Effective field theory approach to the Higgs boson phenomenology

Transcription

1 Effective field theory approach to the Higgs boson phenoenology Supervisor: Dr. Roberto Contino Roa, October 8th, 013

2 Introduction After the discovery of the Higgs boson, we are looking for New Physics signals It is reasonable to think that NP is related to the E syetry breaking Copatibility with the SM ATLAS Preliinary,Z H bb s s H ττ s s * H lνlν s s H γγ s s * H ZZ 4l s s 1 = 7 TeV: Ldt = 4.7 fb 1 = 8 TeV: Ldt = 13 fb 1 = 7 TeV: Ldt = 4.6 fb 1 = 8 TeV: Ldt = 13 fb 1 = 7 TeV: Ldt = 4.6 fb 1 = 8 TeV: Ldt = 0.7 fb 1 = 7 TeV: Ldt = 4.8 fb 1 = 8 TeV: Ldt = 0.7 fb 1 = 7 TeV: Ldt = 4.6 fb 1 = 8 TeV: Ldt = 0.7 fb H = 15.5 GeV Cobined s s 1 = 7 TeV: Ldt = fb 1 = 8 TeV: Ldt = fb µ = 1.30 ± Signal strength µ

3 Introduction Copatibility with the SM Scaling coupling ass follows naturally if the new boson is part of the sector that breaks the E syetry λ ψ ψ v λ V g VVh v V v

4 Introduction Global fit on couplings Copatibility with the SM The new boson does not look an ipostor It looks like a doublet Gap between H and the New Physics scale

5 Introduction The focus now is on a region of the paraeter space around the SM point. Following a botto-up approach, our ignorance of the ESB sector can be paraetrized in ters of an effective Lagrangian. The couplings of the operators are free paraeters if new particles are discovered they can be included in the Lagrangian

6 My Thesis Study of the Higgs effective Lagrangian Contino, MG, Grojean, Mühlleitner, Spira, Effective Lagrangian for a light Higgs-like scalar, JHEP , [arxiv: ] Ipleentation of the HEL in a nuerical progra for the coputation of the Higgs decay rates Contino, MG, Grojean, Mühlleitner, Spira, ehdecay: an ipleentation of the Higgs effective Lagrangian into HDECAY, in preparation Collider analysis of double Higgs production in the HEL fraework Contino, MG, Moretti, Panico, Piccinini, ulzer, Anoalous couplings in double Higgs production, JHEP , [arxiv: ] Study of the effective operators contributing to gg hh Azatov, Contino, Del Re, MG, work in progress

7 My Thesis Study of the Higgs effective Lagrangian Contino, MG, Grojean, Mühlleitner, Spira, Effective Lagrangian for a light Higgs-like scalar, JHEP , [arxiv: ] Ipleentation of the HEL in a nuerical progra for the coputation of the Higgs decay rates Contino, MG, Grojean, Mühlleitner, Spira, ehdecay: an ipleentation of the Higgs effective Lagrangian into HDECAY, in preparation Collider analysis of double Higgs production in the HEL fraework Contino, MG, Moretti, Panico, Piccinini, ulzer, Anoalous couplings in double Higgs production, JHEP , [arxiv: ] Study of the effective operators contributing to gg hh Azatov, Contino, Del Re, MG, work in progress

8 Effective Higgs Lagrangian Local operators paraetrize the effects of the exchange of new heavy particles: g g M i Y ii h G a µνg aµν H H Higgs coupling Integrate to gluons out theinduced heavyby fields a loop andof obtain assivethe ferions. effective operator SM exaple: the liit of infinite top ass ribution to the Higgs production cross-section fro gluon fusion is given L σgg H SM = α s H Y ggh = g S 48π G µνg a aµν h ii v A 1/ τ i δŝ 576π M i i H, 3. The coefficient is deterined by atching the full theory with the effective theory. τ i h/4m i,

9 Effective Higgs Lagrangian Assuptions: SU L U1 Y is linearly realized at high energies hx is a scalar and it is part of an SU L doublet Hx hx is CP-even flavour alignent to avoid FCNC The list of di-6 operators of Effective Lagrangian has been known since long tie: Buchüller and yler NPB A ore recent coplete and inial classification: Grzadkowski, Iskrzynski, Misiak, Rosiek JHEP Here we will follow the paraetrization of: Giudice, Grojean, Poarol, Rattazzi JHEP

