Higgs Physics at the Large Hadron Collider

Transcription

1 Italo-ellenic School of Physics, Lecce, June 2006 iggs Physics at the Large adron Collider Michael Krämer (RWT Aachen) Electroweak symmetry breaking The profile of the Standard Model iggs boson iggs searches at the LC Michael Krämer Page 1 Italo-ellenic School of Physics 2006

2 Literature I have used the following references to prepare these lectures: Lectures from Maria Laach schools, in particular those by S. Dawson and M.L. Mangano; Lectures from previous Lecce schools, in particular those by C. Oleari and D. Zeppenfeld; Lectures by D. Ross at the Scottish University Summer School SUSSP57; Review articles by: A. Djouadi (hep-ph/ ),. Spiesberger, M. Spira, P.M. Zerwas (hepph/ ); C. Quigg (hep-ph/ ) textbooks, mainly: Peskin & Schroeder, Barger & Phillips. Michael Krämer Page 2 Italo-ellenic School of Physics 2006

3 Introduction: The Standard Model and beyond The SM Lagrangian is determined by the particle content Poincare invariance local gauge invariance under SU(3), SU(2) and U(1) renormalizability and the mechanism of electroweak symmetry breaking L SM = 1F a 4 µνf aµν + i ψdψ gauge sector +ψ i λ ij ψ j + h.c. flavour sector + D 2 V () EWSB sector +N i M ij N j ν-mass sector Michael Krämer Page 3 Italo-ellenic School of Physics 2006

4 The SM Lagrangian looks a bit more complicated when you spell it out (typed by T.D.Gutierrez from Diagrammatica by M.Veltman) L SM = 1 2 ν g a µ ν g a µ g sf abc µg a ν gb µ gc ν 1 4 g2 s fabc f ade g b µ gc ν gd µ ge ν ig2 s ( qσ i γµ q σ j )ga µ + Ḡa 2 G a + gsf abc µḡa G b gµ c ν W µ + ν W µ M2 W µ + W µ 2 1 ν Zµ 0 ν Zµ 0 1 2c 2 M 2 Zµ 0 Z0 µ 2 1 µaν µaν 2 1 µ µ w 1 m 2 2 h 2 µφ + µφ M 2 φ + φ 2 1 µφ 0 µφ 0 1 2c 2 Mφ 0 φ 0 β h [ 2M2 w g 2 + 2M g (2 + φ 0 φ 0 + 2φ + φ )] + 2M 4 g 2 α h igc w [ ν Zµ 0 (W µ + W ν W ν + W µ ) Z0 ν (W µ + ν W µ W µ ν W µ + ) + Z0 µ (W ν + ν W µ W ν ν W µ + )] igsw [ ν Aµ(W + µ W ν W + ν W µ ) A ν (W + µ ν W µ W µ ν W + µ )+A µ(w + ν ν W µ W ν ν W + µ )] 1 2 g2 W + µ W µ W + ν W ν g 2 W + µ W ν W + µ W ν + g2 c 2 w (Z0 µ W + µ Z0 ν W ν Z0 µ Z0 µ W + ν W ν ) + g2 s 2 w (A µw + µ A ν W ν A µaµw + ν W ν ) + g 2 sw cw [AµZ 0 ν (W + µ W ν W + ν W µ ) 2A µz 0 µ W + ν W ν ] gα[3 + φ 0 φ 0 + 2φ + φ ] 1 8 g2 α h [ 4 + (φ 0 ) 4 + 4(φ + φ ) 2 + 4(φ 0 ) 2 φ + φ φ + φ + 2(φ 0 ) 2 2 ] gmw + µ W µ 1 2 g M c 2 w Z 0 µ Z0 µ 1 2 ig[w + µ (φ0 µφ φ µφ 0 ) W µ (φ0 µφ + φ + µφ 0 )] g[w + µ ( µφ φ µ) W µ ( µφ + φ + µ)] g 1 cw (Z0 µ ( µφ 0 φ 0 µ) ig s2 w c w MZ0 µ (W µ + φ W µ φ+ )+igsw MAµ(W µ + φ W µ φ+ ) ig 1 2c2 w 2cw Z0 µ (φ+ µφ φ µφ + )+igsw Aµ(φ + µφ φ µφ + ) 4 1 g2 W µ + W µ [2 +(φ 0 ) 2 +2φ + φ ] 4 1 g2 1 c 2 Z µ 0 Z0 µ [2 +(φ 0 ) 2 +2(2s 2 w 1)2 φ + φ ] 2 1 g2 s2 w c w Z0 µ φ0 (W µ + φ + w W µ φ+ ) 1 2 ig2 s2 w c w Z0 µ (W µ + φ W µ φ+ ) g2 sw Aµφ 0 (W µ + φ + W µ φ+ ) ig2 sw Aµ(W µ + φ W µ φ+ ) g 2 sw c w (2c2 w 1)Z0 µ A µφ + φ g 1 s 2 w A µaµφ + φ ē λ (γ + m λ e )eλ ν λ γ ν λ ū λ j (γ + mλ u )uλ j d λ j (γ + mλ d )dλ j + igsw Aµ[ (ē λ γ µ e λ )+ 2 3 (ūλ j γµ u λ j ) 3 1 ( d λ j γµ d λ j )]+ ig 4cw Z0 µ [( νλ γ µ (1+γ 5 )ν λ )+(ē λ γ µ (4s 2 w 1 γ5 )e λ )+(ū λ j γµ ( 4 3 s2 w 1 γ 5 )u λ j ) + ( d λ j γµ (1 3 8 s2 w γ5 )d λ ig )] + j 2 2 W µ + [( νλ γ µ (1 + γ 5 )e λ ) + (ū λ j γµ (1 + γ 5 )C λκ d κ j γ 5 )ν λ ) + ( d κ j C λκ γµ (1 + γ 5 )u λ j )] + iφ 0 (ē λ γ 5 e λ )] + ig 2 2 m λ e M [ φ+ ( ν λ (1 γ 5 )e λ ) + φ (ē λ (1 + γ 5 )ν λ )] g 2 ig 2M 2 φ+ [ m κ d (ūλ j C λκ (1 γ5 )d κ j ) + mλ u (ūλ j C λκ (1 + γ5 )d κ j ] + m κ u ( d λ j C λκ (1 γ5 )u κ j ] g m λ u (ū 2 λ M j uλ j ) g m λ d 2 M ( d λ j dλ j ) + ig 2 m λ u M φ 0 (ū λ j γ5 u λ j ) ig 2 )] + ig 2 2 W µ [(ēλ γ µ (1 + m λ e M [(ēλ e λ ) + ig 2M 2 φ [m λ d ( d λ j C λκ (1 + γ5 )u κ j ) m λ d M φ0 ( d λ j γ5 d λ j ) + X + ( 2 M 2 )X + + X ( 2 M 2 )X + X 0 ( 2 M2 c 2 )X 0 + Ȳ 2 Y + igcw W µ + ( µ X 0 X µ X + X 0 ) + igsw W µ + ( µȳ X w µ X + Y ) + igcw W µ ( µ X X 0 µ X 0 X + ) + igsw W µ ( µ X Y µȳ X+ ) + igcw Zµ 0 ( µ X + X + µ X X ) + igsw Aµ( µ X + X + µ X X ) 1 2 gm[ X + X + + X X + 1 c 2 w X 0 X 0 ] + 1 2c2 w 2cw igm[ X + X 0 φ + X X 0 φ ] + 1 2cw igm[ X 0 X φ + X 0 X + φ ] + igmsw [ X 0 X φ + X 0 X + φ ] igm[ X + X + φ 0 X X φ 0 ] Michael Krämer Page 4 Italo-ellenic School of Physics 2006

