deep inelastic scattering cteq summer school madison, wi, july 2011 cynthia keppel hampton...
TRANSCRIPT
![Page 1: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/1.jpg)
Deep Inelastic ScatteringCTEQ Summer SchoolMadison, WI, July 2011
Cynthia KeppelHampton University / Jefferson
Lab
![Page 2: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/2.jpg)
40 years of physicsMaybe 100 experiments
...in an hour…..
QuickTime™ and a decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
![Page 3: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/3.jpg)
How to probe the nucleon / quarks?
• Scatter high-energy lepton off a proton: Deep-Inelastic Scattering (DIS)
• In DIS experiments point-like leptons + EM interactions which are well understood are used to probe hadronic structure (which isn’t).
• Relevant scales:
m 10 18−≈=∝p
dprobedh
D
QuickTime™ and a decompressor
are needed to see this picture.
large momentum -> short distance (Uncertainty Principle at work!)
![Page 4: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/4.jpg)
DIS Kinematics• Four-momentum transfer:
• Mott Cross Section (c=1):
22
2'
2
22
sin'4
)cos|'| ||'(2
)'()'()'(
QEE
kkEEmm
kkkkEEq
ee
−≡−≈
=−−+=
=−⋅−−−=
2θ
θrr
rrrr
sorhadron ten :
sorlepton ten :
μν
μν
W
L
)sin2(11
sin4
cos
)cos1(112
sin'16'4
'2'4
22
242
222
2422
22
4
22
cos
cos)(
θθ
θ
θ
α
θθα
θασ
ME
ME
E
EEE
EE
QE
Mottdd
+
−+2
2Ω
⋅=
⋅=
⋅=
Electron scattering of a spinless point particle
a virtual photon of four-momentum q is able to resolve structures of the order /√q2
![Page 5: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/5.jpg)
• Effect of proton spin:
– Mott cross section:
– Effect proton spin • helicity conservation
• 0 deg.: σep(magnetic) 0
• 180 deg.: spin-flip!
σmagn ~ σRuth sin2(θ/2)
~ σMott tan2(θ/2)
• with
• Nucleon form factors:
with:
• The proton form factors have a substantial Q2
dependence.
Electron-Proton Scattering
]2
tan21[ 2
21
θτσσ +⋅∝−− Mottspine
22
2
4 cM
Q=τ
2222
2 2)( 1
)( and MME GQB
GGQA τ
ττ
=++
=
]2
tan)()([ 222 θσσ QBQAMottep +=
22 ≡⋅= θθα σσ 2'2'4 coscos4
22
RuthEE
QE
Mott
Mass of target = proton
NNgn
MnE
NN
gpM
pE
n
p
GG
GG
μμ
μμ
91.1- )0( 0)0(
2.79 )0( 1)0(
2
2
and
and
===
===
![Page 6: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/6.jpg)
Measurement kinematics…
ep collision
Q2=-q2=-(k-k’)2=2EeE’e(1+cosθe)
Initial electron energy
Final electron energy
Electron scattering angle
Everything we need can be reconstructed from themeasurement of Ee, E’e and θe. (in principle) ->
try a measurement!….
W2=(q + Pp)2= M2 + 2M(Ee-E’e) - Q2 = invariant mass
of final state hadronic system
![Page 7: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/7.jpg)
Excited states of the nucleon
• Scatter 4.9 GeV electrons
from a hydrogen target. At 10
degrees, measure ENERGY
of scattered electrons
• Evaluate invariant energy of
virtual-photon proton system:
W2 = 10.06 - 2.03E’e *
• In the lab-frame: P = (mp,0) 2222 2)( qPqPqPW p ++=+=
222 2 QmmW pp −+= ν → What do we see in the data for W > 2 GeV ?
(1232)
• Observe excited resonance states:
Nucleons are composite
* Convince yourself of this!
![Page 8: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/8.jpg)
• First SLAC experiment (‘69):– expected from proton form factor:
• First data show big surprise:– very weak Q2-dependence– form factor -> 1!– scattering off point-like objects?
)71.0/1(
1
)/(
'/ 8
2
22Mott
−∝⎟⎟⎠
⎞⎜⎜⎝
⎛+
=Ω
ΩQ
QddddEd
σσ
…. introduce a clever model!
