Exploring Extended Scalar Sectors with Di Higgs Signals: A Higgs EFT Perspective

Transcription

1 Exploring Extended Scalar Sectors with Di Higgs Signals: A Higgs EFT Perspective Tyler Corbett Melbourne Node arxiv: , with Aniket Joglekar (Chicago), Hao-Lin Li (Amherst), Jiang-Hao Yu (Amherst). Tyler Corbett (Melbourne) June 20, 2017

2 Motivation Single Higgs data constrains operators relevant to single Higgs processes No measurement of tri Higgs coupling independent measurement of λ or wilson coefficient of Q H = (H H) 3 are not possible We consider simplest UV completions which shift the tri Higgs coupling and work from an EFT point of view See e.g. T.C. OJP Éboli, J. Gonzalez-Fraile, M.C. Gonzalez-Garcia arxiv: , or A. Butter, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, T Plehn, M Rauch arxiv: Tyler Corbett (Melbourne) June 20, / 14

3 Motivation Single Higgs data constrains operators relevant to single Higgs processes No measurement of tri Higgs coupling independent measurement of λ or wilson coefficient of Q H = (H H) 3 are not possible We consider simplest UV completions which shift the tri Higgs coupling and work from an EFT point of view See e.g. T.C. OJP Éboli, J. Gonzalez-Fraile, M.C. Gonzalez-Garcia arxiv: , or A. Butter, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, T Plehn, M Rauch arxiv: Tyler Corbett (Melbourne) June 20, / 14

4 Motivation Single Higgs data constrains operators relevant to single Higgs processes No measurement of tri Higgs coupling independent measurement of λ or wilson coefficient of Q H = (H H) 3 are not possible We consider simplest UV completions which shift the tri Higgs coupling and work from an EFT point of view See e.g. T.C. OJP Éboli, J. Gonzalez-Fraile, M.C. Gonzalez-Garcia arxiv: , or A. Butter, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, T Plehn, M Rauch arxiv: Tyler Corbett (Melbourne) June 20, / 14

5 Workflow Topologies generating H 6 operator (tree level) UV models generating H 6 operator (tree level) UV and IR Lagrangians Single Higgs Constraints Di Higgs predictions Tyler Corbett (Melbourne) June 20, / 14

6 Q H = (H H) 3 topologies Note: Lorentz Invariance will prevent tree level Q H from fermions or vectors: µ µ g 6 16π 2 M 2 g 6 16π 2 M 2 g4 M 4 p 2 (H H) 2 2 (H H) Tyler Corbett (Melbourne) June 20, / 14

7 Q H = (H H) 3 at Tree Level, cont. With scalars tree level Q H is possible: Then the question is: (λ ) 2 M 2 µ2 λ M 4 (µ)3 µ M 6 What extended scalar sectors can generate these topologies? Must be an SU(3) c singlet, the Higgs is uncolored. Must be in rep. of SU(2) L w/ λ (H 3 Φ) and/or µ(h 2 Φ) invariant From there hypercharge is a given: H 3 Φ Y φ = {±3Y H, ±Y H } H 2 Φ Y φ = {0, ±2Y H } Tyler Corbett (Melbourne) June 20, / 14

8 Q H = (H H) 3 at Tree Level, cont. With scalars tree level Q H is possible: Then the question is: (λ ) 2 M 2 µ2 λ M 4 (µ)3 µ M 6 What extended scalar sectors can generate these topologies? Must be an SU(3) c singlet, the Higgs is uncolored. Must be in rep. of SU(2) L w/ λ (H 3 Φ) and/or µ(h 2 Φ) invariant From there hypercharge is a given: H 3 Φ Y φ = {±3Y H, ±Y H } H 2 Φ Y φ = {0, ±2Y H } Tyler Corbett (Melbourne) June 20, / 14

9 Some Group Theory... Clearly a SM singlet and a 2HDM work as we can form H 3 Φ. What other representations work? 2 2 = 3 S + 1 A = 4 S + 2 So triplets will work! R triplet w/ H Hφ must have Y φ = 0 C triplet w/ H 2 Φ must have Y Φ = 2Y H Quadruplets will also work! R quadruplet won t work, because we have either (H H)HΦ or H 3 Φ so Y φ 0 C quadruplet can have H 3 Φ and Y Φ1 = 3Y H C quadruplet can also have (H H)HΦ and Y Φ2 = Y H However, we neglect quadruplet models (haven t completed the analyses yet)... Tyler Corbett (Melbourne) June 20, / 14

