drell yan cteq final 1 - smu
TRANSCRIPT
![Page 1: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/1.jpg)
CTEQ summer 01| brock | michigan state university | No. 1front nine
• we’re going to take a walk–“unspoiled”–on a tough course
• our walk will have only good lies, avoiding the rough
• we start in wide fairways, but dogleg to a difficult approach
• we’ll take drops, in order to stay in the fairway and avoid the rough
• we’ll use “gimmes” to quickly skip through material that Sopercovered (he’s already holed out)
• we’ll occasionally be schematic - it’s the broad lay of the land that Iwant to get across as this is highly technical stuff - doesn’t naturallyrecommend itself in full glory to lectures …
![Page 2: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/2.jpg)
CTEQ summer 01| brock | michigan state university | No. 2front nine
W and Z Boson Production and Resummation
1. a bit of history
2. Drell-Yan formalism
3. multiple gluon emission - Sudakov exponential
4. resummation: “CSS” formalism
5. W/Z boson production
6. global fitting of all Drell-Yan data - new
7. conclusions
naïve DY - kinematics and cross section
kinematics, corrected for finite pT
Compton and annihilation cross sections
www.pa.msu.edu/ ~brock/cteq01.pdf
The game is the Royal and Ancient:
![Page 3: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/3.jpg)
CTEQ summer 01| brock | michigan state university | No. 3front nine
It started innocuously enough…
Searching for the W
the idea was mature by 1960
• Heisenberg’s notion of an exchange force, 1932
• Fermi’s theory of b decay, 1934
• Yukawa’s notion of an exchanged boson, 1935
Feynman and GellMann, 1958
• an audacious paper - so enamored of the “Universal V-A”interaction that they introduced, that they concluded that along-standing experiment on He was wrong: A not themeasured T.
Lee and Yang
• didn’t predict parity violation in 1957, but indicated that ithadn’t been tested
• in 1960, fleshed out the properties of the W (W 0 & W ± ) andproposed production scenarios
![Page 4: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/4.jpg)
CTEQ summer 01| brock | michigan state university | No. 4front nine
Lee and Yang considered W production
p
Fe
mn K, p decays a serious low pT bkgnd
but W should produce high pT m’s
pTMW/2
n m n
n
N N W
h N pW
Æ Æ
Æ Æ
( )
( )
l
lthey suggested
no evidence of W, but what Lederman and Pope found was a little unsettling:• unrelated to the W search, at a suggestion that there would be a gggg
continuum, they looked…
An experiment was mounted in 1970 at BNL with a 30 GeV/cproton beam.
the search was on…
![Page 5: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/5.jpg)
CTEQ summer 01| brock | michigan state university | No. 5front nine
lotsa muons, 2 by 2
investigated by forming mass-pairs of muons
at very high pT’smomenta from range…
![Page 6: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/6.jpg)
CTEQ summer 01| brock | michigan state university | No. 6front nine
so what was it?
it’s not the W
the only known source was photons…but at such high pT?
