Origins of the Mass ofOrigins of the Mass of Baryonic MatterBaryonic Matter

Xiangdong JiXiangdong Ji

The TQHN GroupThe TQHN Group

Mass and Energy of the UniverseMass and Energy of the Universe

According to the modern cosmology, the According to the modern cosmology, the energy density of the universe is at critical,energy density of the universe is at critical,

Among which 73% come from the Among which 73% come from the cosmological constant—dark energy.cosmological constant—dark energy.

And 23% comes from dark matter of non-And 23% comes from dark matter of non-baryonic origin (axions, susy-partners)baryonic origin (axions, susy-partners)

4% comes from the 4% comes from the baryonic matterbaryonic matter that both that both luminous (less than 0.5%) and dark. luminous (less than 0.5%) and dark.

25 2 -3

1 1

31.05 10 GeV cm

8

100 km s Mpc , 0.73 0.03

cN

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H h h

Forms of Baryonic MatterForms of Baryonic Matter

Earthly Matter Earthly Matter – Atoms, Molecules in gas, liquid and solids Atoms, Molecules in gas, liquid and solids

which include everything we know in daily which include everything we know in daily lifelife

Neutron Stars Neutron Stars – Nuclear matter made of neutronsNuclear matter made of neutrons

Quark MattersQuark Matters – High-density nuclear matter in which quarks High-density nuclear matter in which quarks

and gluons are not confined to inside of a and gluons are not confined to inside of a hadron.hadron.

……

Mass and EnergyMass and Energy

Mass: Mass: one of the most fundamental concepts one of the most fundamental concepts first introduced in physics, as in first introduced in physics, as in F=MaF=Ma. .

EnergyEnergy: a concept introduced to describe : a concept introduced to describe motion (motion (kinetic energykinetic energy) and interactions ) and interactions ((potential energypotential energy). ).

According to Einstein, mass and energy is According to Einstein, mass and energy is intimated connection through intimated connection through

E=McE=Mc22

Which is more fundamental? Mass or energy?Which is more fundamental? Mass or energy?

Making a point: Hydrogen AtomMaking a point: Hydrogen Atom

The mass of the hydrogen atom is NOT equal toThe mass of the hydrogen atom is NOT equal to

Rather, it is equal to Rather, it is equal to

Therefore, mass is a reflection of energy and energy Therefore, mass is a reflection of energy and energy seems to be more fundamental!seems to be more fundamental!

The difference is small, 10The difference is small, 10-8-8. It is difficult to . It is difficult to measure the difference at such a scale. measure the difference at such a scale.

(except M(except MKKLL-M-MKKss where the accuracy is 10 where the accuracy is 10-14 -14 !)!)

2 2938.272029(80) MeV/c 0.510998918(44) MeV/c

p eM M

213.6 eV/cp eM M

Mass of Baryonic MatterMass of Baryonic Matter

Let us consider baryonic matter composed of Let us consider baryonic matter composed of electrons protons and neutrons. electrons protons and neutrons.

The mass of the baryonic matter will be The mass of the baryonic matter will be affected by the energy of interactionsaffected by the energy of interactions– GravityGravity– ElectromagnetismElectromagnetism– Strong Strong – Weak Weak

Mass of Baryonic MatterMass of Baryonic Matter

GravityGravity– Plays extremely important role at short distance Plays extremely important role at short distance

(blackhole) and cosmic scale. However, it can be (blackhole) and cosmic scale. However, it can be ignored for the earthly matter. ignored for the earthly matter.

Electromagnetic Interactions Electromagnetic Interactions – Long range Coulomb interactions among Long range Coulomb interactions among

electrons and nuclei can be ignored. Very small electrons and nuclei can be ignored. Very small effect just like in hydrogen atom. effect just like in hydrogen atom.

– However, larger effects inside nuclei.However, larger effects inside nuclei.

To a good approximation, the mass of baryonic To a good approximation, the mass of baryonic matter is the sum of those of the electrons and matter is the sum of those of the electrons and nuclei!nuclei!

Mass of NucleiMass of Nuclei

Nuclei are consists of protons and neutrons. Nuclei are consists of protons and neutrons. Their masses are equal to the sum of those of Their masses are equal to the sum of those of nucleons plus binding energies.nucleons plus binding energies.

The mass of the deuteronThe mass of the deuteron

MMdd= M= Mpp + M + Mnn – 2.2 MeV/c – 2.2 MeV/c

the binding here has the effect of order 10the binding here has the effect of order 10-3-3..

The typical nucleon binding energy is on the The typical nucleon binding energy is on the order of 8 MeV per nucleon. Therefore, it is on order of 8 MeV per nucleon. Therefore, it is on the order of 1 percent or so. It is a huge the order of 1 percent or so. It is a huge effect. effect. This is the reason for the huge energy This is the reason for the huge energy release in nuclear reactions (atomic bomb)release in nuclear reactions (atomic bomb)

Nuclear Binding EnergyNuclear Binding Energy

Nuclear dynamicsNuclear dynamics

Binding is the effect of the nuclear dynamics.Binding is the effect of the nuclear dynamics.

