From the SM Lagrangian to Phenomenology, including SM Higgs Boson. Fulvio Piccinini

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1 From the SM Lagrangian to Phenomenology, including SM Higgs Boson Fulvio Piccinini INFN, Sezione di Pavia PhD course 2014, Pavia Bibliography G. Montagna, O. Nicrosini and F. P., arxiv:hep-ph/ LEP and SLD Collaborations, arxiv:hep-ex/ S. Dittmaier and M. Schumacher, arxiv: LEP, SLD and Tevatron Collaborations, arxiv: LEP(2) Collaborations, arxiv: CDF and D0 Collaborations, arxiv: F. Piccinini (INFN) PhD course 2014, Pavia May / 34

2 Outline 1 From the SM Lagrangian L matter +L gauge +L Higgs +L gauge int. +L Yukawa inter. +L Higgs sel int. L = + + Lkin Lkin L Lkin V ± LN LC R L V V LH LH L V V + + LY LHV how do we test it with experiments? (rom LEP to LHC) 2 General eatures o event generators/simulation tools or LHC physics F. Piccinini (INFN) PhD course 2014, Pavia May / 34

3 Map o LEP( CERN Jura Mountains ALEPH LEP OPAL 1 km Switzerland France L3 SPS DELPHI PS Geneva Airport F. Piccinini (INFN) PhD course 2014, Pavia May / 34

4 Linking theory and experiment σ theory hh 1 σ exp 1 Ldt N obs A ɛ = σtheory a,b 0 dˆσ a,b (x 1, x 2, Q 2 /µ 2 F, Q 2 /µ 2 R) + O Φ dx 1 dx 2 a,h1 (x 1, µ 2 F, µ 2 R) b,h2 (x 2, µ 2 F, µ 2 R) ( Λ n ) QCD Q n PDF s itted rom data ˆσ calculated perturbatively Campbell, Huston, Stirling, hep-ph/ σ = σ 0 (1 + α s δ QCD 1 + αsδ 2 QCD 2 + αδ1 EK +...) F. Piccinini (INFN) PhD course 2014, Pavia May / 34

5 LEP1: e + e s M Z ( ) e - e - γ Z e + e + Primary observables absolute cross sections or dierent species o ermions σ (s) Forward-backward asymmetries A F B (s) σ = σ F + σ B A F B = σ F σ B σ F + σ B σ F = 2π 1 0 d cos ϑ dσ dω, σ B = 2π 0 1 d cos ϑ dσ dω F. Piccinini (INFN) PhD course 2014, Pavia May / 34

6 LEP1 observables dσ dω = dσγ dω + dσγz dω + dσz dω dσ γ dω dσ γz dω dσ Z dω = α 2 Q 2 N c 4s ( 1 + cos 2 ) ϑ, = αgµm 2 Z Q N c 4 2πs Re ( χ(s) ) [ g e v g v ( 1 + cos 2 ) ϑ + 2g e ] a g a cos ϑ, = G 2 µ M Z 4 Nc 32π 2 χ(s) 2 [ ( e (g v s )2 + (g e a )2)( (g v )2 + (g ( a )2) 1 + cos 2 ) ϑ +8g e ] v ge a g v g a cos ϑ g i v = Ii 3 2Q i sin 2 ϑ, g i a = Ii 3 s χ(s) = (s MZ 2 ) + iγ Z M Z F. Piccinini (INFN) PhD course 2014, Pavia May / 34

7 Z peak σ had [nb] ALEPH DELPHI L3 OPAL Γ Z σ 0 A FB (µ) A FB rom it QED corrected average measurements 0 A FB ALEPH DELPHI L3 OPAL 10 measurements (error bars increased by actor 10) σ rom it QED corrected -0.2 M Z E cm [GeV] -0.4 M Z E cm [GeV] F. Piccinini (INFN) PhD course 2014, Pavia May / 34

8 Pseudo-observables Idea: extract as much as possible inormation on the Z properties independently o the event selection details Γ = 4N cγ 0 [(g V )2 R V + (g A )2 R A ] Γ inv = Γ Z Γ e Γ µ Γ τ Γ h Observable hadronic peak cross-section partial leptonic and hadronic widths total width hadronic width invisible width ratios orward-backward asymmetries polarization asymmetries let-right asymmetry (SLC) eective sine Symbol σ h Γ l (l = e, µ, τ), Γ c, Γ b Γ Z Γ h Γ inv R l, R b, R c A l F B, Ab F B, Ac F B P τ, P b A e LR sin 2 ϑ l e, sin2 ϑ b e R l = Γ h Γ l R b,c = Γ b,c Γ h σ 0 had = 12π ΓeΓ h M 2 Z Γ2 Z 2g V A = g A (g V )2 + (g A )2 A F B = 3 4 AeA A e LR = Ae P = A 4 Q sin 2 ϑ e = 1 g V g A F. Piccinini (INFN) PhD course 2014, Pavia May / 34

