HKIAS Jan Higgcision. Higgs Boson Pair Production

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1 HKIAS Jan Higgcision & Higgs Boson Pair Production KC, Jae-Sik Lee, Po-Yan Tseng:: , , , Jung Chang, KC, Jae-Sik Lee, Chih-Ting Lu Jung Chang, KC, Jae-Sik Lee, Chih-Ting Lu

2 HKIAS Jan Outlines 1. Present status of the Higgs boson Higgcision. 2. Single top plus Higgs production. 3. Higgs boson pair production.

3 HKIAS Jan Higgs Mechanism So far the Higgs mechanism for masses of gauge bosons and fermions, and interactions of Higgs with gauge bosons and fermions are consistent with a simple Higgs doublet. The scalar sector Lagrangian where and L Φ = D µ Φ 2 V (Φ) + L Y V (Φ) = µ 2 Φ 2 + λ Φ 4 D µ = µ + ieqa µ + i g 2 (τ + W + µ + τ W µ ) + i g cos θ w Φ develops a true vacuum at Φ = 1 2 ( 0 v + H(x) The mass and interactions of gauge bosons are fixed ) ( τ 3 2 sin2 θ w ( 1 L = (v 2 + 2vH + H 2 ) 4 g2 W + µ W µ + 1 ) 8 g2 z Zµ Z µ ) Z µ, where v = µ 2 /λ.

4 HKIAS Jan The mass and interactions of fermions are also fixed in L Y : L Y = y ev 2 (e L e R + e R e L ) y e 2 H (e L e R + e R e L ) So far, the gauge boson couplings and b, τ, t Yukawa couplings are consistent with data. We have no information about V (Φ) except that it gives a nontrivial VEV. In the SM, V (ϕ) = λ 4 v m2 H H2 + m2 H 2v H3 + λ 4 H4 This is the simplest structure. The self couplings are fixed. But for extended Higgs sector it is not the case.

5 HKIAS Jan Higgs Precision Higgcision KC, JS Lee, PY Tseng , , , , We have established formalism to compare the Higgs signal strengths versus the Higgs boson couplings, including CP-even and CP-odd ones, in model-independent, 2HDMs, MSSM. Formalism: Fermionic couplings L H ff = f=u,d,l gm f 2M W 3 i=1 H f ( ) g S H ff + igp H ff γ 5 f. For the SM g S H ff = 1 and gp = 0. H ff gauge boson couplings: L HV V = g M W ( g HW W W + µ W µ + g HZZ 1 2c 2 W Z µ Z µ ) H.

6 HKIAS Jan two photons: M γγh = αm 2 H 4π v { S γ (M H ) ( ϵ 1 ) ϵ 2 P γ (M H ) 2 } MH 2 ϵ 1 ϵ 2 k 1k 2, S γ (M H ) = 2 f=b,t,τ P γ (M H ) = 2 f=b,t,τ N C Q 2 f gs H ff F sf (τ f ) g HW W F 1 (τ W ) + S γ, N C Q 2 f gp H ff F pf (τ f ) + P γ, Numerically, taking M H = GeV, we find that S γ 8.35 g HW W g S H tt + ( i) gs H bb +( i) g S H ττ + ( i) gs H cc + Sγ P γ 2.78 g P H tt + ( i) gp H bb +( i) g P H ττ + ( i) gp H cc + P γ giving S γ SM = i and P γ SM = 0.

