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Quantum Chromodynamics (QCD) QCD Is the Theory That Describes the Action of the Strong Force

Quantum Chromodynamics (QCD) QCD Is the Theory That Describes the Action of the Strong Force

Quantum chromodynamics (QCD) QCD is the theory that describes the action of the strong force. QCD was constructed in analogy to (QED), the quantum theory of the electromagnetic force. In QED the electromagnetic interactions of charged are described through the emission and subsequent absorption of massless (force carriers of QED); such interactions are not possible between uncharged, electrically neutral particles. By analogy with QED, predicts the existence of , which transmit the strong force between particles of that carry color, a strong .

The was introduced in 1964 by Greenberg to resolve -statistics contradictions in spectroscopy. In 1965 Nambu and Han introduced the octet of gluons. In 1972, Gell-Mann and Fritzsch, coined the term quantum chromodynamics as the of the . In particular, they employed the general field theory developed in the 1950s by Yang and Mills, in which the carrier particles of a force can themselves radiate further carrier particles. (This is different from QED, where the photons that carry the electromagnetic force do not radiate further photons.) First, QED Lagrangian…

µ ! # 1 µν LQED = ψeiγ "∂µ +ieAµ $ψe − meψeψe − Fµν F 4

µν µ ν ν µ : • F =∂ A −∂ A EM field when an index variable µ • A four potential of the field appears twice in a single term, it implies summation µ •γ Dirac 4x4 matrices of that term over all the values of the index •ψe Dirac four-spinor of the field • e = 4πα, 1/α ≈ 137, ! = c =1

µ µ electromagnetic four-current density of the electron: J = e ψeγ ψe

From the Euler–Lagrange equation of motion for a field, we get:

µ µ (iγ ∂µ − me )ψe = eγ Aµψe for the electron

□Aµ = e ψ γ µψ Maxwell equations for the EM fields e e in the Lorentz gauge

µ d'Alembert □ =∂ ∂µ polarization in QED

force between two + (in natural units) + +

p - e = 4⇡↵ - -

+ - + - + - - + - + +

QED vacuum is dielectric: is screened; interaction becomes weak at large distances

In QED the presence of an electric charge eo polarizes the vacuum and the charge that is observed at a large distance differs from eo and is given by e = eo/ε with ε>1 the dielectric constant of the vacuum. QED vacuum

Let us consider empty space. In a , we cannot just say that the of the empty space is the state with no quanta - we have to solve the proper field equations, with proper boundary conditions, and determine what is the state of the field. Such a state may or may not contain quanta. In particular, whenever the space has a boundary, the ground state of the field does contain quanta - this fact is called the effect.

In QED, this is a very well known, and experimentally verified effect. For example, two conducting parallel plates attract each other, even if they are not charged and placed in otherwise empty space (this is called the Casimir effect). Here, the vacuum fluctuations of the electron field may create in an empty space virtual electron- pairs. These charged particles induce virtual polarization charges in the conducting plates (it means virtual photons are created, travel to plates, and reflect from them). Hence, the plates become virtually charged, and attract one another during a short time when the existence of the virtual charges, and virtual photons, is allowed by the Heisenberg principle. All in all, a net attractive force between plates appears.

d − distance between the plates

Also: QCD Lagrangian

1 L = ψ iγ µ !δ ∂ +ig Gαt $ψ − m ψ ψ − Gα Gµν QCD ∑( qi "# ij µ ( µ α )ij %& qj q qi qi ) 4 µν α q

µ ! # 1 µν LQED = ψeiγ "∂µ +ieAµ $ψe − meψeψe − Fµν F 4

µν µ ν ν µ αβγ µ ν •Gα =∂ Gα −∂ Gα − gf Gβ Gγ color fields tensor µ four potential of the fields (a=1,..8) •Gα

• tα 3x3 Gell-Mann matrices; generators of the SU(3) color group •f αβγ structure constants of the SU(3) color group

•ψi Dirac spinor of the field (i represents color)

• g = 4παs (! = c =1) color charge (strong )

