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Home , Color charge, Force carrier, Weak charge, Weinberg angle

Particle 627: Ordering

Dr. Rupak Mahapatra Week 4 Chapter 3 Particle Classification: and

• Fermion – ½ particle – Obeys Fermi Statistics

– No two can exist in the same quantum state (Pauli’s exclusion principle) • Boson – Integral spin – Obeys Bose statistics Spin Statistics

• are integral spin particles • Two particle wave function is identical under exchange of two particles.

• Symmetric wave function : Ψ12 ↔Ψ21

• are spin ½ particles

• Assymmetric wave function: Ψ12 ↔ ‐Ψ21 Elementary Particles and

+2/3 Neutral ‐1/3 charge Neutral Neutral Neutral ‐ve Charge +/‐ charge

Fermions Bosons Particle Properties • Mass: All particles have mass (may be zero) – Mass is typically written in terms of energy mc2 – Unit eV: energy required to move an e‐ across 1V – Typicall y use MeV as the scale: rest mass is ½ MeV/c2 or simply often stated as ½ MeV – Recall p is E/c, so p has unit MeV/c • Charge : All have charge (electric, weak, strong) • Lifetime: Probability that a particle created at t=0 is still alive after time P(t) = e‐t/τ

– Half life t1/2 = 0.693 τ Flavors (spin ½)

• The have lepton number conservation and come in 3 types ((heach type is conserved) – Electron type – type – type • Leptons may or may not carry – Neutral (()) – Charged (electron, muon, tau) • No “”, hence no – More on Color in next lecture Lepton Flavors Conservation Laws • Charge and Lepton Number conserved Flavors ((pspin ½)

• Number is conserved • Unlike leptons, where each generation has a separate fully conserved lepton number, come in only one • Thus quark can mix between generations, whereas leptons can’t Quark Flavors ((pspin ½) Masses: Huge Range

Leptons

Quarks

Precise mass measurement of quarks difficult due to presence of Flavor eigenstates ≠ Mass eigenstates • ⊗ means the “partner” of top row is NOT an eigen state of the TOTAL Hamiltonian • For neutrinos: solar and atmospheric neutrinos show oscillations ddeue to mismatch of flavor and mass eigenstates

Flavor eittigenstates Mass eigenstates Called the Maki‐Nakagawa‐Sakata matrix. Lots of interest in this mixing matrix Not an Identity Matrix Quark Mixing

• CbibbCabibbo KbKobayashi MkMaskawa (CKM) miiixing matrix 2 2 2 • Mdc ~5 MeV, Msc ~ 100 MeV, Mbc ~ 4.5 GeV CKM Matrix • Mostly diagonal. But some significant mixing across generations 2008 Physics Nobel Prize Cabibbo: Missed Nobel Prize? • Cabibbo introduced the the cabibbo angle in 1963 for 2 generations of quarks to explain down and decays to

• Or using Cabibbo angle

2 2 Vud and Vus didn’t add up to exactly 1, • Kobayashi and Maskawa but less than 1! generalized this to 3 generations Liftetime: Physics is in life time! • EitllExperimentally often know iittnstant of bir th t0t=0 • Repeatedly make particle at t=0, measure decay time and bin • Can measure exponential slope (independent of start time) • Lifetimes generally more interesting than masses Lepton Lifetimes • Electron: stable – charge can not go to lower energy (mass) state • Neutrinos: Mix among themselves

• Muon lifetime : τμ ~ 2.2 μs – Used to determine the – Almost always decays to an electron and two neutrinos – cτ ~ 1 km! Muon is effectively stable inside detectors (size <=10m). Notice, it is longer than atmospheric thickness! ‐12 • τ Lepton lifetime: ττ ~ ps (10 sec) – Tests “Universality” of weak charge – cτ ~ 100 μm. In most experiments τ decays inside detectors. Huge effort starting mid‐80s to measure this Universality of weak interactions? More dldetails in later lectures • Do all leptons and quarks carry

the same unit of weak chh?arge? τ ντ

– Yes, for leptons and no for W − quarks e− ge ν e

„ for quarks, the couplings to the weak gauge bosons depend on the quark flavors, due to “quark‐mixing” Î CKM mechanism Quark Lifetimes • U, d, s, c, b, t quarks always unstable • All can be unstable. The question is : • Is there lower mass (rest energy) state available? • Yes, in • Hadrons (more later) – (3 quarks) – (quark‐antiquark) Career Lifetimes • γ, and : Mass ≡ 0 • W± : mass = 80.4 GeV • Z0: mass = 91.2 GeV • Dealing with these massive force careers is hard ‐1 • θw = cos (mw±/mZ0) is called the Weak Angle or 0 • θw : Mixing angle between fields that make up γ, Z