7 HKIAS Jan two gluons M ggh = α s M 2 H δab 4π v S g (M H ) = f=b,t { S g (M H ) ( ϵ 1 ) ϵ 2 P g (M H ) 2 } MH 2 ϵ 1 ϵ 2 k 1k 2, g S H ff F sf (τ f ) + S g, P g (M H ) = f=b,t g P H ff F pf (τ f ) + P g S g g S H tt + ( i) gs H bb + Sg P g g P H tt + ( i) gp H bb + P g

8 HKIAS Jan Signal Strengths: The signal strength can be written as the product of µ(p, D) µ(p) µ(d) where P = ggf, VBF, VH, tth denote the production mechanisms and D = γγ, ZZ, W W, b b, τ τ the decay channels. On the production side: µ(ggf) = Sg (M H ) 2 + P g (M H ) 2 S g SM (M H) 2 µ(vbf) = g 2 HW W,HZZ µ(vh) = g 2 HW W,HZZ ( ) µ(tth) = g S 2 ( H tt + g P H tt ) 2 On the decay side µ(d) = B(H D) = B(H D) B(H SM D) Γ(H D) Γ tot (H) + Γ tot

9 HKIAS Jan Experimentally observed signal strength is a sum over all production mechanisms: µ(q, D) = C QP µ(p, D) P=ggF,VBF,VH,ttH the decomposition coefficients C QP may depend on the relative Higgs production cross sections for a given Higgs-boson mass, experimental cuts, etc.

10 HKIAS Jan Fitting analysis Ratios of Yukawa and gauge couplings Cu S = ghūu S, Cd S = g S H dd, Cl S = g S H ll ; C v = g HV V ; Cu P = ghūu P, Cd P = g P H dd, Cl P = g P H ll. Extra loop contributions other than the Yukawa and gauge couplings: S g, S γ ; P g, P γ Γ tot

11 HKIAS Jan Combined µ = 1.00 ± fb (8 TeV) fb (7 TeV) CMS Preliminary m H = 125 GeV H bb tagged µ = 0.93 ± H ττ tagged µ = 0.91 ± 0.27 H γγ tagged µ = 1.13 ± 0.24 H WW tagged µ = 0.83 ± H ZZ tagged µ = 1.00 ± Best fit σ/σ SM

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13 HKIAS Jan The SM: χ 2 /dof = 16.76/29, p-value = Cases CPC 1 CPC 2 CPC 3 CPC 4 CPC 6 Vary Γ tot S γ, S γ, C S u, CS d, CS u, CS d, CS l, C v Parameters S g S g, Γ tot C S l, C v S γ, S g C S u C S d C S l C v S γ S g Γ tot χ 2 /dof 16.76/ / / / /23 p-value

14 HKIAS Jan CPC1: Vary only Γ tot This can be used to constrain some dark matter model, in which the Higgs boson decays invisibly. The χ 2 /dof = 16.72/27, p-value = The 95% allowed range of Γ tot = MeV The central value consistent with zero, so the 95% C.L. upper limit is Γ tot < 0.97 MeV For a M H = 125 GeV the standard width is about MeV. So nonstandard decay branching ratio has to be less than B(H nonstandard) < 19%

15 HKIAS Jan CPC4: Vary C S u, C S d, C S l, C v Only modified Yukawa and gauge couplings while no light particles running in the triangle loops. Approximate symmetry in the results: Cd S Cd S, Cl S Cl S Sign of Cu S is important. The W and the top contributions are in opposite sign.

16 HKIAS Jan C S u > 0 is preferred but C S u < 0 is still allowed at 95% CL; C v =

17 HKIAS Jan CPV3: Vary C S u, C P u, C v The χ 2 /dof = 16.03/26, p-value =

18 HKIAS Jan Remarks The HV V coupling is the most restrictive: C v = with 7 12% uncertainty. The CPC top-yukawa coupling Cu S is preferred to be positive in those fits with S γ and S g fixed at zero. Cu S < 0 is ruled out at 68.3% CL, but allowed at 95%CL. The nonstandard Higgs decay is limited to be below 19%. The Higgs signal strengths cannot rule out the pseudoscalar couplings, and only a combination of Cu S and Cu P is constrained in the form of an elliptical equation.

