W/Z hmm… • Invent new particles! • Superpartners must have the same mass! hmm… • Supersymmetry must be broken! gluino photino wino gravitino u d n e c s n higgsinos m t n b t squarks sleptons gluino photino wino u d e n c s m n h higgsinos b t t n u d e n nd c s m n g g W/ 2 Z higgs t higgs b t n gravitino Standard Model: Minimal Supersymmetry Standard Model: 18 particles, 30 parameters 40 particles, 140 parameters “With 4 parameters I can fit an elephant, with 5 parameters I can make him wiggle his trunk” -- Carl Friedrich Gauss Tanβ and charged Higgs mass smuon and neutralino mass gluino and squark masses mSUGRA parameterers Jets at LEP Old Way (Brute Force) New Way (Effective Field Theory) MDS, T. Becher,: JHEP: 0807.2477 (2008) World’s best measurement of a (m )= 0.1134 ± 0.0013 strong coupling constant: s Z Old value from LEP New model-independent bound on the gluino Old value: mg > 5 GeV New value: mg > 50 GeV Factor of 10 improvement! MDS, D. Kaplan PRL 101.022002 (2008) Photons at the LHC Old Way (Brute Force) New Way (Effective Field Theory) MDS and T. Becher, appears at 8pm Predictions Problems • detectable dark matter • where are the sparticles? • proton decay • m problem • calculable Higgs mass • SUSY flavor problem • B meson decays and mixings • Little hierarchy problem • new sources of CP violation • Proton decay • muon anomalous magnetic moment (g-2) • CP problems • flavor changing neutral currents • Moduli problems • collider signatures • … Solutions • Gauge/Gravity/Anomaly/Gaugino mediation • R-parity • Hidden sectors • NMSSM 1000s of models! • A terms, D terms • … If supersymmetry is relevant to TeV scale physics, Why is it hiding? Yes. But we hope not. Clues to new physics 1. Dark Matter 2. Unification 3. The Higgs is weird 4. Quantum Gravity The Higgs boson is a spinless particle. It naturally wants to clump together. It also clumps around fermions to give them mass u d (bad) e (good) Scale of gravity This makes it very heavy (1019 GeV) W/Z + but it has to be light to cancel strong W/Z scattering = small This is known as the hierarchy problem: •Why is the weak scale (100 GeV) so much smaller than the Planck scale (1019 GeV)? •Why is the Higgs so light? supersymmetry: = higgsino fermions don’t clump Electromagnetism The Higgs is just an order parameter for electroweak symmetry breaking = Magnetization is an order parameter for spin-alignment symmetry breaking Weak force Not magnetized magnetized Does a “magentization particle” exist? No. There are electrons with spins. What are the “electrons” for electroweak symmetry breaking? What if the order parameter is a fermion condensate? = Solves the Hierarchy Problem: fermions don’t clump! Weak scale (100 GeV) can be much smaller than Planck scale (1019 GeV) Weak scale is generated by pairs of virtual techniquarks and technigluons (We already know that the strong scale is generated by pairs of virtual quarks and gluons) Beautiful idea. •But it cannot explain fermion masses. u d Theories like e ?? technicolor with strong dyanmics are very hard to •Huge problem with flavor-changing neutral currents study •Ruled out by precision measurements Many more types that we don’t understand 2 Typical technicolor prediction Extra dimensions •Why not? •Must be tiny and curled up hard to visualize •Fun to think about, but not particularly well-motivated Warped Extra dimensions • Randall-Sundrum models • Related to technicolor by duality • Thousands of parameters AdS/CFT • Current bounds are strong correspondence •hard to see at the LHC Leptoquarks Little Higgs models Yes. But we hope not. Clues to new physics 1. Dark Matter 2. Unification 3. The Higgs is weird 4. Quantum Gravity Recall weak boson scattering grows growth canceled by Higgs with energy W/ Z - Graviton scattering grows with energy what cancels the growth? too h ??? strings? maybe. Sadly, there is little chance that the LHC will tell us anything about quantum gravity… …but who knows? proton electron photon Electromagnetism gravity Three particles: p+ g e- Two forces: Nuclei are made up of protons and electrons n = Heluim n + neutron p p+ = n Simple explanation of b decay (Occam’s razor) Dirac equation (1928) + e- 3He • explains spin tritum + • predicts positron e • Klein-Nishina formula •explains details of Compton scattering (g e → g e) •requires virtual positrons + e+ •Dirac (1930): Maybe proton is the positron! p = Bohr (1930) Perhaps energy only conserved Three problems on average 1. Nuclear spins and magnetic moments made no sense n neutron discovered (1932) 2. If p+ = e+, nuclei can implode e+ positron discovered Hydrogen Light (1932) 3. b decay spectrum continuous neutrino z n (theory 1930) n ( discovery 1956) Three separate solutions Needed EXPERIMENTS to find out There is a lot we don’t understand today 1. Dark Matter 2. Unification 3. The Higgs What will the LHC find? 4. Quantum Gravity •supersymmetry •technicolor •extra-dimensions • … Will we need a new principle? Quantum Field Theory FAILS no Higgs (m = ∞ ) From A&E’s “The Next Big Bang” • no Higgs The Higgs is missing QFT fails • Quantum field theory fails without a Higgs. • The Higgs is weird Higgs clumping (Hierarchy problem) • None of our “better” ideas seem to work • The LHC must either find the Higgs, find something else, or disprove quantum field theory “There are more things in Heaven and in Earth than are dreamt of in our philosophy” -- Ernest Rutherford, 1914, from Hamlet.
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