Constraints on UED Models

Transcription

1 KAIST TF, C. Pasold, PRD85 (2012) TF, A. Menon, Z. Sullivan, arxiv: TF, KC Kong, SC Park, arxiv:1210.xxxx KIAS-SNU Workshop on Particle Physics and Cosmology

2 Outline UED Review Modifying the UED mass spectrum Constraints from pp W tb at the LHC Some pre-lhc constraints

3 UED: The basic setup Review Modifying the UED mass spectrum UED models are models with flat, compact extra dimensions in which all fields propagate. 5D and 6D: [Appelquist, Cheng, Dobrescu,(2001)] see [Dobrescu, Ponton (2004/05), Cacciapaglia et al., Oda et al. (2010)] for further 6D compactifications. The Standard Model (SM) particles are identified with the lowest-lying modes of the respective Kaluza-Klein (KK) towers. Here, we focus on one extra dimension. Compactification on S 1 /Z 2 ; x 5 y [ πr/2, πr/2] [ L, L] allows for chiral zero mode fermions allows for gauge field zero modes without additional scalars The presence of orbifold fixed points breaks 5D translational invariance. KK-number conservation is violated, but a discrete Z 2 parity (KK-parity) remains. The lightest KK mode (LKP) is stable.

4 (M)UED pheno review Review Modifying the UED mass spectrum Phenomenological constraints on the compactification scale R 1 Lower bounds: FCNCs [Buras, Weiler et al. (2003); Weiler, Haisch (2007)] R GeV at 95% cl. Electroweak Precision Constraints [Appelquist, Yee (2002); Gogoladze, Macesanu (2006); Gfitter (2011)] R GeV for m H = 125 GeV at 95% cl. no detection of KK-modes at LHC, yet [Murayama et al. (2011)] R GeV at 95% cl. Upper bound: preventing too much dark matter by B (1) dark matter R 1 1.5TeV [Belanger et al. (2010)] UED vs. SUSY at the LHC: Determining the spin of new resonances [Barr et al. (2004) and many follow-ups] Studying the influence of 2 nd KK mode particles [Datta, Kong, Matchev (2005), Kim, Oh, Park (2011), Chang, Lee, Song (2011) Measuring total cross sections [Kane et al. (2005)], some follow-ups]

5 the MUED spectrum Review Modifying the UED mass spectrum The UED mass spectrum at the 1 st KK mode (R 1 = 500 GeV, ΛR = 20). [Cheng, Matchev, Schmaltz, PRD 66 (2002) , hep-ph/ ]

6 Relevance of the detailed mass spectrum Review Modifying the UED mass spectrum!h a0) " (1) annihilation (tree; w/o FS level 2) a1) " (1) annihilation (1!loop; w/o FS level 2) b0) Coannihilation (tree; w/o FS level 2) b1) Coannihilation (1!loop; w/o FS level 2) c0) Coannihilation (tree; w/ FS level 2) c1) Coannihilation (1!loop; w/ FS level 2) a b0 a0 b1 c0 WMAP 0.1 c m h = 120 GeV, #R = R!1 (GeV) [Cheng, Matchev, Schmaltz, PRD66 (2002) ] The KK mass spectrum determines decay channels, decay rates, branching ratios and final state jet/lepton energies and MET at LHC. [Belanger, Kakizaki, Pukhov, JCAP 1102 (2011) 009] The DM relic density is highly sensitive to mass splittings at the first and between the first and second KK level.

7 Review Modifying the UED mass spectrum modifying the UED mass spectrum - why? and how? UED is a five dimensional model non-renormalizable. It should be considered as an effective field theory with a cutoff Λ. Naive dimensional analysis (NDA) result: Λ 50/R. A light Higgs and vacuum stability even implies Λ 6/R. [ Ohlsson et al. (2011)] if higher dimensional operators and a Higgs brane mass are not included. Assumption in MUED: all higher dimensional operators vanish at Λ. Effective field theory include all operators allowed by symmetries. 1. Bulk mass terms for fermions (dim = dim(l)) split UED (sued), 2. kinetic and mass terms at the orbifold fixed points, (dim = dim(l) + 1; radiatively induced in MUED) nonminimal UED (nued), 3. bulk or boundary localized interactions (dim > dim(l) + 1) The former two operator classes modify the free field equations and thereby alter the Kaluza-Klein decomposition different mass spectrum and different KK wave functions.