19 HKIAS Jan Zoom in for the Higgs boson Use EDMs to constrain the pseudoscalar Higgs couplings, such as Cu P and P γ. Search for non-standard decays of the Higgs boson, e.g. dark matter, Goldstone bosons, etc. Investigate the W W scattering. The associated production of Higgs with W, Z, t t, or a single top. Probe the Yukawa couplings. Use the single top + Higgs production to determine the sign and the size of top-yukawa coupling. Higgs boson pair production: (Chang, Cheung, Lee, Lu, )

20 HKIAS Jan Confronting Higgcision with Electric dipole moments KC, Jae-Sik Lee, Eibun Senaha, Po-Yan Tseng Higgs signal strength data cannot restrict the pseudoscalar coupling. But the EDM predicted is mostly proportional to Cu S Cu P. By limiting the predictions to be less than the current limits of Thallium, neutron, Mercury, and Thorium monoxide EDMs, one can constrain the Cu P.

21 HKIAS Jan KC, Lee, Senaha, Tseng

22 HKIAS Jan Associated Production of Higgs with a single top quark Jung Chang, KC, Jae-Sik Lee, Chih-Ting Lu, The associated Higgs production with a single top quark can indeed probe the size and the sign of the top Yukawa.

23 HKIAS Jan q qb thq q q q q q q t t t qg thq b ø ø ø gb thw q t q t q t q q th b øq ø øq ø øq ø

24 HKIAS Jan Variations of Cross section Vs C S,P t L hv V = gm W ( g hw W W + µ W µ + g hzz 1 L hff = f=t,b,c,τ gm f 2m W f 2c 2 W ) (g hff S + ighff P γ 5 f h Z µ Z µ ) h, We can understand the process qb q th by looking at the near-shell region of the W : W b ht At high energy, it is dominated by longitudinal W : g2 m t M = 2 2m 2 W [ (C v C S t ) + ic P t ] ū(p t )P L u(p b )

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26 HKIAS Jan C S t and CP t are roughly constrained by 1 = ( C t S ) 2 (0.86) 2 + ( C t P ) 2 (0.56) 2. We can parameterize by the angle tan ϕ CP t C t S allowed 2π/3 ϕ 2π/3 at 68% CL = 0.56 sin θ 0.86 cos θ = 0.66 tan θ, with the

27 HKIAS Jan Potential at the LHC Many decay channels: t blν, t bjj; h b b, γγ, τ + τ, ZZ 4l, W W l + νl ν Focus on pp thj production, and and t blν, t bjj, h b b, γγ, τ + τ h ZZ 4l We use MADGRAPH, Pythia, Delphes 3 for calculations, parton showering, and detector simulations. Detection efficiencies Mistag probability ϵ b ϵ τ ϵ l ϵ γ P c b P udsg b P j τ P j γ 0.7 (0.6) (0.08) (0.004)

28 HKIAS Jan h b b Mode with t blν Basic cuts: R ij > 0.4, p Tb > 25 GeV, η b < 2.5, p Tl > 25 GeV, η l < 2.5, p Tj > 25 GeV, η j < 4.7 Forward jet tag and top mass constraint

29 HKIAS Jan Backgrounds: t t t( bj 1 j 2 ) tb bj Apply: M b1 b 2 m h < 15 GeV, t tj t( bj 1 j 2 ) tb bj M b1 b 2 j > 300 GeV

30 HKIAS Jan The cut flow Cuts Signals (fb) Backgrounds (fb) Ct S = 1 Ct S = 0 Ct S = 1 t t t tj (1) Basic cuts and p Tb1,2 > 25 GeV, η b1,2 < (2) 2.5 < η j < (3) (M bl ) min < 200 GeV (4) M b1 b 2 m h < 15 GeV (5) M b1 b 2 j > 300 GeV S/ S + B for 300 fb

31 HKIAS Jan h γγ Mode with t blν Diphoton mode has much less QCD background, but the BR is Backgrounds: tjγγ, tjjγ, W bjγγ, W jjγγ. Further cuts: M γγ m h < 5 GeV, p T γ > 20 GeV, η γ < 2.5

