Download Mass of the hadron

Origins of the Mass of
Baryonic Matter
Xiangdong Ji
The TQHN Group
Mass and Energy of the Universe
 According to the modern cosmology, the energy
density of the universe is at critical,
3H 2
c 
 1.05 105 h 2 GeV cm-3
8 GN
H  100h km s 1 Mpc1 , h  0.73  0.03
 Among which 73% come from the cosmological
constant—dark energy.
 And 23% comes from dark matter of non-baryonic
origin (axions, susy-partners)
 4% comes from the baryonic matter that both
luminous (less than 0.5%) and dark.
Forms of Baryonic Matter
 Earthly Matter
– Atoms, Molecules in gas, liquid and solids which
include everything we know in daily life
 Neutron Stars
– Nuclear matter made of neutrons
 Quark Matters
– High-density nuclear matter in which quarks
and gluons are not confined to inside of a
hadron.
 …
Mass and Energy
 Mass: one of the most fundamental concepts first
introduced in physics, as in F=Ma.
 Energy: a concept introduced to describe motion
(kinetic energy) and interactions (potential
energy).
 According to Einstein, mass and energy is
intimated connection through
E=Mc2
Which is more fundamental? Mass or energy?
Making a point: Hydrogen Atom
 The mass of the hydrogen atom is NOT equal to
M p M e
 938.272029(80) MeV/c2  0.510998918(44) MeV/c2
 Rather, it is equal to
M p M e  13.6 eV/c2
Therefore, mass is a reflection of energy and
energy seems to be more fundamental!
 The difference is small, 10-8. It is difficult to
measure the difference at such a scale.
(except MKL-MKs where the accuracy is 10-14 !)
Mass of Baryonic Matter
 Let us consider baryonic matter composed of
electrons protons and neutrons.
 The mass of the baryonic matter will be affected
by the energy of interactions
– Gravity
– Electromagnetism
– Strong
– Weak
Mass of Baryonic Matter
 Gravity
– Plays extremely important role at short
distance (blackhole) and cosmic scale. However,
it can be ignored for the earthly matter.
 Electromagnetic Interactions
– Long range Coulomb interactions among
electrons and nuclei can be ignored. Very small
effect just like in hydrogen atom.
– However, larger effects inside nuclei.
 To a good approximation, the mass of baryonic
matter is the sum of those of the electrons and
nuclei!
Mass of Nuclei
 Nuclei are consists of protons and neutrons. Their
masses are equal to the sum of those of nucleons
plus binding energies.
 The mass of the deuteron
Md= Mp + Mn – 2.2 MeV/c
the binding here has the effect of order 10-3.
 The typical nucleon binding energy is on the order
of 8 MeV per nucleon. Therefore, it is on the
order of 1 percent or so. It is a huge effect. This
is the reason for the huge energy release in
nuclear reactions (atomic bomb)
Nuclear Binding Energy
Nuclear dynamics
 Binding is the effect of the nuclear dynamics.
pi 2
H i
  ij Vij   ijk Vijk
2m
QUANTUM MONTE CARLO CALCULATIONS OF A = 8 NUCLEI.
By V.R. Pandharipande et al, Phys.Rev.C62:014001,2000
Where does it the nucleon mass comes from?
 Nucleons are made of quarks and gluons which
interact with a theory called
Quantum Chromodynamics (QCD)
 Building blocks
– Quarks (u,d,s…, spin-1/2, 3 colors)
– Gluons (spin-1, massless, 32 −1 colors)
 Interactions
1  a
L   (i    mq )  F F a  g s  A
4
Scales in QCD
 Quark masses:
– The up and down quark masses are much smaller
than that of the nucleon, and hence contribute
only a small fraction.
 A hidden QCD scale ΛQCD
QCD coupling is not really a constant (next slide),
but depends on the momentum scale
2
g
4
2
s
 s (Q ) 

4  0 ln Q 2 /  QCD 2
 Asymptotic freedom! (Gross, Politzer, Wilczek)
– As Q, αs(Q)0
Physics of the running couplings
 In quantum field theory, the vacuum is not a
constant. Rather it is a medium full of particles.
