Physics at the LHC bdelhak DJOUDI ( LPT Orsay) Standard Physics at the LHC 1 The Standard Model QCD at the LHC 3 Tests of the SM at the LHC The SM Higgs at the LHC SUSY and SUSY Higgs at the LHC Physics at the LHC Djouadi p1/6
+,? B B @ 6??? F @ @ @ OP I F Q S + S L R M S 1 The Standard Model brief introduction The SM is based on a local gauge symmetry invariance under describes the strong force The group interaction between q, q, q which are SU(3) triplets corresponding to 8 generators of mediated by 8 gluons,, ) ( matrices GellMan 354 687 /1 asymptotic freedom interaction weak at high energy, The Lagrangian of the theory is given by D B C D B K B JI HG F CED B?@? D B = <;? F @? G with O LNM fermion gauge boson couplings P @ P P @ P F @ + LNM triple gauge boson couplings P @ P quartic gauge boson couplings Physics at the LHC Djouadi p/6
6 + F F ( @ @ @ C,, @ @ 6 1 The SM brief introduction describes the electroweak interaction between the three familles of quarks and leptons,, Same holds for the two other generations (and neutrinos are and stay exactly massless) There is no (hypercharge) gauge bosons (isospin) and mediated by the the gauge bosons, corresp to generators, are exactly massless, )(, Lagrangian simple with fields strenghs and covariant derivatives F @ @ G F @ @, O 1 / HG HG F O 54 I C3 I @ B B B @ 6 Physics at the LHC Djouadi p3/6
S S ) ) / 1 The Higgs in the SM the potential But if gauge boson and fermion masses are put by hand in R S S and/or terms breaking of gauge symmetry We need a less brutal way to generate particle masses in the SM In the SM, for the mechanism of spontaneous EW symmetry breaking, introduce a doublet of complex scalar fields ) ( with a Lagrangian that is invariant under 4 scalar particles develops a vev, +, + S ( ( Physics at the LHC Djouadi p4/6
3, B 1 B, G G, 3 3 1 The Higgs in the SM the physical fields with the true vacuum To obtain the physical states, write and H(x) at 1st order, in terms of four fields Write B,, B B to go to the unitary gauge Make a gauge transformation on, B of the Lagrangian Then fully develop the term 1 3 HG F 3 3 3 4 3 4 3 3 3 4 3 3 3 4,, G,, F, ] is the orthogonal of [ and Define the new fields 3 3, 3 3 3 3 ) G, G G ) G ( + Physics at the LHC Djouadi p5/6
G 1 The Higgs in the SM the masses nd pick up the terms which are bilinear in the fields,, and thus 3 degrees of freedom for, G G,,,? ) with the value of the vev given by is preserved = ; The photon stays massless, and its conjugate field For fermion masses, use same doublet field and introduce which is invariant under SU()xU(1) C C C C C C, C C C, K K K With same, we have generated gauge boson and fermion masses, while preserving SU()xU(1) gauge symmetry (which is now hidden) What about the residual degree of freedom? Physics at the LHC Djouadi p6/6
6 G G G G G 1 The Higgs in the SM the Higgs boson It will correspond to the physical spin zero scalar Higgs particle, H The kinetic part of H field, F, Mass and selfinteraction part from, comes from term 3 Doing the exercise you find that the Lagrangian containing H is, 6 F, F F, The Higgs boson mass is given by The Higgs triple and quartic self interaction vertices are ) ) What about the Higgs boson couplings to gauge bosons and fermions? They were almost derived previously, when we calculated the masses ) K ) ) ) ) K Since v is known, the only free parameter in the SM is or Physics at the LHC Djouadi p7/6
/ I I S S P Status of the SM parameters at tree level In the SM, there are 18 free parameters ( ; = sector) fermions masses, 4 CKM parameters (see below for details) 3 coupling L L S More precise inputs, and parameters from scalar potential L R / S and Weak interactions of fermions with gauge bosons (unknown) S I R S I R I with 3families complication in CC as current eigenstates connected by a unitary transformation mass eigenstates ) ( P /) / ( / unitarity matrix; NC are diagonal in both bases (GIM) Parametrized by 3 angles and 1 CPV phase tests at B factories Physics at the LHC Djouadi p8/6
3 3 Status of the SM precision tests 7 S ( + S predicted S ( + S and R at tree level in the SM In fact, they are related by To have very precise predictions, include the radiative corrections parameter, the one to the The dominant correction is, besides DC 5 8 7 65 4 1 / 1 / EF F F B?@ ; < ;=<,+ )( Physics at the LHC Djouadi p/6
