Higgsless Vector Boson Fusion at the LHC beyond leading order

Transcription

1 Higgsless Vector Boson Fusion at the LHC beyond leading order Christoph Englert GGI Conference The Search for New States and Forces of Nature, Florence INSTITUTE FOR THEORETICAL PHYSICS KIT the cooperation of Forschungszentrum Karlsruhe GmbH and Universität Karlsruhe (TH) Forschungszentrum Karlsruhe in der Helmholtz - Gemeinschaft Universität Karlsruhe (TH) Research University founded 1825

2 Outline 1 Overview over Higgsless Symmetry Breaking 2 Higgsless VBF signatures 3 Summary based on CE, B. Jäger and D. Zeppenfeld JHEP 0903 (2009) 060 CE, B. Jäger, M. Worek and D. Zeppenfeld, Phys. Rev. D 80 (2009) C.Englert Higgsless VBF at the LHC beyond LO /22

3 EWSB & hierarchies via... i) SUSY ii) Technicolor iii) Extra dimensions unresolved spacelike dimension(s) [Arkani-Hamed, Dimopoulos, Dvali 98], [Randall, Sundrum 99] RS1: 5d Einstein equations exhibit 4d Lorentz-invariant solution, S 1 /Z 2 orbifold slice of AdS 5 Planck TeV ds 2 = R2 y 2 g µνdx µ dx ν dy 2 m eff = R y m 0 AdS y RS1 bulk-gauging [Pomarol et al. 99, 00], [Chang et al. 99],... dictionary of duality via AdS/CFT [Rattazzi, Zaffaroni et al. 00], [Arkani-Hamed et al. 00] C.Englert Higgsless VBF at the LHC beyond LO /22

4 AdS/CFT Bulk-gauged RS1 AdS/CFT conjecture [Maldacena 97], [Witten 98] AdS 5 framework strongly-coupled CFT Realistic Higgsless model [Csáki et al. 04, Agashe et al. 03] T, U 0 Planck TeV Break symmetry by DBCs unbroken directions NBCs R SU(2) x U(1) U(1) R B L Y SU(2) x SU(2) x U(1) L R B L AdS 5 S 0 fermiophobic KKs ( bulk-fermions) SU(2) x SU(2) Break symmetry by DBCs unbroken directions NBCs R SU(2) L R D SU(2) L SU(2) R U(1) B L global symmetry SU(2) L U(1) Y subgroup weakly gauged Strong CFT dynamics causing spontaneous breaking of CFI which also higgses the electroweak sector. Walking extended technicolor vectors an axial-vectors: e.g. Kaluza-Klein W k (ρ-like bound states) C.Englert Higgsless VBF at the LHC beyond LO /22

5 Notes on deconstruction [Arkani-Hamed, Cohen, Georgi 01] SU i (M) SU i (N) SU i+1 (M) SU i+1 (N) SU i+2 (M) χ i,i ψ i,i+1 χ i+1,i+1 ψ i+1,i+2 Connections with deconstruction [Randall, Shadmi, Weiner 02] Seminal to continuum model-building (delocalization,... ) [Chivukula et al. 05] Popular candidates to model higgsless LHC phenomenology [He et al. 08] Phenomenologically quite identical to continuum theory [Belyaev al. 09] Drawbacks, model-building issues 3rd generation new discovery modes, flavor physics,... [Csáki et al. 06] Tension between minimal models and electroweak precision data [Barbieri, Pomarol, Rattazzi 03], [Barbieri et al. 08] C.Englert Higgsless VBF at the LHC beyond LO /22

6 Higgsless ELW mass spectrum 5d gauge fields decompose under the unbroken 4d Lorentz group A M (x, y) = A k µ, A k 5 = 4d vectors 4d scalars Action mixes 4d scalar and 4d vector (cf. SM) Z S d 4 x Z R R dy R y j 1 4 F a,µν Fµν a 1 ff 2 F a,µ5 Fµ5 a -conditions & gauge fixing A 5 becomes the longitudinal component of A µ, i.e. A 5 decouples in unitary gauge no scalars in theory s spectrum, Gauge boson mass operator ˆm 2 = y 1 y 2 y reg. SLP along additional dimension KK decomposition of gauge fields, e.g. A 3L µ (x, y) = az µ (0) (x) + X ψ B (k) k (y)z µ (x) k 1 massless mode massive modes C.Englert Higgsless VBF at the LHC beyond LO /22

7 The Higgsless model - masses & couplings Model is determined by a single parameter, chosen to be the localization of the UV brane R (T Parameter bound 10 7 GeV 1 ). [CE, B. Jäger, D. Zeppenfeld 08] W k WZ coupling ratio wrt to WWZ coupling for m W2 = 700 GeV C.Englert Higgsless VBF at the LHC beyond LO /22