• The have three basic color-charge states, which can be labeled as i=red, green, and blue. Three color states form a in a 3-dimensional . A general color state of a quark is then a vector in this space. The color state can be rotated by 3 × 3 unitary matrices. All such unitary transformations with unit determinant form a Lie group SU(3). • A crucial difference between the QED and QCD is that the gluon field contain the additional term representing interaction between color-charged gluons. • While sources of the electromagnetic field depend on currents that involve a small parameter, gluons are sources of the color field without any small parameter. Gluons are not only color-charged, but they also produce very strong color fields. –15–

Quark masses

PDG, 2010

Figure 3.Thevaluesofeachquarkmassparametertaken fromt mass: the Data 172.44 Listings. Points ± 0.13 from (stat) papers reporting± 0.47 no (syst error ) bars are colored grey. Arrows indicate limits reported. The grey regions indicate values excluded by our evaluations; some regions were determined in part though examination of Fig. 2.

July 30, 2010 14:34 Vacuum polarization in QCD

The left diagram is shared by QED and QCD which renders the interaction stronger at shorter distance (screening). The second diagram arising from the nonlinear interaction between gluons in QCD has the antiscreening effect, which makes the coupling weaker at short distance.

• Color is anti-screened • Color builds up away from a source • Interaction becomes strong at large distances (low momenta) • Confinement of quarks; quarks are not observed as isolated particles g2 Strong coupling constant α = s 4π In quantum field theory, the coupling constant is an effective constant, which depends on four-momentum Q2 transferred. For strong interactions, the Q2 dependence is very strong (gluons - as the field quanta - carry color and they can couple to other gluons). A first- order perturbative QCD calculation (valid at very large Q2) gives:

2 12π running coupling α Q = s ( ) 2 2 constant! (22 − 2n f )⋅ ln(Q / ΛQCD )

nf =6 − number of quark flavors LQCD − a parameter in QCD (~0.22 GeV), an infrared cutoff

The spatial separation between quarks goes as " ! = Q2 Therefore, for very small distances and high values of Q2, the inter- quark coupling decreases, vanishing asymptotically. In the limit of very large Q2, quarks can be considered to be “free” (). On the other hand, at large distances, the inter-quark coupling increases so it is impossible to detach individual quarks from (confinement). Asymptotic freedom was described in 1973 by Gross, Wilczek, and Politzer (Nobel Prize 2004). It is customary to quote as at the 91 GeV energy scale (the mass of the Z )

In QED, coupling increases with increasing energy. At low energies, the fine structure constant a≈ 1/137, whereas at the scale of the Z boson, about 90 GeV, one gets a ≈ 1/127. Chiral

For massless quarks, QCD Lagrangian preserves helicity. Indeed, since a massless quark travels at the speed of light, the handedness or of the quark is independent of any Lorentz frame from which the observation is made. L = L (ψ )+L (ψ ) the QCD interaction does not couple the QCD QCD L QCD R left and right-handed quarks

The mass term explicitly breaks the chiral symmetry as:

mqψqψq = mqψqLψqR + mqψqRψqL

The main origin of the chiral , however, may be described in terms of the condensate (vacuum condensate of bilinear expressions involving the quarks in the QCD vacuum) formed through nonperturbative action of QCD gluons.

Spontaneous symmetry breaking due to the strong low-energy QCD dynamics, which rearranges the QCD vacuum: 3 ψqLψqR ∝ ΛQCD ≠ 0 QCD vacuum The QCD vacuum polarization effect is extremely strong, and the empty space is not empty at all - it must contain a soup of spontaneously appearing, interacting, and disappearing gluons. Moreover, in the soup there also must be pairs of virtual quark-antiquark pairs that are also color-charged, and emit and absorb more virtual gluons. It turns out that the QCD ground state of an “empty” space is extremely complicated. At present, we do not have any glimpse of a possibility to find the vacuum analytically. Some ideas of what happens are provided by the QCD lattice calculations, in which the gluon and quark fields are discretized on a four-dimensional lattice of space-time points, and the differential field equations are transformed into finite-difference equations solvable on a computer.

http://www.physics.adelaide.edu.au/theory/staff/leinweber/VisualQCD/Nobel/index.html

