Transcript Deep Inelastic Scattering in Lepton
Deep Inelastic Scattering in Lepton-Hadron Collisions
— Probing the Parton Structure of the Nucleon with Leptons • Basic Formalism (indep. of strong dynamics and parton picture) • Experimental Development – Fixed target experiments – HERA experiments • Parton Model and QCD – Parton Picture of Feynman-Bjorken – Asymptotic freedom, factorization and QCD • Phenomenology – QCD parameters – Parton distribution functions – Other interesting topics http://user.pa.msu.edu/wkt/talks/04/CTSS04.pdf
Basic Formalism
(leading order in EW coupling) Lepton-hadron scattering process
B
Effective fermion-boson electro weak interaction Lagrangian:
(B = g, W, Z)
EW SU(2)xU(1) gauge coupling constants
Basic Formalism: current operators and coupling Fermion current operator: V-A couplings: or, Left-right (chiral) couplings: Charge Weak isospin Weinberg angle CKM mixing matrix
Basic Formalism: Scattering Amplitudes Scattering Amplitudes
B
Spin 1 pro jection tensor Lepton current amplitude (known): Hadron current amplitude (unknown): Object of study: * Parton structure of the nucleon; * QCD dynamics at the confinement scale (short distance) (long dis.
)
Cross section Basic Formalism: Cross section (amplitude) 2 phase space / flux Lepton tensor (known): Hadron tensor (unknown): Object of study: * Parton structure of the nucleon; * QCD dynamics at the confinement scale S X
Basic Formalism: Structure Functions Expansion of W m n in terms of independent components Cross section in terms of the structure functions Charged Current (CC) processes (neutrino beams): W-exchange (diagonal); left-handed coupling only ; ….
Neutral Current (NC) processes (e, m scat.)---low energy: (fixed tgt): g -exchange (diagonal); vector coupling only ; … Neutral Current (NC) processes (e, m (hera): g & Z exchanges: G 1 2 , G 1 G scat.)---high energy 2 , G 2 2 terms; ….
Basic Formalism: Scaling structure functions Kinematic variables
E 2 E 1 q P
Scaling (dimensionless) structure functions Scaling form of cross section formula: ( )
Basic Formalism: Helicity Amplitudes Scattering Amplitudes
B
Spin 1 rotation matrix Lepton current amplitude (known): Hadron current amplitude (unknown): Object of study: * Parton structure of the nucleon; * QCD dynamics at the confinement scale
Basic Formalism: Helicity structure functions l l Relations between invariant and helicity S.F.s
Where at high energies Should have been absorbed into the definition of the scaling S.F.’s
F 2,3 !
Conversely, Cross section formula: where
Experimental Development
Interesting and comprehensive description of the entire history of probing the structure of nuclei 70’s (SLAC), …SPS, Fermilab, HERA —from (pre-) Rutherford scattering … 1930’s …50’s (Hofstadter) …60’s, Highly recommended!
2-lecture series by E. Tassi at CTEQ2003 http://www-zeus.desy.de/~tassi/cteq2003.html
The SLAC-MIT Experiment
Under the leadership of Taylor, Friedman, Kendall (Nobel prize, 1990)
First SLAC-MIT results
Two unexpected results…
~ 1969
Experimental Development — modern experiments (high Q)
NuTeV
The highest energy (anti-) neutrino DIS experiments
CCFR and NuTeV Fermilab
The highest energy (anti-) neutrino DIS experiment
Fixed targets results: An overview (PDG)
F 2 : 1< Q 2 < 200 GeV 2 F 3 : 1< Q 2 < 200 GeV 2 F L
H1
The HERA Collider
The first and only ep collider in the world Zeus
e ± p 27.5 GeV 920 GeV √s = 318 GeV Equivalent to fixed target experiment with 50 TeV e ±
Two independent storage rings
H1 HERA-B HERMES ZEUS
H1 – ZEUS Colliding beam experiments HERA-B Uses p beam on wire target Goal: B - physics HERMES Uses e ± beam on gas jet target Both lepton and target polarized Measurement of polarized structure functions
The Collider Experiments
H1 Detector
Complete 4π detector with Tracking Si-μVTX Central drift chamber Liquid Ar calorimeter
î E=E = 12%= p î E=E = 50%= p E[GeV ] (e:m:) E[GeV ] (had)
Rear Pb-scintillator calorimeter
î E=E = 7:5%= p E[GeV ] (e:m:)
μ chambers and much more…
ZEUS Detector
Both detectors asymmetric Complete 4π detector with Tracking Si-μVTX Central drift chamber Uranium-Scintillator calorimeter
î E=E = 18%= p î E=E = 35%= p E[GeV ] (e:m:) E[GeV ] (had)
μ chambers and much more…
Kinematic Regions of DIS
NC:
NC and CC incl. Processes measured at HERA
NC :
e
p
e
X
, CC :
e
p
n
e
( n
e
)
X
missing n momentum CC:
Measurement of F
g 2
(x,Q
2
)
• For
Q 2 « M Z 2 → xF 3
negligible; •
F L
only important at high y; • Both
F L
and
xF 3
~ calculable in QCD • Correct for higher order QED radiation • Extract
F 2 (x,Q 2 )
from d 2 s ep measurement of 2 These are difficult measurements: nevertheless precision level has reached: errors of 2-3%
A major finding at Hera: rise of F 2 (x,Q) at small x Early fixed-target results: F 2 rise towards low-x established with ~20 nb -1 in early Hera run Recent precise determination of F 2 (1996-97 data samples)
F 2 At high-Q limited… 2 → still statistics priority to the measurements at high-Q 2
Physical Interpretations of DIS Structure Function measurements • The Parton Model (Feynman-Bjorken) • Theoretical basis of the parton picture and the QCD improved parton model high energy (Bjorken) limit
Features of the DIS structure functions due to SM couplings For CC processes, only one helicity vertex (out of 2x2x3=12) is non-zero : In Brick-Wall (Breit) frame: Vector g coupling: y Lorentz boost with
v = tanh
y Allowed spin configurations: m n
W + u d W +
Left-handed W coupling:
continued Consequences on CC Cross sections (parton model level): These qualitative features were verified in early (bubble chamber) high energy neutrino scattering experiments.
