Nuclear Physics: Strangeness
enhancement observed by ALICE at
the LHC in proton-proton collisions
https://www.nature.com/nphys/journal/vaop/nc
urrent/full/nphys4111.html
Published in Nature Physics,
April 24, 2017
The effect is
strongest in
high
multiplicity
events.
Omega’s seem
to be
enhanced
No dependence on
collision energy or
type of projectile.
This “strangeness enhancement is
interpreted as a signal of the QGP
(Quark Gluon Plasma) production
Surprisingly, do
not need heavy
ions to see the
effect.
Nuclear Physics from ALICE
Today’s plan
More Chapter 9 material
Reminder: Final Exam
(Friday May 5, time 13:30-15:30).
Schedule for presentations:
Friday April 28
Tommy (CPV in the B system);
Makana (discovery of the Higgs)
Y. Nambu 1921-2015
2008 Nobel Prize
Monday May 1
Anirvan (LHCb pentaquark);
Tyler (discovery of the top quark),
James (MWPC)
Practice Final now posted
Francois Englert and Peter Higgs,
2013 Nobel Prize
Review question: How do we make
neutrino or anti-neutrino beams ?
295 km to SuperK
Use negative pions for anti-neutrino beams
and positive pions for neutrino beams
Question:
Does the Z boson decay into two identical pseudoscalar
mesons ?
How about into two identical scalar mesons ?
Hint: what is the JPC of the Z boson ?
Hint: what is the JPC of a pseudoscalar meson ?
Hints: 1- - and 0 - Hint: Is a Z a fermion or a boson ?
Widths of the W boson
Given the leptonic widths,
2
G en = G mn
3
æ g ö M W 1 GF M W
= Gtn = ç
=
» 225MeV
÷
è 2 ø 24p 2 3 2p
Question: What are the components of the hadronic width
and the total hadronic width ? (Drawing the relevant
diagrams may help).
Hint: What are the quark level hadronic decay
processes of the W boson ?
Hint: Do not forget the color factors.
Do not forget the CKM factors.
G ud º G(W ® ud) = 3´ |Vud |2 G en = 640.4MeV
G cs º G(W ® cs) = 3´ |Vcs |2 G en = 660MeV
Widths of the W boson
Question: What are the components of the hadronic width and the total
hadronic width ? (Drawing the relevant diagrams may help).
G en = G mn = Gtn » 225MeV
G ud º G(W ® ud) = 3´ |Vud |2 G en = 640.4MeV
G cs º G(W ® cs) = 3´ |Vcs |2 G en = 660MeV
Let’s not forget the singly Cabibbo suppressed components
(this will give a 10% correction to the width.)
G us º G(W ® us) = 3´ |Vus |2 G en = 3´ 0.224 2 ´ 225MeV » 35MeV
G cd º G(W ® cd) = 3´ |Vcd |2 G en = 3´ 0.22 2 ´ 225MeV » 33MeV
Let’s put all the contributions together
G en + G mn + G tn » 3(225 MeV ); G ud + G cs = 640 MeV + 660MeV
G us + G cd = 35MeV + 33MeV
G tot @ 2043MeV
Read the section on the Z
width in Bettini
Grows linearly
with energy and
violates unitarity.
This diagram now diverges at
high energy (different from γγ
scattering). Longitudinal
polarization of W gives an E/m
factor.
Including the W
contribution solves
the problem from
a) but introduces
new problems.
Adding this
diagram helps
a bit but does
not solve the
problem
Need the triple gauge
boson coupling to solve
the problem.
W. –M. Yao et al. (2006); J. Phys. G. 33 1
Run LEP at energies
above the W pair
threshold and verify
this is correct.
Cross-section is
unitarity because of
the triple gauge
boson coupling
(ZWW). The
position of the
threshold also gives a
precise determination
of the W mass.
But there is a new problem
The contribution of the 4-W vertex violates unitarity of
the electroweak model
Need a scalar
Higgs boson to
solve this
problem.
Precise measurements of electroweak
observables demand a light Higgs
Spontaneous symmetry breaking
Abdus Salam’s analogy: The table setting is symmetrical until
someone takes a serviette (napkin) from his/her left or right side.
