Arnaud Ferrari. Uppsala, April Department of Physics and Astronomy Uppsala University, Sweden. Advanced Particle Physics:

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1 Department of Physics and Astronomy Uppsala University, Sweden Uppsala, April

2 Outline and E miss

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4 (1) In order to interpret the experimental observations of a high-energy particle collision, one needs to accurately measure: the four-vectors of the incident particles (initial state), the four-vectors of all outgoing particles (final state). he mass of intermediate short-lived particles can be reconstructed from the energy-momentum balance of the four-vectors of the final state decay products: E 2 = (mc 2 ) 2 + (pc) 2. In addition, one needs a good time resolution to separate the collision events from each other. 4

5 (2) must measure accurately all decay products of the particle(s) created at the collision point. However: In a detector, the basic experimental observables are NO four-momenta! One detector can not provide enough information on its own in order to identify all final state particles and measure their energies and momenta! One must gather information from several sub-, each providing some level of particle identification and kinematical measurement. 5

6 (3) 6 his lecture is organized with the same structure as the Chapter 5 in Elementary Particle Physics in a Nutshell: 1, 2.,. 3, 4.,. 5 Special objects:, E miss. It will be followed by a basic overview of experimental methods and statistical treatments used in high-energy physics. data-analysis

7 Kinematics at hadron colliders At a pp or p p collider, the longitudinal momentum of the partons in collision is unknown one needs kinematical variables that are invariant under longitudinal boosts: the transverse energy or momentum (E or p ) with: E = m 2 + p 2 the azimuthal angle φ, ( the pseudo-rapidity η = ln tan θ z 2 η is an ultra-relativistic approximation of y = 1 2 lne + p z. E p z With these kinematic variables, the four-momentum of an (ultra-relativistic) object is defined by: ( E p ) = E coshy p cos φ p sin φ E sinhy p ). coshη cos φ sin φ sinhη 7

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9 particle interactions (1) Both electrons and photons can be detected via their electromagnetic interaction with a non-zero nuclear charge in the medium through which they pass. Starting from high-energy electrons and photons, two processes are dominant: e + e pair production for high-energy photons, Bremsstrahlung (braking radiation) emission for high-energy electrons and positrons. 9

10 particle interactions (2) he pair production by photons and the Bremsstrahlung emission by electrons/positrons lead to the development of an electromagnetic (EM) shower: A high-energy photon produces one electron and one positron in the vicinity of a non-zero nuclear charge, Each electron/positron radiates a Bremsstrahlung photon in the vicinity of a non-zero nuclear charge, Each new photon produces one e + e, etc... 10

11 particle interactions (3) Important remark: Bremsstrahlung emission is the same process as synchrotron radiation in a circular accelerator, i.e. electromagnetic radiation emitted when a charged particle is accelerated radially, by a nucleus in matter or by an external magnetic field... he radiated power is very collimated and proportional to E 2 /m 4 with E the energy and m the mass of the incoming particle important for high-energy electrons, negligible for low-energy and/or heavier particles such as protons, muons, etc... 11

12 Radiation length (1) If σ r is the Bremsstrahlung emission cross-section, the cross-section for e + e pair production is a factor of 7/9 smaller. For a medium with N atoms per cm 3, the characterisitic radiation length X 0 is defined as: the mean distance over which a high-energy electron has lost 63% of its energy through Bremsstrahlung emission, a fraction 7/9 of the mean free path for e + e pair production by a high-energy photon. X 0 is inversally proportional to Nσ r. 12

13 Radiation length (2) Values of radiation lengths can be found on the PDG website: A A good approximation is: X 0 = ) Z (Z + 1)ln( 287 Z with A the atomic mass (g/mol). he radiation length is in g/cm 2, or in cm when divided by the density ρ. For a composite material, using the mass fractions w i of each component: 1 = X 0 i w i X 0,i. Exercise: what is the radiation length of the epoxy C 60 H 79 N 2 O 3 with density 1.33 g/cm 3? 13

14 Molière radius and critical energy What about the transverse extension of EM showers? he Molière radius R M is another characteristic constant of a material, related to the transverse dimension of EM showers initiated by a high-energy electron or photon: 21 MeV R M X 0 E c where the critical energy E c is the energy at which an electron loses as much energy via the Bremsstrahlung emission as through ionization: E c 710 MeV Z (gas) or E 610 MeV c Z (liquid/solid). Or check: In order to contain an electromagnetic shower, one needs 20 25X 0 in the longitudinal direction, and 2 3R M in each transverse direction. 14

