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Lecture 15 – Next steps ● The Higgs boson ● Review of the Standard Model Problems of the Standard Model Proposed Solutions FK7003 1 The Standard Model Goal: a theory which describes all of the fundamental constituents of nature and their interactions with the minimum of assumptions and free parameters. Ultimately describe all interactions over small distance scales and cosmological observations. The Standard Model is our best attempt at this - assess how successfult in this lecture. 6 quarks, 6 leptons, 3 exchange bosons + antiparticles. Two independent forces (electroweak and QCD). 19 free parameters: particle masses, mixing angles, CP-violating term, couplings.... Consistent method of introducing interactions via so-called gauge invariance and Feynam diagram formalism (next lecture course). The Standard Model assumes massless neutrinos but this is easily fixed. Barring neutrino oscillations, the Standard Model has never failed a single experimental test. There is still one test left to pass - finding the Higgs boson. FK7003 2 The Higgs boson The missing particle in the Standard Model. Explains mass generation of the fundamental particles. The Higgs mechanism is a way of explaining why, in an apparently unified electroweak theory, the W and Z 0 are heavy and the is massless. Some consequences: A spin-0 massive boson, the Higgs particle H 0 , is required. A Higgs field pervades space: fermions interacting with the field acquire mass. A fermion with mass m f can also couple to the Higgs boson with strength g Hff . mf g Hff 2 gW (15.01) mW Couplings to other particles, with strength proportional to particle mass. FK7003 3 How do we look for the Higgs ? How is it produced and how does it decay ? At LEP: e e H 0 Z 0 208 GeV centre-of-mass energy Sensitive to Higgs masses up to 120 GeV. Production mechanism b H bb 0 bb FK7003 4 Have we already found it ? Lots of excitement around 2000/2001 as LEP reached the end of its life. FK7003 5 Observation of a Higgs ? An excess of events was seen at mass 115 GeV but reanalysis of data and rigorous statistical calculation of significance means it is impossible (and stupid) to conclude a Higgs was seen. Lower mass limit MH > 113.5 GeV (15.02) FK7003 6 Been here before - top quark nondiscovery… ● 1984 CERN ● UA1 experiment ● pp (630 GeV cm energy) ● Something they would rather forget FK7003 7 Race for the Higgs The Tevatron (pp at 2 TeV centre-of-mass energy) is now hunting the Higgs. The LHC (pp at 14 TeV centre-of-mass energy) will take up the chase in 2009. Different production mechanisms compared with LEP and different decays sought. FK7003 8 Where is the Higgs ? Excluded by direct search. Most likely Higgs mass value from fits to measured electroweak quantities in the Standard Model. The Higgs is either just around the corner or nature is more complicated than we suppose. FK7003 9 How good is the Standard Model ? Criteria Predictivity and testability U,G or VG VG – the only ’failure’ is neutrino masses and we can patch that up by adding extra parameters. Higgs yet to be found. The SM can be killed but is still v. much alive! Completeness* U – no quantum theory of gravity ? Dark matter ? …. Compactness G - Based on 19 free parameters – not bad for describing EM,weak and strong forces below 1TeV. * The focus of the rest of this lecture FK7003 10 Speculation strategy We have few answers but that doesn't mean we can't ask sensible questions. (1) At which energies can we expect that the Standard model will not describe subatomic particle interactions ? (2) In which areas is the Standard Model incomplete and which theories have been proposed address these problems ? FK7003 11 How well can we localise a particle ? To what precision can we know the position of a particle, eg electron ? In quantum mechanics the position can be known to infinite accuracy if we accept we have no knowledge of its momentum. Eg from basic quantum mechanics: Heisenberg's microscope. 