Deep Scattering of Hadrons. Hadroproduction from e + e  Proton formfactor e  p scattering Parton Model and scaling Quark distributions
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Hadroproduction from e+e
Proton formfactor
ep scattering
Parton Model and scaling
Quark distributions
These notes are not original, and rely heavily on information and examples in the texts “Introduction to Particle Physics” by David Griffiths, “Introduction to High Energy Physics” by Donald H. Perkins and “Quarks and Leptons” by A. Martin and Halzen.
Much of the content of these slides is acknowledged to come from
“Introduction to Elementary Particles”
By David Griffiths, Wiley, 1987
e+eqq
Time
Time
_
e+eqqg
Hadron Production from e+e AnnihilationBrian Meadows, U. Cincinnati
s ´ q2=(p1+p2)2
Quark charge (+2/3,1/3)
p1
p3
q
Time
p2
p4
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since Qm=1
Sum over
Q flavours
Each quark
Has 3 colours
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Predict:
u+d+s:
3 [(2/3) 2 + (1/3) 2 + (1/3) 2]
= 2
u+d+s+c:
3 [(2/3) 2 + (1/3) 2 + (1/3) 2
+ (2/3) 2]
= 10/3
u+d+s+c+b:
3 [(2/3) 2 + (1/3) 2 + (1/3) 2
+ (2/3) 2 + (1/3) 2]
= 11/3
Recent data
fromBaBar
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Brian Meadows, U. Cincinnati
Events expected to have symmetric cos distribution
+
RH
LH
e +
e 
LH
RH

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p1
p3

p1
p3

Z0
+
+
+
p2
p4
p2
p4
s/ 1/s
Z0 has mass
mZ=m0+ i GZ
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q
Time
Elastic ep Scatteringe 
e 
e 
e 
p formfactor
m
m
p
p
e mass
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q
Time
Proton FormFactore 
e 
e 
e 
p formfactor
m
m
p
p
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Antisymmetric
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(since p12 = p32 = m2c2).
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Using p¢q = q2 / 2 we obtain:
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and we neglect m (<< M)
to obtain (more homework!) – the “Rosenbluth formula”:
K1 = q2 ; K2 = 4M2c2
GM(q 2)
GE(q 2)
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“MV”~ 0.9 GeV/c2
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“Inclusive” (Inelastic) ep Scattering
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where we neglect m (<< M)
electron lab. energies E1 =E and E3 = E0 respectively.
p3
p1
E’
e 
e 
E
p formfactor
p2 =p
p
X (p4, …pn)
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q
Time
Elastic Scattering
Inelastic Scattering
q2 = 2MX(E`E)
p¢ q = q2/2
E’´ E’ (E, , MX)
q2 = 2MX(E`E)  Mp2 + Mx2
Bjorken x (=1 for elastic case)
E’
e 
e 
E’
E
E
e 
e 
E, p
E’, p’
p
X (p4, …pn)
Mp
Mp
Mp
p
p
MX
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Time
“Infinite Momentum System” (IMS)p3
p1
E
E 0
P
P
W = MX
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for massless e ,in proton rest frame, where:
All possible
X ’s
Not determined
by E and
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Chooseq2andx =  0.5 q2/ p¢ q
To get Rosenbluth formula, we need:
Inelastic structure functions
W1,2´W 1,2(q2, x)
“Bjorken x”
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Define:
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[ “ “ 0 “ ]
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nW2 (¼ F2) vs. q2
at x = 0.25
(Friedman & Kendall, 1972)
For perfect “scaling” there is no
q2dependence.
2xW1/F2vs. q2 /(2Mn)
For spin ½ partons, this is equal to 1.0.
(For spin 0 it is = 0)
1.0
1.5
1.0
0.5
0
2xF1/F2
0.5
0.4
0.3
0.2
0.1
0
n W2
0 2 4 6 8
0 0.5 1.0
q2 (GeV/c2) 2
x = q2/(2Mn)
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p = x P (P is momentum of parent hadron)
inside the hadron given by a distribution function f(x) with
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with
Analogous to
Rosenbluth scattering
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with terms for c, b and t quarks that are small due to their large masses (small propagators).
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1.0
0.1
F2(x)
ed 15 GeV
N 100 GeV
0 0.25 0.50 0.75 1.00
x
Structure Function F2(x)Structure function F2(x) for various beam energies
Of eN and n N scattering experiments. (N is
a nucleon)
The shrinkage is apparent as the beam energy
increases.
x 3 GeV nN  Gargamelle
(bubble chamber at CERN)
15 GeV e d  SLAC
(fixed target experiment)
100 GeV nN  CDHS at Fermilab
(fixed target experiment)
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