The typical four-dimensional structure of gluon-field configurations averaged over in describing the vacuum properties of QCD. The volume of the box is 2.4 by 2.4 by 3.6 fm, big enough to hold a couple of . Color, Gluons Gluons are the exchange particles which couple to the color charge . They carry simultaneously color and anticolor. red antigreen antiblue

blue green antired

http://www.particleadventure.org Gluons

What is the total number of gluons? According to SU3, 3x3 color combinations form a singlet and an octet. The octet states form a basis from which all other color states can be constructed. The way in which these eight states are constructed from colors and anticolors is a matter of convention. One possible choice is:

RG , RB , GB , GR , BR , BG , 1/ 2 ( RR − GG ), 1/ 6 ( RR + GG − 2 BB )

The color singlet:

1/ 3( RR + GG + BB )

is invariant with respect of a re-definition of the color names (rotation in color space). Therefore, it has no effect in color space and cannot be exchanged between color charges. emission of a gluon splitting of a gluon self-coupling of gluons by a quark into a quark-antiquark pair q → q + g g → q + q g → g + g g + g → g + g

http://www.particlezoo.net/shop.html Quarks In 1968, deep inelastic scattering experiments at the Stanford Linear Accelerator Center showed that the contained much smaller, point-like objects and was therefore not an elementary Flavor A t t S C B T Q(e) Mc2 (GeV) z MeV u (up) 1 1 + 1 0 0 0 0 + 2 0.002 − 0.003 3 2 2 3 2.3(5) d (down) 1 1 − 1 0 0 0 0 − 1 0.004 − 0.006 3 2 2 3 4.8(5) s (strange) 1 0 0 −1 0 0 0 − 1 0.08− 0.13 3 3 95(5) c () 1 0 0 0 1 0 0 + 2 1.2 −1.3 3 3 b (bottom) 1 0 0 0 0 −1 0 − 1 4.1− 4.3 3 3 t (top) 1 0 0 0 0 0 1 + 2 173±1 3 3 • The least massive are u- and d-quarks (hence the lightest and are made exclusively of these two quarks). • Each quark has number A=1/3. • carries a quantum number called S. Strange particles (such as ) carry this quark. • Six antiquarks complement the list. • Quarks are all ; they carry half-integer spins. • d- and u-quarks form an doublet: τ− u = d τ+ d = u • Strong interactions conserve the total number of each type of quarks. However, quarks can be transformed from one flavor to another through weak interactions (CKM matrix!). baryon

_ _ ! g g u d bg # R R + # _ π = u d " B B b # b _ # u d g b $ G G _ g Meson can exist in three different color g combinations. The actual is a mixture of _ _ these color states. By exchange of gluons, the r g r color combination continuously changes. r Hadrons

baryons mesons fermions made up of three quarks made up of quark-antiquarks* must have half-integer spins must have integer spins

* Bosons can be annihilated; strong interactions conserve the # of quarks

p + p → γ + γ particle- annihilation

• particle and antiparticle have opposite charges, baryon numbers, etc. • they must have opposite intrinsic parities • they must have opposite isospins

A charge number Q = t + 0 2

A third component of isospin u !!→ u d !!→− d τ ± (hadron) → ∑τ ± (qi ) C C i=1

€ Mesons quark wave function of the pion

- Consider p (t=1 and t0=-1). The only possible combination is π − = ud In general, it is possible to find several linearly independent components corresponding to the same t and t0. The appropriate combination is given by isospin coupling rules. Furthermore, the wave function must be antisymmetric among the quarks. This problem is similar to that of a two- wave function! 1 1 π 0 = τ π − = uu − dd + ( ) T=1 triplet: 2 2 π + = − ud

What about the symmetric combination? 1 T=0 singlet: η0 = uu + dd 2 ( )

To produce heavier mesons we have to introduce excitations in the quark-antiquark system or invoke s- and other more massive quarks The is a term coined by Murray Gell-Mann for a theory organizing baryons and mesons into octets (alluding to the Noble Eightfold Path of Buddhism). The Eightfold Way is a consequence of flavor symmetry. Since the strong nuclear force affects quarks the same way regardless of their flavor, replacing one flavor of quark with another in a hadron should not alter its mass very much. Mathematically, this replacement may be described by elements of the SU(3) group. The octets and other arrangements are representations of this group.