10 Some Group Theory... Clearly a SM singlet and a 2HDM work as we can form H 3 Φ. What other representations work? 2 2 = 3 S + 1 A = 4 S + 2 So triplets will work! R triplet w/ H Hφ must have Y φ = 0 C triplet w/ H 2 Φ must have Y Φ = 2Y H Quadruplets will also work! R quadruplet won t work, because we have either (H H)HΦ or H 3 Φ so Y φ 0 C quadruplet can have H 3 Φ and Y Φ1 = 3Y H C quadruplet can also have (H H)HΦ and Y Φ2 = Y H However, we neglect quadruplet models (haven t completed the analyses yet)... Tyler Corbett (Melbourne) June 20, / 14

11 Some Group Theory... Clearly a SM singlet and a 2HDM work as we can form H 3 Φ. What other representations work? 2 2 = 3 S + 1 A = 4 S + 2 So triplets will work! R triplet w/ H Hφ must have Y φ = 0 C triplet w/ H 2 Φ must have Y Φ = 2Y H Quadruplets will also work! R quadruplet won t work, because we have either (H H)HΦ or H 3 Φ so Y φ 0 C quadruplet can have H 3 Φ and Y Φ1 = 3Y H C quadruplet can also have (H H)HΦ and Y Φ2 = Y H However, we neglect quadruplet models (haven t completed the analyses yet)... Tyler Corbett (Melbourne) June 20, / 14

12 R Scalar Singlet Example Taking the R Scalar Singlet as an example: L = (D µ H) (D µh) + µ 2 (H H) λ(h H) 2 + L Where for this model L is given by: L = 1 2 ( µ S)( µs) M 2 2 S2 g 3 S3 g HS (H H)S λ S 4 S4 λ HS 2 (H H)S 2 Integrating out the heavy S at tree level we find, L = g ( HS λhs 2M 2 H 4 gg ) HS ghs 2 3M 2 M 4 (H H) 3 g HS 2M 4 (H H) (H H) Note we generate a finite renormalization of λ We generate (as expected) Q H = (H H) 3, but also Q H = (H H) (H H) Tyler Corbett (Melbourne) June 20, / 14

13 R Scalar Singlet Example Taking the R Scalar Singlet as an example: L = (D µ H) (D µh) + µ 2 (H H) λ(h H) 2 + L Where for this model L is given by: L = 1 2 ( µ S)( µs) M 2 2 S2 g 3 S3 g HS (H H)S λ S 4 S4 λ HS 2 (H H)S 2 Integrating out the heavy S at tree level we find, L = g ( HS λhs 2M 2 H 4 gg ) HS ghs 2 3M 2 M 4 (H H) 3 g HS 2M 4 (H H) (H H) Note we generate a finite renormalization of λ We generate (as expected) Q H = (H H) 3, but also Q H = (H H) (H H) Tyler Corbett (Melbourne) June 20, / 14

14 R Scalar Singlet Example Taking the R Scalar Singlet as an example: L = (D µ H) (D µh) + µ 2 (H H) λ(h H) 2 + L Where for this model L is given by: L = 1 2 ( µ S)( µs) M 2 2 S2 g 3 S3 g HS (H H)S λ S 4 S4 λ HS 2 (H H)S 2 Integrating out the heavy S at tree level we find, L = g ( HS λhs 2M 2 H 4 gg ) HS ghs 2 3M 2 M 4 (H H) 3 g HS 2M 4 (H H) (H H) Note we generate a finite renormalization of λ We generate (as expected) Q H = (H H) 3, but also Q H = (H H) (H H) Tyler Corbett (Melbourne) June 20, / 14

15 R Scalar Singlet Example Taking the R Scalar Singlet as an example: L = (D µ H) (D µh) + µ 2 (H H) λ(h H) 2 + L Where for this model L is given by: L = 1 2 ( µ S)( µs) M 2 2 S2 g 3 S3 g HS (H H)S λ S 4 S4 λ HS 2 (H H)S 2 Integrating out the heavy S at tree level we find, L = g ( HS λhs 2M 2 H 4 gg ) HS ghs 2 3M 2 M 4 (H H) 3 g HS 2M 4 (H H) (H H) Note we generate a finite renormalization of λ We generate (as expected) Q H = (H H) 3, but also Q H = (H H) (H H) Tyler Corbett (Melbourne) June 20, / 14