15 Energy loss for low-energy electrons Below the critical energy E c, electrons primarly lose energy via Coulomb forces with orbital electrons in the material. Each encouter results in energy transfer from the incident electron excitation or ionization of an atom. Positrons lose their energy in the same manner, however annihilation occurs at the end of the positron track. Bethe-Bloch formula for e ± energy losses: ( ) de dx = 2π 2 ( [ ] m e c 2 e 2 n β 2 E m e c 2 4πε 0 β 2 ln 2(1 β 2 )I 2 (ln2)(2 1 β β 2 ) + (1 β 2 ) + (1 ) 1 β 2 ) 2 n is the electron density, given by n = N A (Z ρ/a), where N A is Avogadro s number, I is the average excitation and ionization potential of the absorber (usually tabulated). 8 15

16 Energy loss for low-energy photons (1) Photo-electric absorption: a photon interacts with an atom and disappears, leaving place to an energetic photo-electron, ejected by one of the atomic shells: E e = hν E b An ionized absorber atom is also created with a vacancy in one of its shells, so the photo-electric absorption may be accompanied with X-rays. his is the dominant photon interaction at low energy, with a probability: σ ph Z 5 E 7/2 γ Absorption edges appear at the energies corresponding to the binding energies of various shells. 16

17 Energy loss for low-energy photons (2) Compton scattering: a photon is deflected with an angle θ and transfers a fraction of its energy to an electron. hν hν = 1 + hν (1 cos θ) m e c2 he probability of Compton scattering increases linearly with Z as it depends on the number of available electrons. he Klein-Nishina formula gives the angular distribution of the scattered gamma-rays as a function of θ and hν. here is a strong tendency for forward scattering at high energy. 17

18 wo types of electromagnetic A high-z material is needed to contain the shower within a reasonable volume. he energy of the incident particle is derived from the signal coming from absorbed photons and/or the drifting ions in a high electric field. Homogeneous calorimeter: he entire volume is sensitive and contributes to the detected signal. Inorganic heavy scintillating crystals or ionizing noble liquids with a high Z. Sampling calorimeter: It has both an active medium which generates signal and a passive medium working as an absorber. he active medium is a scintillator, an ionizing noble liquid, a gas chamber, or a semiconductor. he passive medium is a material of high density, such as lead, iron, copper, or depleted uranium. 18

19 he ALAS electromagnetic calorimeter b-jets, τ -leptons and Emiss 19 Sampling calorimeter with an accordion shape, using lead (Pb) as a passive medium and liquid argon (LAr) as an active medium. Central presampler layer to correct for energy losses in dead material upstream.

20 he CMS electromagnetic calorimeter Homogeneous calorimeter made of lead tungstate with a touch of oxygen to make the PbWO 4 crystals transparent and scintillating when hit by electrons or photons. Photo glued onto the back of each crystal detect the scintillation light and convert it to an electrical signal. here is a high-granularity pre-shower layer (Pb with Si-sensors) in the forward regions. 20

21 Energy resolution σ(e) E = N E S E C N is the electronic noise, with also a component from the pile-up (i.e. signals from minimum-bias events in the same or neighbouring bunch crossings). S is a stochastic term (statistical fluctuations, e.g. from the shower, light yield, sampling, etc). C is a constant term, dominant at high-energy: intrinsic non-uniformities, cell-to-cell calibration inaccuracies, radiation damage, etc. ypically, e.g. for ALAS and CMS, N = GeV and C %, but S varies from 2-3% for homogeneous to 10% for sampling. 21

22 Spatial resolution An electromagnetic calorimeter should not only measure accurately the energy but also the position of electrons and photons. he spatial resolution: depends on R M and the transverse granularity, has a dependence a b. E a can vary from a few to 20 mm, b can be below 1 mm. Very important for photon-related physics, because photons do not leave any track in the inner detector... Indeed, the only way of distinguishing electrons from photons is the presence/absence of a matching track upstream of the electromagnetic shower!! *** 22

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24 Basic concepts (1) An electron is distinguished from a photon primarily by the presence of a charged track in the inner detector, pointing to the center of the electromagnetic shower. Basic concept: a charged particle disturbs the material through which it passes, via Coulomb forces. From the track left behind charged particles, a keen observer can deduce: Identity: what made the track? Position: where did it go through? Direction: which way did it go? Velocity: how fast was it moving? 24

