spectroscopy overview Jozef Dudek Old Dominion University & Jefferson Lab thanks for inviting a whinging pom

spectroscopy overview Jozef Dudek Old Dominion University & Jefferson Lab thanks for inviting a whinging pom

spectroscopy? will touch only lightly on precision spectroscopy - masses of (QCD)-stable hadrons with control over systematic errors obvious importance of this work - doesn t need restating will rather focus on areas in which lattice QCD calculations are running alongside (or ahead of) experiments & models looking at the excited hadron spectrum necessitates some (temporary) relaxation in rigour (most interesting states are inelastic resonances) at this stage looking for qualitative patterns in the QCD spectrum (do what we can with the technology we have) (be careful to assess the validity of the results) maturing of finite-volume method for scattering will eventually lead to more rigourous studies (Dan Mohler up next with a survey) 2

the light meson spectrum - experiments GlueX CLAS2 π γ π,η,k... p N π,η,k... p p π,η,k. p N p p BES III ψ,χc π,η,k... γ ψ,χc π,η,k... 3

the light meson spectrum relatively simple models of hadrons: bound states of constituent quarks and antiquarks the quark model empirical meson flavour systematics I=, S= : η,φ,ω,fj... 2. empirical J PC distribution L=3 I=, S= : π,ρ,b,aj... I=½,S=± : K,K*....5 L=2 I, S. L= L=.5 PDG summary (take with a pinch of salt) 4

the light meson spectrum an example of states beyond minimal quark model configurations smoking gun signature - J PC outside the set accessible to hybrid mesons states in which a gluonic excitation is present and many others since many models, many different spectrum predictions... 5

lots of operators + variational analysis... proves rather powerful method to extract a spectrum of excited states e.g. a basis of fermion bilinears with up to three covariant derivatives one possible smearing methodology - distillation distillation smeared quarks - allows for relevantly efficient construction of a large operator basis expensive, but becomes good value for: large operator basis disconnected diagrams computing two-particle correlators with definite inter-particle momentum 6

lots of ops + variational analysis... operators constructed to be irreducible (definite spin) in the continuum theory e.g. subduced into irreducible representations of the cubic group e.g. 7

lots of ops + variational analysis... up to three-derivatives gives 26 operators in 9 subduced from J= 6 subduced from J=3 subduced from J=4 compute the full 26 26 correlation matrix solve the generalised eigenvalue problem anisotropic 2+ Clover (24 3 28) mπ~4 MeV 8

principal correlators - T.2.5..5.95 state.6 state.6 state 2.4.4.2.2.8.8 5 5 2 25 3 5 5 2 5 5 2.6 state 3.6 state 4.6 state 5.4.2.8.4.2.8.4.2.8 5 5 2 5 5 2 5 5 2.6 state 6.6 state 7.6 state 8.4.2.8.4.2.8.4.2.8 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 9

principal correlators - T.2.5..5.95 state.6 state.6 state 2.4.2.8 5 5 2 25 3 5 5 2.5.4.4.2.8 5 5 2.6 state 3.6 state 4.6 state 5.4.2.8.4.2.8.3.4.2.8 5 5 2 5 5 2.2 5 5 2.6 state 6.6 state 7.6 state 8.4.2.8.4.2.8..4.2.8 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8. 2 4 6 8 2 4 6

overlap matrix elements - T subduced from J= subduced from J=3 subduced from J=4 state state state 2 state 3 state 4 state 5 state 6 state 7 state 8 J= J= J= J=3 J= J= J= J=3 J=4

overlap matrix elements - T.5 subduced from J= subduced from J=3 subduced from J=4.4.3.2. some explanation of this observation for smeared operators in Restoration of Rotational Symmetry in the Continuum Limit of Lattice Field Theories Zohreh Davoudi and Martin J. Savage state state state 2 state 3 state 4 state 5 state 6 state 7 state 8 J= J=. J= J=3 arxiv:24.446v2 J= J= [hep-lat] J= J=3 J=4 2

spin identification.5.4.3.2.. 3

spin identification.5 3 operators subduced into three irreps.4 4..3.2 3. state state state 3.. Z 2.. op op op 2 op 3 op 4 op 5 ( 3) ( ) 4

a meson spectrum 25 4 4 3 2 E / MeV 4 3 3 2 2 2 5 2 5 scale setting 25 4 4 3 E / MeV 2 3 2 5 anisotropic clover (2+) 5 3 2 2 4 2 Engel, Lang, Limmer, Mohler, Schafer Phys.Rev. D85 (22) 3458 (Chirally Improved fermions, mπ~33 MeV a~.4 fm, mπl~3.7 smaller volumes in Phys.Rev.D82 3458 (2) 5

a meson spectrum 25 2 25 4 4 3 4 3 2 E / MeV 5 2 3 2 2 5 2 5 5..2.3.4.5 6 3 2 3 so it is technically feasible to extract 24 a 3 highly excited state spectrum...... can we build any experimentally relevant phenomenology from the results? 6

a meson spectrum degeneracy pattern? L=4 25 2 4 4 3 4 3 2 L=3 E / MeV 5 L= 2 3 2 L=2 2 L= 5 7

a meson spectrum what are these extra states? 25 2 4 4 3 4 3 2 E / MeV 5 2 3 2 2 5 8

