Outline – III, The Higgs Boson

1. Outline – III, The Higgs Boson • W-W Scattering • Vacuum Fields • Higgs Mass • W vs. Top Mass • Direct Searches @ LEP • Upper Limits • Higgs Couplings to Bosons and Fermions – Decays and Production • Vector Boson Fusion • Higgs Quantum Numbers • Higgs Pairs?

2. W+W Scattering, sans Higgs The EW interactions diverge and thus violate unitarity. One mechanism proposed to solve this problem is to postulate the “Higgs boson” which cancels the divergences. It also has a vacuum expectation value for the field which is ~ 1/ ~ 300 GeV

3. Heavy Higgs and EW Cross Section In COMPHEP let the Higgs mass get large. Cross section diverges. As before, H mass should be < 1 TeV

4. Higgs Potential, Self Coupling Postulate forces described by a potential with 2 unknown parameters. Postulate a non-zero vacuum expectation value for the field and an excitation of the field, The resulting potential has a ‘cosmological term a Higgs mass term No prediction in the SM for the Higgs mass. There are also triplet plus quartic Higgs particle couplings . Lagrangian density is dimension [M4] So [μ] = M and [λ] = 1

5. How the W and Z get their Mass • Covariant derivative contains EW gauge fields W,Z. Suppose an additional scaler field  exists and has a vacuum expectation value. Quartic couplings give mass to the W and Z, as required by the data [ V(r) ~e(exp(-r/)/r) ] - weak at large r, strength ~e at small r]. Add gauge fields and look at mass terms Photon, W and Z masses are induced by vev and predicted numerically

6. G and Decay Widths Numerical value of G 2 body EW 3 body EW

7. Numerical W, Z Mass Prediction • The masses for the W and Z are specified by the coupling constants. G comes from beta decays or muon decay.

8. Extend to Fermion Masses Free Dirac density Yukawa interaction The Higgs coupling to W,Z are fixed by the gauge symmetry. For fermions we exchange one mass parameter for an unknown coupling constant. Still, it is a compact choice. Except for the top quark these couplings are weak and are proportional to the fermion mass.

9. W Mass Corrections Due to Top, Higgs Klein-Gordon Dirac W mass shift due to top (m) and Higgs (M). Note quadratic (strong) divergence due to fermion loop.

10. 2 - What is MH and How Do We Measure It? • The Higgs mass is a free parameter in the current “Standard Model” (SM). • Precision data taken on the Z resonance constrains the Higgs mass, along with precision top and W masses. Lowest order SM predicts that MZ = MW/cosW.. Radiative corrections due to loops. • Note the opposite signs of contributions to mass from fermion and boson loops. Crucial for SUSY and radiative stability. b t H W W W W W

11. LEP,CDF D0 Data Indicate Light Higgs – 2011 and Beyond b W t W W W H W Quantum mechanics: traces of higher mass states are seen in radiative corrections due to virtual quantum loops, e.g. Lamb shift in atomic spectrum due to virtual e pairs. Note sign – fermion, boson (Quantum Amplitude – phase matters) - SUSY.

12. Snapshot of H Constraints Limits are quoted at 95% exclusion. This is ~ ½ the deviation needed to claim a discovery.

13. Higgs Mass - Upper Limit • The couplings are a function of the mass scale at which they are probed. We require that (Q) is well behaved from = 174 GeV up to a scale , with 1/ () = 0 (strong coupling at ), the running of  includes loops with H and t - with opposite sign. Running coupling constants – Lecture IV Inverse coupling decreases as Q increases. Therefore coupling blows up at some Q

14. Higgs Mass - Upper Limit In quantum field theories the constants are altered in higher order processes (e.g. loops). Asking that the Higgs interactions be well behaved up to a high mass scale (no new Physics) implies a low mass Higgs. Is a high scale plausible? (GUTs ?) Lecture IV H H H H

