Light Higgs wants light top partners [De Curtis, Redi, Tesi 1110.1613 ] f=500 GeV 2500 2500 � moderate mixing � � � ⇥ � � � � ⇥ � � ⇥ ⇥ ⇥ � ⇥ � � large mixing � � ⇥ � � � �� � � � ⇥ ⇥ � � ⇤ ⇥ ⇥ ⇥ � � � � ⇥ � ⇤⇤ � � ⇥ � � � � � � ⇤ � � ⇥ ⇥ ⇥ � � ⇤ ⇤ ⇥ � ⇥ ⇥ � � � ⇥ � ⇥ ⇤ � � � � ⇤ ⇤ ⇥ ⇤ � � ⇥ ⇥ � ⇥ ⇥ � � ⇤ ⇤ � ⇥ � ⇥ � � ⇤ ⇥ ⇤ 2000 � � ⇤ ⇤ � � ⇤ ⇤ � 2000 � ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇤ ⇥ ⇤ � ⇤ � � ⇤ ⇤ ⇤ ⇤ ⇤ � ⇤ � � ⇥ � � ⇥ ⇥ ⇤ ⇤ ⇤ ⇥ ⇥ ⇤ ⇤ ⇥ ⇥ ⇤ � ⇤ � � ⇤ ⇥ ⇤ ⇤ ⇤ ⇤ ⇥ ⇥ ⇤ � � � � ⇥ ⇤ ⇤ � � � ⇥ ⇤ � � � � ⇥ ⇤ ⇤ � ⇤ ⇥ ⇥ ⇤ � ⇤ ⇤ � � ⇤ � � � ⇤ � ⇤ � ⇤ ⇥ � ⇤ ⇤ � ⇥ ⇤ ⇤ ⇤ ⇤ � ⇤ � � � ⇥ � � ⇤ � ⇥ ⇥ ⇤ ⇤ ⇤ � ⇤ ⇥⇥ � ⇥ ⇥ ⇥ � � � ⇤ ⇥ ⇤⇤ � � ⇤ ⇥ ⇥ � ⇥ ⇤ ⇤ ⇤ ⇤ � ⇤ ⇤ � � � ⇤ � ⇥ � ⇥ � ⇤ ⇤ � ⇥ � ⇤ ⇤ � � � � ⇤ ⇤ ⇤ � ⇤ m f � GeV ⇥ � � � � ⇤ ⇤ ⇤ m f � GeV ⇥ ⇥ ⇤ � ⇤ ⇤ ⇥ � � � � � ⇤ ⇤ ⇥ ⇥ � ⇥ ⇤ ⇤ ⇥ ⇥ ⇥ ⇥ � ⇥ ⇤ ⇤ � ⇤ ⇥ � ⇤ ⇤ � ⇥ ⇥ � ⇥ � � ⇤ ⇤ ⇥ ⇥ ⇥ ⇥ ⇤ ⇤ � ⇤ � � ⇥ ⇥ ⇤ ⇤ ⇤ ⇤ ⇤ � � � � ⇥ ⇥ ⇥ ⇥ 1500 � ⇤ ⇤ � � ⇤ 1500 � ⇥ ⇥ ⇤ ⇤ ⇥ ⇥ ⇤ ⇤ ⇤ ⇥ ⇥ ⇤ � ⇤ ⇤ ⇥ � ⇤ ⇤ ⇤ ⇥ ⇥ ⇤ � � ⇤ ⇤ ⇥ ⇤ ⇤ ⇥ ⇥ ⇤ ⇤ � � ⇤ ⇤ ⇥ ⇤ ⇤ � � � � ⇥ ⇤⇤ ⇤ � � ⇥ ⇤ � ⇤ ⇥ ⇥ ⇤ ⇤ ⇤ � ⇤ ⇤ ⇥ ⇥ � ⇥ ⇥ � ⇤⇤ � � ⇤ � ⇤ ⇥ � ⇥ � � � ⇤ ⇥ � � ⇤ � � ⇤ � ⇤ � ⇤ � � � ⇥ ⇤ ⇤ � ⇤ ⇥ ⇥ ⇥ � � ⇤ ⇤ ⇤ ⇥ ⇥ ⇥ ⇤ ⇤ � � ⇤ � ⇤ ⇤ ⇤ ⇥ ⇥ ⇤ � ⇤ ⇥ ⇤ ⇤ ⇤ ⇤ ⇥ � � � � ⇥ ⇥ � ⇤ ⇥ ⇥ ⇥ ⇤ � � � � ⇤ ⇤ ⇥ ⇥ ⇥ ⇤ ⇤ � � ⇤⇤ ⇤ ⇥ 2 7 ⇤ 6 � ⇤ ⇥ ⇥ ⇥ ⇥ 2 7 ⇤ 6 ⇥ ⇤ � � ⇤ � ⇥ � � ⇤ ⇥ ⇥ ⇥ ⇥ ⇤ ⇥ ⇥ ⇤ ⇤ ⇥ � � ⇥ ⇥ ⇥ ⇤ ⇤ ⇤ ⇥ ⇥ � ⇥ � ⇤ ⇤ ⇤ � 1000 ⇤ 1000 � ⇤ ⇤ ⇥ ⇥ ⇤ � ⇤ ⇥ ⇥ ⇥ ⇤ ⇤ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇤ ⇤ ⇤ ⇥ ⇥ ⇥ ⇤ ⇤ � ⇤ ⇤ ⇤ ⇥ � ⇤ ⇥ ⇥ ⇥ ⇤ � ⇥ ⇥ ⇥ ⇥ ⇤ � 2 1 ⇤ 6 � ⇤ � 2 1 ⇤ 6 � ⇥ ⇥ ⇥ ⇤ ⇥ ⇥ ⇤ ⇤ ⇤ ⇤ ⇥ ⇥ ⇤ ⇤ ⇤ ⇥ ⇤ ⇥ ⇤ ⇤⇤ ⇤ ⇥ ⇥ ⇥ ⇤ ⇤ ⇥ ⇥ ⇤ 1 2 ⇤ 3 ⇥ ⇥ ⇥ ⇥ ⇥ ⇤ 1 2 ⇤ 3 ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ 500 ⇥ ⇥ ⇥ 500 ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ 100 120 140 160 180 200 220 240 100 120 140 160 180 200 220 240 m H � GeV ⇥ m H � GeV ⇥ lightest fermion: singlet lightest fermion: doublet ⇤ ⇤ 2500 � ⇤ � ⇤ ⇤ � ⇤ ⇤ � ⇤ ⇤ � ⇤ � � � � � ⇤ � ⇤ ⇤ ⇤ ⇤ � ⇤ ⇤ ⇤ ⇤ � ⇤ � ⇤ � � � � ⇤ ⇤ � ⇤ � ⇤ ⇤ ⇤ � ⇤ � ⇤ � ⇤ ⇤ ⇤ � � ⇤ � � ⇤ ⇤ � � � � 2000 ⇥ ⇤ ⇤ � ⇤ � ⇤ ⇤ � ⇤ � � ⇤ � ⇤ ⇤ � 2 7 ⇤ 6 ⇤ � � � � ⇤ � ⇤ ⇥ � ⇤ ⇤ � � � � ⇤ ⇤ � ⇤ � ⇤ � ⇤ � ⇤ ⇤ � � � � � � � ⇤ ⇤ � ⇤ ⇤ ⇤ � ⇥ � ⇤ ⇤ � ⇤ ⇤ ⇤ � ⇤ ⇤ � � � ⇤ ⇤ � � � ⇤ m T � GeV ⇥ ⇤ ⇤ ⇤ � ⇤ ⇤ � ⇤ ⇥ � � ⇤ � 2 1 ⇤ 6 � � � � � ⇥ � ⇥ ⇤ ⇥ � � ⇤ ⇤ ⇤ � ⇤ � ⇤ ⇤ � � ⇥ ⇤ ⇥ � � ⇤ ⇥ ⇥ ⇤ � ⇤ ⇥ 1500 ⇥ ⇤ ⇤ ⇥ ⇥ � � ⇥ ⇤ ⇤ ⇤ ⇤ ⇤ � ⇤ � � ⇥ ⇥ ⇥ ⇤ ⇤ ⇥ � � ⇤ ⇥ ⇤ ⇤ � ⇤ � ⇤ ⇤ ⇥ ⇤ ⇤ ⇥ ⇤ � ⇤ ⇥ ⇥ f=800 GeV � ⇤ 1 2 ⇤ 3 ⇤ ⇤ � ⇥ ⇤ � � ⇤ � � ⇤ ⇥ ⇥ ⇤ ⇥ ⇤ ⇥ ⇥ ⇥ � � ⇤ � � ⇤ � ⇥ ⇥ ⇥ ⇥ � ⇥ � ⇥ ⇤ ⇤ � ⇥ � ⇥ � ⇥ ⇥ ⇥ ⇥ ⇥ � ⇥ ⇥ � ⇥ ⇥ ⇥ ⇥ ⇤ � ⇥ ⇥ ⇥ ⇤ ⇥ � � ⇤ ⇥ ⇥ ⇥ ⇤ ⇤ � � ⇥ ⇤ ⇥ ⇥ ⇥ � ⇥ ⇥ ⇥ � ⇥ � ⇥ ⇥ � ⇥ ⇤ � ⇥ � ⇥ ⇤ ⇥ ⇥ ⇥ ⇥ � ⇥ ⇥ ⇥ � ⇥ ⇥ � ⇥ � ⇥ ⇥ � ⇥ ⇥ ⇥ ⇤ ⇥ ⇥ ⇥ � ⇥ 1000 � ⇥ ⇥ ⇥ ⇥ ⇤ ⇥ ⇥ ⇤ ⇥ ⇥ ⇥ � ⇤ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ � ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇤ ⇥ ⇥ ⇥ ⇤ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ � ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ -> partners above ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ 500 ⇥ experimental bound ⇥ 116 118 120 122 124 126 128 130 m H � GeV ⇥
Light Higgs wants light top partners [Panico & Wulzer, 1106.2719 ] 4000 3000 2000 M ˜ m H ∈ [115 , 130] T 1000 0 0 1000 2000 3000 4000 2006) M T [Wulzer,2012]
Exotic bi-doublet is even lighter 4000 4000 ξ = 0 . 1 3000 3000 M ˜ M ˜ T T 2000 2000 M H ∈ [115 − 130] GeV 1000 1000 0 0 0 1000 2000 3000 4000 0 1000 2000 3000 4000 [Wulzer,2012]
Present constraints: ~ 550-600 GeV on the mass of b’ and t’ t → l ± l ± b 3 j E T [CMS L=1.14 fb -1 ] B ¯ B → WtW ¯ m B > 495 GeV → lll b 1 j E T PAS-EXO-11-036 update at L=4.6 fb -1 M b 0 & 600 GeV t’b -> bWb ; b’ t -> t bW WbW ; [CMS L=1.1 fb -1 ] t’ t’ -> bWbW ; b’b’ -> t bW Wt bW W PAS-EXO-11-054 m t’ =m b’ > 490GeV M t 0 & 560 GeV [CMS L=4.7 fb -1 ] at least 1 lepton and 4 jets: PAS-EXO-11-099 [CMS L=4.7 fb -1 ] M t 0 & 552 GeV dilepton PAS-EXO-11-050 [CMS L=1.1 fb -1 ] M T & 475 GeV T->tZ 3 leptons PAS-EXO-11-005 M b 0 & 480 GeV arXiv:1202.6540 1 lepton: [ATLAS M b 0 & 450 GeV arXiv:1202.5520 same-sign dilepton + 2 jets L=1.1 fb -1 ] M t 0 & 350 GeV dilepton + 2 jets arXiv:1202.3389 1 lepton: arXiv:1202.3076 M t 0 & 404 GeV [ATLAS L=2 fb -1 ] M b 0 & 400GeV b’->bZ arXiv:1204.1265
ATLAS limits on t’-> bW (with 1 fb -1 ) opposite-sign
ATLAS limits on b’-> tW (with 1 fb -1 ) same-sign
CMS limits on t’->bW (with 4.6 fb -1 ) larger data set + stronger cuts: stronger limits DILEPTON CHANNEL 1 LEPTON + 4 jets CHANNEL -1 -1 [pb] CMS preliminary CL : µ +jets (4.6fb ), e+jets (4.7fb ) S s =7 TeV σ observed 95% C.L. expected 1 expected ± σ 2 expected ± σ 1 t' THEORY -1 10 400 450 500 550 600 M [GeV] t' M t 0 & 552 GeV M t 0 & 560 GeV [CMS L=4.7 fb -1 ] [CMS L=4.7 fb -1 ] PAS-EXO-11-050 PAS-EXO-11-099
CMS limits on b’->tW (with 4.6 fb -1 ) DILEPTON CHANNEL -1 CMS 2011 Preliminary 4.6 fb s = 7 TeV ') [pb] observed limit 2 σ 1 expected limit 1 σ theory prediction b b' → (pp -1 10 σ 2 Limit at 95% CL: M > 600 GeV/c b' -2 10 450 500 550 600 650 2 M [GeV/c ] b' M b 0 & 600 GeV [CMS L=4.6 fb -1 ] PAS-EXO-11-036
