The ``Higgs'' Discovery

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Higgsportal The “Higgs” discovery Johan Rathsman - a portal to new physics

Johan Rathsman

Department of astronomy and theoretical physics, 2012-10-17

1 / 1 Higgsportal

Johan Rathsman The “Higgs” discovery

2 / 1 Now also in the world of particle physics

July 4th 2012 - a historic day in many ways ...

Higgsportal

Johan Rathsman

3 / 1 Now also in the world of particle physics

July 4th 2012 - a historic day in many ways ...

Higgsportal

Johan Rathsman

4 / 1 Now also in the world of particle physics

July 4th 2012 - a historic day in many ways ...

Higgsportal

Johan Rathsman

5 / 1 July 4th 2012 - a historic day in many ways ...

Higgsportal

Johan Rathsman

Now also in the world of particle physics

6 / 1 July 4th 2012 - a historic day in many ways ...

Higgsportal

Johan Rathsman

Now also in the world of particle physics

7 / 1 and in Lund

Higgsportal

Johan Rathsman

8 / 1 Published

Higgsportal

Johan Rathsman

9 / 1 Published

Higgsportal

Johan Rathsman

10 / 1 Published

Higgsportal

Johan Rathsman

11 / 1 LHC data in H → γγ channel

proton proton collider with 7/8 TeV center of mass energy Higgsportal Two multipurpose experiments: ATLAS and CMS Johan Rathsman

H → γγ on-shell ⇒ spin 0 or 2

12 / 1 ATLAS data – exclusion

Standard Model Higgs particle excluded (95 % CL): 111 < mH < 122 GeV and 131 < mH < 559 GeV Higgsportal

Johan Rathsman

13 / 1 ATLAS data – signal

Compatibility with background only hypothesis: observed and expected in standard model

Higgsportal

Johan Rathsman

⇒ mH = 126.0 ± 0.4(stat) ± 0.4(sys) GeV

14 / 1 CMS data – signal

Compatibility with background only hypothesis: observed and expected in standard model

Higgsportal

Johan Rathsman

⇒ mH = 125.3 ± 0.4(stat) ± 0.5(sys) GeV

15 / 1 preLHC experimental results in standard model

Direct LEP-limit: mH > 114 GeV (95% CL)

Indirect electroweak precision tests: mH < 158 GeV (95% CL)

Higgsportal

Johan Rathsman

very good agreement with direct detection!

16 / 1 Higgsportal

Johan Rathsman The standard model of particle physics

17 / 1 The particle content of the standard model Describes the electromagnetic, weak and strong forces

Higgsportal

Johan Rathsman

All particles observed – that’s it?

18 / 1 Gauge symmetries and Lagrangians dynamics of relativistic quantum ﬁeld theory described by Lagrangian (density) L = K − V standard model with U(1)Y ⊗ SU(2)L ⊗ SU(3)C gauge iYf α(x)/2 3 Higgsportal symmetry (local transf. of type e , Yf = 2Qf − 2If ) Johan Rathsman uL LSM = (¯uL, d¯L)iD/ +u ¯RiDu/ R + d¯RiDd/ R + ... dL 1 1 1 − B Bµν − W i W µν − G a G µν 4 µν 4 µν i 4 µν a p 2 2 p 2 2 where (e = g1g2/ g1 + g2 , sin θw = g1/ g1 + g2 ): Y σ λ D = ∂ − ig f B − ig i W i − ig a G a µ µ 1 2 µ 2 2 µ s 2 µ Bµν = ∂µBν − ∂ν Bµ i i i ijk j k Wµν = ∂µWν − ∂ν Wµ + g2 WµWν a a a abc b c Gµν = ∂µGν − ∂ν Gµ + gs f GµGν

explicit mass terms would break SU(2)L gauge symmetry 1 L = −m (¯u u +u ¯ u ) + M2 W 3W 3µ + ... mass u R L L R 2 V µ 19 / 1 Englert–Brout–Higgs–Guralnik–Hagen–Kibble– ... mechanism

Higgsportal

Johan Rathsman

Spontaneous breaking of SU(2)L gauge symmetry weak force carriers W and Z massive quarks and leptons can be given masses through Yukawa interaction with Higgs ﬁeld one more massive particle – the Higgs boson

20 / 1 Spontaneous breaking of global symmetry µ Complex ﬁeld φ with L = ∂µφ∂ φ − V (φ) and potential