QuickTime™ and a decompressor
are needed to see this picture.
![Page 9: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/9.jpg)
The Quark-Parton Model• Assumptions:
– Proton constituent = Parton– Elastic scattering from a quasi-
free spin-1/2 quark in the proton
– Neglect masses and pT’’s,
“infinite momentum frame”
• Lets assume: pquark = xPproton
– Since xP2 M2 <<Q2 it follows:
0')( 222 ≈==+ quarkquark mpqxP
e
P
parton
e’
νM
Q
Pq
QxqqxP
22 02
222 ==⇒≈+⋅
• Check limiting case:
• Therefore:
x = 1: elastic scattering
and 0 < x < 1Definition Bjorken scaling variable
21222 2 px
pp MQMMW ⏐⏐ →⏐−+= →ν
ν = (q.p)/M = Ee-Ee’
![Page 10: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/10.jpg)
Structure Functions F1, F2
• Introduce dimensionless structure functions:
• Rewrite this in terms of : (elastic e-q scatt.: 2mqν = Q2 )
• Experimental data for 2xF1(x) / F2(x)
→ quarks have spin 1/2
(if bosons: no spin-flip F1(x) = 0)
( )⎥⎦⎤
⎢⎣
⎡ +⎟⎠
⎞⎜⎝
⎛Ω
=Ω
⇒== 2/tan)(2
)(1
' and 2
122211 θν
ν
σσν xF
MxF
d
d
ddE
dWFMWF
M
22 4/ quarkmQ=τ
2 )()( if 12 xFxF x=
( )
( )
( ) 2/tan )(1
2/tan)()(1
2/tan)(4
4)(
1
'
22
212
212
2
2
2
2
21
22
2/
⎥⎦⎤
⎢⎣⎡=
⎥⎦⎤
⎢⎣⎡=
=⎥⎥⎦
⎤
⎢⎢⎣
⎡=⎟
⎠
⎞⎜⎝
⎛ΩΩ
+
⋅+
+
θν
θν
θν
ν
σσ
τ
τ
xF
xFxF
xFMQ
m
m
QxF
d
d
ddE
d
x
q
qM
![Page 11: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/11.jpg)
Interpretation of F1(x) and F2(x)
)]( )([)( 221
1 xqxqzxF ff ff∑ +=
• In the quark-parton model:
QuickTime™ and a decompressor
are needed to see this picture.
Quark momentum distribution
![Page 12: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/12.jpg)
The quark structure of nucleons
• Quark quantum numbers:
– Spin: ½ Sp,n = () = ½
– Isopin: ½ Ip,n = () = ½
• Why fractional charges?– Extreme baryons: Z =
– Assign: zup =+ 2/3, zdown = - 1/3
• Three families:
– mc,b,t >> mu,d,s : no role in p,n
• Structure functions:
– Isospin symmetry:
– ‘Average’ nucleon F2(x)
with q(x) = qv(x) + qs(x) etc.
• Neutrinos:
)]()()([
)]()()([
91
94
91
2
91
94
91
2
ssns
ns
nv
ns
ns
nv
n
ssp
sps
pv
ps
ps
pv
p
ssuuudddxF
ssuuudddxF
+++++++=
+++++++=
32
31- 231 +≤≤⇒+≤≤− qq zz
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛b
t
s
c
d
u
bsd
tcu
mmmz
mmmz
;
;
GeV) 3.0(31
GeV) 5.1(32
<<<<−=⇒
<<<<+=⇒
≈
≈
ps
ps
ns
ns
pv
nv
pv
nv duduuddu ===== , ,
)]()([ ))()((
)(
91
,185
2221
2
xsxsxxqxqx
FFF
ssdu
npN
+⋅++⋅=
+=
∑
))()(( )]()[(
)]()()[(
,,
2
xqxqxsudsudx
ssuuudddxF
sdusss
ssssvssv
+=+++++=
+++++++=
∑
ν
)2,1( +−
![Page 13: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/13.jpg)
• Neglect strange quarks
– Data confirm factor 5/18:
Evidence for fractional charges
• Fraction of proton momentumcarried by quarks:
– 50% of momentum due to non-electro-weak particles:
Evidence for gluons
Fractional quark charges
5.0)()(1
0
,25
181
0
,2 ≈= ∫∫ dxxFdxxF NeNν
18
5,
2
,2 ≈N
Ne
FF
ν
ν
μ
![Page 14: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/14.jpg)
The partons are point-like and incoherentthen Q2 shouldn’t matter.
