Hadron Spectroscopy Part I: Conventional Hadrons Tomasz Skwarnicki Syracuse University

National Nuclear Physics Summer School Boulder, Colorado, July 9-22, 2017 Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 2 Introduction • Plan: – Day 1: Conventional Hadron Spectroscopy – Day 2: Exotic Hadron Spectroscopy • Hadron Spectroscopy is a very broad subject. A lot of interesting aspects of various systems. Hundreds of experimentalists and theorists involved in it. • Instead of getting into very specialized topics, try to provide broad guide to various hadron families today. • I apologize for this talk being perhaps too elementary. I start from reviewing atomic spectroscopy, historical intro, … • I am an experimentalists, who has been active in heavy flavor experiments (Crystal Ball at DORIS, CLEO at CESR, LHCb). Selection of topics somewhat biased by my background. Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 3 Hadron? • Hadron = strongly interacting particle Лев Борисович Окунь • The term “hadron” introduced by Lev Borisovich 1929 –2015 Okun at 1962 (11 th ) ICHEP conference in Geneva:

“The point is that "strongly interacting particles" is a very clumsy term which does not yield itself to the formation of an adjective. For this reason, to take but one instance, decays into strongly interacting particles are called non-leptonic. This definition is not exact because "non-leptonic" may also signify "photonic". In this report I shall call strongly interacting particles "hadrons", and the corresponding decays "hadronic" (the Greek signifies "large", "massive", in contrast to which means "small", "light"). I hope that this terminology will prove to be convenient.”

0.5 < 140 < 938 MeV 1777 < 5279 < 5620 MeV M(e) < M( π) < M(p); M( τ) < M(B) < M( Λ ); b lepton hadrons ο α the mass hierarchy which led to this “intermediate” “heavy” meson baryon nomenclature still holds within each “generation” Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 4 Spectroscopy? The Cat's Eye Nebula (Hubble Space Telescope)

• Spectral lines were observed visible light before their origin was understood. • Led to development of

quantum mechanics Intensity

= c h / Eγ Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 5 Hydrogen atom ℏ − − (,,)=(,,)

[eV] = − p [nm] V e = − z Reduced mass: = 1,,3, … 1 = = = 0.0073 = 0,1,, … , − 1 = ( + 1)ℏ 1 ℏ 137 = −, − + 1, … , + = ℏ = ≈ (not to be confused with reduced mass) 1 1 Coulomb potential + ℏ = =0.053 nm

generalized Laguerre polynomials have − − 1zero crossings (“nodes”)

principal vs If it was not due to the energy degeneracy in “principal quantum number” n, it would make more sense radial quantum to define “radial quantum number” = − and use instead of to label eigenstates of the system ( is not restricted by value). number Energy depends on both radial ( ) and orbital momentum ( ) excitations. The degeneracy in + is accidental and happens only for 1/ r potential. Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 6 Hydrogen Spectroscopy 2 Each colored square represents En = −13.6 eV / n a different quantum state 0 ionization threshold n = infinity (ml labels not spelled out) H Hγ β Balmer (visible) Hα

Hβ = 2s 2p photon = 0 = −1,0, +1 transitions

Balmer series 2 | (, , )| Lγ Lyman series Lβ L (ultraviolet) α = 1,,3,… H α = 0,1,,3,…, − 1 −13.6 eV = , , , , … 1s = 0 Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 7 More Hydrogen Electron Orbitals | (, = , )|2 = 1

Notice, how radial quantum number implies specific radial structure, while principal quantum number doesn’t =

= 3

= 4

= 0 = 0 = ±1 = 0 = ±1 = ± = 0 = ±1 = ± = ±3 Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 8 Fine-structure of hydrogen = ( + 1)ℏ Particle with a spin has a magnetic dipole moment: = − = ℏ = = ~ = 0.0005 Magnetic effects due to proton spin can be neglected relative to magnetic effects due to electron spin. = + SPIN-ORBIT INTERACTIONS orbiting electron is like a current loop and sets up magnetic field ∝ which interacts with magnetic dipole of electron = − ∝ ∝ p

very small effect ! FS 0.000045 eV decreases with excitation level = 0.00005 (Lamb shift removes this degeneracy: QED effect suppressed by α~0.01)

Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 9 Single-electron atoms (N-nucleus) • H ( N=p ), deuterium ( N=np ), He + (N=2p2n ), Li 2+ (N=3p3n ),… • Same energy spectrum up to fine structure, except for small shift due to the small change in the reduced mass of the system (H→deuterium), or larger rescaling due to increased charge of nucleus in ions

