An Exploratory study of Higgs-boson pair production

Transcription

1 High-6 KIAS-NCTS Joint Workshop on Particle Physics, String theory and Cosmology An Exploratory study of Higgs-boson pair production Based on : JHEP 58 (5), arxiv : Collaborate with : Prof. Kingman Cheung, Prof. Jae Sik Lee and Dr. Chih-Ting Lu

2 Higgs Pair Production at the LHC R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, P. Torrielli, E. Vryonidou, M. Zaro PLB(4), arxiv : 4.74 [hep-ph] Higgs pair production in hadron hadron collisions: double Higgs production without HHH vertices the contribution due to the Higgs self interaction

3 Higgs Pair Production at the LHC R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, P. Torrielli, E. Vryonidou, M. Zaro PLB(4), arxiv : 4.74 [hep-ph] Higgs pair production in hadron hadron collisions: double Higgs production without HHH vertices the contribution due to the Higgs self interaction Standard Model : g h g h Top/Bottom Yukawa Coupling t/b Destructive interference t/b h Higgs Self Coupling g h g h

4 Higgs Pair Production at the LHC R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, P. Torrielli, E. Vryonidou, M. Zaro PLB(4), arxiv : 4.74 [hep-ph] Total cross sections at the NLO in QCD LHC-4, cross section as function of λ/λsm

5 Higgs Pair Production at the LHC J. Baglio, A. Djouadi, R. Grber, M. M. Mhlleitner, J. Quevillon and M. Spira, JHEP(), arxiv:.558 [hep-ph] Higgs Kinematic distribution HH production with different λ/λsm & HZ production MHH pth ηh

6 Higgs Pair Production at the LHC C. R. Chen and I. Low, PRD(4) arxiv:45.74 [hep-ph] The HH cross section is small because of the Destructive Interference Term Triangle diagram did not increase as much as Box diagram as the CM energy increase Higgs Top quartic coupling tthh quartic coupling will increase with CM energy Be careful, At certain high enough energy, it may upset unitarity safely applied at LHC

7 Higgs Pair Production at the LHC B. Bhat- tacherjee and A. Choudhury, PRD(5), arxiv: [hep-ph] MSSM, H hh

8 Higgs Production, Signal & BG J. Baglio, A. Djouadi, R. Grber, M. M. Mhlleitner, J. Quevillon and M. Spira, JHEP(), arxiv:.558 [hep-ph] Normalized signal and backgrounds distributions in the b bγγ channel. pth MHH ΔRH

9 Higgs Production, Signal & BG J. Baglio, A. Djouadi, R. Grber, M. M. Mhlleitner, J. Quevillon and M. Spira, JHEP(), arxiv:.558 [hep-ph] Normalized signal and backgrounds distributions in the b bττ channel. pth MHH ηh

10 Higgs Production, Signal & BG J. Baglio, A. Djouadi, R. Grber, M. M. Mhlleitner, J. Quevillon and M. Spira, JHEP(), arxiv:.558 [hep-ph] Normalized signal and backgrounds distributions in the b bww channel.

11 Higgs Pair Production at the LHC Best Search Channel can be : b b!! Cross section & Kinematic Distributions depend on SM Coupling : Higgs Self Coupling Top/Bottom Yukawa Coupling New Physics Coupling : Top-Higgs Quartic Coupling New Heavy Color Particle & Heavy Scalar Coupling (Might Show Effect on Triangle diagram or Box diagram)

12 varying C S u, C S d, CS l, C v while keeping S γ = S g =. 68.%C.L. 95%C.L. u 99.7%C.L. v K. Cheung, J. S. Lee, E. Senaha and P. Y. Tseng, Higgcision Electric Dipole Moments HDM framework With no contributions from : other Higgs bosons, supersymmetric particles, other exotic particles pseudoscalar Yukawa coupling than about delicately cancel the current Higgs-mediated contributions C P u less u v u varying C S u, C S d, CS l, C v, S γ and S g Most constrained ghvv/ghvv SM.9-. uncertainty 7%-% varying scalar Yukawa couplings C S u, Higgs gauge couplings C v and the pseudo scalar Yukawa coupling C P u can t rule out C P u CPC case, top Yukawa more prefer positive elliptical equation constraint

13 In Our Work We Study the Higgs Pair Production. Consider : triangle diagram with a Higgs-boson propagator box diagram with colored particles running in it. dim-5 anomalous tthh contact coupling By Vary : Higgs Self Coupling Top-Yukawa Coupling tthh contact coupling (include CP odd contribution in top-yukawa coupling & tthh Coupling) Keep Bottom-Yukawa Coupling as SM value. (One additional destructive interference arises between the top and bottom mediated loops, although the bottom quark effects are very small in the SM. )

