Isospin, a quantum number, is indicated by I (sometimes by T), is related to the number of electrically charged states (N) of a meson or a baryon, and is expressed by the value of I, with Iz directly indicating the charge.

So if proton and neutron forms two charged states of the nucleon, then 2I + 1 = N = 2,Which leads to I = ½ for a nucleon later this was attributed to u,d quarks

The Standard Model, forces, and classifications

Lecture 5, Tues Sep 8, 2015

Old values

Baryons are formed with three quarks and mesons are formed with one quark and one antiquark

Write the quark contents on the board

Strong interactions take place by exchange of the gauge bosons called gluons. A hypothetical quantum number, color (charge), is attributed to be responsible for strong interactions, just like Electric charge is attributed to be responsible for EM interactions. So gluons are known as the mediator of the strong force. Color field/charge: All quarks carry (hypothetical) colors (r, b, g), to be compared with electric charges in EM; gluons carry two color indices, one color one anti-color. They have spin 1, are massless, and being made of a color and an anti-color, there are eight gluons altogether.Because quarks carry color, they interact with another quark or with a gluon via color-fields.

e.g., a green quark turns into a blue quark (of the same flavor), by emitting a gluon with g, and negative b from the green quark. It could likewise have absorbed a gluon with a negative g and a positive b. Color is conserved at the vertex.

So the primitive vertex of a strong interaction is :However, unlike the photon, which itself does not carry electric charge, gluons carry color, thus being able to couple to themselves as shown at right. This gives rise to a very rich spectroscopy, but also makes calculations very difficult in some cases.

4

n

p

Basic QCD primitive vertices

Strength of each vertex is s

Theory of Strong Interactions is called Quantum ChromoDynamics: QCD (chromos color)

??

From Yukawa’s simple pion exchange model to QCD model:

Can have multiple bubbles also

Screening of a charge +q in a dielectric medium with dielectric constant . Outside an intra-molecular distance, qeff = q/

In QED, each vertex contributes a factor of in strength, and as the number of vertices increase, the effective contribution of the particular diagram decreases because 8 6 4 2

So higher order effects are minimal.

The electron charge e measured is not the bare electron charge

Difficulties: The strong coupling constant (at each QCD vertex) is denoted by s. Unlike the value of , the value of is much bigger, can be ~ 1 or even larger inside a nucleus. This makes calculation of higher order diagram by perturbative series impossible.

Now, vacuum is not nothing, in QED :

Inside an atom,

s however, is a different story; it is larger in magnitude. Can have contributions from different flavor of quarks (gluons breaking up into q pairs, just like the electron-positron pairs); but also from different colored gluons from vacuum polarization.

The 6 flavor loops and the 3 color loops work with opposite effects of each otherfor the higher order diagrams. The resulting effect is negative, i.e., as the distance decreases the effective coupling decreases, as the distance increases, the effective coupling increases. [Asymptotic freedom]

At very short distances, when penetrated deeply, the effective coupling is negligible, but as one wants to spilt the quarks apart, the coupling strength is extremely high.[Confinement]

Perturbative and non-perturbative QCD

a 2f 11n = 21

At high momentum transfer Q, (means the basic particles are very close to each other, deep penetration into a proton or a neutron with a quark or a lepton as a probe), then s is small, means perturbative QCD calculations are very successfully applied, e.g., in Deep Inelastic Scattering.Later we will see what scaling is and then scaling violation

While we observe the leptons, we can not observe single isolated (naked) quarks; if we try to pull a hadron apart by pulling them very hard, the quark from it pulls an extra q-qbar pair from the vacuum and dresses itself.

D

D+

(3770)

We can not pull apart the quarks:

proton

neutron

Early Observation (that led to discovery of the existence of the strange quark): Strange mesons are produced in pairs, but decay differently into non-strange mesons.(also holds true for charmed and bottom mesons) . Production by strong interaction, but decay by weak interaction.

Weak Interactions:

udd uud

primitive vertex

uudusd

p + 0

Again, the theory of weak interaction is similar in structure to that of QED. Like charged current, we talk about weak currents, and they are positive or negative depending on the charge of the W exchanged.

