Methods of Experimental Particle Physics

Methods of Experimental Particle Physics Alexei Safonov Lecture #13

Presentations • Two presentations today: • Chris Davis – about the design of the CMS Drift Tubes (DT) muon detector cells • Jeff Roe – on RICH detectors

Chris Davis Drift Tube Electrodes

Review of Drift Tubes • Filled with an Ar/CO2 gas mixture • Charged particles (muons) cause a cascade of ionized electrons • electrons detected at the anode • Question: Why are there electrodes?

Tracking with Drift Tubes • Answer is due to requirements from local trigger algorithms and reconstruction models • Require a constant drift velocity in the cell • The distance x of the track from the anode wire is • is the particle time of passage • is the time when the signal is collected

Tracking (continued) • When the drift velocity is constant • This makes it easy to tell where each track occurs. • Drift velocity is stabilized by the electrode strips on the top and bottom

At the drift velocity saturates • Each cell designed to avoid regions with lower field

Complicating Effects • Track inclination affects the resolution • electrons with the shortest drift time not produced in the middle of the cell • Magnetic field affects the moving electrons • Simulation with 0.5 T magnetic field

Source • Drift Tubes Trigger System of the CMS Experiment at LHC: Commissioning and Performances. Carlo Battilana, PhD Thesis University of Bologna.

Cherenkov Radiation and RICH Detectors Jeffrey Roe 3/18/2013

Cherenkov Radiation Speed of light in medium • Cherenkov radiation occurs when a charge particle traverses a material faster than light in that material • Predicted by Oliver Heaviside in 1888 • Discovered by PavelAlekseyevich Cherenkov (Nobel Prize 1958) • Polarization and de-excitation of molecules in the medium emits photons • In the slower than light case, photons would interfere destructively • When the photons are produced faster than the light travels, the emitted photons interfere constructively, resulting in visible photon emission at a fixed angle

Cherenkov Radiation for Particle ID • Particles lie on curves of constant mass in the “Cherenkov angle vs. momentum plane” • Can uniquely identify particles by measuring: • Cherenkov radiation angle (): RICH detector, etc. • Particle momentum: tracker, etc. The “turn-on” momentum is The “turn-off” angle is

Ring Imaging Cherenkov (RICH) Detectors • Design components • Radiating material • Optical system (optional) • Photodetector • Design considerations • Angular Resolution • Angular dispersion for different frequencies • Flaws in optical systems (mirrors, lenses, etc.) • Position resolution for detector Example RICH detectors with (left, “focusing RICH”) and without (right, “proximity RICH”) optical systemshttp://en.wikipedia.org/wiki/Ring-imaging_Cherenkov_detector • Number of collected photons • Depth of radiating material • Photon transmission trough the material and optical system • Efficiency (quantum) of photon detectors

RICH DetectorsAn Example • RICH at the HADES experiment for e+e- pairs • Relatively low particle momentum • Velocity of electrons/positrons and hadrons much different (easy to make it “hadron blind”) • Radiator: CaF2 • n = 1.0015, χ0 = 32.52 g/cm2 • High UV emittance RICH Design Example from the HADES experiment http://www-np.ucy.ac.cy/HADES/experiment/rich_detector.html • Photodetector • Segmented photocathode (CsI) • Multi-wire proportional chamber (MWPC)

RICH DetectorsMore Examples: LHCb • RICH-1: Lower momentum tracks (10-65 GeV/c) • Radiator: C4F10 • RICH-2: Higher momentum tracks (15-100 GeV/c) • Radiator: CF4 • Hybrid Photon Detectors (HPDs) • Combination of photocathodes and silicon based photodiodes RICH 2 RICH 1

Main lecture: QCD

Quantum ChromoDynamics (QCD) • Another quantum field theory • Much like QED or the electroweak part of the Standard Model • QCD describes interactions of quark and gluons, which are constituents of all hadrons • Hadrons are bound states of quarks (“matter fields”) kept together by gluons (“force carriers”) • Not too different from the hydrogen atom where charged fermions (protons and electrons, the “matter fields”) are kept together by the electromagentic field (photons, the “force carriers”) • Also based on a gauge symmetry • SU(3) in this case, which is like SU(2) but a higher dimension group