• much theoretical scurrying about
• one explanation stuck - that of Drell and Yan in 1971
they extrapolated from the (young, circa. 1970) parton model to suggestthat the mechanism was:
we can quickly reproduce their calculation
![Page 7: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/7.jpg)
CTEQ summer 01| brock | michigan state university | No. 7front nine
immediate plans…
1. work out kinematics for the naïve model
2. calculate the naïve Drell-Yan cross section
– find some measurables
– check predictions
3. un-naïve the calculation a bit
– especially work on the kinematics for finite pT for theproduced photon
![Page 8: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/8.jpg)
CTEQ summer 01| brock | michigan state university | No. 8front nine
the Drell-Yan ansatz:
parton-parton scattering inside of hadrons
i.e, buried inside
Let’s calculate it:first, kinematics.we’ll presume the simple CM:
rp pV V= 3 k
independence and incoherenceof the primary process:
is
![Page 9: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/9.jpg)
CTEQ summer 01| brock | michigan state university | No. 9front nine
hadron/parton/V kinematics
partons
the IVB
hadrons parton-hadron
connection:
![Page 10: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/10.jpg)
CTEQ summer 01| brock | michigan state university | No. 10front nine
kinematics2
![Page 11: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/11.jpg)
CTEQ summer 01| brock | michigan state university | No. 11front nine
invariants
hadron invariants
parton invariants
here: t x x= a b•which allows for a definition: t = M s2 /
from equation (3)
![Page 12: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/12.jpg)
CTEQ summer 01| brock | michigan state university | No. 12front nine
rapidity
define:y
E p
E pVV V
V V
a
b
∫+
-
Ê
ËÁ
ˆ
¯˜
=Ê
ËÁ
ˆ
¯˜
12
12
ln
lnx
x
the familiar “rapidity”, additiveunder Lorentz boosts…
in this simple case:
= -( )x xa b P for thissimplecase
pM u
P
M t
PV3
2 2
4 4=
-Ê
ËÁ
ˆ
¯˜ -
-Ê
ËÁ
ˆ
¯˜so:
&
x ta bye, = ±using the above…
also, there are connections among invariants:
![Page 13: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/13.jpg)
CTEQ summer 01| brock | michigan state university | No. 13front nine
kinematical boundaries
for one early Drell-Yan experiment - E288
xF = 0
fixed xb/xa or y
xF > 0
xF < 0
t
t
![Page 14: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/14.jpg)
CTEQ summer 01| brock | michigan state university | No. 14front nine
world’s experimental regions
![Page 15: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/15.jpg)
CTEQ summer 01| brock | michigan state university | No. 15front nine
the Drell-Yan calculation
simple Feynman diagram:
colinear beams
integrate away “d”
detect angular distribution of “c”
d
T d
flux normalizationfi
s
r
=◊( )
ÂÂ2
2
___
with cross section
In CM of a+b:
d P P p p p p dP dPc d a b c d c d242r p d
r r r r, ( )( ) = + - -( )and
flux normalization p p m m p sa b a b◊( ) = ◊( ) - =4 42where
![Page 16: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/16.jpg)
CTEQ summer 01| brock | michigan state university | No. 16front nine
phase space reminder
my definitions…
d pc d p d p p d pc c c d d2 2 23r r r( ) ( , ) ( , )
r r r r= ∫ ÚW
ds
p
PT dc
fi
sp
= ÂÂ1
641
22
W___
so,
and then
d d p dp
p
sd
c c c
cc
2 2
216
r r
p
( ) ( )W
W
=
=
Úr
Kwhere
d p dp dE p
E p p p EE E
E E p p m
cc c c
a c a c cR c c
R
cR
a a c d
2 3 2
2
2
2 2
12 4
rp
d( )( )
( )r
r r
r r
=- ◊
Ê
ËÁ
ˆ
¯˜ -
= - -( ) +
W
![Page 17: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/17.jpg)
CTEQ summer 01| brock | michigan state university | No. 17front nine
matrix element
the whole enchilada
with our frame choice:
indicative of 1/2-1/2 scattering: a prediction
![Page 18: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/18.jpg)
CTEQ summer 01| brock | michigan state university | No. 18front nine
putting it together
the real inspiration:
a function which incoherently sums all quarks:
must average over colors - DY didn t know this
where is theprobability of finding an a-type parton in hadron Acarrying fraction of PA equalto xa
![Page 19: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/19.jpg)
CTEQ summer 01| brock | michigan state university | No. 19front nine
find some measurables…
in order to get the differential cross section:
use
d d d dx dQa b Fx x tÆ Æ 2
which allows us to calculate the Jacobian to take
We have a prediction:
this quantity is
independent of
Q … only t
(or ) plus
![Page 20: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/20.jpg)
CTEQ summer 01| brock | michigan state university | No. 20front nine
it worked!
