Viability of strongly coupled scenarios with a light Higgs like boson

Transcription

1 Beijing IHEP, January 8 th 2013 Viability of strongly coupled scenarios with a light Higgs like boson J.J. Sanz Cillero (PKU visitor) A. Pich, I. Rosell and JJ SC [arxiv: [hep ph]]

2 OUTLINE 1) Motivation: EWSB and oblique parameters S and T 2) Chiral Lagrangian for resonances 3) Oblique parameters 30 (s) (s) (0) - (s) (+) S sum-rule T disp-rel. for lightest cuts 4) High-energy Constraints 5) Phenomenology

3 Motivation: EWSB and (S,T)-parameters

4 A new Higgs like boson (possibly a scalar) discovered Mass m S =126 GeV Still many questions: Spin? Coupling to gauge bosons? SM Higgs?

5 Does this exclude strongly coupled EWSB models? Not yet THEORETICALLY: NOT YET E.g., the meson in the L Min QCD doesn t imply the absence of other hadrons (although here the has completely different properties!!) EXPERIMENTALLY: NOT YET The EWPO Oblique Parameters don t exclude them at all NDA dangerous for precision physics!! We will see that, more precisely,?

6 What? One-loop calculation of the oblique (S,T)-parameters in strongly-coupled EWSB* Why? Origin of mass generation? strongly-coupled models How? Effective approach a) EWSB: SU(2) L x SU(2) R SU(2) L+R : similar to ChSB in QCD ChPT *** b) Strongly-coupled models: Resonances like in QCD RChT (+) c) Lagrangian with at most two derivatives + short-distance information (+) + d) Just the lightest two-particle cuts: + S for S-param. Dispersive representation from Peskin and Takeuchi 92 + Dispersion relation for T (for the lightest cuts) B + BS for T-param. (impact of heavier channels neglected (x) ) * Gfitter *** Weinberg 79 (+) Ecker et al. 89 * LEP EWWG *** Gasser & Leutwyler (+) Cirigliano et al. 06 * Zfitter *** Bijnens et al (+) Pich, Rosell, SC 08 (x) Pich, Rosell, SC 12

7 THEORETICAL FRAMEWORK: Chiral Lagrangians with resonances

8 EW resonance models i) Many BSM constructions contain a Tower of V and A resonances * Strongly-coupled models: Higgsless It seems not any more non-perturbative EWSB Composite resonances instead of a fundamental Higgs. Many possibilities in the market: Technicolor (Original/Walking/Conformal/Holographic ), Composite SO(5)/SO(4), Extra Dimensions, etc. * Arkani-Hamed et al. 01 * Csaki et al. 04 * Cacciapaglia et al. 04 * Hirn,Sanz 06

9 ii) EWSB similar to Chiral Symmetry Breaking (ChSB) in QCD: SU(2) L xsu(2) R SU(2) L+R At low energies, same EFT pion Lagrangian, Chiral Perturbation Theory (ChPT)** E.g., in the SM ** Weinberg 79 ** Gasser & Leutwyler ** Bijnens et al

10 iii) EFT for the Goldstones (SM gauge symmetry non-linearly realized) + Lighest resonances from strongly-coupled models * Similar to Resonance Chiral Theory (RChT) in QCD ** Incidentally, the most naive rescaling F =0.090 GeV v=0.246 TeV from QCD to EW scale yields: M =0.770 GeV M V1 =2.1 TeV M a1 =1.260 GeV M A1 =3.4 TeV //////////////////////////// m S =0.126TeV *Matsuzaki et al. 07 *Barbieri et al. 08 *Catà, Kamenik 11 *Orgogozo, Rychkov 12 **Ecker et al. 89 ** Cirigliano et al. 06

11 Field content of the theory: SU(2) L SU(2) R / SU(2) L+R Goldstones Gauge fields V and A resonances (antisym. tensor formalism) SU(2) singlet scalar S SU(2) L SU(2) R transformation properties: NOTATION:

12 Effective theory with at most two derivatives (x) + short-distance info: EW Goldstones + SM gauge bosons + lightest V and A resonances + one SU(2) singlet scalar S Relevant resonance Lagrangian S + sector* V + sector A+S+ sector We will have 7 resonance parameters: F V, G V, F A,, SA 1, M V and M A The high-energy constraints will be crucial (x) Ecker et al. 89 (x) EoM simplifications: Xiao, SC 07 (x) Georgi 91

13 Oblique parameters S and T: Calculation

14 Oblique EWPO s Universal oblique corrections via the EW boson self-energies (transverse in the Landau gauge) * ** In pure SM In BSM, usually stated But it s more precise * Peskin and Takeuchi 92. ** Barbieri et al. 93

15 1.) Estimation of the S parameter in strongly-coupled EW models: Equivalent to the determination of L 10 ( )-L 10 ( ref ) in ChPT/RChT * S-parameter New physics in the difference between the Z self-energies at Q 2 =M Z2 and Q 2 =0. Notice the running with reference scale ref Only recovered if the loop included Tree-level ambiguity on the ref running 2.) Estimation of the T parameter in strongly-coupled EW models: Equivalent to the determination of F +2 F 02 in ChPT/RChT T-parameter It parametrizes the Custodial symmetry breaking Again, running with reference scale ref : B loop; tree-level ambiguity on ref * Pich,, Rosell, SC 08

16 S-parameter sum-rule * In this work, dispersive representation introduced by Peskin and Takeuchi*. The convergence of the integral requires S-parameter defined for an arbitrary reference value m H,ref Higher threshold cuts in Im 30 will be suppressed in the dispersive integral * Peskin and Takeuchi 92.

