Quarks, , and the Strong Force Physics 245C Prof. Conway

1 1950’s-1960’s: “ Zoo”

Life was simple back when we just had two elementary ! Discovery of the . How did they do it? Great project!

Mesons were thought to explain how nuclei were held together - was this it?

By the 1950’s cyclotrons opened our eyes to a plethora of particles...what the $&%$^ ??

2 Rutherford’s Nucleus

• Geiger and Marsden, in 1911, sat for days in a darkened room recording flashes... • many came out at a large angle • Ernest Rutherford realized the significance of this, and calculated the scattering cross section versus angle:

scattering center must be smaller than rmin 3 (Deeply) Inelastic eN Scattering • do the Rutherford experiment with and ! • e-p scattering has inelastic part 4-vectors!

elastic: q2 = 2Mν inelastic: q2 < 2Mν

interaction is via intermediate virtual

4 (Deeply) Inelastic eN Scattering

• results show resonance structure • ep → eX (X can be delta resonance, e.g.)

∆+ → p + π0 ∆+ → n + π+ m(∆+) = 1232 MeV/c2

...or X could be a bunch of hadrons, etc.

5 (Deeply) Inelastic eN Scattering

e- p

e-

hadrons

mass of recoil system

Phys. Rev. Lett. 23, 930–934 (1969) 6 (Deeply) Inelastic eN Scattering

• we measure the in-elastic-ness of the process using the Bjorken scaling variable x

Q2 Q2 x ≡ = ; Q2 = −q2 2Pq 2Mν

2 2 2 d σ dσ × F2(Q ,ν) F1(Q ,ν) 2 θ ! = + 2 tan dΩdE !dΩ"Mott # ν Mc 2$

structure functions 7 BJ’s “Parton” Model

2 • at large Q , when F1 and F2 were extracted from SLAC data, it was observed that they depend weakly on Q2 - mainly on ν • this implies that the electrons are being scattered from point charges...much smaller than the ! • BJ called them “partons” • since it was found that 2xF1 = F2 , and this is expected for spin-1/2 particles, the partons have spin 1/2

8 BJ’s Parton Model

• let’s think about this from the point of view of an infinite- momentum frame • each parton (whatever it is) carries some fraction of the total momentum in this limit

x is now seen to be that fraction!

but what are the partons? 9 Gell-Mann’s • “three quarks for Muster Mark!” - James Joyce, Finnegan’s Wake • Gell-Mann proposed that the properties of could be accounted for if they were constituted of quarks • initially needed only three: u - up , charge +2/3 d - charge -1/3 s - charge -1/3

10 Quark Structure baryons are particles made from three quarks: n p

- 0 Σ Σ + Λ0 Σ

Ξ- Ξ0

(antibaryons are made from three antiquarks) 11 Quark Structure

• are particles made from a quark and and antiquark - ds us-

ud- Text ud- - us- ds more explanation needed here

12 The Strong Force

• quarks interact via the weak, force the electromagnetic force, and the strong force • the charge associated with the strong force is called color: red green blue • quarks have color; antiquarks have anticolor • the color force grows with separation • quarks can be thought of as the ends of color flux tubes or strings (not string th.!) • if the tube breaks, new quarks are produced

13 The Strong Force

electric dipole field color dipole field

This is how we pop a qq- pair out of the vacuum!

14 Mark I at SLAC • Mark I was installed at the SPEAR e+e- collider at SLAC in the early 1970’s • the machine was able to run at cm energies of up to about 3.5 GeV • the goal: study qq - production and nail down the existence of quarks They succeeded beyond their wildest dreams... 15 e+e- → qq-

• we can pair produce quarks via the electromagnetic interaction, exactly in analogy to pair production:

well above threshold: 2 − π ¯hQcα σ(e+e → qq¯)= 3 ! E "

• what happens to color string in this case? • need to consider resonances also 16 Breit-Wigner Resonances • the “point-like” cross section (γ*) drops like 1/Ecm = 1/s • s-channel exchange of a vector meson is governed by the Breit-Wigner formula:

∝ Γ σ(E) 2 2 (E − E0) +Γ /4

width related to lifetime: ¯h τ = Γ

17 The November Revolution

• in late 1974, the Mark I was plugging away, scanning in energy • at Brookhaven, an experiment was underway to look for muon pair production using a beam on a target • they saw something totally unexpected: a large, narrow resonance at about 3.1 GeV/c2 • the SLAC folks found out...tuned to 3.1 GeV • SLAC called it the “ψ”, Sam Ting called it the “J” ... we now call it the J/ψ

18 The November Revolution • the ψ is a of a new quark, called 2 charm (mc ~ 1.8 GeV/c ) • very narrow resonance: 91 keV • higher resonances ψ’, ψ’’,...