14 C.T. Lu, JC, K. Cheung, J. S. Lee, JHEP 58 (5) [arxiv: [hep-ph]]. Formalism Lagrangian involved for the Higgs Pair Production In the SM, λh=g S t =, g P t = and g S,P tt =. The differential Cross section with the extended couplings

15 The production cross section normalized to the corresponding SM cross section, with or without cuts, can be parameterized as follows: Where the numerical coefficients c,, (s), d,,,4 (s), e,, (s), and f,,,4 (s) depend on s and experimental selection cuts. Here the coefficients c(s) and C(s) are for the SM contributions from the triangle and box diagrams, c(s) for the interference between them. Once we have the coefficients c i, d i, e i, and f i s, the cross sections can be easily obtained for any combinations of couplings. Upon our normalization, the ratio should be when λh=g S t =, g P t = and g S,P tt = or c(s)+ c(s)+ c(s) =

16 Behavior of each piece of cross sections versus Energies triangle box tthh c (s)[" c (s)[" c S (g ) ] H t S (g ) ] H t S 4 ) ] t S S (s)[(g e (s)[" H g tt g t S ] t tt S S e (s)[g (g ) ] e (s)[(g tt ) ] 5 5 d (s)[" d (s)[" H g (g P H t S P t S t (g t P d (s)[(g ) (g ) d 4 (s)[(g f (s)[" t P ) ] ) ) ] ] 4 ] t g P g P H t tt S P ] f (s)[g (g ) ] f (s)[g tt t S g P g P t t tt P ] f 4 (s)[(g ) ] tt!/! SM!/! SM s (TeV) - s (TeV)

17 CM energy (kinematically equals to the invariant mass MHH) lower MHH triangle higher MHH box and contact MHH can be used to enhance or reduce the triangle and box diagrams contributions

18 The higher the MHH the relatively larger proportion comes from the box and contact diagrams. MHH correlates with the boost energy of each Higgs boson. A more energetic Higgs boson will decay into a pair of particles, which have a smaller angular separation between them than a less energetic Higgs boson.

19 CPC σ/σ SM λ H g S t g S tt 5 the contact diagram interferes constructively with the triangle diagram but destructively with the box diagram Σ Σ SM Λ H = gs t = 4 Σ Σ SM Λ H = 4 gs tt = Σ Σ SM gs t = gs tt = 5 Give constructive interference Give destructive interference 5 gs tt g S tt gs t g S t 5 5 Λ H λh The dominance of the box diagram leads to the totally destructive interference the interference term strongly cancels the triangle and box diagrams

20 CPC "/" SM =±5% λ H g S t g S tt (g S t,g S tt) (λ H,g S tt) (λ H,g S t ) Σ Σ SM.5,.5 Λ H = gs tt Σ Σ SM.5,.5 gs t = gs tt Σ Σ SM.5,.5 gs tt = gs tt = gs t Same as SM +5% +5% +5% -5% +5% -5% -5% -5% gs t Λ H 5 5 the contact diagram contributes significantly to the cross section 5 5

21 CPV λ H g S t g P t

22 CPV λ H g S t g P t In most of the measurements of the Higgs boson production cross sections, (ggf, tth), both real and imaginary parts of the coupling come in the form g S t + g P t therefore one cannot tell the phase in the coupling Σ Σ SM (gs t, gp t = (,) (gs t, gp t = (,) (gs t, gp t =, ) 5 5 Λ H

23 CPV λ H g S t g P t (g S t,g P t ) (λ H,g S t ) (λ H,g P t ) Σ Σ SM Λ H = Λ H = Λ H = 5 Λ H = - Λ H = - Λ H = -5 gp t Σ Σ SM gp t = gp t =.5 gp t = gs t Σ Σ SM gs t = gs t =.5 gs t = gp t gs t Λ H

24 We consider the SM NLO HH cross section: σ SM (pp HH) 4fb p T and η dependent b-tagging efficiency τ tagging efficiency as.5 mis-tagging P j τ =. used modified MADGRAPH implementation PDF : CTEQ6L, renormalization/factorization scales μ = MH cross sections decrease by about % if μ = MHH 4 TeV with fb - luminosity It would be challenging to measure this size of cross section only in the bb!! mode and one may need to combine the measurements in different Higgs-decay channels.

