Lecture 23. November 16, Developing the SM s electroweak theory. Fermion mass generation using a Higgs weak doublet

Transcription

1 Lecture 23 November 16, 2017 Developing the SM s electroweak theory Research News: Higgs boson properties and use as a dark matter probe Fermion mass generation using a Higgs weak doublet Summary of the Standard Model with one generation More generations Composite Higgs models Michael 1

2 Class Plans Date Lecture Essay presentation (15 minutes) Nov Michael Composite Higgs models Nov Ping Family/flavor symmetry in the SM Nov. 23 Thanksgiving break Nov Nov (last class) 2

3 Research news 3

4 Is the Higgs boson real? Up until 2012 there were serious questions about the existence of a Higgs boson, with people willing to make bets against it. Alternate explanations of EWK symmetry breaking were on the theory market (e.g., technicolor). For the first year after the observation of a 125 GeV boson it was called a Higgs-like particle. But now after four years more of studies at the LHC the particle observed so far has all the properties expected for the Higgs boson that was predicted in As you have seen, once the mass has been measured, all the production cross sections and decay rates are fixed and can be compared to experiment. 4

5 Check of spin etc. The most basic measurements involve the quantum numbers expected for a Higgs boson. These are: spin = 0, parity P = +1 and charge conjugation C = +1. That is, the Higgs field has quantum numbers of the vacuum. The spin is measured by studying 2-body decays into particles of known spin. Decay modes used for this are: H! + H! Z + Z! e + e + µ + µ etc. H! W + + W! e e + µ + µ etc. Tests are made for spin 0 + vs 0 - and 2 + ( spin = 1 is excluded by the observation of H à γ + γ ). 5

6 Check of spin etc. Studies using decays in individual channel studies are not compelling, but a combined 3-channel fit favors J P = 0 + at 99.9% CL over alternative hypotheses. See arxiv: v2 [hep-ex] for the ATLAS experiment results. Studies of the spin and parity of the observed Higgs boson in the H ZZ 4l, H WW eνµν and H γγ decay processes are presented. The investigations are based on4.5 fb 1 and 20.3 fb 1 of pp collision data collected by the ATLAS experiment at the LHC at s = 7TeVand s = 8TeV, respectively. The SM Higgs boson hypothesis, corresponding tothequantumnumbersj P = 0 +,istested against several alternative spin and parity models. The models considered include non-sm spin-0 and spin-2 models with universal and non-universal couplings to quarks and gluons. The combination of the three decay processes allows the exclusion of all considered non-sm spin hypotheses at a more than 99.9% CL in favour of the SM spin-0 hypothesis. 6

7 Check of spin etc. Arbitrary normalisation ATLAS ZZ* 4l 1 Data SM H s = 7 TeV, 4.5 fb s = 8 TeV, 20.3 fb H WW* eνµν s = 8 TeV, 20.3 fb Arbitrary normalisation ATLAS H ZZ* 4l 1 Data + 0 SM + 0 h s = 7 TeV, 4.5 fb s = 8 TeV, 20.3 fb H WW* eνµν s = 8 TeV, 20.3 fb ~ q (a) ~ q (b) Arbitrary normalisation ATLAS Data + 0 SM + 2 (κ q =κ g ) H ZZ* 4l s = 7 TeV, 4.5 fb s = 8 TeV, 20.3 fb H WW* eνµν s = 8 TeV, 20.3 fb H γ γ s = 7 TeV, 4.5 fb s = 8 TeV, 20.3 fb Arbitrary normalisation ATLAS Data + 0 SM + 2 (κ q =2κ g, p <125 GeV) T H ZZ* 4l s = 7 TeV, 4.5 fb s = 8 TeV, 20.3 fb H WW* eνµν s = 8 TeV, 20.3 fb H γ γ s = 7 TeV, 4.5 fb s = 8 TeV, 20.3 fb ~ q ~ q 7 (d)