25 Basic concepts (2) he footprint of a charged particle in a tracking detector (e.g. a bubble chamber) is an excitation/ionization of the material. 25

26 Basic concepts (3) 1) A charged particle transfers energy to an atom, creating a ion-e pair (in a gas) or a hole-e pair (in a semi-conductor). 2) An ambient electric field is applied across the medium to separate electrons from ions/holes. 3) he drifting charges are collected on anodes and cathodes, where a signal is measured. 26

27 Bethe-Bloch formula (1) We generalize the Bethe-Bloch formula to any particle of charge ze... With the relativistic formalism (β = v/c and γ = 1/ 1 β 2 ): de dx = K Z ( [ ] ) 1 z2 A β 2 max ln β 2 I With Avogadro s number N A and r e = e 2 /(4πɛ 0 m e c 2 ): K = 4πN A r 2 e m e c 2 = MeV.g 1.cm 2, max = 2m e c 2 β 2 γ 2 is the maximal kinetic energy that can be transferred to a free electron, I is the average excitation and ionization potential of the material (tabulated). 27

28 Bethe-Bloch formula (2) he energy loss rate is in MeV/(g.cm 2 ), or in MeV/cm when divided by the density ρ. 28 For a given material, the energy loss rate depends on β and z only. Low β: de/dx 1/β 2. High β: de/dx grows slowly, then saturates. he energy loss rate has a minimum for βγ 4, where all charged particles behave as Minimum Ionizing Particles (MIPs), with de/dx 1-2 MeV for each g/cm 2 of material (except hydrogen).

29 Additional effects (1) An orbital electron scattered by a charged particle may have enough energy to ionize more atoms, so the total number (N ) of electron-ion pairs is usually larger than the number of primaries (N P ). 29

30 Additional effects (2) A charged particle passing through a material may change its direction as a result of multiple scattering. For a material layer of length x, the change of direction θ with respect to the incident charged particle follows a Gaussian distribution with a rms value: x θ rms = 13.6 MeV z βpc X 0 For relativistic particles, θ rms 1/p, ( ln xx0 ). o minimize multiple scattering, the tracking detector should be light, i.e. x X 0. his latter requirement also helps reduce energy losses via Bremsstrahlung emission for electrons inside the inner detector, before reaching the electromagnetic calorimeter. 30

31 Drift velocity and spatial positioning (1) Knowing the drift velocity of the charges in the material, then the drift time (that elapses before the charges are incident on the collection electrode) is used to compute the spatial coordinates where ionization first occurred. 31

32 Drift velocity and spatial positioning (2) In a gas detector with pressure p: For ions: v D = µe p where µ is the mobility (fairly constant over wide ranges of E and p). For free electrons: acceleration between encounters, much larger mobility than ions and dependent on E... but it saturates at high values of the electric field for some gases. In a semi-conductor: Both for holes and electrons can drift, with v h D = µ he and v e D = µ ee of roughly the same order. he mobilities may depend on E, but saturate at high values of the electric field. In both cases, the diffusion of charge carriers (random fluctuations of their drift path) limits the precision of the measurement. 32

33 ransverse momentum measurement and resolution (1) A tracker is a detector that measures spatial coordinates along the trajectory of a charged particle. hese spatial coordinates need to be associated with one same track to measure the properties of the trajectory: proximity of the track to a (primary or secondary) vertex, impact point on the calorimeter, curvature due to the motion of charged particles in a magnetic field measurement of the transverse momentum p. 33

34 ransverse momentum measurement and resolution (2) For a circular trajectory in the bending plane, with a radius of curvature R (m) in a magnetic field B (): p = 0.3BR [GeV/c] he sagitta (maximum deviation of the track from a straight line) for a tracker level arm L (m) is: s 0.3BL 2 /(8p ) he tracker provides a (second) measurement of the energy/momentum of charged particles! 34

35 ransverse momentum measurement and resolution (3) σ(p ) p = C 0 C 1 p he most degrading effect from the material in the tracker is multiple scattering, with random deflecting angles depending on the thickness and density of the detector, but reduced in high magnetic fields: C 0 = 0.5 2%. High-p tracks have little deflection in the magnetic field, leading to possible charge misidentification: C 1 = (GeV/c) 1. Note that tracks with less than MeV/c in p curl in the magnetic field and do not reach the. 35