Search for neutral current was finally successful around 1973 it was observed in a bubble chamber neutrino experiment at CERN, it was soon confirmed by other neutrino experiments and in electron positron collision experiments.

, , q

e+ + e +

The Z-exchange process and the -exchange processes interfere, which shows up in an asymmetric angular distribution of the outgoing particles.

n + n n + p

Neutral current Charged current

Weak interactions of quarks and mixingExperiments showed the existence of a charged electroweak coupling between an up and down quark and between an up and strange quark

K

From the branching fraction measurements ratio, the u into W rate was higher than that of u rate, so Nicola Cabibbo declared :

The weak eigenstates are different from the mass eigenstates of the quarks. The Cabibbo angle represents the rotation of the mass eigenstate vector space formed by the mass eigenstates into the weak eigenstate vector space formed by the weak eigenstates . The rotation angle is θC 13°.

sincos sd

u

d

ucosθc ≈ 0.97, sin θc ≈ 0.22

With the discovery of the charm quark, the basic idea as a rotation between the electroweak eigenstates of the quark and the flavor eigenstates can be written as :

s

dV

s

d

s

d

CC

CC

cossin

sincos

Generalizing to the three generations, the matrix is 3 3 and is known as the Cabibbo-Kobayashi-Maskawa (CKM) matrix, and is a unitary matrix. Unlike the 2 2 matrix, which only contains an angle, the CKM matrix contains three angles and one phase. It is because of this phase that we observe CP-violation, which we will learn later. This has been measured (by the BaBar experiment at SLAC and the Belle experiment in KEK) and agree with the predictions. Kobayashi and Maskawa received Nobel prize in

The CKM matrix

the magnitudes of the CKM matrix elements :

The diagonal elements are close to 1.The off-diagonal elements between generation 1 and 3 are very small. Top quark to down quark transition is almost non-existent, as is the b-quark decaying into an up quark.

Similar to the CKM matrix there is the Pontecorvo–Maki–Nakagawa–Sakata matrix (also called the PMNS or simply MNS matrix (Uij) , which describes the neutrino oscillations among the three generations of neutrinos. CP-violation is a possibility in the neutrino sector also.Our Sun produces 2 1038 e /sec. About 400 billion pass thru our body each sec. Experiments proved that there is a deficit in the number reaching us. Now SuperKamiokande, SNO, and many others measured accurately that some of the e from the Sun oscillate into . They do then have mass. Even though the masses have not been measured, upper limits have been measured. Other experiments showed many changing into …etc. A deficit was observed in atmospheric muon neutrinos () (in ratio of the flux of to e). Super-Kamiokande made an accurate measurement of the oscillation of , announced in 1998. Anti-electron-neutrino flux, produced in nuclear reactors have been measured (KamLand, Daya Bay, also Double Chooz).Intense neutrino beams produced at particle accelerators have been used to study neutrino oscillation (MINOS (CERN), K2K (KEK), OPERA at Gran Sasso, MiniBoone). OPERA experiment observed a produced in a beam, meaning

oscillating into .Many new experimental results are now available.

Conservation laws :Photon is stable, no lighter particle than photonElectron is stable, lightest charged particleProton is presumably stable, lightest baryonOther particles are short (and shorter) livedEspecially the exotic ones

lifetime 2.2 106 sec [Weak interaction] lifetime 2.6 108 sec [Weak interaction]0 lifetime 8.3 1017 sec [EM interaction] decays into two s++ lifetime 1023 sec [Strong interaction] decays into and pRelated to “decay width” , the fatter the width the faster the decayMany particle have several decay modes, the total decay width = Branching ratio/Branching fraction in ith decay channel =

1) Electric charge is conserved at each vertex2) Color charge is conserved at each vertex3) Baryon number is conserved (quark number is conserved)4) Lepton number is conserved (generation number approximately

conserved)5) Flavor is conserved at Strong and EM vertex, but not in Weak

vertex6) Okubo-Zweig-Izuka (OZI) rule