The hierarchy problem. (On the origin of the Higgs potential)

Transcription

1 The hierarchy problem (On the origin of the Higgs potential)

2 Electroweak symmetry breaking (EWSB) in the SM is triggered by the Higgs VEV: V (h) = 1 2 µ2 h λh4 µ 2 = λv 2 = λ g 2 4M 2 W 10 4 GeV 2 << M 2 P GeV 2 Why so different?

3 Even worse, at the quantum level, scalar masses are extremely sensitive to heavy states h h 1 16π 2 M 2 mass of the particle in the loop

4 Not the same situation for fermions or gauge bosons gauge symmetries can protect them No symmetry in the SM protects the Higgs mass In general: m Ψ L Ψ R vs µ 2 H 2 { { Not a singlet if ΨR transform: Always a singlet under phase transformations Ψ R e iθ Ψ R (chiral symmetry) Expected: µ 2 heavier scale² ~ MGUT², MP², Mstring² This is the hierarchy problem

5 Let me emphasize that is not a problem of consistency but of naturalness Example: Fine-tune system

6 Analogy with Superconductivity EWSB Breaking of U(1)EM Higgs Model GL Model h = e e Give the GL Model a good description of superconductors? Bc B N phase h =0 SC phase h =0 Tc T

7 Analogy with Superconductivity EWSB Breaking of U(1)EM Higgs Model GL Model h = e e Give the GL Model a good description of superconductors? Bc B N phase h =0 NO, it only works close to the critical line SC phase only there h is small and it makes sense to Taylor-expand the potential: h =0 Tc T V (h) =m 2 h 2 + λ h 4 +

8 Possibilities that theorists envisage to tackle the Hierarchy Problem: 1) Supersymmetry: Protecting the Higgs mass by a symmetry 2) Composite Higgs: The Higgs is not elementary: As in superconductivity: h ~ ee or QCD: pions ~ qq - 3) Large extra dimensions: Gravity strong at the EW-scale: Λ ~ Mstring ~ TeV In all cases New Physics at ~TeV Strong motivation for the LHC!

9 Supersymmetry Following notation and formulae of A Supersymmetry Primer, Stephen P. Martin (hep-ph/ )

10 We want a symmetry to protect the Higgs mass: Idea: Scalar Fermion symmetry trans. since fermion masses It exists, it is a Supersymmetry: protected by chiral symmetry Simplest case: L = µ Φ 2 + i 1 2 Ψ/ Ψ Invariant under: Ψ Φ = Majorana fermion = Complex scalar Φ Φ + δφ Ψ Ψ + δψ δφ ξ (1 γ 5 )Ψ δψ i(1 γ 5 )γ µ ξ µ Φ The scalar must be massless!! Parameter of the trans. being a Majorana fermion

11 Supersymmetry Algebra (Maximal extension of Poincare in a QFT) Minimal SUSY (N=1): One extra generator Q Q Boson = Fermion, Q Fermion = Boson. Schematic form: [Q, M µν ]=Q {Q, Q } = P µ, {Q, Q} = {Q,Q } =0, [P µ,q]=[p µ,q ]=0, Q commutes with P² and any generator of the gauge symmetries: The Fermion and Boson have equal masses and charges

12 Minimal Supersymmetric SM (MSSM) Imposing supersymmetry to the SM MSSM The spectrum is doubled: SM fermion New scalar (s-... ) SM boson New majorana fermion (... -ino)

13 ... but not yet realistic: The model has a quantum anomaly (due to the Higgsino) and the down-quarks and leptons are massless Extra Higgs needed Two Higgs doublets: H u : (1, 2, 1) H d : (1, 2, 1) give mass to the up quarks give mass to the down quarks and leptons + two Higgsino doublets: H u : (1, 2, 1) H d : (1, 2, 1)

14 MSSM Spectrum (ũ L d L ) (u L d L ) Squarks ũ R d R u R d R Sleptons ( ν ẽ L ) (ν e L ) ẽ R e R (H + u H 0 u ) ( H + u (H 0 d H d ) ( H 0 d H 0 u ) H d ) Higgsinos g g Gauginos W ± W 0 W ± W 0 B 0 B 0 particles: R-parity = 1 superpartners: R-parity = -1 1) Superpart. interact in pairs 2) Lightest superpart. stable