5 From W W -scattering to the iggs boson Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ e ν e ν µ L = G F 2 [ ν µ γ λ (1 γ 5 )µ][ēγ λ (1 γ 5 )ν e ] with G F GeV 2 (Fermi coupling) Fermi theory at high energies: M[ ν µ e µ ν e ] G F 2 2π s violates unitarity Solution: interaction mediated by heavy vector boson W ± M[ ν µ e µ ν e ] G F s 2 2π M 2 W M 2 W s (with M W 100 GeV) Michael Krämer Page 5 Italo-ellenic School of Physics 2006

6 From W W -scattering to the iggs boson Consider W W W W M[W L W L W L W L ] s violates unitarity Solution: strong W W interaction at high energies or new scalar particle with g W W M W M GF M 2 4 2π Unitarity properties of : coupling g XX particle mass M X M < 1 TeV Michael Krämer Page 6 Italo-ellenic School of Physics 2006

7 Spontaneous symmetry breaking I: the ABEGK t Mechanism (Anderson, Brout, Englert, Guralnik, agen, iggs, Kibble, t ooft) Generating particle masses requires breaking the gauge symmetry M W,Z 0 0 X 0 0 Standard Model: Spontaneous symmetry breaking through scalar isodoublet Φ ( Φ = 1 2 φ 1 + iφ 2 φ 3 + iφ 4 ) with scalar potential V = µ 2 Φ 2 + λ Φ 4 If µ 2 < 0 (why?), then the minimum of the potential is at ( Φ = v ) where v = µ 2 / λ spontaneous symmetry breaking 3 Goldstone bosons mass for W ±, Z 1 physical scalar (iggs) particle Michael Krämer Page 7 Italo-ellenic School of Physics 2006

8 Spontaneous symmetry breaking I: U(1)-Example Or: ow to generate masses for gauge bosons without violating gauge invariance? Recall structure of U(1) local gauge theory with single spin-1 gauge field A µ : L = 1 4 F µνf µν where F µν = ν A µ µ A ν mass term m 2 A µ A ν not gauge invariant massless gauge boson A Possible solution: add complex scalar field φ with charge e: L = 1 4 F µνf µν + D µ φ 2 V (φ) where V (φ) = µ 2 φ 2 + λ φ 4 If µ 2 > 0: unique minimum at φ = 0 QED with M A = 0 and M φ = µ Reverse sign of µ 2 so that V (φ) = µ 2 φ 2 + λ φ 4 minimum of potential at µ2 2λ v 2 Expand φ around vacuum expectation value: φ = 1 2 (v + + iχ) L = 1 4 F µνf µν µ µ + µ χ µ χ e2 v 2 A µ A µ + eva µ µ χ ea µ (χ µ µ χ) e2 A µ A µ ( 2 + χ 2 ) V (φ) Michael Krämer Page 8 Italo-ellenic School of Physics 2006