32 HKIAS Jan h τ + τ Mode with t blν Tau has a BR Tau decays always contain neutrino, thus the momentum cannot be fully reconstructed. But it can estimated in fast moving tau and in hadronic decay. Currently, the scale factor is 1.37 in Delphes 3. The M ττ peak at m h is broad. We apply the cuts: 110 GeV < M ττ < 150 GeV, p T τ > 25 GeV, η τ < 2.5

33 HKIAS Jan h ZZ 4l Mode with t bj 1 j 2 Cuts on leptons: p Tl > 5 GeV, η l < 2.5, M 4l m h < 5 GeV

34 HKIAS Jan Required luminosity at LHC-14 to achieve S/ S + B > 1

35 HKIAS Jan Higgs boson Pair Production Jung Chang, KC, Jae-Sik Lee, Chih-Ting Lu

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37 HKIAS Jan Formalism Interactions: L = 1 3! ( 3M 2 H v ) λ 3H H 3 + m t v t ( g S t + iγ 5g P t ) t H m t v t ( ) g S 2 tt + iγ 5g P tt t H 2 In the SM, λ 3H = g S t = 1 and gp t The SM result: dˆσ(gg HH) dˆt = G2 F α2 s 512(2π) 3 = 0 and gs,p tt = 0. [ λ3hg S t D(ŝ)F S + (gs t )2 F SS 2 + (g S t )2 G SS 2] where D(ŝ) = 3M H 2 ŝ M H 2. +im H Γ H Extensions to CP-odd and contact terms: dˆσ(gg HH) G 2 { F = α2 ( ) s λ dˆt 512(2π) 3 3H g S t D(ŝ) + gs tt F S + (gs t )2 F SS + (g S t )2 G SS + (gp t )2 G P P 2 + ( ) λ 3H g P t D(ŝ) + gp tt F P + gs t gp t F SP 2 + g S t gp t GSP + (gp t )2 F P P } 2. 2

38 HKIAS Jan Production cross section normalized to the SM one is σ(gg HH) σ SM (gg HH) = λ 2 3H [ c 1 (s)(g S t )2 + d 1 (s)(g P t )2] + λ 3H g S t [c 2 (s)(g S t )2 + d 2 (s)(g P t )2] + [c 3 (s)(g S t )4 + d 3 (s)(g S t )2 (g P t )2 + d 4 (s)(g P t )4] ] +λ 3H [e 1 (s)g S t gs tt + f 1(s)g P t gp tt + g S tt [e 2 (s)(g S t )2 + f 2 (s)(g P t )2] + [e 3 (s)(g S tt )2 + f 3 (s)g S t gp t gp tt + f 4(s)(g P tt )2]

39 HKIAS Jan Behavior of cross sections The triangle diagram has the 1/s behavior of the Higgs propagator, more suppressed at high s. The contact term t t HH will saturate unitarity at high enough s: ŝ im(t t HH) gtt S m t Requiring a 0 < 1/2: ŝ 17.6 g S tt TeV. v 2

40 HKIAS Jan s c1 (s) c 2 (s) c 3 (s) d 1 (s) d 2 (s) d 3 (s) d 4 (s) (TeV) λ 2 3H (gs t )2 λ 3H (g S t )3 (g S t )4 λ 2 3H (gp t )2 λ 3H g S t (gp t )2 (g S t )2 (g P t )2 (g P t ) s e1 (s) e 2 (s) e 3 (s) f 1 (s) f 2 (s) f 3 (s) f 4 (s) (TeV) λ 3H g S t gs tt g S tt (gs t )2 (g S tt )2 λ 3H g P t gp tt g S tt (gp t )2 g S t gp t gp tt (g P tt )

41 HKIAS Jan CPC1: g S t and λ 3H Attempt to isolate the Higgs self coupling in the triangle diagram. The triangle diagram has the 1/s behavior, so more profound at low invariant mass region. Thus, the angular separation between the decay product is larger: HH (γγ)(b b) We can make use of simultaneous cross section measurements: (i) no cuts, (ii) σ( R γγ > 2), (iii) σ( R γγ < 2). Repeat using R b b, and both R γγ and R b b.

