at the LHC OUTLINE Vector bosons self-couplings and the symmetry breaking connection

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1 Trilinear and Quartic Gauge Boson Couplings at the LHC Fawzi BOUDJEMA OUTLINE LAPTH-Annecy, France Vector bosons self-couplings and the symmetry breaking connection Gauge Invariance and the Hierarchy of couplings: Higgs vs Higgsless description Present indirect limits as a yardstick for a meaningful future measurement/constraint Important channels. Outlook. Conclusions F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. /

2 Self-couplings: the Higgs and Symmetry Breaking Connection W + L W L W+ L W L Without Higgs If g V V V V g 2 V V V = M LLLL E 4 W In the SM M LLLL 2G F u E 2 W Unitarity without Higgs requires s WW.2TeV Slight departure of the vector bosons self-couplings from SM values is enhanced at high energies F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 2/

3 Higgs and Delayed Unitarity Higgs in SM Extra-dim with special boundary cdts W W À M LLLL 2G F M 2 H À ( s s M H 2 Unitarity implies M H 4π 2 3G F + t t M 2 H 700GeV tower of KK W W Unitarity is delayed up to a few TeV cancellation from underlying 5-d gauge symmetry. expect some collective modes to effectively affect the self-interaction of the gauge bosons watch out for the longitudinal modes F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 3/

4 Gauge Invariance: g ffv = g V V V σ(e + e W + W (γ [pb] 20 0 LEP s 89 GeV: preliminary Data GENTLE YFSWW3 RACOONWW no ZWW vertex only ν e exchange e - W s [GeV] LEP legacy: We know that WWV can not deviate too much (0% from SM gauge value. But slightest deviations are revealed at higher energies (LHC? e + e - Z, γ W - W - W + e + F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 4/

5 s 2 W Gauge Invariance: Indirect Limits Z =M W M ? l = MeV Dittmaier, Schildknecht and Weiglein 996. F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 5/

6 Origin of VVVV and VVV: Gauge Invariance, Symmetry Breaking. I. SM L Gauge = 2 [Tr(W µνw µν + Tr(B µν B µν ] GI kinetic term W µν = ( µ W ν ν W µ + i 2 2 g[w µ, W ν ] = τi ( µ Wν i ν Wµ i gǫ ijk W j 2 µw B µν = 2 ( µb ν ν B µ τ 3 B µ = τ 3 B µ L Gauge describes transverse states (field strength longitudinal states, Z L µ µφ 3 ǫ L µ = k µ M Z M Z s µ s.k do not contribute much to L Gauge BUT to the mass and Symmetry Breaking Lagrangian L M = M 2 W W+ µ W µ + 2 M2 Z Z µz µ L H,M=SB = (D µ Φ (D µ Φ λ ] 2 [Φ Φ µ2 2λ Self interacting Goldstone Bosons Self-interacting V L V L V L V L Symmetry Breaking has a custodial SU(2 symmetry ρ = Gauge invariance of Mass and SB: Covariant Derivatives F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 6/

7 Origin of VVVV and VVV: Gauge Invariance, Symmetry Breaking. II. SM without Higgs kinetic term still there but mass and longitudinals through a system of Goldstones without the Higgs (still gauge invariant: Non-Linear realisation of SB Σ = exp( iωi τ i (v = 246 GeV is the vev and D µ Σ = µ Σ + i v 2 L M = v2 4 Tr(Dµ Σ D µ Σ v2 4 Tr (V µv µ with V µ = (D µ ΣΣ ( gwµ Σ g B µ Στ 3 F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 7/

8 Hierarchy of Operators: Most important effects POST-LEP &2: The SM is a gauge invariant (GI theory with a custodial SU(2 symm. as in QED any deviation should be parameterized as a (higher order GI operators This approach defines a hierarchy of couplings and order of magnitude for deviations QED example L QED eff. = 4 F µνf µν + β m 2 e 2 6π 2 ( F µν F µν + ǫ 2 m 2 F µν 2 F µν + e 4 ( m 4 6π 2 β 2 (F µν F µν 2 + β 3 (F µν F µν L gauge fixing SM need to describe new physics of longitudinal modes decide about Linear (with Higgs or Non-Linear (without Higgs of Symm. Breaking F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 8/

9 Operators forw Physics Linear Realisation, Light Higgs Non Linear-Realisation, No Higgs L B = ig ǫ B Λ 2 (D µ Φ B µν D ν Φ L 9R = ig L 9R 6π 2 Tr(B µν D µ Σ D ν Σ L W = ig ǫ w Λ 2 (D µ Φ (2 W µν (D ν Φ L 9L = ig L 9L 6π 2 Tr(W µν D µ ΣD ν Σ L λ = 2i 3 L λ Λ 2 g 3 Tr(W µν W νρ W µ ρ L = L ( 6π Tr(D µ 2 Σ D µ Σ 2 L 6π 2 O L 2 = L ( 2 6π Tr(D µ 2 Σ D ν Σ 2 L 2 6π 2 O 2 F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 9/