15 i Type of interactions he couplin. (3 riant derivative; they come f gian. Figure 3.3c show am is traditiona bosons and fermion and scalar field i i re 3.3: Supersymmetric gauge interaction vertices. and [mass] 2. First, there are (scalar) 3 couplings in Figure 3.2a,b, vertices supersymmetric and renormalizable to corresponding actions discussed in the Introduction [compare Figure 1.1, and eq. (1.11)]. quantum in divergences quadratic the cancel to needed type special the supersymmetry; asdepictedinfigure3.2e,ifonetreats Figure 3.2c,d. There is no such arrow-reversal in arrows he erms in eq. (3.50). The propagators of the fermions and scalars, ijk y couplings Yukawa and ij M parameters mass superpotential and Mij each lead to a chirality-changing insertion in the mass squared scalar and ij M mass fermion the using way al supersymmetric theory. Figures 3.3a,b,c occur only preserved. is direction arrow the propagator, the Getting them from supersymmetrization : k H 0 u j k i j i H 0 u j j H 0 u i (a) (b) (c) (d) (e) guret3.2: Supersymmetric L t dimensionful couplings: (a) (scalar) R t 3 interaction L t vertex Mt R L in yjkn and (b) e conjugate interaction M in yjkn,(c)fermionmasstermmij and (d) conjugate fermion mass term ij,and(e)scalarsquared-masstermm ik M kj. Figures 3.3a and 3.3b are the interactions of gauge bosons, the gauge group is non-abelian, for example for SU(3)C color and igure 3.3 shows the gauge interactions in a supersymmetric theory. Figu direction arrow the propagator, the in insertion an as term squared-mass scalar asdepictedinfigure3.2 supersymmetry; exact with theory a in propagator scalar a or es 3.3c,d,e,farejustthestandardinteractions interactionsofghostfields,which the show not of gauge bosons, which derive from the first term the in isospin weak SU(2)L and color SU(3)C for e ) and (3.65)-(3.67) inserted in the kinetic the of because theory gauge any in occur ust e as the well-known QCD gluon and electroweak t R gauginos (f) slepton, squark (a) (b) (c) (d) (e) slepton, squark M ij,and(e)scalarsquared-masstermm ik M kj. e conjugate interaction M in y jkn,(c)fermionma 3.2: Supersymmetric dimensionful couplin (b) k (a) (b) (c) corrections to scalar masses, as discussed in the Introduction [compare Figure 1.1, a quadratic dive the cancel to needed type special the of exactly is 3.1c Figure of tion (f) (g) (h) Figure 3.3: Supersymmetric gauge interaction vertices. (f) (g) (h) (i) gauginos Figure 3.3: Supersymmetric gauge interaction vertices. ik fermion propagator; note the directions of the arrows in Figure 3.2c,d. There is no such arrow chirality-changing insertion a to lead each Mij and ij M terms mass fermion The. kj M M ugino to a gauge boson; the gaugino line in the theory are constructed in the usual way using the fermion mass M ij and scalar squ fermions the of propagators The (3.50). eq. in terms third and second the by indicated as which are entirely determined by the superpotential mass parameters M ij and Yukawa c in couplings 3 (scalar) are there First,. 2 [mass] and [mass] of dimensions coupling with Figure 3.2 shows the only interactions corresponding to renormalizable and supersy n and a complex scalar [the first term In nlinesuperimposedonawavyline. n vertices of the Standard Model. (We do not s we the as same the exactly are these MSSM the In 7). (g) (h) (i) ersymmetrization of Figure 3.3e or only for consistent loop amplitudes.) Fig (d) (e) Higgs Higgs n of Figure 3.1c is exactly of the special type needed to cancel the quadratic divergences in quantum rrections to scalar masses, as discussed in the Introduction [compare Figure 1.1, and eq. (1.11)]. gauginos Figure 3.2 shows the only interactions corresponding to renormalizable and supersymmetric Higgsino vertices th coupling dimensions of [mass] and [mass] 2. First, there are (scalar) 3 couplings in Figure 3.2a,b, ich are entirely determined by the superpotential mass parameters M ij and Yukawa couplings y ijk,

16 Up to scalar trilinear and quartics: i j k

17 How supersymmetry works? h 0 t + h 0 t Fermion loop Boson loop μ² = + A μ² = - A μ²total = 0{

18 Its not the first time that symmetries force doubling the known spectrum: Relativistic quantum field theories: Particle Antiparticles Made the electron-mass corrections not linearly divergent: e γ e + e e γ e m e m e

19 But if supersymmetry is exact: MF = MB e.g. M e = Mẽ It must be broken to give masses to the superpartners Supersymmetry breaking must afford soft terms : (terms that do not spoil the good UV properties of the Susy) = 1 2 ( M 3 g g + M W W 2 + M B B ) 1 +c.c. (ũ au QH u d a d QH d ẽ a e LH d +c.c. Q m 2 Q Q L m 2 L L ũ m 2 u ũ d m 2 d ẽ m 2 d e ẽ m 2 H u Hu H u m 2 H d Hd H d (bh u H d +c.c.). ) +µ H u Hd for 3 families, more than100 terms are possible!!