9 Spontaneous symmetry breaking I: U(1)-Example L = 1 4 F µνf µν µ µ + µ χ µ χ e2 v 2 A µ A µ + eva µ µ χ ea µ (χ µ µ χ) e2 A µ A µ ( 2 + χ 2 ) V (φ) The theory now has: a photon of mass M A = ev a scalar field with M 2 = 2µ2 > 0 a massless scalar field χ (Goldstone boson) The mixed A χ propagator can be removed by a gauge transformation: A µ A µ 1 ev µχ and φ e i χ v φ (unitary gauge) the χ field has been absorbed by a redefinition of A (jargon: χ has been eaten to give photon mass) Counting of degrees of freedom: before symmetry breaking: massless gauge boson (2 dof) and complex scalar (2 dof) after symmetry breaking: massive gauge boson (3 dof) and physical scalar (1 dof) Michael Krämer Page 9 Italo-ellenic School of Physics 2006

10 Spontaneous symmetry breaking I: the ABEGK t Mechanism? John Earman, Philosopher, on the need to choose a specific gauge to suppress Goldstone bosons and generate masses for gauge bosons: A genuine property like mass cannot be gained by eating descriptive fluff, which is just what gauge is Michael Krämer Page 10 Italo-ellenic School of Physics 2006

11 The birth of the iggs boson Michael Krämer Page 11 Italo-ellenic School of Physics 2006

12 Spontaneous symmetry breaking II: superconductivity Ginzburg-Landau description: F super (B = 0) = F free (B = 0) + α Ψ 2 + β Ψ 4 T > T c : α > 0 Ψ 0 = 0 T < T c : α < 0 Ψ 0 0 Microscopic mechanism (Bardeen, Cooper, Schrieffer): electromagnetic gauge invariance is broken by Cooper pairs of electrons with 0 ēe 0 0 Weisskopf, Cornell seminar (recalled by Brout), 1960: Particle physicists are so desperate these days that they have to borrow from the new things coming up in many-body physics - like BCS. Perhaps something will come of it... Michael Krämer Page 12 Italo-ellenic School of Physics 2006

13 Spontaneous symmetry breaking III: chiral symmetry in QCD For m up, m down = 0: L QCD = q L D/ q L + q R D/ q R (q L,R =(1 γ)q/2) independent left and right rotations permitted: U(2) L U(2) R (chiral) symmetry Spontaneous breaking of chiral symmetry through quark condensate: 0 qq 0 0 q L q R + q R q L 0 Λ 3 QCD (250 MeV) massless Goldstone bosons: π 0, π ± dynamical quark masses heavy nucleons QCD lite TM (2 massless quarks and gluons) 90% of mass of ordinary matter (without the iggs particle... ) In the real world m up, m down 0 and chiral symmetry is not exact. But m up, m down Λ QCD and m π m proton,neutron,... Michael Krämer Page 13 Italo-ellenic School of Physics 2006

14 Dynamical electroweak symmetry breaking: Technicolour SSB in condensed matter physics and QCD through fermion condensate 0 F F 0 0 EWSB through new strong interactions of new massless fermions ( technicolour ): 0 T T 0 Λ 3 TC (1 TeV) 3 0 massless technipions masses for W ±, Z via Brout-Englert-iggs mechanism new bound states ( technihadrons ) with M 1 TeV To give masses to the Standard Model quarks and leptons must add interactions between T, q, l ( extended technicolour ) Features + no fundamental scalar needed + dynamical generation of hierachy Λ TC /M Planck through RGE running What breaks extended technicolour? ow to accommodate FCNC and electroweak precision tests? ( walking technicolour ) ow to accomodate the large top quark mass? ( topcolour assisted technicolour ) Michael Krämer Page 14 Italo-ellenic School of Physics 2006

15 EWSB: fundamental iggs boson or fermion condensate? fundamental iggs boson + simple and predictive + consistent with precision data no dynamical explanation of EWSB fundamental scalar has never been observed in nature fermion condensate + analogous to existing mechanisms (BCS, QCD) + no fundamental scalar no naturalness problem less predictive (strongly interacting theorie) no realistic and compelling models(?) iggs mass unstable under radiative corrections: why is M iggs M Planck? (naturalness problem) Michael Peskin, EPS 99: The idea that the data drives us to a weak-coupling picture of the iggs boson was controversial at EP99. Among the people arguing vocally on the other side were olger Nielsen and Gerard t ooft. So if you do not wish to accept this argument, you are in good company (but still wrong). Michael Krämer Page 15 Italo-ellenic School of Physics 2006

16 The profile of the Standard Model iggs boson Consider first the iggs kinetic term L D µ Φ 2 with the covariant derivative of the SU(2) U(1) gauge theory D µ = µ + i g W 2 σi W i µ + i g W 2 B µ Expanding Φ about its vacuum expectation value ( Φ = v + ) the covariant derivative may be written (in unitary gauge) ( D µ Φ = 1 µ + i g W 2 2 ( W 0 µ 2W µ 2W + µ W 0 µ ) + i g W 2 B µ ) ( 0 v + ) which leads to L D µ Φ 2 = 1 2 ( µ) 2 + g2 W v 2 W +µ Wµ 4 + v2 8 (g W W 0 µ g W B µ ) 2 + interaction terms Michael Krämer Page 16 Italo-ellenic School of Physics 2006

