Inflation models after the Higgs discovery

Transcription

1 Inflation model after the Higg dicovery Fedor Bezrukov CERN & Univerity of Connecticut & RIKEN-BNL Reearch Center

2 Outline LHC and the Standard Model for Particle Phyic Experimental tatu of the SM Minimal extenion to incorporate everything Can SM be a good model up to the Planck cale? Inflationary model and the Higg Boon Role of the Higg at early Univere Higg inflation I Higg inflation dead? Concluion

3 LHC i nicely compatible with the Standard Model ma charge name Quark Lepton ⅔ Left Left Left Left Three Generation of Matter (Fermion) pin ½ I II III 2.4 MeV u 1.27 GeV c GeV t ⅔ ⅔ up charm top Right Right Right Left 4.8 MeV 14 MeV -⅓ -⅓ d down trange ν e ev ν electron neutrino Left Left Left μ ev ν muon neutrino Right Right Right Left 4.2 GeV -⅓ b bottom Left Left Left τ ev tau neutrino.511 MeV 15.7 MeV GeV e μ τ electron muon tau Right Right Right Boon (Force) pin 1 g gluon γ photon 91.2 GeV Z weak force 8.4 GeV W ± ±1 weak force H GeV Higg boon pin Decribe all laboratory experiment electromagnetim, nuclear procee, etc. all procee in the evolution of the Univere after the Big Bang Nucleoynthei (T < 1 MeV, t > 1ec) July 4, 212 Dicovery wa announced by LHC Lat particle of the Standard Model found Firt fundamental calar found

4 LHC CMS a Higg boon reult H! ZZ 13 Event / 3 GeV CMS Data Z+X Zγ*, ZZ m H =125 GeV -1 = 7 TeV, L = 5.1 fb Event / 3 GeV = 8 TeV, L = 5.3 fb m 4 (GeV) 6 K D > m (GeV) 4 σ/σ SM -1 CMS = 7 TeV, L = 5.1 fb 6 H γγ + H ZZ = 8 TeV, L = 5.3 fb Combined H γγ (untagged) H γγ H ZZ (VBF tag) m X (GeV) H γγ H ZZ H WW H ττ H bb CMS -1 = 7 TeV, L = 5.1 fb -1 = 8 TeV, L = 5.3 fb Bet fit σ/σ SM m H = GeV ure 4: Ditribution of the four-lepton invariant ma for the ZZ! 4` analyi. The int repreent the data, the filled hitogram repreent the background, and the open hiram how the ignal expectation for a Higg of mh = 125 GeV, added to the ckground expectation. New The inetboon how the m 4` ditribution ma after election of event with >.5, a decribed in the text. ble 3: The number of elected event, compared to the expected background yield and excted number of ignal event (mh = 125 GeV) for each final tate in the H! ZZ analyi. The imate of the Z + X background are baed on data. Thee reult are given for the ma range m 11 to 16 GeV. The total background and the oberved number of event are alo hown the three bin ( ignal region ) of Fig. 4 where an exce i een (121.5 < m 4` < 13.5 GeV). CMS 13 hannel 4e 4µ 2e2µ 4` Z background 2.7 ± ± ± ± X ll background (11 < m 4` < 16 GeV) 4. ± ± ± ± 3 berved (11 < m 4` < 16 GeV) ignal (mh = 125 GeV) 1.36 ± ± ± ±.78 Figure 19: Value of /SM for the combination (olid vertical line) and for individual decay mode (point). The vertical band how the overall /SM value.87 ±.23. The ymbol /SM denote the production cro ection time the relevant branching fraction, relative to the expectation. The horizontal bar indicate the ±1 tandard deviation uncertaintie on the /SM value for individual mode; they include both tatitical and ytematic uncertaintie. M h = ±.4(tat) ±.5(yt)GeV

