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,  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=Mc 2 E=Mc 2 Which is more fundamental? Mass or energy?

Making a point: Hydrogen Atom  The mass of the hydrogen atom is NOT equal to  Rather, it is equal to Therefore, mass is a reflection of energy and energy seems to be more fundamental! Therefore, mass is a reflection of energy and energy seems to be more fundamental!  The difference is small, It is difficult to measure the difference at such a scale. (except M K L -M K s where the accuracy is !) (except M K L -M K s where the accuracy is !)

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 M d = M p + M n – 2.2 MeV/c M d = M p + M n – 2.2 MeV/c the binding here has the effect of order the binding here has the effect of order  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. 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) Quantum Chromodynamics (QCD)  Building blocks –Quarks (u,d,s…, spin-1/2, 3 colors) –Gluons (spin-1, massless, 3 2 −1 colors)  Interactions

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 Λ QCD QCD coupling is not really a constant (next slide), but depends on the momentum scale  Asymptotic freedom! (Gross, Politzer, Wilczek) –As Q  , α s (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 Λ GUT ~ GeV. –Λ QCD is determined by the value of α s at Λ GUT –For example, if we take α em ~ 1/40 at Λ GUT the Λ QCD will be about a few hundred MeV. the Λ QCD will be about a few hundred MeV.  The precise value of the proton mass depends on QCD dynamics at α s (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 one of the daunting challenges in theoretical physics Clay Math. Inst., Cambridge, MA $1M prize to solve QCD! (E. Witten) $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 left- handed quarks and right-handed quarks. They are independent species, and do not talk to each other in the hamiltonian, which 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 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  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 SU 2 X U 1. This symmetry is spontaneously broken at scale Λ EM which is about 100 GeV. 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.