Transcript Slide Title Goes Here - University of California, San Diego

High PT Hadron Collider Physics
Outline
• 1 - The Standard Model and EWSB
• 2 - Collider Physics
• 3 - Tevatron Physics
• QCD
• b and t Production
• EW Production and D-Y
FNAL Academic Lectures - May, 2006
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Backup Text
FNAL Academic Lectures - May, 2006
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Units
Recall that coupling constants indicate the strength of the interaction and characterize a
particular force. For example, electromagnetism has a coupling constant which is the electron
charge, e and a “fine structure” constant   e 2 / 4c that is dimensionless. The
electromagnetic potential energy is U (r )  eV (r )  e2 / r and V(r) is the electromagnetic
potential. The dimensions of e2 are then energy times length, [e2 ]  [U (r )r ] , the same as those of
c . Thus, in the units we adopt,  c  1 , e is also dimensionless. With  ~ 1/137, we find e ~
0.303. Coupling constants for the two other forces, the strong and the weak, will be indicated by
gi, and the corresponding fine structure constants by i with i = s, W.
The units for cross section, , which we will use are barns (1 barn = 10-24 cm2). Note that
( c)2  0.4 GeV 2mb where 1 mb  1027 cm2 . The units used in COMPHEP are pb = 10-12 b for
cross section and GeV for energy units. As an example, at a center of mass, C.M., energy, s ,
of 1 TeV = 1000 GeV, in the absence of dynamics and coupling constants, a cross section scale
of  ~ 1 / s ~ 400 pb is expected simply by dimensional arguments.
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Tools Needed
We will extensively use a single computational tool, COMPHEP. The aim was to expand a
slightly formal academic presentation to a more interactive mode for the student, giving “hands
on” experience. The plan was that the student would work the examples and then be fully
enabled to do problems on her own. COMPHEP runs on the Windows platform, which was why
it was chosen since the aim was to provide maximum applicability of the tool. A LINUX version
is also available for students using that operating system
(will use both during lecture demonstrations)
The COMPHEP program is freeware. We have taken the approach of first working through the
algebra. That way, the reader can make a “back of the envelope” calculation of the desired quantity.
Then she can use COMPHEP for a more detailed examination of the question. The use and description
of COMPHEP is explained in detail. A web address where the executable code (zipped) and a users
manual are available. The author has also posted these items: http://uscms.fnal.gov/uscms/dgreen.
Freeware to unzip files can be found at http://www.winzip.com/ and http://www.pkware.com/.
( Google them all – also Ghostview and Acrobat reader )
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COMPHEP – Models and Particles
Can edit
the
couplings
– e.g. ggH
Use SM
Feynman
gauge
Watch for
LOCK
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COMPHEP - Process
1-> 2,3
1-> 2,3,4
1,2 ->3,4
1,2 ->3,4,5
1,2-> 3,4,5,6 (slow)
*x options
No 2 -> 1
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COMPHEP –Simpson, BR
Find simple 2>2. Graphs
(with menu)
Results can be
written in .txt
files
Several PDF, p
and pbar,
Check stability
of results
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COMPHEP - Cuts
May be needed to avoid poles or to simulate
experimental cuts, e.g. rapidtiy or mass or Pt.
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COMPHEP - Cuts
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COMPHEP - Vegas
Full matrix element
calculation –
interference. Watch
chisq approach 1.
Setup plots, draw
them and write
them.
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COMPHEP - Decays
Strictly tree level. Does not do “loops” or “box” diagrams.
Explore this very useful tool. If there are problems bring
them to the class and we’ll try to fix them.
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1 - The SM and EWSB
• 1.1 The Energy Frontier
• 1.2 The Particles of the SM
• 1.3 Gauge Boson Masses and
Couplings
• 1.4 Electroweak Unification
• 1.5 The Higgs Mechanism for Bosons
and Fermions
• 1.6 Higgs Interactions and Decays
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The Energy Frontier
Constituent CM Energy (GeV)
10
4
Accelerators
10
LHC
electron
hadron
3
Higgs boson
Tevatron
10
SppS
2
LEPII
SLC
TRISTAN
t quark
W, Z bosons
PEP
CESR
10
1
ISR
SPEAR
10
b quark
c quark
0
Prin-Stan
s quark
10
-1
1960
1970
1980
1990
2000
2010
Historically
HEP has
advanced
with
machines that
increase the
available C.M.
energy. The
LHC is
designed to
cover the
allowed Higgs
mass range.
Colliders give
maximum
C.M. energy.
Starting Year
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The Standard Model of Elementary
Particle Physics
•
•
Matter consists of half integral spin fermions. The strongly interacting
fermions are called quarks. The fermions with electroweak interactions are
called leptons. The uncharged leptons are called neutrinos.
The forces are carried by integral spin bosons. The strong force is carried
by 8 gluons (g), the electromagnetic force by the photon (), and the weak
interaction by the W+ Zo and W-. The g and  are massless, while the W and
Z have ~ 80 and 91 GeV mass respectively.
g,, W+,Zo,W-
J=1
Force Carriers
u
c
t
2/3
d
s
b
-1/3
J = 1/2
Quarks
Q/e=
e