16 Preliminary Summary We can summarize our derived EFTs as follows, Q H = (H H) (H H) Q eh = (H H)( LHe R ) Q HD = (D µ H) HH (D µh) Q uh = (H H)( Q Hu R ) Q HD2 = (H H)(D µ H) (D µh) Q dh = (H H)( QHd R ) Q H = (H H) 3 W/ each model generating these operators as follows: Theory c H c H c HD c HD2 c ψh R Singlet C Singlet 2HDM, Type I R Triplet C Triplet Tyler Corbett (Melbourne) June 20, / 14

17 Preliminary Summary We can summarize our derived EFTs as follows, Q H = (H H) (H H) Q eh = (H H)( LHe R ) Q HD = (D µ H) HH (D µh) Q uh = (H H)( Q Hu R ) Q HD2 = (H H)(D µ H) (D µh) Q dh = (H H)( QHd R ) Q H = (H H) 3 W/ each model generating these operators as follows: Theory c H c H c HD c HD2 c ψh R Singlet C Singlet 2HDM, Type I R Triplet C Triplet Tyler Corbett (Melbourne) June 20, / 14

18 Higgs Global Fits Since the Higgs discovery, global fits of the Higgs EFT to single Higgs experimental results has become an industry... TC, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, arxiv: & I Brivio, TC, OJP Éboli, MB Gavela, J Gonzalez-Fraile, et al. arxiv: TC, OJP Éboli, D Gonçalves, J Gonzalez-Fraile, T Plehn, M Rauch, arxiv: But also including EWPD and triple gauge boson processes, TC, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, arxiv: A Butter, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, et al., arxiv: this is clearly a pretty biased list... Tyler Corbett (Melbourne) June 20, / 14

19 Higgs Global Fits Since the Higgs discovery, global fits of the Higgs EFT to single Higgs experimental results has become an industry... TC, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, arxiv: & I Brivio, TC, OJP Éboli, MB Gavela, J Gonzalez-Fraile, et al. arxiv: TC, OJP Éboli, D Gonçalves, J Gonzalez-Fraile, T Plehn, M Rauch, arxiv: But also including EWPD and triple gauge boson processes, TC, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, arxiv: A Butter, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, et al., arxiv: this is clearly a pretty biased list... Tyler Corbett (Melbourne) June 20, / 14

20 Higgs Global Fits Since the Higgs discovery, global fits of the Higgs EFT to single Higgs experimental results has become an industry... TC, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, arxiv: & I Brivio, TC, OJP Éboli, MB Gavela, J Gonzalez-Fraile, et al. arxiv: TC, OJP Éboli, D Gonçalves, J Gonzalez-Fraile, T Plehn, M Rauch, arxiv: But also including EWPD and triple gauge boson processes, TC, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, arxiv: A Butter, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, et al., arxiv: f/λ 2 [TeV -2 ] O GG O WW LHC-Higgs, 95% CL LHC-Higgs + LHC-TGV + LEP-TGV, 95% CL O BB O W O B O φ2 O WWW Λ/ f [TeV] f/λ 2 [TeV -2 ] O t O b O τ Λ/ f [TeV] O GG = (H H)G A,µν G A µν O W W = (H H)W I,µν W I µν O BB = (H H)B µν B µν O W (D µ H) τ I (D ν H)W I,µν O B (D µ H) (D ν H)B µν O φ2 = 2Q H O W W W = W µν W νρw ρ µ this is clearly a pretty biased list... Tyler Corbett (Melbourne) June 20, / 14

21 Higgs Global Fits Since the Higgs discovery, global fits of the Higgs EFT to single Higgs experimental results has become an industry... TC, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, arxiv: & I Brivio, TC, OJP Éboli, MB Gavela, J Gonzalez-Fraile, et al. arxiv: TC, OJP Éboli, D Gonçalves, J Gonzalez-Fraile, T Plehn, M Rauch, arxiv: But also including EWPD and triple gauge boson processes, TC, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, arxiv: A Butter, OJP Éboli, J Gonzalez-Fraile, MC Gonzalez-Garcia, et al., arxiv: f/λ 2 [TeV -2 ] This list is too long for our EFTs... O GG O WW We only need three operators, Q H, Q HD, and Q ψh... Λ/ f f/λ 2 Λ/ f but at leading order (but [TeV] not [TeVtree level) -2 ] 2HDM and[tev] triplet Ochange 15 GG = Hγγ (H H)G A,µν G A µν µ γγ (most recent from ATLAS) O W W = (H H)W I,µν W I µν so we include an operator 0.5 Q γγ c γγ hf µν F µν also helps constrain parameters of models: O BB = (H H)B µν B µν coefficients of Q HD, depend on diff. parameters than Q γγ O W (D µ H) τ I (D ν H)W I,µν LHC-Higgs, 95% CL LHC-Higgs + LHC-TGV + LEP-TGV, 95% CL 0.3 O B (D µ H) (D ν H)B µν O BB O W O B O φ2 O WWW O t O b O τ 0.25 O φ2 = 2Q H O W W W = W µν W νρw ρ µ this is clearly a pretty biased list... Tyler Corbett (Melbourne) June 20, / 14