8 In the Standard Model these cancellations are a consequence of the underlying, spontaneously broken gauge symmetry. As it turns out, this is also true for the Higgsless Thescenarios, warped wherehiggsless the 5d gauge symmetry model protects the Unitarity effective 4d theory from the bad high energy behavior. A a i (k1) A c k (k3) A e k (p 0 (A) )0 A b j(k 2) A d l (k4) Figure 4.1: Tree level gauge boson scattering topologies. Necessary SM sum rules for s m k 1 Here Pl is the lth Legendre Polynomial. As all gauge boson helicities [Birkedal, areperelstein, equal no reduced Matchev Wigner 04, Chivukula et al. 08] functions are to be included. g W1 W 1 W 1 W = X g 2 1 W 1 W 1 Z O(s) k k 0 4m 2 W 1 g W1 W 1 W 1 W 1 = 3 X k 1 m 2 Z k g 2 W 1 W 1 Z k O( s) g W1 W 1 Z 1 Z = X g 2 1 W k W 1 Z O(s) 1 k 1 0 2(m 2 Z + m 2 1 W )g 1 W1 W 1 Z 1 Z = X g 2 1 W k W 1 2 (mz 2 m 1 W 1 W 2 ) A k m k 1 W 2 O( s) k...obeyed as consequence of the regular SLP in the continuum C.Englert Higgsless VBF at the LHC beyond LO /22

9 In the Standard Model these cancellations are a consequence of the underlying, spontaneously broken gauge symmetry. As it turns out, this is also true for the Higgsless Thescenarios, warped wherehiggsless the 5d gauge symmetry model protects the Unitarity effective 4d theory from the bad high energy behavior. A a i (k1) A c k (k3) A e k (p 0 (A) )0 A b j(k 2) A d l (k4) Figure 4.1: Tree level gauge boson scattering topologies. Unitarity violation postponed to several TeV (upper limit). 1 Here Pl is the lth Legendre Polynomial. As all gauge boson helicities are equal no reduced Wigner functions 0.5 are to be included Partial wave projection for m W2 = 700 GeV, J = 0, J = 1, J = 2, J = s 1/2 [TeV] C.Englert Higgsless VBF at the LHC beyond LO /22

10 In the Standard Model these cancellations are a consequence of the underlying, spon- warped brokenhiggsless gauge symmetry. model As it turns out, Unitarity this is also true for the Higgsless Thetaneously scenarios, where the 5d gauge symmetry protects the effective 4d theory from the bad high energy behavior. A a i (k1) A c k (k3) A e k (p 0 (A) )0 A b j(k 2) A d l (k4) Figure 4.1: Tree level gauge boson scattering topologies. Extract upper limit on NDA O(1) determined from AdS 5 1 Here Pl is the lth Legendre Polynomial. As all gauge boson helicities are equal no reduced Wigner functions12are to be included. Cut-off scale [TeV] Ratio NDA cut-off scale [TeV] NDA cut-off scale [TeV] C.Englert Higgsless VBF at the LHC beyond LO /22

11 Higgsless WW, WZ cross sections Phenomenology with W, Z - saturated sum rules: W is smoking gun Saturation in very good agreement with full calculation: [Birkedal, Perelstein, Matchev 04] WW WW WZ WZ cos < [nb] 1 [nb] s 1/2 [GeV] s 1/2 [GeV] [CE, 07] Phenomenology entirely dominated by the first non-sm mode ( unitarity!) flat space warped space C.Englert Higgsless VBF at the LHC beyond LO /22

12 VBF signatures in general Weak Boson fusion processes access gauge boson scattering. sensitivity to the mechanism of EWSB Clean and distinct signatures of gold and silver plated modes at the LHC. [Bagger et al. 94], [Rainwater, Zeppenfeld 99] cut on typical VBF signature highly reduces QCD backgrounds pseudorapidity azimuthal angle VBF processes provide prominent discovery channels of extra vector bosons, especially for suppressed Drell-Yan production. C.Englert Higgsless VBF at the LHC beyond LO /22

13 Higgsless WWjj signatures VBF cuts p j T 20 GeV, η j 4.5, η jj 4, η j1 η j2 < 0, m jj 600 GeV, pt l 20 GeV, η l 2.5, R ll 0.2, R jl 0.4, leptons in jet rapidity gap σ tot (µ F = Q) = 1.70, 2.28, 2.03 fb [CE, B. Jäger, D. Zeppenfeld 08] smearing: CMS-Note 2006/035,036 C.Englert Higgsless VBF at the LHC beyond LO /22

14 Higgsless W + Zjj signatures VBF cuts p j T 20 GeV, η j 4.5, η jj 4, η j1 η j2 < 0, m jj 600 GeV, pt l 20 GeV, η l 2.5, R ll 0.2, R jl 0.4, leptons in jet rapidity gap σ tot (µ F = Q) = 0.18, 0.35, 0.24 fb [CE, B. Jäger, D. Zeppenfeld 08] smearing: CMS-Note 2006/035,036 C.Englert Higgsless VBF at the LHC beyond LO /22