4 1 / Status of the SM high precision data Z boson lineshape parameters at LEP1 ( ) ( hadrons) Partial decay widths and asymmetries in Z decays at LEP1 ; 4 ; ; E ; ; Left right polarized asymmetries in Z decays at SLC ; 4 ; boson parameters and at LEP and Tevatron Other observables at low energy () DIS, PV in Cs and Th Use top quark mass value from Tevatron +, GeV Use value of from LEP and elsewhere /1 354 3 1 3 3 4 Use with 873 3 3 3 4 6 1 3 3 4 from low energy data Very high precision tests of the SM at the quantum level 1 1 SM describes precisely (almost) all available experimental data Physics at the LHC Djouadi p1/6
Status of the SM high precision tests Measurement Fit O meas O fit /σ meas 1 3 α (5) had (m Z ) 758 ± 35 766 m Z [GeV] 11875 ± 1 11874 Γ Z [GeV] 45 ± 3 457 σ had [nb] 4154 ± 37 41477 R l 767 ± 5 744,l fb 1714 ± 5 164 l (P τ ) 1465 ± 3 147 R b 16 ± 66 1585 R c 171 ± 3 17,b fb ± 16 137,c fb 77 ± 35 741 b 3 ± 35 c 67 ± 7 668 l (SLD) 1513 ± 1 147 sin θ lept eff (Q fb ) 34 ± 1 314 m W [GeV] 83 ± 8371 Γ W [GeV] 147 ± 6 1 m t [GeV] 1714 ± 1 1717 1 3 Physics at the LHC Djouadi p11/6
E 3 @ = < @ Q Q P P Q P P ^ ] d e T b f ] Tests of the SM gauge structure 11/7/3 LEP PRELIMINRY 3 σww (pb) WW production at at LEP 1 YFSWW/RacoonWW no ZWW vertex (Gentle) only ν e exchange (Gentle) 16 18 1, /, + )( s (GeV) ;, ; 56 8 7, 43 5 λγ κγ 15 15 D CB @ CB?( 1 1 5 5 5 5 1 1 JLO HN G M JLK HI FG 15 15 5 W VU Q 1 1 1 1 R T S R g 1 Z g 1 Z DELPHI L3 OPL 3D Fit Preliminary 5 κγ \ T Q QY P [ Z QY X 15 5 cl 1 68 cl 5 3d fit result W VU Q cb 5 ^ _a` 1 15 e VU Q QY T QYg 5 1 1 λ γ LEP charged TGC Combination Physics at the LHC Djouadi p1/6
3 Physics at LHC generalities LHC pp collider Huge cross sections for QCD processes Small cross sections for EW Higgs signal S/B a needle in a haystack Need some strong selection criteria Trigger get rid of uninteresting events Select clean channels Use different kinematic features for Higgs Combine different decay/production channels Have a precise knowledge of S and B rates Gigantic experimental (+theoretical) efforts σ (fb) 1 15 1 14 1 13 1 1 1 11 1 1 1 1 8 1 7 1 6 1 5 1 4 1 3 1 1 1 1 1 pp/pp _ cross sections σ tot σ bb _ jet σ jet (E s /) T σ W σ jet (E T σ Z jet 1GeV) jet σ jet (E s /4) T σ tt _ σ Higgs (M H =15GeV) σ Higgs (M H =5GeV) Tevatron pp _ pp LHC 1 3 1 4 s (GeV) Physics at the LHC Djouadi p13/6
B 1 + 3 5 1 1 / < <? 1 ) 3 Physics at LHC generalities Example of process at LHC to see how things work B B For a large number of events, all these numbers should be large Two ingredients hard process (, B) and soft process (PDF, hadr) Factorization theorem Here discuss production/decay process The partonic cross section of the subprocess,, is +,, / 87 6 43 ) ( ) ( Flux factor, color/spin average, matrix element squared, phase space Convolute with gluon densities to obtain total hadronic cross section = + 3 6 ; ; ; <; Physics at the LHC Djouadi p14/6
+ The calculation of 3 Physics at LHC generalities is not enough in general at pp colliders need to include higher order radiative corrections which introduce terms of order Since B? @ where Q is either large or small is large, these corrections are in general very important Choose a (natural scale) which absorbs/resums the large logs Since we truncate pert series only NLO/NNLO corrections available The (hopefully) not known HO corrections induce a theoretical error The scale variation is a (naive) measure of the HO must be small lso, precise knowledge of kinematical distributions (eg is not enough need to calculate some ) to distinguish S from B In fact, one has to do this for both the signal and background (unless directly measurable from data) the important quantity is a lot of theoretical work is needed But most complicated thing is to actually see the signal for S/B 1 Physics at the LHC Djouadi p15/6