1 1 V (φ) = − µ2|φ|2 + λ|φ|4 Higgsportal 2 4 Johan Rathsman L unchanged under φ → φeiα µ minimum: v = √ λ expand around minimum φ = v + H + iG and identify term in 2 2 front of H and G √ ⇒ “Higgs” mass: mH = 2λv (radial excitations) Nambu-Goldstone mass: mG = 0 (angular excitations) Symmetry broken by ground state – spontaneous symmetry breaking (Nobel prize 2008) ⇒ equations of motion unchanged If the symmetry is local (φ → φeiα(x)) the Nambu-Goldstone boson is “eaten” by the gauge ﬁeld making it massive

21 / 1 Electroweak symmetry breaking in Standard Model Higgs sector in Standard Model √ Higgsportal 1 2G + Johan Rathsman Add complex doublet Φ = √ 2 v + H + iG 0 2 with Lagrangian LHiggs = |DµΦ| − V (Φ) where Y σ D Φ = ∂ − ig f B − ig i W i Φ µ µ 1 2 µ 2 2 µ and the potential contains all the self-interactions of Φ 2 † 1 † 2 V (Φ) = −µ Φ Φ + 2 λ Φ Φ

Higgs mechanism in Standard Model µ2 > 0 ⇒ vacuum expectation value v ≈ 246 GeV/c2 ⇒ SU(2)L⊗U(1)Y “spontaneously” broken to U(1)e.m. three would be Nambu-Goldstone bosons G 0 and G ± (longitudinal components of Z and W ) 2 2 one massive Higgs ﬁeld H, mH = λv

22 / 1 Vector boson masses and interactions with Higgs ﬁeld 1 0 In unitary gauge Φ = √ 2 v + H Higgsportal 1 1 W ± = √ (W 1 ∓ iW 2) and Z = (g W 3 − g B ) Johan Rathsman µ µ µ µ p 2 2 2 µ 1 µ 2 g1 + g2 couple to the Higgs ﬁeld through 1 1 |D Φ|2 = g 2W +W −µ(v + H)2 + (g 2 + g 2)Z Z µ(v + H)2 + ... µ 4 2 µ 8 1 2 µ giving masses 1 1q m = g v , m = g 2 + g 2v W 2 2 Z 2 1 2 and interactions

2 2 2mW + −µ 2mZ µ L 2 = W W H + Z Z H + ... |DµΦ| ,int v µ v µ

23 / 1 Fermion masses and interactions with Higgs ﬁeld Add Yukawa type interaction (example d-quark)

Higgsportal LY = −yd (¯u, d¯)LΦdR + h.c. Johan Rathsman In unitary gauge

v H H LY = −yd √ (d¯LdR + d¯RdL) 1 + = −md dd¯ 1 + 2 v v giving mass v md = yd √ 2 and coupling to Higgs m L = − d ddH¯ Y,int v

24 / 1 Why is the Higgs boson so “light”?

Standard Model is an eﬀective theory ⇒ expect it to break Higgsportal down at some high scale Λ (e.g. Planck mass ∼ 1019 GeV ) Johan Rathsman Calculating the one-loop corrections to the Higgs boson mass one ﬁnds

3Λ2 m2 = m2 + 4m2 − 2m2 − 4m2 − m2 H H,0 8π2v 2 t W Z H ⇒ “natural scale” for Higgs boson mass given by Λ and not v 2 2 (tree-level mH = λv ) Solutions: 2 ﬁne-tuning – mH,0 cancels one-loop correction “exactly” Higgs boson is not a fundamental scalar (e.g. Technicolor) There is a symmetry that protects the Higgs boson from acquiring a large mass

25 / 1 Higgsportal

Johan Rathsman Theory beyond the standard model

26 / 1 Supersymmetry - one possible solution Why is this not a problem for fermions? Protected by Chiral symmetry:

Higgsportal the Lagrangian gets an additional symmetry if mf → 0 ⇒ higher order corrections have to be proportional to m Johan Rathsman f ⇒ only log(Λ) dependence ⇒ no ﬁne-tuning

SUSY solution introduce Higgsino – SUSY fermion partner to Higgs boson

Higgsino mass mH˜ is protected by the Chiral symmetry

Imposing (exact) SUSY mH = mH˜ is also stabilized

SUSY complications Anomaly cancelation and analytic structure of SUSY Lagrangian ⇒ the SM cannot be supersymmetrized as is – have to add an additional Higgs doublet No supersymmetric partners observed ⇒ Supersymmetry has to be softly broken ⇒ plethora of parameters

27 / 1 Particle content minimal supersymmetric model

Higgsportal

Johan Rathsman

28 / 1 Higgs sector of minimal supersymmetric model

Two complex Higgs doublets: Hu and Hd ⇒ 5 scalar degrees of freedom after electroweak symmetry breaking

