Higgs Short Notes. Higgs Field, Vacuum Nightmares, End of the World Production, Decays Strategies, Detectors Observation.

Transcription

1 Higgs Short Notes 1 Higgs Field, Vacuum Nightmares, End of the World Production, Decays Strategies, Detectors Observation

2 About the Higgs Field - I Universal, constant field Lorentz scalar Same value in any frame, rotation invariant Non-standard feature: Vacuum expectation value v 0 Usual analogy: Spontaneously magnetized ferromagnet: M 0 below Curie temperature Pick up a direction Ground state rotationally not symmetric, in spite of H being symmetric

3 About the Higgs Field - II Better analogy: Superconductor Energy difference between normal and s.c. state at two different temperatures 1 4 E= a( T) ψ + b( T) ψ +... Landau theory of phase transitions 3 ψ is the Cooper pair wave function ψ density of Cooper pairs Below T c, the minimum energy state ( vacuum ) occurs for ψ = ψ 0 0, phase undefined U(1) QED gauge invariance spontaneously broken Photon becomes massive B = 0 inside

4 About the Higgs Field - III ψ Higgs field of superconductivity: <ψ> 0 Permanent supercurrents Superconductive state: Higgs field = Wave function of Cooper pairs Not a fundamental field Composite field of fundamentals fermions (electrons) Why there is the composite? e-e effective interaction: Attractive (!) due to e lattice interaction Is the real Higgs field a genuine, fundamental field or a composite? Good question..no answer (yet): Take it as a fundamental field 4

5 About the Higgs Field - IV A couple of questions: 1) What about the nonzero VEV of the Higgs field? 5 Higgs: Unique field whose VEV 0 Similar to magnetization M 0 in a ferromagnet But: In a vacuum Not related to many body effe cts Lorentz scalar No preferred direction, reference frame ) Does it involve a new force? 'Giving mass to all the fundamental constituents'?? i Part of the standard EW interaction, often as a neglig ible contribution: Higgs particle exchange diagrams between Fermion lines normally strongly suppressed ( ) 0 ± by mf mw factors as compared to γ, Z, W exchange Not true for t quark! 3 & 4 boson diagrams with and without H similar i Crucial role as 'Background' interaction: For most particles Higgs field coupling translates into inertial mass!

6 About the Higgs Field - V 6 Apparently contributing to vacuum energy density: ( ) Beware: Take potential energy V φ Constant term: Usually not considered Does not enter field equations, where only energy differences count But: Taken into account by gravity Cosmological term? Cosmological constant : Possibly additiona l term in Einstein's field equations May yield long range attraction/repulsion, according to sign Invented by Einstein in order to guarantee static universes Rejected by Einstein at the time of discovery of expansion of the Universe Recently resurrected following the discovery of accelerated expansion

7 About the Higgs Field - VI 1 Zero point energy = mh v ρhiggs 8 1 E Indeed: m v = E = E( E ) Energy density 3 8 L ρ Higgs h 4 GeV 8 4 By assuming ρ to be a cosmological term, compare: ρ observed ρ Higgs GeV GeV ! 55 ord ers of magnitude too big ( and with the wrong sign... ) Quick fix: V( v) can be set = 0 by adding a constant to V( φ) 7 Constant apparently unrelated to m, v to be chosen to an accuracy of 1 part out of 10! Fi ne tuning problem, still essentially unsolved h Something missing?

8 About the Higgs Field - VII Higgs boson: Quantum excitation of the field, mass m not given by the field ( φ) Further issue: V appearing in L: Classical potential Must be quantized Will be used perturbatively Radiative corrections will modify the classical V( φ) Similar to vacuum polarization corrections to Coulomb potential in QED (Uehling potential & Lamb shift) Standard effect: Running constants, including λ L = D D µ H λ= λ m H ( ) µ φ φ µφφ λφφ ( q ) modified by radiative corrections ( ) Upon taking µ < 0, λ 0> 0 λ evolution depending on β functions H 8