The Dharma wheel (represents the Noble Eightfold Path) The lightest strange mesons are kaons or K-mesons. Since s-quark has zero isospin, kaons come in two doublets with t=1/2: {K + (us ), K 0 (ds )}, {K − (us), K 0 (ds)} Y = A + S +C +B +T hypercharge 1 Q = t0 + Y 2 the SU(3) symmetry limit is met for massless u,d,s quarks

π − (ud)+ p(uud) → K 0 (ds )+ Λ(uds) strangeness is conserved! Pseudoscalar mesons ! J total angular momentum ! ! ! ! ! ! ! J = ℓ + S, S = s + s ℓ orbital angular momentum q q ! S total spin

S can be either 0 or 1. The mesons with the relative zero orbital angular momentum are lower in energy. For the pion, S=0, hence J=0. Consequently, are “scalar” particles. But what about their ? The parity of the pion is a product of intrinsic parities of the quark (+1), antiquark (-1) and the parity of the spatial wave function is +1. Hence, the pion has negative parity: it is a . With (u,d,s) quarks, one can construct 9 pseudoscalar mesons (recall our earlier discussion about the number of gluons!): 9 (nonet)=8 (octet)+1 (singlet) Members of the octet transform into each other under rotations in flavor space (SU(3) group!). The remaining meson, h0, forms a 1-dim irrep. (us ) 1 497.61 π 0 = uu − dd (ds ) 2 ( ) 493.68 1 η = uu + dd − 2 ss 8 6 ( ) 1 547.86 134.98 η = uu + dd + ss (ud ) 0 3 ( ) (du )

139.57 In reality, since the SU3 (flavor) symmetry 957.78 is not exact one, the observed mesons are: (su ) � = � cos � − � sin � (sd )

�′ = � sin � + � cos � � = −15∘ masses are in MeV/c2 The eta was discovered in pion-nucleon collisions at the Bevatron (LBNL) in 1961 at a time when the proposal of the Eightfold Way was leading to predictions and discoveries of new particles.

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(Q=0)

Hmmm… Those are not CP eigenstates

Long Short

69% 31% The main decay modes of KS are:

… and both decays conserve CP. What about KL ? Three-body decay, very slow!

These decays are called semileptonic decays, producing one meson and two . They account for about 67% of KL decays compared to 33% for the 3π mode.

−11 1m T(KS)=(8.954±0.004)×10 s

−8 T(KL)=(5.116±0.021)×10 s

Cronin & Fitch experiment, 1964

17 m beamline; KS should not be observable more than ~1m down the beam line Given the disparity of the lifetimes of the two kaon species, you expect to see only the long-lived version at the end of the beam tube, but they found about 1 in 500 decays to be 2-pion decays, characteristic of the short-lived species.

Vector mesons

Here S=1, hence J=1. They have negative parity. The vector mesons are more massive than their pseudoscalar counterparts, reflecting the differences in the interaction between a quark and an antiquark in the S=0 and S=1 states.

J π =1− 896 (us ) (ds ) 1 892 ρ 0 = uu − dd 2 ( ) 775 1 783 (ud ) ω = uu + dd (du ) 2 ( ) 775 ϕ = ss 1019

(su ) (sd )

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€ € 2 Flux tubes and confinement “ ” 1.5 Lattice measurement of the quenched static potential 1 linear region Phys. Rev. D 51, 5165 (1995)

0.5

0 V = kr (k =16 T) ñ0.5 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 r (fm) Phys. Rev. D 79, 114029 (2009)

The origin of the linear potential between quarks may be traced to the flux tube: a string of gluon energy density between the quark pair. The QCD vacuum acts like a dual superconductor, which squeezes the color electric field to a minimal geometrical configuration, a narrow tube. It costs energy for the flux to spread out in space. The tube roughly has a constant cross section and with constant energy Regge trajectories density. Because of this, the energy stored in the flux (Nambu 1970) increases linearly with the length of the flux. energy: This animation shows the suppression of the QCD vacuum from the region between a quark-antiquark pair illustrated by the coloured spheres. The separation of the quarks varies from 0.125 fm to 2.25 fm, the latter being about 1.3 times the diameter of a proton. The surface plot illustrates the reduction of the vacuum action density in a plane passing through the centers of the quark-antiquark pair. The vector field illustrates the gradient of this reduction. The tube joining the two quarks reveals the positions in space where the vacuum action is maximally expelled and corresponds to the famous "flux tube" of QCD. As the separation between the quarks changes the tube gets longer but the diameter remains approximately constant. As it costs energy to expel the vacuum field fluctuations, a linear confinement potential is felt between quarks. http://www.fair-center.eu

