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A Lecture on the Standard Model Higgs

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A Lecture on the Standard Model Higgs A Lecture on the Standard Model Higgs Eduardo Pontón IFT-UNESP & ICTP-SAIFR The Higgs in the SM Goal: To cover the theory of Electroweak Symmetry Breaking, understand the main properties of the Higgs boson resonance within the Standard Model (SM), and to review the experimental status pos-LHC Run I… Outline: • The Standard Model: Highlights • SM Higgs Properties • Production • Decay Channels • The Higgs Boson Discovery and Experimental Status • Further Remarks on the SM Structure • Further Reading (sample bibliography) The Standard Model of Particle Physics (Highlights) The Standard Model The theory describing the properties of, and interactions between all known elementary particles (… hence, in principle, of everything made of these particles!) A theory based on a gauged SU(3) SU(2) U(1) ``symmetry" C ⇥ L ⇥ Y Physics Translation: Describes spin-1 (quantum) fields coupled to the other fields (i.e. spin-1/2 and spin-0) through the Noether currents of a global SU(3) SU(2) U(1) internal symmetry: C ⇥ L ⇥ Y = + J µaGa + J µiW i + J µB + LSM ··· 3 µ 2 µ 1 µ ··· 8 color currents hypercharge current 3 weak isospin currents Until recently: all collider-experiment results could be understood just in terms of these interactions! The Standard Model Furthermore: The electroweak (EW) sector, i.e. SU(2) U(1) , is ``spontaneously broken” L ⇥ Y Translation: the vacuum we live in is not invariant under the EW transformations, so that it selects a particular direction in the internal SU(2) U(1) space… L ⇥ Y … much as the ground state of a ferromagnet, at sufficiently low temperatures, selects one direction, even if the underlying physics is perfectly rotationally invariant. Consequence: three of the EW spin-1 particles are massive (hence mediate short-range interactions) and one is massless (mediating long range interactions). + 0 These are the W ,W−, the Z and the photon. Physics: ``weak” lifetimes (e.g. beta-decay or muon decay) much longer than those of EM or strongly induced decays. The Symmetry Breaking Sector 0 A striking difference between the (massless) photon and the (massive) W ± and Z : • The photon has two physical polarizations • The massive vector bosons have three physical polarizations Clearly, the three extra d.o.f. must arise from the EW symmetry breaking sector (and we have been studying their properties for decades) These, together with the 125 GeV resonance discovered in 2012, nicely fit into the simplest imaginable picture (at least as measured by counting d.o.f.) for the symm. breaking sector! The Standard Model posits the existence of a scalar (spin-0) field, transforming as a doublet of SU(2)L and with hypercharge Y =1/2 . In the vacuum, this ``Higgs doublet” has a vacuum expectation value (VEV): 0 (The direction is conventional H = and arbitrary, given the h i v SU(2) x U(1) invariance) ✓ ◆ The Symmetry Breaking Sector The Standard Model posits the existence of a scalar (spin-0) field, transforming as a doublet of SU(2)L and with hypercharge Y =1/2 . In the vacuum, this ``Higgs doublet” has a vacuum expectation value (VEV): 0 (The