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pH V V

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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 Where does it the nucleon mass comes from?from?

Nucleons are made of quarks and gluons Nucleons are made of quarks and gluons which interact with a theory called which interact with a theory called

Quantum Chromodynamics (QCD) Quantum Chromodynamics (QCD)

Building blocksBuilding blocks– Quarks (u,d,s…, spin-1/2, 3 colors)Quarks (u,d,s…, spin-1/2, 3 colors)– Gluons (spin-1, massless, 3Gluons (spin-1, massless, 32 2 −−1 colors)1 colors)

InteractionsInteractions

1( )

4a

q a sL i m F F g A

Scales in QCDScales in QCD

Quark masses:Quark masses:– The up and down quark masses are much The up and down quark masses are much

smaller than that of the nucleon, and hence smaller than that of the nucleon, and hence contribute only a small fraction.contribute only a small fraction.

A hidden QCD scale A hidden QCD scale ΛΛQCDQCD

QCD coupling is not really a constant (next QCD coupling is not really a constant (next slide), but depends on the momentum scale slide), but depends on the momentum scale

Asymptotic freedom!Asymptotic freedom! (Gross, Politzer, Wilczek) (Gross, Politzer, Wilczek)

– As QAs Q, , ααss(Q)(Q)00

22

2 2QCD0

4( )

4 ln /s

s

gQ

Q

Physics of the running couplingsPhysics of the running couplings

In quantum field theory, the vacuum is not a In quantum field theory, the vacuum is not a constant. Rather it is a medium full of particles.constant. Rather it is a medium full of particles.

In such a medium, the interaction strength is In such a medium, the interaction strength is modified by the vacuum polarization and hence modified by the vacuum polarization and hence is distance dependentis distance dependent

Screening:Screening: the charge gets screened at large the charge gets screened at large distance, and hence distance, and hence is weakeris weaker (electricity) (electricity)

Anti-ScreeningAnti-Screening: the charge gets anti-screened : the charge gets anti-screened at large distance, and hence at large distance, and hence grows strongergrows stronger (QCD)(QCD)

What sets the scale for strong What sets the scale for strong interactionsinteractions

There has not been a clear answer!There has not been a clear answer!

Speculations:Speculations: – The electromagnetic, weak and strong The electromagnetic, weak and strong

coupling constants might be unified at some coupling constants might be unified at some grand unification scale grand unification scale ΛΛGUT GUT ~ 10~ 101616 GeV. GeV.

– ΛΛQCDQCD is determined by the value of is determined by the value of ααss at at ΛΛGUTGUT

– For example, if we take For example, if we take ααem em ~ 1/40 at ~ 1/40 at ΛΛGUT GUT

the the ΛΛQCDQCD will be about a few hundred MeV. will be about a few hundred MeV.

The precise value of the proton mass depends The precise value of the proton mass depends on QCD dynamics at on QCD dynamics at ααss(Q) ~ 1.(Q) ~ 1.

Quark confinement Quark confinement The other side of the coin of asymptotic freedomThe other side of the coin of asymptotic freedom

Because of the strong coupling, the colored Because of the strong coupling, the colored quarks and gluons can never be librated from quarks and gluons can never be librated from inside of a hadron.inside of a hadron.

In the low-energy region, QCD represents an In the low-energy region, QCD represents an extremely relativisticextremely relativistic, , strongly coupledstrongly coupled, , quantum many-body problemquantum many-body problem

oneone of the daunting challenges in theoretical of the daunting challenges in theoretical physicsphysics

Clay Math. Inst., Cambridge, MAClay Math. Inst., Cambridge, MA

$1M prize to solve QCD! (E. Witten)$1M prize to solve QCD! (E. Witten)

Spontaneous Symmetry BreakingSpontaneous Symmetry Breaking

One idea to get the mass of proton is the so-One idea to get the mass of proton is the so-called called chiral symmetry breakingchiral symmetry breaking, which is a , which is a phenomenon of phenomenon of spontaneous symmetry spontaneous symmetry breakingbreaking. .

Consider a double-well potential in which the Consider a double-well potential in which the barrier is finite. The ground state wave barrier is finite. The ground state wave function is symmetric. However, when the function is symmetric. However, when the barrier goes to infinity, the ground state has barrier goes to infinity, the ground state has no parity symmetry. no parity symmetry.

Chiral Symmetry breakingChiral Symmetry breaking

When the quarks are massless, there are left-When the quarks are massless, there are left-handed quarks and right-handed quarks. They are handed quarks and right-handed quarks. They are independent species, and do not talk to each independent species, and do not talk to each other in the hamiltonian, which is symmetric other in the hamiltonian, which is symmetric under-exchange of them---under-exchange of them---chiral symmetrychiral symmetry!!

