Introduction to Deep Inelastic Scattering DIS

1
Introduction to Deep Inelastic Scattering (DIS)

• Rik Yoshida
• Argonne National Laboratory
• CTEQ summer school 07
• May 30, 2007

2
Some preliminary remarks

• This is not a historical review
• for a very nice historical review see
  EnricoTassis lectures from 2003
• http//www-zeus.desy.de/tassi/cteq2003.ppt
• Nor a review of experimental status
• Enricos second lecture (same place)
• Max Kleins DIS lecture from CTEQ 2006
• Nor a theoretical discussion
• Morning lectures from George Sterman
• Aim to leave you with some intuitive feeling for
  what is happening in Deep Inelastic Scattering
  (DIS). Going to stick to electron- (positron-)
  proton DIS

3
Partons in the proton
Feynmans parton model the nucleon is made up of
point- like constituents (later identified with
quarks and gluons) which behave incoherently. The
probability f(x) for the parton f to carry the
fraction x of the proton momentum is an intrinsic
property of the nucleon and is process
independent.
If I were thinking about an experiment where
we collide protons with protons at, say, 14 TeV
then this is great! Because -Protons are just
a beam of partons (incoherent) -The f(x)s, the
beam parameters, could be measured in some
other process. (process independent)
4
Quarks and Gluons as partons
u(x) up quark distribution u(x) up
anti-quark distribution etc.
Momentum has to add up to 1 (momentum sum rule)
?xu(x)u(x)d(x)d(x)s(x)s(x).dx 1
Quantum numbers of the nucleon has to be right
So for a proton
?u(x)-u(x)dx2
?d(x)-d(x)dx1
?s(x)-s(x)dx0
5
DIS kinematics
ep collision
proton in 8 momentum frame
No transverse momentum
0 x 1
x fractional longitudinal momentum
carried by the struck parton
vs ep cms energy
Q2-q2 4-momentum transfer squared
(or virtuality of the photon)
6
DIS kinematics
Final electron energy
ep collision
Initial electron energy
Q2-q2-(k-k)22EeEe(1cos?e)
Ee Ee (1cos?e)
x Q2/2Pq
EP 2Ee-Ee(1-cos?e)
Initial proton energy
Electron scattering angle
Everything we need can be reconstructed from
the measurement of Ee and ?e. (in principle)
7
Deep Inelastic Scattering experiments
HERA collider H1 and ZEUS experiments 1992
2007 (will complete July 2, 2007)
Fixed target DIS at SLAC, FNAL and CERN
completed 10-20 years ago
8
e-p Neutral Current (NC) cross-section
Has to do with long. photon. Only large at
largest y
Well come back to these
Has to do with Z0 exchange small for QltltMZ
d2s 2pa2

YF2(x,Q2)-y2 FL(x,Q2)Y-xF3(x,Q2)
dxdQ2 xQ4
yQ2/xs 0 y 1 inelasticity
Y1(1-y)
So for now
d2s 2pa2