direction is conventional H = and arbitrary, given the h i v SU(2) x U(1) invariance) ✓ ◆ The observed d.o.f. can be parametrized as follows: 0 H+ H = ei ~ ~⌧ · v + 1 h 0 p2 ⌘ H ``eaten NGB's" ✓ ◆ ✓ ◆ The 125 resonance (the ``Higgs boson") 2 ``Higgs field” potential: V (H)=λ H H v2 H = v 174 GeV † |h i| ⇡ (Most general renormalizable one) − The Symmetry Breaking Sector 2 2 V (H)=λ H†H v H = v 174 GeV − |h i| ⇡ 1 =2λv2h2 + p2λvh3 + λh4 m2 =4λv2 4 h Thus, within the SM, a measurement of the Higgs mass fixes the remaining free parameter: mh 125 GeV λ 0.13 ⇡ ⇡ But so far we have no direct evidence for λ , i.e. from cubic and quartic Higgs self-interactions! Measuring these interactions directly would constitute a non-trivial check of the SM h h hhhh h h Alternatively: any deviations would indicate a h hh more complicated symmetry breaking sector, h hh i.e. physics beyond the SM! 0-0 0-0 The Higgs Mechanism (or how massive gauge bosons acquire a third polarization) Gauge boson masses arise from the Higgs “kinetic term”: µ (D H)†D H where DµH =(@µ igWµ ig0/2 Bµ)H LSM ⊃ µ − − Minimal coupling prescription: @ D µ ! µ The construction that leads to consistent interactions of spin-1 fields: µ⌫ a ⌫ a @µW = JNoether conserved source Can use gauge invariance to choose: 0 0 i ~ ~⌧ i ~ (x) ~⌧ H = e · 1 H0 = U(x)H = 1 with U(x) = e v + h ! v + h − · ✓ p2 ◆ ✓ p2 ◆ In this (unitary) gauge: µ 1 µ 1 2 2 0 (DµH0)†D H0 = @µh@ h +(v + h) 01(gW 0 + g0/2 B0 ) 2 p2 ⇥ µ µ 1 ✓ ◆ The Higgs Mechanism In this (unitary) gauge: µ 1 µ 1 2 2 0 (DµH0)†D H0 = @µh@ h +(v + h) 01(gW 0 + g0/2 B0 ) 2 p2 ⇥ µ µ 1 ✓ ◆ From the h-independent terms, we read the gauge boson masses: 2 2 MW = gv/p2 MZ = g + g0 v/p2 p where 1 1 2 0 3 Wµ± =Mass(W generationµ MassiWµ ) generation andZ Higgs= andcW couplingsW Higgs+ s couplingsW inB theµ SM intW the= SM tan ✓W = g0/g p2 ⌥ µ µ Gauge bosonsGauge (V = bosonsW ± or (VZ=)acquiremassviainteractionwiththeHiggsW or Z)acquiremassviainteractionwiththeHiggs This leads to one important prediction: MW± = cW MZ vacuum condensate.vacuum condensate. The interactionsVVVVVV betweenVVVVVV the Higgs boson and the massive igMV ⌘µ⌫ 0 0 0 gauge bosons are also fixed: h 0 h h0 0 vvv vvv h h h Thus, Thus, 2 2 2 2 2 i(MV /v )⌘µ⌫ ghV V =2mV /v ,Knowsand2 aboutg hhVEWSB! V =2mV /v , 2 2 ghV V =2mV /v , and ghhV V =2mV /v , i.e., the Higgsi.e., the couplings Higgs| to couplings vector tobosons{z vector are bosons proportional} are proportional to the to the correspondingcorresponding boson squared-mass. boson squared-mass. 0 Likewise, byLikewise, replacing byV replacingwith theV Higgswith field theh Higgsin the field aboveh0 in diagrams, the above the diagrams, the Higgs self-couplingsHiggs self-couplings are also proportional are also proportional to the square to of the the square Higgs of mass: the Higgs mass: 2 2 3 3mh 2 3 3mh 2 g = λv = 3, and3mh g = λ = .3 3mh hhh 2 g = λv = , hhhhand 2 g 2= λ = . hhh v 2 v hhhhv 2 v2 The Rest of the SM (with apologies to neutrinos) The SM fermions come in the simplest (smallest) representations: singlets or fundamental i i } u YQ =1/6 Qi = L uR L i {z d i SU(3)C triplets Y =2/3 L dR u ✓ ◆ | i } Yd = 1/3 i ⌫L i − L = l {z SU(3)C singlets L li R YL =1/2 L | ✓ ◆ Y = 1 l − ( i =1, 2, 3 label the three generations) SU(2)L