eHDECAY: an Implementation of the Higgs Effective Lagrangian into HDECAY Margherita Ghezzi University of Torino in collaboration with: R. Contino, C. Grojean, M. M¨ uhlleitner, M. Spira arXiv:1403.3381 Workshop of LHC Higgs Cross Section Working Group, June 12th - 13th, 2014 Margherita Ghezzi (University of Torino) eHDECAY Geneva, Jun 12th 1 / 13 eHDECAY http://www.itp.kit.edu/~maggie/eHDECAY/ It has been obtained from extending HDECAY 5.10 Fortran program for the calculation of the partial decay widths and branching ratios of the Higgs boson according to the Higgs effective Lagrangian QCD and EW higher order contributions are consistently included Included parametrizations are: Effective Lagrangian for a light Higgs-like scalar (non-linear σ-model) Effective Lagrangian for a light Higgs weak doublet (Strongly-Interacting Light Higgs Lagrangian) Benchmark Composite Higgs Models: MCHM4 and MCHM5 Margherita Ghezzi (University of Torino) eHDECAY Geneva, Jun 12th 2 / 13 General Lagrangian for a light Higgs-like scalar Assumptions: CP is conserved vector fields couple to conserved currents L= 1 2 µ ∂µ h ∂ h − 2 + + mW Wµ W + + 1 2 2 2 mh h − c3 −µ + cWW Wµν W 1 3mh2 6 v h 1 + 2cW −µν − + cW ∂W Wν Dµ W v cZZ 2 +µν 3 ¯ (i) ψ (i) m (i) ψ ψ h − ψ=u,d,l + cW 2 h2 v2 + 1 2 2 mZ Zµ Z + cZ γ Zµν γ µν + h.c. + cZ ∂Z Zν ∂µ Z µν Zµν Z µν + ... + cγγ 2 µ 1 + cψ h v + cψ2 1 + 2cZ + cZ 2 γµν γ µν + cZ ∂γ Zν ∂µ γ + µν cgg 2 h v h2 v2 h2 h v2 v a Gµν G + ... + ... + ... aµν + ... h v (unitary gauge) Standard Model c3 = cψ = cW = cZ = 1 cψ 2 = cW 2 = cZ 2 = 0 cWW = cZZ = cZ γ = cgg = cW ∂W = cZ ∂Z = cZ ∂γ = 0 Contino, Grojean, Moretti, Piccinini and Rattazzi, JHEP 05 Alonso, Gavela, Merlo, Rigolin and Yepes, Phys.Lett. B722 Contino, MG, Grojean, M¨ uhlleitner and Spira, JHEP 1307 Buchalla, Cat` a and Krause, Nucl.Phys. B880 Margherita Ghezzi (University of Torino) eHDECAY (2010) (2013) (2013) (2014) Geneva, Jun 12th 089 330 035 552 3 / 13 Minimal Composite Higgs Models f v SO(5) → SO(4) → SO(3) 1 free parameter: (custodial symmetry) v2 ξ ≡ 2 ∈ [0, 1] f f ≡ M g∗ MCHM4: spinorial representation cV = cψ = c3 = 1 − ξ, cV 2 = 1 − 2ξ, cψ2 = − ξ 2 MCHM5: fundamental representation cV = 1 − ξ, cV 2 = 1 − 2ξ, 1 − 2ξ cψ = c3 = √ , 1−ξ cψ2 = −2ξ Agashe, Contino and Pomarol, Nucl. Phys. B 719 (2005) 165 Contino, Da Rold and Pomarol, Phys. Rev. D 75 (2007) 055014 Margherita Ghezzi (University of Torino) eHDECAY Geneva, Jun 12th 4 / 13 Effective Lagrangian for a Higgs doublet L = LSM + c¯i Oi ≡ LSM + ∆LSILH + ∆LF1 + ∆LF2 + ∆LV + ∆L4F i ∆LSILH = c¯H 2v 2 + + + + ∂ † µ c¯u v2 † c yu H H q ¯L H uR + i c¯W g 2 2mW i c¯HW g 2 mW c¯γ g 2 2 mW ✞ † H H ∂µ H H → † i← µ H σ D H µ † + c¯d v2 ← → H†DµH c¯T 2v 2 ✝ ν ν i i (D H) σ (D H)Wµν + † H HBµν B µν Expansion at the first order in Margherita Ghezzi (University of Torino) + v2 f2 c¯l † yd H H q ¯L HdR + (D Wµν ) + i ← → H† D µH c¯g gS2 2 mW † i c¯B g 2 2mW i c¯HB g 2 mW a H HGµν G v2 − ✆ c¯6 λ v2 † H H 3 † ¯ yl H H L L HlR + h.c. → †← µ H D H µ ☎ † ν (∂ Bµν ) ν (D H) (D H)Bµν aµν flavour alignment 1 Buchm¨ uller and Wyler, NPB 268 (1986) 621 Giudice, Grojean, Pomarol and Rattazzi, JHEP 0706 (2007) 045 Grzadkowski, Iskrzynski, Misiak and Rosiek, JHEP 1010 (2010) 085 Contino, MG, Grojean, M¨ uhlleitner and Spira, JHEP 1307 (2013) 035 eHDECAY Geneva, Jun 12th 5 / 13 LSILH Higgs couplings cW cZ c ( = u, d, l) c3 1 1 c¯H /2 c¯H /2 1 MCHM4 