15 NLO-QCD?! Why NLO corrections LO = Order of magnitude approximation scale dependence (lower bound on uncertainty!) Hadron-colliders total QCD quantum corrections are sizable 2 Differential QCD-corrections even more important: differential shapes jet-definition,... MLO 2 Experiment hard fixed-order QCD RG-improved LO analysis, i.e. µ F,R = µ F,R (typical scales; Observable) C.Englert Higgsless VBF at the LHC beyond LO /22

16 NLO-QCD?! Why NLO corrections LO = Order of magnitude approximation scale dependence (lower bound on uncertainty!) Hadron-colliders total QCD quantum corrections are sizable 2 Differential QCD-corrections even more important: differential shapes jet-definition,... MNLO 2 Experiment hard fixed-order QCD RG-improved LO analysis, i.e. µ F,R = µ F,R (typical scales; Observable) C.Englert Higgsless VBF at the LHC beyond LO /22

17 Higgsless NLO-QCD u c γ,z γ,z (a) u µ ν µ ν e e + c u c γ,z γ,z (b) u µ ν µ ν e e + c Anatomy of NLO-QCD corrections ( external QCD no gluon tower) Handle IR-divergencies à la Catani-Seymour [Catani, Seymour 96], [KLN 62 64] Z σ NLO = σ LO + `dσ R dσ A Z Z «+ dσ Virt + dσ A n+1 n 1 {z } {z } finite (a) finite (b) Subtraction term reproduces IR-divergencies of the real emission matrix element dσ Virt M B 2 αs(µ R) π 4πµ 2 R Q 2! ɛ» Γ(1 + ɛ) C F ɛ 2 γq + 2 Re [ M f V M B ɛ ] Loop corrections in terms of process-universal building blocks [Jäger, Oleari, Zeppenfeld 06] [Campanario, CE, Spannowsky, Zeppenfeld 09] C.Englert Higgsless VBF at the LHC beyond LO /22

18 Higgsless NLO-QCD Total NLO correction for W + Zjj with leptonic decay: σ NLO /σ LO Scale µ σ LO [fb] σ NLO [fb] K factor (m W + m Z )/ Q m W RG improvement!? [CE, B. Jäger, D. Zeppenfeld 08], cf. SM [Bozzi et al. 07] C.Englert Higgsless VBF at the LHC beyond LO /22

19 Higgsless NLO-QCD Total NLO correction for W + Zjj with leptonic decay: σ NLO /σ LO Scale µ σ LO [fb] σ NLO [fb] K factor (m W + m Z )/ Q m W RG improvement!? [CE, B. Jäger, D. Zeppenfeld 08] C.Englert Higgsless VBF at the LHC beyond LO /22

20 Can we separate the signal from the background? VBF provides clean enough signatures to cope with very general BSM-EWSB [Bagger et al ] Dedicated refinement of the analysis for all LHC [CE, Jäger, Worek, Zeppenfeld 08] Signal procs background procs pp W ± Zjj 3l/p T jj pp W + W jj 2l/p T jj taking into account pp ZZjj 4l/p T jj full matrix elements for signal and backgrounds double jet tagging full off-shell effects & leptonic final states t t + jets QCD pp VVjj incl. leptonic decays central jet veto b-tag efficiencies, RG improvements C.Englert Higgsless VBF at the LHC beyond LO /22

21 Can we separate the signal from the background? Process σ S σ B S/B S/ B S/ S + B N SM signal N bkgd. W ± Zjj W + W jj ZZjj 4l jj ZZjj 2l2ν jj : fb Cross 1 sections for the Higgsless Kaluza-Klein scenario and overall background for various channels (in fb), after all selection cuts have been applied. Also listed are several ratios for signal and background LHC rates is together highly sensitive with the number to the of scenario! signal and background events for an assumed integrated luminosity of 300 fb 1 at the LHC. Combined analysis of LHC sheds light on EWSB These two channels provide excellent possibilities for the study of strongly interacting gauge boson systems via scalar resonances, see Table 9. Particularly encouraging is the signal rate for the ZZjj 2l2ν jj mode. The absence of a significant enhancement in the WZjj channel is a crucial factor in identifying the iso-scalar character of such a resonance. C.Englert Higgsless VBF at the LHC beyond LO /22

22 Can we separate the signal from the background? QCD-impact on the signal for these selection cuts? C.Englert Higgsless VBF at the LHC beyond LO /22

23 Summary Higgsless EWSB defines phenomenologically appealing BSM scenarios If VBF phenomenologically dominates (fermiophobic KKs), the signatures are (i) (ii) (iii) clearly visible and perturbatively stable, largely independent of the fermionic sector, rather model independent Additional KKs generically too weakly coupled no d > 4 VBF-proof The MC Code is publicly available at [Arnold et al., 08] vbfnloweb/ and features all the stuff you need... (GNU-build system, libraries, LHA, manual,... ) Use your own scenario switch plug in your scenario and get differential NLO-QCD cross sections C.Englert Higgsless VBF at the LHC beyond LO /22