9 About the Higgs Field - VIII 9 Running couplings and β functions: dg dlnq 4 6 ( g ) bg O( g ) 4πβ = + + dg i = 4πβ dlnq ( g ) 1 loop 4 i i i i For the EW interaction: bg loop bg =, b =+ 6 16π 6 16π Higgs couplings: g' ( ) dλ = ( λ + ht ht ) 3λ( 3 g + g' ) + g + ( g + g' ) Self dlnq 3π 8 dh t = 9h 8 ' Top (Yukawa) t h t gs+ g + g dlnq 3π 4 1

10 About the Higgs Field - IX dλ 3λ dlnq 4π dln Q + ln ( Q) ( ) F H ( ) = λ( Q) 10 Neglect smaller contributions at large λ dλ Q λ 4π λ λν 4π ν Q ln λ λν 4π ν λν G m ( Q) ( ) ( ) λν 3 Q 1 λν ( ) ln 4π ν 3 Q λ as λν ( ) ln 1 Diverging at 'Landau pole' 4π ν exp π ( ) exp π QLP = v v = 3 λν 3 GF m H Λ New physics required at scale Λ< QLP ln < < v ν 1 19 π O( 140 GeV), mplanck 1.10 GeV m π Λ H 3G Fm Λ H 3G ln O ( 650 GeV ), Λ 1 TeV F

11 About the Higgs Field - X dλ 3h dlnq 4π 4 t 4 3h t dλ dlnq 4π 3h Q λ( Q) λν ( ) ln 4π ν 11 Neglect smaller contributions at small λ 4 t λ must stay + ve in order to keep vacuum stable (!): Don't like a too quick End of the World h λν ( ) > 4π m H> 4 3 t ln 3h 4 t π G F Q ν G m 3h Q > ln for some Q Λ 4π ν 4 F H t 1 ln Λ ν

12 About the Higgs Field - XI Running couplings: 1 Sombrero: λ>0 Relax Dog Bowl: λ<0 End of the World (sometime) Λ

13 About the Higgs Field - XII 13 Radiative corrections leading to major changes in the effective Higgs potential at large φ values: Details tied to m, m H t Might induce vacuum instability/metastability through fast/slow tunneling Classical Higgs potential Metastable vacuum Unstable vacuum

14 About the Higgs Field - XIII Upper & lower bounds on m H : 14 m H = 16 GeV Is the Universe metastable??

15 Higgs Production - I Start from H coupling to Fermions: 15 0 Compare to coupling to Z : H mf coupling down by a factor as compared to Z m W 0

16 Higgs Production - II First mode: s-channel formation: 16 f f Ideal for lineshape scan, provided cross-section is big enough Lepton colliders: Tough requirements on luminosity, energy resolution

17 Higgs Production - III Second mode: H radiation from quarks, sizeable contribution from Top: 17 f f f f tt signature might be useful to tag

18 Higgs Production - IV Shift to gauge bosons: Exclude massless photon, gluon at tree level [ Photon, gluon loop contribution to be taken into account: See later ] 18 More promising: W, Z mass very large

19 Higgs Production - V 19 Best modes: 'Higgsstrahlung', 'Gauge boson fusion' f f f f f f

20 Higgs Production - VI Beyond tree level: Very Important Loops Lepton machines: Interesting diagrams, also quite relevant to detection 0 H Parton machines: Dominant diagram at LHC t

21 Higgs Decays - I 1

22 Higgs Decays - II

23 Higgs Decays - III 3 3-body phase space factor 3-body phase space factor

24 Higgs Decays - IV 4 3-body phase space factor ( H Z / γγ, ) Γ

25 Higgs Decays - V H decays entirely determined by Higgs mass: 5 (GeV) M H =16 GeV Γ H 5 MeV!

26 Higgs Decays - VI H branching ratios: 6

27 Higgs Decays - VII 7

28 Parton Collider - I Dominant diagrams for H production: 8 Gluon-Gluon fusion Vector Boson fusion t Higgsstrahlung Htt t t

