Download Why is the proton mass interesting?

STRUCTURE OF THE
PROTON MASS
Xiangdong Ji
University of Maryland
WHY IS THE PROTON MASS INTERESTING?
 How to communicate the lofty goals of
nuclear physics to general public?
Long-range plan:
One of the purposes of modern nuclear physics
is to understand the origin of the masse of the
visible matter.
 Quark masses only contribute ~1-2% of the
proton mass?
MASS AND ENERGY: WHICH IS MORE
FUNDAMENTAL?
 In non-relativistic theory, mass is a more
fundamental concept, as it is introduced
before the concept of energy. It is needed
for the second law of Newton’s,
F = ma
 However, according to Einstein, E = mc2,
mass is a source of energy. Hence, one has
a fundamental reason for harnessing the
nuclear energy.
ENERGY IS MORE FUNDAMENTAL

 Thus, studying the mass structure of the
nucleon is, in a sense, to understand the
energy structure or energy sources in a
fundamental theory.
ENERGY STRUCTURE IN CLASSICAL
THEORY

FIRST HINT OF DARK MATTER
While examining the Coma galaxy
cluster in 1933, Zwicky was the first to
use the virial theorem to infer the
existence of unseen matter, which he
referred to as dunkle Materie‘ dark
matter'.[2] He calculated the
gravitational mass of the galaxies
within the cluster and obtained a value
at least 400 times greater than
expected from their luminosity, which
means that most of the matter must be
dark
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 already
NUCLEAR MASS AND DYNAMICS
pi 2
H i
  ij Vij   ijk Vijk
2m
Binding is the effect of the nuclear dynamics.
QUANTUM MONTE CARLO CALCULATIONS OF A = 8 NUCLEI.
By V.R. Pandharipande et al, Phys.Rev.C62:014001,2000
MASS IN STRONG INTERACTIONS
Nucleons are made of quarks and gluons
 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
MASS 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, 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)
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.
MASSLESS QCD PREDICTIONS

LATTICE QCD AND DIMENSIONAL
TRANSMUTATION

CHIRAL SYMMETRY BREAKING
When the quarks are massless, there are left-handed
quarks and right-handed quarks. They are independent
species, and do not talk to each other in the Hamiltonian.
There is symmetric under-exchange 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
righhanded quark---Thus the quark gets
dynamical mass!
CONSTITUENT QUARKS
When massless quarks travel in the vacuum
where the chiral symmetry is broken, they
acquire a mass of order 300 MeV (must be
proportional to ΛQCD) and become the socalled constituent quark.
The mass of the proton is roughly the sum of 3
constituent quarks!
However chiral symmetry breaking happens?
 Instantons, near zero modes of Dirac operator
QUARK CONFINEMENT
THE OTHER SIDE OF THE COIN
Because of the strong coupling, the colored
quarks and gluons can never be liberated
from inside of a hadron.
In the low-energy region, QCD represents
an extremely relativistic, strongly coupled,
quantum many-body problem
 Lattice QCD is the only approach.
 Understanding the energy structure is useful.
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 go 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!
BAG CONSTANT VS. DARK ENERGY
The bag constant is represented by the
energy momentum tensor density Bg which is
mathematically the same as the cosmological
constant (CC) term Λg introduced by
Einstein.
 It is known today that
the dark energy contributes
about ¾ of the energy density
of the Universe.
A QCD VIEW ON PROTON MASS
THE QCD ENERGY
One can calculate the proton mass through
the expectation value of the QCD
hamiltonian,
Quark energy
Quark mass
Gluon energy
Trace anomaly
TRACE AND TRACE-LESS PARTS

MASSLESS QCD AND TRACE ANOMALY

VACUUM CONDENSATE AND
COSMOLOGICAL CONSTANT

A “VIRIAL THEOREM”

QUARK AND GLUON ENERGY
 The traceless part contribution to the
nucleon mass can be extracted from the
parton distribution, since it is the matrix
element of a twist-2 operator.
 In the rest frame of the proton, it measures
quark kinetic energy and gluon energy
(scheme and scale dependent).
MEASURING THE ENERGY OF THE QUARKS:
DEEP INELASTIC SCATTERING
The highly virtual photon knocks out a quark in the
proton
Feynman: Measuring the momentum density of the
quarks q(x)
PARTON DISTRIBUTIONS
OTHER INGREDIENTS
The quark mass contribution to the proton
mass can be determined from
Pion-N sigma term m p u u  dd p
Chiral perturbation theory for masses of baryon
octect
ms p s s p
One can also consider ms as heavy.
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!
COLOR FIELDS IN THE PROTON
 From the gluon energy and the anomaly,
one can get the individual contribution of
the color electric and magnetic fields.
 Color electric field contribution is positive
<E^2> > 0
 And the color magnetic field contribution is negative,
<B^2> < 0
 What does this tell us?
THE PROTON MASS BUDGET
Trace
Anomaly
20%
Gluon
Energy
34%
Quark
Energy
29%
Quark
Mass
17%
WHY IS THE PROTON MASS INTERESTING?
 How to communicate the lofty goals of
nuclear physics to general public?
Long-range plan:
One of the purposes of modern nuclear physics
is to understand the origin of the mass of the
visible matter.
 Quark masses only contribute ~1-2% of the
proton mass.