1
e


0
J=0
FNAL Academic Lectures - May, 2006
Leptons
H
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Gravity – Hail and Farewell
UG(r) = GNM2/r, depends on mass in comparison to the electrical energy U EM(r) = e2/r. The
quantity GN is Newton’s gravitational constant. The fine structure constants of the forces
appearing in the SM, such as electromagnetism, where   e 2 / 4c ~ 1/ 137, are dimensionless
and mass independent. The gravitational analogue, Gr  GN M 2 / 4 c , is not.
Ignore gravity. However, gravity is a precursor gauge
theory which is non-Abelian. The gauge quanta are
“charged”  non-linearity. The gravity field carries
energy, or mass. Therefore, “gravity gravitates”. This is
also true of the strong force (gluons are colored) and
the weak force (W,Z carry weak charge). The photon is
the only gauge boson which is uncharged.
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How do the Z and W acquire mass and not
the photon?
Gravity - Physics is the same in any local general coordinate system
--> metric tensor or spin 2 massless graviton coupled universally
to mass = GN.
Electromagnetism - Physics is the same regardless of wave function
phase assigned at each local point --> massless, spin = 1, photon
field with universal coupling = e
These are “gauge theories” where local invariance implies massless
quanta and specifies a universal ( GN, e ) coupling of the field to
matter.
Strong interactions are mediated by massless “gluons” universally
coupled to the “color charge” of quarks = gs.
Weak interactions are mediated by massive W+,Z,W- universally
coupled to quarks and leptons. gWsinW = e. How does this
“spontaneous electroweak symmetry breaking” occur? (Higgs
mechanism)
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Lepton Colliders - LEP
Z peak
L and R leptons have
different couplings
to the Z. There is Zphoton interference
which leads to a F/B
asymmetry. A way to
measure the
Weinberg angle. gW
measured from muon
decay.
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Field Theory
To describe quantum fields we will use  for fermion (J = ½) fields,  for scalar (J = 0)
fields, and  for vector (J = 1) gauge fields in this text. For masses, m is used for fermions and
M for bosons.
E  P 2  M 2 , P  P   M 2
Classical Special Relativity
 ( )  M 2
Lagrangian density, P is an
operator
 

P by P  eA
   D     ieA
( )( )  ( D )( D )
~ g ( ) , g 
2
I
FNAL Academic Lectures - May, 2006
Classical gauge replacement
Quantum gauge replacement
ggg, gggg
W W  , W W  Z
W W  , W W Z , WW  ZZ , W W W W 
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WW in e+e- Collisions
Test of self-coupling of
vector bosons. There
are s channel Z and
photon diagrams, and t
channel neutrino
exchange. Test of VVV
couplings.
In COMPHEP play
with the Breit-Wigner
option as s dependence
of the cross section
depends crucially on
the W width – i.e.
technique to measure
W width..
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Simpson –Angular Dist
Cross section without
neutrino exchange in the t
channel. Note divergent C.M.
energy dependence – voilates
unitarity.
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WW Cross Section at LEP
COMPHEP point shown.
Proof that the WWZ triple
gauge boson coupling is
needed and that there are
interfering amplitudes
that themselves violate
initarity.
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WW at LEP
Probe of quartic couplings.
LEP data confirms SM
WWAA, WWZA
Cross section in COMPHEP
with all final state bosons
having Pt > 5 GeV is 0.36 pb
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ZZ at LEP
SM has only the single
Feynman diagram. There
are no relevant triple or
quartic couplings – in
the SM. Use the data to
set limits on couplings
beyond the SM.
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e+e- Cross Sections
WW, ZZ, and
WW are seen at
LEPII. At even
higher C.M.
energies, WWZ
and ZZZ are
produced indicating triple
and quartic V
couplings. New
channels open up
at the proposed
ILC.
Try a few (red
dots) processes
yourself…..
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ILC Process - Example
Cross section ~ 1 fb at 500 GeV in COMPHEP.
Approximate agreement with full calculation.
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The Higgs Boson Postulated
Potential
V ( )   |  |  |  |
2
2
4
Minimum at a non-zero vev
  2   2 / 2
Lagrangian density
~ ( )   V ( )
“cosmological term”
V (  ) ~    4
This is Landau-Ginzberg
superconductivity – much
too simple?
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How the W and Z get their Mass
Covariant derivative contains gauge fields W,Z. Suppose an
additional scaler field  exists and has a vacuum expectation value.
Quartic couplings give mass to the W and Z, as required by the
data [ V(r) ~e(exp(-r/)/r) - weak at large r, strength e at small r].
( )( )  ( D )( D )
0

~






( D )( D ) ~  g 22   2 / 2 W W  ( g12  g 22 )   2 / 2  ZZ  e2 (0) 
M  0
MW  g2    / 2
M Z     g12  g 22 / 2  M W / cosW
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Numerical W, Z Mass Prediction
The masses for the W and Z are specified by the coupling
constants. G comes from beta decays or muon decay.
G / 2  gW2 / 8M W2 , G  105 GeV 2
M W / gW     / 2
  2  2 / 4G,     174 GeV
sin 2 W ~ 0.231, W ~ 28.7o , sin W  0.481
 ~ 1/137, W   / sin 2 W ~ 1/ 31.6, gW ~ 0.63
M W  gW    / 2 ~ 80 GeV
M Z  M W / cosW ~ 91 GeV
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Higgs Decays to Bosons
Field excitations ==> interactions with gauge bosons VVH,
VVHH, VVV, VVVV
0