29 Parton Collider - II 9 Basic ingredient: PDFs Quarks: Look for heavy ones Tree diagrams: Best bet is with b Factor m M b W encouraging But: No b-quark beams, must rely on bb sea inside the nucleon b-quark partonic density small... Taking H production at small rapidity y 0, with a 7 TeV beam x 10 Incident flux of sea b-quarks very small Gluons: Main contribution Loop diagrams, dominated by t quark PDF somewhat dependent on Q

30 Parton Collider- III 30

31 Parton Collider- IV 31

32 Parton Collider - V 3 Parton densities:

33 Parton Collider - VI 33

34 Parton Collider - VII Expected cross sections for parton colliders: 34

35 Parton Collider - VIII 35 Results for LHC cross sections

36 Parton Collider - IX Cross-sections for a 16 GeV Higgs 36

37 LHC: Machine - I 37

38 LHC: Machine - II 38 LHC dipole field 8.3 T (HERA/Tevatron ~4 T) LHC pp ~ cm - s -1 (Tevatron pp 3x10 3 cm - s -1 ) (SppbarS pp 6x10 30 cm - s -1 )

39 LHC: Machine - III R= Lσ L= kn f * * 4πσσ x y Rate, Luminosity,Cross-Section k = number of bunches = 808 N = no. protons per bunch = f = revolution frequency = 11.5 khz σ* x,σ* y = beam sizes at collision point (hor./vert.) = 16 mm High L: Many bunches (k) Many protons per bunch (N) A small beam size σ* u = (β * ε) 1/ β * : Beam envelope (optics) ε : Phase space volume occupied by the beam (constant along the ring) 39 High beam brilliance N/ε (particles per phase space volume) Injector chain performance Small envelope Strong focusing Optics property Beam property

40 LHC: Machine - IV 40 LHC: ρ =.8 km given by LEP tunnel To reach p = 7 TeV/c given a bending radius of ρ = 805 m: Bending field : B = 8.33 T Superconducting magnets I I I B

41 LHC: Machine - V 41 p B field B F force Two-in-one magnet design F p 41

42 LHC: Machine - VI Superconducting coils: 4

43 LHC: Machine - VII 43 LHC main dipole: Two magnets in a single module

44 LHC: Machine - VIII RF system: Superconducting RF cavities 400 MHz 0.5 MeV/turn 0' for 450 GeV 7 TeV 44 Synchrotron radiation loss E (t) s 3.5 TeV 7 TeV 104 GeV 0.4 kev/turn 6.7 kev /turn ~3 GeV /turn

45 LHC: Machine - IX 45 Superconducting cavity

46 H - I 46 Selecting best decay channels for detection: Strongly dependent on (unknown) M By taking M < M H W H bb : Large BR > 50 %, good signature (secondary vertexes), lots of QCD background ττ + γγ :Large BR 7 %,som ewhat harder than bb (neutrinos) BR 3 : Tiny 10, small background, experimentally challenging gg : Large BR 5 %, jets, lots of QCD background ZZ*: Small BR 3 %,small background in the 4 lept ons mode WW *:Large BR 0 %,sizeable QCD background in the 4 jets mode, harder than ZZ * in leptonic modes (neutrinos)

47 H - II 47 1 Total integrated luminosity: 30 fb /experiment Phenomenal performance: Record luminosity (> 5 x ) obtained soon after startup in 01 Sustained data collection rate of > 1.0 fb -1 /wk 8 TeV = [ 3.3 / 1.3 (ATLAS), 1.8 (CMS) ] fb -1

48 H - III 48 4 leptons: ~7σ observation

49 H - IV 49 γ s: ~6 σ observation

50 H - V 50 Signal strength: Channel ATLAS (expected) h γγ ATLAS (observed) CMS (expected) CMS (observed) γγ h ZZ h WW h ττ h bb 1.6 ~0.1.1

51 H - VI 51 Combined mass: All modes m H ( ) ATLAS = ± 0.37 (stat) ± 0.18 (sy st) m H (CMS) = (stat) (syst) Many more results on spin/parity, couplings, width......next time!