Sam Ting Nobel 1976 19 Clearly it should be called ψ ! R

• needle in haystack problem? • measure ratio of multihadron production to muon pair production: σ(e+e− → hadrons) R ≡ σ(e+e− → µ+µ−) • can’t use e+e- in denominator...why? 2 R = 3ΣQi

20 R • measurement of R shows clear steps as we cross the threshold for the next heavier quark

21 Charmed Hadron Structure

22 The b Quark • In 1977 the highest energy e+e- colliders were still < 10 GeV cm energy • Leon Lederman and his group were studying Drell-Yan production of muon pairs in proton- collisions at high Leon Lederman energy at FNAL (Nobel 1988) • having founded the “I missed the J/psi club”, Leon and Co. found something new and not entirely unexpected: another new quark, dubbed the b quark (beauty, or bottom) • this is the Υ (upsilon = “oops - Leon!”) 23 Drell-Yan and Structure

• even before the was fully established, Drell and Yan worked out the consequences of hard collisions of hadrons:

x1 = mom. fraction of antiquark in p x2 = mom. fraction of quark in N quark momentum mµµ = x1x2Ecm fraction distributions xF = x1 − x2

2 2 d σ 4πα 2 2 = 2 ! ef [qf (x1)¯qf (x2)+...] dm dxF 9sm µµ µµ f 24 Quark Structure of Hadrons

• Did we just say that there were antiquarks inside protons? • Strong force holding together hadrons carried by • If we look deep inside a hadron, we can sometimes catch the gluons:

25 Quark Structure of Hadrons

• if we look even deeper, we can see the gluons undergo quantum fluctuations to quark antiquark pairs • this happens in QED too but the strong force is, well, stronger

26 Fundamental , ca. 1979

• by the close of the seventies, a tantalizing picture had emerged:

• clearly nature had more in store... 27 Colors and QCD

• QCD = • two ways to make “white” (color neutrality): • red-antired, blue-antiblue, green-antigreen • red-green-blue (rgb) • clearly this is the basis of mesons/baryons • gluons carry color and anticolor simultaneously

28 Gluons

• How many gluons are there? Nine?

• No...the color-neutral ones can’t be gluons... • color charge is governed by an SU(3) symmetry • SU(3) - special unitary group of 3x3 matrices with determinant • ana1ogous to Pauli matrices: SU(2)

29 Gluons

• there are 32 - 1 = 8 gluons which transform under the SU(3) matrices • Griffiths lists the states in eq. 9.4, and the matrices (Gell-Mann’s version) in 9.9 • to learn/use QCD fully you will need to have studied group theory and Lie algebras in particular • http://www.answers.com/topic/color-charge has links to any desired depth... • what do you need to know? Gluons in Hadrons

• inside a hadron you can imagine the gluons moving color charge around:

• this is not completely accurate...but not a bad way to think about hadrons Structure Functions • the complete structure function of the proton has three components:

This is how the structure GLUONS functions look at a particular Q2 - at higher VALENCEQUARKS values, the shapes change:

PARTONDENSITY the valence distribution

SEAQUARKS drops and the gluon and sea components are enhanced

  Feynman Rules - QCD

• these vertices are allowed in QCD:

• the first has a counterpart in QED...the gluon self-coupling ones are new

33 Typical QCD Processes • in hadron collisions we find processes of the form

• these lead to hadron jets Jets and QCD

• at lower energies, get ~few hadrons • at high energies, get tightly collimated “jets” • particle multiplicity scales logarithmically with jet energy • significant chance of gluon radiation from quark line:

35 Discovery of the Gluon

• TASSO experiment at PETRA (Hamburg), in e +e- collisions at Ecm = 27 GeV :

This and a handful of similar events with three jets established the existence of the gluon in 1979

S.L. Wu, G. Zobernig

36

Running Coupling

• we have a coupling constant in QCD, αs define in analogy to α in QED • however, it turns out that both of these coupling constants “run” with Q2 ! • potential is “screened” by quantum fluctuations to pairs in both cases