8 Check of production Another class of tests compares the measured production cross sections to SM predictions. 8

9 Check of production 9

10 Check of production

11 Check of decay All the decay widths of the Higgs boson are predicted: b b m b t m t BR(WW) = 21% BR(ZZ) = 2.6% H BR( bb) = 58% H BR( ) = 0.23% 11

12 Check of decay H! (discovery channel) H! ZZ (useful for spin analysis) H! bb (coupling to fermions) 12

13 Check of decay µ = data/sm prediction 13

14 Is it the SM Higgs? With limited precision, all checks to date agree 14

15 Is it the SM Higgs? However it could be a member of a more complex (e.g. SUSY) Higgs sector. Ø The measured couplings from observed production and decay rates have large errors ( s of %) Ø No fermion couplings to first or second generations leptons/quarks have been measured (as expected with the current statistics). Ø No Higgs self-couplings have been measured. Ø No quartic Higgs-EWK boson couplings have been measured. 15

16 Using the Higgs as a portal to DM Since the Higgs boson couples democratically to all particles with a strength proportional to mass, it seems like a great candidate to bridge connections between SM particles and WIMP-like dark matter (Higgs portal to DM). This process is independent of any QCD/EWK interaction properties of the WIMPS, and depends only on the assumption that the WIMP mass couples to the Higgs boson as it does to all other massive particles. 16

17 Generating fermion masses 17

18 Generation of fermion masses As we have observed previously the normal mass term in a fermion Lagrangian is not invariant under SU L (2): L f =i µ - m f where = R L + L R This can be repaired by dropping the explicit mass term and introducing an interaction of the fermions with the Higgs field weak doublet. This will be the final modification required to complete the SM EWK theory (for one generation). 18

19 Generation of fermion masses Use the same notation introduced previously: L EWK = B µ B µ W aµ W a µ + i µ D µ +(D µ )(D µ ) -[-µ 2 + ( ) 2 ] + terms with Ψ Φ interaction = = apple apple u d + 0 Also define: = i 2 = i apple 0 i i 0 apple + 0 = apple o 19

20 Generation of fermion masses Lagrangian terms that are invariant under U Y (1)xSU L (2) and also renormalizable are: - g u [ u R ( )+( ) L - g d [ d R ( )+( L ur ] ) L L d R ] Here the subscripts L and R denote the usual ½(1 γ 5 ) and ½(1 + γ 5 ) projections. Also note carefully the use of upper case Ψ for the weak doublet and lower case ψ u and ψ d for the lower fermion member of the doublet. apple The g u and g d are dimensionless coupling constants of the scalar field to the ψ u and ψ d fermion fields. = u d 20

21 As before, express the Higgs field doublets using the expansion about the field value producing the potential minimum and then the unitary gauge for the fields. apple = p v + H(x) and = 1 p 2 apple v + H(x) 0 Substitute these into the scalar field fermion interactions at the top of the previous page. The result is: [- g u ( u R ul + u L ur )-g d ( d R dl + d L dr )] 1 p2 (v +H) =- g uv p 2 Generation of fermion masses u u - g dv p 2 fermion mass d d - p g u 2 H u u - p g d 2 H d d H fermion interaction 21

22 SUMMARY The SM s theory for one quark/lepton generation 22

23 Overview Particle content: q 8 fermions: u i,d i, e, e where i = 1,2,3 (colors) q 12 vector bosons: G µ a, A µ, Z µ, W µ, W +µ where a = 1-8 q 1 scalar boson: H Experimental input parameters = 7 masses and couplings Dynamics structure from gauge symmetries: L SM = L QCD + L EWK + L Higgs SU c (3) U Y (1) xsu L (2) 23

24 The QCD part L QCD =- 1 4 F µ a F aµ +iū j µ D µ jk u k +i d j µ D µ jk d k F µ a µ G G µ a g s f abc G µ b G c Include separate terms for the u and d 3-colored quarks. Describes u and d quark interactions with gluons and gluon self-interactions. 24