20 μ²total ~ mstop²{ How supersymmetry works? (including soft-masses) t t h 0 + h 0 Fermion loop Boson loop μ² = + A μ² = - A + mstop² B Superpartners expected around v ~ 100 GeV

21 Constraints on superpartner masses from flavor physics: Breaking of lepton symmetry: µ R ẽ R µ B γ e Exp: BR(µ eγ) < mẽ m µ up to 1% - 0.1% Large contributions _ s s R d R d to K-K mixing: d g d R s R g s m s m d up to 0.1% %

22 Soft terms must be generated in a clever way Most interesting possibilities: 1) Gauge mediation 2) Gravity/Moduli/Extra-dim mediation

23 The famous scenario minimal sugra not a model, just an Ansatz: At Q=MGUT { All gaugino masses equal = M1/2 All scalar masses equal = M0 All trilinear equal = A0 Why? At Q=MZ 600 Mass [GeV] H d H u M 2 M 3 M 1 squarks (µ 2 +m 0 2 ) 1/2 m 1/2 I don t know, but experimentalists like it a lot! 100 sleptons m Log 10 (Q/1 GeV)

24 1) Gauge mediation New sector Susy breaking sector gauge bosons MSSM Gauge interactions are flavor blind : Universal masses for squarks/sleptons with equal charges

25 Very predictive (in the minimal case). Just calculate loops: B, W, g F S S gaugino masses scalar masses Depends on 3 parameters: 1) μ-term: Higgsino mass 2) Susy-breaking scale: F 3) Scale where the soft-terms are induced: M ~ m / M ~ g ~ u R ~ d L ~ t 1 ~ t 2! = 74 TeV N = 1 tan" = 3 µ < 0 ~ el 2 ~ e R Giudice,Rattazzi M (GeV)

26 Predicts a very light gravitino = Mass suppressed by MP: partner of the graviton m 3/2 = F k 3M P = 1 k ( ) 2 F 2.4 ev 100 TeV k = model-dependent coefficient Lightest Superparticle

27 2) Gravity/Moduli/Extra-dim mediation: gauge or gravity...to be discussed later Susy-breaking AdS 5 R H MSSM Matter Spectrum at high-energies (Q~1/R) model dependent An example: Scalar masses = 0 (at tree-level) Lightest superpartner: Gaugino masses = M1/2 0 Neutralino (mixture of gaugino and Higgsino)

28 Only 3 parameters: Higgs sector V = ( µ 2 + m 2 H u )( H 0 u 2 + H + u 2 )+( µ 2 + m 2 H d )( H 0 d 2 + H d 2 ) +[b (H + u H d H0 u H0 d )+c.c.] (g2 + g 2 )( H 0 u 2 + H + u 2 H 0 d 2 H d 2 ) g2 H + u H 0 d + H 0 uh d 2. Spectrum: quartic coupling related to gauge-couplings 2 x 4 = 8 scalars = 3 Goldstones (eaten by W, Z) +3 neutral Higgs = h, H, A + Charged Higgs = H+, H

29 2 unknown parameters (since ): v 2 = H u 2 + H d 2 1) 2) At tree-level: tan β = H u H d m A { m 2 H + = m 2 A + m 2 W 1 2 m 2 h,h= 1 m 2 A + m 2 Z ± 2 (m 2 A m2 Z )2 + 4sin 2 2βm 2 A m2 Z m h m Z Was a great prediction for Higgs hunters at LEP!

30 ... but quantum effects (mostly loops of top/stop) t t modify the bound: Upper bound ~130 GeV Djouadi 05

31 LEP searches: e + Z Z e + Z A e h e h with decays to taus and bottoms tan! m h -max tan! m h -max Excluded by LEP 1 Theoretically Inaccessible 1 Excluded by LEP m h (GeV/c 2 ) m A (GeV/c 2 )

32 After LEP, a heavy stop is essential to keep the MSSM alive Higgs bound: m 2 h = m 2 Z + 3m4 t < 2π 2 v 2 ln(m stop/m t )+ Needed to be large to be above the experimental bound Higgs searches rules out a big chunk of the parameter space of the MSSM!