9 High exp. precision and th. precision Exp. precision at the level o 0.1% How accurate are theoretical predictions? we have to rely on perturbation theory the theoretical accuracy is given by the size o the next (not calculated) perturbative order the tree-level approximation has an uncertainty o the order o several %, as proved by the calculated eects at one-loop approximation = we need to include higher order eects γ, Z γ, Z in the loop we have to sum over all possible (also heavy) particles which couple to γ and/or Z theoretical predictions depend also on top quark mass! (not yet discovered at the start o LEP1) and other possible heavy ermions F. Piccinini (INFN) PhD course 2014, Pavia May / 34

10 Not only ermions but also bosons... γ, Z γ, Z Z Z Z γ, Z, Z γ, Z H H γ, Z γ, Z Z Z γ, Z γ, Z, H H γ, Z, Z γ, Z, Z Theoretical predictions become sensitive to all the spectrum and structure o the theory: m t, number o light neutrinos, m H, non abelian γ and Z vertices Precision physics at the Z peak is eectively discovery physics F. Piccinini (INFN) PhD course 2014, Pavia May / 34

11 SM One-loop calculations (in a nutshell) irst step: regularization and renormalization according to a chosen renormalization scheme in the gauge sector three input parameters needed to be ixed with three experimental data (like in QED the electric charge is ixed order by order through the ine structure constant) the experimental error on the input parameters will induce parametric uncertainties on the theoretical predictions the three typically used input experimental measurements are: α, G F and M Z ater ixing the parameters we can calculate every observable order by order in perturbation theory also M is calculated: M 2 = 4 2πα 8G µ sin 2 (1 + r) ϑ r = r(α, G µ, M Z, m top, m H, α s (M 2 Z)) F. Piccinini (INFN) PhD course 2014, Pavia May / 34

12 subtlety in the QED running coupling the parameter e is ixed at Q 2 0 and used at Q 2 MZ 2 = large correction terms o O(α log s ) rom Renormalization Group m 2 evolution r = α +... where α is the contribution to the QED running coupling α(0) α(s) = 1 α(s) α(s) = 4πα(0)Re [Π γ (s) Π γ (0)] (q µ q ν q 2 g µν )Π γ (q 2 ) = i d 4 xe iq x 0 T (j µ (x)j ν (0)) 0 F. Piccinini (INFN) PhD course 2014, Pavia May / 34

13 QED vacuum polarization k q µ ν k-q α(s) = α l (s) + α (5) h (s) + α t(s) leptonic masses well known top quark contribution s according to the m 2 t Appelquist-Carazzone theorem or light quark masses the perturbative expression can not be used (QCD is not ree in the inrared limit) escape way: exploit the analyticity properties o the two-point Green unction through dispersion relations F (q 2 ) = 1 2πi ds F (s) C s q 2 F. Piccinini (INFN) PhD course 2014, Pavia May / 34

14 QED vacuum polarization II Under the assumption that F (s) is real or real s, up to a threshold M 2, F (s) has a branch cut or real s > M 2, F (s) is olomorphic except along the branch cut, and taking as integration contour Im s. q 2 M 2 Λ 2 Re s we can derive the once subtracted dispersion relation F (q 2 ) = F (q 2 0) + q2 q 2 0 π M 2 ds s q 2 0 ImF (s) s q 2 iε F. Piccinini (INFN) PhD course 2014, Pavia May / 34

15 R had Bacci et al. Cosme et al. Mark I Pluto Cornell,DORIS Crystal Ball MD-1 VEPP-4 VEPP-2M ND DM2 A connection between low energy and high energy the optical theorem gives a link between the imaginary part o the hadronic vacuum polarization amplitude and the total cross section e + e hadrons σ(s) = 16π2 α 2 (s) ImΠ γ (s) s ρ,ω,φ Ψ's Υ's 7 Burkhardt, Pietrzyk ' relative 15 % 15 % 6 % 3 % error in continuum s in GeV measurements at low energy are extremely important or high energy tests o the SM F. Piccinini (INFN) PhD course 2014, Pavia May / 34

16 Sensitivity to the number o light neutrinos σ had [nb] ALEPH DELPHI L3 OPAL average measurements, error bars increased by actor 10 2ν 3ν 4ν E cm [GeV] F. Piccinini (INFN) PhD course 2014, Pavia May / 34