36 Example: the ALAS inner detector (2) Pixel detector High granularity and high precision measurements near the interaction point. Very helpful to detect the secondary vertices from short-lived particles. 3 layers of semi-conductor pixels with radii between 5 and 15 cm. he 80 million pixels cover an area of 1.7 m 2. he pixel detector must withstand over neutrons per cm 2 during 10 years of operation. At normal incidence, the thickness of each layer is about 0.025X 0. 36

37 Example: the ALAS inner detector (3) 37 Semi-Conductor racker Gas detector with straws of 4 mm diameter with a tiny central wire. Spatial resolution of 170 µm per straw. ransition radiation from e ± in a dielectric radiator between the straws help to reject charged hadrons. 4 double-sided layers of Si micro-strip, each of cm 2 with 780 readout strips of 80 µm. Modules mounted at radii between 30 cm and 52 cm, covering an area of 61 m 2. ransition Radiation racker

38 EXERCISE A photon with an energy E = 10 GeV interacts with the material of the beam pipe and produces an e + e pair, where the electron and the positron have a transverse momentum p = 5 GeV/c each: What is the electromagnetic calorimeter energy resolution for the photon if N = 0.1 GeV, S = 5% and C = 0.05%? What is the transverse momentum resolution for the electron or positron if the tracking system has C 0 = 1.5% and C 1 = (GeV/c) 1? For which photon energy would the two resolutions above be comparable? 38

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40 Basic concepts QCD tells us that one can not observe single quarks and gluons... Instead they hadronize into composite objects: pions, protons, neutrons, etc. In order to detect primary quarks or gluons, one must reconstruct hadronic jets. Charged hadrons leave tracks in the inner detector, but neutral hadrons don t incomplete information about hadronic jets from tracking. For the same calorimeter material, the cross-section for hadrons is about one order of magnitude smaller than for an electron or a photon: an electromagnetic calorimeter is mostly blind to hadronic jets. hick and dense hadronic are needed to measure the energy and position of jets. 40

41 showers (1) he physical processes causing the propagation of hadronic showers rely on the strong interaction, and differ from the processes in electromagnetic showers. Inelastic hadronic interactions include multiparticle production, nuclear decays of excited nuclei, etc... hese processes yield many secondary particles, mostly pions and nucleons. In hadronic showers, as neutral pions decay into photons, there is an electromagnetic component: π 0 γγ. Charged pion decays via the electroweak interaction lead to some loss of signal: π ± µν. Back-scattering and nuclear excitation, break-up or evaporation a large amount of the initial energy is not converted into a measurable signal. 41

42 showers (2) showers are characterized by the nuclear interaction length λ, which is the mean free path of a particle before undergoing a nuclear absorption, in a given medium: A λ = σ abs N A ρ A is the atomic mass (g/mol), N A is Avogadro s number and ρ is the density, σ abs is the cross-section for nuclear absorption. λ is energy- and particle-dependent: it can be 1.5 times longer for pions than for protons. If σ abs is replaced by the total nuclear cross-section σ, one obtains the collision length λ. 42

43 showers (3) In general, λ X 0 so a hadronic calorimeter needs more depth than an electromagnetic calorimeter. Longitudinal development of hadronic showers: strong peak around λ, followed by an exponential decrease. For example, 350 GeV pions need about 8λ to deposit 95% of their energy. Lateral development of hadronic showers: about λ at the peak, with a well-defined core of radius R M from the electromagnetic component. showers develop in less than 1 ns... but hadronic showers need up to 1 µs. 43

44 Constraints on hadronic (1) must be: massive, thick (about 10 λ) and hermetic, sampling, i.e. made of repetitive layers of dense absorbers for hadronic shower development and of active material (e.g. scintillators) for the signal collection. ALAS and CMS (central) hadronic : both use plastic scintillating tiles as active material, where the ionization energy from charged particles is converted into an optical signal, then measured by photo. the absorbers are steel or brass for CMS, iron for ALAS. 44

45 Constraints on hadronic (2) he ALAS ile Calorimeter: 8 m in diameter + covers 12 m along the beam axis. In the far-forward sections, the hadronic calorimeter uses liquid argon (as the electromagnetic calorimeter) with copper and tungsten as absorbers. 45