Hα photon lines Reduced mass:

1 = ≈ (1 − ) 1 1 + Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 10 Hyperfine structure of hydrogen Due to magnetic dipole moment of proton. Suppressed relative to fine structure by: = + = 0.0005 . 8 = 0.0015 = + - anomalous magnetic moment of proton since not a point-like particle

= + Hyperfine structure will be due to: ∝

Hyperfine structure splits even = states = 1 1 1 HS 0.000006 eV

1 = 0 Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 11 Positronium – (e+e-) = + • In the leading order, the same energy spectrum as for hydrogen except for a factor of 2 smaller = + (larger) energies (sizes) of states: 1 1 Reduced mass: = ≈ 1 1 +

• Hyperfine and fine structures are of the same order of magnitude:

– total spin = + is a “good quantum number” – spin-orbit interactions:

– spin-spin interactions:

– tensor interactions: 3( ) ( ) − • New element – even ground state is meta-stable and can annihilate to photons: 1 3 – τ(1 s0→γγ ) =0.125 ns, τ(1 s1→γγγ ) =142 ns Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 12 Pauli exclusion principle and periodic table

Z Periodic table of elements: Dmitri Mendeleev 1834-1907 “magic Russia numbers” shell-3 …

2 shell-2 8e 8 …

x 2 for =±

Wolfgang Pauli 1925 Identical fermions cannot occupy the same quantum state within a quantum system shell-1 2e simultaneously. (this also led to development of spin concept) Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 13 First hadrons discovered • Alpha particles (~1900): (Nobel prize in 1908)

rays from α radioactive decays β classified γ according to Ernest Rutherford their penetration at McGill University in 1905 ability Manchester University in • Nuclei (1909-) 1909 α

hard scattering Hans Ernest α centers in Rutherford + atoms Geiger - nucleus

p 1919: proton as nucleus of hydrogen n alpha particles as nucleus of helium 1932: neutrons (highly penetrating radiations but not gammas) Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 14 Isospin symmetry - 1932 • Rotation in the isospin space is a symmetry of strong interactions. • Total isospin is conserved in strong interactions. pion predicted by Yukawa in 1934 = ( + 1) ℏ = ℏ = + IZ + IZ π Q – electric charge A – baryon number M(p)=938.3 MeV identified p in cosmic rays +ℏ by Powell in 1946 +ℏ/ IY π0 0

M( π0)=135.0 MeV -ℏ/ IX -ℏ n M(n)=939.5 MeV 1 π− = = 1 M( π±)=139.6 MeV (N – nucleon) Any nucleus has a definite isospin. Isospin (“Isotopic spin”) very useful in nuclear physics. Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 15 ρρρ resonance: short-lived particle • 1961: scattering charged pion beam (E=2 GeV) on stationary proton target and looking for two pions and a proton (or neutron) coming out: π−p →π −π0p π−p →π−π+n Thought to happen: = 1

time ~770 MeV Γρ ~150 MeV Relativistic Breit-Wigner ~ formula for a resonance Γ The ρ resonance is a very short-lived particle: τ - average lifetime -24 τρ = ħ / Γρ =4.4x10 s unmeasurably small cτρ === 1.3 fm

MeV -8 vs. long-lived ν ν 2 1/2 τπ± = 2.6x10 s mππ =[ (P π1 +P π2 ) ] particle cτπ± = 7.8 m -8 unmeasurably small Γπ± = 2.5x10 eV Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 16 Strange mesons and baryons Bubble chamber photograph

p π−

0 -10 Λ τΛ = 2.6x10 s lives long cτΛ = 7.8 cm

Lots of particles Incoming produced; most of them short-lived resonances p beam Λ0 baryon lives “strangely” long.