YF2(x,Q2)
dxdQ2 xQ4
quark charge
2
F2 x?(q q) eq Z-exchange
quark and anti-quark distributions
9
IF, proton was made of 3 quarks each with 1/3 of
protons momentum
no anti-quark!
2
F2 x?(q(x) q(x)) eq
q(x)d(x-1/3)
F2
or with some smearing
x
1/3
The partons are point-like and incoherent then Q2
shouldnt matter. ? Bjorken scaling F2 has no Q2
dependence.
Lets look at some data?
10
Proton Structure Function F2
F2
Seems to be.
NOT
11
So what does this mean..?
QCD, of course
q
quarks radiate gluons
q
q
gluons can produce qq pairs
q
gluons can radiate gluons!
12
Proton
e
1.6 fm (McAllister Hofstadter 56)
?(Q2)
e
r
Virtuality (4-momentum transfer) Q gives the
distance scale r at which the proton is probed.
r hc/Q 0.2fm/QGeV
CERN, FNAL fixed target DIS rmin 1/100
proton dia. HERA ep collider DIS
rmin 1/1000 proton dia.
HERA Ee27.5 GeV, EP920 GeV
13
F2
Higher the resolution (i.e. higher the Q2) more
branchings to lower x we see.
So what do we expect F2 as a function of x at a
fixed Q2 to look like?
14
F2(x)
Three quarks with 1/3 of total proton momentum
each.
x
1/3
F2(x)
Three quarks with some momentum smearing.
x
1/3
F2(x)
The three quarks radiate partons at low x.
x
1/3
15
Proton Structure Function F2
How this change with Q2 happens quantitatively
described by the Dokshitzer-Gribov-Lipatov-Alta
relli-Parisi (DGLAP) equations
16
DGLAP equations are easy to understand
intuitively
First we have the four splitting functions
z
z
z
z
1-z
1-z
1-z
1-z
Pab(z) the probability that parton a will
radiate a parton b with the fraction
z of the original momentum carried by a.
17
Now DGLAP equations (schematically)
convolution
dqf(x,Q2)
o
o
as qf Pqq g Pgq
d ln Q2
strong coupling constant
Change of quark distribution q with Q2 is given
by the probability that q and g radiate q.
Same for gluons
dg(x,Q2)
o
as ?qf Pqg g Pgg
o
d ln Q2
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DGLAP fit (or QCD fit) extracts the
parton distributions from measurements.
(Lectures by Jeff Owens next week)
Heres a 1 min description
Step 1 parametrise the parton momentum desity
f(x) at some Q2. e.g. uv(x) u-valence
dv(x) d-valence g(x) gluon
S(x) sum of all sea (i.e. non valence)
quarks Step 2 find the parameters by fitting
to DIS (and other) data using DGLAP equations to
evolve f(x) in Q2.
f(x)p1xp2(1-x)p3(1p4vxp5x)
The orginal three quarks
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At xltlt1/3, quarks and (antiquarks) are all
sea. Since F2 eq ?x(q q), xS is very much
like F2
2
Sea PDF
xS
Fractional uncertainty
x
20
Gluons, on the other hand, are determined
from the scaling violations dF2/dlnQ2 via the
DGLAP equations.
Gluon PDF
xg
Uncertainties are larger. Scaling violations
couple as and gluon g
Fit with as also a free param.
x
21
So far F2 ?(qq) S (sea quarks)
measured directly in
NC DIS Scaling
violations dF2/dlnQ2 asg Scaling
violations gives gluons
(times as). DGLAP
equations. What about valence quarks?
?(q-q) uv dv can we determine them
separately? Can we decouple as and g ?
22
Return to Neutral Current (NC) cross-section
Now write out the ep and e-p separately
(keep ignoring FL for now..)
Y1(1-y)
d2s(ep) 2pa2

YF2(x,Q2) Y-xF3(x,Q2)

dxdQ2 xQ4
xF3 ?(q(x,Q2)-q(x,Q2)) xBq The valence quarks!
Bq -2eqaqae?Z 4vqaqveae?Z
2
Bq -2eqaqae?Z 4vqaqveae?Z
2
1 Q2
?Z ( ) Keeps xF3 small
if QltMZ
2
sin2?W MZQ2
23
Return to Neutral Current (NC) cross-section
Now write out the ep and e-p separately
(keep ignoring FL for now..)
Y1(1-y)
d2s(ep) 2pa2

YF2(x,Q2) Y-xF3(x,Q2)

dxdQ2 xQ4
xF3 ?(q(x,Q2)-q(x,Q2)) xBq The valence quarks!
Bq -2eqaqae?Z 4vqaqveae?Z
2
Bq -2eqaqae?Z 4vqaqveae?Z
2
?-Z interference
Z-exchange
eq electric charge of a quark aqvq axial-vector
and vector couplings of a quark aeve
axial-vector and vector couplings of an electron
24
Return to Neutral Current (NC) cross-section
Now write out the ep and e-p separately
(keep ignoring FL for now..)
Y1(1-y)
d2s(ep) 2pa2

YF2(x,Q2) Y-xF3(x,Q2)

dxdQ2 xQ4
xF3 ?(q(x,Q2)-q(x,Q2)) xBq The valence quarks!
Lets look at the reduced NC cross-section
sNC F2(x,Q2) (Y-/Y)xF3(x,Q2)