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45 HKIAS Jan Only with both R γγ and R b b can one really tell if δ 3H is significantly distinct from zero.

46 HKIAS Jan CPC2: g S t, λ 3H, g S tt The contact diagram contributes in the same way as the triangle diagram, except for the 1/s propagator. Also becomes important at high ŝ. We can make use of simultaneous cross section measurements: (i) Basic cuts, (ii) σ( R γγ, R b b > 2), (iii) σ( R γγ, R b b < 2).

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50 HKIAS Jan CPV1: g S t, g P t, and λ 3H, Unless stringent EDM constraints are imposed, the pseudoscalar coupling cannot be ruled out. Again, we can make use of simultaneous cross section measurements: (i) no cuts, (ii) σ( R γγ, R b b > 2), (iii) σ( R γγ, R b b < 2).

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53 HKIAS Jan s : 14 TeV c1 (s) c 2 (s) c 3 (s) d 1 (s) d 2 (s) d 3 (s) d 4 (s) Cuts λ 2 3H (gs t )2 λ 3H (g S t )3 (g S t )4 λ 2 3H (gp t )2 λ 3H g S t (gp t )2 (g S t )2 (g P t )2 (g P t )4 Basic Cuts R γγ > R γγ < R bb > R bb < R bb,γγ > R bb,γγ < s : 14TeV e1 (s) e 2 (s) e 3 (s) f 1 (s) f 2 (s) f 3 (s) f 4 (s) Cuts λ 3H g S t gs tt g S tt (gs t )2 (g S tt )2 λ 3H g P t gp tt g S tt (gp t )2 g S t gp t gp tt (g P tt )2 Basic Cuts R γγ > R γγ < R bb > R bb < R bb,γγ > R bb,γγ <

54 HKIAS Jan TeV pp Collider s : 100 TeV c1 (s) c 2 (s) c 3 (s) d 1 (s) d 2 (s) d 3 (s) d 4 (s) Cuts λ 2 3H (gs t )2 λ 3H (g S t )3 (g S t )4 λ 2 3H (gp t )2 λ 3H g S t (gp t )2 (g S t )2 (g P t )2 (g P t )4 Basic Cuts R γγ > R γγ < R bb > R bb < R bb,γγ > R bb,γγ < s : 100TeV e1 (s) e 2 (s) e 3 (s) f 1 (s) f 2 (s) f 3 (s) f 4 (s) Cuts λ 3H g S t gs tt g S tt (gs t )2 (g S tt )2 λ 3H g P t gp tt g S tt (gp t )2 g S t gp t gp tt (g P tt )2 Basic Cuts R γγ > R γγ < R bb > R bb < R bb,γγ > R bb,γγ <

55 HKIAS Jan Conclusions It is just the beginning of an exciting era. Global fitting of Higgs parameters Higgcision. If the W W scattering becomes strong, it means the light Higgs boson is only partially responsible for EWSB. The associated Higgs production with a single top quark has the potential to measure the size and sign of the top Yukawa. Non-standard decay of the Higgs boson is still exciting. Higgs boson pair production is the beginning of probing into the Higgs sector itself.

56 HKIAS Jan Backup Slides

57 HKIAS Jan Signal strengths of H γγ (full data set) Channel Signal strength µ M H (GeV) χ 2 SM (each) ATLAS (4.5fb 1 at 7TeV fb 1 at 8TeV): (Aug. 2014) µ ggh 1.32 ± µ V BF 0.8 ± µ W H 1.0 ± µ ZH µ tth CMS (5.1fb 1 at 7TeV fb 1 at 8TeV): (July 2014) µ ggh µ V BF µ V H µ tth Tevatron (10.0fb 1 at 1.96TeV): (Nov. 2012) Combined subtot: 6.30

58 HKIAS Jan Search for Goldstone Boson in Higgs Decay KC, Wai-Yee Keung, Tzu-Chiang Yuan Typically, the Higgs boson can decay into non-sm particles, which further decay into SM particles. Signatures include γγb b, τ + τ b b, ππ E T, µµ E T, etc.

