HIGGS RATES AND NEW QUARKS Elisabetta Furlan Brookhaven National - PowerPoint PPT Presentation

HIGGS RATES AND NEW QUARKS Elisabetta Furlan Brookhaven National Laboratory In collaboration with S. Dawson and I. Lewis Galileo Galilei Institute, June 6 2013

MOTIVATION LHC experiments: “habemus Higgs!” “a light fundamental scalar is not natural”: the hierarchy problem many extensions of the Standard Model introduce new particles that can alter the LHC phenomenology (supersymmetry, extra dimensions, little/composite Higgs models,...) direct W − production Q ¯ t t ¯ x loop x ¯ t t effects W +

MOTIVATION constraints from W − ¯ t t ➡ direct searches ¯ x x t ¯ t W + ➡ effects on loop mediated processes (S, T, U parameters, ) Z → b ¯ b e + ¯ q e − q ➡ measured Higgs rates! ( (ATLAS) ( 1 . 4 ± 0 . 3 1 . 7 ± 0 . 3 σ σ H → γγ σ SM = = 0 . 8 ± 0 . 3 σ SM 0 . 88 ± 0 . 21 (CMS) H → γγ 1 . 1 ± 0 . 3

MOTIVATION the new particles typically ✦ couple to the Higgs boson ✦ mix with the Standard Model top quark, modifying its coupling to the Higgs boson ➡ can significantly affect Higgs production and decays SM4 σ CH gg → h σ SM q → ht ¯ gg, q ¯ t qq → hqq q ¯ q → hW, hZ SM4, composite ξ = v 2 /f 2 Higgs

MOTIVATION the new particles typically ✦ couple to the Higgs boson ✦ mix with the Standard Model top quark, modifying its coupling to the Higgs boson ➡ can significantly affect Higgs production and decays ➡ but.. do they have to ? ➡ if they do, can we use these effects to learn something about their properties?

MOTIVATION idea: A. Pierce, J. Thaler, L.-T. Wang, JHEP 0705:070, 2007 ✦ up to dimension six, there are only two operators that describe the effective gluon-Higgs interaction ‣ dimension 6 ‣ renormalizable (SM) ‣ not present in the SM ✦ they are related to different mass generation mechanisms

MOTIVATION ✦ they contribute differently to Higgs single and pair production v + H 2 ✓ H ◆ O 1 ∝ G a µ ν G a,µ ν 2 v 2 v − H 2 ✓ H ◆ O 2 ∝ G a µ ν G a,µ ν 2 v 2 ➡ combine this two channels to gain insights on the nature of the mass of the new heavy quarks A. Pierce, J. Thaler, L.-T. Wang, JHEP 0705:070, 2007

OUTLINE single and pair Higgs production ✦ approximate leading order results vector singlet chiral mirror families ✦ the model ✦ the model ✦ experimental bounds ✦ experimental bounds ✦ Higgs phenomenology ✦ Higgs phenomenology gluon-Higgs effective operators

SINGLE HIGGS PRODUCTION main mechanism: gluon fusion for heavy ( ) quarks, the leading order 2 m q >m H amplitude depends on the mass and the Yukawa m q coupling as y qq m 2  2 � y qq 3 + 7 X H A gg → H ∝ + . . . 4 m 2 m q 45 q q ➡ neglecting finite-mass effects, In the SM ◆ A gg → H y qq ✓ X = y tt = m t A SM m q gg → H q

DOUBLE HIGGS PRODUCTION Standard Model like contributions NEW y ij y ii f i q i q i g H g H g H g g H H q i t H q j q i q i q i q i f i t f j H q i H H t g g g g g H H q i q i f i at leading order, the amplitude is known with the full mass dependance Glover, van der Bij, NPB309:282, 1988 in the infinite quark mass approximation, y 2 gg → HH ∝ y 2 gg → HH ∝ − 3 m 2 y ii A box,ii ij ii A box,ij A tri H gg → HH ∝ m 2 s − m 2 m i m i m j i H ➡ neglecting finite-mass effects, A box y 2 gg → HH ij X = A box,SM m i m j gg → HH i,j