Note: Presented limits assume 100% BR t' -> Wb and 100% BR b' -> Wt Presented limits on b’ apply to Presented limits on t’ apply to vector-like doublets, where B -> charge -4/3 quarks in a doublet, tW @ 100%, but not to singlets, but not to T singlets which also which also decay into bZ and bH. decay into tZ and tH [J-A Aguilar-Saavedra]
CMS limits on T->tZ at the Large Hadron Collider (LHC). The decay tZ ! b � bW þ W � ZZ , pp ! T � TX , with T � T ! tZ � PRL 107, 271802 (2011) Z -1 CMS 1.14 fb s = 7 TeV 10 observed limit 1 σ Theory expected limit 2 X) [pb] σ T 1 T → (pp σ 2 Limit at 95% C.L.: M > 475 GeV/c -1 T 10 250 300 350 400 450 500 550 2 M [GeV/c ] T
' ¡→ ¡ ATLAS limits on b’->bZ (with 2 fb -1 ) with to ¡ ¡Z(→ ee) + b-jet b'b ' ¡→ ¡ Zb + X 2 10 Zb) [pb] (BR = 100%) � × � to ¡ ¡Z(→ HATHOR (BR VLS) � × � HATHOR � expected limit (b’ 10 observed limit � expected limit 1 ± � × ’) expected limit 2 ± � b b’ � 1 (pp � ATLAS Preliminary Data 2011 ( s = 7 TeV ) -1 10 � -1 L dt = 2.0 fb -2 10 200 300 400 500 600 700 m [GeV] b’ M & 400GeV if BR=100% M & 358GeV if B is singlet mixing with 3rd generation only
Prospects for T-> tH & B-> bH with H->bb [Aguilar-Saavedra, 0907.3155] q ′ , T ¯ T → Ht W − ¯ b → HW + bW − ¯ H → b ¯ b b, WW → ℓν q ¯ T ¯ t → HW + b V W − ¯ H → b ¯ T → Ht V ¯ q ′ , V → q ¯ b b, WW → ℓν q ¯ q/ ν ¯ ν q ′ . B ¯ t → Hb W + W − ¯ H → b ¯ B → Hb W + ¯ 250 b b, WW → ℓν q ¯ 14 TeV, 30 fb − 1 T s 200 B s TB d 1 Events / 50 GeV l ± + 4 b final state TB d 2 150 XT d BY d 100 SM bkg 50 ± (4 b ) l 0 0 1000 2000 500 1500 2500 H T q ′ , T ¯ t → HW + b HW − ¯ H → b ¯ T → Ht H ¯ b b, WW → ℓν q ¯ l ± + 6 b final state
Prospects for T->tH [Azatov et al, Les Houches report, 1203.1488] + 1204.0455 l: thbW/thtZ/thth , h → γγ -1 Delphes Fast-Simulation 2012 s = 14 TeV L= 20.00 fb th, h → 2 γ Events / 5 GeV point A1 point A2 10 W + 2 + jets γ t t + 2 γ + jets ± W + t t + 2 γ + jets 8 6 4 2 0 100 150 200 250 300 M [GeV] 2 γ
Prospects for B->bH [Vignaroli 1204.0468] � el pp → ( ˜ q q B → ( h → bb ) b ) t + X . W � L pp ! l ± + n jets + 6 E T , n � 4 , At least 2 b -tag ˜ B λ t ¯ t s = 8 TeV 5 5 s 30 fb - 1 3 s 30 fb - 1 15 fb - 1 4 30 fb - 1 5 s 15 fb - 1 3 L = 100 fb - 1 s = 14 TeV l 5 2 5 s 4 3 s 1 3 0 200 300 400 500 600 700 800 900 l 2 m B é H GeV L 1 0 200 400 600 800 1000 1200 1400 1600 é H GeV L m B
Single production may start to play q q ′ an important role for M>~600 GeV W + L / W − L λ T 5 / 3 /B t g t λ = M X g 2 sin θ √ M W CMS limit on B->tW [L. Gauthier]
ATLAS search for singly produced vector-like coupled to light quarks arXiv:1112.5755 -like quarks, Q , coupling to light quarks, q . The s es, pp → Qq → Wqq ′ and pp → Qq → Zqq ′ 2011 by the ATLAS experiment at a center-of-m although new vector quarks expected to couple sizably only to third generation 14000 Data ATLAS q W +jets CC Channel q 12000 q" t t q Single Top ∫ -1 q" Ldt = 1.04 fb s = 7 TeV Multijet 10000 Z +jets Events/50 GeV W * /Z * Diboson Signal (600 GeV) × 100 8000 l l W * * Stat + Sys Uncertainty /Z l Q 6000 W/Z q' ν / l 4000 ν /l W/Z q' Q q 2000 q q negligible dominant q" 0 1.4 0 200 400 600 800 1000 1200 Data / BG 1.2 miss m(lepton, E ,leading jet) [GeV] 1 W q) [pb] 0.8 ∼ LO Cross Section, =1 κ 0.6 uD 2 10 0 200 400 600 800 1000 1200 Expected 95% CL upper limit miss s m(lepton, E ,leading jet) [GeV] ± 1 σ Uncertainty → BR(D ± 2 σ Uncertainty Observed Limit × 10 D q) → (pp σ 1 M > 900 GeV from CC ATLAS ∫ -1 Ldt = 1.04 fb s = 7 TeV M > 760 GeV from NC -1 10 200 300 400 500 600 700 800 900 1000 D mass [GeV]
Associated production (via a heavy gluon) [Bini, Contino , Parisse, Vignaroli, 1110.6058] q → G ∗ → ˜ t + ˜ B ¯ T ¯ q ¯ b [Barcelo, Carmona, Masip, Santiago, 1110.5914] - - ->Wbt ->Wtb ˜ T/B - same final state as tt G ∗ Mass reach depends on: M G ∗ /M ˜ -the ratio t / ¯ ¯ b g 3 tan θ 3 T ,B -on coupling between G* and the light fermions, 1 at M G ∗ = 1 . 5 , 2 . 0 , 3 . 0 TeV. -1 ⇤ 10 -on the top degree of compositeness d σ /dm tot [fb/GeV] -2 10 -> model-dependence -3 10 -4 10 -5 10 -6 10 0 1000 2000 3000 4000 m tot [GeV] m tot ≡ m ( W t b t W 6 t b 6 t ), [Contino et al ]
Associated production (via a heavy gluon) [Bini, Contino , Parisse, Vignaroli, 1110.6058] q → G ∗ → ˜ t + ˜ B ¯ T ¯ q ¯ b [Barcelo, Carmona, Masip, Santiago, 1110.5914] - - ->Wbt ->Wtb ˜ T/B - same final state as tt G ∗ Mass reach depends on: -the ratio M G ∗ /M ˜ t / ¯ ¯ b g 3 tan θ 3 T ,B -on coupling between G* and the light fermions, T LHC √ s = 7 GeV L = 10 fb − 1 L ⇤ 10 fb ⇥ 1 Discovery Reach s ⇤ 7 TeV 1.0 -on the top degree of compositeness -> model-dependence s R ⇤ 0.6 0.8 s R ⇤ 0.8 0.6 Much better reach s R ⇤ 1 tan ⇥ ⌅ 3 ⌅ reach: M T 5 / 3 ,B ∼ 1 . 5 TeV ([1 - 1.4 TeV]) 0.4 in comparison with the previous 0.2 single+pair production process M G ∗ if 0.0 ∼ 1 . 5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 M ˜ M G � � TeV ⇤ T ,B [Contino et al ]