Question: Can you give some other examples of spontaneous
symmetry breaking ? (preferably in physics)
Some debate between Anderson and
Peierls whether this is fully correct or not.
Spontaneous symmetry breaking
The electroweak lagrangian is perfectly gauge invariant, but the physical
vacuum i.e. the lowest energy state is a member of a set of physically
equivalent states.
A field theory potential density
with scalar particles of mass μ but
no interactions
A field theory with
particle interactions
Not stable
equilibrium
In the SU(2) x U(1) quantum field theory, the spontaneous
symmetry breaking is obtained by including a potential V(Φ)
that contains a complex scalar field Φ that is an isospin doublet.
What is an weak
isospin doublet ?
æ f+
F=ç 0
çè f
ö æ f + + if +
1
2
÷ =ç 3
÷ø çè f0 + if04
ö
÷
÷ø
F 2 enters in the Lagranian
F 2 º F + F = (f *-
æ f+
f *0 ) ç 0
çè f
ö
÷
÷ø
There are two cases:
1 2 2 1
V(F) = m F + lF4
2
4
m 2 > 0; boring
m 2 < 0; EW physics and Higgs potential
Question: What do the graphs of the two cases look like ?
1 2 2 1
V(F) = m F + lF4
2
4
m 2 < 0; EW physics and Higgs potential
Let’s find the minima of this potential, which correspond to the
ground state (after spontaneous symmetry breaking)
Question: How do we find the minima of the Higgs potential ?
¶V
= 0 = Fm 2 + lF3 = F(m 2 + lF2 )
¶F
Question: So what are the minima ?
Fmin = ±
-m2
l
º ±v
The quantity v is called the “vev” or
vacuum expectation value.
The Higgs boson can be considered as
an excited state above the ground
state.
Add a constant to the Higgs potential and
then perturb the vacuum.
4
1 2 2 1
m
V (F) = m F + lF 4 2
4
2l
l
2
m
l 2 2 2
2
2
V(F) = (F - ) = (F - v ) where v is the vev.
4
l
4
Now let’s do our perturbation Φ= v +σ
(note that Φ2 is constant in the valley)
F = v + s Þ F2 - v2 = 2vs + s 2
V=
l
4
Read off the 1/2m2σ2
term
(2vs + s )
2 2
1 4
d V = l v s + l (vs + s )
4
2
2
3
M H = 2l v = -2 m 2
What is the vev (numerical calculation)
and the Higgs potential ?
1
1 2
M W = gv; M Z =
g + g '2 v
2
2
1
Þv=
= 246 GeV
2GF
Assuming l =1,
- l v4
V(Fmin ) =
~ -10 54 GeV / m 3
4
Question: How does this compare to the energy density in
nuclear matter ?
Very important, terms
involving the Higgs field and
109 times
fermions give mass.
nuclear
Fermion-fermion coupling
density
terms cannot have mass. But
(remember 1
masses of hadrons (e.g. p,n)
GeV/fm3)
are mostly from QCD.
1
me =
fe v
2
Here fe is the
Yukawa coupling
QED versus electroweak theory (Qualitative).
In QED, consider a photon propagating down the z-axis.
The z and time components of the A (the vector potential) are gauge
dependent and are NOT physical. The physical components are the
transverse parts Ax and Ay.
In the EW theory, the longitudinal degrees of freedom of the massive
vector bosons are related to the Higgs.
Nambu and Goldstone found that spontaneous symmetry
breaking leads to massless scalars, which are not observed.
With the Higgs potential, three of its real components
turn into the longitudinal components of the W+, Wand Z bosons and give them masses. The fourth vector
boson, the photon remains massless. The remaining
component of Φ is neutral and a scalar becomes the
physical Higgs boson.
The W and Z gauge bosons are said to “eat” the Nambu-Goldstone
bosons from the scalar potential and thus became the longitudinal
degrees of freedom of the massive vector gauge bosons (W, Z). No
massless scalars are left over in the EW theory.
Y. Nambu
Higgs couplings
How to produce the Higgs boson at the LHC