10 Effective Higgs Lagrangian Assuptions: SU L U1 Y is linearly realized at high energies hx is a scalar and it is part of an SU L doublet Hx hx is CP-even flavour alignent to avoid FCNC The list of di-6 operators of Effective Lagrangian has been known since long tie: Buchüller and yler NPB A ore recent coplete and inial classification: Grzadkowski, Iskrzynski, Misiak, Rosiek JHEP Here we will follow the paraetrization of: Giudice, Grojean, Poarol, Rattazzi JHEP

11 Effective Higgs Lagrangian L = L SM + i c i O i L SM + L SILH + L F1 + L F L SILH = c H v µ H H µ H H + c T v H D µ H H D µh c 6 λ v H 3 H cu + v yu H H q L H c u R + c d v y d H H q L Hd R + c l v y l H H L L Hl R + h.c. + i c g + i c H g H σ i D µ H D ν µν i + i c B g H D µ H ν B µν D µ H σ i D ν H i µν + i c HB g D µ H D ν HB µν cγ g + H HB µν B µν + cg g S H HG a µν G aµν

12 Effective Higgs Lagrangian L = L SM + i c i O i L SM + L SILH + L F1 + L F L SILH = c H v µ H H µ H H + c T v H D µ H H D µh c 6 λ v H 3 H cu + v yu H H q L H c u R + c d v y d H H q L Hd R + c l v y l H H L L Hl R + h.c. + i c g + i c H g H σ i D µ H D ν µν i + i c B g H D µ H ν B µν D µ H σ i D ν H i µν + i c HB g D µ H D ν HB µν cγ g + H HB µν B µν + cg g S H HG a µν G aµν flavour alignent

13 hy this basis? L SILH = c H v µ H H µ H H + c T v H D µ H H D µh c 6 λ v H 3 H cu + v yu H H q L H c u R + c d v y d H H q L Hd R + c l v y l H H L L Hl R + h.c. + i c g + i c H g cγ g + H σ i D µ H D ν µν i + i c B g H D µ H ν B µν D µ H σ i D ν H i µν + i c HB g D µ H D ν HB µν H HB µν B µν + cg g S H HG a µν G aµν oblique corrections can be described in ters of L SILH operators instead of operators with ferionic currents ɛ 1 ρ = c T Z ɛ 3 = c Z + c B Z

14 hy this basis? L SILH = c H v µ H H µ H H + c T v cu + + i c g + + H D H µ H D µh c 6 λ v H 3 H v yu H H q L H c u R + c d v y d H H q L Hd R + c l v y l H H L L Hl R + h.c. i c H g H σ i D µ H D ν µν i + i c B g H D µ H ν B µν D µ H σ i D ν Hµν i + i c HB g D µ H D ν HB µν cγ g H HB µν B µν + cg g S H HG a µν G aµν contribution to the decays h γγ fro O γ and h γz fro O γ and O H O HB can easily be isolated

15 hy this basis? it is appropriate to establish the nature of the Higgs boson and deterine the strength of its interactions eak or strong dynaics? g M/f eak: Strong: g g SM e.g. SUSY g g SM e.g. coposite Higgs

16 Naive Diensional Analysis Starting fro the Higgs kinetic ter D µh D µ H derivatives + Higgs fields: pay a factor 1/M for each extra derivative and a factor 1/M for each gauge field strength insertion pay a factor g /M 1/f for each extra power of Hx pay an extra loop factor if the effective operator is generated at one loop Exaple: O H = µh H µ H H generated at tree level extra Higgs fields 1/f h h Vµ h t g h h a g FIG. : Feynan diagras for contributions to the Higgs prod vector V µ and a heavy scalarsapienza Φ are shown Università in a di and Roa b, resp depend on the PNGB nature of the Higgs.

17 Estiates of the coefficients estiates valid at the UV scale M c H, c T, c 6, c ψ O c Hψ, c Hψ O λ ψ g v f v f c, c B O M λuλd v c Hud O g f c H, c HB, c γ, c g O 16π f c ψ, c ψb, c ψg O 16π f c,b, c Hψ, c Hψ, c T : valid when generated at tree-level c H,HB,g,γ : suppressed by an additional loop factor g /16π weak dynaics: g g f M strong dynaics: g 1 f M leading New Physics effects: O H,T,6,ψ and ferionic operators if λ ψ g also O,B in case of weak dynaics