L ⇤ 10 fb ⇥ 1 s ⇤ 7 TeV 1.0 5 σ discovery region for the signal s R ⇤ 0.6 0.8 G ∗ 3 al pp → G ∗ → ˜ s R ⇤ 0.8 Tt + Bb → Wtb 0.6 s R ⇤ 1 tan ⇥ ⌅ 3 ⌅ 0.4 0.2 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 M G � � TeV ⇤ M G ∗ /m ˜ T = 1 . 5 and Y ∗ = 3. L ⇤ 100 fb ⇥ 1 s ⇤ 14 TeV 1.0 5 σ discovery region for the signal s R ⇤ 0.6 0.8 G ∗ 3 al pp → G ∗ → ˜ Tt + Bb → Wtb s R ⇤ 0.8 almost 3 TeV 0.6 s R ⇤ 1 tan ⇥ ⌅ 3 ⌅ reach for top 0.4 partner! 0.2 0.0 0 1 2 3 4 5 6 M G � � TeV ⇤ [Bini, Contino , Parisse, Vignaroli, 1110.6058]
Other signature: Gluonic resonance pp → G ∗ → t ¯ t decay mainly into tops which have sizable coupling to the strong sector d # (pp t t b b l jj) " " ! 4 10 dm t t # of events / 200 GeV $ -1 Ldt = 100 fb 3 10 Signal + Background Possible 2 10 up to 4 TeV Agashe et al Background 1000 1500 2000 2500 3000 3500 m / GeV t t
Let us now imagine the top partners are too heavy to be accessible at the LHC (i.e >~1.5-2 TeV), and heavy gluons also too heavy (>~4 TeV ) Where shall we search for signs of top compositeness ?
F o r-top events at t LHC spectacular events with 12 partons in the final state
Four-top production in the Standard Model t t g q t t + + .... t t g q t t 88 % σ LHC ~ 7.5 fb @ 14 TeV σ LHC ~ 0.2 fb @ 7 TeV σ tevatron < 10^-4 fb ➾ 4 top final state sensitive to several classes of new TeV scale physics ~ - e.g. SUSY (gluino pair production with g → t t χ 0 ) top compositeness
well-motivated class of composite higgs models where new heavy resonances have a preference for the top quark Low energy effective theory approach 1 After integrating out heavy resonances, we are Λ 2 ( t R γ µ t R )( t R γ µ t R ) left with higher dimensional operators such as t g - t t leading to: X t t g t [Pomarol-Serra,’08] [Lillie-Shu-Tait,’08]
Four-top events from a top-philic and Dark Matter-philic Z’ Jackson, Servant, Shaughnessy,Tait, Taoso,’09 Z’ has suppressed couplings to light quarks - -> no observable resonances t t instead: t - t Z’ t ν (DM) or - - t ν (DM) Z � → νν tt + E T gg → tt + Z � Z � tttt → t t
A simple UV completion All SM fermions are uncharged under U(1)’ ~ Add T (vector-like) charged under U(1)’ with same gauge SM quantum numbers as t R to realize coupling of top quark to Z’ and h: yHQ 3 t R + µ ˜ T L ˜ T R + Y Φ ˜ T L t R higgs of U(1)’ the light mass eigen state identified with top ~ quark is an admixture of t and T
production cross section at the LHC Use top-philic Z’ as benchmark model Z’ 14 TeV ( g Z � t R = 3) pp tt tt → Z’ 10 TeV 1 Z’ 7 TeV SM 14 TeV Cross section [pb] SM 10 TeV -1 SM 7 TeV 10 -2 10 -3 10 -4 10 400 600 800 1000 1200 1400 1600 1800 2000 mass of Z’ [GeV]
- t t invariant mass distribution of M(t t ) 0.04 0.04 t t from the Z’ for M(Z’)=1.2TeV spectator t t for M(Z’)=1.2TeV 0.035 0.035 random combination for M(Z’)=1.2TeV 0.03 0.03 four-top SM ] ] -1 -1 [GeV [GeV effective model for = 500GeV � 0.025 0.025 maximum of M(t t )versus m(Z’) ) ) 0.02 0.02 t t dM(t dM(t 2 2 / ndf / ndf � � χ χ 0.2768 / 5 0.2768 / 5 1000 d d origine origine 306.5 306.5 74.97 74.97 ± ± 0.015 0.015 slope slope 0.3794 0.3794 0.1187 0.1187 ± ± 900 1 1 � � ) t maximum of M(t 800 0.01 0.01 700 0.005 0.005 600 500 0 0 400 400 600 600 800 1000 1200 1400 1600 1800 800 1000 1200 1400 1600 1800 400 M(t M(t t t ) [GeV] ) [GeV] 400 600 800 1000 1200 1400 1600 mass of Z’ [GeV] for random combination
0.08 M(Z’) = 1.2 TeV spectator t t 0.07 random combination pp->tt tt 0.06 pp->t t + jets normalized to 1 0.05 0.04 0.03 0.02 0.01 0 0 500 1000 1500 2000 M(t t ) [GeV]
top polarization In the models of interest, 4-top production yields an excess of right-handed tops 1 d cos θ = A d σ 2 (1 + cos θ ) + 1 − A (1 − cos θ ) 2 σ A: fraction of RH tops θ is the angle between the direction of the (highest p T ) lepton in the top rest frame and the direction of the top polarisation Polarisation of the top 0.8 0.8 Value of the polarisation versus M Z’ Z’ Model 1 0.7 0.7 SM 0.9 0.6 0.6 0.8 value of A 0.7 0.5 0.5 0.6 0.4 0.4 Z’ Model : A=0.78 0.5 0.4 0.3 0.3 SM : A=0.50 0.3 500 1000 1500 2000 2500 -1 -1 -0.8 -0.6 -0.4 -0.2 -0.8 -0.6 -0.4 -0.2 0 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 1 M cos( cos( ) ) θ θ Z’
background in same-sign dilepton channel @LHC final state: l ± l ± + n jets + E T ➙ (of which 4 are b-jets) σ .BR ( l ± l ± ) [fb] process σ [fb] signal m(Z’)=500GeV 838 35 signal m(Z’)=1TeV 61 2.6 signal + 1jet m(Z’)=500GeV 164 6.9 signal + 1jet m(Z’)=1TeV 21.5 0.9 tt ¯ 7.5 0.3 tt tW + W − + 0 , 1 , 2 jets t ¯ 450 13.7 tW ± + 0 , 1 , 2 , 3 jets t ¯ 595 18.4 W + W − W ± + 0 , 1 , 2 jets 603 18.7 W ± W ± + 0 , 1 , 2 , 3 jets 340 15.5 t ¯ 442 657 203 t t ¯ t + 1 jet 315 999 145 t ¯ t + 2 jets 182 868 84 t ¯ t + 3 jets 101 057 46 t ¯ t + 4 jets 36 236 17 - tt+jets with charge mis-ID is the main background (more precisely ttbar+ 2 hard jets)