   H 
( D )( D )  g 22 (   H ) 2 W W / 2  ( g12  g 22 )(   H ) 2  Z  Z / 2
,  ~ gW2 <>[ WWH ] ~ gWMW [ WWH ].
( H  WW ) / M H ~ (W /16)(M H / MW )2 
Higgs couples to
mass. Photons and
gluons are
massless to
preserve gauge
symmetry
unbroken. Thus
there is no direct
gluon or photon
coupling.
Using the Higgs potential, V(), expanding about the minimum at     , and
identifying the mass term in
as M H2 H H , we find that the mass is,
M H     2  246GeV . Since  is an arbitrary dimensionless coupling, there is no
prediction for the Higgs mass in the SM.
FNAL Academic Lectures - May, 2006
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ZZH Coupling and ILC Production
ILC at 500 GeV
C.M. Higgs
production by off
shell Z production
followed by H
radiation, Z* >Z+H.
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Higgs Coupling to Fermions
•The fermions are left handed weak doublets and right handed singlets.
A mass term in the Lagrangian,
m( L R  R L ) is then not a weak
singlet as is required.
•A Higgs weak doublet is needed, with Yukawa coupling, ~ g f [ L R ]
 ~ g f    [  ]  m f [  ],
Yukawa
Mass from Dirac
Lagrangian density
m f  g f     g f [ 2 MW / gW ]
g f  gW (m f / MW ) / 2
FNAL Academic Lectures - May, 2006
 (  m)
Fermion weak
coupling constant
31
Higgs Decay to Fermions
• The threshold factor is for P wave, 2l+1 since
scalar decay into fermion pairs occurs in P wave
due to the intrinsic parity of fermion pairs.
• The Higgs is poorly coupled to normal (light)
matter
•
gt ~ gW (mt/ MW)/2 ~ 1.0, so top is strongly
coupled to the Higgs.
( H  qq ) / M H ~ (3W /8)(m f / MW )2  3
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The Higgs Decay Width
The Higgs decay width, 
scales as MH3. Thus at low
mass, the detector defines
the effective resonant
width and hence the time
needed to discover a
resonant enhancement. At
high masses, the weak
interactions become
strong and /M ~ 1.
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Higgs Width - WW + ZZ
Higgs decays to
V V have widths
 ~ M3
Try this as a
COMPHEP
example
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Higgs Width Below ZZ Threshold
Below ZZ threshold, decays
can occur in the tails of the
Breit Wigner Z resonance,
with  ~ 2.5 GeV, M ~ 91
GeV. This compares to the
width to the heaviest
quark, b at a Higgs mass of
~ 150 GeV. Means that
W*W is an LHC strategy.
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Early LHC Data Taking
• We have seen that the Higgs couples to
mass. Thus, the cross section for
production from gluons or u, d quarks
is expected to be small.
• Therefore, it is a good strategy to
prepare for LHC discoveries by
establishing credibility. The SM
predictions , extrapolated from the
Tevatron, should first be validated by
the LHC experimenters.
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Vector Bosons and Forces
The 4 forces
appear to be of
much different
strength and
range. We will see
that this view is
largely a
misperception.
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2 - Collider Physics
• 2.1 Phase space and rapidity - the
“plateau”
• 2.2 Source Functions - protons to
partons
• 2.3 Pointlike scattering of partons
• 2.4 2-->2 formation kinematics
• 2.5 2--1 Drell-Yan processes
• 2.6 2-->2 decay kinematics - “back to
back”
• 2.7 Jet Fragmentation
FNAL Academic Lectures - May, 2006
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Kinematics - Rapidity
One Body Phase Space
NR

dP  P 2 dPd  dP|| PT dPT d
Relativistic

4
2
2
d P P  m   dP / E
 dydPT2 
dy  dP|| / E
If transverse momentum is
limited by dynamics, expect
a uniform distribution in y
FNAL Academic Lectures - May, 2006
Rapidity
E  mT cosh y
mT2  m 2  PT2
max y at PT  0, beam m om entum
pp @ 2, 14 TeV ,
ymax  7.7, 9.6
Kinematically
allowed range in
y of a proton
with PT=0
39
Rapidity “Plateau”
Monte Carlo results
are homebuilt or
COMPHEP running under
Windows or Linux
Region around y=0
(90 degrees) has a
“plateau” with
width y ~ 6 for
LHC
LHC
FNAL Academic Lectures - May, 2006
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Rapidity Plateau - Jets
For ET small
w.r.t sqrt(s)
there is a
rapidity
plateau at the
Tevatron with
y ~ 2 at ET <
100 GeV.
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Parton and Hadron Dynamics
Proceed left to right
FNAL Academic Lectures - May, 2006
For large ET, or
short distances,
the impulse
approximation
means that
quantum effects
can be ignored.
The proton can
be treated as
containing
partons defined
by distribution
functions. f(x) is
the probability
distribution to
find a parton
with
momentum
fraction x.
42
The “Underlying Event”
d / dydpT2 ~ A /( pT  po ) n
A ~ 450m b/ GeV 2 , po ~ 1.3 GeV , n ~ 8.2
s dependence
for PT < 5 GeV
is small
FNAL Academic Lectures - May, 2006
The residual fragments of the pp
resolve into soft - PT ~ 0.5 GeV
pions with a density ~ 5 per unit of
rapidity (Tevatron) and equal
numbers of +o-. At higher PT,
“minijets” become a prominent
feature
43
COMPHEP - Minijets
p-p at 14 TeV,
subprocess
g+g->g+g, cut
on Ptg> 5
GeV. Note
scale is
mb/GeV
FNAL Academic Lectures - May, 2006
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Minijets - Power Law?
pp(g+g) -> g + g
The very low PT
fragments change to
“minijets” - jets at
“low” PT which have
mb cross sections at ~
10 GeV. The boundary
between “soft, log(s)”
physics and “hard
scattering” is not very
definite. Note log-log,
which is not available
in COMPHEP – must
export the histogram
FNAL Academic Lectures - May, 2006
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The Distribution Functions
•Suppose there was very weak binding of the u+u+d
“valence” quarks in the proton.
x ~ 1/3, f(x) is a
delta function
•But quarks are bound, .xPx ~ , x ~1 fm, Px ~ 0.2 GeV ~ QCD
•Since the quark masses are small the system is
relativistic - “valence” quarks can radiate gluons ==>
xg(x) ~ constant. Gluons can “decay” into pairs ==> xs(x)
~ constant. The distribution is, in principle, calcuable but
not perturbatively. In practice measure in lepton-proton
scattering.
FNAL Academic Lectures - May, 2006
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Radiation - Soft and Collinear
,k
P
(1-z)P
E  P 2  m2  P  m2 / 2P
 ~ 1 / E  1 /( E f  Ei )
E ~ P  (1  z ) P
 ~ 1/ z
E  E  
  