Note the change of sign from ep to e-p
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Reduced Neutral Current Cross-section
sNC
x
Measurements are at relatively high x
26
Recent (Spring 07) preliminary result from HERA
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Charged Current Cross-Sections
2
2
dsCC(ep) GF MW
2sCC
dxdQ2 2px MWQ2
2
Skip a few steps.
sCC x u c (1 - y)2(d s) d
sCC- x u c (1 y)2(d s) u
charm
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Reduced Charged-Current Cross-Section
sCC
sCC d
sCC- u
x
Now lets look at the valence quarks from the QCD
fits ?
29
Valence PDFs
xf
x
The momenta from valence quarks are
producing gluons and sea quarks at low x
30
Jet production in DIS (HERA)
sjet asf(x)
Sensitive to as
Sensitive to gluon 10-3 lt x lt 10-2
Sensitive to quarks 10-2 lt x lt 10-1
complementary to gluon from F2
Same range as NC and CC
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Jet measurements in Breit frame
No ET in Breit Frame
Jet production cross-section used in QCD fit ?
32
Gluon distributions
x
x
Using only HERA (ZEUS) data including NC,CC and
jets
Using HERA (ZEUS) F2 data and FNAL, CERN fixed tgt
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Finally
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Proton Structure Function F2
F2
Now we understand what is happening here.
35
Some remarks about DGLAP equations
The incoherence of the original parton model is
preserved. i.e. a parton doesnt know
anything about its neighbor.
never happens
The process independent partons also survive.
But now parton densities must be evolved in
Q2. What does this mean? ?
36
A parton at x at Q2 is a source of partons at x
lt x at Q2 gt Q2.
In fact, any parton at x gt x at Q2 is a source.
unknown
Q2
known
To know the parton density at x, Q2 its
necessary (and sufficient) to know the parton
density in the range x x 1 at some lower
Q2.
Q2
measured
1
x
x
If you know the partons in range x x 1 at
some Q2, then you know the partons in the range
x x 1 for all Q2 gt Q2.
What does this mean for the LHC? ?
37
Tevatron jets
known
HERA DIS
Fixed target DIS
safe Q2
38
LHC (or hadron-hadron) parton kinematics
rapidity
1 EPZ
y ln( )
2 E-PZ
pseudo-rapidity
?-ln tan(?/2)
2
4
angle wrt beam
parton1(x1) parton2(x2) ? State with mass M
x1 (M/vs) exp (y)
x2 (M/vs) exp (-y)
39
s(pp?W,ZX) q,q(x1,MW,Z) q,q(x2,MW,Z)
s(qq?W,Z)
2
2
So if I want to predict Z or W production cross-se
ction at LHC at some rapidity y, say, -4
need
and
2
4
2
2
q,q(x110-4,Q2MW,Z)
q,q(x20.3,Q2MW,Z)
40
Evolving PDFs up to MW,Z scale
xf(x)
xg(x)
evolved
xS(x)
measured
measured
xg(x)
xS(x)
41
Examples of predictions for LHC using partons
from DIS
Jet production at LHC
Z production at LHC
Uncertainty 5
s(arb. scale)
-6
6
?
A. Cooper-Sarkar (HERA-LHC workshop 2007)
42
Final remarks I

• Weve just gone through an informal tour of
  QCD-improved parton model and its application to
  data from ep Deep Inelastic Scattering.
• Some health warnings
• Most of what I talked about is a leading-order
  picture. In practice, most things are done at
  least to next-to-leading order. At NLO, the
  interpretation of the results are not as
  straight-forward.
• Many people worry about whether we are not
  missing something fundamentally with the picture
  of DGLAP equations.
• Much of the data are at very low x DGLAP is a
  lnQ2 approximation. Why arent ln(1/x) terms
  importantor are they? ? BFKL equations.
• The density of the partons, especially that of
  the gluons is getting very high. When and where
  should we worry about shadowing, gluon
  recombination etc.
• The idea of incoherence of partons may be
  breaking down in some kinematic regions
  phenomenon of hard diffraction is difficult to
  understand in terms of partons without
  correlations to each other.

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Final remarks II

• There are many other DIS physics topics I did not
  cover here.
• Electoweak physics
• Heavy quark production
• Diffraction, Vector Meson production, low Q2
  physics
• Beyond the SM searches.
• Polarized DIS
• I hope I have refreshed your memory about some
  familiar DIS physics, and got you ready for the
  rest of the school.
• Thanks to the organizers for their kind
  invitation. Thanks to Claire Gwenlan for
  preparing some of the plots animation for me.
• You can find the animated gifs in
• http//www.hep.anl.gov/ryoshida/animated_proton.ht
  m

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Extras (FL)
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Longitudinal cross-section
FL(Q2/4p2a) sL
46
QCD predicts a relationship between scaling
violations and FL through the gluon density.
increasing y
47
You can determine FL from a NLO DGLAP fit to NC
cross-section.
Indeed, we also only determine F2 the same way,
in principle
We measure this only
x
48
HERA measurement of FL on-going now
Normally 920 GeV
C. Diaconu DIS 07 conference April 07