Quarks do not exist in isolation. Attempts The theory of the strong interaction to separate quarks from one another predicts the existence of - require huge amounts of energy and particles that consist only of gluons results in the production of new quark- (above), and so-called hybrids composed antiquark pairs. of two quarks and a gluon (below). Baryons (qqq)

With three flavors, one can construct a total of 3×3×3=27 baryons

baryon singlet t = 0

Completely asymmetric under flavor 1 Λ1 = { uds + dsu + sud − dus − usd − sdu } rotations 6 The color and flavor wave-functions should be antisymmetric and thus zero orbital angular momentum and spin-1/2 are not possible if the wave-functions is to be overall 1 − antisymmetric as required by Fermi–Dirac statistics. Hence, L=1 J π = L (1405) 2 baryon decuplet

(ddd) (udd) (uud) (uuu)

3 + (dds) (uds) (uus) J π = 2

(dss) (uss)

(sss)

The discovery of the omega baryon was a great triumph for the of baryons since it was found only after its existence, mass, and decay products had been predicted by Murray Gell-Mann in 1962. It was discovered at Brookhaven in 1964.

€ baryon octet The remaining 16 baryons constructed from u-, s-, and d-quarks have mixed symmetry in flavor. The lower energy octet contains protons and as its members. The wave functions for each member in the group is symmetric under the combined exchange of flavor and intrinsic spin (the quarks are antisymmetric in color!)

939.6 938.3

(udd) (uud) (ddd)

1115.7 (uds) + 1197.4 π 1 J = 1189.4 2 (dds) 1192.5 (uus)

1321.3 1314.9 (dss) (uss)

1 p = 2 u↑u↑d ↓ + u↑d ↓u↑ + d ↓u↑u↑ 18 { ( ) example: proton wave function −( u↑u↓d ↑ + u↑d ↑u↓ + d ↑u↑u↓ ) +( u↓u↑d ↑ + u↓d ↑u↑ + d ↑u↓u↑ )} Magnetic dipole moments of the nucleon The magnetic dipole moment of a baryon comes from two sources: the intrinsic dipole moment of the constituent quarks and the orbital motion of the quarks. For the baryon octet, L=0. ! ! q! µ = gsµD, µD = 2mqc For Dirac particles (I.e., particles devoid of internal structure), g=2 for s=1/2. Unfortunately, we do not know quark masses precisely. Assuming that the masses of u- and d-quarks are equal, one obtains: µu = −2µd Consider the proton wave function written in terms of u- and d-quarks. The net contribution from u-quarks is 4/3 and that from d-quarks is -1/3. Hence 4 1 µ = µ − µ p 3 u 3 d 4 1 By the same token µ = µ − µ n 3 d 3 u µ 2 This gives n = − µ p 3 (=-0.685 experimentally)

quark magnetic moments New relatives of the proton

http://www.fnal.gov/pub/ferminews/ferminews02-06-14/selex.html

Two New Particles Enter the Fold http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.114.062004 The Roper resonance [N(1440)P11] is the proton's first radial excitation. Its lower- than-expected mass owes to a dressed-quark core shielded by a dense cloud of pions and other mesons. The positions of the three quarks composing the proton are illustrated by the colored spheres. The surface plot illustrates the reduction of the vacuum action density in a plane passing through the centers of the quarks. The vector field illustrates the gradient of this reduction. The positions in space where the vacuum action is maximally expelled from the interior of the proton are also illustrated by the tube-like structures, exposing the presence of flux tubes. A key point of interest is the distance at which the flux-tube formation occurs. The animation indicates that the transition to flux-tube formation occurs when the distance of the quarks from the center of the triangle is greater than 0.5 fm. Again, the diameter of the flux tubes remains approximately constant as the quarks move to large separations. • Three quarks indicated by red, green and blue spheres (lower left) are localized by the gluon field. • A quark-antiquark pair created from the gluon field is illustrated by the green-antigreen (magenta) quark pair on the right. These quark pairs give rise to a meson cloud around the proton.

http://www.physics.adelaide.edu.au/theory/staff/leinweber/VisualQCD/Nobel/index.html Nucl. Phys. A750, 84 (2005) 1000000 QCD mass 100000 Higgs mass

10000

1000

100 Mass (MeV) Mass

10

1 u d s c b t

GeV

HOW does the rest of the proton mass arise?