Gargamelle (CERN)
Refined measurements reveal QCD corrections to the approximate naïve parton model results. These are embodies in all modern “QCD fits” and “global analyses”.
Leading (diagonal) EM NC scattering processes: a
F long = 0
no parity violation (y is the hyperbolic “angle” connecting the lepton and hadron vertices.) Analogous to the familiar angular distribution of scat tering of spin ½ elementary particles in the CM frame: At HERA, the g
-Z
interference term also contribute, giving rise to more complicated patterns for the “angular” (y) distribution.
Features of the partonic interactions revealed by DIS experiments have firmly established that the lepton probes interact primarily with spin ½ quark partons inside the nucleons with couplings of the SM.
Structure functions: Quark Parton Model
Quark parton model (QPM) NC SFs for proton target: [
F
2
γ
,
F
2
γ Z
,
F
2
Z
]
=
x
∑
[
e
2
q
, 2
e q v q
,
q v
2
q
+
a
2
q
]{
q
+
q
} [
xF
3
γ Z
,
xF
3
Z
]
=
2
x
∑
[
e q a q
,
v q a q q
] {
q
-
q
}
=
QPM CC SFs for proton targets: 2
x
∑
q
=
u
,
d
[
e q a q
,
v q a q
]
q v xF CC
2 ,
e
+
+
=
x
{
u
+
c
+
d
+
s
},
xF
3 ,
CC e
+
+
=
x
{
d
+
s
(
u
+
c
)}
xF
CC 2 ,
e -
-
=
x
{
u
+
c
+
(
d
+
s
)},
xF
3 ,
CC e -
-
=
x
{
u
+
c
(
d
+
s
)} For neutron targets, invoke (flavor) isospin symmetry: _
u
d and u
_
d
High-Q2 CC cross section from HERA
Comparing NC and CC Xsec’s at HERA: EW Unification
NC cross section sharply decreases with decreasing Q 2 (dominant γ exchange): ~ 1/Q 4 CC cross section approaches a constant at low Q 2 ~[M 2 W /(Q 2 +M 2 W )] 2 Dramatic confirmation of the unification of the electromagnetic and weak interactions of the SM in Deep Inelastic Scattering.
Manifestation of g Z interference: xF 3 (NC) at Hera
xF
3
NC
=
1 2
Y
[ (
e
-
p
) (
e
+
p
)]
Needs better e
-
data!
d
2
σ NC Born
(
dxdQ
2
e
±
p
)
=
2
πα
2
xQ
4 [
Y
+
F
2
NC
(
x
,
Q
2 ) -
y
2
F L NC
(
x
,
Q
2 )
Y
-
xF
3
NC
(
x
,
Q
2 )]
xF 3 γZ (NC)
xF
3
NC
=
-
a e
(
Q
2
κ Q
2
+
M
2
Z
)
xF
3
γ Z
+
( 2
v e a e
)(
Q
2
κ Q
+
2
M
2
Z
) 2
xF
3
Z xF
3
γ Z
≈
-
F
3
NC
(
Q
2
+
M
2
Z
) /(
a e κ Q
2 )
Helicity structure
Needs e data
QCD and DIS
Cf. Introductory course by Sterman m is the factorization scale. Usually choose m
= Q
: that is how
f(x,Q)
acquires
Q
-dep .
F
2
: “Scaling violation” — Q-dependence inherent in QCD
Renormalization group equation governs the scale dependence of parton distributions and hard cross sections.
(DGLAP) Rise with increasing Q at small-x Flat behavior at medium x decrease with increasing Q at high x
QCD evolution
Cf. Introductory course by Sterman Evolution performed in terms of (1/2/3) non-singlet, singlet and gluon densities: ln m
F
2
q NS
P NS
q NS
ln m
F
2 S
g
Where
P
(
x
)
a S P
( 0 ) (
x
)
a S
2
P
( 1 ) (
x
) 0 ln m m
F R
2 2
P qq P gq P qg P gg
S
g P
( 0 ) (
x
) with
a S
P q a
S
4 ( m
R
2 )
d da
ln
S
m
R
2 (
a S
)
l
0
a S l
2
l
a S
2 0
a S
3 1 w here 0 11 2 3
N F
and 1 102 38
N F
3
Parton Distribution Functions (PDF): most significant physical results derived from DIS (with help from other hard scattering processes) A common misconception: Parton distribution functions “Structure functions” These are the hard Xsecs.
These are the (process-dep) S.F.s
These are the (universal) PDFs There is a convo lution integral and a summation over partons here!
Parton Distributions: one example
Cf. course on global analysis and PDFs
Outline of the course: • Basic Formalism • Experimental Development – Fixed target experiments – HERA experiments • Parton Model and QCD
Summary and Conclusion
Important to know the model indep. foundation of the measured structure There is a long and distinguished history, dating back to Rutherford These highest energy and highest statistics expts. provide the basis for modern precision phenomenology – Asymptotic freedom, factorization and QCD the nucleon, and confirmed every • Phenomenology aspect of the SU(3)xSU(2)xU(1) SM. – QCD parameters – Parton distribution functions – Other interesting topics Cf. the rest of the Summer School courses for exciting consequences of PQCD as well as other modern theories to follow.