17 i) At leading-order (LO)* W 3 B correlator = V,A NGB self energies = 0 (s) (0) (s) (+) =0 * Peskin and Takeuchi 92.

18 ii) At next-to-leading order (NLO)* W 3 B correlator NGB self energy * Barbieri et al. 08 * Cata and Kamenik 10 * Orgogozo and Rynchov 11,

19 W 3 B correlator Reconstruction through dispersion relations * Once-subtract. dispersive relation from tree+1-loop spectral function:, S (higher cuts suppressed) F Rr and M Rr are renormalized couplings which define the resonance poles at the one-loop level. NGB self energy Ward identity relation for T ** Pich, Rosell, SC 12 Orgogozo, Rychkov 11, 12 ** Barbieri et al. 93

20 W 3 B correlator S parameter sum rule VFF + VFF + NGB self energies Convergent dispersion relation for T for the lightest absorptive diagrams with B + BS

21 High energy constraints

22 We have 7 resonance parameters: F V, G V, F A,, SA 1, M V and M A. The number of unknown couplings can be reduced by using short-distance information. In contrast with the QCD case, we ignore the underlying dynamical theory. i) Weinberg Sum Rules (WSR)* i.i) LO i.ii) Imaginary NLO i.iii) Real NLO: fixing of F V,A r or lower bounds** (1 / 2 constraints) (1 / 2 constraints) ( constraints on F V,Ar ) * Weinberg 67 * Bernard et al. 75. ** Pich, Rosell, SC 08

23 ii) Additional short-distance constraints ii.i) Vector Form Factor** ii.ii) W L W L W L W L scattering* (NOT CONSIDERED HERE, studied in a previous work***) 1 st + 2 nd WSR determination: 7 parameters (only lowest cuts +S ): M V,M A,F V,F A & G V,, 1 SA constraints: F V,F A & G V,M A,(F A 1 SA ) 2 free parameters: M V, Only 1 st WSR lower bound for M V <M A : 6 parameters (only lowest cuts +S ): M V,M A,F V & G V,, (F A 1 SA ) constraints: F V & G V,(F A 1 SA ) 3 free parameters: M V,M A, * Bagger et al. 94 * Barbieri et al. 08 * Guo, Zheng, SC 07 * Pich, Rosell, SC 11 ** Ecker et al. 89 *** Pich, Rosell, SC 12

24 Phenomenology

25 S = 0.03 ± 0.10 * (m H,ref =0.126 TeV) i) LO results i.i) 1st and 2nd WSRs ** i.ii) Only 1st WSR *** (lower bound for M A >M V ) At LO M V > 2.4 TeV at 68% CL ( M V > 3.6 TeV if T LO =0 also considered ) * Gfitter * LEP EWWG * Zfitter ** Peskin and Takeuchi 92. *** Pich, Rosell, SC 12

26 ii) NLO results: 1st and 2nd WSRs M V T 0.0 [ terms O(m S2 /M 2 V,A) neglected ] Ω 1 st and 2 nd WSRs at LO and NLO + -VFF: 2 nd WSR: =M V2 /M 2 A [ ] Free parameters: M V and S At NLO with the 1 st and 2 nd WSRs M V > 5.4 TeV, >0.97 at 68% CL Small splitting M V /M A

27 ii) NLO results: only 1 st WSR [ terms O(m S2 /M 2 V,A) neglected ] Assumption M A >M V for the S lower-bound Only 1 st WSRatLOandNLO+ -VFF: Free parameters: M V, M A and

28 < M V /M A < < M V /M A <1 0.02< M V /M A < Ω M V TeV At NLO with only 1 st WSRs M V > 1 TeV, (-0.36,+0.30) at 68% CL for moderate splitting 0.2 < M V /M A < 1 BACKUP PLOTS 5 Ω M A TeV Ω M A M V MA TeV M V TeV

29 < M V /M A <1 0.02< M V /M A < M V TeV MA TeV M V TeV M A M V M A TeV

30 0.9 < M V /M A <1 0.02< M V /M A <0.9

31 Further comments: 1<M A /M V <2 yields M V >1TeV, [-0.16,+0.30] The limit only reached for M V /M A 0 =0 incompatible with data (independently of whether 1 st +2 nd WSR s or just 1 st WSR) Calculation equivalent to that in SO(5)/SO(4) with =cos <1 * Orgogozo, Rychkov 12

32 Conclusions

33 Strongly-coupled EW models still allowed by the EWPO Only 1 st WSR: In reasonable scenarios with M A M V 1 M V >1TeV In any scenario M A >1.5TeV (68% CL) 1 st +2 nd WSR s: Tiny splitting (M V /M A ) 2 =, with 0.97 < <1 (68% CL) M V >5.4TeV Even wider phase-space if the UV-constraints are released

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35 BACKUP SLIDES

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37 ii) At next-to-leading order (NLO)* V V V V A A A A V V V V V V V V A A A A Once-subtract. dispersive relation from tree+1-loop spectral function:, V, A (higher cuts suppressed) F Rr and M Rr are renormalized couplings which define the resonance poles at the one-loop level. * Barbieri et al. 08 * Cata and Kamenik 10 * Orgogozo and Rychkov 11

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39 * = W in Cacciapaglia et al. 12