17 The profile of the Standard Model iggs boson L D µ Φ 2 = 1 2 ( µ) 2 + g2 W v2 4 W +µ W µ + v2 8 (g W W 0 µ g W B µ ) 2 + interaction terms massive gauge bosons: W µ ± and Z 1 µ = (g 2 )(g W W W +g 2 µ 0 g W B µ) W with masses: M ± W = 1 2 g W v and M Z = 1 2 (g 2 W + g 2 W ) v 1 Orthogonal superposition to Z: massless photon A µ = (g 2 W +g 2 W )(g W W µ 0 + g W B µ ) Introduce the electroweak mixing angle so that sin θ W = g W (g and cos θ W = 2W + g 2W ) g W (g 2 W + g 2 W ) g W = g W tan θ and M W = M Z cos θ W The iggs vacuum expectation value can be determined from the Fermi constant G F : ( ) 2 G F gw = MW 2 = v = 1 2GF GeV Michael Krämer Page 17 Italo-ellenic School of Physics 2006

18 The profile of the Standard Model iggs boson The iggs kinetic term L D µ Φ 2 also includes iggs gauge-boson interactions: D µ Φ 2 ( g 2 W 4 W + µ W µ + gw 2 ) ( 8 cos 2 Z µ Z 2 µ + 2v ) θ W = g W M W W + µ W µ + g W 2 cos θ W M Z Z µ Z µ + g2 W 4 W + µ W µ 2 + g 2 W 8 cos 2 θ W Z µ Z µ 2 The iggs potential V = µ 2 φ 2 + λ φ 4 expanded around the vacuum state Φ = 1/ 2(0, v) becomes V = 1 2 (2λv2 ) 2 + λv 3 + λ 4 4 λ 4 v4 yielding a iggs mass M = 2λv 2 and cubic and quartic iggs self-couplings. Michael Krämer Page 18 Italo-ellenic School of Physics 2006

19 The profile of the Standard Model iggs boson Fermion masses are generated through so-called Yukawa interactions, e.g. for electrons L G e li L Φ i e R + h.c. which, in unitary gauge, is L G e ν L 2 ē L T 0 v + e R + h.c. This yields an electron mass term L G ev 2 (ē L e R + ē R e L ) = G ev 2 ēe The Yukawa coupling G e is related to the electron mass m e by G e = g W m e 2MW There is also an interaction between the electron and the iggs L g W m e 2M W ēe Michael Krämer Page 19 Italo-ellenic School of Physics 2006

20 The profile of the Standard Model iggs boson Quark masses are also generated through Yukawa interactions with masses L G d q i LΦ i d R + h.c. }{{} d-quark mass G u ɛ ij q i LΦ j u R + h.c. }{{} u-quark mass m d = G d 2 v = 2 G dm W g W and m u = G u 2 v = 2 G um W g W There is also an interaction between the quarks and the iggs: L g W m u 2M W ūu g W m d 2M W dd Adding more generations will introduce mixing in the Yukawa interactions, e.g. L G ds ūl d L T Φs R Michael Krämer Page 20 Italo-ellenic School of Physics 2006

21 The profile of the Standard Model iggs boson Three-point couplings with iggs bosons W Z f W Z f = ig W M W g µν g W = i M cos 2 W g µν θ W = ig W m f 2M W = 3ig W M 2 2M W Four-point couplings with iggs bosons W Z W Z = 1 2 ig2 W g µν = ig2 W 2 cos 2 θ W g µν = 3ig W M 2 4M 2 W Michael Krämer Page 21 Italo-ellenic School of Physics 2006

22 The profile of the Standard Model iggs boson SM iggs decay modes and branching ratios [DECAY: Djouadi, Kalinowski, Spira].0/1!!" " # (*) $ $% 2 3, : ; ; & ' 5; 5 4 # 5; 4 % 4 dominant decay into { b b W W, ZZ for M < 130 GeV for M > 130 GeV Michael Krämer Page 22 Italo-ellenic School of Physics 2006

23 The profile of the Standard Model iggs boson SM iggs total decay width < C D E F G 0IJ K L M N N N NO N NP N Q N N R N N M S N M Q N M N N M N N N M N N M N M NT M NT N M NT N N M Michael Krämer Page 23 Italo-ellenic School of Physics 2006

24 The profile of the Standard Model iggs boson The SM iggs mechanism is testable because all couplings are known: fermions: g ff m f /v gauge bosons: g V V MV 2 /v with vacuum expectation value v 2 = 1/ 2G F (246 GeV) 2 (from µ-decay) The iggs sector and the properties of the iggs particle (lifetime, decay branching ratios, cross sections) are fixed in terms of the iggs boson mass M. [Express the iggs potential in terms of (µ, λ) (v 2, M )] Extended iggs models (eg. 2-iggs-doublet models like the MSSM) have a more complicated structure Michael Krämer Page 24 Italo-ellenic School of Physics 2006