# of jets M = 500 GeV M = 500 GeV Z’ Z’ 0.6 M = 1 TeV 0.25 M = 1 TeV Z’ Z’ background background 0.5 0.2 0.4 dN σ dN σ 0.15 d d 1 σ 1 σ 0.3 0.1 0.2 0.05 0.1 0 0 0 1 2 3 4 5 6 7 0 2 4 6 8 10 12 14 number of b-jets if P >30GeV total number of jets if P >30GeV T T
Distinguishing variable 0.22 t t M = 500 GeV 0.3 t t + 1 jet Z’ 0.2 M = 1 TeV t t + 2 jets Z’ 0.18 background t t + 3 jets 0.25 t t + 4 jets 0.16 0.14 0.2 dN σ 0.12 dN σ d d 1 σ 1 0.15 σ 0.1 0.08 0.1 0.06 0.04 0.05 0.02 0 0 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 3000 3500 H [GeV] H [GeV] T T
g n j ≥ 6 , p T > 30 GeV n b jets � 3 H T & 1 . 2 TeV H T & 700 GeV 4.5 45 -1 -1 L = 10fb , s =14TeV L = 10fb , s =14TeV background, b-efficiency=1 background, b-efficiency=1 4 40 signal, b-efficiency=1 signal, b-efficiency=1 3.5 background, b-efficiency=0.6 35 background, b-efficiency=0.6 signal, b-efficiency=0.6 Number of events Number of events 3 signal, b-efficiency=0.6 30 M = 1 TeV Z’ 2.5 25 M = 500 GeV Z’ 4-top production cross 2 20 section: ~ 60 fb 4-top production cross 1.5 section: ~ 800 fb 15 1 10 0.5 5 0 0 1000 2000 3000 4000 5000 6000 7000 8000 0 0 1000 2000 3000 4000 5000 6000 7000 8000 M [GeV] tot M [GeV] tot ∼ 2 σ ∼ 20 σ 5 σ excess luminosity 5 σ excess luminosity ~ 45 fb -1 ~ 1 fb -1
top reconstruction With cut nb jet ≥ 6 and nb bjet ≥ 3 : e after finding the 2 leptonic tops 4 10 4 10 -1 -1 L = 10fb , s =14TeV L = 10fb , s =14TeV signal M =500GeV signal M =500GeV Z’ background Z’ 3 10 background t t only 3 10 number of events number of events 2 10 t t only 10 2 10 1 10 -1 10 -2 10 1 0 1 2 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 number of distinct hadronic tops number of distinct tops 3 -1 L = 10fb , s =14TeV signal M =500GeV 2.5 Z’ background t t only number of events 2 1.5 1 0.5 0 0 500 1000 1500 2000 st M (1 hadronic top + leading lepton + b-jet) [GeV] inv
Back to top polarisation (requires top momentum reconstruction) Polarisation of the top polarisation of the top pola_top pola_top Entries Entries 6085 6085 Mean Mean 0.09888 0.09888 RMS RMS 0.556 0.556 0.8 0.8 0.8 Signal Z’ Model 0.7 0.7 Background 0.7 SM 0.6 0.6 0.6 0.5 0.5 0.5 0.4 0.4 0.4 Z’ Model : A=0.78 0.3 0.3 0.3 SM : A=0.50 0.2 -1 -0.8 -0.6 -0.4 -0.2 -1 -0.8 -0.6 -0.4 -0.2 0 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 cos( cos( ) ) θ θ cos( θ ) after top reconstruction at generator level in 1-lepton channel
four-top events from different models Z’ model M =500GeV Z’ 0.18 Z’ model M =1TeV Z’ Susy M =800GeV 0.16 Gluino effectif model = 500GeV Λ 0.14 exotic model M(T )=500GeV 5/3 background 0.12 dN σ 0.1 d 1 σ 0.08 0.06 0.04 0.02 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 H [GeV] T
four-top events from gluino pair production is easily distinguishable Z’ model M =500GeV 0.09 Z’ Z’ model M =1TeV Z’ Susy M =800GeV 0.08 Gluino effectif model = 500GeV Λ 0.07 exotic model M(T )=500GeV 5/3 background large E_Tmiss 0.06 dN σ 0.05 d 1 σ 0.04 0.03 0.02 0.01 0 0 100 200 300 400 500 600 700 800 900 1000 miss E [GeV] T
four-top events from gluino pair production Z’ model M =500GeV 0.09 Z’ Z’ model M =1TeV Z’ 0.16 signal Susy M =800GeV 0.08 Gluino effectif model = 500GeV pp->t t + jets Λ 0.14 0.07 exotic model M(T )=500GeV 5/3 background 0.12 0.06 dN σ 0.1 0.05 d dN σ 1 σ d 1 σ 0.04 0.08 0.03 0.06 0.02 0.04 0.01 0.02 0 0 0 100 200 300 400 500 600 700 800 900 1000 0 200 400 600 800 1000 1200 1400 1600 miss E [GeV] miss E {GeV} T T M=800 GeV
four-top events at 7 TeV σ .BR ( l ± l ± ) [fb] process σ [fb] signal m(Z’)=500GeV 41 1.7 tt ¯ 0.74 0.031 tt t ¯ 93 142 42.7 t t ¯ t + 1 jet 71 746 32.90 t ¯ t + 2 jets 37 190 17.06 t ¯ t + 3 jets 15 851 7.27 t ¯ t + 4 jets 4 215 1.93 and nb jets ≥ 6 , nb bjets ≥ 3 , H T > 500 GeV -1 L = 10fb , s =14TeV background, b-efficiency=1 3 signal, b-efficiency=1 background, b-efficiency=0.6 signal, b-efficiency=0.6 2.5 Number of events with 10 /fb: 2 S= 3 1.5 B= 0.3 1 0.5 0 500 1000 1500 2000 2500 3000 3500 4000 M [GeV] tot
T e top quark-Dark Ma t er connection if the WIMP hypothesis is correct: likely to be connected to the physics of EW symmetry breaking and Dark Matter may have enhanced couplings to massive states
A very simple effective theory Jackson, Servant, Shaughnessy,Tait, Taoso,’09 see also Belanger-Pukhov-Servant ’07 The WIMP is a Dirac fermion, ν , singlet under the SM, charged under a new spontaneously broken U(1)’. L = L SM − 1 t γ µ P R Z � µ t + χ µ ν F � µ ν + M 2 µ Z � µ + i ¯ µ ν F µ ν νγ µ D µ ν + g t R ¯ 4 F � Z � Z � 2 F � Y D µ L P L ) Z � µ ∂ µ − i ( g ν R P R + g ν ≡ The only SM particle charged under the Z’ is the top quark There is no SM state the WIMP can decay into: ν is stable. This model can be UV completed as an SO(10) RS model Agashe - Servant ’04 More generally, in models of partial fermion compositeness, natural to expect that only the top couples sizably to a new strongly interacting sector.