10 Projecting on the multipole moments, phenomenological parameters W + W Z, W + W γ couplings κ γ = e2 s 2 w κ Z = e2 s 2 w v 2 4Λ 2 (ǫ W + ǫ B = e2 s 2 w v 2 4Λ 2 (ǫ W s2 w c 2 ǫ B = e2 w s 2 w g Z = e2 s 2 w 4Λ 2 (ǫ W c 2 = e2 w s 2 w 32π 2 ( e 2 MW 2 λ γ = λ Z = L λ Λ 2 v 2 s 2 w 32π 2 (L 9L + L 9R 32π 2 ( L9L c 2 w ( L 9L s2 w c 2 L 9R w At this order no C violating tri-linear couplings in particular no ZZZ, ZZγ, Zγγ couplings. These appear at higher orders. Should not receive high priority. For LHC fits and measurements better to switch to the L i parameters F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 0/

11 Pheno of tri-linear couplings L WWV = ie A µ (W µν W ν + W +µν Wν + c W sw g Z {}}{ ( + g Z Z µ (W µν W ν + W +µν Wν + + κ γ {}}{ ( + κ γ F µν W +µ W ν κ Z {}}{ ( + κ Z Z µν W +µ W ν + M 2 W ( } λ γ F νλ c + λ W Z sw Z νλ W + λµ W µ ν L L No ZZZ, ZZγ, Zγγ(higher order L L κ Z, κ γ complementarity g Z, g Z LT + e - W + W - + e pp W - Z (, γ T T ( ( T Tλ Z λ γ λ Z, λ γ κ Z, κ γ LT F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. /

12 Current direct limits as a guide λ γ κ γ κ γ LEP charged TGC Combination 2003 g Z λ γ g Z LEP Preliminary 95% c.l. 68% c.l. 2d fit result 5 0% accuracy = L 9 50 F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 2/

13 L WWV V 2 e 2 {( A µ A µ W ν + W ν A µ A ν W µ + Wν + 2 c w ( + l 9l s w c 2 (A µ Z µ W +ν W ν 2 Aµ Z ν (W +µ W ν + W+ν W µ w + c2 w s 2 ( + 2l 9l w c 2 l w c 4 ( Z µ Z µ W ν + W ν Z µ Z ν W µ + W ν w + ( + 2l 9l l ( W +µ Wµ W +ν Wν W +µ W µ + W ν Wν + 2s 2 w l + 2s 2 w 2 c 2 w (( 3W +µ W µ W +ν W ν + W +µ W + µ W ν W ν ( Zµ Z µ W + ν W ν + Z µ Z ν W + µ W ν with l 9l = e 2 32π 2 s 2 L 9L ; l ± = w + e 2 c 4 w Z µ Z µ Z ν Z ν } 32π 2 s 2 (L ± L 2 w No Anomalous WWγγ, No V V 2 γγ New ZZZZ, New WWWW and WWZZ structures. Best probed in WW scattering (L,2 = = (higher order structures see Bélanger et al., F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 3/

14 Catch 22: Contribution to 2-point functions?...! I only listed operators giving contribution to V V V and V V V V but... A general approach would also include contributions to 2-point function (see QED example L WB = gg ǫ W B Λ 2 ( Φ W µν Φ B µν L 0 = gg L 0 6π 2 Tr(B µν Σ W µν Σ L 0 = πs New 4πs W α ǫ 3 LEP-Tevatron precision EW physics implies strong constraint on S New (L 0 and consequently on the other operators This constraint could be considered as a yardstick for future measurements F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 4/

15 Present Limit on S New Preliminary 68 % CL sin 2 θ lept eff m W Chanowitz U 0 T New Γ l T 0 S New m t -0.5 m H SM with SNew, T New Ref. values m H = 50GeV m t = 75GeV LEP EWWG Winter 2004 S For M H = TeV need S New = 0.07 and T New = +0.3 = Constraint L 0 < future L i measurements of this order! L i unless some global symmetry makes L 0 = 0 (SU(2 A? F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 5/

16 Future measurements I. The S, T, U Post-LEP From WW scattering LHC F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 6/

17 Future measurements and Conclusions. Especially if Higgs not found precision measurements of (longitudinal vector bosons self-couplings is crucial Update simulations in the channels pp WZ, Wγ(WW? including NLO (MCFM pp (W, ZX (VV fusion to single V: worth it? Can more be done to optimize WW WW? Quartic through pp W W Z, ZZZ,. though falls like /ŝ could it help? combined with WW fusion? work out in detail consequences of some extra-dim models, (Little Higgs?......could constitute a nice subgroup at Les Houches Official deadline for registration TOMORROW F. BOUDJEMA, Trilinear and Quartic Gauge Boson couplings at the LHC p. 7/