c¯T (¯ cH /2 + c¯ ) 1 + c¯6 3¯ cH /2 MCHM5 p 1 ⇠ p 1 ⇠ p 1 ⇠ p 1 ⇠ p 1 ⇠ 1 p 1 2⇠ ⇠ p 1 ⇠ 1 p 1 2⇠ ⇠ cgg 8 (↵s /↵2 ) c¯g 0 0 c 8 sin2 ✓W c¯ 0 0 0 0 cZ c¯HB Margherita Ghezzi (University of Torino) c¯HW 8 c¯ sin2 ✓W tan ✓W eHDECAY Geneva, Jun 12th 6 / 13 NLO corrections Beyond the tree level: Short-distance corrections: RG evolution - not included in eHDECAY for the c¯i The input values c¯i must be given at the low-energy scale µ2 = mh2 Long-distance corrections: multiple perturbative expansion QCD corrections: they generally factorize with respect to the expansion in the number of fields and derivatives ✞ ✝ Multiple perturbative expansion: Margherita Ghezzi (University of Torino) eHDECAY αSM 4π , 2 E , v M f2 ☎ ✆ Geneva, Jun 12th 7 / 13 ¯ A simple example: h → ψψ General case: ψ¯ h Coupling rescaled by cψ cψ = 1 + δcψ ψ QCD: the same as in the SM EW: not factorized ¯ Γ(ψψ) NL QCD ¯ = cψ2 ΓSM 0 (ψψ) 1 + δψ κ Margherita Ghezzi (University of Torino) eHDECAY δψ = 1 0 X ψ = quark ψ = lepton Geneva, Jun 12th 8 / 13 ¯ A simple example: h → ψψ SILH case (Higgs doublet close to the SM): Perturbative expansion in v2 f2 and α2 4π ψ¯ h h h ψ O v2 f2 ¯ Γ(ψψ) SILH ψ O α2 4π ¯ = ΓSM ¯H − 2¯ cψ + 0 (ψψ) 1 − c Margherita Ghezzi (University of Torino) ψ¯ ψ¯ ψ O 2 Re A∗SM ASM 0 1,ew 2 |ASM 0 | eHDECAY α2 v 2 4π f 2 X 1 + δψ κQCD Geneva, Jun 12th 9 / 13 A loop-process example: h → γγ General case: γ cψ h h ψ NL = GF α2em mh3 √ 128 2π 3 q=t,b,c cγγ h W γ γ Γ(γγ) γ cW γ 4 4 4π NLO cq 3Qq2 AQCD (τq )+ cτ Qτ2 A1/2 (ττ )+cW A1 (τW )+ cγγ 1/2 3 3 αem QCD corrections: NLO AQCD (τq ) = A1/2 (τq )(1 + κQCD ) 1/2 EW corrections: not factorized and not available Margherita Ghezzi (University of Torino) γ eHDECAY Geneva, Jun 12th 2 10 / 13 A loop-process example: h → γγ SILH case: Γ(γγ) SILH = GF α2em mh3 √ 128 2π 3 2 SM∗ SM |ASM QCD NLO (γγ)| + 2 Re AQCD LO (γγ) Aew (γγ) + 2 Re ASM∗ QCD NLO (γγ) ∆A(γγ) + SM ASM QCD NLO ∼ ALO 1 + O ASM ew ∼ O 32π sin2 θW c¯γ αem αS 4π α2 4π ∆A(γγ) + 32π sin2 θW c¯γ αem ∼O v2 f2 γ h γ h γ Margherita Ghezzi (University of Torino) γ h W γ eHDECAY γ Geneva, Jun 12th 11 / 13 Approximated formulas Higgs decays into vector bosons Γ(h → W (∗) W ∗ ) Γ(h → W (∗) W ∗ )SM Γ(h → Z (∗) Z ∗ ) Γ(h → Z (∗) Z ∗ )SM Γ(h → Z γ) Γ(h → Z γ)SM 1 − c¯H + 2.2 c¯W + 3.7 c¯HW , 1 − c¯H + 2.0 2 c¯W + tan θW c¯B 1 − c¯H + 0.12 c¯t − 5 · 10 −4 2 + 3.0 c¯HW + tan θW c¯HB −5 c¯c − 0.003 c¯b − 9 · 10 2 + 4.2 c¯W + 0.19 c¯HW − c¯HB + 8 c¯γ sin θW Γ(h → γγ) Γ(h → γγ)SM Γ(h → gg ) Γ(h → gg )SM c¯τ 4π √ − 0.26 c¯γ , α2 αem , 1 − c¯H + 0.54 c¯t − 0.003 c¯c − 0.007 c¯b − 0.007 c¯τ + 5.04 c¯W − 0.54 c¯γ 1 − c¯H − 2.12 c¯t + 0.024 c¯c + 0.1 c¯b + 22.2 c¯g √ α2 ≡ Margherita Ghezzi (University of Torino) 2 2GF mW π 4π α2 4π αem , . 2 αem ≡ αem (q = 0) eHDECAY Geneva, Jun 12th 12 / 13 Conclusions We have presented eHDECAY, a numerical program for the calculation of the Higgs branching ratios according to the Higgs effective Lagrangian. Parametrizations included: General non-linear effective Lagrangian Efffective Lagrangian for a weak Higgs doublet Minimal Composite Higgs Models MCHM4 and MCHM5 QCD corrections are included EW corrections are included in the SILH case, according to the multiple perturbative expansion Enjoy eHDECAY! Thanks for your attention! Margherita Ghezzi (University of Torino) eHDECAY Geneva, Jun 12th 13 / 13
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