33 In minimal Sugra: M 2 0 /µ 2 Only the thin withe spike is left! M 2 1/2 /µ2 Giudice, Rattazzi

34 MSSM Higgs hunting at the LHC Bad news: h too light to decay to WW/ZZ A, H+ have very small couplings to WW/ZZ H small regions with sizable couplings to WW/ZZ Good news: Regions where the decays of H, A, H+ to leptons are enhanced (Large Tanβ region) Due to: m τ = Y τ H d can be larger than in the SM, if H d is smaller than v

35 Near future: 5# discovery 95% exclusion More interestingly: MSSM could be ruled out if a Higgs WW/ZZ with mass ~160 GeV is discovered in the first LHC run

36 In the long run... tan! h 0 H A h H

37 Superpartners at Hadron Colliders

38 Superpartners at Hadron Colliders Neutral gaugino + Higgsino mix: Mass-eigenstate = χ 0 neutralino Charged gaugino + Higgsino mix: Mass-eigenstate = χ + chargino

39 Main consideration: Due to R-parity superpartners are produced in pairs, and decay, in cascade, down to the lightest one (neutral) that, being stable, goes away from the detector A classic:

40 Strategy: Detect leptons or jets + Missing ET Final states with same-charge dilepton due to the Majorana nature of the gluino

41 Tevatron From P. Wittich at Physics at the LHC 2010 conference

42 susy in jets + met:generic squark/gluino production Large production cross section, bkgnds from multi-jet, Z νν, top Optimize searches as a function of (Missing ET, njet) No excess seen so far Limits for 2 (2.1)/fb of data for CDF (D0) interpret results in msugra-like SUSY scenario!"# 20

43 Trileptons: Chargino-Neutralino Search, 3.2/fb Very clean signature: Missing E T due to undetected ν, χ isolated leptons, lower momentum ~ ~ 3 identified leptons (e,μ) 2 identified leptons + track (l) Tight and loose e,μ categories Rejection using kinematic selections on: ml+l-, njets, Missing ET, Δφ between leptons... Good agreement between data and SM prediction set limit Peter Wittich Channel SM expected Data Trilepton 1.5 ± Lepton+trk 9.4± 1.2 6!"# 16

44 Chargino-neutralino results interpret null result in msugra SUSY scenario as a convenient/conventional benchmark PRL 101, (2008) excluded region in msugra m 0 -m! space m 0 = 60 GeV, tan β=3, A 0 =0, μ>0 ~ 2 fb -1 ~ ~ ~ Excludes mχ ± 1 < 164 (154 Exp.) GeV/c 2 Limits depend on relative χ 0 2-l masses! m χ2 > m l ~ increases BR to e/μ! m χ2! m l reduces acceptance D0 limit in 2.3/fb: Phys. Lett. B 680, 34 (2009) Peter Wittich!"# 17

45 2 b jets + ET Miss - ~q and LQ ZH ν νb b Final state familiar from Higgs searches missing ET and b quarks Also good signal for leptoquarks and SUSY event selection: b tagging (D0: neural-net algo) two b-tagged jets, ET miss, Sign., ΣET optimize pt, ET miss, HT, Xjj for SUSY/LQ3 signals p p b 1 b1 b χ 0 1 b χ 0 1 LQ 3 ν τ b X jj = pjet1 T + p jet2 T H T pre-tag tagged low δm(lsp, b squark) hi δm(lsp, b squark) SM Total Syst. Uncertainty Peter Wittich H T + E/ T [GeV] -1 CDF RunII DATA (L=2.65 fb ) SM + MSSM!"# 21

46 Supersymmetric top in the e+μ+bb+met, 3.1/fb 3 rd generation again - special role in SUSY Look for decay mode in e μ final state with ET Miss >18 GeV Low SM backgrounds (Z ττ,ttbar) Reject with δφ(lepton, ET Miss ) cuts no explicit b tag required Consider small and large δm(stop, sneutrino) drives kinematics of accepted events p p t 1 t 1 B( t 1 νb) = 100% R parity conserving Bin events in two kinematic variables HT: scaler sum of jet pt ST: scalar sum of lepton pt, ET Miss Null result: set limits in sneutrino/stop mass plane events Sneutrino mass (GeV) e!+ee Obs (1.1 fb -1 e!+ee Exp (1.1 fb ) e! Obs (3.1 fb e! Exp (3.1 fb <S ) ZZ T -1 D ) Run II Preliminary, 3.1 fb -1 ) M(t ~ 1 ) = M(b) + M( ) D Preliminary Result -1 WZ WW Z TOP W Z!! Z ee QCD Dzero data M[110,80] M[150,50] 60 4 LEP II excluded D0 Conference Note 5937-CONF Peter Wittich 240 LEP I excluded H T [GeV] Stop mass (GeV) Blue: this result 23

47 LHC From P. Jenni at Physics at the LHC 2010 conference

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50 Other MSSM goodies: Gauge coupling unification The lightest supersymmetric particle (LSP) can be Dark matter Local supersymmetry must incorporate gravity: {Q, Q } = P µ, { } { Fits well EWPT from LEP/Tevatron It has allowed us to write more than 20,000 papers