25 Vacuum Instability The profile of the Standard Model iggs boson Theoretical constraints on the iggs boson mass 0 ambye, Riesselmann Running of the iggs coupling: dλ dln µ 2 = 3 8π 2 [λ2 + λg 2 t G 4 t ] with λ = M 2 /v 2 and G t = 2m t /v. Landau Pole For M > m t one has dλ/dln µ 2 λ 2 and thus λ(µ 2 ) = λ(v 2 ) 1 3λ(v2 ) 8π ln µ2 2 v 2 Requiring λ(λ) < yields M 2 < 8π 2 v 2 3 ln (Λ 2 /v 2 ) Michael Krämer Page 25 Italo-ellenic School of Physics 2006

26 U W U U V X iggs boson hunting: indirect search Quantum corrections to precision observables give access to high mass scales: m 2 top ln M iggs More precisely: calculate M W from M Z and G F including quantum corrections ( ) MW 2 1 M W 2 πα = MZ 2 MZ 2 2GF MZ 2 (1 r) where the quantum correction r is composed of The leading top contribution is quadratic in m top : r = α cot θ W ρ top + r iggs + ρ top = 3G F m 2 top 8π The iggs contribution is screened, depending only logarithmically on M iggs r iggs = G F M 2 W 8π sin 2 θ W 3 cos 2 θ W ln ( ) M 2 iggs + M 2 W Michael Krämer Page 26 Italo-ellenic School of Physics 2006

27 iggs boson hunting: indirect search Indirect top hunting works well: (C. Quigg, arxiv:hep-ph/ ) direct observation: m top = ± 2.9 GeV (CDF & D0) indirect observation: m top = ± 11 GeV (LEP & SLD) Michael Krämer Page 27 Italo-ellenic School of Physics 2006

28 iggs boson hunting: indirect search Indirect iggs hunting is harder: 200 igh Q 2 except m t 68% CL m t [GeV] 180 m t (Tevatron) 160 Excluded m [GeV] Michael Krämer Page 28 Italo-ellenic School of Physics 2006

29 iggs boson hunting: indirect search Indirect iggs hunting is harder: 80.5 igh Q 2 except m W /Γ W 68% CL m W [GeV] 80.4 m W (LEP2 prel., pp ) Data consistent with SM M < 219 GeV (95% CL) (LEPEWWG) 80.3 Excluded m [GeV] Michael Krämer Page 29 Italo-ellenic School of Physics 2006

30 iggs boson hunting: indirect search Precision SM measurements are important to constrain the iggs sector... what we hope to see (maybe?) (Bentvelsen, Grünewald) Repeat the electroweak fit with smaller uncertainties δm W = 15 MeV δm top = 1 GeV same central values Michael Krämer Page 30 Italo-ellenic School of Physics 2006

31 iggs boson hunting: past and present colliders search at the CERN LEP2 (e + e collider with s < 200 GeV) e + e / Z M > GeV (95% CL) (LEPIGGSWG) search at the Fermilab Tevatron (p p collider with s = 2 TeV) current L 1 fb 1 expectation in 2008: L = 4 6 fb 1 Michael Krämer Page 31 Italo-ellenic School of Physics 2006

32 Italo-ellenic School of Physics, Lecce, June 2006 iggs Physics at the Large adron Collider Michael Krämer (RWT Aachen) Electroweak symmetry breaking The profile of the Standard Model iggs boson iggs searches at the LC Michael Krämer Page 32 Italo-ellenic School of Physics 2006

33 Summary of lecture 1: SM iggs boson properties The SM iggs mechanism is testable because all couplings are known: fermions: g ff m f /v gauge bosons: g V V MV 2 /v with vacuum expectation value v 2 = 1/ 2G F (246 GeV) 2 (from µ-decay) The iggs sector and the properties of the iggs particle (lifetime, decay branching ratios, cross sections) are fixed in terms of the iggs boson mass M. [Express the iggs potential in terms of (µ, λ) (v 2, M )] Extended iggs models (eg. 2-iggs-doublet models like the MSSM) have a more complicated structure Michael Krämer Page 33 Italo-ellenic School of Physics 2006

34 Summary of lecture 1: SM iggs boson properties Three-point couplings with iggs bosons W Z f W Z f = ig W M W g µν g W = i M cos 2 W g µν θ W = ig W m f 2M W = 3ig W M 2 2M W Four-point couplings with iggs bosons W Z W Z = 1 2 ig2 W g µν = ig2 W 2 cos 2 θ W g µν = 3ig W M 2 4M 2 W Michael Krämer Page 34 Italo-ellenic School of Physics 2006

35 Y Z Z Z Summary of lecture 1: SM iggs boson properties SM iggs decay modes and branching ratios [DECAY: Djouadi, Kalinowski, Spira] l0mn ``a \ a b g*h c cd \ [\ [ ] ] ^ ^ o p j k u r r r t r r s r q r r q u r q w r v r r q r r r rx r r r q rx r r q i e f rx r q b \ rx q d q dominant decay into { b b W W, ZZ for M < 130 GeV for M > 130 GeV Michael Krämer Page 35 Italo-ellenic School of Physics 2006

36 iggs boson hunting Ellis, Gaillard, Nanopoulos, A Phenomenological Profile of the iggs Boson, 1976: We should perhaps finish with an apologie and a caution. We apologize to experimentalists for having no idea what is the mass of the iggs boson... and for not being sure of its couplings to other particles except that they are probably all very small. For these reasons we do not want to encourage big experimental searches for the iggs boson... Michael Krämer Page 36 Italo-ellenic School of Physics 2006

