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/9802302 LEP and SLD Collaborations, arxiv:hep-ex/0509008 S. Dittmaier and M. Schumacher, arxiv:1211.4828 LEP, SLD and Tevatron Collaborations, arxiv:1012.2367 LEP(2) Collaborations, arxiv:1302.3415 CDF and D0 Collaborations, arxiv:1204.0042 F. Piccinini (INFN) PhD course 2014, Pavia May 2014 1 / 34
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 V1 + + + ± LN LC R L V V2 + + + 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 2014 2 / 34
Map o LEP( LHC) @ CERN Jura Mountains ALEPH LEP OPAL 1 km Switzerland France L3 SPS DELPHI PS Geneva Airport F. Piccinini (INFN) PhD course 2014, Pavia May 2014 3 / 34
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/0611148 σ = σ 0 (1 + α s δ QCD 1 + αsδ 2 QCD 2 + αδ1 EK +...) F. Piccinini (INFN) PhD course 2014, Pavia May 2014 4 / 34
LEP1: e + e collisions @ s M Z (1989-1995) 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 2014 5 / 34
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 2014 6 / 34
measurements @ Z peak σ had [nb] 40 30 20 ALEPH DELPHI L3 OPAL Γ Z σ 0 A FB (µ) 0.4 0.2 0 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 86 88 90 92 94 E cm [GeV] -0.4 M Z 88 90 92 94 E cm [GeV] F. Piccinini (INFN) PhD course 2014, Pavia May 2014 7 / 34
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 2014 8 / 34
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 2014 9 / 34
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 2014 10 / 34
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 2014 11 / 34
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 2014 12 / 34
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 2014 13 / 34
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 2014 14 / 34
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 '95 6 5 4 3 2 1 relative 15 % 15 % 6 % 3 % error in continuum 0 0 1 2 3 4 5 6 7 8 9 10 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 2014 15 / 34
Sensitivity to the number o light neutrinos σ had [nb] 30 20 10 ALEPH DELPHI L3 OPAL average measurements, error bars increased by actor 10 2ν 3ν 4ν 0 86 88 90 92 94 E cm [GeV] F. Piccinini (INFN) PhD course 2014, Pavia May 2014 16 / 34
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 2014 17 / 34
time evolution o indirect and direct top-quark mass 200 M t [GeV] 150 100 Tevatron SM constraint 68% CL Direct search lower limit (95% CL) 50 1990 1995 2000 2005 Year Tevatron was a p p collider @ s 2 TeV (1989-2011) F. Piccinini (INFN) PhD course 2014, Pavia May 2014 18 / 34
hat about the Higgs boson? we can calculate total width and branching ratios as unctions o m H 10 2 Γ(H) [GeV] 10 0 10 1 ZZ tt _ 10 1 10-1 10-2 10-3 50 100 200 500 1000 M H [GeV] Branching Ratio 10 2 10 3 10 4 10 5 γ γ _ bb _ cc τ + τ 100 200 300 400 500 600 M H (GeV) F. Piccinini (INFN) PhD course 2014, Pavia May 2014 19 / 34
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 2014 20 / 34
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 2014 21 / 34
m H as at the end o LEP1 6 theory uncertainty 4 χ 2 2 Excluded Preliminary 0 10 10 2 10 3 m H [GeV] F. Piccinini (INFN) PhD course 2014, Pavia May 2014 22 / 34
From LEP1 to LEP2 (1996-2001) 2M s 208 GeV Cross-section (pb) 10 5 10 4 Z e + e hadrons 10 3 10 2 CESR DORIS PEP + - 10 KEKB PEP-II PETRA TRISTAN SLC LEP I LEP II 0 20 40 60 80 100 120 140 160 180 200 220 Centre-o-mass energy (GeV) F. Piccinini (INFN) PhD course 2014, Pavia May 2014 23 / 34
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) 30 20 10 0 LEP YFS/Racoon no Z vertex (Gentle) only ν e exchange (Gentle) 160 180 200 s (GeV) Cross section (pb) 10 4 10 3 10 2 10 1 10-1 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) 80 100 120 s 140 160 180 200 (GeV) F. Piccinini (INFN) PhD course 2014, Pavia May 2014 24 / 34
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 35000 30000 25000 20000 15000 10000 5000 1 D0 Run II, 4.3 b Fit Region χ 2 /do = 37.4/49 DATA FAST MC >τν Z >ee 0 50 60 70 80 90 100 m T, GeV 4 3 2 1 0 1 2 3 1 D0 Run II, 4.3 b 4 50 60 70 80 90 100 m T, GeV MJ Events/0.5 GeV 70000 60000 50000 40000 30000 20000 10000 1 D0 Run II, 4.3 b Fit Region χ 2 /do = 26.7/31 DATA FAST MC >τν Z >ee 0 25 30 35 40 45 50 55 60 e p, GeV T 4 3 2 1 0 1 2 3 1 D0 Run II, 4.3 b 4 25 30 35 40 45 50 55 60 p e, GeV T MJ CDF and D0, arxiv:1204.3260[hep-ex] CDF and D0, arxiv:1204.3260[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 2014 25 / 34
