M. Cobal, PIF 2006/7 Quarks

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M. Cobal, PIF 2006/7

Quarks

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Quarks

• Quarks are s = ½ fermions, subject to all kind of interactions.

• They have fractional electric charges

• Quarks and their bound states are the only particles which interact strongly

• Like leptons, quarks occur in 3 generations:

• Corresponding antiquarks are:

 

 



 



 



 



 





b t s

c d

u

 

 



 



 



 



 





t b c

s u

d

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The quark model:

Baryons and antibaryons are bound states of 3 quarks

Mesons are bound states of a quark and an anti-quark

Barions and Mesons are: Hadrons

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Hadrons

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Quantum Numbers and flavours

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Strangeness is defined so that S=-1 for s-quark and S =1 for the anti s-quark. Further, C=1 for c-quark, B=-1 for b-quark and T=1 for t-quark

Since t-quark is a very short living one, there are no hadrons containg top, i,e, T=0 for all

Quark numbers for up and down quarks have no name, but just like any other flavour, they are conserved in strong and em interactions Baryons are assigned own quantum number B :

B =1 for baryons, B =-1 for antibaryons, B =0 for mesons

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Theory postulated in 1964 (Gell-Mann)

e

p

e’ In the 70’s, deep inelastic scattering of electrons on p and bound n show evidence for the quark model

• Strange, charmed, bottom and top quarks each have an additional quantum number:

strageness S, charm C, beauty B and truth T respectively.

• In strong interactions the flavour quantum number is conserved

• Quarks can change flavours in weak interactions (S =1, C =1)

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Particles and Interactions

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Hadrons and lifetime

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• Majority of hadrons are unstable and tend to decay by the strong interaction to the state with the lowest possible mass ( ~ 10

^-23

s)

• Hadrons with the lowest possible mass for each quark number (S, C, etc.) may live much more before decaying weekly

( ~ 10

^-7-

10

^-13

s) or electromagnetically (mesons, ~10

^-16-

10

^-21

s)

Such hadrons are called stable particles

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Brief history of hadron discoveries

• First known hadrons were proton and neutron

• The lightest are pions . There are charged pions +, -, with mass of 0.140 GeV/c

²

, and neutral ones 

⁰

, with mass of 0.135 GeV/c

²

• Pions and nucleons are the lightest particles containing u- and d- quarks were discovered in 1947 in cosmic rays, using

photoemulsion to detect particles

Some reactions induced by cosmic rays:

Same reactions can be reproduced in accelerators, with higher rates (but cosmics may provide higher energies)

















 p

p

p p

n p p

p

⁰

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Nobel Prize 1936: C. D. Andersson (Berkeley)

“for his discovery of the positron”

Plate of steel

positron

B

Positron Discovery

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Pion discovery

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Charged pions decay mainly to the muon-neutrino pair (BR ~99.99%) having lifetimes of 2.6x10

^-8

s.

In quark terms:

Neutral pions decay mostly by the electro- magnetic interaction, having shorter lifetime of 0.8x10

^-16

s

At the beginning discovered pions were believed to be responsible for the nuclear forces

However, at ranges comparable with the size of nucleons this description fails.

  u d  

^

 

_



 ⁰  

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Strange mesons and baryons

Were called so because, being produced in strong interactions, had quite long lifetimes and decayed weakly rather than strongly

The most light particles containing s-quark

 mesons K

⁺

, K

^-

and : Kaons, lifetime of K

⁺

= 1.2x10

^-8

s

 baryon , lifetime of 2.6x10 s

Principal decay modes of strange hadrons:

0 0

, Κ Κ

) 36 . 0 (

) 64 . 0 (

) 21 . 0 (

) 64 . 0 (

0

































B n

B p

B K







_

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Strange particles: kaon discovery

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Problem:

While the first decay in the list is clearly a weak one, decays of

 can be very well described as strong ones, if not the long lifetime:

However, this decay should have  ~ 10

^-23

s.

Thus,  cannot be another sort of neutron....

Solution:

To invent a new quark, bearing a new quark number –“strangeness”- which does not have to be conserved in weak interactions

In strong interactions, strange particles have to be produced in pairs to save strangeness:

 ^udd    ^ ^d ^u ^ ^(uud ⁾









 p K

0



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More strange particles: S=2

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The charm quark

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• Bubble chambers turned out to be a great tool for particle

discovery. Numerous hadrons, all fitting the u-d-s quark scheme until 1974

• In 1974 a new particle was discovered, which demanded a new flavour to be introduced.

Since it was detected simultaneously by two rival groups in

Brookhaven (BNL) and Stanford (SLAC), it received a double name:

The new quark was called “charmed” and the corresponding quark number is charm, C. J/ itself has C=0

• Shortly after other particle with “naked” charm were discovered:

c c J /  ( 3097 ) 

udc

c u D

c d D

u c D

d c D

c













) 2285 (

) 1865 (

, )

1869 (

) 1865 (

, )

1869 (

0 0

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J/

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J/Width

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Even heavier charmed mesons were found which contained strange quark as well:

Lifetimes of the lightest charmed particles are of ~10

^-13

s, well in the expected range of weak decays

• Discovery of “charmed” particles was a triumph for electroweak theory, which demanded number of quarks and leptons to be equal