• τ W± and τZ0 very small life times • Energy –time Uncertainty principle tells us the uncertainty in energy must be high • This is the decay width, which is inversely proportional to the life time • ΔE * Δt ~ h • Large width implies lots of ways for these particles to decay • Decay width measured with fantastic accuracy and tells us presence or lack thereof new physics • Z0 width ΔE ~ 2.5 GeV, so cτ ~ 0.1 fm (10‐15m) – Not physically measurable! • Sim ilar ly, W± decay width: 2142.14 GVGeV Z0 width END OF LECTURE 02/09/2009 Charges and Feynman Diagrams • Feyman diagrams: Many levels (tree, loop) give most precise calculations ever • Allows computation of , <Ψ|H|Ψ> ppyerturbatively Solid straight line = fermion e‐ γ Vertex Time Charge of OdOrder e or ‐√α amplitud e Coupling ‐e or ‐√α e‐ Arrow forward ⇒ Particle Conserved Quantities

Many quantities that go in to the vertex must also come out: e‐ •Energy‐Momentum e •Electric Charge mm γ •SifiSpecific LLtepton NNbumber or Ti electron‐ness here •Others (Baryon number, e‐ Helicity, etc)

Vector boson (s) couple to the lepton at the vertex

Is the above process allowed, as is? If not, why not? e‐ → e‐ + γ Quiz 2 Amplitude for Interaction • If it did happen, the amplitude would be proportional to –e (charge)

Dimensionless –e/√hc = ‐√α Not Conserved ⇒ Not Allowed • Flip all additive quantum numbers Antiparticles Antiparticles e‐e+ annhiliation

γ Can not happen, due to Energy‐ Momentum conservation me Ti

e‐ e+ e‐e+ annhiliation

Two vertices : Amplitude ∝ (√α)2 Rate or Cross‐section ||2 ∝ α2 γ γ

√α √α

Time ‐ e e+ EM is Not the Only Force! Evidence of non‐EM Force

γ γ e‐

√α e‐ γ √α √α Z√α e‐ e‐ Rutherford : Thomson Scattering: σ∝Z2α2 σ∝α2 Evidence of non‐EM Force

π π e‐

√α √αs √α√αs

pp

Pion Scattering (1951) Clearly, a new type of interaction was σ Experimental is 3 orders of at play, with very different coupling magnitude higher than the previous 2 strength or charge. This is evidence for EM calculation involving α ! strong force, with strength called αs.

αs is of the order Unity! Much larger than α (1/137) Comparison between EM and Nuclear

Electromagnetic Nuclear • Massless force carrier • Massive force carrier

• Long range (infinite) • Short range (We know this force binds and • Interaction has 1/k2 term inside nucleus

• Interaction has 1/(k2+m2) term (known as propagator, where m is the mass of the boson Range of Interaction and Mass • Uncertainty Principle: ΔE*Δt ≅ h • Range of interaction Δx = c*Δt ≅ (c*h/ ΔE) → 0 (for ΔE → 0), when m → 0 for EM interaction e‐ e+

M γ = 0 Propagation speed c + e‐ e Exchange particle (γ) Short Range of Force • between proton and was known to be of short range, inside the nucleus

• Yukawa proposed it is due to a massive scalar particle as the nuclear force carrier, thus limiting the range of the force

• He estimated it to be around 200MeV in mass. Estimate led to a Huge Coincidence!