5 1 = 7 TeV: Ldt = 4.7 fb 1 = 8 TeV: Ldt = 13 fb 1 = 7 TeV: Ldt = 4.6 fb 1 = 7 TeV: Ldt = fb 1 = 8 TeV: Ldt = fb 1 1 = 8 TeV: Ldt = 13 fb 1 = 7 TeV: Ldt = 4.8 fb 1 = 7 TeV: Ldt = 4.6 fb 1 1 = 8 TeV: Ldt = 2.7 fb dence of thee uncertaintie on the four-lepton invariant Overview ma pectrum ha been taken into account a dicued Inflationary model and the Higg Boon Concluion in Ref. [53]. Though a mall exce of event i oberved for m4l > 18 GeV, the meaured ZZ ( ) 4l cro ection [93] i conitent with the SM theoretical prediction. The impact of not uing the theoretical contraint on the ZZ LHC ATLAS a Higg boon reult ( ) yield on the earch for a Higg boon with mh < 2mZ ha been tudied in Ref. [87] and ev] ha been found to be negligible. The impact of the interference between a Higg ignal and the non-reonant gg ZZ ( ) background i mall and become negligible for mh < 2mZ epton pair [94]. didate and mbination aceofthe. Iolation are applied the dataribution of wn. itie are nd 3.6% ribed in tion and m cale of W, certainty ainty on iency i e) chan- ±.9% arly, the ue to the identifir the 4e reache The unn an un cale channel. n energy 6 Event/5 GeV Data (*) Background ZZ Background Z+jet, tt Signal (m =125 GeV) H Syt.Unc. -1 = 7 TeV: Ldt = 4.8 fb -1 = 8 TeV: Ldt = 5.8 fb ATLAS (*) H ZZ 4l m 4l [GeV] Figure 2: The ditribution of the four-lepton invariant ma, m4l, for the elected candidate, compared to the background expectation in the 8 25 GeV ma range, for the combination of the = 7TeV and = 8TeVdata.TheignalexpectationforaSMHiggwith mh = 125 GeV i alo hown. New particle ma 4.4. Reult The expected ditribution of m4l for the background and for a Higg boon ignal with mh = 125 GeV are compared to the data in Fig. 2. The number of oberved and expected event in a window of ±5 GeV around mh = 125 GeV are preented for the combined ATLAS 13 Signal trength (µ) ATLAS Preliminary -1 = 7 TeV: Ldt = fb -1 = 8 TeV: Ldt = 2.7 fb Combined H (*) H ZZ 4l Bet fit 68% CL 95% CL m H [GeV] ATLAS Preliminary W,Z H bb H ττ = 8 TeV: Ldt = 13 fb (*) H WW lνlν H γγ = 8 TeV: Ldt = 2.7 fb (*) H ZZ 4l Combined µ = 1.43 ± M h = ±.2(tat) ±.6(yt)GeV.21 m H = GeV 1 +1 Signal trength (µ)

6 Reult till arriving tth production Lat week on Moriond Electroweak: Reult ATLAS Preliminary -1 =8 TeV, L dt=2.3 fb ATLAS Preliminary -1 =8 TeV, L dt=2.3 fb Dilepton tot. tat. ( tot ) ( tat ) Dilepton 2.9 ± 2.3 ( 1.4 ) Lepton+jet Expected ± 1σ Expected ± 2σ Lepton+jet 1.3 ± 1.6 (.8 ) Combination Oberved Expected ( µ=1) Combination 1.7 ± 1.4 (.7 ) % CL limit on σ/σ SM at m H =125 GeV bet fit µ=σ/σ SM for m H =125 GeV Reminder of 7 TeV analyi `+jet channel 95% CL oberved (expected) limit: 13.1 SM (1.5 SM) ATLAS-CONF Combination of `+jet and dilepton channel 95% CL oberved (expected) limit: 4.1 SM ( 2.6 SM) Bet fit µ =1.7±1.4 ATLAS-CONF Reult conitent with SM prediction. 2/3/214 Eve Le Ménédeu 11/12

7 LHC for now one lide ummary Standard Model Higg boon with the ma about 125 GeV

8 Minimal extenion of the SM to account for everything Should explain everything Neutrino ocillation Dark Matter Baryon aymmetry of the Univere Inflation in a minimal way νmsm Introduce minimal amount of new particle/parameter Simple Predictive No new cale up to gravity/inflation With cale invariance remove hierarchy problem Allow to make relation between inflation and particle phyic

9 Standard Model up to Planck cale Renormalization evolution of the Higg elf coupling λ Coupling contant evolution: (4π) 2 β λ = 24λ 2 6y 4 t Strong coupling (2g4 2 + (g2 2 + g2 1 )2 ) + ( 9g 2 2 3g y 2 t )λ High M h trong coupling Low M h our (EW) vacuum i metatable. Boundary ituation M h = M min M h mmax M h m min Zero Planck Higg potential V (φ) λ(φ) φ 4 V φ Fermi Planck Fermi Planck V 4 φ Μ

10 Λ Higg ma i within 2σ from critical ± V Μ Strong coupling Α S M Z Higg ma M h 125.3±.6 GeV Pole top ma M t, GeV [ ] M h critical = y t (173.2GeV) α GeV FB, Kalmykov, Kniehl, Shapohnikov 12, Degrai et.al 12, Buttazzo et.al 13

11 If the Higg tart at electroweak vacuum, it jut tay there 128 p decay e S bounce e 8π8 3λ(h) Even if the vacuum i metatable, it live much longer than the Univere age m h, GeV t 1 8 t 1 2 U U t U Decay at hot tage after inflation lightly tronger bound M h 116 GeV Epinoa, Giudice, Riotto 7 Even tronger bound for conformally coupled Higg, M h ±... Gorbunov, Tokareva 12 t

12 Should go earlier in time! Preent day laboratory experiment can not ditinguih table/metatable electroweak vacuum Evolution of the Univere after reheating can proceed in any ituation Let u go earlier Inflation Somewhat implitic view: Inflation may (or may not) force the Higg field to get large value. Thi would lead to the Univere to get into the Planck cale minimum if the Higg ma i below critical M h < M crit Inflation may be otherwie related to the ingle calar field we know

13 Inflationary model and the Higg boon Additional m 2 φ 2 2, Bound inglet ξ φ 2 R 2 + λ φ 4 4, or inflaton... no bound any R 2 inflation M 2 P R 2 + ar2 Higg ma i ok inflation ξ H HR + λ(h H) 2, Bound uing cg µν µ H ν H + λ(h H) 2, or Higg fale Planck-cale vacuum, prediction!...