Seeing the light from Dark Matter Jackson, Servant, Shaughnessy,Tait, Taoso,’09 Dirac Dark Matter annihilation into γ H � � DM M 2 � ⇥ X E γ = M DM 1 − 4 M 2 DM Z, Z’ t h � DM ~ O(1) couplings
Hi gh s in Space! γ -ray lines from the Galactic Center Δ Ω℧ = 10 -5 sr Z’ H Z Z ' = g t Z ' = 3 L M n = 162 GeV H g n Z ' = g t Z ' = 1 L M n = 149 GeV H g n 10 - 4 g h - M h = 170 GeV g Z g Z ¢ - M Z ' = 220 GeV 10 - 5 Spectra for parameters leading to EGRET 10 - 6 E 2 d F ê dE @ GeV cm - 2 s - 1 D correct relic density and satisfying 10 - 7 FERMI direct detection constraints 10 - 8 HESS 10 - 9 10 - 10 10 - 11 10 - 12 NFW profile 10 - 13 adiabatically 10 - 14 contracted 10 - 15 10 - 16 1 10 10 2 Jackson, Servant, Shaughnessy,Tait, Taoso,’09 E g @ GeV D
and a very recent claim ... “A Tentative γ -Ray Line With E~ 130 GeV from Dark Matter Annihilation at the Fermi Large Area Telescope.” [Weniger 1204.2797] Z’ H Z Z ' = g t Z ' = 3 L M n = 162 GeV H g n Z ' = g t Z ' = 1 L M n = 149 GeV H g n 10 - 4 g h - M h = 125 GeV g Z g Z ¢ - M Z ' = 220 GeV 10 - 5 EGRET 10 - 6 E 2 d F ê dE @ GeV cm - 2 s - 1 D 10 - 7 FERMI 10 - 8 HESS 10 - 9 10 - 10 The additional line due to 10 - 11 Z’ disappears if the Z’ is 10 - 12 heavier than 300 GeV 10 - 13 10 - 14 10 - 15 10 - 16 1 10 10 2 E g @ GeV D Jackson, Servant, Shaughnessy,Tait, Taoso,’09
If gauge resonances are heavier -> Effective Field Theory (EFT) approach
EW precision data together with constraints from flavour physics make plausible if not likely that there exists a mass gap between the SM degrees of freedom and any new physics threshold. In this case, new physics can be integrated out and simply gives new (higher dimensional) interactions among the SM degrees of freedom effective 4-fermion interaction @ E<M 2 g g g SM 2 M 1 2 # 2 p M 2 g " # M !!!! L L SM 2 dim " 6 in the rest of the talk: no bias on what the TeV new physics should be
Low-energy effective field theory approach to BSM Buchmuller-Wyler ‘86 New interactions are assumed to respect all symmetries of the SM. & 60 : operators c c $ ! " L L i O SM i # 2 i dim ! ( 6 4 Good news: Only a few operators contribute to top quark physics
Our goal: - study new physics in tt final state in the most general model-independent approach
Dimension 6 operators for top physics Zhang & Willenbrock’10, Aguilar-Saavedra ‘10 , Degrande & al ’10 ... There are only 15 relevant operators: CP-even operator process O (3) φ q = i ( φ + τ I D µ φ )(¯ q γ µ τ I q ) top decay, single top q σ µ ν τ I t )˜ φ W I O tW = (¯ µ ν (with real coe ffi cient) top decay, single top O (1 , 3) q i γ µ τ I q j )(¯ q γ µ τ I q ) = (¯ single top qq q σ µ ν λ A t )˜ q, gg → t ¯ c hg φ G A O tG = (¯ µ ν (with real coe ffi cient) single top, q ¯ t h gg → t ¯ O G = f ABC G A ν µ G B ρ ν G Cµ t ρ gg → t ¯ O φ G = 1 2 ( φ + φ ) G A µ ν G Aµ ν t c V v q → t ¯ 7 four-quark operators q ¯ t c Aa c Av CP-odd operator process q σ µ ν τ I t )˜ φ W I O tW = (¯ µ ν (with imaginary coe ffi cient) top decay, single top q σ µ ν λ A t )˜ q, gg → t ¯ φ G A O tG = (¯ µ ν (with imaginary coe ffi cient) single top, q ¯ t G = g s f ABC ˜ gg → t ¯ G A ν µ G B ρ ν G Cµ O ˜ t ρ 2 ( φ + φ ) ˜ gg → t ¯ G = 1 G A µ ν G Aµ ν O φ ˜ t We will only consider those which affect top pair production at tree level by interference with the SM (QCD) amplitudes (we neglect weak corrections) ner
Dimension 6 operators for top physics Zhang & Willenbrock’10, Aguilar-Saavedra ‘10 , Degrande & al ‘10 There are only 15 relevant operators: CP-even top-philic operators: modifying top couplings and operator process not only-gluon O (3) φ q = i ( φ + τ I D µ φ )(¯ q γ µ τ I q ) top decay, single top couplings q σ µ ν τ I t )˜ φ W I O tW = (¯ µ ν (with real coe ffi cient) top decay, single top O (1 , 3) q i γ µ τ I q j )(¯ q γ µ τ I q ) = (¯ single top qq q σ µ ν λ A t )˜ q, gg → t ¯ c hg φ G A O tG = (¯ µ ν (with real coe ffi cient) single top, q ¯ t h gg → t ¯ O G = f ABC G A ν µ G B ρ ν G Cµ t ρ gg → t ¯ O φ G = 1 2 ( φ + φ ) G A µ ν G Aµ ν t c V v q → t ¯ 7 four-quark operators q ¯ t c Aa c Av CP-odd operator process q σ µ ν τ I t )˜ φ W I O tW = (¯ µ ν (with imaginary coe ffi cient) top decay, single top q σ µ ν λ A t )˜ q, gg → t ¯ φ G A O tG = (¯ µ ν (with imaginary coe ffi cient) single top, q ¯ t G = g s f ABC ˜ gg → t ¯ G A ν µ G B ρ ν G Cµ O ˜ t ρ 2 ( φ + φ ) ˜ gg → t ¯ G = 1 G A µ ν G Aµ ν O φ ˜ t We will only consider those which affect top pair production at tree level by interference with the SM (QCD) amplitudes (we neglect weak corrections) ner
Effective Field Theory for Top Quark Pair production Degrande & al ‘10 We calculate top pair production at order O(1/ Λ 2 ) � 1 � | M | 2 = | M SM | 2 + 2 � ( M SM M ∗ NP ) + O Λ 4 i.e. we assume new physics manifests itself at low energy only through operators interfering with the SM We focus on top-philic new physics (and therefore ignore interactions that would only affect the standard gluon vertex ) r O G = f ABC G A µ ν G B νρ G C µ ρ ction). Hence we consider t We are left with only two classes of dim-6 gauge invariant operators (when working at order O(1/ Λ 2 ))
Effective Field Theory for Top Quark Pair production We are left with only two classes of dim-6 gauge invariant operators (when working at order O(1/ Λ 2 )) � � − − g - t t ● op. with t, t and one or H ¯ σ µ ν T A t G A g �� � � = Q O hg µ ν two gluons g t t (chromomagnetic moment) � ¯ O (8) Q γ µ T A Q u γ µ T A u �� � = ¯ , Qu � ¯ �� ¯ O (8) Q γ µ T A Q d γ µ T A d LL ¯ ¯ � = , LL : Qd O (8) �� ¯ � q γ µ T A q t γ µ T A t � = ¯ , tq RR ¯ ¯ O (8) � ¯ t γ µ T A t u γ µ T A u �� � RR : = ¯ , tu however only 7 ● 4-fermion op. �� ¯ O (8) � ¯ t γ µ T A t d γ µ T A d � = , independent td operators � ¯ − q t O (8 , 1) LL ¯ ¯ Q γ µ T A Q q γ µ T A q �� � = ¯ , RR : Qq � ¯ O (8 , 3) Q γ µ T A σ I Q q γ µ T A σ I q �� � = ¯ , Qq − t q � ¯ : negligible (QCD is chirality diagonal) LR ¯ ¯ O (8) QT A t qT A d �� � LR : = ¯ , d