1 Resolution in position x (2.36) ; probing photon wavelength. p p =photon momentum xpx px maximum change in momentum in x-direction of particle. 1 (2.12) Above picture assumes reaction: e e Quantum field theory changes this picture. If p 2me (me =electron particle) kinematically feasible reaction: e e e e Two identical particles in final state. No longer possible to say anything about electron position for p 2me . Fundamental limitation on knowledge of position: x FK7003 1 (15.03) 2m 12 Compton Wavelength More formally (and don't worry about factors of ) 2 Compton wavelength of a particle: c (15.04) m Introduced in lecture 12 as the distance below which the electromagnetic coupling constant starts to change i.e. the distance at which quantum field theory below important in describing particle behaviour. 2 Electron: c 2.43 1010 m. (12.03) me Different ways to think about this number but the point is that c that a quantum description of matter says that we can localise a particle of 2 mass m to a region of size: c . m FK7003 13 Gravity From general relativity: any object of mass m contained within its Scharzschild radius leads to a gravitational singularity (black hole): Scharzschild radius : rs 2Gm. G Gravitational constant. Quantum description of nature implies that a particle position be known to accuracy: C 2 . m However, for C rc the particle is contained within such a small size that a gravitational singularity occurs. The quantum prediction of a particle localised to a certain distance must be invalid if that localisation is taking place inside a black hole :). (naively) quantum gravity becomes important at: rc C 2Gm 2 m (15.05) m G 1 1.2 1019 GeV (15.06) (drop the ) G The Standard Model must fail for masses and energies > Planck mass and a theory of quantum gravity is needed. Formally define the Planck mass FK7003 14 Question Compare the values of the electromagnetic and gravitational attractive forces between two stationary massive particles with charges e and - e if the particles have (a) mass=1 GeV and (b) Planck mass. The particles are separated by a macroscopic distance. e2 Fem 4 0 r 2 e2 R m 2G Fgrav 4m 2 0G r2 G 6.67 1011 m3kg-1s-2 0 8.85 10 12 Fm1 e 1.602 10 19 C m 1 GeV 1.5 10 27 kg 1.602 10 R 4 3.14 1.5 10 8.85 10 19 2 27 2 12 6.67 10 11 1036 m m p 1019 GeV 1.5 10 8 kg R 102 Gravity is extremely weak until we get to the Planck scale. FK7003 15 Eg strong force becomes weak at short distances (<1fm) asymptotic freedom. measurements From lecture 12: The coupling constants vary with momentum transfer (or distance) 1/coupling Other possible energy scales E Electromagnetic Weak GUT scale Strong Log(Momentum transfer, Q(GeV) ) 33 2 N f Q s Q s M Z 1 s M Z ln 6 MZ 1 (12.05) Couplings appear to unify for Q 1016 GeV. Grand unified theories (GUTs) unify em, weak and strong forces (to come). FK7003 16 Speculation strategy We have few answers but that doesn't mean we can't ask sensible questions. (1) At which energies can we expect that the Standard model will not describe subatomic particle interactions ? Quantum gravity effects must play a role for masses and energies at and above the Planck scale ( 1019 GeV). The GUT scale ( 1016 GeV) looks a promising energy for "new physics" to appear. (2) In which areas is the Standard Model incomplete and which theories have been proposed address these problems ? FK7003 17 Problems of the Standard Model A subjective selection of three open areas in particle physics about which the Standard Model has nothing to say. (i) Cosmology: Dark matter. 