8 mass modifying operators Review Modifying the UED mass spectrum In sued, a KK parity conserving fermion bulk mass term is introduced. [Park, Shu (2009); Csaki et al. (2001)] S d 5 x µθ(y)ψψ. In nued one includes the boundary kinetic action ( S bd = d 5 x r B B µνb µν r W WµνW a a,µν r G GµνG A A,µν 4ĝ1 2 4ĝ2 2 4ĝ3 2 M S 1 /Z 2 ) [ ( +r h Ψ h /DΨ h + r H (D µh) D µ H δ y πr 2 ) ( + δ y + πr 2 where h = R, L represents the chirality. For simplicity, in what follows we consider a common electroweak boundary parameter r B = r W = r H r ew. For the generic case, c.f. [TF,Menon,Phalen(2009)]. )],

9 Kaluza-Klein decomposition Review Modifying the UED mass spectrum KK decomposition: Ψ R (x, y) = Ψ (n) R n=0 (n) (x) f R (y), Ψ L(x, y) = Ψ (n) L n=0 (n) (x) f (y). Bulk mass terms modify the 5D EOM. BLKTs modify the boundary conditions of this Sturm-Liouville problem. KK-masses and wave-functions are modified. Solutions for a fermion with left-handed zero mode: KK zero modes even numbered KK-modes odd numbered KK-modes f ( 0 ) L (y) = N (0) L eµ y f (n) (n) L (y) = N L (cos(k ny) f (n) (n) ) L (y) = N L sin(k ny) + µ sin(k k n n y ) f (0) R (y) = 0 (n) (n) f R (y) = N R sin(kny) (n) (n) f R (y) = N R (cos(kny) ) µ sin(k k n n y ) k 2 0 = µ2 tan(k nl) = (1+rµ) rk n tan(k nl) = (rm2 n +µ) k n and m n = k 2 n + µ 2. (Solutions for left-handed zero mode: L R and µ µ, Solutions for gauge bosons / scalars: µ 0) L

10 Masses Review Modifying the UED mass spectrum Masses of the first and second KK mode for different µ (m n vs. r/l) Masses of the first and second KK mode (r/l vs. µl for R 1 = 500 GeV)

11 Couplings Review Modifying the UED mass spectrum Coupling g (1) f (1) f (0) (normalized w.r.t. g (0) f (0) f (0) coupling) Coupling g (2) f (0) f (0) (normalized w.r.t. g (0) f (0) f (0) coupling)

12 Constraints from pp W (2) tb [TF, Menon, Sullivan (2012)] The KK number violating couplings in nued and sued imply W, Z, g,... - like signatures from the s-channel resonances of W (2), Z (2), γ (2), G (2) at LHC. We first focus on pp W tb. tb) [pb] R σ(pp W' CMS Preliminary 5.0 fb at s = 7 TeV Boos et. al., PLB 655 (2007) % C.L. observed 95% C.L. expected ±1σ expected ±2σ expected g200 g BDT Analysis e/µ+jets N 1 b tags W' R Mass [GeV] CMS bounds on pp W tb CMS bounds on pp W tb, 5fb s = 7 TeV, [CMS PAS EXO ] converted into a bound on g /g for ATLAS bounds, c.f. [arxiv: ] for earlier W bounds c.f. Sullivan (2003) W

13 Resulting sued bounds 2.5 BR 1 BR BR min 2.0 ΜQL 1.5 Μ QL Upper bounds on µ Q L for different branching ratios σ(w (2) QQ)/σ(W (2) all) Contours of maximally allowed R 1 in the µ Q L vs. µ L L plane Contours: R 1 = (.925,.9,.8,.6) TeV Μ L

14 Resulting nued bounds r f L r f L rw L Bounds in the r f L vs. rw L plane Bounds in the r f L vs. rw L plane for m W (2) = (0.8, 1.0, 1.2, 1.5) TeV for m LKP = (0.4, 0.5, 0.6,.7) TeV (for BR QQ = 3/4) (for BR QQ = 3/4) rw L

15 Electroweak precision I: S, T, U parameters [TF, Pasold (2012); TF, Kong, Park (in prep.)] In the presence of bulk masses and boundary terms, electroweak corrections are not oblique but if we assume a common boundary term r and a common boundary term µ, corrections are universal. can be treated in terms of effective S, T, U parameters: [Carena, Ponton, Tait, Wagner (2002)] S eff = S UED Experimental values: [Gfitter(2011)] T eff = T UED + T UED = T UED 1 δg f α G obl f U eff = U UED = U UED = U UED + 4 sin2 θ W α δg f G obl f S BSM = 0.04 ± 0.10 T BSM = 0.05 ± 0.11 U BSM = 0.08 ± 0.11 reference point: m h = 120 GeV, m t = 173 GeV, with correlations of (S T ), 0.45 (S U), and 0.69 (T U).

16 At tree level in nued/sued, the only contributions to the effective parameters arise from W KK excitations, so that δg f G obl f = m 2 W (F 002n ) 2 mw 2 + ( ) 2n 2, R where again, F 002n are the overlap integrals which depend on µ (sued) or respectively r f, r ew (nued). The leading one-loop contributions are [ S UED 4 sin2 θ W 3g 2 α 4(4π) 2 [ T UED 1 3g 2 mt 2 α 2(4π) 2 mw 2 U UED 4g2 sin 4 θ W (4π) 2 α ( 2 9 n ( 2 3 n [ 1 6 n n=1 m 2 t m 2 t m 2 t (n) ) ) ( + g2 1 4(4π) 2 6 m 2 + g2 sin 2 θ W (4π) 2 cos 2 θ t (n) W ] mw 2 m 2 1 mh 2m2 W 15 W (n) n m 4. W (n) n ( m 2 h m 2 h (n) 5 12 n )], m 2 h m 2 h (n) Compare to experimental values (χ 2 -test) Constraints on parameter space. )],