Higgsportal ± CP conserved: h, H (CP-even, mh ≤ mH ), A (CP-odd), H Johan Rathsman supersymmetry ⇒ Higgs potential very constrained – only two parameters at tree-level:

0 vu hHu i mH± , tan β = = 0 vd hHd i Other masses determined at tree-level

2 2 2 mA = mH± − mW 1 q m2 = m2 + m2 ∓ (m2 + m2 )2 − 4m2 m2 cos2 2β h,H 2 A Z A Z A Z

2 2 2 ⇒ mh ≤ mZ cos 2β (equality in decoupling limit, mH± → ∞)

approximate custodial symmetry mA ≈ mH ≈ mH±

29 / 1 Couplings and mixings

mixing of CP-even Higgs bosons 0 H cos α sin α Hd Higgsportal = 0 h − sin α cos α Hu Johan Rathsman 2 2 mH + mh at tree-level sin 2α = − 2 2 sin 2β mH − mh

Couplings relative to standard model ZZh, WWh: sin(β − α) ZZH, WWH: cos(β − α) uuh : cos(α)/ sin(β) = sin(β − α) + cot β cos(β − α) uuH : sin(α)/ sin(β) = cos(β − α) − cot β sin(β − α) ddh : − sin(α)/ cos(β) = sin(β − α) − tan β cos(β − α) ddH : cos(α)/ cos(β) = cos(β − α) + tan β sin(β − α)

standard model limit: sin(β − α) → 1, mH± → ∞

30 / 1 Higher order corrections to Higgs sector

All particles enter through loops Higgsportal Sensitivity to supersymmetry breaking parameters Johan Rathsman 4 2 2 2 2 2 3mt mS Xt Xt mh = mh,tree + 2 2 log 2 + 2 1 − 2 + ... 2π vu mt mS 12mS where m˜ + m˜ - m = t1 t2 with ˜t the two stop mass eigenstates S 2 1,2 - Xt = At − µ cot β, At is a supersymmetry breaking contribution to the Higgs-stop-stop coupling, µ is the Higgsino mass parameter 2 2 Maximal mixing: Xt = 6mS ⇒ mh . 135 GeV 2 No mixing: Xt = 0 ⇒ mh . 120 GeV Supersymmetry predicts at least one light Higgs boson

31 / 1 Higgsportal

Johan Rathsman Interpretation of data beyond the standard model

32 / 1 ��

�� 2 2 2 M M M ± , β ΔM MSUSY,X ,... Higgsportal h = h,tree ( H tan )+ h( t )

Johan Rathsman ��

MSUSY = 1 TeV ��

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�� courtesy Oscar St˚al(Stockholm) from H+2012 in Uppsala

33 / 1 ��

�� Higgsportal ��

Johan Rathsman

�� H/A→ ττ �� 2 2 2 MH± =M A +M W

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MH± > 161 GeV tanβ>4

�� courtesy Oscar St˚al(Stockholm) from H+2012 in Uppsala

34 / 1 ��

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Higgsportal ��

Johan Rathsman ��

µ = 1 TeV

MSUSY = 1 TeV

Xt = 2.3 MSUSY �� courtesy Oscar St˚al(Stockholm) from H+2012 in Uppsala

35 / 1 Diﬀerent “Higgs” boson decay channels

Higgsportal Johan Rathsman Branching fraction in SM

Experimental sensitivity

36 / 1 Signal strength relative to standard model expectation

Higgsportal

Johan Rathsman

depends also on production mode (gluon-gluon fusion, vector-boson fusion (VBF) , Higgs strahlung (VH))

37 / 1 ��

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Higgsportal

Johan Rathsman

�� courtesy Oscar St˚al(Stockholm) from H+2012 in Uppsala

38 / 1 ��

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Higgsportal

Johan Rathsman

�� courtesy Oscar St˚al(Stockholm) from H+2012 in Uppsala

39 / 1 ��

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Higgsportal

Johan Rathsman

�� courtesy Oscar St˚al(Stockholm) from H+2012 in Uppsala

40 / 1 Conclusions

The discovery of a Higgs-like particle marks a new era in (particle) physics

Higgsportal Completes the particle content of the standard model – time Johan Rathsman to look beyond So far experimental data in agreement with standard model expectations – still room for surprises Supersymmetric models give equal or better description of available data Precision measurements of all possible combinations of production and decay channels will test if standard model is correct at LHC energies Higgs physics has gone from discovery mode to precision measurements (also possible at hadron collider) LHC will continue running until February 2013 and then have a break until November 2014 to go to design energy Stay tuned

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