15. Higgs Decays to Bosons - Direct • Field excitations  interactions with gauge bosons VVH, VVHH, VVV, VVVV due to W, Z fields in the covariant derivative Higgs couples to mass. Photons and gluons are massless to preserve gauge symmetry unbroken. Thus there is no direct gluon or photon coupling. This is an extension of the W,Z mass with the vev to interactions with the Higgs excitation. As with W, Z masses and vev, now look at excitation in the Higgs Lagrangian density “kinetic term” and EW gauge replacement

16. Higgs - Loop Decays to Bosons • There are decay modes that are not accessible through diagrams with a single coupling constant - zero mass states. • The coupling is to the heaviest quark in the loop. For a light Higgs, (H --> )/MH ~ 2W/2(MH/MW)2(mt/MH)8 [sin-1(MH/2mt)]4 • (H --> gg)/MH can be estimated by replacing  by s. This diagram is the major production mode at the LHC, g + g from p + p fusing into a Higgs boson. The loop integral |I| is ~ O(1). • For a light Higgs, (H --> gg)/MH ~ [s2W/722](MH/MW)2. COMPHEP does not do loops

17. Higgs - Production via gg Fusion • The formation cross section is (Lecture I), • Using the expression for (H-->gg) and normalizing the gluon distribution with a = 6, • Note that the MH3 behavior of  cancels the 1/ MH3 behavior of d/dy , leaving a roughly constant cross section, d/dy ~ 2(Hgg)/(MH3)[xg(x)]x1[xg(x)]x2 d/dy ~ 492[(Hgg)/(4MH3)][(1 - MH/s)12] ~ 492(Hgg)/(4MH3) d/dy ~ 49|I|2s2W/[288MW2].

18. Higgs Cross Section CDF and D0 successfully found the top quark, which has a cross section ~ 10-10 the total cross section. A 500 GeV Higgs has a cross section ratio of ~ 10-11, which requires great rejection power against backgrounds and a high luminosity. Rate = luminosity * cross section LHC at design has ~ 30 times the luminosity of the Tevatron and 7 times the energy.

19. Higgs Production Modes The Higgs cross section has as largest contribution g+g with an internal top loop. Note that qqH is quite large, followed by associated production modes including DY production of W, Z with H bremmstrahlung and H with top pairs.

20. Higgs Decay Rates - Direct and Loop Direct: Quarks and Leptons Gauge Bosons Loop Decays - Gauge Bosons: Higgs couples to mass, with no direct H or Hggcoupling. Gauge – Higgs mass squared coupling. fermion coupling – quark mass squared coupling

21. Higgs Decay Widths

22. Higgs Branching Ratios Note that q,l width ~ M while W,Z width ~ M3. Hence bb dominates below WW “threshold”.  is down by ~ 9 due to coupling to mass, and 1/3 color factor. Similarly for WW*

23. Higgs Decay, H -> ZZ ->4 Muons should be the cleanest signal at the LHC: Momentum in tracker * momentum in CSC * match in Multiple redundant measurements for rare processes

24. Use H --> ZZ --> 4e Higgs couples to mass -> most strongly to W and Z. Next strongest is to heavy quarks such as t, b. H natural width is < energy resolution ->Fully active crystals are the best resolution possible -needed for 2 photon decays of the Higgs and Z+Z-> 4 e decays. Z Z

25. Higgs Strategy and BR LEP-II H--> is a clean decay mode for low mass Higgs. The ZZ --> 4l mode is clean when it is above threshold at ~ 150 GeV. The dip in ZZ is due to WW rise above threshold at ~ 160 GeV. The WW decay mode does not have a mass peak and is unused save just at threshold, except in the VBF mode where it is a discovery mode. VBF VBF, H ->WW* -> 2l

26. Higgs Decay into Di-Photons t W,Z Yang’s theorum, J=1 Cannot decay into 2 photons

27. Higgs Discovery Limits The main final state is ZZ --> 4l. At high masses larger branching ratios are needed. At lower masses the ZZ*, qqWW* and  final states are used. LEP II has set a limit ~ 113 GeV. LHC will cover the full range from LEPII to 1 TeV. 1/20 year at design luminosity – CMS and ATLAS are designed to find the Higgs.