Pion was discovered to be approximately of that mass and was thought for a while as the nuclear force carrier Lifetime • Lets use uncertainty principle to estimate the life time of Strong Interaction • Distance between proton and neutron, which are held by the strong force is ~ 1F (10‐15m) • The force carrier has to carry this message within the typical decay time or interaction time of say a baryon Δ++ • Ballpark time constant τ = 1F/c = 10‐23 secs • Strong interaction has a fast characteristic decay time of 10‐23 secs. • Characteristic decay time of EM: 10‐16 secs • Ratio of coupling strengths provides ratio of time 2 6 constants: τe/τs = (αe/ αs) ≅ 10 Problem with Strong Interaction • Baryons are bound states of three quarks, held together by the strong force • Examples of baryons: proton (uud), neutron (udd), etc. • A baryon Δ++ was dddiscovered in 1951 in the resonance from π+ and proton scattering • The particle matched the configuration uuu giving rise to charge of +2 and the spin J=1/2 was obtained by combining 3 idential J=1/2 up quarks in ground stttate • Here lies the problem: quark scheme forces us to combine 3 identical fermions (u) in their symmetric ground state in order to make up the known Δ++ Δ++ Violates Pauli’s Exclusion Principle? • To fix this problem, a new charge (quantum number) was introduced, namely “color” • Quarks come in 3 primary colors: red, green and blue • Utilizing the color, we solve the problem with Pauli’ s exclusion principle ++ • Δ = uRuGuB • Introduction of color also solved a few other problems such as non‐observance of uu with charge 4/3 Color is nice • ClColor provides a way to mathtch experitlimental dtdata on stable bound states of quark • It is ffdound tha t bbdound stttates only occur as Baryons (3 quarks) and Mesons (quark‐anti quark) • Why does not proton come in many differen t formats, since there are 3x3x3 options available? • RiRequire tha t all stbltable partic les be COLORLESS! – Equal mixture of R, G, B (or their anti‐colors): Baryons – ElEqual miitxture of color and complimen tary color (RRbar) : Mesons • 8 Types of gluons (color combinations), such as RRbar Quantum Colordynamics

• Just like the (γ) is the carrier of Electromagnetic interaction and responsible for the Electromagnetic force • Gluon (massless like γ ) is the carrier of Strong Force • Gluon carries “Strong Charge”: Color • Theory is very much like and is a renormalizable • For now, simply imagine QCD is exactly QED with a single gluon exchange between quarks at short dis. The Strong Interaction

Flow of color in an itinteracti on Gluons can self interact due to their color! You may even have a glue ball made entirely out of gluons. None found yet! Self coupling of gluons makes QCD so distinct from QED in terms of interaction strength • No self coupling by QED carrier • Self coupling by QCD carrier QED • In QED, an electron can emit a γ and the γ can pair produce and electron hole pair and so on • Thus, the electron is surrounded by e‐e+ pairs, which make it like a diaelectric • The electron charge is screened • At long distances the electron is mostly screened and the interaction strength is minimum • At short distances, one sees the full charge and the maximum strength of interaction with the electron • Self coupling by QCD carrier QCD • In QCD, due to the self coupling, an emitted gluon from a quark can further produce gluons and so on! • The additional diagrams reverse the screening phenomenon from QED and produce anti screening • At short distances, only the bare quark is visible • At long distances the quark is surrounded by lots of gluons and thus make the quark appear stronger • The longer the distance, the stronger “effective” strong charge of the quark! END OF LECTURE 02/011/2009 HEP Journal Club

• Starts March 6 noon‐1, room 426

• More details by email Particle Data Group (PDG)

• Order PDG Handbook 2008 Edition. Invaluable resource for the class • It contains summary of all particles, easy to understand reviews on various topics • http://pdg.lbl.gov/ QCD Similar to and Different from QED • QED and QCD both have massless mediators – If a single mediator is exchanged, both theories are ident ica l – This is essentially what happens with heavy quarks at short distances, such as heavy mesons. “Effective” cross‐ section simple to calculate • QCD different from QED – Mediator of QED γ does not carry the QED charge – Mediator of QCD g carries QCD charge (color) • Higher order Feynman diagrams: Multiple mediator exchange leads to differences – Less and less dominant in QED (α << 1)

– More and more dominant in QCD (αs > 1) in QCD • No free quarks ever observed. They are bound inside hadrons (Baryons and Mesons) • Is there evidence that this is positively due to confinement? Confinement and Asymptotic Freedom are essentially same concepts wihith two sides • What happens when we try to separate two quarks? Experimental Evidence of Confinement