25 The EWK part L EWK =- 1 4 B µ B µ W aµ W a µ +i q µ D µ q +i l µ D µ l D µ µ 1 + ieqa µ + ig w [T + L W + µ + T L W µ ] + ig z [T 3L x w Q]Z µ Describes quark and lepton interactions with EWK bosons and EWK boson self interactions. B µ µ B B µ W aµ µ W a W aµ - g w f abc W bµ W c apple T + = p Q = W ± µ =(W 1µ iw 2µ )/ p 2 Z µ = cos w W 3µ -sin w B µ A µ =sin w W 3µ + cos w B µ apple Q1 0 0 Q 2 1 = apple T = p apple T 3 = 1 2 apple Note: multiply T s by ½ (1 γ 5 ); exclude term in D µ for quarks. 25

26 The Higgs field part D µ µ 1 + ieqa µ + ig w [T + W + µ + T W µ ] + ig z [T 3 x w Q]Z µ apple = p v + H(x) and = 1 p 2 apple v + H(x) 0 Generates mass terms for the Z, W + and W - bosons, quarks, and leptons. Includes interaction of the Higgs field with the Z, W + and W - bosons, the quarks, and leptons, and Higgs field self interactions. 26

27 Completing the SM 27

28 More generations The observation of additional quark/lepton generations is not predicted by the SM or other theory options. It is purely driven by what we observe experimentally. However they bring along one highly desirable bonus. With three generations CP violation can be introduced into the predictions. This is true for quarks and might be true for leptons. CP violation is one of the requirements for generation of a slight imbalance between matter and anti-matter in cosmological models of the early-universe. The next step is to introduce a second generation of quarks/leptons. This can be used to illustrate the concepts of fermion mass and flavor mixing without being burdened with 3x3 mixing matrices. 28

29 Discovery of the 2 nd generation A brief tour through discovery of the particles in the second generation. The muon: The first member of the 2 nd generation was discovered in 1937 from a study of charged particles in cosmic rays using a cloud chamber in a magnetic field. The observation was that when charged particles were sent through as lead plate, some showered, as expected for electrons, and some penetrated the plate. Anderson and Neddermeyer, Phys. Rev. 52, 02 (1937) 29

30 Discovery of the 2 nd generation The strange quark: The neutral kaon decay to two pions was observed in 1947 as a strange particles with a long lifetime decaying to strongly interacting particles. Strange because if the particle was strongly interacting it should decay with a very short lifetime. The Kaon is the lightest particle containing a strange quark, carrying a flavor quantum number (strangeness) conserved by the strong interaction, but violated by the weak interaction. Nature 160, 855 (1947) 30

31 Discovery of the 2 nd generation The muon neutrino: Explict evidence for the muon neutrino was found in A beam of neutrinos from pion decays was directed into a detector built from spark chambers with dense steel plates for identifying muons. Nobel Prize in 1988 to Lederman, Scharwartz and Steinberger 31

32 Discovery of the 2 nd generation The charm quark : In 1973 a narrow resonance of mass 3.1 GeV, was discovered simultaneously at SLAC and Brookhaven labs. At SLAC it was produced from an electron-positron collider and at Brookhaven from proton Beryllium collisions. J.J. Augustin et al. PRL 33 (1974) 1406 J.J. Auber et al. PRL 33 (1974) 1404 BNL SLAC e + e - " hadrons p+be! e + e - + X T p = 30 GeV e + e - " e + e - M J =3.1 GeV σ M 20 MeV e + e - " µ - µ +, π + π -, K + K - Particle Data Book (2007): M J/ψ = ±0.011 MeV Γ J/ψ = 93.4±2.1 kev M ψ =3.1±0.003 GeV FWHM 1.3 MeV Nobel Prize in 1976 to Richter and Ting 32

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34 End Lecture 23 Next: Including the second generation in the SM 34