17 m top determination For a gauge theory with SSB rad. corrections G F (m 2 t m 2 b ) G. Montagna, O. Nicrosini, G. Passarino and F. P., Phys.Lett. B335 (1994) 484 F. Piccinini (INFN) PhD course 2014, Pavia May / 34

18 time evolution o indirect and direct top-quark mass 200 M t [GeV] Tevatron SM constraint 68% CL Direct search lower limit (95% CL) Year Tevatron was a p p s 2 TeV ( ) F. Piccinini (INFN) PhD course 2014, Pavia May / 34

19 hat about the Higgs boson? we can calculate total width and branching ratios as unctions o m H 10 2 Γ(H) [GeV] ZZ tt _ M H [GeV] Branching Ratio γ γ _ bb _ cc τ + τ M H (GeV) F. Piccinini (INFN) PhD course 2014, Pavia May / 34

20 hat about the Higgs boson? Direct search up to the possible Higgs boson mass; i not discovered lower bounds can be set or low m H (accessible at LEP energies) the branching ratio is saturated by H b b e - b e - ν e Z H b H b Z µ - b e + µ + e + ν e Indirect search through global it o all the pseudo-observables dependence o the radiative corrections on m H is only logarithmic, so very high precision is necessary F. Piccinini (INFN) PhD course 2014, Pavia May / 34

21 m H determination G. Montagna, O. Nicrosini, G. Passarino and F. P., Phys.Lett. B335 (1994) 484 F. Piccinini (INFN) PhD course 2014, Pavia May / 34

22 m H as at the end o LEP1 6 theory uncertainty 4 χ 2 2 Excluded Preliminary m H [GeV] F. Piccinini (INFN) PhD course 2014, Pavia May / 34

23 From LEP1 to LEP2 ( ) 2M s 208 GeV Cross-section (pb) Z e + e hadrons CESR DORIS PEP KEKB PEP-II PETRA TRISTAN SLC LEP I LEP II Centre-o-mass energy (GeV) F. Piccinini (INFN) PhD course 2014, Pavia May / 34

24 Direct study o the non-abelian gauge sector o the SM For s 2M we can investigate processes involving trilinear as well as quadrilinear sel-couplings e + + e + + e + + e + + e + + e ν e e γ e Z e γ/z γ e γ/z Z σ (pb) LEP YFS/Racoon no Z vertex (Gentle) only ν e exchange (Gentle) s (GeV) Cross section (pb) e + e + e + e ZZ e + e + γ e + e γγ e + e HZ m H = 115 GeV L3 e + e e + e qq e + e qq (γ) e + e µ + µ (γ) s (GeV) F. Piccinini (INFN) PhD course 2014, Pavia May / 34

25 Measurement o mass at LEP2 and Tevatron χ χ precise mass determination through the analysis o the invariant mass distribution measurement also at Tevatron p (e,µ) M = p l /p (1 cos φ l/p ) Events/0.5 GeV D0 Run II, 4.3 b Fit Region χ 2 /do = 37.4/49 DATA FAST MC >τν Z >ee m T, GeV D0 Run II, 4.3 b m T, GeV MJ Events/0.5 GeV D0 Run II, 4.3 b Fit Region χ 2 /do = 26.7/31 DATA FAST MC >τν Z >ee e p, GeV T D0 Run II, 4.3 b p e, GeV T MJ CDF and D0, arxiv: [hep-ex] CDF and D0, arxiv: [hep-ex] needed a change o input parameters in the theoretical calculations: G F, M Z and M F. Piccinini (INFN) PhD course 2014, Pavia May / 34

26 -1-1 mass and width ater LEP2 and Tevatron Summary o direct measurements Mass o the Boson Measurement M [MeV] CDF-0/I ± 79 D -I ± 83 D -II (1.0 b ) ± 43-1 CDF-II (2.2 b ) ± 19 D -II (4.3 b ) ± 26 Tevatron Run-0/I/II ± 16 LEP ± 33 orld Average ± 15 idth o the Boson Measurement Γ [MeV] CDF Ia 2,032 ± 329 CDF Ib 2,043 ± 138 D I 2,242 ± 172 CDF II 2,033 ± 72 D II 2,034 ± 72 χ 2 / do = 1.4 / 4 Tevatron Run I/II 2,046 ± 49 LEP 2* 2,196 ± 83 SM orld Av.* = 2,085 ± 42 * (Preliminary) M [MeV] March Γ [MeV] February 2010 TEVEG: arxiv: [hep-ex] TEVEG: arxiv: [hep-ex] F. Piccinini (INFN) PhD course 2014, Pavia May / 34