P  P  k

  k cos
FNAL Academic Lectures - May, 2006
The amplitude for
radiation of a
gluon of
momentum
fraction z goes as ~
1/z. The radiated
gluon will be ~
collinear -  ~ k
==>  ~ 0. Thus,
radiated objects
are soft and
collinear.
Cherenkov relation
47
COMPHEP, e+t->e+t+A
Use heavy
quark as a
source of
photons –
needed to
balance E,P.
See strong
forward
(electronphoton) peak.
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Parton Distribution Functions
In the proton, u
and d quarks have
largest probability
at large x. Gluons
and “sea” antiquarks have large
probability at low
x. Gluons carry ~
1/2 the proton
momentum.
Distributions
depend on
distance scale
(ignore).
“valence”
“sea”
gluons
xg ( x)  7 / 2(1  x) 6
 xg( x)dx  1 / 2
xf ( x) ~ (1  x)
FNAL Academic Lectures - May, 2006
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Proton – Parton Density
Functions
g dominates for x < 0.2
At large x, x > 0.2, u dominates
over d and g.
Points are simple xg(x)
parametrization.
“sea” dominates for x < 0.03 over
valence.
FNAL Academic Lectures - May, 2006
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2-->2 Formation Kinematics
x  2 P|| / s ,
x1 x2  M 2 / s   , x1  x2  x
x  0  x1  x2    M / s
s ~ 4P2
x1
M 2 ~ P 2 [( x1  x2 ) 2  ( x1  x2 ) 2 ]
E  mT cosh y
x2
P||  mT sinh y, x ~ ( M / s )e y , y ~ 2 ln( s / M )
mT  m 2  PT2
2
  E / m,   P / E
m  0:
cosh y  1 / sin 
sinh y  1 / tan
FNAL Academic Lectures - May, 2006
E.g. for top quark
pairs at the Tevatron,
M ~ 2Mt ~ 350 GeV.
<x> ~ ~350/1800 ~
0.2
Top pairs produced
by quarks.
51
Linux COMPHEP
g + g->g + g with Pt of final state gluons
> 50 GeV at 14 TeV p-p
n.b. To delete diagrams use d, o to turn
them back on one at a time
Cross section is 0.013 mb (very large)
Write out full events – but no
fragmentation. COMPHEP does not
know about hadrons.
FNAL Academic Lectures - May, 2006
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gg -> gg in Linux COMPHEP
Note the
kinematic
boundary,
where <x> ~
0.007 is the
y=0 value for
x1=x2 for M =
100, C.M. =
14000.
FNAL Academic Lectures - May, 2006
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CDF Data – DY Electron Pairs
DY Plateau
x1,x2 at Z mass ~ 0.045
FNAL Academic Lectures - May, 2006
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The Fundamental Scattering
Amplitude
Fourier transform of the interaction potential, VI(r) where q  k f  ki , q ~ k is the
magnitude of the momentum transfer in the reaction. A familiar example is the 1/r Coulomb
potential, which yields a Born amplitude ~ 1/q2 describing how the virtual exchanged photon
propagates in momentum space. In turn this leads to a cross section (Rutherford scattering)
which goes as the square of the amplitude ~ 1/q4~ 1/4 , which should be familiar.
A   f | H I | i  ~  eiq. rVI ( r )dr
1 ~ x1 x2 x vertex
 2 ~ xx3 x4 vertex
[ ]  [ L ]  [1/ M ]  1/ s
2
FNAL Academic Lectures - May, 2006
2
55
Pointlike Parton Cross Sections
Point-like cross sections for parton - parton scattering. The entries have the generic dependence
already factored out. At large transverse momenta, or scattering angles near 90 degrees (y ~ 0),
the remaining factors are dimensionless numbers of order one.
Pointlike partons have
Rutherford like
behavior
Process
A
q  q  q  q
4 2
[s  u 2 ] / t 2
9
4 2
8
[( s  u 2 ) / t 2  ( s 2  t 2 ) / u 2 ]  ( s 2 / ut )
9
27
4 2
[t  u 2 ] / s 2
9
4 2
8
[( s  u 2 ) / t 2  (t 2  u 2 ) / s 2 ]  (u 2 / st )
9
27
32 2
8 2
2
2
2
[t  u ] / tu  [t  u ] / s
27
3
1 2
3
[t  u 2 ] / tu  [t 2  u 2 ] / s 2
6
8
4 2
 [ s  u 2 ] / su  [u 2  s 2 ] / t 2
9
9
[3  tu / s 2  su / t 2  st / u 2 ]
2
8 2
[t  u 2 ] / tu
9
1
 [ s 2  u 2 ] / su
3
qqqq
q  q  q  q
qq qq
qq  gg
 ~ (12
)|A|2/s
s,t,u are Mandelstam
variables. |A|2 ~ 1 at
y=0.
gg qq
gq gq
gggg
qq   g
g q  q
FNAL Academic Lectures - May, 2006
2
Value at   
2.22
3.26
0.22
2.59
1.04
0.15
6.11
30.4
56
Hadronic Cross Sections
To form the system need x1 from A and x2 from B picked out of
probability distributions with the joint probability PAPB to form a
system of mass M moving with momentum fraction x. C is a color factor
(later). The cross section is  ~ (d/dy)y=0y. The value of y varies
only slowly with mass ~ ln(1/M)
d  PA PB dˆ  Cf1 ( x1 ) f 2 ( x2 )dx1dx2 dˆ (1  2  3  4)
dx1dx2  dsˆ / sdy  ddy
  sˆ / s  M 2 / s
d  Cf1 ( x1 ) f 2 ( x2 )ddydˆ (1  2  3  4)
d / ddyy 0  Cf1 (
FNAL Academic Lectures - May, 2006
 ) f 2 (  )dˆ (1  2  3  4)
57
2-->2 and 2-->1 Cross Sections
2  2:
M 3  d / dydM  y 0  2C  xf1 ( x) xf 2 ( x) x 

 dˆ sˆ 
dˆ  1 2 / sˆ
M (d / dydM ) y 0 ~ C[ xf1 ( x) xf 2 ( x)]x   (1 2 )
4
2
2  1:
ˆ  4
2
(2 J  1),
partial wave unitarity
2
ˆ
ˆ

