Probing Higgs Self Coupling at the LHC and future Colliders. Jung Chang, KC, Jae Sik Lee, Chih-Ting Lu, ; in preparation.

Transcription

1 Probing Higgs Self Coupling at the LHC and future Colliders Jung Chang, KC, Jae Sik Lee, Chih-Ting Lu, ; in preparation.

2 Higgs Mechanism The most important pillar of the Standard Model. The SM fermions and bosons acquire a mass. The theory obeys the SM symmetries, but just the vacuum state takes on a specific configuration chosen by the Nature.

3 Current Status of Higgs Mechanism The scalar sector Lagrangian L Φ = D µ Φ 2 V (Φ) +L Y where V (Φ) =µ 2 Φ 2 + λ Φ 4 and ( D µ = µ + ieqa µ + i g ) (τ + W + µ + τ W µ )+i g τ 3 2 cos θ w 2 sin2 θ w Φ develops a true vacuum at Φ = 1 2 ( The mass and interactions of gauge bosons are fixed Z µ ( ) 0,wherev = µ 2 /λ. v + H(x) ( 1 L =(v 2 +2vH + H 2 ) 4 g2 W + µ W µ + 1 ) 8 g2 z Zµ Z µ

4 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.

5 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 The HV V coupling is the most restrictive: with 7 12% uncertainty. C v =

6 Higgs Sector Itself 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. Probing self interactions of the Higgs boson becomes an important avenue to understand the Higgs sector.

7 Channels for testing HHH coupling 10 4 HH production at pp colliders at NLO in QCD HH production at 14 TeV LHC at (N)LO in QCD σ NLO [fb] M H =125 GeV, MSTW2008 NLO pdf (68%cl) pp HH (EFT loop-improved) pp HHjj (VBF) pp tthh pp tjhh pp WHH pp ZHH MadGraph5_aMC@NLO σ (N)LO [fb] pp HH (EFT loop-improved) pp HHjj (VBF) pp tthh pp ZHH M H =125 GeV, MSTW2008 (N)LO pdf (68%cl) pp WHH pp tjhh MadGraph5_aMC@NLO s[tev] λ/λ SM. 2. From Ref.[5]: (HH) = 34.8 fb, (HHjj : VBF)=2.017 fb, (tthh) =0.981 ± HH)=0.565 fb, (ZHH)=0.356 fb. Frederix et al

8 SM Cross sections [4] p s [TeV] NLO gg!hh [fb] NLO qq 0!HHqq [fb] NNLO 0 q q 0!WHH [fb] NNLO q q!zhh [fb] LO q q/gg!t thh [fb]

9 FIG. 2. From Ref.[5]: (HH) = 34.8 fb, (HHjj : VBF)=2.017 fb, (tthh) =0.981 fb, (W ± HH)=0.565 fb, (ZHH)=0.356 fb. s ssm s H pp Æ HH + X L ê s SM s =14 TeV, M H =125 GeV gg Æ HH qq ' Æ HHqq ' q q ' Æ WHH q q Æ ZHH q q ê gg Æt t HH s ssm s H pp Æ HH + X L ê s SM s gg Æ HH =14 TeV, M H =125 GeV qq ' Æ HHqq ' q q ' Æ WHH q q Æ ZHH q q ê gg Æt t HH l l l SM l SM The ggf has the largest FIG. 3. Chih-Ting: cross section, of order 10 - O(100) fb. The VBF has the best sensitivity to Lambda_3H, but the cross section is one order smaller.

10 ggf Higgs pair production Jung Chang, KC, Jae Sik Lee, Chih-Ting Lu ; works in progress Interactions: L = 1 3! ( 3M 2 H v ) λ 3H H 3 + m t v t ( g S t + iγ 5g P t ) th m t v t ( ) g S 2 tt + iγ 5g P tt th 2 In the SM, λ 3H = g S t = 1 and gp t = 0 and gs,p tt = 0. The SM result: dˆσ(gg HH) dˆt = G2 F α2 s 512(2π) 3 [ λ 3Hg S t D(ŝ)F S +(gs t )2 F SS 2 + (g S t )2 G SS 2] where D(ŝ) = 3M 2 H ŝ M 2 H +im H Γ H. { ( )

11 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]

12 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 )

13 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

14 Decay channels: Decay channels HH! bb HH! bb HH! bbw W HH! bbbb Branching ratios 0.263% 7.29% 24.8% 33.3%!!! Due to background consideration and clean HH reconstruction we focus on HH! bb To some extent other modes should be considered to increase the significance of the already-small signal.

15 Kinematics of the signal diagram 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)

16 Chang, KC, Lee,Lu 2015 Signal-only study assuming 25% and 50% uncertainties in cross section measurements. Can probe ~ -1 < lambda_3h < 3.

