Does Nature respect (gauge) Symmetry? DISCOVERY and beyond: What ’ s next in Higgs physics

1. Does Nature respect (gauge) Symmetry?DISCOVERY and beyond:What’s next in Higgs physics Regina Demina (University of Rochester)

2. Phase of the wave function • First lecture on quantum mechanics – introduce wave function, but only define (Wave function Y)2dV=probability to find particle in volume dV. • While probability is a real number, wave function is a complex number. It has a phase. • When two matter waves meet we add wave functions, not probabilities! Interference can be observed phase is important!

3. Gauge invariance = non-observability of the phase • Gauge invariance - Fundamental symmetry of nature, so Langrangian must be invariant under gauge (phase) transformation: • According to Noether’s theorem, symmetry (==non-observability) leads to conserving quantity • If a is the same everywhere – global gauge invariance (leads to e.g. baryon number conservation) For some reason Nature goes to great length to hide the phase of the wave function from us Preserve gauge invariance

4. Local Gauge invariance • Local gauge invariance: a(x) –– phase depends on 4 dimensional space-time coordinate x • Demanding local gauge invariance leads to interactions via gauge fields • E.g. U(1) gauge group, leads to EM interactions and charge conservation

5. Electro-weak interactions Transformation group Conserved quantity Gauge field Group properties Fermion masses U(1) – QED Q (scalar) electric charge EM interaction Photons M(g)=0 Abelian (commutative) group – photons do not interact with each other added by hand without breaking gauge invariance SU(2)L –Weak T (doublet) weak isospin Weak interactions W-boson M(W)=80GeV Z-boson M(Z)=91 GeV Non-Abelian group – W and Z do interact with each other cannot be added by hand without breaking gauge invariance

6. Electroweak symmetry breakingF. Englert and R. Brout, Phys. Rev. Lett. 13 (1964) 321P.W. Higgs,, Phys. Rev. Lett. 13(1964) 508, G. S. Guralnik, C. R. Hagen, and T.W. B. Kibble, Phys. Rev. Lett. 13 (1964) 585 Problem #1: W and Z boson masses violate SU(2)L gauge invariance Solution: Postulate #1 There exists a scalar complex field doubletf • Mexican hat (bottle’s bottom) potential • The Universe chose to roll into a minimum at • Non-zero v generates masses for W and Z-bosons • Absorb 3/ 4 degrees of freedom • Given W mass (muon decay rate) v is constrained to be 246 GeV • Predict ratio between W and Z masses - verified in experiment • One remaining d.o.f. – H (aka Higgs) boson (s=0, P=+)

7. Expand f near its minimum Lagrangian (g2v2/2)AmAm – mass term for gauge bosons lv2h2– mass term for the scalar boson itself h3,h4 –self interaction terms hAA, h2AA – interaction with gauge fields terms This is what we were after Byproducts Strength of these terms is predicted given l (MH) H Boson v constrained by MW l- free parameter Higgs mass is not predicted

8. Higgs mechanism of fermion mass generation Problem #2: fermion masses violate SU(2)L gauge invariance Solution: Postulate #2 • Yukawa-like couplings to fermions – generate fermion masses in a gauge invariant way through interaction with Higgs field • This mechanism does not reduce the number of free parameters in the model, masses are traded for the strength of interaction with the Higgs field (gf)

9. Testable predictions • Existence of a true scalar boson (s=0, P=+1) • Find the resonance • measure its spin, parity • Couplings to gauge bosons • Probing custodial symmetry (between W and Z-bosons) – one of best motivated symmetries given that the new state is responsible for breaking the EW symmetry • Couplings to fermions • New state can be responsible for EW symmetry breaking but NOT for generation of fermionic masses – fermiophobic Higgs • Self coupling • h3,h4 –self interaction termsarise from the same assumption as couplings to gauge fields. Interesting to test their absolute and relative strength • Require large statistics to observe

10. Higgs Production @ LHC Gluon Fusion - dominant process Vector Boson Fusion 20% of gg @ 120GeV Associated Production W or Z (1-10% of gg) Associated Production ttbar or bbbar (1-5% of gg) 4 production mechanism key to measure H-boson parameters

11. LHC at CERN Alps • Large Hadron Collider located in Europe (France and Switzerland) • Circumference 27 km; • 7TeV(2010-2011)8TeV (now)14 Tev(2014) • LHC has uncovered the mechanism behind mass - 2012 • Discovery of a particle that might be known as Higgs boson Lecture I

12. Apparatus: LHC Lecture I

13. Apparatus: CMS Lecture I

14. 4 July, 2012 F. Englert, P.W. Higgs, C. R. Hagen, G. S. Guralnik J. Incandela

15. Higgs to two photons CMS collaboration: Phys. Lett. B 716 (2012) 30-61Atlas collaboration: Phys. Lett. B 716 (2012) 1-29

16. Di-photon spectrum Lecture XII

17. HZZ*4l Lecture XII

18. HZZ*4l Lecture XII

19. Combined p-value Lecture XII

20. Projected signal Current status: signal observed in ZZ, gg and WW modes There is some evidence (Tevatron) for bbbar coupling Projected signal by the end of the run

21. Observables • the framework to probe the Higgs couplings issued by the “low mass” LHCXS WG and endorsed by both CMS and ATLAS: arXiv:1209.0040 • Overall signal strength m

22. Disentangling coupling from production and decay VBF production – sensitive to vector boson couplings ggH – sensitive to quark loops; Hgg – fermion+W loop HWW, ZZ – vector boson coupling at decay

23. Disentangling coupling from production and decay kVkF - scale vector and fermion coupling Kg(kV, kF) – coupling to g, depends on W and fermion loops (Hgg) ggH – sensitive to quark loops; HWW, ZZ – vector boson coupling No direct Higgs to fermion couplings observed yet, limits on Htt, Hbb

24. Current status: Testing custodial symmetry • lWZ: ratio of scale factors for W and Z • The measurement of the HWW/HZZ ratio is mostly driven by the ratio of the Higgs couplings to WW and ZZ, which is protected by custodial symmetry • Combination of “inclusive” WW and ZZ yields gives Rww/zz=0.9+1.1-0.6

25. More tests to come • llq: ratio of scale factors for leptons and quarks • kV left floating in the fit • ldu: ratio of scale factors for down and up type of fermions • kV left floating in the fit • kg- kg: contour of loop scale factors • BRInv,Undet: same as kg- kg but with a scale factor in the total width accounting for invisible or undetectable decay modes

26. spin measurementarXiv:1208.4018 • Xgg excludes s=1 option (Landau-1948, Yang -1950) • XZZ4l system is described by 5 non-trivial angles Different scenarios result in distinct angular distributions 2+m 0- 2+h 0+m 0+m 2+h 2+m

27. Comparing spin-parity hypotheses • Matrix Element Likelihood Analysis (MELA) allows for optimal separation of different sP hypotheses XZZ4l 0+(SM) vs 0- hypothesis Expected significance of hypotheses separation based on 35 fb-1

28. MELA – was already used to separate signal from bg SM H(125 GeV) Bg:ZZ Data w.r.t 126 GeV Higgs Expectation

29. Summary • Observed narrow resonance at 125.3+-0.6 GeV couples to weak gauge bosons, hence it is potentially responsible for the EW symmetry breaking • To verify this hypothesis it is necessary to show that its properties are consistent with the predictions: • Spin=0, Parity =+ • An angular based analysis is developed that has a potential to exclude pseudoscalar and tensor hypotheses based on 35 fb-1 • The framework is developed to independently measure • Vector and fermion couplings • W and Z boson couplings • Lepton and quark couplings