-1-1 mass and width ater LEP2 and Tevatron Summary o direct measurements Mass o the Boson Measurement M [MeV] CDF-0/I 80432 ± 79 D -I 80478 ± 83 D -II (1.0 b ) 80402 ± 43-1 CDF-II (2.2 b ) 80387 ± 19 D -II (4.3 b ) 80369 ± 26 Tevatron Run-0/I/II 80387 ± 16 LEP-2 80376 ± 33 orld Average 80385 ± 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) 80200 80400 80600 M [MeV] March 2012 1600 2000 2400 Γ [MeV] February 2010 TEVEG: arxiv:1204.0042[hep-ex] TEVEG: arxiv:1003.2826[hep-ex] F. Piccinini (INFN) PhD course 2014, Pavia May 2014 26 / 34
SM consistency checks -Boson Mass [GeV] TEVATRON 80.387 ± 0.016 LEP2 80.376 ± 0.033 Average 80.385 ± 0.015 χ 2 /DoF: 0.1 / 1 NuTeV 80.136 ± 0.084 LEP1/SLD 80.362 ± 0.032 LEP1/SLD/m t 80.363 ± 0.020 80 80.2 80.4 80.6 m [GeV] March 2012 -Boson idth [GeV] TEVATRON 2.046 ± 0.049 LEP2 2.195 ± 0.083 Average 2.085 ± 0.042 χ 2 /DoF: 2.4 / 1 pp indirect 2.141 ± 0.057 LEP1/SLD 2.091 ± 0.003 LEP1/SLD/m t 2.091 ± 0.002 2 2.2 2.4 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 2014 27 / 34
Summary o constraints on m H at the end o LEP2 6 5 4 Theory uncertainty α (5) had = 0.02758±0.00035 0.02749±0.00012 incl. low Q 2 data χ 2 3 2 1 Excluded 0 30 100 500 m H [GeV] F. Piccinini (INFN) PhD course 2014, Pavia May 2014 28 / 34
some year later, ater switching on LHC χ 2 6 5 4 3 2 March 2012 Theory uncertainty α (5) had = 0.02750±0.00033 0.02749±0.00010 incl. low Q 2 data 1 LEP LHC excluded excluded 0 40 100 200 m H [GeV] m Limit = 152 GeV [GeV] M 80.5 80.45 80.4 80.35 80.3 80.25 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 =125.7 1σ M H =300 GeV M H =600 GeV Tevatron average 140 150 160 170 180 190 200 m t [GeV] kin m t ± 1σ G itter SM Sep 12 F. Piccinini (INFN) PhD course 2014, Pavia May 2014 29 / 34
SM consistency checks (II) m [GeV] 80.5 80.4 March 2012 LHC excluded LEP2 and Tevatron LEP1 and SLD 68% CL M (GeV) 80.46 Not excluded at 95% C.L. by direct searches 80.44 80.42 80.40 80.38 M new A, M: Tevatron t 68% C.L. 115.5 < M H < 127 GeV 80.3 m H [GeV] α 114 300 600 1000 155 175 195 m t [GeV] 80.36 80.34 80.32 80.30 M H > 600 GeV 165 170 175 180 185 190 M t (GeV) LEPEG homepage F. Piccinini (INFN) PhD course 2014, Pavia May 2014 30 / 34
to bear in mind at LHC: relative size o PDF s A.D. Martin,.J. Stirling, R.S. Thorne and G. att, arxiv:0901.0002[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 2014 31 / 34
Cross sections at e + e and hadron colliders σ (b) 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 e + e - cross sections _ ( t) HZ 30 GeV HZ 60 GeV maximum energy o LEP collider + - ZZ HZ 110 GeV 115 GeV 120 GeV 1 0 25 50 75 100 125 150 175 200 s 225 250 (GeV) σ (b) 10 15 10 14 10 13 10 12 10 11 10 10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 10-1 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 10 3 10 4 s (GeV) F. Piccinini (INFN) PhD course 2014, Pavia May 2014 32 / 34
Higgs production Cross sections at Tevatron and LHC 10 2 10 1 10-1 10-2 10-3 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 10-4 10-4 80 100 120 140 160 180 200 10 2 10 1 10-1 10-2 10-3 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 0 200 400 600 800 1000 M H [GeV] F. Piccinini (INFN) PhD course 2014, Pavia May 2014 33 / 34
Higgs production Cross sections BR s @Tevatron BR [pb] σ 10 1 s = 7TeV SM ± l νqq LHC HIGGS XS G 2011 σ x BR (b) 10 2 10 H lνbb ZH ννbb ZH llbb H lνlν -1 10-2 10 + - l νl ν + - ZZ l l qq + - ZZ l l νν H γγ tth lνqqbb H 3(lν) 1 H ZZ 4l 10-1 10-2 100 110 120 130 140 150 160 170 180 190 200 M H (GeV) - H τ + τ + - + - ZZ l l l l -3 10 - VBF H τ + τ l = e, µ ± H l νbb ν = ν e,ν µ,ν - τ + γγ ZH l l bb q = udscb -4 10100 200 300 400 500 [GeV] M H F. Piccinini (INFN) PhD course 2014, Pavia May 2014 34 / 34
Higgs discovery Events / 2 GeV 3500 3000 2500 2000 1500 1000 500 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 200 100 0 100 200 100 110 120 130 140 150 160 m γγ [GeV] F. Piccinini (INFN) PhD course 2014, Pavia May 2014 35 / 34