ds


(2 J  1)( / M ), int egrate over narrow width

“scaling”
behavior –
depends only
on  and not
M and s
separately
M 2  d / dy  y 0  C  xf1 ( x) xf 2 ( x) x    2  ff (2 J  1) / M 
 / M ~ "12 "
M 2  d / dy  y 0  C  xf1 ( x) xf 2 ( x) x    212 (2 J  1) 
FNAL Academic Lectures - May, 2006
58
DY Formation: 2 --> 1
At a fixed
resonant mass,
expect rapid rise
from “threshold”  ~
(1-M/s)2a
- then slow
“saturation”. W ~
30 nb at the LHC
FNAL Academic Lectures - May, 2006
u  u  Z  e  e , u  d  W   e    e
59
DY Z Production – F/B Asymmetry
CDF – Run I
The Z couples to L and R
quarks differently -> parity
violating asymmetry in the
photon-Z interference.
FNAL Academic Lectures - May, 2006
60
F/B Asymmetry
 
e  , eR Q  I 3  Y / 2, YL  1, YR  2
 L
u 
YL  1/ 3, YuR  4 / 3, YdR  2 / 3
 d  , uR , d R
 L
Coupling of leptons and quarks to Z specified in SM by gauge
principle.
gW / cosW [ I3  Q sin 2 W ]
Coupling to L and R fermions differs => P violation ~ R-L
coupling. Predict asymmetry , A ~ I3/Q. Thus, A for muons = 1,
that for u quarks is 3/2, while for d quarks it is 3.
FNAL Academic Lectures - May, 2006
61
COMPHEP
At 500 GeV the asymmetry
is large and positive – here
not p-p but u-U
FNAL Academic Lectures - May, 2006
62
COMPHEP - Assym
Option in “Simpson” to get F/B
asymmetry in COMPHEP
FNAL Academic Lectures - May, 2006
63
DY Formation of Charmonium
g

g
FNAL Academic Lectures - May, 2006
Cross section =  ~
2(2J+1)/M3 for W,
width ~ 2 GeV,  =
47 nb. For
charmonium,
width is 0.000087
GeV, and estimate
cross section in gg
formation as 34 nb.
The PT arises from
ISR and intrinsic
parton transverse
momentum and is
only a few GeV, on
average. Use for
lepton momentum
scale and
resolution.
64
Charmonium Calibration
Cross section in |y|<1.5 is ~ 800 nb at the LHC. Lepton calibration – mass scale,
width?
FNAL Academic Lectures - May, 2006
65
Upsilon Calibration
Cross section * BR about 2 nb at the LHC. Resolve the spectral peaks? Mass
scale correct?
FNAL Academic Lectures - May, 2006
66
ZZ Production vs CM Energy
VV production
also has a steep
rise near
threshold.
There is a 20
fold rise from
the Tevatron to
the LHC.
Measure VVV
coupling. ZZ
has ~ 2 pb cross
section at LHC.
Not much gain in using anti-protons
once the energy is high enough that
the gluons or “sea” quarks
dominate.
FNAL Academic Lectures - May, 2006
67
WWZ – Quartic Coupling
Not accessible at Tevatron. Test quartic couplings at the
LHC.
FNAL Academic Lectures - May, 2006
68
Jet-Jet Mass, 2 --> 2
Expect 1/M3
behavior at low
mass. When M/s
becomes
substantial, the
source effects
will be large. E.g.
for M = 400 GeV,
at the Tevatron,
M/s=0.2, and
(1-M/s)12 is ~
0.07.
p p gg
M 3d / dM ~ (1  M / s )12
FNAL Academic Lectures - May, 2006
69
Jets - 2 TeV- |y|<2
ET ~ M/2 for large
scattering angles.
FNAL Academic Lectures - May, 2006
1/M3[1-M/s]12
behavior
70
COMPHEP Linux
PT  M / 2
FNAL Academic Lectures - May, 2006
71
Scaling ?
Tevatron runs at 630 and 1800 GeV in Run I. Test of
scaling in inclusive jet production. Expect a function of
xT  2PT / s
FNAL Academic Lectures - May, 2006
only in lowest order.
72
Direct Photon Production
Expect a similar
spectrum with a rate
down by ratio of
coupling constants
and differences in u
and g source
functions. /s~14
u/g~6 at x~0.
FNAL Academic Lectures - May, 2006
73
D0 Single Photon
Process
dominated
by q + g – a
la Compton
scattering.
FNAL Academic Lectures - May, 2006
COMPHEP – 2 TeV p-p
74
2--> 2 Kinematics - “Decays”
Formation
x1
x2
System
x,y,M
Decay
y3, y4
x1  [ M / s ]e y , y  ( y3  y4 ) / 2
x2  [ M / s ]e  y
yˆ  ( y3  y4 ) / 2
cos ˆ  tanh( yˆ )
FNAL Academic Lectures - May, 2006
CM Decay
y*, *
The measured
values of y3, y4 and
ET allow one to
solve for the initial
state x1 and x2 and
the c.m. decay
angle.
75
COMPHEP - Linux
g+g-> g+ g, in pp at 14 TeV with cut of Pt of jets of 50 GeV.
See a plateau for jets and the t channel peaking. Want to
establish jet cross section, angular distributions and to look
at jet “balance” – missing Et distribution in dijet events.
MET angle ~ jet azimuthal angle and no non-Gaussian
tails.
FNAL Academic Lectures - May, 2006
76
Parton-->Hadron Fragmentation
For light hadrons (pions)
as hadronization products,
assume kT is limited (scale
~. The fragmentation
function, D(z) has a
radiative form, leading to a
jet multiplicity which is
logarithmic in ET
FNAL Academic Lectures - May, 2006
zk/P
z min  z  1, z min  m / P
zD ( z )  a (1  z )
1
 n   D ( z )dz ~ a  dz / z ~ a ln(P / m)
m/ P
dy  dP|| / E ~ dz / z
 n  ~ y ~ ln( s / M )
Plateau widens
with s, <n>~ln(s)
77
CDF Analysis – Jet Multiplicity
Different
Cone radii
Jet cluster multiplicity within a cone increases
with dijet mass as ~ ln(M).
FNAL Academic Lectures - May, 2006
78
Jet Transverse Shape
There is a
“leading
fragment” core
localized at
small R w.r.t.
the jet axis 40% of the
energy for R<
0.1. 80% is
contained in R
< 0.4 cone
R
FNAL Academic Lectures - May, 2006
y 2   2
79
Jet Shape - Monte Carlo
Simple model with
zD(z) ~ (1-z)5 and <kt>
~ 0.72 GeV. “Leading
fragment” with <zmax>
~ 0.24. On average the
leading fragment takes
~ 1/4 of the jet
momentum.
Fragmentation is soft
and non-perturbative.
FNAL Academic Lectures - May, 2006
80
Low Mass LHC Rates
Total Re actionRate :
 ~ 100 mb
L ~ 1034 /(cm 2 sec)
t ~ 25 n sec
 L ~ 109 Hz
 nx ~ 25 min bias events / cros sin g
" Minijet " Rate :
For small x and strong
production, the cross
section is a large
fraction of the inelastic
cross section.
Therefore, the
probability to find a
“small Pt “minijet” in
an LHC crossing is not
small.
( c) 2  0.4 mbGeV 2 , 1 mb  1027 cm 2
M 3 (d / dMdy ) y 0  2[ xg ( x)]2 C (d s )( c) 2
 ( M  M o ) ~ y[ xg ( x)]2 [ s 2 | A |2 / M o2 ]
xg ( x) ~ 7 / 2, y ~ 10,  s ~ 0.1, C ~ 1
for M o  10 GeV , | A |2  30 ( gg    gg )
 ~ 0.4 mb
FNAL Academic Lectures - May, 2006
81
V V Production - W + 
The angular distribution at the
parton level has a zero. The SM
prediction could be confirmed
with a large enough event
sample. – pp at 2 TeV with Pt > 10
GeV, 0.6 pb
Asymmetry somewhat washed out by the contribution of sea
anti-quarks in the p and sea quarks in the anti-proton.
FNAL Academic Lectures - May, 2006
82
3 –Tevatron -> LHC Physics
•
•
•
•
•
•
3.1 QCD - Jets and Di - jets
3.2 Di - Photons
3.3 b Pair Production at Fermilab
3.4 t Pair Production at Fermilab
3.5 D-Y and Lepton Composites
3.6 EW Production
W Mass and Width
Pt of W and Z
bb Decays of Z, Jet Spectroscopy
• 3.7 Higgs Mass from Precision EW Measurements
FNAL Academic Lectures - May, 2006
83
Kinematics - Review
Initial State
M 2  ( p1  p2 )   ( p1  p2 )  ~ (e1  e2 ) 2  ( p1  p2 ) 2 ~ P 2 [( x1  x2 ) 2  ( x1  x2 ) 2 ]
x  p|| / P ~ 2 p|| / s
x1x2  M 2 / s   , x1  x2  x
FNAL Academic Lectures - May, 2006
84
Review Kinematics - II
Final State
pT 3  pT 4  ET  (M / 2)sin ˆ
M 2  2ET2[cosh( y 3  y4 )  cos(3  4 )]