17 Current status at LHC ATLAS-CONF Higgs-boson pair production in the bb bb final state Non-resonant cross section is constrained < 330 fb, 29x SM. *** Using final state with 3.2 fb^-1, the upper limit is 3.9 pb h reson b b

18 HL-LHC s = 14 TeV, L =3000 fb -1 Focus on H( b b)h( γγ) Analysis

19 Background Analysis ATL-PHYS-PUB Samples Generated/ σ BR Showered With (fb) H(b b)h(γγ)(λ/λ SM = 1) MadGraph5/Pythia H(b b)h(γγ)(λ/λ SM = 0) MadGraph5/Pythia H(b b)h(γγ)(λ/λ SM = 2) MadGraph5/Pythia H(b b)h(γγ)(λ/λ SM = 10) MadGraph5/Pythia b bγγ MadGraph5/Pythia8 338 c cγγ MadGraph5/Pythia b bγ j MadGraph5/Pythia b bjj MadGraph5/Pythia jjγγ MadGraph5/Pythia t t( 1 lepton) MC@NLO/Herwig t tγ MadGraph5/Pythia t th(γγ) POWHEG/Pythia Z(b b)h(γγ) Pythia b bh(γγ) MadGraph5/Pythia8 1.32

20 Events/arb. unit 0.18 ATLAS Simulation Preliminary H(bb)H(γ γ ) bbγ γ ttγ s= 14 TeV tth(γ γ ) Z(bb)H(γ γ ) bbh(γ γ ) m bbγ γ [GeV] Events/arb. unit ATLAS ATLAS Simulation Preliminary s= s= TeV TeV H(bb)H(γ H(bb)H(γ γ ) γ ) tth(γ tth(γ γ ) γ ) bbγ γ Z(bb)H(γγ ) bbγ tt γ Z(bb)H(γ bbh(γγ ) γ ) ttγ bbh(γγ ) γ γ R Events/arb. unit 0.6 ATLAS Simulation Preliminary Small m(hh) for triangle s= diagram 14 TeV doesn t work because backgrounds s= 14 TeV H(bb)H(γγ ) bbγ γ ttγ tth(γγ ) Z(bb)H(γγ ) bbh(γγ ) Events/arb. unit also focus there. Yet, small Delta(R) works ATLAS Simulation Preliminary 0.2 H(bb)H(γγ ) tth(γγ ) 0.18 bbγ γ Z(bb)H(γγ ) ttγ bbh(γγ )

21 Simulation results for HL-LHC Expected yields (3000 fb 1 ) Total Samples H(b b)h(γγ)(λ/λ SM = 1) 8.4±0.1 H(b b)h(γγ)(λ/λ SM = 0) 13.7±0.2 H(b b)h(γγ)(λ/λ SM = 2) 4.6±0.1 H(b b)h(γγ)(λ/λ SM = 10) 36.2±0.8 b bγγ 9.7±1.5 c cγγ 7.0±1.2 b bγ j 8.4±0.4 b bjj 1.3±0.2 jjγγ 7.4±1.8 t t( 1 lepton) 0.2±0.1 t tγ 3.2±2.2 t th(γγ) 6.1±0.5 Z(b b)h(γγ) 2.7±0.1 b bh(γγ) 1.2±0.1 Total Background 47.1±3.5 S/ B(λ/λ SM = 1) 1.2 background and of the signal contribution for λ/λ SM = events. N is the parameter of interest of the model. This limit (dashed line) on the total number of HH e events summed with the λ/λ SM = 1 signal contribution) shown in Figure 8. It is overlaid on the parametrization coupling) HH events as a function of the λ/λ SM ratio af Projected limit on the total HH yield (events) ATL-PHYS-PUB in the previous sections (red line). The minimum of th the dependence of the cross-section including the initial m effects seen on Projected Figure 2 due Sensitivity to the effects at HL-LHC of the analysis The projections of the analysis described in the note models with λ/λ SM 1.3 and λ/λ SM 8.7. ATLAS Simulation Preliminary -1 s = 14 TeV: 3000 fb Exp. 95% CLs ± 1 σ ± 2 σ λ 10 / λ SM

22 100 TeV pp Collider: US/Europe vs China Date

23 Kinematic distributions are similar to 14 TeV

24 3 2 25% & 50% for s ê s SM = 1 Detector Level -- ATLAS, LHC-100 Basic Cuts DR gg,bb > 2 DR gg,bb < 2 gs t 1 0 l 3 H Chang, KC, Lee, Lu TeV: Signal-only study assuming 25% and 50% uncertainties in cross section measurements. Can probe ~ -1 < lambda_3h < 3.

25 Vector Boson Fusion at 100 TeV Bishara, Contino, Rojo q q V V h h q q V V 100 h h q q LHC h V V h s!14 TeV d /d j max [arbit. u.] TeV 100 TeV j max c 3 = / sm TLAS searc C 2V = g VVhh "#pp$hh%&"#pp$hh%sm c 2V c 2V 1 c "1.0 "

26 Outlook Probing the self-interactions of the Higgs boson is necessary for understanding the EWSB sector. The sensitivity in VBF is better than ggf, but event rate is low. Need to combine with other channels, e.g. tthh, WHH, ZHH, etc. HL-LHC, 100 TeV, ILC analyses are all needed.