46 Constraints on hadronic (3) Energy resolution: σ(e) E = A E B A = (statistical) fluctuations of: shower shape, particle content and multiplicity, electromagnetic component in hadron showers (f EM ), invisible energy... B = inhomogeneities and shower leakage. * For ALAS, A 50% and B 3%. * For CMS, A 100% and B 5% (not as deep hadronic calorimeter, inside the solenoidal coil). he term C/E is usually negligible in hadronic. 46

47 Constraints on hadronic (4) A significant contribution to the energy resolution is e/h: he electromagnetic component from π 0 γγ has a higher response than the hadronic component (due to its invisible energy): ε EM ε HAD. he effects of fluctuations in f EM and non-linearities are worsened when the e/h ratio differs from 1: E shower = E true [f EM ε EM + (1 f EM )ε HAD ]. Compensating have ε EM = ε HAD but are not easy to achieve: add materials that decrease ε EM or increase ε HAD, offline corrections when the shower profile is known: calibration, weighting of individual cells with more or less signal, etc. 47

48 Jet algorithms (1) Until recently, the most commonly used algorithms to reconstruct.. hadronic jets were cone algorithms: 1 Start from a seed p i (for instance a high-e calorimeter object). 2 Use all objects p j inside a cone of radius R. centered on the seed to build a proto-jet: R ij = (η i η j ) 2 + (φ i φ j ) 2 < R. 3 Use this proto-jet as a new seed, and repeat the procedure above until a stable solution is found (in terms of energy and direction for the proto-jet). 4 Repeat until all objects above a seed threshold are used once! Such algorithms need a seed threshold and a cone size. But,. they can run into trouble when choosing a seed and dealing with overlapping cones. 48

49 . Jet algorithms (2) Clustering. algorithms are now commonly used: 1 For two objects p i and p j (e.g. calorimeter cells, high-p tracks), define a distance:. D ij = Min(p 2p i, p2p j ) R2 ij R 2 ; D i = p 2p i 2 If the minimum distance is D i, then the object p i is a jet and is removed from the list of objects. Otherwise, p i and p j are merged into a new object. 3 Repeat until all objects are used.. wo parameters need to be set: the distance R (usually 0.1 1) reflects the level of detail for the jet sub-structure. p = 1, 0, 1 correspond to various algorithms: k, Cambridge-Aachen, anti-k. 49

50 EXERCISE Compute the number of Gaussian sigma separations between the reconstructed mass peaks of a W boson and a Z boson decaying at rest into a pair of jets with equal energies. Use the hadronic calorimeter energy resolution of ALAS first, and then of CMS. Assume that the angular resolution is negligible in both cases. 50

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52 interactions s are the only long-lived charged particles with a minimal cross-section up to nearly ev energies minimum ionizing particle through the whole detector! In addition to the track left in the inner detector, muons are identified using a large muon spectrometer placed around the. 52

53 Basic concepts (1). In order. to detect muons, one needs: 1 a large magnetic field to bend the muon trajectories and thereby measure their charge and transverse momentum. 2 drift chambers to detect the ionization signals from muons: these must be precisely aligned to minimize. errors on the sagitta.. 3 resistive plate chambers for triggering purposes: the electrons from the ionization hit other atoms causing an avalanche, then a signal is picked up by external metallic strips after a small but precise time delay to give a quick measure of the muon momentum. 4. enough material upstream (in the ) to suppress the probability that some charged hadrons punch through, leaving tracks in the muon chambers. 53

54 Basic concepts (2) Reminder: σ(p ) p = C 0 C 1 p the stand-alone muon spectrometer usually has a somewhat larger multiple scattering term C 0 than the inner detector, the muon spectrometer provides an additional level arm and thereby reduces the effective term C 1 with respect to using only the tracker. he primary function of the muon chambers is to identify muons escaping the and to improve the measurement with respect to the stand-alone tracker. 54

55 he CMS muon spectrometer use the return flux of the solenoid field concentrated within layers of iron between tracking chambers, drift tubes and cathode strip chambers are used in the central and forward sections to detect muons, resistive plate chambers for triggering purposes. 55

56 he ALAS muon spectrometer (1) he design is similar to the CMS muon spectrometer, with a different technology for the magnetic field. three superconducting air-core toroids to create a strong magnetic field, drift tubes and cathode strip chambers are used in the central and forward sections to detect muons, resistive plate chambers for triggering purposes. 56

