Theory of the ElectroWeak Interactions

Transcription

1 Theory of the ElectroWeak Interactions Riccardo Barbieri 1st Summer School of ITN Corfu, September 4-15, The Standard Model: the indirect informations 2. Higgsless Grojean 3. The Higgs boson as a PGB Grojean 4. Beyond msugra Pokorski All at a hopefully simple and self-contained level, to be complemented by other lectures this same week

2 Particle Physics in one page L SM = 1 4 Fa µνf aµν + i ψ Dψ +ψ i λ ij ψ j h + h.c. + D µ h 2 V (h) +N i M ij N j The gauge sector (1) The flavor sector (2) The EWSB sector (3) The ν-mass sector (4) (if Majorana) Anybody NOT familiar with this? Almost all the focus of these lectures on (3), with, maybe, an incursion on (2) towards the end

3 The impact of the Large Hadron Collider on EWSB 1. The first thorough exploration of the energy scales well above G 1/2 F Λ QCD, G 1/2 F 2. No comparable prior situation at the SppS or at the TEVATRON 1984: W, Z 1994: top 201?: the Higgs boson of the SM Which indirect informations so far?

4 The famous ElectroWeak Precision Tests the Gfitter group CERN-Fermilab-Stanford precision often better than 10 3 In fact: from l max 10 8 cm to (APV) l min cm A naive p-value of 0.23

5 The Higgs boson mass in the SM M Higgs = GeV M Higgs = GeV with LEP and Tevatron direct searches included

6 χ 2 -distributions the Gfitter group (ATLAS and CMS not included)

7 LHC exclusion plots 95% CL limits on σ σ SM

8 The indirect determination of the Higgs mass m W m t m h Rad Corr predict and well. Also? th m t = ± 3.3m W = (13) M Higgs = GeV exp m t = ± 1.1m W = (23)? (the exact meaning of this plot in a while)

9 The main Standard Model effects summarized Ŝ = g g Π 30(0) ˆT = Π 33(0) Π WW (0) π + 0 m 2 W B W 3 h B π + 0 h π 0 W 3 Ŝ G Fm 2 W 12 2π 2 logm h ˆT 3G Fm 2 W 4 2π 2 tan2 θlogm h ρ 1 = ˆT = 1 + 3G Fm 2 t 8 2π 2 t π + π 0 b t Equivalence Theorem W L π

10 A more general use of the EWPT 1 Λ SB Consider a theory characterized by a scale with its virtual effects likely significant in the vac. pol. amplitudes of the vector bosons. At q 2 < Λ 2 SB!"' The dominant effects in:!"&!"#!"$ )!"% *+,-,./, 0',-,./, (with some care when extra light particles, O(m W ), are present) ( T 1,S 3, although not quite)!!!"%!!"$ m h %!!, '!!, SM!!"#!!"#!!"$!!"%!!"%!"$!"#!"& (

11 2 L ef f = L SM +L NP ef f Taking c i = ±1 L NP ef f = Σ i c i Λ 2 O i NP and considering one operator at a time T S 1σ-bounds a light Higgs More conservatively: Λ > ~5 TeV flavour (see below)

12 Current flavour constraints : The CKM picture quantitatively successful Lef NP c i f = Σ i Λ 2 O i NP L ef f = L SM +L NP ef f Isidori, Nir, Perez 2010 A problem and an opportunity

13 On the meaning of these bounds c? i = ±1 The stronger case: fermion compositeness at Λ NP c i 16π 2 The weaker case: NP only induced by loop effects c i α 4π An intermediate case: NP from perturbative tree level c i 1 Need to consider specific models to be more precise also because of possible cancellations

14 The naturalness problem of the Fermi scale There is certainly New Physics (NP) at short distances Λ NP =...,M GUT, M Pl Λ NP >> G 1/2 F to be included in a suitably Extended SM (ESM) How to keep the beautiful consistency of the SM with exp.s? No problem, even not knowing which NP at all, provided: 1. SU(3) SU(2) U(1) kept intact 2. The low energy spectrum of the ESM coincides with the one of the SM, with the inclusion of the Higgs boson Why this is the case? the naturalness problem of the Fermi scale Why the focus on the Higgs boson only? Why we call this a problem? h }SM

15 Why a problem? 1. To address it at all, need a calculable Higgs mass 2. In the SM δm 2 h = α t Λ 2 t + α g Λ 2 g + α h Λ 2 h with known coeff.s for a given cut-off 3. Even though Λ, whatever will cutoff these div.s is likely to leave a significant contribution to (see below) Too big? m 2 h ( ) 4. Using the naive estimate of ( ) and barring accidental cancellations Λ t 5. Especially low enough that one might have already seen its (indirect)signs Λ t 3.5m h Λ g 9m h > Λ t Λ h 1.3 TeV

16 SM in isolation A more refined analysis m 2 h(phys) =m α t Λ µ d µ m2 h(µ) =α t m 2 h(µ), µ > m h >m t SM + (e.g.) a heavy Fermion coupled to the Higgs boson m 2 h(phys) =m α F Λ µ d µ m2 h(µ) =α F m 2 h(µ), µ < m F m 2 h(µ) m 2 h m 2 h(µ) m 2 F µ µ d µ m2 h(µ) =α F m 2 F, µ > m F m 2 h µ a very precise initial condition at the high scale if m F >> m h on a physical renormalized quantity

17 The Fine Tuning problem of the Fermi scale 1999: the LEP Paradox 2001: the little hierarchy problem B, Strumia While all indirect tests (EWPT, flavour) indicate no new scale below several TeV s, the Higgs boson mass is apparently around the corner and is normally sensitive to any such scale m h 115 GeV ( Λ cutoff 400 GeV )? Λ NP Λ cutoff Λ NP? T ev 2011: the problem still there, more than ever, driving our view about what can/will happen at the LHC

18 The (many) reactions to the FT problem 0. Ignore it and view the SM in isolation (untenable) In case you doubted of its relevance: 1. Cure it by symmetries: SUSY, Higgs as PGB, little Higgs 2. A new strong interaction nearby 3. A new strong interaction not so nearby: quasi-cft 4. Warp space-time: RS 5. Saturate the UV nearby: ADD, classicalons 6. Accept it: the multiverse, the vacua of string theory Anything else?

19 The proposed relevant symmetries 1 Supersymmetry (φ,ψ) m 2 φ 2 if ψ massless 2 Global symmetry h h + α m 2 h 2 3 Gauge symmetry in higher dim.s A µ A µ + d µ α m 2 A 2 µ h = A 5 (likely related to 2 anyhow)

20 EWSB: weak or strong? weak a relatively light Higgs boson exists perturbativity extended high E ( M GUT,M Pl ) perhaps (probably) embedded in susy gauge couplings (perhaps) unify strong EWSB related to new forces, new degrees of freedom or even new dimensions opening up in the TeVs perturbativity lost in the multi-tev range high E extrapolation highly uncertain