y  ( y3  y4 ) / 2, y  ( y3  y4 ) / 2
x1  [ M / s ]e y
x2  [ M / s ]e  y
FNAL Academic Lectures - May, 2006
85
Jet Et Distribution and Composites
Simplest jet measurement inclusive jet ET . Jet defined
as energy in cone, radius R.
Classical method to find
substructure. Look for wide
angle (S wave) scattering.
Limits are  ~ s.
FNAL Academic Lectures - May, 2006
86
CDF Run II – Data Reach
FNAL Academic Lectures - May, 2006
87
Dijet Et Distribution – Run I
As |3 - 4|
increases MJJ
increases and
the cross
section
decreases. The
plateau width
decreases as ET
increases
(kinematic limit)
FNAL Academic Lectures - May, 2006
88
Dijet Mass Distribution
Falls as 1/M3 due to
parton scattering
and ~ (1- M/s)12
due to structure
function source
distributions. Look
for deviations at
large M (composite
variations or
resonant structure
due to excited
quarks). Limits at
Tevatron and LHC
will increase as
C.M. energy.
FNAL Academic Lectures - May, 2006
89
Initial, Final State Radiation
The initial state has ~ no
transverse momentum. Thus
a 2 body final state is backto-back in azimuth. Take the
2 highest Et jets in the 2 J or
more sample. At the higher
Pt scales available at the
LHC ISR and FSR will
become increasingly
important – determined by
the strong coupling constant
at that Pt scale.
FNAL Academic Lectures - May, 2006
90
“Running” of s - Measure in 3J/2J
1/ s (2QCD )  0
QCD ~ 0.2 GeV ~ 1 fm
Energy below
which strong
interaction is strong
 S ((1 GeV ) 2 )  0.55
 S ((10 GeV ) 2 )  0.23
 S ( M Z 2 )  0.15
s (Q2 )  [12 /(33  2n f )]/ ln(Q2 / QCD2 )]
FNAL Academic Lectures - May, 2006
91
Excited Quark Composites
q  g  q*  q  g
q
q*
g
Look for
resonant J - J
structure, with
a limit ~ C.M.
energy
FNAL Academic Lectures - May, 2006
92
t Channel Angular Distribution
( p1  p3 )  ( p1  p3 )   2 p 2 (1  cos )
  4 /  2 , tˆ  ( pˆ )2 ,   (2 pˆ )2 / tˆ
FNAL Academic Lectures - May, 2006
If t channel
exchange
describes the
dynamics, then 
distribution is flat
- as in Rutherford
scattering.
Deviations at
large scattering
angles would
indicate
composite quarks.