14 Chaotic inflation a calar field λ (2M P ) 4 4 ȧ 2 a 2 H 2 1 ( ) 3MP 2 V (φ) + φ 2 /2, φ + 3H φ + V (φ) = V λ 4 φ 4 3M P Slow roll inflation 2M P φ δt /T 1 5 normalization: quartic coupling: λ 1 13 Can not be the SM Higg field? (or ma: m 1 13 GeV)

15 With large non-minimal coupling no new particle are needed Standard Model Higg boon itelf can be ued a inflaton Scalar part of the (Jordan frame) action S J = d 4 x { } g M2 P h2 R ξ 2 2 R +g µ h ν h µν λ 2 4 (h2 v 2 ) 2 h i the Higg field; M P 1 8πGN large ξ allow for large λ ξ λ 47 = GeV SM higg vev v M P / ξ FB,Shapohnikov 7

16 Conformal tranformation nice way to calculate It i poible to get rid of the non-minimal coupling by the conformal tranformation (change of variable) ĝ µν = Ω 2 g µν, Ω ξ h2 M 2 P Redefinition of the Higg field to get canonical kinetic term { dχ dh = Ω 2 + 6ξ 2 h 2 /MP 2 h χ for h < MP /ξ Ω 4 = ( ) Ω 2 exp 2χ 6MP for h > M P /ξ Reulting action (Eintein frame action) S E = d 4 x ĝ { } M2 P 2 ˆR + µ χ µ χ λ h(χ) Ω(χ) 4

17 Potential different tage of the Univere λm 4 P 4ξ 2 U λ(χ 2 v 2 ) 2 ( ) 2 4λM4P 4ξ 2 1 e 2χ/ 6M P M P/ξ M P χ WMAP 5.4M P χ Hot Big Bang Preheating (matter dominated) Slow roll inflation δt /T 1 5 normalization ξ λ 47 n.967 r.32

18 Higg Inflation nice in the center of the allowed region ξ= ξ=.1 Prediction of inflationary model: Higg inflation 2 R inflation ξ=.1 Non-minimal derivative coupling ξ=.1

19 Higg can not be too light!.6 Radiative.4 correction to inflationary potential: Higg inflation work Λ V ± V M H >M crit only.2 for λ(m P / (ξ)) >. Numerically,M H >M crit withφ extra. theoretical uncertainty of δm H 1 GeV..2 Fermi Planck V Μ M H >M crit V M H <M crit V (h) = λ(h)h4 4 = U(h(χ)) = φ V (h) Ω 4 (h) φ Fermi Planck Fermi Planck

20 BICEP2 reult Higg inflation no more? ξ= ξ=.1 Prediction of inflationary model: Higg inflation 2 R inflation ξ=.1 ξ=.1.4 Non-minimal derivative coupling Planck+WP+highL Planck+WP+highL+BICEP2.3 r n

21 Higg inflation better than ever! You could have gueed: Of coure it i alive! Only thank to a nontrivial et of coincidence! λ min at about Planck cale good top quark ma good Higg boon ma [Hamda, Kawai, Oda, Park ; FB, Shapohnikov 143.next Tueday]

22 Radiative correction are important for the critical Higg ma λ Radiatively corrected potential U(χ) λ(µ)m4 P 4ξ 2 µ 2 = κ 2 y t(µ) 2 2 (1 e 2χ 6MP ) 2 MP 2 ) (1 e 2χ 6MP ξ (µ) (λ at top quark ma in the higg background) λ q µ Parameter in particle phyic: λ, q (or M h, M t ), ξ comology: P R, r, n

23 Ξ Potential: U M P Work jut in the critical point And only for a light top quark! M P n r h (Preliminary) mt,gev

24 Two regime of Higg inflation Large ξ Prediction for comology r =.3, n =.96 For particle phyic jut bound on the Higg ma M h > M crit Small ξ Prediction for comology n related to r For particle phyic very precie relation between the M h and M t. Prediction of M t once r (or n ) i known.

25 Concluion LHC Standard Model Higg with M h 125 EW vacuum can be metatable or table Inflation Depending on the model May ay nothing (e.g. R 2 ) May are ok only if M h (M t 173.2) GeV (e.g. Higg inflation in large ξ regime, many model with additional inflaton) Or even predict Higg an top quark mae! (Higg inflation in the mall ξ regime) Needed in the future Good meaurement of n and r Meaure M t and M h