we assume new physics manifests itself top pair production in EFT at order O(1/ Λ 2 ) at low energy only through operators � 1 interfering with the SM � | M | 2 = | M SM | 2 + 2 � ( M SM M ∗ NP ) + O Λ 4 − − − q g t t t New g vertices: − t g t q t Chromomagnetic operator O hg = ( H ¯ Q ) σ µ ν T A t G A Four-fermion operators µ ν top pair production from gluon fusion: corrections from c hg only g t + + top pair production from q anti-q annihilation: corrections from g ¯ t SM SM SM both c hg and 4-fermion operators q t + + + + ¯ ¯ q t SM + +
gluon fusion (contribution from one operator only) The new physics and SM contributions for gluon fusion have a common factor � � 1 − 3 d σ t ) = d σ SM vm t c hg √ dt ( gg → t ¯ + 2 α s g s 6 τ 1 τ 2 8 s 2 Λ 2 dt � � → 9 s 2 dt t ) = πα 2 ρ 2 � 1 − 3 � d σ SM ( gg → t ¯ s ( ρ + τ 2 1 + τ 2 ) 2 − s 2 6 τ 1 τ 2 8 4 τ 1 τ 2 dt Common factor mainly τ 1 = m 2 τ 2 = m 2 ρ = 4 m 2 t − t t − u t , , s . responsible for the shape s s of the distributions t: Mandelstam variable t − t = s related to θ angle m 2 2 (1 − β cos θ ) . (between incoming parton and outgoing top quark) The operator O hg can hardly be distinguished from the SM in gluon fusion Distortions in the shape of the distributions can only - come from q q annihilation ➙ small effect at LHC
- θ q q annihilation (contribution from the 8 operators) Only two linear combinations of 4-fermion operators actually contribute to the differential cross section after averaging over the final state spins some vector combination some axial combination of of operators that is operators is asymmetric - - symmetric under q <-> q under q <-> q c � � � 1 + c V v ± + 1 �� � � d σ t ) = d σ SM V v s α s c Aa ± c � √ q → t ¯ Aa 2 dt ( q ¯ s ( τ 2 − τ 1 ) + 4 g s c hg 2 vm t 9 s 2 2 dt g 2 Λ 2 Λ 2 s even part in the odd part in the scattering angle scattering angle θ comes from comes from ¯ t γ µ T A t ¯ q γ µ T A q t γ µ γ 5 T A t ¯ ¯ q γ µ γ 5 T A q. This dependence vanishes after integration over t vector combination of the light quarks axial combination of the light quarks involving the RH and LH top quarks involving the RH and LH top quarks ← u+d → c V v = c Rv + c Lv c Aa = c Ra − c La ← u-d → Av = ( c tu − c td ) / 2 − ( c Qu − c Qd ) / 2 − c (8 , 3) V v = ( c tu − c td ) / 2 + ( c Qu − c Qd ) / 2 + c (8 , 3) c � c � Qq , Qq � c Ra = − c tq / 2 + ( c tu + c td ) / 4 � c Rv = c tq / 2 + ( c tu + c td ) / 4 with with c La = − c (8 , 1) c Lv = c (8 , 1) Qq / 2 + ( c Qu + c Qd ) / 4 . Qq / 2 + ( c Qu + c Qd ) / 4
total cross section Tevatron � 2 � 1 TeV σ ( pp → t ¯ t ) / pb = 6 . 15 +2 . 41 �� 0 . 87 +0 . 23 � � 1 . 44 +0 . 47 � � 0 . 31 +0 . 08 � � − 1 . 61 + c V v + c hg + c � . − 0 . 16 − 0 . 33 − 0 . 06 V v Λ LHC 7 TeV � 2 � 1 TeV σ ( pp → t ¯ t ) / pb=94 +22 4 . 5 +0 . 7 25 +7 0 . 48 +0 . 068 �� � � � � � c � � − 17 + c V v + c hg + . V v − 0 . 6 − 5 − 0 . 056 Λ � � LHC 14 TeV �� � � � � � � � 2 � 1 TeV σ ( pp → t ¯ t ) / pb = 538 +162 15 +2 144 +34 1 . 32 +0 . 12 �� � � � � � � c � − 115 + c V v + c hg + . − 1 − 25 − 0 . 12 V v Λ LO with CTEQ6L1 pdfs chromo In fits, we’ll use NLO+NLL SM u+d u-d results but in interference, magnetic (isospin 0) (isospin 1) we’ll keep LO SM amplitude moment
Tevatron constraints - - The pp -> tt total cross section at Tevatron depends on both c hg and c Vv and constrains thus a combination of these parameters. 4 Region allowed by the Tevatron at 2 σ 2 c Vv × (1 TeV / Λ ) 2 total cross (4-fermion section 0 operator) -2 O hg (chromomagnetic moment operator) -4 -4 -2 0 2 c hg × (1 TeV / Λ ) 2
σ Tevatron constraints - - The pp -> tt total cross section at Tevatron depends on both c hg and c Vv and constrains thus a combination of these parameters. 4 Region allowed by the Tevatron at 2 tt invariant mass shape 2 c Vv × (1 TeV / Λ ) 2 (4-fermion 0 operator) -2 O hg (chromomagnetic moment operator) -4 -4 -2 0 2 c hg × (1 TeV / Λ ) 2
σ The LHC - Tevatron complementarity ● The Tevatron cross section depends on both c hg and c Vv and constrains thus a combination of these parameters. - ● At the LHC, the pp -> tt total cross section mostly depends on c hg and can be directly used to constrain the allowed range for c hg Region allowed by the Tevatron at 2 4 total cross section � 20 � � 10 � 0 � 0 � 10 � 20 � tt invariant mass shape 2 c Vv � � 1TeV � � � 2 (4-fermion operator) 0 O hg � 2 (chromomagnetic moment operator) � 4 LHC total cross � 4 � 2 0 2 4 section limits (7 TeV: thin c hg � � 1TeV � � � 2 line, 14 TeV: thick line)
The LHC - Tevatron complementarity ● The Tevatron cross section depends on both c hg and c Vv and constrains thus a combination of these parameters. - ● At the LHC, the pp -> tt total cross section mostly depends on c hg and can be directly used to constrain the allowed range for c hg 4 total cross section 2 c Vv × (1 TeV / Λ ) 2 0 (4-fermion operator) -2 tt invariant mass shape O hg -4 (chromomagnetic -4 -2 0 2 4 moment operator) LHC total cross c hg × (1 TeV / Λ ) 2 section limits (assuming no deviations observed compared to SM prediction)
Constraining Non-resonant New Physics in top pair production [Degrande, Maltoni, Gérard, Grojean, Servant’10] 4 measured σ tt = σ SM Tevatron yellow region is excluded by Tevatron � 20 � (4-fermion � 20 � 2 operator) � 10 � c Vv � � 1TeV � � � 2 � 10 � 0 � 0 0 � green (blue) region 10 � O hg 10 � excluded by LHC at 7 TeV (chromomagnetic � 2 20 � (14 TeV) after a precision moment operator) 20 � LHC LHC of 10% is reached on σ tt 14TeV 7TeV � 4 � 4 � 2 0 2 4 c hg � � 1TeV � � � 2 A 10% uncertainty on the total cross section at the LHC already rules out a large region of parameter space
Minor effect on shapes of distributions at the LHC 0.20 0.20 SM SM O hg 0.15 c Vv � � 2, c hg � 1, 0.15 O Rv � O Lv �� 1 TeV d m tt d Σ d m tt d Σ 0.10 0.10 � Σ 1 Σ 1 0.05 0.05 0.00 0.00 300 400 500 600 700 800 900 1000 300 400 500 600 700 800 900 1000 m tt � GeV � m tt � GeV � 0.14 0.14 SM SM 0.12 O hg 0.12 c Vv � � 2, c hg � 1, 0.10 O Rv � O Lv 0.10 �� 1 TeV d p T d Σ d p T d Σ 0.08 0.08 � � Σ 0.06 1 Σ 0.06 1 0.04 0.04 0.02 0.02 0.00 0.00 0 100 200 300 400 500 0 100 200 300 400 500 p T � GeV � p T � GeV � 0.10 0.10 0.08 0.08 0.06 0.06 d Σ d Η d Σ d Η � Σ 1 Σ 0.04 1 SM 0.04 O hg SM 0.02 0.02 c Vv � � 2, c hg � 1, O Rv � O Lv �� 1 TeV 0.00 0.00 � 4 � 2 0 2 4 � 4 � 2 0 2 4 Η Η