27 SM consistency checks -Boson Mass [GeV] TEVATRON ± LEP ± Average ± χ 2 /DoF: 0.1 / 1 NuTeV ± LEP1/SLD ± LEP1/SLD/m t ± m [GeV] March Boson idth [GeV] TEVATRON ± LEP ± Average ± χ 2 /DoF: 2.4 / 1 pp indirect ± LEP1/SLD ± LEP1/SLD/m t ± Γ [GeV] March 2012 LEPEG homepage LEPEG homepage LEP1/SLD values results rom theory: highly non trivial test! M 2 = 4 2πα 8G µ sin 2 (1 + r) ϑ input parameters: α, G µ, M Z, m top, m H, α s (M 2 Z ) F. Piccinini (INFN) PhD course 2014, Pavia May / 34

28 Summary o constraints on m H at the end o LEP Theory uncertainty α (5) had = ± ± incl. low Q 2 data χ Excluded m H [GeV] F. Piccinini (INFN) PhD course 2014, Pavia May / 34

29 some year later, ater switching on LHC χ March 2012 Theory uncertainty α (5) had = ± ± incl. low Q 2 data 1 LEP LHC excluded excluded m H [GeV] m Limit = 152 GeV [GeV] M M M H =50 GeV 68% and 95% CL it contours w/o M and m t measurements 68% and 95% CL it contours w/o M, m and M H measurements t world average ± M H = σ M H =300 GeV M H =600 GeV Tevatron average m t [GeV] kin m t ± 1σ G itter SM Sep 12 F. Piccinini (INFN) PhD course 2014, Pavia May / 34

30 SM consistency checks (II) m [GeV] March 2012 LHC excluded LEP2 and Tevatron LEP1 and SLD 68% CL M (GeV) Not excluded at 95% C.L. by direct searches M new A, M: Tevatron t 68% C.L < M H < 127 GeV 80.3 m H [GeV] α m t [GeV] M H > 600 GeV M t (GeV) LEPEG homepage F. Piccinini (INFN) PhD course 2014, Pavia May / 34

31 to bear in mind at LHC: relative size o PDF s A.D. Martin,.J. Stirling, R.S. Thorne and G. att, arxiv: [hep-ph] measured by means o its to ixed target data, DIS and Tevatron data on jets F. Piccinini (INFN) PhD course 2014, Pavia May / 34

32 Cross sections at e + e and hadron colliders σ (b) e + e - cross sections _ ( t) HZ 30 GeV HZ 60 GeV maximum energy o LEP collider + - ZZ HZ 110 GeV 115 GeV 120 GeV s (GeV) σ (b) σ jet (E T jet > s /20) pp/pp _ cross sections σ tot σ bb _ σ σ Z σ jet (E T jet > 100GeV) σ jet (E T jet > s /4) σ tt _ σ Higgs (M H =150GeV) σ Higgs (M H =500GeV) Tevatron pp _ pp LHC 7 TeV LHC 14 TeV s (GeV) F. Piccinini (INFN) PhD course 2014, Pavia May / 34

33 Higgs production Cross sections at Tevatron and LHC gg h SM qq h SM qq gg,qq _ h SM tt _ gg,qq _ h SM bb _ bb _ h SM M h [GeV] SM σ(pp _ h SM +X) [pb] s = 2 TeV M t = 175 GeV CTEQ4M qq _ h SM qq _ h SM Z gg H qq _ H qq Hqq gg,qq _ Hbb _ σ(pp H+X) [pb] s = 14 TeV M t = 175 GeV CTEQ4M gg,qq _ Htt _ qq _ HZ M H [GeV] F. Piccinini (INFN) PhD course 2014, Pavia May / 34

34 Higgs production Cross sections BR BR [pb] σ 10 1 s = 7TeV SM ± l νqq LHC HIGGS XS G 2011 σ x BR (b) H lνbb ZH ννbb ZH llbb H lνlν l νl ν + - ZZ l l qq + - ZZ l l νν H γγ tth lνqqbb H 3(lν) 1 H ZZ 4l M H (GeV) - H τ + τ ZZ l l l l VBF H τ + τ l = e, µ ± H l νbb ν = ν e,ν µ,ν - τ + γγ ZH l l bb q = udscb [GeV] M H F. Piccinini (INFN) PhD course 2014, Pavia May / 34

35 Higgs discovery Events / 2 GeV ATLAS 1 s=7 TeV, Ldt=4.8b 1 s=8 TeV, Ldt=5.9b Data Sig+Bkg Fit (m =126.5 GeV) H Bkg (4th order polynomial) H γγ Events Bkg m γγ [GeV] F. Piccinini (INFN) PhD course 2014, Pavia May / 34