25 CPC λ H g S t Since the shape of the three bands are not exactly the same, we can make use of three simultaneous measurements in order to obtain more useful information for the couplings. - 5% & 5% for Σ Σ SM Detector Level -- ATLAS, LHC-4 Basic Cuts R ΓΓ,bb R ΓΓ,bb gs t g S t Λ H #hhh

26 CPC λ H g S t Basic Cuts, R ΓΓ, bb, R ΓΓ, bb Detector Level -- ATLAS, LHC-4 Σ Σ SM Σ Σ SM 5 Σ Σ SM Σ Σ SM Σ Σ SM.5 g S t gs t 5% 5% 5% 5% 5% 5% 5% 5% 5% 5% Λ H #hhh If the measured cross sections being multiples of the SM predictions

27 CPC λ gt S gtt S H - - 5% & 5% for Σ Σ SM gs tt = - Detector Level -- ATLAS, LHC-4 Basic Cuts R ΓΓ,bb R ΓΓ,bb % & 5% for Σ Σ SM gs tt = Detector Level -- ATLAS, LHC-4 Basic Cuts R ΓΓ,bb R ΓΓ,bb gs t gs t (#h,g S t) g S tt= (#h,g S t) g S tt= Λ H Λ H gs tt 5% & 5% for Σ Σ SM gs t = Detector Level -- ATLAS, LHC-4 Basic Cuts R ΓΓ,bb R ΓΓ,bb gs tt (#h,g S tt) -5 5 (g S t,g S tt) 5% & 5% for Σ Σ SM Λ H = Detector Level -- ATLAS, LHC-4 Basic Cuts R ΓΓ,bb R ΓΓ,bb Λ H - gs t

28 CPV λ gt S gt P H 5% & 5% for Σ Σ SM Λ H = Detector Level -- ATLAS, LHC-4 Basic Cuts R ΓΓ,bb R ΓΓ,bb gp t 5% & 5% for Σ Σ SM gs t = Detector Level -- ATLAS, LHC-4 Basic Cuts R ΓΓ,bb R ΓΓ,bb (g S t,g P t) (#h,g P t) gp t gs t Λ H - - #h= % & 5% for Σ Σ SM gp t = Detector Level -- ATLAS, LHC-4 Basic Cuts R ΓΓ,bb R ΓΓ,bb - gs t 5% & 5% for Σ Σ SM gp t =.5 Detector Level -- ATLAS, LHC-4 Basic Cuts R ΓΓ,bb (#h,g S t) R ΓΓ,bb gs t (#h,g S t) Λ H Λ H - g P t= - g P t=

29 gp tt CPV up: #h=, g S t=, g P t=.5. 5% & 5% for Σ Σ SM Λ H =, gs t =, gp t = Detector Level -- ATLAS, LHC-4 Basic Cuts R ΓΓ,bb R ΓΓ,bb (g S tt,g P tt) λ H g S t g P t g P tt down left: g S t=, g P t=, g P tt= gs tt All coefficients relevant. down right: g S t=, g P t=, g S tt= Fixed some of the variable got simpler results. For example, g S t=, g P t= coefficients : c,c,c,e,e,e and f4 4 gs tt 5% & 5% for Σ Σ SM gs t =, gp t =, gp tt =.5 Detector Level -- ATLAS, LHC-4 Basic Cuts R ΓΓ,bb R ΓΓ,bb (#h,g S tt) Λ H % & 5% for Σ Σ SM gs t =, gp t =, gs tt = Detector Level -- ATLAS, LHC-4 Basic Cuts R ΓΓ,bb R ΓΓ,bb gp tt (#h,g P tt) Λ H

30 LHC-4 v.s. LHC-

31 Conclusion The triangle diagram, which contains an s-channel Higgs propagator, does not increase as much as the box diagram or the contact diagram with the center-of-mass energy Thus the open angle of Higgs decay product is useful to separate the triangle and box diagram, and helps to isolate the Higgs trilinear coupling The contact diagram contains a dim-5 operator tthh, which actually breaks the unitarity at about CM energy ~7.6/g S tt TeV. This implies that it could become dominant at high invariant mass. Suppose we take a measurement of cross sections, we can map out the possible region of parameter space. Since in different kinematic regions the regions of parameter space are mapped out differently, such that simultaneous measurements can map out the intersected regions. With measurement uncertainties less than 5% one can statistically show a nonzero value for the Higgs trilinear coupling, and also obtain the sensitivity regions of

32 We found that the behavior of the distributions of the invariant mass and angular separation at 4 TeV are very similar to those at TeV. We can then use the same method as in 4 TeV to isolate the Higgs trilinear coupling. It is difficult, if not impossible, to determine the Higgs trilinear coupling uniquely at the LHC and TeV pp machine even in the simplest case assuming very high luminosity and precise independent input for the top- Yukawa coupling. We suggest to combine the LHC results with information which can be obtained at a future e+elinear collider. If the couplings deviate from their SM values, the Higgsboson pair production cross section can easily increase by an order of magnitude.

33 Thanks!