37 The Large adron Collider LC Michael Krämer Page 37 Italo-ellenic School of Physics 2006

38 iggs boson search at the LC The days of the iggs boson are numbered! Signal significance 10 2 γ γ tt ( bb) ZZ (*) 4 l WW (*) lνlν ZZ llνν WW lνjj Total significance 10 5 σ ATLAS L dt = 30 fb -1 (no K-factors) m (GeV) Michael Krämer Page 38 Italo-ellenic School of Physics 2006

39 z y { { z y } ~ ƒ } ~ y } ~ iggs boson production at the LC gg σ(pp + X) [pb] s = 14 TeV NLO / NNLO { { qq _ ' W qq qq gg/qq _ tt _ qq _ Z MRST M [GeV] z y Michael Krämer Page 39 Italo-ellenic School of Physics 2006

40 iggs production cross sections: theoretical status iggs production in gluon-gluon fusion NLO corrections: K NLO 1.7 [Spira, Djouadi, Graudenz, Zerwas; Dawson, Kauffman] 10 2 σ(pp +X) [pb] [arlander, Kilgore 02] s = 14 TeV NNLO corrections: K NNLO (m top M ) 2 [arlander, Kilgore; Anastasiou, Melnikov 02; Ravindran et al. 03] NNLO scale dependence < 15% Soft-gluon summation 5% [MK, Laenen, Spira; Catani, de Florian, Grazzini] Electroweak corrections 5% [Aglietti, Bonciani, Degrassi, Vicini; Degrassi, Maltoni] 10 LO NLO NNLO M [GeV] Michael Krämer Page 40 Italo-ellenic School of Physics 2006

41 ˆŠ Œ ˆŠ iggs production cross sections: theoretical status Vector boson fusion Associated V production Ž discovery channel & measurement of iggs couplings [Zeppenfeld, Kauer, Plehn, Rainwater] NLO QCD corrections (cf DIS) +10% [an, Valencia, Willenbrock; Figy, Oleari, Zeppenfeld; Berger, Campbell] crucial for Tevatron search (M < 130 GeV) NLO QCD corrections +(30 40)% [an, Willenbrock] NNLO QCD corrections +10% [Brein, Djouadi, arlander] NLO electroweak corrections 10% [Ciccolini, Dittmaier, MK] Michael Krämer Page 41 Italo-ellenic School of Physics 2006

42 š iggs production cross sections: theoretical status iggs production in association with top quarks small cross section but distinctive final state direct measurement of top-iggs Yukawa coupling need precise theoretical cross section prediction NLO scale dependence < 15% [Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas; Dawson, Jackson, Orr, Reina, Wackeroth] [Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas] σ(pp tt _ + X) [fb] s = 14 TeV M = 120 GeV µ 0 = m t + M /2 LO NLO µ/µ 0 Michael Krämer Page 42 Italo-ellenic School of Physics 2006

43 iggs boson search at the LC σ tot Tevatron LC QCD background: σ b b 10 8 pb σ (nb) σ bbar σ jet (E T jet > s/20) σ W σ Z σ jet (E T jet > 100 GeV) σ ttbar σ jet (E T jet > s/4) events/sec for L = cm -2 s -1 iggs signal: σ +X 10 pb iggs bosons/year ( L = 30 fb 1 ) 10-5 σ iggs (M = 150 GeV) σ iggs (M = 500 GeV) s (TeV) iggs-search through rare decays or/and associate production Michael Krämer Page 43 Italo-ellenic School of Physics 2006

44 iggs boson search at the LC P X γ, W, Z Inclusive channels P X γ, W, Z pp ( γγ) + X important for M < 150 GeV pp ( W W l + νl ν) + X important for 140 GeV < M < 200 GeV pp ( ZZ l + l l + l )+X important for M > 130 GeV and M 2M W X P jet, top b, τ, γ, W, Z,... Associated production P X jet, top b, τ, γ, W, Z,... pp t t( b b) + X important for M < 140 GeV pp qq( ττ, b b, γγ, W W, ZZ) + X important for whole iggs mass range Michael Krämer Page 44 Italo-ellenic School of Physics 2006

45 Inclusive search channels: γγ g γ γ W top g γ γ small branching ratio BR( γγ) 10 3 large background from QCD processes + excellent photon-energy resolution in CMS and ATLAS iggs discovery through resonance peak + determine background from sideband of data Events / 500 MeV for 10 5 pb CMS, 10 5 pb -1 iggs signal S/ B = 2.8 to 4.3 σ ( L = 30 fb 1) m γγ (GeV) Michael Krämer Page 45 Italo-ellenic School of Physics 2006

46 Inclusive search channels: W W l + νl ν g g W W + ν l l + ν neutrinos in final state no invariant iggs mass peak large background from QCD process q q W W Events / 5 GeV exploit lepton rapdity distributions and angular correlations to suppress background 100 (Dittmar, Dreiner) S/ B = 3 to 15 σ ( L = 30 fb 1) m T (GeV) Michael Krämer Page 46 Italo-ellenic School of Physics 2006