QCD Charge • The QCD Charge is “color” • In QED, the charge is electric charge • All QED interactions preserve conservation of the electric charge (can’t convert an electron into a positron by interacting with the force carriers) • In EWK theory, the electroweak hypercharge preserves the leptons and quarks from converting into each other (a muon can convert into a neutrino via interaction with W, which is the generator of the group, but it doesn’t allow it to convert into a quark as those interactions are explicitly not allowed) • QCD preserves quark flavor (a top quark cannot convert into a charm or up quark) • Quarks interact with each other by exchanging gluons but gluons do not change the flavor of the quark, it remains what it was • In some sense QCD is like QED, electrons can emit photons to interact with other electrons or positrons but you can’t kill an electron or convert it into a positron • Each quark can have three colors (that’s why it is SU(3)) • Quarks can change colors by exchanging gluons, 32-1=8 gluons as they are the generators of SU(3)

Asymptotic Freedom and Confinement • QCD is an attractive force that grows with distance • That’s why you can’t have a free quark, they always appear in “colorless” combinations • Any free hanging color will cause a huge force • This is “confinement” in QCD, it takes infinite amount of energy to separate two quarks • At very small distances (high energies), QCD force all but disappears – “asymptotic freedom”: • Quarks inside a proton are much like three pool balls inside a shell

Energy Behavior • QCD does not have the usual QFT troubles at high energy • As the force drops at small distances (large energies), there are no ultraviolet divergences and so no worries about renormalizability • Running coupling: • Where k is the usual momentum transfer (same as q2 we used before) and L is “Lambda QCD” • There are some details to it but L is about 250 MeV • But it has troubles at low energies: • Alpha becomes too large to do perturbative calculations at already a few GeV scale • Any bound states (hadrons) have typical energy transfers much smaller than several GeV’s (most of them have their entire mass smaller than a GeV)

Bound States • Despite being a nice theory, for a long time QCD has been only partially usable • What’s good in a theory that can’t predict the masses of mesons and baryons? • The issue is that we aren’t good at dealing with regimes where perturbative methods don’t work • QCD is one of them • “Lattice QCD” is an area of calculational particle physics where they calculate these using non-perturbative methods

Path Integral • This is another way to do quantum field theory • Solution functions are those that minimize action • Much like in regular mechanics • In QFT you will write something like: • An “integral over all possible functions over all possible points in space”

Path Integral in Discrete Case • It is a little difficult to grasp what is an “integral over all possible functions over all possible points in space” • It makes more sense if instead of all space, you do it on a discrete lattice, so that you sum over values at specific xi and so you are trying to find a function that gives such values f(xi) that minimize action: • Lattice QCD is effectively calculating path integrals for “x to x” transitions which are dominated by the ground state as time (T) is infinite • And so they can find masses of the ground states (mesons)

QCD Interactions • For high energy collisions, there are two main implications: • You can produce quarks in colliding beams and something needs to happen with them as they can’t live by themselves • If your collider is a hadron machine, you need to know how to calculate cross-sections as what interacts in QCD is quarks and gluons and not protons

QCD Jets • Let’s separate the problems: first lets make quarks/gluons with a e+e- machine • What will happen with it? • Turns out you get “jets” • Gluon discovery at Petra

Number of Quark Colors • Stay away from QCD yet, look at EW production of quarks at an e+e- machine • Note we can check how many colors are there:

Jet Fragmentation • As quarks can’t live by themselves, they need to bleach their color • They do it by “showering” emitting gluons that can produce quark pairs • One would have the right color to form a color neutral hadron (meson), the other one will have to get another quark from somewhere to bleach itself • As in the beginning you had a colorless system, you can always find a pair for each quark/gluon to end up with a set of colorless hadrons

Jet Production • Two things to note: • Each quark showers a lot as the QCD coupling is strong • Means we would have to do calculations to some potentially very high orders • Even though the two initial quarks give the direction and energy to two jets, they still “talk” • As they need to cancel each other’s color the color string is getting stretched producing some particles flying far from the directions of the parent quarks

Factorization • Doing any calculable predictions would be impossible without simplifications: • Break into two stages with very different energy scales: • Produce two energetic quarks • Hard process as energies are high • Very perturbative regime, calculations should work fine • Let each quark independently shower (called fragmentation) – difficult: • This is much softer process, one would wonder if QCD would even work there • At the end of it the groups of quarks/gluons form hadrons (very soft process, perturbative methods can’t work – need some modeling) • Then apply correction to account for broken strings (add particles between main quarks that are there to cancel the color flow)

Next time • QCD fragmentation • QCD in higher orders: LO, NLO, LL, NLL • Parton model and parton distribution functions

Methods of Experimental Particle Physics