Bjorken scaling: F2 has no Q2 dependence.
IF, proton was made of 3 quarks each with 1/3 of proton’smomentum:
F2 = x∑(q(x) + q(x)) eq
no anti-quark!
F2
1/3 x
q(x)=δ(x-1/3)
or with some smearing
2
![Page 15: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/15.jpg)
Thus far, we’ve covered: Some history Some key results Basic predictions of the parton model The parton model assumes: Non-interacting point-like particles → Bjorken scaling, i.e. F2(x,Q2)=F2(x) Fractional charges (if partons=quarks) Spin 1/2 Valence and sea quark structure (sum rules) Makes key predictions that can be tested by experiment…..
![Page 16: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/16.jpg)
Proton Structure Function F2
F2
Seems to be….…uh oh…
Let’s look at some data
Lovely movies are from R. Yoshida, CTEQ Summer School 2007
![Page 17: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/17.jpg)
Deep Inelastic Scattering experiments
Fixed target DIS at SLAC, FNAL, CERN, now JLab
HERA collider: H1 and ZEUS experiments 1992 – 2007
![Page 18: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/18.jpg)
Modern data • First data (1980):
• Now..“Scaling violations”:– weak Q2 dependence– rise at low x– what physics??
PDG 2002
….. QCD
![Page 19: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/19.jpg)
g
Quantum Chromodynamics (QCD)• Field theory for strong interaction:
– quarks interact by gluon exchange
– quarks carry a ‘colour’ charge
– exchange bosons (gluons) carry
colour self-interactions (cf. QED!)
• Hadrons are colour neutral:– RR, BB, GG or RGB
– leads to confinement:
• Effective strength ~ #gluons exch.
– low Q2: more g’s: large eff. coupling
– high Q2: few g’s: small eff. coupling
forbidden |or | ,| ⟩⟩⟩ qqqqqq
q
q
sα
sαg
QuickTime™ and a decompressor
are needed to see this picture.
![Page 20: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/20.jpg)
The QCD Lagrangian
aas Ggi μμμ λ2
1+∂=D4 34 2144 344 21
aaabcs
aaaìí GGfgGGG νμμννμ −∂−∂=
μνμνμ
μ ψψψγψ aa
q
kq
jqq
kqjk
q
jqqcd GGmi 4
1) −−= ∑∑ (DL
(j,k = 1,2,3 refer to colour; q = u,d,s refers to flavour; a = 1,..,8 to gluon fields)
Covariant derivative:
Gluon kineticenergy term
Gluon self-interaction
Free quarks
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛−=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛ −=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛−=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛ −=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
200
010
001
3
1
00
00
000
010
100
000
00
000
00
001
000
100
000
010
001
000
00
00
000
001
010
8765
4321
λλλλ
λλλλ
i
i
i
i
i
iqg-interactionsSU(3) generators:
)],([ 21
cabcba fi λλλ =
![Page 21: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/21.jpg)
So what does this mean..?
QCD brings new possibilities:
quarks can radiate gluons
q
q
q
q
gluons can produce qq pairs
gluons can radiate gluons!
![Page 22: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/22.jpg)
r≈ hc/Q = 0.2fm/Q[GeV]
rγ*(Q2)
Virtuality (4-momentum transfer) Q gives the distancescale r at which the proton is probed.
~1.6 fm (McAllister & Hofstadter ’56)
CERN, FNAL fixed target DIS: rmin≈ 1/100 proton dia.HERA ep collider DIS: rmin≈ 1/1000 proton dia.
e
e’
Proton
HERA: Ee=27.5 GeV, EP=920 GeV(Uncertainty Principle again)
![Page 23: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/23.jpg)
Higher the resolution (i.e. higher the Q2) more low x partons we “see”.