Drell and Yan’s explanation of the Lederman/Poperesults proved substantially correct
early results demonstrated scaling…
…later results, even moreimpressively
…including the demonstrationof point -like 1/2-1/2 scattering
![Page 21: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/21.jpg)
CTEQ summer 01| brock | michigan state university | No. 21front nine
why “naïve”?
well, because of two approximations:
1. scale invariant parton distribution functions
2. presumption of the g produced with pT=0
and
![Page 22: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/22.jpg)
CTEQ summer 01| brock | michigan state university | No. 22front nine
loss of naiveté, 1
scale-violating pdf’s
The Factorization Theorem (Collins, Soper, Sterman) puts the physicallyappealing quark - parton model on a firm, formal basis:
physical cross section:
calculable, to a particular order in aS
separate short-distance (calculable) from long distance(not calculable) using a scale, mmmm f…hard part is only
implicitly dependent on mmmm f - in practice, mmmm f set = mmmm .
measurable, universal not calculated, long-distanceeffects are absorbed into pdf’s
finite effects - the infamous “k-factor”
from now on, we’ll presume scale-violating pdf’s
![Page 23: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/23.jpg)
CTEQ summer 01| brock | michigan state university | No. 23front nine
loss of naiveté, 2
finite pT … comes in 2 ways:
hard emission (think: “perturbative”)…(we’ll do it next)
soft emission (think: “complicated”!)…(we’ll do it later)
![Page 24: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/24.jpg)
CTEQ summer 01| brock | michigan state university | No. 24front nine
take it a bit at a time…
to first order in aaaaS, the elementary processes are:
for example, emission is 1 gluon
This is a familiar fundamental process: annihilation
…one of a set of order-aaaaSaaaaEM hard processes which can be treated perturbatively
Compton graphs, “C”
Annihilation graphs, “A”
![Page 25: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/25.jpg)
CTEQ summer 01| brock | michigan state university | No. 25front nine
more kinematics
it’s harder this time…
in principle, n states, for thei th particle…
presume cm and consider that the ith is V
![Page 26: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/26.jpg)
CTEQ summer 01| brock | michigan state university | No. 26front nine
kinematics, 2
from solution for t,
express the
longitudinal p
as a fractional
difference of P
different from before:
![Page 27: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/27.jpg)
CTEQ summer 01| brock | michigan state university | No. 27front nine
kinematics, 3
to get…
solving for M2:
so,
and therefore,
also,
![Page 28: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/28.jpg)
CTEQ summer 01| brock | michigan state university | No. 28front nine
kinematics, 4
solving…
(recalling only in the zero pT case…)
![Page 29: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/29.jpg)
CTEQ summer 01| brock | michigan state university | No. 29front nine
immediate plans…
1.set up the hadronic QCD “Compton” process
2.but, be lazy: calculate the eg Compton cross section
– everyone has done this, don’t need to really calculate…
– …except we’ll do it to a “heavy” photon
3.convert it to the QCD process by simple substitutions
4.use crossing to infer the Annihilation cross section
5.put it together…and then look at low pT for trouble
![Page 30: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/30.jpg)
CTEQ summer 01| brock | michigan state university | No. 30front nine
from our earlier phase space outline:
Compton process:
set up to ignore d, and embed the process inside hadrons:
for the simple 2-2:
a+b V+d
a trick
integrate trivially:
note!
![Page 31: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/31.jpg)
CTEQ summer 01| brock | michigan state university | No. 31front nine
compton, 2
mess with the delta function:
you can show that
so,
you remember
so…
is the root…
is the derivative…
so: allows us to do the xa integration
![Page 32: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/32.jpg)
CTEQ summer 01| brock | michigan state university | No. 32front nine
compton, 3
so, putting it together:
for 2 body kinematics
where
integrating and changing variables…
the physics lives here…
![Page 33: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/33.jpg)
CTEQ summer 01| brock | michigan state university | No. 33front nine
“regular” Compton scattering
textbook, but for keeping the outgoing photon mass
kinematics
rememberthe plan
![Page 34: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/34.jpg)
CTEQ summer 01| brock | michigan state university | No. 34front nine
“regular” Compton scattering, 2
actually, an exercise in Halzen and Martin…
standard 2 body kinematics
Jacobian to go to invariants
so:
mass only
affects theinterference term
![Page 35: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/35.jpg)
CTEQ summer 01| brock | michigan state university | No. 35front nine
from QED to QCD with hadrons…
now exploit our laziness...