28. Higgs Quantum Numbers If the Higgs is seen in the 2 photon decay mode , it cannot be a J=1 state (Yang’s theorem). Recall that the 2 photon state is a quantum number filter. A Higgs must have the quantum numbers of the vacuum Suppose the Higgs is found in the WW decay mode. Look at the spin correlations expected for a 0++ state. The emission of the 2 leptons is then preferentially in the same direction, with small mass.

29. H --> ZZ --> 4l, Spin and Parity • Recall the classical pion parity in • for J = 0 into ZZ, CP requires that S = 0 for the ZZ, with a longitudinal and transverse Z polarization

30. Pion Parity - 1962

31. Spin of an Enhancement -> Z+Z? Measure decay angular distribution and extract L and T components

32. Full Monte Carlo Results 0- - decay planes are perpendicular 0+ - decay planes are parallel. Used to determine the “Higgs” parity in Z+Z decays.

33. Higgs Partial Widths For a light Higgs several partial widths can be determined at the 10-20% level. If the VBF method is successful with the WW and ZZ final state, then gHWW can be determined unambiguously.

34. EW – W Emission Weizacher-Williams approx – virtual W. Source function has coupling strength, EW, and a radiative 1/x behavior. Transverse virtual W dominate. This is like 2 photon physics in electron-positron colliders Luminosity of transverse W >> that for longitudinal W – but H couples preferentially to longitudinal W. Luminosity of WW in quark- antiquark pair, WW mass M

35. WW in pp Luminosity of WW in pp system and cross section to produce X through VBF in pp reactions. VBF of H has a WW width which grows a cube of H mass – cancels the cross section falloff as M cubed. Falloff of H cross section via VBF with energy is slow. At high enough energy VBF is the dominant process.

36. VBF and Other H Cross Sections Estimated for 400 GeV Higgs. Some numerical work needed – use the plots in “The Higgs Hunter’s Guide”

37. “Tag” Jets Forward calorimetry needed at the LHC in order to have sufficient hermeticity. Also for good efficiency to detect the “tag” jets – forward going quarks recoiling against an emitted virtual W

38. Tag Jets and Parity – HWW Coupling Azimuthal correlation between tag jets

39. VBF and H Quantum Numbers The H is a scalar object. That means, in VBF that the “tag jets” reflect the W, and thought of as inverse decays to W+W, their azimuthal correlation makes them back-to back. Other quantum numbers give other patterns.

40. WW Scattering Use VBF to study WW scattering at all WW masses? Find HWW coupling constant. If H mass is large, effectively study strong WW scattering as unitarity limit is approached . Can we use VBF to explore strong WW scattering? SM quartic background and t channel H exchange for example.

41. Higgs Pair Production at SLHC Higgs potential vevat potential minimum Expand about the minimum Aside from mass term for H there are triplet and quartic self couplings Therefore the Higgs self couplings in the SM are completely specified because the Higgs mass specifies the parameter λ. There are 2 parameters in the potential and μis fixed by G. Verify the SM by exploring the triple and quartic Higgs self-couplings?

42. Higgs – Self-Couplings at the SLHC Cross section is ~ 20 fb @ 160 GeV H mass. If SLHC is 1000 fb-1/yr, then 20,000 HH produced/yr. There are ~ 400 events with 2 leptons, missing energy and 4 jets (2 W mass peaks in the quark pair spectra).

43. Final State for Higgs Pairs Some final states are clean but rare. The ability to definitively find Higgs pairs will require large luminosities – perhaps SLHC….

44. Problems - III • Evaluate the ratio of decay widths of a Higgs boson into W and quark pairs. • Use Calchep to compute a “tag jet” cross section - process: u+d->d+u+H. • Use Calchep to explore branching fractions, H->2*x for several different masses.

45. Higgs Coupling to Fermions • The fermions are left handed weak doublets and right handed singlets. A mass term in the Lagrangian, mff = m(fLfR + fRfL) is then not a weak singlet as is required. • A Higgs weak doublet is needed, with Yukawa coupling, L ~ gf[(fL)fR + h.c.]. Yukawa Mass from Dirac Lagrangian density Fermion weak coupling constant