New Physics at the Large Hadron Collider

Transcription

1 New Physics at the Large Hadron Collider Riccardo Barbieri Paris, April 2-3, 2008 For Summary and References: arxiv:

2 New physics at the Large Hadron Collider 1. The first thorough exploration of the energy scales well above G 1/2 F Λ QCD, G 1/2 F 2. Any comparable prior situation at the SppS or at the TEVATRON? 1983: W, Z 1993: top

3 A road map 1. Higgsless: a conservative view 2. The naturalness problem of the Fermi scale a. Supersymmetry b. Goldstone symmetry c. Gauge symmetry in extrad 3. Dark Matter 4. The Planck/Fermi hierarchy extrad a. Gravity weak by flux in extrad b. G 1/2 F /M Pl as a red shift effect c. Symmetry breaking by boundary conditions

4 Plan (in logical order) 0. Introduction and preliminaries 0 1. Higgsless: a conservative view 2. The naturalness problem of the Fermi scale a. Supersymmetry 4 b. Goldstone symmetry c. Gauge symmetry in extrad 3. Dark Matter 3 4. The Planck/Fermi hierarchy extrad 2 (No flavour for reasons of time) Bs mixing and decays 1

5 The famous ElectroWeak Precision Tests Measurement Fit O meas!o fit /" meas #$ (5) had (m Z ) ! m Z "GeV# ! % Z "GeV# ! " 0 had "nb# ! R l ! A 0,l fb ! A l (P & ) ! R b ! R c ! A 0,b fb ! A 0,c fb ! A b 0.923! A c 0.670! A l (SLD) ! sin 2 ' lept eff (Q fb ) ! m W "GeV# ! % W "GeV# 2.140! CERN-Fermilab-Stanford precision often better than 10 3 In fact: from l max 10 8 cm to (APV) l min cm m t "GeV# 170.9! % probability χ 2

6 The main Standard Model effects summarized Ŝ = g g Π 30(0) ˆT = Π 33(0) Π WW (0) m 2 W π + 0 B W 3 h B π + 0 h 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

7 The Higgs boson mass in the SM Pull distribution = Normal Gaussian? Mean: 0.22 ± 0.28 Sigma: 1.1 ± 0.4 LEPHWG M Higgs direct 114.4GeV

8 The indirect determination of the Higgs mass m W m t m h Rad Corr predict and well. Also? predicted measured m t = m W = (20) m t = ± 2.1 m W = (29) m h = ? A heavier Higgs would require a positive ΔT LEPEWWG - Summer 2006

9 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',-,./,! %!!, The SM as function of the Higgs boson mass in GeV!!"%!!"$ m h '!!,!!"#!!"#!!"$!!"%!!"%!"$!"#!"& (

10 2 L e f f = L SM +L NP e f f Taking c i = ±1 L NP e f 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

11 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

12 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

13 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

14 Once again: The naturalness problem of the Fermi scale Why the agreement data SM is unaffected by short distance physics, whatever it may be?

15 The proposed relevant symmetries Supersymmetry (φ,ψ) m 2 φ 2 if ψ massless Global symmetry h h + α m 2 h 2 Gauge symmetry in higher dim.s A µ A µ + d µ α m 2 A 2 µ h = A 5 We shall see

16 Higgsless models: a conservative view 1. Preliminaries: the SM as m h 2. A gauge invariant Higgsless SM 3. A model in 5D 4. Signals

17 The SM as m h gets large Γ(H) [GeV] gg"h!(pp"h+x) [pb] #s = 14 TeV M t = 174 GeV CTEQ6M qq _ "HW qq"hqq gg,qq _ "Htt _ M H [GeV] gg,qq _ "Hbb _ qq _ "HZ W W VV scattering W W W W W H W W (but see also the EWPT)

18 If the Higgs boson is as expected, it will be found N X = L σ(p X) One month at design luminosity enough to explore the entire range

19 Without the Higgs boson diagram A(W + W ZZ) = A(s, t, u) A(W + W W + W ) = A(s, t, u) + A(t, s, u) A(ZZ ZZ) = A(s, t, u) + A(t, s, u) + A(u, s, t) A(W W W W ) = A(t, s, u) + A(u, s, t). a IJ a 00 = + s 16πv 2 a 11 = + s 96πv 2 a 20 = s 32πv 2. for the partial wave the central process Perturbation theory lost at A(s, t, u) = s v 2 + α 4 q/e q/e W W 4(t 2 + u 2 ) v 4 + α 5 8s 2 v 4 +, W W if we knew something about it s 1.2 TeV I = 0, 2 J even I = 1 J odd A(s, t, u) s v 2.