HIGGS PRODUCTION these approximate results are useful to understand the source of the (potential) deviations from the SM in our analysis we will use the “exact” cross section ✦ for single Higgs production, through NNLO Graudenz, Spira, Zerwas, Harlander, Kilgore, PRL88, 201801 (2002) PRL70, 1372 (1993) Anastasiou, Melnikov, NPB646, 220 (2002) Spira, Djouadi, Graudenz, Zerwas, Ravindran, Smith, van Neerven, NPB665, 325 (2003) NPB453, 17 (1995) EF , JHEP 1110 (2011) 115 ihixs Anastasiou, Bülher, Herzog, Lazopoulos

HIGGS PRODUCTION these approximate results are useful to understand the source of the (potential) deviations from the SM in our analysis we will use the “exact” cross section ✦ for single Higgs production, through NNLO ✦ for double Higgs production, at LO with full mass dependence Glover, van der Bij, NPB309:282, 1988

VECTOR SINGLET introduced for example in little Higgs and composite Higgs models notation ✓ T 1 ◆ , T 1 R , B 1 L SM-like chiral fermions ψ L = B 1 R L vector singlet with Y=1/ 6 T 2 L , T 2 R mass eigenstates of mass t, T, b = B 1 m t , M T , m b the fermion mass terms are 2 2 R + λ 2 ψ L ˜ R + λ 3 ψ L ˜ − L S M = λ 1 ψ L H B 1 H T 1 H T 2 L T 1 L T 2 R + λ 4 T R + λ 5 T R + h . c . } − L SM M

VECTOR SINGLET the fermion mass terms are 2 2 R + λ 2 ψ L ˜ R + λ 3 ψ L ˜ − L S M = λ 1 ψ L H B 1 H T 1 H T 2 L T 1 L T 2 R + λ 4 T R + λ 5 T R + h . c . the charge 2/3 mass eigenstates are an t, T admixture of and , T 1 T 2 ✓ t i ◆ ✓ c i ◆ ✓ T 1 ◆ − s i i = cos( θ i ) , c i = T 2 T i s i c i = sin( θ i ) i s i ( i = L, R ) 2 L T 1 the term can be rotated away by a T R redefinition of the right handed fields  4 independent parameters ( m b , m t , M T , θ L )

CONSTRAINTS Contribution to the Peskin-Takeuchi S, T, U parameters M T = 1 TeV 1 0.1 D T D U 0.01 D S 0.001 } D T app m b → 0 , 10 - 4 D U app M T >> m t 10 - 5 D S app 10 - 6 0.0 0.1 0.2 0.3 0.4 s L ∆ T app = T SM s 2 rs 2 L + 2 c 2 L log r − 1 − c 2 r = ( M T /m t ) 2 � � L L ∆ S app = − N c ∆ U app = N c 18 π s 2 1 − 3 c 2 + 5 c 2 18 π s 2 3 s 2 L log r + 5 c 2 ⇥ � � ⇤ � � log r L L L L L

CONSTRAINTS Contribution to the Peskin-Takeuchi S, T, U parameters 0.1 0.01 D T , s L = 0.1 D U , s L = 0.1 0.001 D S , s L = 0.1 D T , s L = 0.01 10 - 4 } D U , s L = 0.01 10 - 5 D S , s L = 0.01 600 800 1000 1200 1400 1600 M T ∆ T app = T SM s 2 rs 2 L + 2 c 2 L log r − 1 − c 2 r = ( M T /m t ) 2 � � L L ∆ S app = − N c ∆ U app = N c 18 π s 2 1 − 3 c 2 + 5 c 2 18 π s 2 3 s 2 L log r + 5 c 2 ⇥ � � ⇤ � � log r L L L L L