  (1  cos ) /(1  cos )


t ~ (1  cos ), ˆ from y3 , y 4 and ET

 
d / dt ~ 1 / t 2 ,  propagator


d / dt ~ 1 / t 2

d / d ~ constant
93
Diphoton, CDF Run II
2--> 2 processes similar to
jets. Down by coupling
and source factors Also
useful in jet balancing for
calibration. Important SM
background in Higgs
searches. Must establish
SM photon signals
u+g-->u+ (Lecture 2)
u+u-->+
FNAL Academic Lectures - May, 2006
94
COMPHEP – Tree Only
Tevatron, 2 TeV
||<1, ET>10 GeV
FNAL Academic Lectures - May, 2006
95
B Production @ FNAL
d/dPT ~ 1/PT3 so (>)
~ 1/PT2
 ( PT  PT min ) ~ 1/ PT2min
FNAL Academic Lectures - May, 2006
Spectrum is as
expected with PT ~
M/2, g+g --> b + b.
Adjustment in b -> B
fragmentation
function resolves the
discrepancy. Establish
a b jet signal and b
tagging efficiency
using 1 tag to 2 tag
ratio. Many LHC
searches and SM
backgrounds (e.g. top
pairs) require b
tagging.
96
B Production – Rapidity
Distribution
Note
rapidity
plateau
which
extends to
y ~ 5 at this
low mass, ~
2mb scale. At
the LHC
tracking and
Si vertexing
extends to
|y| < 2.5.
FNAL Academic Lectures - May, 2006
97
B Lifetimes
Use Si tracker to
find decay
vertices and the
production
vertex. (B) ~
(b). For Bc both
the b and the c
quark can decay
==> shorter
lifetime. At LHC
establish
lifetime scale.
Bc  cb
 ~ b  c ,   1/    b
FNAL Academic Lectures - May, 2006
98
Weak Decay Widths
   e   e   
     W     (e  e )
Fermi theory
Standard
m
Model
W
G2
2 5
3
2 5m /192
3


G


  G m /192

 ~| A |2 ~ G2

~ W2 (m / M W ) 4 m
[G]  1/ M 2 , []  M
m5 scaling for q and l
except t  below 2 body threshold
 ~ G2m5
t  Gmt3 / 8 2
~ W /16(mt / M W ) 2 mt
t -> W b
fast decays,
2 body weak
decay
no toponium
Q / t ~ W [mQ5 / mt3MW2 ]
FNAL Academic Lectures - May, 2006
99
Top Mass and Jet Spectroscopy- Run I
D0 lepton +
jets
t-->Wb
W-->JJ, l
FNAL Academic Lectures - May, 2006
100
Jet Spectroscopy - Top
CDF - Lepton +
jets (Si or
lepton tags)
t-->Wb so 2 b’s
in the event
b c


FNAL Academic Lectures - May, 2006
101
tt --> Wb+Wb, W--> qq or l
CDF + D0
Top quark
mass from
data taken
in the
twentieth
century
FNAL Academic Lectures - May, 2006
102
Top Mass @ FNAL
Run I
FNAL Academic Lectures - May, 2006
Run II
103
Top Production Cross Section
Are the mass and the cross
section consistent with a quark
with SM couplings?
FNAL Academic Lectures - May, 2006
> 100x gain in going to the
LHC. The discovery at the
Tevatron becomes a nasty
background at the LHC.
However, W-> J+J in top
pair events sets the
calorimeter energy scale at
the LHC.
104
Run II Top Cross section
No evidence for deviation
from SM coupling of a
heavy quark. At the LHC top
pair events have jets, heavy
flavor, missing energy and
leptons. They thus serve as a
sanity check that the
detector is working correctly
in many final state SM
particles. The LHC
experiments must establish
a top pair sample before
contemplating, for example,
SUSY discoveries.
FNAL Academic Lectures - May, 2006
105
DY and Lepton Composites
Run I
u  u   * / Z* 
FNAL Academic Lectures - May, 2006
Drell-Yan:



Falls with the
source function. For
ud the W is
prominent, while
for uu the Z is the
main high mass
feature. Above that
mass there is no SM
signal, and searches
for composite
leptons or
sequential W’, Z’
are made.
106
Extract V,A Coupling to Fermions
F/B asymmetry
allows an extraction
of the A and V
couplings, gA, gV of
fermions to the Z at
high mass – compare
to SM. If a Z’ is seen
at the LHC, use the
F/B distribution to
try to extract the A
and V couplings.
FNAL Academic Lectures - May, 2006
107
Run II – DY High Mass
FNAL Academic Lectures - May, 2006
108
Run II – DY High Mass
Whole “zoo” of new Physics candidates – all still null. At LHC
establish muon and electron momentum scale and resolution with Z
mass and width. Explore tail when backgrounds are under control.
FNAL Academic Lectures - May, 2006
109
W - High Transverse Mass
Run I
Search DY at
high mass for
sequential W’.
Mass calculated
in 2 spatial
dimensions only
using missing
transverse
energy.
MT2  2PTl E T (1  cos lE T )
FNAL Academic Lectures - May, 2006
110
W - SM Mass and Width Prediction
Mass:
   1/ 2G 2  174 GeV
G / 2  gW2 /8MW2 , gW sinW  e
M  2W    , MW ~ 80 GeV
2
W
e uc
2
W
Width;
(W   e    e )  (W /12) M W ~ 0.21 GeV
W ~ 9(W  e   e )