4 SM physics at the LHC Tests of the SM and background calibration for New Physics search High jets, allows to measure physics and QCD, PDFs and check perturbation theory production for QCD dynamics (resummation, quarkonia) The physics of the bottom quarks study of QCD (as above), CKM matrix and CP violation (LHCb) The physics of the top quark plays a key role origin of EWSB and clue to SM flavour problem? since lifetime shorter than hadronisation scale, QCD laboratory The physics of bosons production allow to measure precisely and allow to measure the TGC and allow to test a strong interaction sector Physics at the LHC Djouadi p16/6
+ < 5 ; 66? 4 = 4 SM physics the top quark pp/pp _ cross sections 1 15 pp _ pp σ tot 1 14 σ (fb) LHC Tevatron 1 13 1 1 1 11 σ bb _ 1 1 1 σ jet (E T jet s /) 1 8 σ W σz 1 7 σ jet (E T jet 1GeV) 1 6 () 1 5 1 /, 1 4 _ σ tt jet σ jet (E s /4) T 1 3 1 1 σ Higgs (M H =15GeV) 1 σ Higgs (M H =5GeV) 1 1 78 5 4 3 s (GeV) 1 3 1 4 GF FFF BCED @ Physics at the LHC Djouadi p17/6
7 7 4 SM physics the W/Z bosons Single W/Z production Very large number of events Include RC Systematical errors ( cancell in the ratio, PDF s, etc) Use Z parameters from LEP1/SLC Precise measurements of Ex parameters MeV (3 MeV now) σ (fb) 1 15 1 14 1 13 1 1 1 11 1 1 1 1 8 1 7 1 6 1 5 1 4 1 3 1 1 1 1 1 pp/pp _ cross sections σ tot σ bb _ jet σ jet (E s /) T σ W σ jet (E T σ Z jet 1GeV) jet σ jet (E s /4) T σ tt _ σ Higgs (M H =15GeV) σ Higgs (M H =5GeV) Tevatron pp _ pp LHC 1 3 1 4 s (GeV) Physics at the LHC Djouadi p18/6
4 SM physics boson Physics WW/ZZ/Z production important to check SM gauge structure WW/ZZ scattering important to check a strongly interacting sector (in case where there is no Higgs boson found at the LHC) Physics at the LHC Djouadi p1/6
4 SM physics TGCs General form of the trilinear gauge boson couplings and with overall couplings In practice introduce deviations from their tree level SM values decays, distributions and Use all production processes, spin correlations (many observables) to probe Physics at the LHC Djouadi p/6
4 SM physics constraints on TGCs κ γ λ γ κ Z λ Z g 1 Z 1 1 1 1 1 1 3 1 3 1 3 1 3 1 3 1 4 LEP TEV LHC TESL TESL 5 8 1 4 LEP TEV LHC TESL TESL 5 8 1 4 LEP TEV LHC TESL TESL 5 8 1 4 LEP TEV LHC TESL TESL 5 8 1 4 LEP TEV LHC TESL TESL 5 8 Physics at the LHC Djouadi p1/6
5 4 SM physics strong W/Z sector In SM with Higgs field integrated out (too heavy or absent), non linear EWSB at scale below realisation of EWSB and (and if no resonance appears) is given by / 1 + + by ) related to the NP scale (, Coefficients, ) 43 ( data precisison by constrained, Some operators,, contribute to TGC; probed in contribute to quartic couplings and parametrize strongly interacting gauge bosons; probed in Physics at the LHC Djouadi p/6
) ) ) 4 SM physics strong W/Z sector Propagators of gauge and Goldstone bosons in a general gauge Landau gauge t HooftFeynman In unitary gauge, Goldstones do not propagate and gauge bosons have usual propagators of massive spin 1 particles (old IVB theory) t very high energies,, an approximation is components of V can be replaced by the Goldstones, The In fact, the electroweak equivalence theorem tells that at high energies, massive vector bosons are equivalent to Goldstones In VV scattering eg Thus, we simply replace + by in the scalar potential and use, + ( Physics at the LHC Djouadi p3/6
, +,, + 4 SM physics strong W/Z sector Scattering of massive gauge bosons at highenergy Because w interactions increase with energy ( Decomposition into partial waves and choose J= for terms in V propagator), unitarity violation possible, For unitarity to be fullfiled, we need the condition t high energies,, we have, For a very heavy or no Higgs boson, we have Otherwise (strong?) New Physics should appear to restore unitarity Physics at the LHC Djouadi p4/6
4 SM physics strong W/Z sector 1 75 W + W +, W W 5 W + Z, W Z α 5 5 W + W combined limit 5 5 75 ZZ 1 1 75 5 5 5 5 75 1 α 4 Physics at the LHC Djouadi p5/6
5 (e) 4 SM physics strong W/Z sector 6 8 1 1 14 16 18 4 WW Mass (GeV) (f) 4 1 3 4 5 6 7 WW cosin Cross section (fb/gev) 5 4 3 Vector (C) Continuum (E) Cross section (fb) 14 1 1 8 6 4 1 6 8 1 1 14 16 18 4 WW Mass (GeV) 1 3 4 5 6 7 WW cosin Figure 1 Differential cross section measurements at LHC assuming of luminosity and ) TeV (left) and (right) The green circles are measurements assuming a single 1 TeV vector resonance, while the red squares are measurements assuming a model without resonances Physics at the LHC Djouadi p6/6