 In such a medium, the interaction strength is
modified by the vacuum polarization and hence is
distance dependent
 Screening: the charge gets screened at large
distance, and hence is weaker (electricity)
 Anti-Screening: the charge gets anti-screened at
large distance, and hence grows stronger (QCD)
What sets the scale for strong interactions
 There has not been a clear answer!
 Speculations:
– The electromagnetic, weak and strong coupling
constants might be unified at some grand
unification scale ΛGUT ~ 1016 GeV.
– ΛQCD is determined by the value of αs at ΛGUT
– For example, if we take αem ~ 1/40 at ΛGUT
the ΛQCD will be about a few hundred MeV.
 The precise value of the proton mass depends on
QCD dynamics at αs(Q) ~ 1.
Quark confinement
The other side of the coin of asymptotic freedom
 Because of the strong coupling, the colored quarks
and gluons can never be librated from inside of a
hadron.
 In the low-energy region, QCD represents an
extremely relativistic, strongly coupled, quantum
many-body problem
one of the daunting challenges in theoretical
physics
Clay Math. Inst., Cambridge, MA
$1M prize to solve QCD! (E. Witten)
Spontaneous Symmetry Breaking
 One idea to get the mass of proton is the so-called
chiral symmetry breaking, which is a phenomenon
of spontaneous symmetry breaking.
 Consider a double-well potential in which the
barrier is finite. The ground state wave function is
symmetric. However, when the barrier goes to
infinity, the ground state has no parity symmetry.
Chiral Symmetry breaking
 When the quarks are massless, there are lefthanded quarks and right-handed quarks. They are
independent species, and do not talk to each other
in the hamiltonian, which is symmetric underexchange of them---chiral symmetry!
 However, when the chiral symmetry is
spontaneously broken, the vacuum is no longer
symmetric under exchange of left and right
quarks.
– In particular, when a left-handed quark
propagates in the vacuum, it can emerge as a
right handed quark---Thus the quark gets mass!
Constituent Quarks!
 When massless quarks travel in the vacuum where
the chiral symmetry is broken, they acquire a mass
of order 300 MeV and become the so-called
constituent quark.
 The mass of the proton is roughly the sum of 3
constituent quarks!
 However chiral symmetry breaking happens?
– Instantons, zero modes, lattice QCD…
Color Confinement---In a Bag!
 The quark confinement leads to that a quark in the
nucleon must move in a small region of space.
 Therefore, a hadron looks like a bag inside which
the quarks move, but cannot get to the outside.
The Mass of A bag, Along with 3 Quarks
 A free quark inside of the nucleon has a kinetic
energy 1/R, according to the uncertainty principle.
 However, the free space of volume V has energy
BV—you must pay for the bag!
 Therefore, the total energy is
3 4
M    R3 B
R 3
 Minimizing with respect to R, one finds that the
second term contributes 1/4 and M=4/R. And since
R is about 1 fm, one gets about 900 MeV!
QCD Hamiltonian
 One can write done a QCD hamiltonian in term of
various contributoins
 Matrix elements of various operators can be
determined by experimental data.
– Deep-inelastic scattering
– pi-N sigma term,
– Baryon mass spectrum.
An Anatomy of the proton mass
 Contributions to the proton mass from various
sources. Strange quark has been considered both
as heavy and light.
There is a significant contribution from gluons!
Can we calculate this? Lattice QCD
Lattice QCD
 Solve QCD numerically
 Four important ideas
– Feynman Path Integral
– Wick Rotation
– Discretization of Space and Time
– Monte Carlo
Some Precision Latttice Results
What sets the scale of quark masses?
 The electro-weak symmetry is SU2X U1. This
symmetry is spontaneously broken at scale ΛEM
which is about 100 GeV.
 This symmetry breaking is the origin of the
masses of quarks and leptons (charged leptons and
neutrinos).
 Although this source of mass might be very
important for non-baryonic matter, but is not the
dominant one for baryonic matter.
 This is what LargeHadronCollider will study.
Conclusion
 Most of the mass of the luminous matter comes
for the masses of the protons and neutrons.
 Most of the masses of the protons and neutrons
comes from QCD.
 Chiral symmetry breaking and quark confinement
are essential for understanding the nucleon
masses.
 Experimental data and lattice QCD help us to
understand the importance of the various
contributions to the proton mass.