There are also strangely long-living mesons - kaons Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 17 Quark hypothesis – SU(3) flavor symmetry “Eightfold Way” symmetry – Gell-Mann 1961 “hypercharge” Y=S+A (not really a “charge”) P 3 + JP = 0- Y=S JP = ½+ Y=S+1 J = ½ Y=S+1 Q +1 Q I = ½ +1 Q +1 I = 3½ I = 1 0 0 0 I = 1 I = 0 -1 I = ½ -1 -1 I = ½ Strangeness Strangeness

the lightest version) lightest lightest the the version) version) -1 0 1 -1 0 1 -2 I = 0 Isospin projection Q = + ½ Y -1Y=S+1/3 0 1 (“charge index” in multi-charged particles) (how lifetimelifetimeis the is the long long of of (how (how “strangely” “strangely” Meson Not known at that time: Baryon (sss) S = -3 octet octet decuplet JP = ½+ Y=S+ ½

()+1 3 Q () Murray d u Gell-Mann Quark triplet I = ½ Nobel Prize 0 1969 I = 0 s including baryonic molecules These are “non-exotic” hadrons -1 -1 0 1 i.e. nuclei (( )( )…) Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 18 Experimental discovery of ΩΩΩ−−− −−−1964 • The discovery convinced some physicists that Gell-Mann was on the right track • Quarks initially treated as mathematical abstraction. Many doubted that they existed since free quarks are not observed.

“strange” decays understood later as mediated via “weak” forces as opposed to “strong” (super short lifetimes) or electromagnetic forces (longer but still undetectably short decay paths) Ξ0 s su

d − W− u π Ω− s s s • Ω- is a ground state of three s quarks. Since their spins (1/2) have to add up to 3/2, they must be lined-up. Three identical fermions in identical quantum state? • This was later understood as each s quark having a different charge of strong interactions. Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 19

QCD: SU(3) color symmetry Nobel Prize 2004

• Fundamental parts of SU(3) flavor symmetry: – Quark flavor independence of strong interactions – Rules for making hadrons out of quarks Hugh David David Gross • Near degeneracy of u,d,s quark masses coincidental Politzer Frank Wilczek

• Exact theory of strong interactions: QCD based on SU(3) color symmetry 1 = q ( i D - m ) q - FFF FFF Asymptotic q freedom QCD q=u,d,s, 4 c,b,t V~ r

Unfortunately perturbative methods don’t work at large quark separations (relevant to hadron creation) – need V(r) numerical methods i.e. Lattice QCD calculation. LQCD methods have their own limitations, especially V~1/r Static qq potential when dealing with highly excited hadrons. in Lattice QCD 0.5 1.0 [fm] Observable hadrons Hadrons spectra are often subject of QCD- are color neutral. motivated phenomenological modeling. Raising potential energy must lead to a quark pair creation, and Quarks: 3 different color charges confinement of color charge at Gluons: 8 different color+anticolor charges large distances Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 20 Mesons from quarks & antiquarks in QCD color octet

1 i − 2 2 color color color 1 i triplet antitriplet singlet 2 2 1 1 i 1 2 − 3 − _ 2 6 2 2 3 8 3 ⊗ = 1 ⊕ 1 1 1 1 1 1 i 3 3 − 2 6 6 2 2 quark antiquark attractive color force i 1 − q q 2 2 (qq) meson 1 i +++ e.g. K 2 2 _ Color flux tube s stretched between repulsive color force quark and antiquark quarks will pull apart _in any with attractive u octet configuration potential gluons happen to belong to the color octet Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 21 Light meson excitations? (q=u or d) q,s π,K “OZI allowed decay” q,s q ρ,K* Such fall-apart strong decays happen super fast, = + q leading to a large mass indeterminacy q i.e. large particle widths q π Γ ~ℏ MeV MeV = + 1000 The higher the excitation, the more 1300 decay channels open. 13s 1 Such decays effect the properties ρ(770) of bound states in a way which is 3 difficult to deal with theoretically. 600 900 1 s1 π transitions K*(892) Expect positronium-like energy ππ Kπ (i.e. mass) spectrum, though with 1 _ 1 _ 200 1 s 500 1 s0 different energy splittings 0 q q MeV 140 π q K s 2S+1 Theoretical models of higher light hadron excitations tend to be qualitative only. • Hyperfine mass splittings among light mesons are huge! – Reflects relativistic nature of light mesons, ~1, while positronium is essentially non-relativistic, ~0. Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 22 Initial impact of heavy flavors on hadron spectroscopy: Dispute over quarks ended in 1974.