18 Estiates of the coefficients estiates valid at the UV scale M c H, c T, c 6, c ψ O c Hψ, c Hψ O λ ψ g v f v f c, c B O M λuλd v c Hud O g f c H, c HB, c γ, c g O 16π f c ψ, c ψb, c ψg O 16π f c,b, c Hψ, c Hψ, c T : valid when generated at tree-level c H,HB,g,γ : suppressed by an additional loop factor g /16π weak dynaics: g g f M strong dynaics: g 1 f M leading New Physics effects: O H,T,6,ψ and ferionic operators if λ ψ g also O,B in case of weak dynaics

19 Estiates of the coefficients If the Higgs doublet is a coposite Nabu Goldstone boson of a spontaneously-broken syetry G H: c 6 λ v H 3 H c ψ v y ψ H H ψ L Hψ R c γ g H HB µν B µν c g gs H HG a µν G aµν c ψb g y ψ ψ L Hσ µν ψ R B µν c ψ g y ψ ψl σ i Hσ µν ψ R i µν c ψg g S y ψ ψl Hσ µν λ a ψ R G a µν These operators violate the shift syetry H i H i + ζ i part of the G/H transforation they cannot be generated in absence of an explicit breaking additional suppression factor g G : c γ, c g O 16π f g g G g

20 Running of the coefficients The coefficients ust be evaluated at the scale of the experient copared to the SM, additional divergences are present because of the non-renoralizability of the effective theory divergences are absorbed by the renoralization of the coefficients of the local operators the only one-loop diagras which generate logarithic divergences are the ones which contain one insertion of effective vertices. c i µ = δ ij + γ 0 α SM µ µ ij log c j M 4π M with α SM = α e, α, α s

21 Running of the coefficients Exaple: one-loop diagras with inserction of O H and O Hψ renoralize O +B O H 1 v µ H H µh H O Hψ i µ ψγ ψ H D µh v O +B O + O B = ig [ H σ i D µ H D ν µν i + g H ] D µ H ν B µν g a b a fro O H : c +B = 1 α 6 4π log µ ch M M c +B c +B g 16π log M µ b fro O Hψ : c,b N c α 4π log µ M chψ M c +B c +B λ ψ 16π log M µ

22 Effects on physical observables O H = 1 v µ H H µh H O T = 1 v H D µ H H D µh O ψ = 1 v y ψ H H q L Hψ R O 6 = λ 3 v H H L = 1 µh µ h 1 h h c h v + + µ µ 1 + c h v +... h 3 ψ i ψi ψ i h 1 + c ψ v +... ψ=u,d,l + 1 Z ZµZ µ h 1 + c Z v c = 1 c H / c Z = 1 c H / c T c ψ = 1 c H / c ψ c 3 = 1 + c 6 3 c H / δc i g v = v M f

23 Effects on physical observables O = i g H σ i D µ H D ν µν i O B = i g H D µ H ν B µν generated at tree level sensitive to the scale of new physics δγh V V Γh V V O O,O B M V V =, Z Z, Z γ, γγ

24 Effects on physical observables O H = i g D µ H σ i D ν H i µν O HB = i g D µ H D ν HB µν O γ = g H HB µνb µν O g = g S H HGµν a G aµν generated at one loop V V =, Z Z δγh V V Γh V V O Oγ,O H,O HB 16π f δγh Zγ Γh Zγ v O Oγ,O H,O HB f δγh gg, γγ Γh gg, γγ O Og,O γ v f g SM g

25 Searching for New Physics Use the effective Lagrangian for the precision Higgs physics Leading effects in case of strong dynaics: tree-level couplings and Z γ rate v Γ h Zγ v c V, c u, c d = 1 + O = 1 + O f Γ SM f Angular distributions: dγh VV dω / dγh VV 16π 1 + c,b dω SM g Dipole operators: c tg O tg = c tg g S / y t q L H c σ µν λ a t R G a µν δσgg h σgg h ĉ tg δσgg t t s σgg t t ĉ tg t δσgg t th σgg t th ĉ tg s t ĉ tg Re c tg t / v/f

26 Conclusions e have reviewed the construction of the effective Lagrangian for a light Higgs doublet. By eans of a naive power counting we have estiated the coefficients of the various operators at the UV scale, and the contribution due to their RG evolution. This analysis allows one to identify which operators can probe the Higgs coupling strength to the new states and which instead are sensitive only to the ass scale M. Hence, it gives the possibility to distinguish between weakly-coupled UV copletions of the Standard Model like SUSY and theories where the E syetry is broken by a strongly-interacting dynaics which fors the Higgs boson as a bound state.