57 he ALAS muon spectrometer (2) b-jets, τ -leptons and Emiss 57

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59 Detection of b-jets (1) he behavior of the heaviest quarks is special from the detector s point of view. op quarks decay before they have time to hadronize: t Wb in nearly 100% of the cases detection and reconstruction of its decay products (W also decays immediately). Bottom quarks form B-hadrons with a finite lifetime and hence a decay length of a few mm identification of heavy-flavor jets with a displaced vertex. 59

60 Detection of b-jets (2) B-hadrons usually decay within the beam pipe: the displaced vertex must be reconstructed by extrapolating charged particle tracks. his is performed by a vertex detector installed very close to the beam pipe, with at least 3 radial layers of measurements. Vertex handle a high flux of closely spaced particles as well as processes such as γ conversion in the beam pipe, in a very exposed environment! Silicon pixel sensors are used for this purpose, with up to 100 million channels. 60

61 Detection of b-jets (3) Pixel can help reconstruct primary vertices (from the collisions) with a resolution of µm. Pixel can find secondary (even tertiary) vertices from the finite lifetime of B-hadrons (even D-mesons and kaons) measurement of an impact parameter of tracks to the primary vertex, with a resolution of µm. a hadronic jet matched to a collection of associated tracks with large impact parameters (and thereby a low probability to come from a primary vertex) is a signature for b-jets! Several b-jet algorithms exist... he rate for mistagging light-quark or gluon jets as b-jets is usually in the 0.1-1% range, depending on the b-tagging efficiency. 61

62 Detection of τ-leptons (1) Decay modes and branching ratios of charged leptons: Lepton Decay mode Branching ratio e stable - µ e ν e ν µ 100% τ e ν e ν τ 17.8% µ ν µ ν τ 17.4% hadronic 1-prong 50.1% hadronic 3-prong 14.6% hadronic 5-prong 0.1% 1-prong: π ν τ, π π 0 ν τ, π π 0 π 0 ν τ, etc... 3-prong: π π + π ν τ, π π + π π 0 ν τ, etc... he τ-lepton is unique among the leptons because it can decay hadronically! 62

63 Detection of τ-leptons (2) he electrons/muons coming from a leptonic τ decay are usually hard to distinguish from prompt electrons/muons. 63 A hadronically decaying τ has properties similar to hadronic jets, but with some important differences: a low track multiplicity (1 or 3), some energy deposition in the electromagnetic calorimeter, due to π 0 γγ, a high p boost leading to a narrow and well isolated jet of particles... Identification algorithms can identify hadronically decaying τ-leptons with efficiencies up to 40% and mistag rates around 0.1%. Problem: the momentum of the hadronic τ is not fully reconstructed (neutrinos)...

64 Missing transverse energy (1) Neutrinos (and possibly other hypothetical weakly interacting stable particles) escape the without leaving any trace of their passage... ANY??? At hadron colliders, the longitudinal momenta of the colliding partons is unknown it is impossible to measure any missing energy in the longitudinal direction! However, the transverse energy (un)balance can be measured and used as a physics signature for one or several non-interacting particles. he missing transverse energy/momentum E miss is also a detector object. 64

65 Missing transverse energy (2) he E miss vector is calculated by summing individual calorimeter clusters: E miss = ( ) En cos φ n E n sin φ n i + j coshη n n coshη n = Ex miss i + E miss y j s are taken into account by subtracting the expected minimum ionizing calorimeter energy deposit and adding p from each muon track. Any correction made to a reconstructed detector object must be propagated to E miss. 65

66 Missing transverse energy (3) he E miss resolution depends on the overall activity in the event, measured by E : more objects high chance to mismeasure the missing transverse energy: for events which have no intrinsic E miss, one finds σ(ex,y miss ) S E, with the stochastic term S in the range %, in the high- E region, a constant term of 1-2% dominates the E miss resolution. In events with large missing transverse energy, it is common to use the E miss significance to reject events where the missing transverse energy may come from mismeasurements: Sig(E miss ) E miss E 66

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68 (1) b-jets, τ -leptons and Emiss 68 Differences between the ALAS and CMS : in terms of design, in terms of performance.