HOW does the rest of the proton spin (magnetic moment,…), arise? Mass from nothing

Dyson-Schwinger and Lattice QCD

mass off bare quark mass of constituent quark constituent of mass

It is known that the dynamical ; namely, the generation of mass from nothing, does take place in QCD. It arises primarily because a dense cloud of gluons comes to clothe a low- momentum quark. The vast bulk of the constituent-mass of a light quark is contained in a cloud of gluons, which are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies acquires a large constituent mass at low energies. Low-lying Hadron Spectrum Dürr, Fodor, Lippert et al., BMW Collaboration Science 322, 1224 (2008) More than 99% of the mass of the visible universe is made up of protons and neutrons. Both particles are much heavier than their quark and gluon constituents, and the of should explain this difference. We present a full ab initio calculation of the masses of protons, neutrons, and other light hadrons, using lattice quantum chromodynamics. Pion masses down to 190 mega–electron volts are used to extrapolate to the physical point, with lattice sizes of approximately four times the inverse pion mass. Three lattice spacings are used for a continuum extrapolation. Our results completely agree with experimental observations and represent a quantitative confirmation of this aspect of the Standard Model with fully controlled uncertainties Isospin Splittings in the Light-Baryon Octet from Lattice QCD and QED (ab initio calculation of the -proton mass difference) Neutron = 939.56563 MeV Proton = 938.27231 MeV experiment 8 QCD+QED Electron = 0.51099906 MeV

6 D

4 M [MeV]

cc 2 N

CG 0 Science 347, 1452 (2015)

BMW 2014 HCH

“The neutron–proton mass difference, one of the most consequential parameters of physics, has now been calculated from fundamental theories. This landmark calculation portends revolutionary progress in .” Wilczek, Nature 520, 303 (2015) Synopsis: Strong Force Model for Weak Force Reactions

https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.119.062002 Theorists have used lattice-QCD calculations to predict two weak-force-driven reactions—proton fusion and tritium decay

+ p + p → d + e + νe

sha1_base64="3YNOukEzga4+XmeM4RjNtow8qI0=">AAACHHicbZDNSgMxFIUz/tb6V3Wpi2ARhIEyI4JdFty4rGB/oK1DJr3ThiaZIckopXTjg7h2q8/gTtwKPoJvYdrOQtseCBzOuZdwvzDhTBvP+3ZWVtfWNzZzW/ntnd29/cLBYV3HqaJQozGPVTMk

AAACHHicbZDNSgMxFIUz/tb6V3Wpi2ARhIEyI4JdFty4rGB/oK1DJr3ThiaZIckopXTjg7h2q8/gTtwKPoJvYdrOQtseCBzOuZdwvzDhTBvP+3ZWVtfWNzZzW/ntnd29/cLBYV3HqaJQozGPVTMkGjiTUDPMcGgmCogIOTTCwfWkbzyA0iyWd2aYQEeQnmQRo8TYKCicJG7SVqzXN0Sp+BF3sQv3LnbbMg0gKBS9kjcVXjR+ZoooUzUo/LS7MU0FSEM50brle4npjIgyjHIY59uphoTQAelBy1pJBOjOaHrFGJ/ZpIujWNknDZ6mfzdGRGg9FKGdFMT09Xw3CZd2oVgWt1ITlTsjJpPUgKSz/6OUYxPjCSncZQqo4UNrCFXMnoBpnyhCjeWZt2z8eRKLpn5R8r2Sf3tZrJQzSjl0jE7ROfLRFaqgG1RFNUTRE3pBr+jNeXbenQ/ncza64mQ7R+ifnK9fqFWgpg== The spin structure of the nucleon Rev. Mod. Phys. 85, 655 (2013)