doublets singlets | {z } | {z } The EW part is chiral, i.e. the quantum numbers for LH and RH fermions are different! With the SM Higgs doublet, we can write the following gauge invariant terms: 0 ˜ 2 H ⇤ SM Q H˜ λuuR Q HλddR LLHλelR +h.c. H iσ H⇤ = L L ⌘ H− L ⊃− − − ✓− ◆ Yukawa matrices The Rest of the SM (with apologies to neutrinos) With the SM Higgs doublet, we can write the following gauge invariant terms: Q H˜ λ u Q Hλ d L Hλ l +h.c. LSM ⊃− L u R − L d R − L e R 1 The generation of masses for quarks and leptons is especially elegant in = (v + h) u λ uthe+ SMd (inλ otherd + approachesl λ l to+h EWSB,.c. fermion(in mass unitary generation gauge) is often − p L u R L d R L e R 2 achallenge).ThefermionscoupletotheHiggsfieldthroughthegauge One can furthermore diagonalize⇥ the Yukawainvariant matrices Yukawa couplings, (and choose e.g., real,⇤ positive eigenvalues) by rotating independently the LH and RH components (in generation space) 0 + 0 Yukawa = hu(¯uRuLΦ u¯RdLΦ ) hd(d¯RdLΦ ∗ + d¯RuLΦ−)+h.c. (the rotation matrices appear only in the interactionsL with the− charged W’s: the− CKM matrix)− The quarks and charged leptons acquire mass when Φ0 acquires a vacuum One notices that: the eigenvalues above expectation value: • The Higgs VEV leads to fermion masses: mf = λf v ffff • There are Yukawa interactions proportional to the fermion mass: v h0 Thus, Hence the discovery of the Higgs boson amounts to the discovery of new, non-gauge interactions! ghff¯ = mf /v , … and with a veryi.e.,Higgscouplingstofermionsareproportionaltothecorresponding distinctive pattern of strengths! fermion mass. Particle content of the Standard The SM Field ContentModel Particle Something is content of missing… the Standard Model Something is missing… Higgs Production h hh h h hhh hh h Singlehhe−,u,d Higgs Production h h h h hh We have seenh that the Higgs hhcoupleshe+, u,¯ d¯ most stronglyhh to the heavier particles… − e−,u,d e−,u,d e ,u,d h h ∗ … but our beams (and, moduloe−,u,d DM, our universe) hare made mostly of the lightest particles! Z h h Z∗ hh h + ¯ − + ¯ ¯ e , u,¯ d e ,u,d e+, u,¯ d¯ e , u, d + ¯ ¯ Z e , u, d Z h Hopeless! e−,u,d h e− h q′ − ∗ h Z∗ e+, u,¯ d¯ e h Z Z∗,W∗ Z∗ e+Rather,, u,¯ d¯ look for processese−,u,d involving the heavy gauge bosons: e+ q¯ Z e+ h Z Z, W Z∗ Z − ′ e h q h f1 f3 Z∗ + ¯ ¯ ∗ ∗ V e , u, d Z Z ,W h + − ¯ V e e Z q h Z, W f2 f4 Z∗ ′ q(At leptons colliders) h 0-0 ∗ ∗ (At hadron colliders) (Vector Boson Fusion or VBF) Z ,W + e Z q¯ ′ q Z, W h Z∗,W∗ 0-0 0-0 ¯ q Z, W 0-0 h hh h h hhh hh h hhe−,u,d h h h h hh h hhe+, u,¯ d¯ − e−,u,d e−,u,d e ,u,d h ∗ e−,u,d h Z h Z∗ h + ¯ + ¯ ¯ e , u,¯ d e+, u,¯ d¯ e , u, d + ¯ ¯ Z e , u, d Z e−,u,d h e− h q′ − ∗ h Z∗ Singleh eHiggshh Productionh Z Z∗,W∗ Z∗ h hh h h e+, u,¯ d¯ e+ q¯ Rather, look for processesZ involvingh ethe+ heavyhh gauge bosons: Z Z, W h Z hh − − − e ,u,d e ,u,d ′ −h e h q− ∗ h e ,u,d f1 f3 ∗ e ,u,d ∗ ∗ Z h Z Z ,W Z∗ V h h h + ¯ + ¯ ¯ e , u,¯ d e , u, d + ¯ V + +¯¯ ¯ eZ, u,¯ d e Z e q, u, d Z, W f2 Z f4 − ′ ′ e h − q h ′ ∗ e ∗ ∗ h0-0 q h q(At leptons colliders) hZ (At hadron∗ Zcolliders),W (Vector∗ ∗ Boson Fusion or VBF) Z∗,W∗ Z Z ,W + Or the heavier efermions: e+ q¯ q¯ ¯ Z Z Z, W Z, W q Z, W ¯ ¯ ¯ ¯ t t b b
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