However, when the chiral symmetry is However, when the chiral symmetry is spontaneously broken,spontaneously broken, the vacuum is no longer the vacuum is no longer symmetric under exchange of left and right symmetric under exchange of left and right quarks. quarks. – In particular, when a left-handed quark In particular, when a left-handed quark

propagates in the vacuum, it can emerge as a propagates in the vacuum, it can emerge as a right handed quark---Thus the quark gets right handed quark---Thus the quark gets mass!mass!

Constituent Quarks!Constituent Quarks!

When massless quarks travel in the vacuum When massless quarks travel in the vacuum where the chiral symmetry is broken, they where the chiral symmetry is broken, they acquire a mass of order 300 MeV and become acquire a mass of order 300 MeV and become the so-called constituent quark.the so-called constituent quark.

The mass of the proton is roughly the sum of 3 The mass of the proton is roughly the sum of 3 constituent quarks! constituent quarks!

However chiral symmetry breaking happens?However chiral symmetry breaking happens?– Instantons, zero modes, lattice QCD…Instantons, zero modes, lattice QCD…

Color Confinement---In a Bag!Color Confinement---In a Bag!

The quark confinement leads to that a quark in The quark confinement leads to that a quark in the nucleon must move in a small region of the nucleon must move in a small region of space.space.

Therefore, a hadron looks like a bag inside Therefore, a hadron looks like a bag inside which the quarks move, but cannot get to the which the quarks move, but cannot get to the outside.outside.

The Mass of A bag, Along with 3 The Mass of A bag, Along with 3 QuarksQuarks

A free quark inside of the nucleon has a kinetic A free quark inside of the nucleon has a kinetic energy 1/R, according to the uncertainty energy 1/R, according to the uncertainty principle. principle.

However, the free space of volume V has However, the free space of volume V has energy BV—you must pay for the bag! energy BV—you must pay for the bag!

Therefore, the total energy isTherefore, the total energy is

Minimizing with respect to R, one finds that the Minimizing with respect to R, one finds that the second term contributes 1/4 and M=4/R. And second term contributes 1/4 and M=4/R. And since R is about 1 fm, one gets about 900 MeV! since R is about 1 fm, one gets about 900 MeV!

33 4

3M R B

R

QCD HamiltonianQCD Hamiltonian

One can write done a QCD hamiltonian in term One can write done a QCD hamiltonian in term of various contributoinsof various contributoins

Matrix elements of various operators can be Matrix elements of various operators can be determined by experimental data. determined by experimental data. – Deep-inelastic scatteringDeep-inelastic scattering– pi-N sigma term, pi-N sigma term, – Baryon mass spectrum. Baryon mass spectrum.

An Anatomy of the proton massAn Anatomy of the proton mass

Contributions to the proton mass from various Contributions to the proton mass from various sources. Strange quark has been considered sources. Strange quark has been considered both as heavy and light.both as heavy and light.

There is a significant contribution from gluons!

Can we calculate this? Lattice QCD

Lattice QCDLattice QCD

Solve QCD numericallySolve QCD numerically

Four important ideasFour important ideas– Feynman Path IntegralFeynman Path Integral– Wick RotationWick Rotation– Discretization of Space and TimeDiscretization of Space and Time– Monte CarloMonte Carlo

Some Precision Latttice ResultsSome Precision Latttice Results

What sets the scale of quark What sets the scale of quark masses?masses?

The electro-weak symmetry is SUThe electro-weak symmetry is SU22X UX U11. This . This symmetry is spontaneously broken at scale symmetry is spontaneously broken at scale ΛΛEMEM

which is about 100 GeV.which is about 100 GeV.

This symmetry breaking is the origin of the This symmetry breaking is the origin of the masses of quarks and leptons (charged leptons masses of quarks and leptons (charged leptons and neutrinos).and neutrinos).

Although this source of mass might be very Although this source of mass might be very important for non-baryonic matter, but is not important for non-baryonic matter, but is not the dominant one for baryonic matter.the dominant one for baryonic matter.

This is what This is what LargeHadronColliderLargeHadronCollider will study. will study.

ConclusionConclusion

Most of the mass of the luminous matter Most of the mass of the luminous matter comes for the masses of the protons and comes for the masses of the protons and neutrons.neutrons.

Most of the masses of the protons and Most of the masses of the protons and neutrons comes from QCD.neutrons comes from QCD.

Chiral symmetry breaking and quark Chiral symmetry breaking and quark confinement are essential for understanding confinement are essential for understanding the nucleon masses.the nucleon masses.

Experimental data and lattice QCD help us to Experimental data and lattice QCD help us to understand the importance of the various understand the importance of the various contributions to the proton mass. contributions to the proton mass.