22 Reduced Global Fits Clearly our EFTs are simpler, and they call for fits to a reduced basis of operators... We employ Lilith to perform simple fits to the relevant operator bases. ρ = v 2 c th v 2 c bh v 2 c τh v 2 c HD v 2 c H c γγ = ± ± ± ± ± ± 1.891, Tyler Corbett (Melbourne) June 20, / 14

23 Projected into the Models ( 2logL) g/ 2v or (g/v) Z Z 6 c β ( 2logL) λ HΦ ( 2logL) 5λ HΦ +λ / ( 2logL) g/v g/v 2 0 Tyler Corbett (Melbourne) June 20, / 14

24 DiHiggs Analysis The motivation for studying the operator Q H = (H H) 3 is to enhance the DiHiggs signal, Simulation Details: performed in bbγγ channel FeynRules Madgraph Pythia Delphes Further details on simulations, cuts, etc. available in arxiv: Tyler Corbett (Melbourne) June 20, / 14

25 DiHiggs Analysis The motivation for studying the operator Q H = (H H) 3 is to enhance the DiHiggs signal, Simulation Details: performed in bbγγ channel FeynRules Madgraph Pythia Delphes Further details on simulations, cuts, etc. available in arxiv: Tyler Corbett (Melbourne) June 20, / 14

26 DiHiggs Analysis, R Scalar Singlet Looking at the R Scalar Singlet at a future 100 TeV collider: S 100TeV 3ab -1 B v 2 c H 0. Real Singlet v 2 (c HD -4c H ) Tyler Corbett (Melbourne) June 20, / 14

27 DiHiggs Analysis, All Models 0.15 S B 100TeV 3ab HDMs 0.05 Complex Triplet Real Singlet v 2 c H 0. Complex Singlet Real Triplet v 2 (c HD -4c H ) An error in implementing tth and tthh vertices from EFT may shift these... Tyler Corbett (Melbourne) June 20, / 14

28 Conclusions We have studied (simple) scalar extensions of the SM from an EFT perspective, only theories which generate tree level dimension six Q H = (H H) 3 operator colored scalars won t give tree level amplitudes there were 4 different representations of SU(2) L we considered Singlet Doublet Y φ = Y H Triplet Y φ = 0, 2Y H Quadruplet (still need to include) Y φ = {3Y H, Y H } all other representations won t give tree level amplitudes We simplified the basis of operators using the EOM, Q H = (H H) 3 Q H = (H H) (H H) Q HD = (D µ H) HH (D µh) Q ψh = (H H)Ψ L Hψ R Simplified fit to single Higgs data relation between the parameters of the UV models We simulated the DiHiggs signals Simulate dihiggs processes at 100 TeV Have identified the regions in c H (c HD 4c H ) plane relevant to our UV models Identified the significances with which the di Higgs signal could be observed in plane Tyler Corbett (Melbourne) June 20, / 14

29 Conclusions We have studied (simple) scalar extensions of the SM from an EFT perspective, only theories which generate tree level dimension six Q H = (H H) 3 operator colored scalars won t give tree level amplitudes there were 4 different representations of SU(2) L we considered Singlet Doublet Y φ = Y H Triplet Y φ = 0, 2Y H Quadruplet (still need to include) Y φ = {3Y H, Y H } all other representations won t give tree level amplitudes We simplified the basis of operators using the EOM, Q H = (H H) 3 Q H = (H H) (H H) Q HD = (D µ H) HH (D µh) Q ψh = (H H)Ψ L Hψ R Simplified fit to single Higgs data relation between the parameters of the UV models We simulated the DiHiggs signals Simulate dihiggs processes at 100 TeV Have identified the regions in c H (c HD 4c H ) plane relevant to our UV models Identified the significances with which the di Higgs signal could be observed in plane Tyler Corbett (Melbourne) June 20, / 14