Domain of validity of results 1) when O(1/ Λ 4 ) terms are subdominant At the Tevatron, our results apply to a region of parameter space bounded by ⇥ 2 � TeV | c i | � 7 Λ At the LHC, since the center of mass energy is larger, the reliable region ⇥ 2 ⇥ 2 shrinks to and � TeV � TeV | c hg | � 3 | c V v | � 2 Λ Λ 0 � 1 2) For which typical mass scale � 2 does the effective field theory �Σ � pb � � 3 treatment apply? � 4 W ' -> ~ 1.5 TeV � 5 Operators � 6 1000 1500 2000 2500 3000 3500 4000 correction to SM cross section at the LHC due to a W’ and comparison with EFT computation M W �
⇔ Effective Field Theory Approach to the Forward-Backward asymmetry A F B ≡ σ (cos θ t > 0) − σ (cos θ t < 0) σ (cos θ t > 0) + σ (cos θ t < 0) A SM F B = 0 . 05 ± 0 . 015 . A EXP F B = 0 . 15 ± 0 . 05(stat) ± 0 . 024(syst) , -> top quarks are preferentially emitted in the direction of the incoming quark � c � � 1 + c V v ± V v + 1 �� c Aa ± c � � � d σ t ) = d σ SM s α s √ q → t ¯ Aa 2 dt ( q ¯ s ( τ 2 − τ 1 ) + 4 g s c hg 2 vm t g 2 Λ 2 Λ 2 9 s 2 2 dt s � 2 � 1 TeV δ A dim 6 0 . 0342 +0 . 016 − 0 . 009 c Aa + 0 . 0128 +0 . 0064 � � − 0 . 0036 c � = × F B Aa Λ [Degrande, Maltoni, Gérard, C Aa and C ’ Aa are only constrained by the asymmetry and not Grojean, Servant’10] by the total cross section or the invariant mass distribution 0.00 � 0.02 Link to axigluon models: � 0.04 � 0.06 A FB : c Aa / Λ 2 = − 2 g q A g t A /m 2 Axigluon � 0.08 A � 0.10 Operators � 0.12 � 0.14 AFB prediction at the Tevatron due to an axigluon 1000 1500 2000 2500 3000 3500 4000 and comparison with the EFT computation M A
Most general expression at order O( Λ -2 ) � 2 �� 1 TeV 0 . 023 + 3 − 1 c Aa + 0 . 0081 + 6 � − 4 c � δ A ( m t ¯ t < 450 GeV ) = , Aa [Degrande et al’10,’11] Λ � 2 �� 1 TeV 0 . 087 + 10 − 9 c Aa + 0 . 032 + 4 � − 3 c � δ A ( m t ¯ t � 450 GeV ) = . Aa Λ ( 30 inclusive C' Aa ¥ TeV 2 ê L 2 20 M tt > 450 GeV 10 M tt < 450 GeV 0 - 10 (using CDF data) - 10 - 8 - 6 - 4 - 2 0 2 4 C Aa ¥ TeV 2 ê L 2 Including O( Λ -4 ) terms can alleviate the tension. See analysis by Aguilar-Saavedra & Perez-Victoria, 1103.2765 and Delaunay et al, 1103.2297 . consistent to ignore σ ( t ¯ t ) = σ SM + δσ int + δσ quad δσ int + δσ quad � 0 SM × Dim 8 terms if c - is large This requires A new ∼ − 2 A SM tt tail at LHC more details in JA Aguilar-Saavedra’s talk
Spin correlations 4. The three observables σ , d σ /dm t ¯ t and A F B are unable to disentangle between theories coupled mainly to right- or left-handed top quarks. However, spin correlations allow us to determine which chiralities of the top quark couple to new physics, and in the case of composite models, whether one or two chiralities of the top quark are composite. 1 d σ = 1 4 (1 + C cos θ + cos θ − + b + cos θ + + b − cos θ − ) d cos θ + d cos θ − σ + re θ + ( θ − ) is the angle between the charged lepton l + ( l − ) resulting from the top (antitop) − + � a ( � decay and some reference direction � b ). � 1 C = σ ( σ RL + σ LR − σ RR − σ LL ) , 1 b + = σ ( σ RL − σ LR + σ RR − σ LL ) , 1 b − = σ ( σ RL − σ LR − σ RR + σ LL ) . � 2 � 1 TeV C × σ / pb = 2 . 82 +1 . 06 0 . 37 +0 . 10 0 . 50 +0 . 13 �� � � � � − 0 . 72 + c hg + c V v , × − 0 . 08 − 0 . 10 Λ � 2 � 1 TeV allows to distinguish 0 . 45 +0 . 12 � � b × σ / pb = c Av × , − 0 . 09 Λ between LH and RH quarks proportional to e c Rv − c Lv
∆ C at the Tevatron b at the Tevatron 2 2 0.15 0.1 0.1 1 1 0.05 c Vv � � 1TeV � � � 2 c Av � � 1TeV � � � 2 0 0 0 0 � 0.05 � 1 � 1 � 0.1 � 0.1 � 2 � 2 � 3 � 3 � 0.2 � 0.15 � 0.3 � 4 � 4 � 4 � 2 0 2 4 � 4 � 2 0 2 4 c hg � � 1TeV � � � 2 c hg � � 1TeV � � � 2 ∆ C at the LHC b at the LHC 2 2 0.25 0.05 0.2 0.15 0.025 1 0.1 1 c Vv � � 1TeV � � � 2 c Av � � 1TeV � � � 2 0.05 0 0 0 0 � 0.05 � 1 � 1 � 0.025 � 2 � 2 � 2 � 1 0 1 2 � 2 � 1 0 1 2 c hg � � 1TeV � � � 2 c hg � � 1TeV � � � 2
Spin correlations SM at the Tevatron c Rv �� 2, c Lv � 0, c hg � 1 and �� 1 TeV at the Tevatron 0.015 0.015 0.01 0.01 0.005 0.005 0 0 1 � 1 1 � 1 0 0 0 0 cos � Θ � � cos � Θ � � cos � Θ � � cos � Θ � � � 1 1 � 1 1 c Rv �� 2, c Lv � 0, c hg � 1 and �� 1 TeV at the LHC SM at the LHC 0.015 0.015 0.01 0.01 0.005 0.005 0 0 1 � 1 1 � 1 0 0 0 0 cos � Θ � � cos � Θ � � cos � Θ � � cos � Θ � � � 1 1 � 1 1 Figure 11: Distribution of events at the Tevatron/LHC (top panel/bottom panel) for the SM (on the left) and for c Rv = − 2, c Lv = 0, c hg = 1 and Λ = 1 TeV (on the right) with µ F = µ R = mt .
Summary Non-resonant top philic new physics can be probed using measurements in top pair production at hadron colliders This model-independent analysis can be performed in terms of 8 operators. Observables depend on different combinations of only 4 parameters: σ ( gg → t ¯ t ) , d σ ( gg → t ¯ t ) /dt c hg ↔ q → t ¯ σ ( q ¯ t ) c hg , c V v ↔ q → t ¯ d σ ( q ¯ t ) /dm tt c hg , c V v ↔ A F B c Aa ↔ spin correlations c hg , c V v , c Av ↔
Note: Previous studies had looked at the phenomenology of part of the operators e.g: Zhang et al, Kumar et al, Cao et al, Jung et al, Hioki et al, 1008.3869 0901.3808 1003.3461 0912.1105 0910.3049 Ref. [24] Ref. [19] Ref. [51] Ref. [20] Ref. [21] 1 2 C 33 c hg 2 C tG g 1 g s uG φ g 2 g 2 1 C 1 u + C 2 u + C 1 d + C 2 − g 2 g 2 � � 4 ( κ u R + κ d R + κ u L + κ d s (*) L )(*) 2 ( C 1 + C 2 ) c V v s s 4 d g 2 g 2 1 C 1 u − C 2 u + C 1 d − C 2 � � 4 ( κ u R + κ d R + κ u L + κ d L )(*) 2 ( C 1 − C 2 ) c Aa s s 4 d g 2 1 � C 1 u + C 2 u − C 1 d − C 2 � 2 ( κ u R − κ d R + κ u L − κ d c � L )(*) s V v d 2 g 2 1 C 1 u − C 2 u − C 1 d + C 2 2 ( κ u R − κ d R + κ u L − κ d � � c � L )(*) s Aa d 2 Listed all operators although did not study the phenomenology
Effective Field Theory Approach to Same-sign top pair production Like-sign top pair production is a golden channel for early discovery at the LHC u t d, s, b uu->tt is absent in the SM at tree level SM contribution to uu->tt ~ |V ub | 4 W W u t d, s, b