morph from: to:
coupling change: decay to muons
![Page 36: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/36.jpg)
CTEQ summer 01| brock | michigan state university | No. 36front nine
ÆÆÆÆ annihilation
use crossing symmetry to go Compton ÆÆÆÆ Annihilation:
“C” “A”
plus color changes…
![Page 37: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/37.jpg)
CTEQ summer 01| brock | michigan state university | No. 37front nine
total order-aaaaS Drell-Yan cross section
putting it together…
where
this leads to trouble… the annihilation hard cross section goes like:
which, since leads to behavior for
![Page 38: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/38.jpg)
CTEQ summer 01| brock | michigan state university | No. 38front nine
ubiquitous logarithms
perhaps not surprisingly, logs float to the surface…
factor out the 1/pT2 behavior and as xT Æ 0, the leading terms go like:
(There’ll be others later)
so,in that limit, the form of the order-aS Drell Yan cross section is:
where:
includes leading
log pdf’s
which live here…
here’s a scale (pT)
which cannot beabsorbed into the pdf’s:
the dreaded
“two scale problem”
BUT
kT dependenceas kTÆ 0
![Page 39: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/39.jpg)
CTEQ summer 01| brock | michigan state university | No. 39front nine
sounds like a good theory
what about data? R209 at the ISR, 1982
badbehavior atlow pT
best fit for aGaussian-smeared model
hmm…
![Page 40: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/40.jpg)
CTEQ summer 01| brock | michigan state university | No. 40front nine
immediate plans…
1. an interlude, of sorts…
– calculate the probability of the emission of a low-pt gluon
– then calculate the probability of an infinite number oflow-pt gluons
– call them “Sudakov” and identify the approximations asLeading Pole and Leading Double Log
![Page 41: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/41.jpg)
CTEQ summer 01| brock | michigan state university | No. 41front nine
itty, bitty gluon radiation
a side calculations - dealing with soft gluon radiation(s)
define x1 and x2 to be themomentum fractionscarried by
q(p1) and q(p2)…then
x3 = 1 - x1 - x2 is the
fraction carried by g.
then:
log divergence when
x1,2 Æ 1/2
so,
define: (which is small)
(invariant qa-g mass, which is small)
![Page 42: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/42.jpg)
CTEQ summer 01| brock | michigan state university | No. 42front nine
details, details…
wave some hands here…
change variables, for photon “lifetime”:
log divergence, jÆ0when j small (mqg small) and z near 1 (Eg small)
the middle term dominates…
called the “Leading PoleApproximation”, (LPA)
related to the Pqg splitting function
q qª = @tan/||
k
k
k
QT T
2and so,
small
![Page 43: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/43.jpg)
CTEQ summer 01| brock | michigan state university | No. 43front nine
summing glue
add up a series of emissions
in the limit, the angle is small
define:
so…
as a function of kT, the probability of > q
so,
![Page 44: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/44.jpg)
CTEQ summer 01| brock | michigan state university | No. 44front nine
calculate T a
change variables
from
likewise, then
so,
remember
again, with at least k2T<<Q2
leading double logapproximation, LDLA
![Page 45: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/45.jpg)
CTEQ summer 01| brock | michigan state university | No. 45front nine
add ‘em up
treat radiations as independent
the probability of n, with < q
adding the probabilities for all possible n’s
which is an exponential:
SO
a significant result: as pT Æ 0, cross s Æ 0!