69 (2) While ALAS uses two magnet systems for the inner detector and for the muon spectrometer, CMS uses one solenoid (with a return yoke) and must be much more compact. 69

70 (3) Magnets: 2 solenoid + three toroids (0.5 to 1 ) for ALAS, 4 solenoid + return yoke for CMS. Inner detector: Silicon pixels and strips + R for ALAS, Full silicon tracker for CMS. calorimeter: LAr + Pb for ALAS, PbWO 4 crystals for CMS. calorimeter: Fe + scintillators or Cu/W + LAr (10 λ) for ALAS, Brass + scintillators (7 λ + catcher) for CMS. spectrometer: Similar designs, different magnetic fields. 70

71 (4) Differences in energy resolution: racker: σ(p )/p p 0.01 for ALAS, σ(p )/p p for CMS. calorimeter: σ(e)/e 10%/ E 0.7% for ALAS, σ(e)/e 3%/ E 0.3% for CMS. calorimeter: σ(e)/e 50%/ E 3% for ALAS, σ(e)/e 100%/ E 5% for CMS. s: σ(p )/p 2% at 50 GeV, 10% at 1 ev for ALAS, σ(p )/p 1% at 50 GeV, 10% at 1 ev for CMS. 71

72 (5) racker: CMS has a better momentum resolution than ALAS; Vertexing and b-tagging performances are similar; ALAS has better reconstruction efficiencies for electrons and pions than CMS. calorimeter: CMS has a better intrinsic resolution than ALAS, but ALAS has a better e/γ identification. calorimeter: ALAS has a twice better resolution than CMS, both for jets. s: ALAS has better stand-alone capabilities for its spectrometer (less multiple scattering), but CMS has a better combined momentum resolution. 72

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74 Some challenges at the LHC (1) It is impossible to keep all events produced in a detector trigger menus to keep events with interesting physics and reduce the rate of events from several MHz to about 200 khz. he higher the luminosity, the tighter the trigger menus. 74

75 Some challenges at the LHC (2) Each proton bunch-crossing yields several pp collisions, most of them are not interesting from the physics point of view pile-up of minimum-bias events! Pile-up leads to several primary vertices, extra energy depositions in the... 75

76 Simulations and data-analysis (1) he first step of any analysis in particle physics is to choose a model to be tested, and to implement all its predictions into an event generator (usually done with theorists/phenomenologists). he event generators for a specific model and for all backgrounds are then interfaced to a detailed detector simulation framework. Millions of events are generated, simulated and stored on the world-wide grid (this can take weeks). Using simulations, event selections must be optimized to obtain the best sensitivity of the signal with respect to the Standard Model backgrounds. 76

77 Simulations and data-analysis (2) Control regions (that are free of signal!) are used for a first comparison of simulations and data, in the case of known Standard Model processes. Discrepancies may indicate systematic errors in the detector simulation. A set of corrections is derived and then applied to the simulations, with associated systematic uncertainties. hen, a signal region (i.e. an event selection sensitive to the signal) is defined. here, the distributions of some discriminative variables are compared to assess the compatibility of the data with the predictions from the simulations, in the absence/presence of a new signal. Exclusion plots... which can be used for a discovery! 77

78 Simulations and data-analysis (3) Let s compare some hypothetical data with the predictions of the Standard Model, with or without a signal. black points close to the green curve: evidence for new physics, black points on or below the dashed black curve (i.e. background): no evidence for new physics some parameters in the corresponding model can be ruled out, with some level of confidence. 78

79 : exclusion plot Horizontal and vertical axes Parameters from a new theory to be excluded, e.g. m H and σ H for a Higgs boson. 79

80 : exclusion plot Solid black line Exclusion with a 95% certainty that a Higgs boson with the given mass does not exist. 80

81 : exclusion plot Dotted black line Expected limit in the absence of a Higgs boson (derived from simulation). 81

82 : exclusion plot Green and yellow bands 68% and 95% certainty on the value of the expected limit. 82

83 : exclusion plot Deficit Less data than the expected background. he observed limit is below the expected limit. 83

84 : exclusion plot Excess More data than the expected background. he observed limit is above the expected limit. 84

85 : exclusion plot White vertical bands = non-excluded Higgs boson masses... but it does not mean discovery! 85

86 Recipe for a discovery What is needed in order to discover new physics? the solid black line must be above the dotted black line (excess of data with respect to the background), in the case of a comparison with the Standard Model, the solid black line must be above the Standard Model reference. For a given point, when the solid black line is at the upper edge of the yellow band, there is a 95% certainty that the observed data exceed the background expectations. So, there is still a 5% chance that background processes or systematic errors in the detector are not well understood. For a discovery, we want the chance that the observed data come from background fluctuations or systematic errors to be less than one in a million: %! 86