**Origins of the Mass ofBaryonic 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=Mc2 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! • 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. 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

**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 • 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 oneof 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 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 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.