How do the proton’s various constituents contribute to its overall spin? As illustrated by the diagram, the quarks, antiquarks, and gluons are all believed to have their own intrinsic spins, and these must contribute. But so also must the relative orbital motions of the quarks and gluons inside the proton. The first measurements of the proton’s spin substructure have been made recently, employing the technique of deep inelastic scattering with spin-polarized beams bombarding spin-polarized targets. By combining these measurements with constraints from other data, one can infer the fraction of the proton’s spin carried by the intrinsic spin of quarks (and antiquarks) of different flavors. The results of experiments performed at CERN, SLAC, and DESY, summarized in the graph, point to an unexpected outcome: all the quarks and antiquarks together account for no more than one-third of the total spin. More direct probes of the spin alignment of different flavors of quarks, separation of the contributions from quarks and antiquarks, and extraction of information on the gluon spin contributions are goals of ongoing and planned second-generation experiments. http://physicsworld.com/cws/article/news/2014/jul/11/gluons-get-in-on-proton-spin http://www.scientificamerican.com/article/proton-spin-mystery-gains-a-new-clue1/ Viewpoint: Spinning Gluons in the Proton http://physics.aps.org/articles/v10/23

Computer simulations indicate that about 50% of the proton’s spin comes from the spin of the gluons that bind its quark constituents

Phys. Rev. Lett. 118, 102001 (2017) 4 Where is the glue? Search for exotic particle

negative parity positive parity exotics

2.5

?

2.0

1.5

1.0

isoscalar

0.5 Phys. Rev. D 84, 074023 (2011) isovector YM

http://www.gluex.org FIG. 1. A compilation of recent lattice QCD computations for both the isoscalar and isovector lightA glueball mesonsis from made Ref. up [1 ],purely of gluons including ``¯ ``¯ ( uu¯ + dd¯ )/p2 and ss¯ mixing angles (indicated in degrees). The dynamical computation is carried out with two flavors| i⌘ of quarks,| i light| i (`) and strange (s). The s quark mass parameter is tuned to match physical ss¯ masses, while • Non-quarkthe light model quark mass mesons parameters are include heavier, giving exotic a pion mass mesons, of 396 MeV. The black brackets with upward ellipses represent regions of the spectrum where present techniques make it dicult to extract additional states. The dotted boxes indicate states + which havethat are quantum interpreted as the numbers lightest hybrid multipletnot possible – the extraction for of clear 0 states in this region is dicult in practice. mesons in the quark model. • glueballs or gluonium, which have no valence quarks. • hybrid mesons, which contain a valence quark- antiquark pair and one or more gluons. http://phys.org/news/2015-10-particle-purely-nuclear.html

FIG. 2. Spectrum of gluonic excitations in hybrid mesons (gray) and hybrid baryons (red, green, and orange) for three light quark masses. The mass scale is m m⇢ for mesons and m mN for baryons to approximately subtract the e↵ect of di↵ering numbers of quarks. The left calculation is performed with perfect SU(3)-flavor symmetry, and hybrid members of the flavor octets (8F ), decuplet (10F ), and singlet (1F ) are shown. The middle and right calculations are performed with a physical ss¯ mass and two di↵erent values of m⇡. The rise and fall (and rise) of the http://www.symmetrymagazine.org/article/september-2006/the-rise-and-fall-of-the-pentaquark

http://physics.aps.org/articles/v8/77

LHCb produces charmonium : Phys. Rev. Lett. 115, 072001 (2015) http://physics.aps.org/articles/v8/77 http://phys.org/news/2015-07-cern-lhcb-exotic-pentaquark-particles.html http://www.sciencedaily.com/releases/2015/07/150714082858.htm http://physicsworld.com/cws/article/news/2016/feb/29/fermilab-bags-a- http://physicsworld.com/cws/article/news/2016/mar/21/cern-fails-to-confirm-- tetraquark-discovery http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.117.082003 Confirmed! The Structure

s=1/2 J=2

proton nucleus hadron spectroscopy nuclear spectroscopy

The origin of confinement The origin of nuclear force The origin of mass, spin The origin of binding, spin Quantum numbers and Quantum numbers and symmetries

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