Five Effective Operators for Same-Sign Top-Pair Production Degrande et al, 1104.1798 Aguilar-Saavedra, 1008.3562 � � + h . c . dim = 6 = 1 + c ( 1 ) LR O ( 1 ) LR + c ( 8 ) LR O ( 8 ) L qq → tt c RR O RR + c ( 1 ) LL O ( 1 ) LL + c ( 3 ) LL O ( 3 ) � LR LL Λ 2 � u t t R γ µ u R � ¯ � [¯ t R γ µ u R ] , O RR = � ¯ O ( 1 ) Q L γ µ q L � [ ¯ Q L γ µ q L ] , LL = u t � ¯ �� ¯ O ( 3 ) Q L γ µ σ a q L Q L γ µ σ a q L � LL = , � ¯ O ( 1 ) Q L γ µ q L � [¯ t R γ µ u R ] , LR = � ¯ O ( 8 ) Q L γ µ T A q L t R γ µ T A u R �� ¯ � LR = (1) (3) c LL = c LL + c LL ][¯ ] (1) (3) O LL and O LL contain which contributes to B d mixing n [¯ b L γ µ d L ][¯ b L γ µ d L ] , di-jet production. For and are therefore constrained: |c LL | (1 TeV/ Λ ) 2 < 2.1 10 -4
pp -> tt cross section σ grows like ~ s | c RR | 2 + | c LL | 2 � ( s − 2 m 2 d σ �� dt = 1 t ) Λ 4 3 π s t − t ) 2 + ( m 2 � ( m 2 t − u ) 2 �� � 2 + 2 � 2 � c ( 1 ) � c ( 8 ) � � � + LR LR 16 π s 2 9 � m 2 ~ m t2 �� � � 2 + 8 − 2 ∗ � � 2 � c ( 1 ) c ( 1 ) LR c ( 8 ) � c ( 8 ) t � � � � − 3 � . LR LR LR 9 24 π s A large part of the cross section at the LHC comes from the region where m tt ~ 1 TeV, where the 1/ Λ cannot be trusted for Λ ~ 1TeV - � 1 � ; O LL tt 7 TeV � 3 � O RR ; O LL 0.100 ( no such concern at the � 1 � O RL 0.050 Tevatron where m tt <~ 500 GeV) tt � 8 � O RL � 1 � � 2 O RL � 8 � O RL d m tt d Σ 0.010 � : int. 4 � F t t � 0.005 Σ 1 � : SM t t 0.001 5 � 10 � 4 1000 2000 3000 4000 5000 m tt � GeV �
σ pp->tt with an upper cut on M tt 1000 7 TeV 500 � 1 � ; O LL � 3 � O RR ; O LL � 1 � O RL 100 Σ � m tt �� � 3 �� fb � � 8 � O RL 50 � 1 � O RL � 8 � Int. O RL c i = 1 10 5 1 2 4 6 8 10 12 14 � � TeV � For Λ ~ 2 TeV and c~ 1, cross sections are of order O(pb) at 7 TeV
Spin correlations Very efficient to discriminate among the contributions from the various operators which have a well-defined chirality � structure and no interference with the SM is possible d σ 1 = 1 + b ( cos θ 1 + cos θ 2 ) � , � 1 + C cos θ 1 cos θ 2 σ d cos θ 1 d cos θ 2 4 � C = 1 σ ( σ ++ + σ −− − σ + − − σ − + ), b = 1 σ ( σ ++ − σ −− ), C = 1 b = 0 . 997 O RR O (1) LL , O (3) C = 1 b = − 0 . 997 LL O (1) LR , O (8) C ≈ 1 b ≈ 0 LR
Link to resonant models In general, no relation exists between same and opposite sign top pair (1) (8) production i.e. c RR , c LL , c LR , c LR cannot be related to c Vv, c Aa � �� �� � c � c � � c V v �� ¯ � c Aa �� ¯ q → t ¯ t = L q ¯ V v t γ µ T a t q γ µ T a q Aa t γ µ γ 5 T a t q γ µ γ 5 T a q �� ¯ � �� ¯ � ± + 2 ± , 2 4 4 � � � t-channel s-channel c (1) c (3) c (1) c (8) Spin SU(3) SU(2) Y c (1) c (3) c (1) c (8) c RR Spin SU(3) SU(2) Y c RR LL LL LR LR LL LL LR LR − ξ 2 − 1 1 1 1 0 − ξ ¯ 2 2 5 − 1 1 1 3 2 − ξ 2 − ξ 2 − 1 1 8 1 0 − ξ 6 6 2 6 24 8 5 − 1 − 1 1 6 2 1 − 1 0 1 2 6 ξ − ξ 6 3 2 2 1 − 2 1 0 8 2 9 ξ 6 ξ 4 1 0 6 1 2 3 4 − ξ 2 1 1 3 0 2 1 − 3 − 1 0 6 3 − 3 8 ξ 2 24 ξ 2 5 1 8 3 0 3 8 8 u t u t u t u t 8 , 1 Q = 0 8 , 1 Q = 0 Q = 4 Q = 0 3 ¯ u t u ¯ t 6 , ¯ 1 , 8 3 ¯ u t u t ¯ link to AFB in ttbar |c Vv |=|c Aa |, |c’ Vv |=|c’ Aa | Spin SU(2) Y c � c � c V v c Aa V v Aa − 1 − 1 1 1 0 − 1 − 1 2 2 | ξ | 2 + 1 | ξ | 2 + 1 1 − 1 � � − 1 1 � � 1 0 2 2 2 2 2 2 2 2
Connection with composite top models In models of composite tops, the operators contributing directly to top pair production are subdominant compared to four-top operators (from Naive Dimensional Analysis) 1 Λ 2 ( t R γ µ t R )( t R γ µ t R ) (The dominant operators are those which contain only fields 1 � g ρ � 4 π g 2 from the strong sector, scale as ) coupling of the ρ - 4-fermion op. contributing directly to tt production strong sector g − 1 scale at best as while O hg scales as g ρ ρ t g In this case, a much better probe of the dominant - t t dynamics is the direct production of four top quarks X t spectacular events with 12 partons in the final state t g typical LHC cross sections at 14 TeV: 10 - 100 fb t [Pomarol, Serra’08] [Lillie, Shu, Tait ’08]
tb ¯ t ¯ b and t ¯ tt ¯ t production at the LHC t γ µ t )(¯ O R =(¯ t γ µ t ) . if only t R is the color octet composite ( O (8) R = 1/3 O R � ¯ �� ¯ O (1) Q γ µ Q � L = Q γ µ Q if only t L is � ¯ �� ¯ O (8) composite Q γ µ T A Q Q γ µ T A Q � L = � ¯ O (1) (¯ � if both t L and t R = Qt tQ ) S are composite � ¯ O (8) QT A t �� ¯ tT A Q � = S σ Λ − 2 σ Λ − 4 σ Λ − 2 σ Λ − 4 σ cut σ cut b / σ 4 t σ 4 t σ t ¯ tb ¯ tb ¯ tb ¯ tb ¯ tb ¯ 4 t 4 t t ¯ t ¯ t ¯ t ¯ b b b b (fb) (fb) (fb) (pb) (pb) (pb) (pb) cross sections at 14 TeV SM 4 . 86 - - 7.2 - - 0.348 71.6 O (1) - 2.7 138 - - - - - assuming R O (1) - 2.9 48 - < 1.1 7.60 4.40 92 c i = 4 π S O (8) - 0.49 11 - < 0.2 1.28 0.76 71 S Λ = 1 TeV O (1) - 2.7 138 - < 0.5 3.61 2.12 15.6 L O (8) - 0.91 15 - 0.49 0.77 0.42 28.2 L
- - ttbb - b b pair produced with invariant mass larger than in the SM LHC s � 14TeV 1.000 0.500 SM � 1 � O S � 8 � O S 0.100 � 1 � O L 0.050 d m bb � 8 � d Σ O L � Σ 1 0.010 0.005 0.001 0 200 400 600 800 1000 m bb � GeV � only relevant if t L is composite (constrained scenario)
Testing O hg 1-loop generation of the chromo-magnetic operator L R R S ( T ) R L R Lv H ¯ H ¯ o δ c hg � � � � r Qt Qt L L R L L + R L R R R L R
- tt + jets g q t q ¯ ¯ t g g t g ¯ t 2 M t ¯ t √ s [Flament’11]
Constraints from higgs searches on top-philic new physics Degrande et al, to appear ................. ............ ............ � ¯ σ µ ν T a t R G a � H ¯ O hg = Q L H µ ν , O Hy = H † H � � Q L t R . H † H ∂ µ � H † H � � � O H = ∂ µ O HG = 1 2 H † HG a µ ν G µ ν a . 0.2 δ c HG ⇡ 0 . 03 < c hg � 0 . 006 c y . c HG � 1TeV � � � 2 � 80 � � 20 � 0.0 v � 20 � c y = c H + p < ( c Hy ) � 80 � 2 m t � 80 � � 0.2 � 20 � � 20 � � 80 � � 0.4 120 140 160 180 200 m H
- Using tth to constrain the chromomagnetic operator Degrande et al, to appear L L L R R L R L ( a ) ( b ) L L constraints from h production R L constraints from tt production L R constraints from tth production ( c ) ( d ) c y H TeV ê L L 2 = 0 c y H TeV ê L L 2 =- 5 c y H TeV ê L L 2 =+ 6 0.2 0.2 0.2 m = 125 GeV m H = 125 GeV m H = 125 GeV H 0.0 0.0 0.0 m = 160 GeV m H c HG H TeV ê L L 2 = 160 GeV c HG H TeV ê L L 2 c HG H TeV ê L L 2 m H = 160 GeV H - 0.2 - 0.2 - 0.2 - 0.4 - 0.4 - 0.4 - 0.6 - 0.6 - 0.6 - 2 - 1 0 1 2 - 2 - 1 0 1 2 - 2 - 1 0 1 2 c hg H TeV ê L L 2 c hg H TeV ê L L 2 c hg H TeV ê L L 2
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