So what do we expect F2 as a function of x ata fixed Q2 to look like?
F2QuickTime™ and a
decompressorare needed to see this picture.
![Page 24: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/24.jpg)
1/3
1/3
1/3
F2(x)
F2(x)
F2(x)
x
x
x
Three quarks with 1/3 of total proton momentum each.
Three quarks with some momentumsmearing.
The three quarks radiate partons at low x.
QuickTime™ and a decompressor
are needed to see this picture.
….The answer depends on the Q2!
![Page 25: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/25.jpg)
Proton Structure Function F2
How this change with Q2 happens quantitatively described by the:
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations
![Page 26: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/26.jpg)
QCD predictions: scaling violations• Originally: F2 = F2(x)
– but also Q2-dependence
• Why scaling violations?– if Q2 increases:
more resolution (~1/ Q2)
more sea quarks +gluons
• QCD improved QPM:
• Officially known as: Altarelli-Parisi Equations (“DGLAP”) = ),( 2
2
x
QxF++
2 2
![Page 27: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/27.jpg)
DGLAP equations are easy to “understand” intuitively..
First we have 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.
These additional contributions to F2(x,Q2) can be calculated.
![Page 28: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/28.jpg)
= αs [qf × Pqq + g × Pgq]
Now DGLAP equations (schematically)
dqf(x,Q2)d ln Q2
convolution
strong coupling constant
qf is the quark density summed over all active flavors
Change of quark distribution q with Q2 is given by the probability that q and g radiate q.
dg(x,Q2)= αs [∑qf × Pqg + g × Pgg]d ln Q2
Same for gluons:
Violation of Bjorken scaling predicted by QCD - logarithmic dependence, not dramatic
![Page 29: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/29.jpg)
DGLAP fit (or QCD fit) extracts the partondistributions from measurements.
(CTEQ, for instance :) )
Basically, this is accomplished in two steps:
Step 1: parametrise the parton momentum density f(x) at some Q2. e.g.
uv(x) u-valence dv(x) d-valence g(x) gluon S(x) “sea” (i.e. non valence) quarks
Step 2: find the parameters by fitting to DIS (andother) data using DGLAP equations to evolve f(x) inQ2.
“The original three quarks”
f(x)=p1xp2(1-x)p3(1+p4√x+p5x)
![Page 30: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/30.jpg)
QuickTime™ and a decompressor
are needed to see this picture.
The DGLAP evolution equations are extremely useful as they allow structure functions measured by one experiment to be compared to other measurements - and to be extrapolated to predict what will happen in regions where no measurements exist, e.g. LHC.
QuickTime™ and a decompressor
are needed to see this picture.
QCD fits of
F2(x,Q2) data
Q2
x
![Page 31: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/31.jpg)
xf(x)
xS(x)xg(x) “measured”
“measu
red”
“evolved”xg(x)
xS(x)
Evolving PDFs up to MW,Z scale
![Page 32: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/32.jpg)
Finally…
Sea quarks and gluons - contribute at low values of x
Valence quarks maximum around x=0.2; q(x) →0 for x→1 and x→0
![Page 33: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/33.jpg)
PDG 2002
QCD predictions: the running of αs
• pQCD valid if αs << 1:
Q2 > 1.0 (GeV/c)2
• pQCD calculation:
– with exp = 250 MeV/c:
asymptotic freedom
confinement
)/ln()233
12)(
222
⋅−(=
QnQ
fs
πα
0 2 →⇒∞→ sQ α
∞→⇒→ sQ α 02
Running coupling constant isquantitative test of QCD.
CERN 2004
![Page 34: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/34.jpg)
QCD fits of F2(x,Q2) data• Free parameters:
– coupling constant:
– quark distribution q(x,Q2)
– gluon distribution g(x,Q2)
• Successful fit:
Corner stone of QCD
16.0)/ln()
122
≈−(33
= 2Qnfs
πα
Quarks
Gluons
![Page 35: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/35.jpg)
What’s still to do?