+ − e e → hadrons November revolution of 1974 Log-scale! ψ J pBe → e+e− X

3 1 s1 state

Samuel Ting

Burton Richter

Nobel Prize, 1976 Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 23 Charmonium p-states

Fine-structure mass splitting (LS dominated) 23s →γ 13p I am switching to use of radial quantum 1 2,1,0 number to label the hadronic states: 3 3 1 p2,1,0 →γ1 s1 2S+1 ′

Eγ [MeV] • In heavy-heavy mesons, photon spectroscopy of hadronic states is an important experimental tool Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 24 Initial impact of heavy flavors on hadron spectroscopy: s,c,b Such fall-apart strong decays happen super fast, leading to a large mass s, c, b q K,D,B K*, ψ’’, °’’’ indeterminacy i.e. large particle widths (“poorly formed” bound states) q, c, b Γ ~ℏ q π, D,B “deeper binding of heavy quarks” MeV (q=u or d) q,c,b MeV °’’’ 3 2S+1 BB 2 S1 n’ L 3 K* (1430) j 1 1 P1,2 2 χ ’’ 2 S0K*(1410) K* (1430) b 0 MeV ψ’’ 1 K (1400) K(1460) 1 P1 1 3 10300 °’’ °2 1300 3 3800 3 DD 1 D1 1 P0 2 S1 10300 ’ K (1270) hb χ ’ 1 21S 13P b q 0 ψ’ χ 0,1,2 Predictions of relativized 11P c2 c,b q potential model hc’ 1 q °’ q 3 vs. _ h χc1 hb’ c,b 1 S c MeV 1160 1 known states c _ q K*(892) χc0 hb q c b cb Kπ MeV 745 b 3 9500 Such strong decays take 1000 times longer. 1 S1 1 _ Narrow widths; well formed bound states. 500 1 S0 1 9500 q MeV 140 3000 1 S0 J/y K ° s hc hb

All excitations above the open flavor threshold. Plenty of excitations below the open flavor threshold. Wide (short-lived) and highly relativistic (light quarks). Narrow (long-lived) and non-relativistic (heavy quarks). Only qualitative spectroscopy. Quantitative spectroscopy. Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 25 Dominant factor in meson mass spectra: n’ , l n’=3 • Near universality of n,l driven mass n’=2 splittings is a reflection of quark- Hydrogen atom: MeV °’’’ Coulomb potential flavor independence of strong n’=1 interactions, and states probing the potential at similar distances for BB χb’’ different meson species 10300 °’’ °2 MeV MeV 3 ’ 3 1 D hb χb’ 2 S1 3800 3 1 ψ’’ 3 2 S1 10300 1 P K* 2(1430) 21S K*(1410) 1,2 21S 3 0 K* 0(1430) DD 0 1 P0,1,2 1 K (1400) ψ’ 1 χc2 °’ K(1460) 1 P1 1 hc’ 1 P1 hb’ 1300 3 1 P0 hc χc1 hb K1(1270) cb χc0

3 3 9500 1 S1 1 S1 K*(892) 11S ° 3000 0 J/y hb • Lack of mass degeneracy in Kπ hc “principal quantum number”, _ _ _ n’=n+L, is a reflection of the 1 c 500 1 S0 q b states probing non-Coulombic 2S+1 b K s c n’ Lj part of the potential Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 26 Fine and hyperfine structure in meson spectra Significant since confining potential is effectively of scalar type Spin-orbit (requires non-zero L and S i.e. n3P,n3D,… ) Tensor Insignificant (requires non-zero L which does not probe small r)

Spin-spin Significant only for states probing Coulomb part, i.e. short distances (L=0 i.e. nS) Hyperfine structure Fine structure

1/r r Spin-orbit Tensor S = 1 usual phenomenology J = L + 1 consistent with data S = 0 Spin-spin n, L and with LQCD J = L uur uur c.o.g Spin-dependent mass splitting reflect magnetic S1⋅ S 2 J = L interactions – they are relativistic effects.

Atoms are highly non-relativistic; tiny effects in QED. mass splittings Can be very large for light-quark mesons. J = L - 1 ur ur uur uuru ur uur 2 $ $ Decrease in importance with quark mass ~1/m Q L ⋅ S S1⋅r S 2⋅ r − SS 12⋅ Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 27 Hyperfine and fine structure in meson spectra 2S+1 n’ lj Hyperfine large only for nS states No splitting MeV °’’’ of S=0 and S=1 states Decreases with n (quarks less likely to for L > 0 BB probe r=0) χb’’