![Page 46: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/46.jpg)
CTEQ summer 01| brock | michigan state university | No. 46front nine
but wait…
this is where we started
for the kT of the radiating quark has the same form as ourorder-aS cross section for the q…but including the effects of
copious radiation of soft glue
we can improve our Drell-Yan cross sectionthe same way:
what we got perturbatively at order-aS
adding infinite-order soft radiation
notice powers of aS
this “RESUMMATION” (the exponential) tames the bad behavior
![Page 47: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/47.jpg)
CTEQ summer 01| brock | michigan state university | No. 47front nine
immediate plans…
1. move to W/Z production
– (ah, to) be naïve again in order to adjust to EWparameters
– get a sense of the rates
– use our results and calculate for finite pT
![Page 48: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/48.jpg)
CTEQ summer 01| brock | michigan state university | No. 48front nine
W/Z production
Drell-Yan process is operative here too
the Feynman rules are slightly different
-ieQig m
vI Q
aI
ii i W
W W
ii
W W
=-
=
( ) sin
sin cos
( )
sin cos
32
3
2
2
2
q
q q
q qie v ai ig gm m-( )
ieW
g gqm ( )
sin1
12 25 2-
siblings
cousins
![Page 49: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/49.jpg)
CTEQ summer 01| brock | michigan state university | No. 49front nine
from photons to W/Z:
just an EW lookup:
propagators:d
dQ Q
s2 4
1µ
12 2 2
s M MV V V-( ) + ( )G
couplings: W bosons Z bosons
plus, the connection between weak and electromagnetic couplings
![Page 50: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/50.jpg)
CTEQ summer 01| brock | michigan state university | No. 50front nine
W cross section - more laziness
write down the, now standard, cross section:
make use of the “narrow width approximation”:
the hard part:
define W-specific parton density combination:
![Page 51: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/51.jpg)
CTEQ summer 01| brock | michigan state university | No. 51front nine
W - cross section
combine with K-M matrix elements for the isospin-changing process
cabbibo cabibbo2 2+( ) angles, actually ~95%
~5%
so,
forget the Cabibbo-disallowed transition…
![Page 52: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/52.jpg)
CTEQ summer 01| brock | michigan state university | No. 52front nine
done…
some details, delta function gymnastics:
defined as thedifferential PartonLuminosity
t = @ ª ¥ -Q
s
2 2
2380
20001 6 10.
s = 2 TeV
Tevatron luminosities
(royal)
and a
ncie
nt;
EH
LQ
st
t= ( ) Ê
ˈ¯
= ( )( ) ÊËÁ
ˆ¯˜
Ê
ËÁ
ˆ
¯˜
=
-
-
6
6 801
0 39
1
10
10100
9 9
22 3
9
nb
nb GeVGeV mb
mb
b
bnb
nb
. nb
ˆˆ
. ( )
ss
d
d
L
s(Z) is about 1/3 s(W)
so, we can integrate
ˆ . /
ˆs c
s
d
d@ fi @0 08 1002TeV nb
t
t
L
![Page 53: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/53.jpg)
CTEQ summer 01| brock | michigan state university | No. 53front nine
Z cross section:
same idea: just follows the previous pattern…
where
so
![Page 54: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/54.jpg)
CTEQ summer 01| brock | michigan state university | No. 54front nine
reasonable description, overall
the calculation is historical…the data and pdf fits aremuch advanced
s n◊ Æ ªBR nb( ) .W l 2 2EHLQ gives…
but, data and phenomenology deserve more attention thanpossible here…
hep-ph/0101051
![Page 55: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/55.jpg)
CTEQ summer 01| brock | michigan state university | No. 55front nine
moving on…
let’s un-naïve the W calculation for finite pT and thenfor radiation:
so that:
everything goes through as before…
so, what’s wrong with this?
![Page 56: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/56.jpg)
CTEQ summer 01| brock | michigan state university | No. 56front nine
aaacckk!!
The Sudakov factor includes the exponentiation of
leading double log approximation
I dropped the power of 2 in the exponentiated form
2
please put that in…the web will be correct…
![Page 57: drell yan cteq final 1 - SMU](https://reader033.vdocuments.us/reader033/viewer/2022052106/628764edf7989a011372a553/html5/thumbnails/57.jpg)
CTEQ summer 01| brock | michigan state university | No. 57front nine
back