DECOUPLING 2 2 R + λ 2 ψ L ˜ R + λ 3 ψ L ˜ − L S M = λ 1 ψ L H B 1 H T 1 H T 2 L T 1 L T 2 R + λ 4 T R + λ 5 T R + h . c . decoupling occurs for λ 4 , λ 5 � λ 2 v 2 , λ 3 v and λ 5 � λ 4 p p 2 √ in this limit M T ∼ λ 5 , m t ∼ λ 2 v/ 2 , s L ∼ λ 3 v/M T ➡ if and is kept fixed, M T → ∞ λ 3 → ∞ s L and the singlet does not decouple! ➡ in the decoupling limit ( constant) λ 3 ∼ T SM s 2 rs 2 � � L − 2 + 2 log r → 0 , ∆ T L r = ( M T /m t ) 2 ∆ S ∼ − N c 18 π s 2 L (5 − 2 log r ) → 0 .

CONSTRAINTS In the singlet model, the strongest constraints come from the oblique parameters

HIGGS PRODUCTION mixing with the singlet reduces the coupling of the top-like quark to the Higgs and yields a coupling to the Higgs also for the heavy top partner m t M T Y tt = c 2 , Y T T = s 2 L L v v m t M T Y T t = s L c L , Y tT = s L c L v v the Higgs production cross section is suppressed with respect to the Standard Model σ ( s ) m 2 1 − m 2 ✓ ◆ ≈ 1 − 7 decoupling gg → H s 2 t H 1 L 4 m 2 M 2 σ SM 15 t T gg → H

HIGGS PRODUCTION potentially large effect, but electroweak observables require a small mixing angle  at most some few % effect

HIGGS PRODUCTION potentially large effect, but electroweak observables require a small mixing angle  at most some few % effect pp → HH, √ S=8 TeV m H =125 GeV, M T =1 TeV, c L =0.987 0.02 SM, Exact SM, LET Singlet Top Partner, Exact Singlet Top Partner, LET 0.015 d σ /dM HH (fb/GeV) 0.01 0.005 0 300 400 500 600 700 800 900 1000 M HH (GeV)

HIGGS DECAYS γ the top partner also affects H loop mediated decays γ only small mixing allowed  below-% effects

MIRROR QUARKS four additional heavy quarks, (charge 2/3), T 1 , 2 (charge -1/3), in the SU(2) L representations B 1 , 2 ✓ T 1 ◆ ✓ T 2 ◆ ψ 1 , T 1 R , B 1 ψ 2 , T 2 L , B 2 L R L = R ; R = B 1 B 2 L . L R } } as Standard Model families left  right assume no mixing with the Standard Model t, b quarks, 1 1 2 2 − L M = λ A ψ L ˜ R ˜ L Φ B 1 Φ T 1 R Φ B 2 Φ T 2 R + λ B ψ R + λ C ψ L + λ D ψ L 1 1 1 L ψ 2 R T 2 R B 2 R + λ F T L + λ G B + λ E ψ L + h . c .

MIRROR QUARKS mass terms: 1 1 ! ! λ B v λ A v T λ E λ E B L L √ √ 2 2 M U = M D = λ D v 2 λ C v 2 λ F λ G T B L L √ √ 2 2 B 1 T 1 T 2 B 2 R R R R the mass eigenstates are obtained T 1 , T 2 ; B 1 , B 2 though unitary rotations  need four rotation angles for simplicity assume M T 1 = M B 1 = M , M T 2 = M B 2 = M (1 + δ ) ➡ six parameters, ± ( θ q L = θ q L ± θ q M, δ , θ t ± , θ b R ) . ➡ one condition, M U, 12 = M D, 12

HIGGS PRODUCTION are large deviations from the Standard Model double Higgs rate compatible with ✦ electroweak bounds ✦ the measured single Higgs production cross section ? e.g., can we have a 15% or larger enhancement in the double Higgs amplitude (from the box contributions) while keeping single Higgs within 10% from the Standard Model?