20 A gauge invariant Higgsless SM The ElectroWeak Chiral Lagrangian In the SM: invariant under H SM = Σ ( ) 0 v + h Σ = expi π τ v H SM U L H SM U L = expiω L τ/2 H SM exp(iω Y /2)H SM Changing notation: Φ (v + h)σ Φ U L Φ Φ Φexp( iω Y τ 3 /2) D µ Φ d µ Φ gŵ µ Φ + g Φ ˆB µ Ŵ µ i/2w µ τ ˆB µ i/2b µ τ 3 H + SM H SM = 1 2 Tr(Φ+ Φ) h D µ H SM 2 = 1 2 Tr(D µφ) + (D µ Φ) Throw away and even forget the doublet origin of EW Chiral Lagrangian In the g 0 limit Σ SU(2) L xsu(2) R Σ U L ΣU + R

21 The EW chiral Lagrangian (continued) An expansion in powers of derivatives and V µ (D µ Σ)Σ + L EW Ch = L G + L Y + L NL + Σ 10 i=0l i L NL = v2 4 Tr[(D µσ) + D µ Σ] L Y = λ ij 1 Tr( Q i LΣQ j R )+λij 2 Tr( Q i LΣτ 3 Q j R )+h.c. 2V-terms 3V-terms 4V-terms T Στ 3 Σ +

22 Some remarks on the EWChL Its symmetries: gauged SU(2) L xu(1) Y exact (surprising?) As g, λ 2 0, global conserved by L G + L Y + L NL + Σ 5 i=1l i Without knowing the underlying dynamics, 11 unknown parameters a 0, a 1,..., a 10 as opposed to a single one in the SM: the Higgs mass m h (v, g, g are in common) m h The SM as is a particular L EWCh At one loop, 4 s diverge logarithmically a i SU(2) L xsu(2) R

23 What is it known of the a i s experimentally? V 2 V 3 a 0, a 1, a 8 T, S, U - terms: see plot and below (in one-to-one correspondence) a 2, a 3, a 9 a 2, a 3 g Z 1, k γ Setting a 9 = 0 - terms: From e + e W + W g Z 1 1 = k γ 1 = at LEP2 (O( 10 3 LEPEWWG ) in the SM) - terms: V 4 a 4, a 5, a 6, a 7, a 10 Nothing known = SU(2) L+R conserving

24 A nearby strong interaction, once again A(W L W L ) (E/v) 2 (E/v) 2 E 0 Gauge Higgs Without a Higgs, perturbation theory saturated at E 4πv Obvious from the point of view of L EWCh ΔL NL = v 2 /4 ( µ + iga µ )e iπa τ a /v 2 g 2 v 2 A 2 µ+( µ π) v 2π2 ( µ π) Λ 4 4πv 4π M W g Unless something happens below Λ 4

25 g 2 v 2 A 2 µ+( µ π) v 2π2 ( µ π) (E/v) 2 (E/v) 2 (E/v) π 2 Λ 4 4πv 4π M W g A better estimate gives Λ 4 4πv ng 1.2 TeV

26 A model in 5D Preliminaries 1: Kaluza-Klein decomposition Consider a real scalar φ(x,x 5 ) To make contact with reality so that φ(x, x 5 ) = φ(x, x 5 ) = φ(x, x 5 + 2πR) n= n= φ n (x)e i nx 5 R. and L φ dx 5 = dx [ [ [( µ ] φ) 2 ( 5 φ) 2] = [ 2 µ φ n 2 + n2 R 2 φ n 2 ] The original 5D field decomposed into a tower of KK 4D fields of mass m n = n R

27 A pictorial view (UV) (IR) Space-time 5D = 4D flat or AdS πr 4D 1 R mass of the KK states Where we (matter) live is model dependent [flat or AdS irrelevant at the weak scale] G UV G 5 G IR

28 Preliminaries 2: Take a 5D gauge theory 1. Where is the strong dynamics? L 5 = 1 4g 2 F MN F MN 5 A gauge Eg2 5 24π 3 1 g 2 5 Λ 5 24π3 g Compactify the 5-th D without breaking G Λ 5 = [mass] (Only IR-physics modified, at 1/R, determined by short distance physics) KK spectrum of vectors M n = n R, n = 0,1,... coupled at g 4 g 5 E 1 R << Λ 5 with strength 2πR Λ 5 24π3 g 2 5 = 12π2 M 1 = 3π 4πM 1 g 4 g 4 g 4 = 3π g 4 Λ 4 by a non trivial dynamics!!!