10300 °’’ °2 MeV MeV 3 ’ 3 1 D hb χb’ 2 S1 3800 3 1 ψ’’ 3 2 S1 10300 1 P K* 2(1430) 21S K*(1410) 1,2 21S 3 0 K* 0(1430) DD 0 1 P0,1,2 1 K (1400) 1 χc2 °’ Fine splitting: K(1460) 1 P1 1 hc’ ψ’ 1 P1 hb’ ur ur 1300 L⋅ S , 13P χ h ur uur ur uur 0 hc c1 b cb $ $ K1(1270) 3srs⋅ ⋅−⋅ r ss χc0 1 2 12 Relativistic nature of 3 3 9500 1 S1 1 S1 hyperfine and fine K*(892) Hyperfine 1 ° 3000 1 S0 J/y hb splittings is apparent splitting: 2 Kπ uur uur hc ~1/m S⋅ S Q 1 2 _ _ 1 _ c b 500 1 S0 q K s c b Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 28

Heavy-Light Mesons (): D, D s, B, Bs • Naively expect light-quark spin effects to dominate over heavy-quark spin effects

In the limit of →0 – Hydrogen-like fine, and hyper-fine structures – Heavy Quark Symmetry: no difference between D and B systems (like symmetry between single-electron atoms!) = + – Transitions do not change heavy quark spin = + • In practice, ~0.2( ~0.07), not as small as in hydrogen, = 0.0015 : – Hyperfine splitting of s-states is still sizable – Heavy-Quark Effective Theory (HQET): use = 0 as the lowest order, then implement corrections Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 29 Status of D meson spectroscopy S. Godfrey, K. Moats PR D93, 034035 (2016) Hadron Spectrum Collaboration (LQCD mπ=240 MeV) Relativized potential Quark Model (revamp of Godfrey-Isgur 1985). JHEP 1612, 089 (2016) (update of the 2012 results) (Includes predictions for decay widths). _ (No 4-quark operators included.) c q c

hybrids _ q

* D2 (3000) * D2 (3000)

* 0 * D3 (2760) DJ (2600) ? D * 0 3 (2760) * 0 * 0 D1 (2680) D1 (2680) D *(2600) ? D *(2460) J * 2 D2 (2460) D (2430) D (2420) D1(2430) D1(2420) 1 1 * * D0 (2400) D0 (2400)

D* D* π Dπ D* D D

• 1S,1P and half of 1D states have been detected • Detecting higher excitations is hard (broad, small production rates, • Like for other spectroscopies of short-lived states, many decay channels open) theoretical predictions, either phenomenological models • Not clear how many of heavier predicted states will ever by or lattice QCD (no couplings to decay channels are detected simulated above), are qualitative in nature Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 30

Status of Ds meson spectroscopy

S. Godfrey, K. Moats PR D93, 034035 (2016) _ Hadron Spectrum Collaboration (LQCD m =240 MeV) c π s JHEP 1612, 089 (2016)

hybrids

* D * * * Ds1 (2700) s3 (2860) Ds1 (2860) Ds3 (2860) D *(2860) s1 * Ds1 (2700) * * Ds2 (2573) Ds2 (2573) D*K Ds1(2536) Ds1(2536) Ds1(2460) D*K Ds1(2460)

* DK * Ds0 (2317) Ds0 (2317)

Ds* The effect of D*K, DK thresholds? Molecular components Ds* Ds in D (2460), D *(2317)? s1 s0 Ds

• No experimental progress in the last 2 years • Status similar to that of D mesons * • Masses of Ds0 (2317) and one of Ds1(2460) states are _ _ • Spectroscopy of B mesons even less shifted relative the expectations to below the DK,D*K c q q s ? (s) thresholds. Molecular components? experimentally developed Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 31 Baryons directly from 3 quarks color singlet color color color 1 triplet triplet triplet 3

= 1 3 ⊗ 3 ⊗ 3 1 ⊕ ... 1 3 3 q q q

Color flux tube in QCD gluons can attractive color force stretched between three quarks couple to each other (qqq) baryon

s u d Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 32 Generic model of baryon excitations

= ′ + = + • In principle two radial quantum numbers n,n’ l,l’ = + and two orbital angular momenta – huge number of excitations ′ = + • Additional symmetrization requirements ′ from SU(3) flavor if quarks are light • Three quark spins to couple to two angular momenta – very complicated (hyper)fine structure

Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 33 Example: ΛΛΛ excitations

s d u Short-lived states (broad). ΛΛΛ* mass predictions by Loring- Metsch-Petry EPJ, A10, 447 (2001) Mostly qualitative spectroscopy. vs KN Well-established ΛΛΛ*s • Mass of ΛΛΛ(1405) significantly shifted relative ΛΛΛ(1405) the expectations to below the KN threshold. πΣ Molecular components? p Λ u d _ s u u K Phenomenological models often restrict some degrees of freedom which has some motivation in QCD. Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 34 (Colored) diquarks in QCD color (antisymmetric) sextet color (symmetric) antitriplet 1 2 color color 1 1 1 triplet 2 triplet 2 2 1 1 − _ − 2 2 1 1 1 3 2 2 ⊗ = 2 1 6 1 3 3 1 ⊕ 2 − 2 2

quark quark 1 q q 1 1 repulsive color force quarks will pull apart in any attractive_ color force sextet configuration (half as strong as in the meson) Color flux tube (qq) diquark stretched between the quarks and Not a particle, just a extending to other s u building block in color partners QCD Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 35 Baryons from quarks and diquarks color singlet color color antitriplet 1 triplet 6 1 1 1 2 2 − 6 Relative importance of 1 1 − _ − this internal baryon 2 2 ⊗ 1 3 = 1 1 1 structure vs more 3 2 6 6 ⊕ ... democratic quark 1 1 1 − − − configuration is a 2 6 6 question mark

Color flux tube attractive color force stretched between the diquark and the quark (q(qq)) baryon third quark attractive color force q (qq) diquark s u e.g. ΛΛΛ d Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 36 Heavy-light-light baryons • Qqq baryons are a perfect place to study light diquark = + structures as the heavy quark spin decouples from light = + quark spins = + • QCD motivated diquarks need to be in the ground state, n =1 , L =0 ,which eliminates a large number of qq qq possible excitations: – States can be labeled with n, L of the diquark orbiting around the heavy quark, which will be a dominant effect in mass – The main mass level hierarchy like among mesons! • Diaquark spin Sqq can be 0 or 1 (scalar and axial vector In usual diaquark model: =0,1 Scalar and axial-vector diquarks): =1 =0 diquarks – Since quarks are light (relativistic), and the diquark is in Lqq =0 state, their hyperfine mass splitting can be large.

• Also important is fine structure from couplings

• Small hyperfine structure from Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 37 000 Heavy-light baryons: excitations of ΩΩΩc LHCb-PAPER-2017-002, CERN-EP-2017-037, arXiv:1703.04639. 1 + 0 3 + 0 • Only two ground states (1S) have been known before: /2 Ωc , /2 Ωc(2770) ∗∗ 0 + − Ωc → Ξc K (Strong decay) (Cabibbo suppressed c→d weak decay) Significance of Ωc(3050) Ωc(3066) each of the narrow resonances + − + > 10 σ Ξc → pK π 3.3 fb -1 Ωc(3000) (csu ). Ωc(3090)

Ωc(3119) (3188) ?? Ωc s s Ξ + c c signal Γ=60±19 MeV ~1M <2.6 MeV <2.6 =8.7±1.3 MeV =8.7±1.3 =3.5±0.4 MeV =3.5±0.4 events Γ <1.2 MeV <1.2 Γ Γ Γ =4.5±0.7 MeV =4.5±0.7 Γ bkg. ~17% Γ=3.5±0.4 MeV + Ξc sidebands

5 narrow, new states in single mass spectrum! Excellent place to test baryon models (long-lived states). Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 38

Interpretation of ΩΩΩc excitations observed by LHCb

Z. Shah et al., Ch.Phys. Ebert,Faustov,Galkin, Ebert,Faustov,Galkin, Roberts,Pervin, Exact predictions for (hyper)fine C40,123102(2016) PRD84,014025(2011). PLB659, 612 (2008). Int.J.Mod.Phys. A23, arXiv:1609.08 2817 (2008). splittings are model dependent. 2P s s • The states newly c observed by LHCb are 1D likely 1P and 2S Ωc(3188) ?? Ξ Ω (3119) • None of the models 2S c Ωc(3090) predicted the mass Ωc(3066) Ω (3050) splitting exactly 1P c Ωc(3000) • Determining their JPs is Ξ important for constraining the models (will be done).