17 Constraints on the UED parameter space r L 0.8 r L Μ Μ Contours of minimally allowed R 1 (at 2σ c.l.) Contours of minimally allowed m LKP (at 2σ c.l.) in the r/l vs. µl plane in the r/l vs. µl plane

18 EWPT II: (non-universal) four-fermi operator bounds Parameterization of the four-fermi interactions: L eff η s 4π f 1 f 2,AB (Λ s f 1,Aγ µ f 1,A f 2,B γ µf 2,B, f1,f2 A,B=L,R f 1,f 2,AB )2 where f 1,2 are the contributing fermions and η s f 1 f 2,AB = ±1. Four-fermi interaction bounds: [PDG 2011] TeV eeee eeµµ eeτ τ llll qqqq eeuu eedd Λ + LL > 8.3 > 8.5 > 7.9 > 9.1 > 2.7 > 23.3 > 11.1 Λ LL > 10.3 > 9.5 > 7.2 > > 12.5 > 26.4 Effective four-fermi operators in UED: L UED eff 4πN c 12π n=1 n=1 ( ) 2 F00 2n (r/l, µl) 3 5 ( ) 2 F00 2n (r/l, µl) 3 α 1 Y ea Y qb 5 MB 2 2n α 1 Y ea Y qb + α 2Te 3 A Tq 3 B Q 2 MB 2 2n Q 2 M 2 W 2n 3 + α 2T 3 e A T 3 q B M 2 W 3 2n,

19 Constraints on the UED parameter space r L r L Μ Μ Contours of minimally allowed R 1 (at 2σ c.l.) Contours of minimally allowed m LKP (at 2σ c.l.) in the r/l vs. µl plane in the r/l vs. µl plane

20 Dark Matter relic abundance Obtaining (at most) as much DM as observed by WMAP yields an upper bound on m LKP. In Minimal UED, the correct relic abundance is obtained for m LKP 1.5 TeV if 2nd KK mode s-channel resonances and co-annihilation are taken into account [Belanger et al. (2010)] m LKP 800 GeV in the absence of co-annihilation [Kong, Matchev (2005); Burnell, Kribs (2005)] s-channel resonances and co-annihilation only occur if the KK mass spectrum is given by m n n/r can be ignored for µl, r/l >.1. In this case, the relic density can be calculated in the standard way from the non-relativistic limit of the annihilation X-section σ treev = a + bv 2 + O(v 4 ) with [Kong,Matchev (2005)] a = b = f f 32πα 2 Y Nc mγ 1 9 4πα 2 Y Nc mγ 1 27 ( ( Yf 4 L (mγ mf 2 L1 ) + Yf 4 R 2 (m 2 γ 1 + m 2 f R1 ) 2 ) Y 4 f L 11m 4 γ m 2 γ 1 m 2 f L1 13m 4 f L1 (m 2 γ 1 + m 2 f L1 ) 4 + Y 4 f R 11m 4 γ m 2 γ 1 m 2 f R1 13m 4 f R1 (m 2 γ 1 + m 2 f R1 ) 4 )

21 Constraints on the UED parameter space r L r L Contours of maximally allowed R 1 in the r/l vs. µl plane Μ Contours of maximally allowed m LKP in the r/l vs. µl plane Μ

22 Combined constraints on the UED parameter space (pre-lhc) r L r L Contours of maximally allowed R 1 in the r/l vs. µl plane ΜL ΜL Contours of maximally allowed m LKP in the r/l vs. µl plane

23 Our W analysis was particularly simple because for the signal, only one resonance (W (2) ) plays a role, the only relevant BSM coupling is the Q (0) Q (0) W (2) coupling. This justifies to simply use model-independent bounds on g 200 g 000 (m W (2)) provided by Atlas/CMS. This does not hold for other channels. Example: resonant pp X ll ( Z searches ) Contributing resonances: Z (2), γ (2), relevant couplings: q (0) q (0) Z (2) /γ (2) and l (0) l (0) Z (2) /γ (2) where q {Q, U, D} and l {L, E}, which are relevant for the process and branching ratios. Resulting bound on the parameter space need to make simplifying parameter choices and use event generators.

24 Example: resonance search in the di-lepton channel We assume universal boundary localized terms r r B = r W = r H = r q = r l and universal bulk mass terms µ µ q = µ l. We use CalcHEP and CTEQ 5M PDF to evaluate cross sections. We compare results to current CMS bounds (CMS PAS EXO ; 7 TeV run and 4.1 fb 1 at 8 TeV) Preliminary Red: contours of maximal R 1 allowed by WMAP Yellow: Parameter region allowed by resonance search in the di-lepton channel

25 and Outlook : Modifications of the KK mass spectrum can occur due to boundary localized kinetic terms or fermion bulk mass terms. In both cases, the KK wave functions are altered, which implies interactions of Standard Model fermions with all even KK modes of the gauge bosons. Combination of DM, electroweak, and W, Z, γ, g,... LHC constraints put substantial bounds on bulk masses while still allowing for large boundary kinetic terms. The presented results are only a first step. There is lots of work to do in terms of precision and more systematic studies of the general parameter space.