22% of universe's energy budget in the form of "dark matter". Current evidence suggests that WIMPs: electrically neutral and weakly interacting massive particles with masses 1 10 TeV may be responsible ( LHC energies) (ii) Forces: unification and gravity Is there hope for a theory which unifies all of the fundamental forces or at least the strong, em and weak forces ? Why is gravity weak until the Planck mass (the hierarchy problem) ? (iii) Properties of particles: electric charge quantisation Why do we never observe particles with charge, eg, 1.5234e ? If the ultimate aim is a theory of everything which predicts particles, forces and cosmological measurements from a single principle/equations then solutions to one of the above problems should address in some way the other problems. *There's loads more, eg matter - antimatter asymmetry, the strong CP problem (why is there no observed CP violation in the strong processes), neutrino masses, dark energy etc. but we'll take (i), (ii) and (iii) as opportunities to show how a problem is defined and solutions proposed. FK7003 18 Supersymmetry Every Standard Model has a supersymmetry partner. Symmetry between bosons and fermion Quarks (fermions) Squarks (bosons) ; W , Z , , g (bosons) W , Z , , g (fermions) Symmetry is broken otherwise SM and SUSY particles (sparticleS) would have the same mass. SM and SUSY particles have different R-parity. Conservation of R-parity stops SUSY sparticles decaying to SM particles. R=(-1)3 B L 2 S 1 SM particles (15.07) = -1 SUSY partner particles. B=baryon number, L=lepton number, S =Spin quantum number. FK7003 19 Why look for SUSY ? Many reasons for looking for SUSY, amongs them... (1) It predicts a dark matter candidate: i.e. a WIMP with mass TeV. Neutralino: 0 a mixed state of SUSY partners of the Higgs, Z and . (2) Unification of the couplings is more exact if SUSY sparticles exist. Can develop SUSY grand unified theories (GUTs) which unify the electromagnetic, Standard Model Electromagnetic E 1/coupling 1/coupling weak and strong forces. Weak Standard Model+SUSY Electromagnetic Weak Strong Strong Log(Momentum transfer, Q(GeV) ) Log(Momentum transfer, Q(GeV) ) (3) Solves the hierarchy problem (beyond this course) Lecture 17 - explore how to look for SUSY at a LHC experiment. FK7003 20 Grand Unified Theories Incorporate strong, electromagnetic and weak forces into a GUT. Simplest model: SU(5) (Georgi-Glashow). Introduce new heavy exchange bosons X and Y : mass 1016 GeV. Prediction of proton decay. Violation of lepton and baryon number. Eg p 0 e Predictions for lifetime 1030 years. Current limits (SuperK- lecture) 1033 years. Other GUTS predict 1033 years. GUTs also predict heavy magnetic monopoles m 1016 GeV and explain charge quantisation. FK7003 21 Extra spatial dimensions Original ideas on extra dimensions from T. Kaluza and O. Klein (1921). Several different models incorporating extra dimensions on the market today. Large Extra Dimensions. Hierarchy problem gravity is weak since it propagates in extra dimensions (bulk) and we see a diluted form of it in our 3+1 dimension world (brane). 1 Gravitational potential V r n 1 (15.08) where r R r n number of extra dimensions. R distance scale for interactions at which the effects of extra dimensions are observed. n 2 R 1 mm (15.09) In general, many extra dimensions theories often predict "new" heavy particles with masses TeV and provide dark matter candidates. FK7003 22 Micro Black Holes at the LHC In general, when two particles pass each other with enough energy, a micro black hole can be formed. For three spatial dimensions, gravity is too weak. With extra dimensions gravity becomes stronger, micro black holes can be created. "Normal" black hole: size km, mass m sun , temperature "Micro" blackhole: size temperature 1016K, 0.01K, 10 18m, mass 1 TeV, 1027 s (evaporate through Hawking radition.) The world won't end when we turn on the LHC. FK7003 23 Electric charge quantisation Maybe its better not to be too ambitious and just focus on one specific problem. Electric charge quantisation. Why is electric charge always meaured in integer multiples of the elementary charge e ? Why are the electron and proton charges the same (barring a sign) ? qelectron q proton The best limits state: 1020 (15.10) qelectron Is there any way to accommodate electric charge quantisation within quantum mechanics ? For clarity - use practical units for following derivation. Also, we'll derive from start to finish... FK7003 24 Maxwell’s equations Electric and magnetic fields from electric charges and currents qe , e , je and magnetic charges and currents qm , m , jm e B E (15.11) ; B 0 m (15.12) ; E -0 jm (15.13) 0 t B 0 0 E je (15.14) t 1 Lorentz force law: F qe E v B qm B 2 v E (15.15) c vB E qe E v B qm v No magnetic monopoles have ever been observed qm m 0, jm 0 E e B E (15.11) ; B 0 (15.16) ; E (15.17) ; B 0 0 je (15.14) 0 t t Lorentz force law: F qE v B (15.18) FK7003 25 Monopoles and charge quantisation Alternative version of Dirac's argument (1931) Electric charge qe at origin monopoe of charge qm z r a distance d away on the z - axis. Electric and magnetic fields from qe and qm , qm respectively, at point P : qe r 0 qm r E (15.19) ; B (15.20) 3 3 4 0 r 4 r 1 2 r ' r dzˆ ; r r d 2rd cos B 2 2 P d r qe 0 qm 4 x r dzˆ r 2 d 2 2rd cos (15.21) 3 2 Momentum density in electromagnetic field : d r zˆ 0 qe qm p 0 E B (15.22) 2 3 4 r 3 r 2 d 2 2rd cos 2 Angular momentum density =r p= 0 qe qm d 4 FK7003 2 r r zˆ r 3 r 2 d 2 2rd cos 3 2 (15.23) 26 r r zˆ r r zˆ r 2 zˆ r 2 cos rˆ r 2 zˆ (15.24) The xˆ and yˆ co-ordinates will integrate to zero. Use: rˆ z cos Angular momentum in the field: L 0 qe qm d 4 2 zˆ (15.25) r 2 cos 2 1 r 2 sin drd d r 3 r 2 d 2 2rd cos 3 2 (15.26) 1 r 1 u dr 0 qe qm d Set u cos L zˆ 2 du (15.27) 2 3 4 1 0 r 2 d 2 2rdu 2 2 0 rdr r 2 d 2rdu 2 3 2 ru d 0 d 1 u r 2 d 2rdu 2 1 2 u d d 1 u 2 d 1 u 2 d u 1 1 (15.28) 2 d 1 u d 1 u 1 u du qq d 1 L 0 e m zˆ 8 d 1 1 u 1 2 2 1 0 qe qm 0 qe qm u2 zˆ 1 u du = zˆ u 8 8 2 1 1 1 0 qe qmQ zˆ (15.29) 4 FK7003 27 Dirac’s quantisation condition z Angular momentum in the field: L= 0 qe qm zˆ (15.29) 4 Obs! Independent of separation d ! Angular momentum is quantised: qe n 4 nh (15.31) 20 qm 0 qm 0 qe qm n (15.30) 4 2 r P qm d r qe x If there's one type of magnetic charge in the universe, anywhere in the universe, this "explains" why electric charge is quantised ; its a consequence of angular momentum quantisation. This is one reason why we look for them. In addition they also turn up just about everywhere else in physics (except in experiments), eg GUTs (m 1015 GeV), quark confinement models.. Possible monopole charge: qe elementary charge e ; n 1 qD h = "Dirac monopole" charge. (15.32) 0 e 0 qD2 Coupling constant for Dirac monopoles: m 34 (15.33) 4 m 1 (1) field theory/Feynman diagram formalism impossible ; (2) several thousand times greater ionisation energy loss than, eg, proton with same momentum (lecture 16). FK7003 28 Speculation strategy We have few answers but that doesn't mean we can't ask sensible questions. (1) At which energies can we expect that the Standard model will not describe subatomic particle interactions ? Quantum gravity effects must play a role for masses and energies at and above the Planck scale ( 1019 GeV). The GUT scale ( 1016 GeV) looks a promising energy for "new physics" to appear. (2) In which areas is the Standard Model incomplete and which theories have been proposed address these problems ? Dark matter, hierarchy problem, force unification, charge quantisation (to name but four) SUSY, extra dimensions, magnetic monopoles are just some of the things we've been speculating..But this is a game - we need data! FK7003 29 So how close are we to a unified theory of all the forces ? At present string theory offers the best hope. It is the most promising candidate theory for quantum gravity. However, its been the most promising theory for over 20 years now... Lecture 9 - hadron masses can be calculated using a picture of hadrons as excitations of string. This formed part of the early ideas which led to string theory. Point-like particles are tiny quantised one-dimensional strings. Extra dimensions and supersymmetry accommodated within string theory. Extremely challenging to come up with a quantitative prediction from string theory which can be tested. Time will tell. FK7003 30 Summary ● ● ● Higgs discovery would be confirmation of the Standard Model Standard Model is incomplete A range of proposed solutions exist which postulate the existence of ”new” particles which could be ”around the corner” at LHC energies. FK7003 31