Ωc(2770) 1S Ωc

1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 39 ∗∗ 000 Why the observed ΩΩΩc states are narrow? • They are below the • They decay to Ξ ,which requires threshold for the preferred ripping apart the diquark – less likely fall-apart mode Ξ process, longer lifetime, smaller width.

s s s s s s s _ u q Ξ c c _ _ u s Ω ∗∗ 0 q ∗∗ 0 c Ωc c c Ξ Except for the possible 6 th one, Their narrowness is the nice evidence for (3188) Ωc , which is broad! QCD-motivated diquarks! Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 40 + ΛΛΛc excitations * Λc s • Recent LHCb amplitude 0 0 − analysis of Λb → D pπ

LHCb-PAPER-2016-61 arXiv:1701.07873

Ν*s

+ Λc(2860) + Λc(2940) First observations u d c

Known before, JP determined for the first time Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 41

Interpretation of ΛΛΛc and of ΞΞΞc excitations Z. Shah et al., Ch.Phys. Ebert,Faustov,Galkin, Z. Shah et al., Ch.Phys. Ebert,Faustov,Galkin, C40,123102(2016) PLB659, 612 (2008). C40,123102(2016) PLB659, 612 (2008). arXiv:1609.08 Ebert,Faustov,Galkin, Roberts,Pervin, arXiv:1609.08 Ebert,Faustov,Galkin, Roberts,Pervin, PRD84,014025(2011). Int.J.Mod.Phys. A23, 2817 (2008). PRD84,014025(2011). Int.J.Mod.Phys. A23, 2817 (2008).

2P pD* 2P Λc(2940) Ξc(3080) 1D Λc(2880) 1D Ξc(3055) Λc(2860) 2S 2S Ξc(2970) Λ (2625) 1P (2815) 1P c Ξc Λc(2595) Ξc(2790)

u d Ξc’ s q Ξc(2645) c 1S c 1S Λc Ξc

1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ? u d Molecular pD* component in Λc(2940) ? _ Ortega,Entem,Fernandez, PL B718, 1381 (2013) 1381. c d J. Zhang, PRD89, 096006 (2014). d Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 42 LHCb JHEP 1605, 161 (2016) Beauty baryons 0 − − + *0 − Ξc → pK K π • Recent measurement: precision determination of Ξb - Ξb *0 (Cabibbo favored mass difference by LHCb ( Ξb first observed by CMS in c→s weak decay) 2012):

Ebert,Faustov,Galkin, PLB659, 612 (2008). − 0 − Ebert,Faustov,Galkin, Roberts,Pervin, Ξb → Ξc π PRD84,014025(2011). Int.J.Mod.Phys. A23, 2817 (2008). (CKM favored b→c weak decay) 2P s q 1D 2S b Ξ *0 → Ξ − π+ b b 1P (Strong decay)

Ξb* • Much fewer excitations Ξb’ known than for charm 1S Ξb • Similar situation for

Λb,Σb 1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 1 1 3 3 5 5 7 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 43 Heavy-baryons and lattice QCD From Stefan Meinel @ Baryons 2016 • Masses of ground states simulated on lattice agree well with the experimental results PRD90,094507 (2014) • Preliminary simulations of excited states have been shown at conferences, but not published Result which is only 1 week old!

− + + Ξ →. Λ K π π

First convincing observation of doubly-heavy baryon! Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 44 Heavy-heavy-light baryons

= + • Light and heavy quark spins decoupled • Place to study heavy diquarks.

– will have its own quarkonium-like excitation spectrum ( nQQ, LQQ ,S QQ ), with radial excitation energies diminished by half. = + = + • Light quark will behave like in heavy-light meson, with replaced by = + – It will have its own n , L ,S structure q q q • Finally, heavy and light total spins will couple Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 45 Example of model predictions for Ξ spectroscopy

(warning: principal used here) = =1

Δ=1

Δ=1 should be Δ =1 relatively narrow Δ =1

diquark excitations cut in half couplings

• No excitations have been detected yet to verify this picture. Many should be detectable in LHCb. Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 46 Conclusions • Conventional hadron spectroscopy can be understood via analogies to atomic spectroscopy. • Hierarchy and magnitude of spin dependent splittings can be very different. • Studies of hadrons with heavy quarks offer hadron families where quantitative spectroscopy is easier: – Heavy quark masses are so well separated from other quark masses, that no mixing of states with different quark content – Many long-lived excitations thanks to “deeper binding” – Less-relativistic systems, intuitive potential model approaches work well • Baryons with different number of heavy quarks offer an insight into diquark substructures suggested by QCD: – So far the data are consistent with diquark picture. More stringent tests with more excitations, hopefully to be detected soon. Hadron Spectroscopy I, NNPSS, Boulder CO 2017, Tomasz Skwarnicki 47

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