![Page 36: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/36.jpg)
LOTS still to do!• Large pdf uncertainties still at large x, low x • pdfs in nuclei• FL structure function - unique sensitivity to the glue
(F2 = 2xF1 only true at leading order)• Spin-dependent structure functions and transversity• Generalized parton distributions• Quark-hadron duality, transition to pQCD• Neutrino measurements - nuclear effects different? F3 structure function (Dave
Schmitz talks next week)• Parity violation, charged current,….• NLO, NNLO, and beyond• Semi-inclusive (flavor tagging)• BFKL evolution, Renormalization
EIC
![Page 37: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/37.jpg)
Large x (x > 0.1) -> Large PDF Uncertainties
u(x) d(x)
d(x) g(x)
![Page 38: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/38.jpg)
Typical W, Q cuts are VERY restrictive….
Current Q2 > 4 GeV2, W2 > 12.25 GeV2, cuts
(Ignore red mEIC proposed data points.)
Essentially leave no data below x~0.75
What large x data there is has large uncertainty
Recent CTEQ-Jlab effort to reduce cuts
![Page 39: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/39.jpg)
The moon at nuclear densities (Amoon ≈ 5x1049)
Nuclear medium modifications, pdfs
![Page 40: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/40.jpg)
The deuteron is a nucleus, and corrections at large x matter….
QuickTime™ and a decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
Differential parton luminosities for fixed rapidity y = 1, 2, 3, as a function of τ = Q2/S, variations due to the choice of deuterium nucleon corrections.
The gg, gd, du luminosities control the “standard candle” cross section for Higgs, jet W- production, respectively.
The extremes of variation of the u,d, gluon PDFs, relative to reference PDFs using different deuterium nuclear corrections
![Page 41: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/41.jpg)
QCD and the Parton-Hadron Transition
Hadrons
Nucleons
Quarks and Gluons
![Page 42: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/42.jpg)
Quark-Hadron Duality
• At high energies: interactions between quarks and gluons become weak(“asymptotic freedom”) efficient description of phenomena afforded in terms
of quarks• At low energies: effects of confinement make strongly-
coupled QCD highly non-perturbative collective degrees of freedom (mesons and baryons)
more efficient• Duality between quark and hadron descriptions
– reflects relationship between confinement and asymptotic freedom
– intimately related to nature and transition from non-perturbative to perturbative QCD
Duality defines the transition from soft to hard QCD.
![Page 43: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/43.jpg)
Duality observed (but not understood) in inelastic (DIS) structure functions
First observed in F2 ~1970 by Bloom and Gilman at SLAC
• Bjorken Limit: Q2, ν
• Empirically, DIS region is where logarithmic scaling is observed: Q2 > 5 GeV2, W2 > 4 GeV2
• Duality: Averaged over W, logarithmic scaling observed to work also for Q2 > 0.5 GeV2, W2
< 4 GeV2, resonance regime
(CERN Courier, December 2004)
![Page 44: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/44.jpg)
Beyond form factors and quark distributions – Generalized Parton Distributions (GPDs)
Proton form factors, transverse charge & current densities
Structure functions,quark longitudinalmomentum & helicity distributions
X. Ji, D. Mueller, A. Radyushkin (1994-1997)
Correlated quark momentum and helicity distributions in transverse space - GPDs
![Page 45: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/45.jpg)
Again, LOTS still to do!• Large pdf uncertainties still at large x, low x • pdfs in nuclei• FL structure function - unique sensitivity to the glue
(F2 = 2xF1 only true at leading order)• Spin-dependent structure functions and transversity• Generalized parton distributions• Quark-hadron duality, transition to pQCD• Neutrino measurements - nuclear effects different? F3 structure function (Dave
Schmitz talks next week)• Parity violation, charged current,….• NLO, NNLO, and beyond• Semi-inclusive (flavor tagging)• BFKL evolution, Renormalization
EIC
![Page 46: Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab](https://reader036.vdocuments.us/reader036/viewer/2022081506/5697bf741a28abf838c7f667/html5/thumbnails/46.jpg)
More challenges….
• If αs >1 perturbative expansions fail…
• Extrapolate αs to the size
of the proton, 10-15 m:
1 >⇒→ sprotonrl α
Non-perturbative QCD:– Proton structure & spin
– Confinement
– Nucleon-Nucleon forces
– Higher twist effects
– Target mass corrections