Λ~150 MeV/c Running Coupling • at the scale of the Z mass (electroweak scale we have

• thus the is about 16 times stronger than the electromagnetic... • in the high Q2 limit, we can perform “perturbative QCD” calculations • QCD “asymptotically free” (Nobel 2004) Loops and Orders • loop diagrams are very important in QCD • even the simplest processes cannot be estimated at leading order only • a very technical specialty...

full set of diagrams at all orders in alpha must be added, w/ interference ! Widths and Decays

• lifetime of a particle related to its total width Γ • total width is the sum of all the partial widths for each possible decay • we write the branching ratio of a particle to a particular final state i as Widths and Decays

• basically impossible to calculate partial widths for hadronic decays due to unknown “hadronization factor”: non-perturbative QCD • however, in ratios of branching ratios (ratios of partial widths) these factors can drop out in certain cases • still, must include all diagrams to all orders in principle...we are left with approximations • works better for heavy quark systems (b mesons and baryons) Strong Decays • particles undergoing decay governed by the strong interaction happen very quickly, O(10-22 sec) • we tend to think of these more as resonances than particles phi resonance width: 4 2. MeV

(~1.5x10-22 sec)

43 Quark-onia

• the phi is “strange- onium”; it has heavier cousins: the psi and the upsilon • each of these exhibits a near-hydrogen-like set of radial excitations at higher masses: • can this tell us the strong potential? The Strong Potential • not really possible to write down a clean functional form for the strong potential; can approximate at long and short scales • very small distances: weakly Coulomb-like • very long distances: linear confining potential See C. Quigg’s article: http://lutece.fnal.gov/Essays/QQM.html So Why is the ψ So Narrow?

• lightest charmed mesons heavier than mψ/2 • must get rid of the c quarks by annihilation: this takes longer • have electromagnetic decays to e, mu pairs • mainly quark pairs: 90% of the decays (17% from photon!) Weak Decays

• for hadrons with only one of the heavier quarks (s, c, b) how do they decay? • must change flavor somehow: cannot happen in strong interaction or electromagnetic • it can happen in the weak interaction! • internal W lines allow s -> u, c -> d, and b -> c transitions • this is weak because the mediator (the W) is so massive: it is far off-shell Weak Decays

• an example of a weak decay involving only hadrons is that of the charged :

• the virtual W allows the strange quark to change to an up-type quark Weak Decays

• generally speaking, decays lead often to D (charm) meson final states, and • decays lead to final states with K’s • lifetimes of these mesons are in the range 10-13 - 10-12 sec • decays of : 10-10 sec • : 10-8 sec

(discuss: plausible pion, kaon decay modes) Proton Decay

• the proton does not decay - no such event has been observed in giant underground water Cerenkov detectors...unless they are simply vanishing

34 τp > 10 years • protons do decay inside nuclei: this is how emission (β+ decay) happens • decay, though this can be enhanced or suppressed inside nuclei Weak Coupling of Quarks

• consider the weak vertex with a W and two quarks: • for quarks (and not ) there is a parameter multiplying the weak vertex factor

• 1961: Cabibbo angle θc ~ 13 degrees • W-u-d vertex: cosθc weak states of quarks rotated w.r.t. em/strong • W-u-s vertex: sinθc CKM Matrix

• we now know that the full three-generation picture of quark weak interactions governed by 3x3 matrix: Cabibbo-Kobayashi-Maskawa quark mixing matrix:

weak quark doublets CKM Phenomenology

• we add several (four, actually) new ad hoc parameters to the theory...but we get • unified picture of quark weak interactions • CP violation in the K system • CP violation in the B system • CP violation in the D system? • current experiments: pin down the “CKM triangle” Measuring CKM Elements

These measurements are being done at the asymmetric B factories (PEP-2 at SLAC: BaBar, and KEK-B in Japan: Belle) Asymmetric B Factories collide e+e- at the Υ(4s) resonance • _ • pairs of B mesons produced (B+B- or B0B0) • moving in lab: measure decay length, asymmetry versus time Asymmetric B Factories

• can fully reconstruct the two B mesons: • BaBar and Belle have recorded millions of these events, and pinned down the CKM elements Unitarity Triangle • current state of the art (a couple weeks ago)

unitarity triangle is in black

measurements are colored

triangle has area = CP violation

triangle closed = no new physics