some (model-dependent) interpretation consider 3 of the 9 J PC = operators > upper component projector non-relativistic two-derivative constructions : > ignoring the gauge-field gauge-invariant version of a D-wave? > ignoring the gauge-field Phys.Rev. D84 7423 (2) 9

some (model-dependent) interpretation 25 2 E / MeV 5 5 2

a meson spectrum extra states are hybrid mesons? 25 2 4 4 3 4 3 2 E / MeV 5 2 3 2 2 5 wouldn t this non-relativistic logic be better justified in charmonium...? 2

charmonium - a similar story (connected contributions) 5 4 4 + 3 ++ 4++ 3+ + + 2 + 2 3 2 + 5 + ++ ++ 2 ++ anisotropic clover (2+) + Liuming Liu & Christopher Thomas, Dublin HUGS 22 arxiv:24.5425 [hep-ph] JHEP in review 22

charmonium 5 4 4 + 3 ++ 4++ 3+ + + 2 + 2 3 2 + 5 + ++ ++ 2 ++ + Bali, Collins & Ehmann Phys.Rev. D84 (2) 9456 HUGS 22 23

charmonium degeneracy & overlap pattern 5 L=4 4 4 + L=3 3 ++ 4++ 3+ + + 2 + 2 3 2 + L=2 5 + ++ ++ 2 ++ L= + L= HUGS 22 24

a QCD phenomenology of hybrid mesons replace model guesswork with something motivated by these lattice calcs... a chromomagnetic field configuration is lowest excitation 5 charmonium + 3+ 2++ ++ 2 + + ++ + + 2 + 25

a QCD phenomenology of hybrid mesons replace the model guesswork with something motivated by these lattice calcs... a chromomagnetic field configuration is the lowest excitation 6 Z 4 2 5 charmonium -- -+ -+ 2 -+ HT 2 L 2 -+ HEL 3+ 2++ ++ 2 + + ++ + + 2 + + 26

a QCD phenomenology of hybrid mesons some candidate states in the experimental spectrum empirical J PC distribution 2. L=3.5 L=2. L= L=.5 in charmonium the Y (426) mass scale looks OK [m(ηc) + 3 MeV] but produced in e + e - - must have 3 S component (need to compute the vector decay constant) 27

isoscalars - η & η mostly a~.2 fm 4 2 8 6 4 2 UKQCD arxiv:2.4384 [hep-lat] noisy sources RBC/UKQCD Phys.Rev.Lett. 5 (2) 246 wall sources Hadron Spectrum Collab. Phys.Rev. D83 (2) 52 [mπl~3.8] unpublished, preliminary [mπl~5.8] distillation..2.3.4.5 28

isoscalars - η & η mostly a~.2 fm 4 2 late-breaking news from ETMC... a~.6,.8,.9 fm 2.6 mπl 5.3 noisy sources.5 8 6 Mη, η [GeV] 4 2.5. experimental values ETMC HSC RBC/UKQCD UKQCD.2.3.4.5 M 2 PS [GeV2 ]..2.3.4.5 29

isoscalars - excited state spectrum Hadron Spectrum Collab. Phys.Rev. D83 (2) 52 negative parity positive parity exotics 2.5 2..5. isoscalar.5 isovector YM glueball small volume (6 3 28) (analysing 24 3 28 now) distillation inversion cost is spread over as large an operator basis as you like glueball operators too noisy? 3

impact on experiment negative parity positive parity exotics 2.5 2..5. isoscalar.5 isovector YM glueball 3

a light baryon spectrum three-quark field operator basis with up to two derivatives 3. 2.5 2..5..5 Phys.Rev. D84 7458 (2) Phys.Rev. D85 546 (22) 32

a light baryon spectrum 3. 2.5 hybrid baryons 2..5..5 33

a light baryon spectrum 3. 2.5 2. 3..5 2.5 2...5.5..5 Engel et al (Graz) 34

hybrids (mesons and baryons) approximately remove the quark mass contribution to the hybrid mass 2 2 5 5 5 5 light hybrid mesons - mρ light hybrid baryon - mn charmonium hybrids - mηc chromomagnetic gluonic excitation scale ~.3-.4 GeV? a model dependent interpretation of lattice QCD calculations 35

including multi-meson operators next step is to include operators that resemble multi-mesons into the basis projected into definite little-group irreps (arxiv:23.64 [hep-ph]) basis of various (relatively straightforward with distillation) solve variational problem in this extended basis... 36

including multi-meson operators e.g. on 24 3.4 local ops local ops & π π- & π π-- local J=3 operator overlaps.3.2. ππ operator overlaps local J= operator overlaps. non-interacting ππ energies promising - clean signals for excited meson-meson state contributions in the spectrum 37

including multi-meson operators e.g. P=[] on 24 3 ( in-flight helicity zero ).4 local ops local ops & ππ.3.2. in the elastic scattering region can use Lüscher formalism see the next talk.... 38

summary a large basis of local operators + variational analysis surprisingly good returns on investment clean excited state spectra possible interpretation of gross structures including hybrids first directly QCD-based phenomenology of hybrids news for COMPASS, JLab, BES... these calculations not complete finite-volume spectrum contains states not well interpolated by these ops including meson-meson ops reveals their presence signals can be statistically very clean 39