47 Inclusive search channels: ZZ l + l l + l g g Z Z l + l l + l + most important and clean search channel for M > 2M Z + only limited background from QCD processes + reconstruction of iggs mass peak S/ B 20 σ ( L = 30 fb 1) for 180 GeV > M < 400 GeV Michael Krämer Page 47 Italo-ellenic School of Physics 2006

48 Associated production: pp t t( b b) g g t,t t t W + W - 0 b b q q ' b b l ν +... events / 10 GeV/c [Drollinger, Müller, Denegri] CMS L int = 30 fb -1 k = 1.5 gen. m : 115 GeV/c 2 const. : ± 3.76 mean : ± 4.14 sigma : ± m inv (j,j) [GeV/c 2 ] g tt /g tt 15% (exp.) small cross section: σ(t t)/σ( + X) 1/100 only relevant for M < 140 GeV + distinctive final state: pp t( W + b) t( W b) ( b b) + cross section g 2 tt unique way to measure top-iggs Yukawa coupling Michael Krämer Page 48 Italo-ellenic School of Physics 2006

49 Associated production: pp qq( τ + τ, b b, γγ, W W, ZZ) q q τ, b, γ, W, Z W, Z W, Z τ, b, γ, W, Z q q + identify signal with forward jet tagging and central jet veto + relevant for many iggs decay channels measurement of iggs couplings Arbitrary units (Asai et al., ATLAS) τ + τ, b b γγ W W ZZ for M < 140 GeV M < 150 GeV M > 130 GeV M > 500 GeV [Eboli, agiwara, Kauer, Plehn, Rainwater, Zeppenfeld; Mangano, Moretti, Piccinini,Pittau, Polosa... ] η Michael Krämer Page 49 Italo-ellenic School of Physics 2006

50 iggs boson search at the LC: signal significance Signal significance 10 2 L dt = 30 fb -1 (no K-factors) ATLAS γ γ tt ( bb) ZZ (*) 4 l WW (*) lνlν qq qq WW (*) qq qq ττ Total significance M < 2M Z gg ( γγ, ZZ, W W ( ) ) gg/q q t t ( b b, ττ) qq qq q q W ( γγ, W W, ττ) ( γγ) 10 M > 2M Z { gg ( ZZ, W W ) qq qq ( ZZ, W W ) m (GeV/c 2 ) [ + diffractive iggs production] Michael Krämer Page 50 Italo-ellenic School of Physics 2006

51 iggs boson search at the LC: signal significance ) -1 5-σ discovery luminosity (fb CMS qq, WW lνjj qq, ZZ llνν WW*/WW llνν, NLO ZZ*/ZZ 4 leptons, NLO 1 qq, γγ, τ + τ - γγ inclusive, NLO tt, W, bb Combined channels m (GeV/c 2 ) Michael Krämer Page 51 Italo-ellenic School of Physics 2006

52 iggs boson search at the Tevatron (revisited) current L = 0.8 fb 1 expectation in 2008: L = 4 6 fb 1 For M < 140 GeV > 140 GeV use p p W /Z and b b p p and W W Michael Krämer Page 52 Italo-ellenic School of Physics 2006

53 iggs boson physics at the LC: the iggs profile To test the iggs mechanism we have to determine the profile of the iggs boson: mass and lifetime external quantum numbers couplings to gauge bosons and fermions iggs self-couplings Michael Krämer Page 53 Italo-ellenic School of Physics 2006

54 iggs boson physics at the LC: the iggs profile The iggs mass Expected precision M/M 10 3 for M iggs < 500 GeV Michael Krämer Page 54 Italo-ellenic School of Physics 2006

55 œ iggs boson physics at the LC: the iggs profile The iggs width Remember: «ª Ÿž ³ ² ± ³ µ measurement of Γ possible only for M > 200 GeV Michael Krämer Page 55 Italo-ellenic School of Physics 2006

56 iggs boson physics at the LC: the iggs profile The iggs width Expected precision Γ/Γ 5 10% for M iggs > 250 GeV Michael Krämer Page 56 Italo-ellenic School of Physics 2006

57 iggs boson physics at the LC: the iggs profile The iggs spin and parity quantum numbers Discovery of γγ J 1 and C = +1 (Landau-Yang) Angular-correlations, e.g. in V V ( ) : φ 3 f 3 θ 3 V V f 1 θ 1 f 4 f 2 Michael Krämer Page 57 Italo-ellenic School of Physics 2006

58 iggs boson physics at the LC: the iggs profile The iggs spin and parity quantum numbers Angular-correlations in V V ( ) : [Choi, Miller, Mühlleitner, Zerwas] ZZ (f 1 f 1 )(f 2 f 2 ) M = 280 GeV /Γ dγ/dϕ SM pseudoscalar π/2 π 3π/2 2π ϕ Michael Krämer Page 58 Italo-ellenic School of Physics 2006

59 iggs boson physics at the LC: the iggs profile The measurement of iggs couplings: The LC measures σ(pp ) BR( X) = σ(pp ) Γ( X)/Γ tot [Zeppenfeld, Kinnunen, Nikitenko, Richter-Was] Michael Krämer Page 59 Italo-ellenic School of Physics 2006