30 Conclusions We have studied (simple) scalar extensions of the SM from an EFT perspective, only theories which generate tree level dimension six Q H = (H H) 3 operator colored scalars won t give tree level amplitudes there were 4 different representations of SU(2) L we considered Singlet Doublet Y φ = Y H Triplet Y φ = 0, 2Y H Quadruplet (still need to include) Y φ = {3Y H, Y H } all other representations won t give tree level amplitudes We simplified the basis of operators using the EOM, Q H = (H H) 3 Q H = (H H) (H H) Q HD = (D µ H) HH (D µh) Q ψh = (H H)Ψ L Hψ R Simplified fit to single Higgs data relation between the parameters of the UV models We simulated the DiHiggs signals Simulate dihiggs processes at 100 TeV Have identified the regions in c H (c HD 4c H ) plane relevant to our UV models Identified the significances with which the di Higgs signal could be observed in plane Tyler Corbett (Melbourne) June 20, / 14

31 Conclusions We have studied (simple) scalar extensions of the SM from an EFT perspective, only theories which generate tree level dimension six Q H = (H H) 3 operator colored scalars won t give tree level amplitudes there were 4 different representations of SU(2) L we considered Singlet Doublet Y φ = Y H Triplet Y φ = 0, 2Y H Quadruplet (still need to include) Y φ = {3Y H, Y H } all other representations won t give tree level amplitudes We simplified the basis of operators using the EOM, Q H = (H H) 3 Q H = (H H) (H H) Q HD = (D µ H) HH (D µh) Q ψh = (H H)Ψ L Hψ R Simplified fit to single Higgs data relation between the parameters of the UV models We simulated the DiHiggs signals Simulate dihiggs processes at 100 TeV Have identified the regions in c H (c HD 4c H ) plane relevant to our UV models Identified the significances with which the di Higgs signal could be observed in plane Tyler Corbett (Melbourne) June 20, / 14

32 Backup: Cut Flow Channel Pre-selection Basic Cuts 110 < m bb < 140 GeV pt bb > 150 GeV ptγγ > 140 GeV σ (fb) + #bjet=2;#γ=2 120 < mγγ < 130 GeV Efficiency σ (fb) Efficiency σ (fb) Efficiency σ (fb) Efficiency σ (fb) Backgrounds b bγγ t th(γγ) c cγγ b bh(γγ) jjγγ Zh(γγ) b bjj Total Signal BMs BM1, (g (1) /v, g(2) HHH HHH v) = (0.0225, 0) BM2, (g (1) /v, g(2) HHH HHH v) = ( 0.032, ) BM3, (g (1) /v, g(2) HHH HHH v) = ( 0.141, ) Cut flow table for the analysis we perform. Basic cuts refer to generator level cuts described in arxiv: In the cross sections we have multiplied by the following NLO k factors (Contino 2016): k zh = 0.87, k t th = 1.3, k bbjj = 1.08, k jjγγ = including fake rate of c b: 10%. 2 including fake rate of j b: 1%. 3 including fake rate of j γ: 0.012%. Tyler Corbett (Melbourne) June 20, / 14

33 Backup: Unitarity and EFTs EFTs are known to violate unitarity, e.g. in Chiral PT: L 2 = F 2 4 Tr [ µu µ U] (2 point) + 1 6F 2 (φ i µ φ i µφ j φ j φ i φ i µφ j µ φ j )φ j with ( ) U = exp i φ, φ = φ F i τ i then, Violates Unitarity at some s! A(s, t, u) = s F 2 π Tyler Corbett (Melbourne) June 20, / 14

34 Backup: Unitarity and EFTs II The operators Q HD and Q H violate unitarity (as they have extra derivatives!), Partial wave unitarity tell us: T J (V 1λ1 V 2λ2 V 1λ1 V 2λ2 ) 2 Calculating all 4V scattering amps we find the largest allowed values of c HD and c H, c H S 67 c HD S 67 For the R scalar singlet this gives, g 2 ( ) HS c H S = 2MS 4 S 67 g HS 2M S TeV 2 (1) So for s 1 TeV and M S 1 TeV we find, Which isn t so useful... g HS 11TeV (2) similar bounds come from performing the search for the other models. Note: 2HDM doesn t generate c H or c HD no unitarity bounds for this model Tyler Corbett (Melbourne) June 20, / 14