59 HKIAS Jan Collider Signatures Nonstandard decay of the Higgs is less than about 20%. Take B(H σσ) 10% and B(σ ππ) 20% we can have gg H σσ (ππ) (αα) The cross section at the LHC-8 would be σ(gg H) B(H σσ) B(σ ππ) B(σ αα) 19 pb fb At the LHC-14, it would be 2.8 times as much. Difficulties: the angular separation between the two pions is very small: 1/60 2m σ /p Tσ It appears to be a microjet having two pions, and experimentally like a τ jet.

60 HKIAS Jan W W Scattering to test the degree of EWSB of the Discovered Higgs Jung Chang, KC, Yuan, ; KC, Chiang, Yuan, If the cancellation from the Higgs diagrams is not complete, due to, e.g., the g hww coupling is smaller than the SM value. The W + L W L scattering amplitude will grow with s. W + L W L Suppose the Higgs-W -W coupling is δ of the SM value, then amplitudes become im gauge = i im higgs = i im all = i g 2 4m 2 W g 2 4m 2 W g 2 4m 2 W u + O((E/m W ) 0 ) u δ + O((E/m W ) 0 ) u(1 δ) + O((E/m W ) 0 )

61 HKIAS Jan Cheung, Chiang, Yuan 10 4 W + L W- L W+ L W- L Cross Section (pb) δ= SM s WW (GeV)

62 HKIAS Jan Cross Sections (fb) for the LHC at 13 TeV Channels sin(β α) = SM (C v = 1) W + W l + νl ν W + W + l + νl + ν W W l νl ν W + Z l + νl + l W Z l νl + l ZZ l + l l + l

63 HKIAS Jan SM cross section value in fb for LHC-14 and LHC-100. SM cross section (fb) 14 TeV 100 TeV Cuts No Cuts 8.92e R(γ 1, γ 2 ) > e e-1 R(γ 1, γ 2 ) < e R(b 1, b 1 ) > e e-2 R(b 1, b 1 ) < e e-1 R(b 1, b 1 ) > 2 & R(γ 1, γ 2 ) > e e-2 R(b 1, b 1 ) < 2 & R(γ 1, γ 2 ) < e e-1

64 HKIAS Jan The cut flow Signals (fb) Backgrounds (fb) C S t = 1 CS t = 0 CS t = 1 tjττ t t t tw (1) Basic cuts and p T τ > 25 GeV, η τ < (2) 2.5 < η j < (3) M bl < 200 GeV (4) 110 < M ττ < 150 GeV S/ S + B for 300 fb

65 HKIAS Jan The cut flow Signals (10 3 fb) Backgrounds (10 3 fb) C S t = 1 CS t = 0 CS t = 1 tj4l ZZ3j ZZb2j (1) Basic cuts and p Tj1,2 > 25 GeV, η j1,2 < 2.5 but with p Tl > 5 GeV (2) 2.5 < η j < (3) M bj1 j 2 < 300 GeV (4) M 4l m h < 5 GeV S/ S + B for 300 fb

66 HKIAS Jan The cut flow Signals (10 3 fb) Backgrounds (10 3 fb) C S t = 1 CS t = 0 CS t = 1 tjγγ tjjγ W bjγγ W jjγγ (1) Basic cuts and p T γ > 20 GeV, η γ < (2) 2.5 < η j < (3) M bl < 200 GeV (4) M γγ m h < 5 GeV S/ S + B for 300 fb