.451 Lecture 11: Quarks inside the proton 9/10/2003 1 Idea: try to identify a kinematic regime in which the electrons scatter from pointlike constituents inside the proton: “deep inelastic scattering” Microscopic scattering mechanism: ) , ( i q Q R E q W , , “virtual” photon has energy and momentum given by the 4 - momentum transfer from the incoming & outgoing electrons! roton absorbs so much energy that he intermediate excited state flies part very quickly afterwards. Mass, momentum, and total energy of the recoiling object after the collision
Transcript
16.451 Lecture 11: Quarks inside the proton 9/10/2003 1
Idea: try to identify a kinematic regime in which the electrons scatter from pointlike constituents inside the proton: “deep inelastic scattering”
Microscopic scattering mechanism:
),( iqQ
REqW ,,
“virtual” photon has energy and momentum given by the 4 -momentum transfer from the incoming & outgoing electrons!
proton absorbs so much energy thatthe intermediate excited state flies apart very quickly afterwards.
Mass, momentum, andtotal energy of the recoiling object afterthe collision
First discovery: for large energy transfer, the form factors are independent of Q2
M. Breidenbach et al., Phys. Rev. Lett. 23, 935 (1969)
Ratio of measuredcross-section topointlike predictionfor the proton =form factor!
Mass of recoiling object is 2 – 3 x themass of the proton!
“Scaling” – in this regime,the form factors areapproximately equal andare almost independentof momentum transfer...
2
),( iqQ
REqW ,,
A measure of “inelasticity” – Ratio of momentum and energy transfer ...
Kinematics result from lecture 10:
22222 2 WMMqQ
• For elastic scattering: 12/
22
2
MQxor
MQWM
• For inelastic scattering: 1 xMW
• The variable x measures the degree of inelasticity: 10 x
3
Generalization of the scattering formalism:
)2/(sin),(
2)2/(cos),(
4 221
2224
2
2
2
QF
MQF
E
E
QddQ
d
New form factors F1 and F2 are called “structure functions” – they
depend on both the 4-momentum transfer and the energy transfer.
cross-section:
10,2
2
xM
Qx
kinematic factor to classify inelasticity:
4
(Note: there are two independent kinematic parameters: Q2 and . The structure-dependent contributions to the cross section can be accounted forin terms of these two variables, or alternatively in terms of Q2 and x.)
The “scaling” discovery is equivalent to finding that the structure functions only depend on x and not on Q2 in this regime.
Illustration: range of x in electron – proton scattering
increasing energy transfer ...
3/1 1M
Qx
2
2
x
structure function F2 (x,Q2)
5
x = 1: Elastic
dashed line: very large Q2
solid line: much smaller Q2
“Deep inelasticregion” x = 1/3;large and smallQ2 have the samestructure function.
Evidence of point-like quarks comes from “scaling” of the structure functions
)GeV( 22Q
.)(25.0 constx
M
QF ),( 22
Idea: pointlike scattering object has a constant form factor or structure function. The proton structure functions are essentially independent of Q2 in the deep inelastic regime, indicating scattering from pointlike constituents with mass approx 1/3 the proton mass u and d quarks!
6
This line is flat!!!
Contrast: elastic and inelastic form factors!
proton electric form factor for elastic scattering, x = 1, falls off rapidlywith increasing Q2 because the protonis not a pointlike object!!! (the whole proton recoils in this case)
proton “F2” structure function,deep inelastic regime, x = 0.25.independent of Q2
(a pointlike object inside the proton recoils after the collision)
7
Broad peak at x = 1/3 ... ?
“Deep inelasticregion” x = 1/3 x = 1: Elastic
increasing energy transfer ...
3/1 1M
Qx
2
2
x
structure function F2 (x,Q2)
Look again at the features in x: 8
Scattering from quarks?
Elastic scattering from the protonis a narrow peak at x = 1
Deep inelastic scattering shows a broad peak at x = 1/3 ... ???
• If the quark has mass m = M/3, then we should see a peak at:
• The peak is broad because the quark is confined in a small space – the quark `target’ is moving in a random direction inside the proton (very fast!!!)
3
1
21
2
22
M
m
m
Qx
m
Q
ee
m
M
!!2~MeVfm
fmMeV250
8.0
197mc
x
cpcxp
Estimate:
9
A bit more about “x”
Feynman’s “parton” model, 1969: viewed in a frame in which the proton is movingrelativistically, deep inelastic scattering (DIS) involves the electron scattering from a single “parton” with a fraction x of the proton’s total momentum.
M
m
M
Qx
2
2
Comparing DIS structure functions for different targets (n, p, 3He, etc...) allows theindividual quark and anti-quark distribution functions to be mapped out, ie, we canmeasure what fraction of the proton’s momentum is carried by each kind of quark.
Observations: 1. only about 60% of the proton’s momentum is carried by quarks 2. only about 30% of the proton’s spin is due to the quarks
Q
m
... so what else is in there ????
10
M
We don’t know exactly, but there is a great deal of effort underway to find out!
Have another look at the NSAC long range plan (web link, lecture 1.) p.14 – 28 –you should be ableto understand a lot more of it now!!!
(N.B. scattering at very small x issensitive to the presence of anti-quarks inside the proton – these areimportant too! (research frontier)...
![eps09 rg reweight · Nucleonstructure: Shortdistances 3 ~ 1 fm 0 0.1 0.2 0.3 10-3 10-2 10-1 distance [fm] αeff • Pointlike objects: Quarks Almost massless mu,d](https://static.documents.pub/doc/80x56/5ee3d659ad6a402d666d6afd/eps09-rg-reweight-nucleonstructure-shortdistances-3-1-fm-0-01-02-03-10-3-10-2.jpg)