• Confinement makes Unique and Spray of Dramatic predictions for how quark Hadrons and antiquark should separate. e+ That is, they can not without producing further characteristic gluonic clouds which were γ confin ing the two quarks e‐ • The confinement simply continues Spray of down the two threads, separately! Hadrons • Two sprays of hadronic jets emanate from the photon and they are back to back! Quark • Without confinement, the antiquarks showers would be isotropic being pulled • Original quarks never reach away. Gluons detector act like rubber band Di‐Jet Event

associates

“jet‐axis” trigger (T2) primary trigger (T1)

associates Weak vs Strong Interaction

• Δ++ , first observed in π+p scattering, decays to π+p with lifetime of Strong interaction ~10‐23 secs – Δ++ →π+p • Δ++ is a Baryon and made of 3 quarks uuu • Take Proton, a baryon with uud quarks • It never decays. Well, we designed a quantum number for this, called Baryon Number • Take another baryon Neutron (udd). Its life time is 15 mins!!! Way longer than typical strong (10‐23 secs) or electromagnetic (10‐16 secs) interaction – n → p+ + e‐ + ν () : Wide range of Lifetimes • Decays are found with a wide range of life times • π‐ → e‐ν decays in 10‐12 secs • Some “strange” particles, with strange quark in them, decay 100 times slower – Σ+ → n + π+ decays in 10‐10 secs • Compare the above decay wihith siilimilar decay – Δ++ →π+p, which has life time of 10‐23 secs • Clearly, a much “weaker” interaction is at play Weak Interaction • Weak interaction is much weaker than color interaction and electromagentic interaction

• αs : αe : αw = 1 : 0.01 : 0.000001 • It couples to quarks and ltleptons

√αw W‐

√αw

n → p+ + e‐ + ν (beta decay) Muon Decay

•So, Weak interaction can change flavors, such as change a u quark to d quark, muon to electron •Additionally, the weak mediator also has charge +/‐ for W and 0 for Z0 Weak Interaction Range

• Heavy mass of W± (80.4 GeV) and Z0 (91.2 GeV) make the range of interaction small • The bosons must be reabsorbed within a time Δt

< h/Mw after it is emitted • During this time, it can travel at most c Δt of 10‐3 fermi (F) • This range is much smaller than the 1F range for strong force Weak Interaction vs QED/QCD

• Force carrier is massive • But, no new charge needed to be introduced to explain Weak Interaction • Weak Interaction couples to electric charge • Contrast this with Maxwell’s equation

– F = eE + eM(v x B) – No new charge needed to be introduced to unify the magnetic interaction. Simply requires e=eM – This unification led to a natural scale c • Our unification of electromagnetic and weak forces also lead to a natural scale, the weak scale MW~100 GeV (More on this later) Review of Particle Ordering and Interaction • QED is the theory of electromagnetic interaction – Electric charge is responsible for the interaction – It emits charge less, massless γ • No self interaction • Long range force

– √αe is the characteristic strength (αe = 1/137) – Higher order Feynman diagrams contribute less • QCD is the theory of Strong interaction – Color charge is responsible for the interaction – It emits massless gluon, which itself has color charge • Self interaction, which leads to confinement/asymptotic free

– √αs is the characteristic strength (αs > 1) • Weak interaction does not need new charge (just e) – Massive (~100 GeV) vector bosons W±, Z0 mediators (charged) – Very short range force ‐6 – √αw is the characteristic strength (αw = 10 ) Saturday Morning Physics

• February 14: "Dark " : Room 202 (9:30‐10:30am) • The is now known to contain mostly unknowns, in the form of and Dark Energy. Matter as we know it makes up for less than 5% of the total Universe, with Dark Matter and Dark Energy accounting for approximately 25% and 70%, respectively. Detecting the nature of the Dark Matter is one of the most highly prized efforts in the of High Energy Physics. Experiments around the world are searching for the most likely particle candida te for the DkDark MttMatter calle d WIMP (Weakl y ItInteracti ng Massive Particle), by detecting very rare collisions of WIMP with ordinary matter. Complimentary experiments also search for the indirect signature of such interactions in space. Finally, the in Europe attempts to produce this WIMP directly in the laboratory. We discuss these different techniques trying to answer one of the biggest fundamental questions in Physics: what makes up the huge missing mass in the Universe. Symmetries and Groups: Next Week