(Z   )  [W / 24][M Z / cos2 W ] ~ 0.16 GeV
FNAL Academic Lectures - May, 2006
e  e ,     ,   
u  d, c  s
Color factor of 3 for
quarks. 9 distinct
dilepton or diquark
final states.
111
COMPHEP – W BR
Check that the naïve estimates are confirmed in
COMPHEP for W and Z into 2*x.
FNAL Academic Lectures - May, 2006
112
W,Z Production Cross Section
Cross section x BR for W is ~ 4 pb for Tevatron Run
II
FNAL Academic Lectures - May, 2006
113
Lumi with W, Z ?
At present in Run II, using W,Z is more accurate than Lumi
monitor. Use W and Z at LHC as “standard candles”. Test of
trigger and reco efficiencies – cross-check minbias trigger
normalization.
FNAL Academic Lectures - May, 2006
114
W and Z - Width and Leptonic B.R.
Expect 1/9 ~ 0.11
FNAL Academic Lectures - May, 2006
Expect 9 (0.21 GeV) = 1.9 GeV
115
Direct W Width Measurement
[ /( M  Mo )]2
decay widths of 1.5 to 2.5 GeV
Monte Carlo
FNAL Academic Lectures - May, 2006
Far from the pole mass the
Breit – Wigner width (power
law) dominates over the
Gaussian resolution
116
W Transverse Mass
D0 and CDF:
Transverse plane
only. Use Z as a
control sample.
At large mass
dominated by
the BW width,
since falloff is
slow w.r.t the
Gaussian
resolution.
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117
W Mass – Colliders, Run I
Hadron
WW (LEP II)
production
near
threshold
(Lecture 1 )
FNAL Academic Lectures - May, 2006
118
W Mass - All Methods
Direct
Precision EW
measurements
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119
I.S.R. and PTW
u  d W   g
FNAL Academic Lectures - May, 2006
u
W+
d
g
2-->1 has no F.S. PT.
Recall Lecture 2 charmonium production.
Scale is set by the FS mass
in 2 -> 1.
120
COMPHEP - PTW
Basic 2 --> 2
behavior,
1/PT3. . Gluon
radiation
from either
initial quark.
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121
Lepton Asymmetry at Tevatron
We must simply assert that the V-A, parity violating, nature of the weak interactions makes
light quarks and leptons, ( u, d , e , e in the first generation) left handed (negative helicity,
where helicity is the projection of spin on the direction of the momentum) and the corresponding
anti-particles, u , d , e , e , right handed (positive helicity).
FNAL Academic Lectures - May, 2006
122
CDF – Lepton Asymmetry
Positron goes in antiproton direction
Electron goes in proton direction
 Charge asymmetry, constrains PDF. Recall u > d at large x.
FNAL Academic Lectures - May, 2006
123
COMPHEP - Asymmetry
COMPHEP generates the
asymmetry in pbar-p at 2
TeV. Can use the PDF that
COMPHEP has available
to check PDF sensitivity.
Generate your own
asymmetry and look for
deviations.
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124
Z --> bb, Run I
Dijets with 2
decay vertices
(b tags). Look
for calorimetric
J-J mass
distribution.
Mass
resolution, dM
~ 15 GeV. This
exercise is
practice for
searches of J-J
spectra such as
Z’ decays into
di-jets, or H
decays into b
quark pairs.
FNAL Academic Lectures - May, 2006
125
Run II Mass Resolution
Using tracker
information to
replace distinct
energy deposit in the
calorimetry for
charged particles
with the tracker
momentum – which
is more precisely
measured. Seems to
gain ~ 20%. This is
quite hard – at LHC
we will use W->J+J
in top pair events.
FNAL Academic Lectures - May, 2006
126
VV at Tevatron - W from D0
The WW  vertex
as measured at
Run II is
consistent with
the SM, as it is at
LEP II.
Transverse mass
in leptonic W
decays with
additional
photon.
FNAL Academic Lectures - May, 2006
127
WW at D0 – Run II
Look at dileptons plus
missing transverse energy.
Tests the WWZ and WW 
vertex as at LEP - II
FNAL Academic Lectures - May, 2006
128
WW Cross Section Measured at
CDF
Extrapolate to LHC
energy. COMPHEP
gives a D-Y WW
cross section at the
LHC of 72 pb. At
LHC will be able to
begin to explore WW scattering
independent of
Higgs searches.
FNAL Academic Lectures - May, 2006
129
W Mass Corrections Due to Top,
Higgs
( P 2  M 2 )  0 Klein( P  M )  0
Gordon
Dirac
We must simply assert that the propagators for fermions (Dirac equation) and bosons (KleinGordon equation) are different, 1/ q , 1/ q2 respectively, for massless quanta. The propagator for
massless bosons can be thought of as the Fourier transform of the Coulomb interaction potential.
The propagator for fermions follows from a study of the Dirac equation.
m
 M ~  d q /(q) ~  q dq / q ~  qdq ~ m 2
2
4
2
3
2
M
 M ~  d q /(q ) ~  q dq / q ~  dq / q ~ ln( M )
2
4
2 2
FNAL Academic Lectures - May, 2006
3
4
W mass shift
due to top
(m) and
Higgs (M)
130
What is MH and How Do We Measure It?
• The Higgs mass is a free parameter in the current “Standard
Model” (SM).
• Precision data taken on the Z resonance constrains the Higgs
mass. Mt = 176 +- 6 GeV, MW = 80.41 +- 0.09 GeV. Lowest order SM
predicts that MZ = MW/cosW.. Radiative corrections due to loops.
M W2  M Z2 cos2 W (1   )
 t ~ [3W ( mt / M W ) 2 ]/16
b
W
 H  [11W tan 2 W / 24 ]ln( M H / M W )
dMW  (3W / 16 )(mt / MW )dmt
W
W
t
H
W
W
2
dM
/
M

[

11

tan
W /of
48contributions
 ](dM H / M H ) to mass from fermion and
Note
the
opposite
signs
W
W
W
boson loops. Crucial for SUSY and radiative stability.
FNAL Academic Lectures - May, 2006
131
CDF D0 Data Favor a Light Higgs
MW vs Mt for 100, 300, 1000 GeV Higgs
80.5
80.45
MH=100
MH=300
MH=1000
MW (GeV)
80.4
80.35
80.3
80.25
80.2
165
FNAL Academic Lectures - May, 2006
170
175
Mt (GeV)
180
185
132
Top and W Mass and Higgs
1 s.d
contours:
all precision
EW data
A light H
mass seems
to be weakly
favored.
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133