60 iggs boson physics at the LC: the iggs profile The measurement of iggs couplings: Different production and decay channels provide measurements of combinations of partial decay widths, for example X γ = Γ W Γ γ Γ tot from qq qq, γγ Y γ = Γ gγ γ Γ tot X τ = Γ W Γ τ Γ tot from qq qq, ττ Y Z = Γ gγ Z Γ tot X W = Γ2 W Γ tot from qq qq, W W ( ) Y W = Γ gγ W Γ tot from gg γγ from gg ZZ ( ) from gg W W ( ) Problem: no direct measurement of Γ tot no observation of some decay modes (e.g. gg) consider ratios of X or Y s Michael Krämer Page 60 Italo-ellenic School of Physics 2006

61 iggs boson physics at the LC: the iggs profile Ratios of iggs couplings can be measured with an accuracy of 10-40% Partial widths can be extracted with additional theoretical assumptions [Dührssen et al.] Michael Krämer Page 61 Italo-ellenic School of Physics 2006

62 iggs boson physics at the LC: the iggs profile Reconstructing the iggs potential at the LC is difficult (impossible) Recall: In the SM we have V = M λ 3 v 3 + λ λ 3 = λ 4 = M 2 2v 2 To determine λ 3 and λ 4 need to measure multi-iggs production, e.g. g g g g Michael Krämer Page 62 Italo-ellenic School of Physics 2006

63 iggs boson physics at the LC: the iggs profile The measurement of λ 3 appears to be very difficult g t t t g t t g t g t The problem is the low cross section and large backgrounds [Baur, Plehn, Rainwater] M iggs < 140 GeV: b bb b overwhelming QCD background GeV < M iggs < 140 GeV: (W W )(W W ) (jjlν)(jjlν) can determine whether λ 3 = 0 Michael Krämer Page 63 Italo-ellenic School of Physics 2006

64 iggs boson physics at the LC: the iggs profile The measurement of λ 4 appears to be impossible Michael Krämer Page 64 Italo-ellenic School of Physics 2006

65 iggs boson physics at the LC: beware of backgrounds! Consider iggs search in pp W W l ν l ν channel W W pair production is the dominant background: σ BR 5 times larger than signal a iggs mass peak cannot be reconstructed from leptonic W decays theoretical control of the background is important experimental selection cuts may enhance the importance of higher-order corrections for background processes example: gg W W l ν l ν [Binoth, Ciccolini, Kauer, MK; Dührssen, Jakobs, van der Bij, Marquard] g d W e d ν µ g d W + u ν e µ + formally NNLO but enhanced by iggs search cuts gg q q (NLO) corr. σ tot 54 fb 1373 fb 4% σ bkg 1.39 fb 4.8 fb 30% Michael Krämer Page 65 Italo-ellenic School of Physics 2006

66 º º ¹» ¹ º º iggs boson physics at the LC: beware of backgrounds! Consider search in VBF channel pp qq important discovery channel provides measurement of V V couplings large iggs + 2 jets background from gg gg [Del Duca, Kilgore, Oleari, Schmidt, Zeppenfeld] need additional kinematic cuts [Del Duca] Michael Krämer Page 66 Italo-ellenic School of Physics 2006

67 ¼ ¼ À À Ã Â Å ¾ The hierarchy problem: why is M iggs M Planck? Quantum corrections to the iggs mass have quadratic UV divergencies ¼ ½ ¼ δm 2 α π (Λ2 + m 2 F ) The cutoff Λ represents the scale up to which the Standard Model remains valid. need Λ of O(1 TeV) to avoid unnaturally large corrections Most popular new physics models Supersymmetry Dynamical EWSB Extra dimensions Little iggs models Quantum corrections due to superparticles cancel the quadratic UV divergences À Á À Ä δm 2 α π (Λ2 + m 2 F ) δm 2 α π (m2 F m2 F ) no fine-tuning if m < O(1 TeV) Michael Krämer Page 67 Italo-ellenic School of Physics 2006

68 A crucial test of the MSSM: the light iggs MSSM iggs sector: two iggs doublets to give mass to up- and down-quarks 5 physical states: h,, A, ± The MSSM iggs sector determined by tan β = v 2 /v 1 and M A. The couplings in the iggs potential and the gauge couplings are related by supersymmetry. At tree level one finds M h M Z. This relation is modified by radiative corrections so that M h < 130 GeV (in the MSSM) The existence of a light iggs boson is a generic prediction of SUSY models. Michael Krämer Page 68 Italo-ellenic School of Physics 2006

69 A crucial test of the MSSM: the light iggs One of the SUSY iggs bosons will be seen at the LC tanβ h 0 A ATLAS ATLAS fb maximal mixing h 0 A 0 0 h h 0 h only LEP 2000 LEP excluded 2 0 h 0 A h but it may look like the SM iggs... m A (GeV) Michael Krämer Page 69 Italo-ellenic School of Physics 2006

70 iggs boson physics at the LC: summary The LC will find the (or a?) iggs boson (or something similar). The LC will measure some of the iggs boson properties. For a more precise and model independent determination of decay widths and a measurement of quantum numbers we will need the ILC. iggs physics is exciting: reveals the mechanism of electroweak symmetry breaking points towards physics beyond the SM (hierarchy problem) Michael Krämer Page 70 Italo-ellenic School of Physics 2006