29 L 5 = 1 4g 2 F MN F MN 5 A µ g 5 A µ L 5 = 1 4 (d MA N d M A N ) 2 + g 5 A M A N d M A N [A M ]=m 3/2 = [mass] g 2 5 Z + g 5 E g 5 Eg 2 5E 1 24π 3 d D P (2π) D f(p 2 ) d 5 x 1 4g 2 F MN F MN = 5 Z Ω D 2(2π) D d 4 x 2πR 1 4g 2 FMNF 0 MN0 5 Λ 5 24π3 g 2 5 dp 2 P D 2 f(p 2 ). g 4 g 5 2πR

30 If 3. Break G by boundary conditions L = L 5 + δ(y)l 0 + δ(y πr)l π ΔL π = F 2 ( µ + iga µ )e iσ/f 2 g 2 F 2 A 2 µ+( µ π) F 2π2 ( µ π) Send 1. Effectively A µ πr = 0 2. No new strong scale The vector spectrum Mn = n + 1/2, n = 0,1,... R M 0 = 1 then 2R = m Z m Z1 = 3 2R = 3m Z!!! 4. Take a big kinetic term on the boundary 0 πr M g n>1 bound M 1

31 SU(2) L SU(2) R U(1) B L 0 πr SU(2) L U(1) Y SU(2) V U(1) B L A Model with fermions at the y=0 boundary SU(2) L SU(2) R U(1) B L SU(2) L U(1) Y (G local ) (G global ) SU(2) V U(1) B L (H global) U(1) em L = L 5 + δ(y)l 0 + δ(y πr)l π L 5 = M L 4 (W I L) MN (W I L) MN M R 4 (W I R) MN (W I R) MN M B 4 B MNB MN, (I = 1,2,3) L 0 = L SM,withoutH L π = Z W (W L ) 2 µν ( Z B L irrelevant) [ L = L 5 + δ(y πr)l π = the EWSB sector ]

32 Spectrum M L = M R = M B 1 >> MR g 2 0 M vector modes W L +W R axial modes W L W R 1 2R 1 R m W g M R Useful to define: Λ 5 = 4π 3 M m KK = Λ 4 N Λ 4 = 4π m W g Λ 5 = π 3/2Λ 4 N N = 24π 3 MR = Λ 5 m KK1 N = O(1)

33 ElectroWeak Precision Tests At tree level, all corrections to EWPT oblique, from p 2 - expansion of Σ s Since custodial symmetry exact in L = L 5 + δ(y πr)l π but ˆT = 0 Ŝ = g 28πRM 3 [ 1 + 3Z ] W 8πMR [ = g2 N 18π Z ] W 8πMR with Z W > 0 to avoid ghosts Conclusion unchanged in the general space of parameters, where the ε s not enough

34 !"'!"&!"#!"$ a loop effect S, T SM (m h Λ 4 ) )!"%! %!!, *+,-,./, 0',-,./, a tree level effect N = 1 Λ 5 m KK1 Λ 4!!"% m h!!"$ '!!,!!"#!!"#!!"$!!"%!!"%!"$!"#!"& ( not really different from standard Technicolour (unless something missing: some proposals, quite ad hoc)

35 Heavy Vector production qq qq V qq WZ qq VZ,VW Γ V = GeV WZ- fusion, since no significant coupling to light fermion Higgs-less: unitarity sum rule saturated by first resonance (note the narrow V-width, relative to a massive h)

36 KK-vector signals ˆV qq qq ˆV qq ˆV ˆV VV, t t, (hv ) ˆV f f probably not useful, because of small BR pp qqŵ qqwz qq jet jet ll (t or b, depending on the charge) Resonance mass - Topo Preliminary SIGNAL+SMbg TTbg: gone after cuts SMbg: 8 events in peak region W4jetsbg: gone after cuts SIGNAL: 15 events in peak region 6 4 Resonance peak at " 649 GeV resolution " 27 GeV 100 fb ! mass [GeV]

37 KKgluons!(pp " KKG) (fb) pp " KKG M KKG (GeV) -1 # events / 200 GeV / 100 fb t t mass distribution total reconstructed total partonic W+jets background SM prediction t t invariant mass / GeV with suitably suppressed qq gkk couplings, 1/5 than normal (when q = light quark) Γ(gKK tt) GeV largely dominant