Slides - Compass - Cern

Hadron Spectroscopy at COMPASSand Related Experiments

Boris Grubefor the COMPASS Collaboration

Physik-Department E18Technische Universität München,

Garching, Germany

International Workshop on Hadron Structure and SpectroscopyErlangen, 23. July 2013

COMPASS

Outline

1 IntroductionQCD and constituent quark modelBeyond the constituent quark model

2 Hadron spectroscopySearch for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction

3 Conclusions and Outlook

2 Boris Grube, TU München Hadron Spectroscopy at and related experiments

COMPASS

IntroductionHadron spectroscopy

Conclusions and Outlook

QCD and constituent quark modelBeyond the constituent quark model

Outline

COMPASS

QCD: The Theory of Strong InteractionQuantum chromodynamics describes interaction of quark and gluon fields

Non-abelian gauge theory: gluons carry charge and self-interactRunning coupling constant αs(Q)

Asymptotic freedom

αs small at short distances (high-energies)Quarks and gluons relevant degrees of freedomLagrangian calculable by series expansion in αs

Confinement of quarks and gluons into hadrons

αs large at distances O(1 fm)

Relevant d.o.f.: color-neutral hadronsSeries in αs does not converge=⇒ non-perturbative regime

Origin of confinement and connection to chiralsymmetry breaking still not understoodExplanation for 98 % of mass of visible matter in theuniverseStudy of hadron spectra provides more insight

PDG 2012

COMPASS

Asymptotic freedom

PDG 2012

COMPASS

Asymptotic freedom

PDG 2012

COMPASS

Mesons in the Constituent Quark Model

Constituent Quark Model (CQM)

Goes back over 40 years to Gell-Mann and Zweig“Constituent” quarks: quasi-particles with additional effectivemass due to interaction with gluon field

E.g. for light-quark mesons mu = md = 310 MeV/c2,ms = 485 MeV/c2 Gasiorowicz et al., AJP 49 (1981) 954

Caveat: no connection to QCD

Mesons in CQM

Color-singlet |qq′〉 states, grouped into SU(N)flavor multiplets

Meson masses are sum of constituent quark masses

Together with hyperfine (spin-spin) interaction, meson spectrumis roughly described

COMPASS

Constituent Quark Model (CQM)

Goes back over 40 years to Gell-Mann and Zweig“Constituent” quarks: quasi-particles with additional effectivemass due to interaction with gluon field

E.g. for light-quark mesons mu = md = 310 MeV/c2,ms = 485 MeV/c2 Gasiorowicz et al., AJP 49 (1981) 954

Caveat: no connection to QCD

Mesons in CQM

Color-singlet |qq′〉 states, grouped into SU(N)flavor multiplets

Meson masses are sum of constituent quark masses

Together with hyperfine (spin-spin) interaction, meson spectrumis roughly described

COMPASS

Spin-parity rules for bound qq system

Quark spins couple to total intrinsic spinS = 0 (singlet) or 1 (triplet)

Relative orbital angular Momentum~Land total spin ~S couple tomeson spin~J = ~L + ~S

Parity P = (−1)L+1

Charge conjugation C = (−1)L+S

Forbidden JPC: 0−−, 0+−, 1−+, 2+−, 3−+, . . .Extension to charged mesons via G parity: G = C (−1)I

I isospin of mesonConvention: assign JPC quantum numbers of neutral partner inisospin multiplet

COMPASS

Light-quark meson spectrum

a2(1320)

K2*(1430)

f2(1270)

f2'(1525)

a1(1260)

K1af1(1285)

f1(1420)

a0(1450)

K0*(1430)

f0(1370)

f0(1710)

b1(1235)

K1bh1(1170)

h1(1380)

p(1300)K(1460)h(1295)h(1440)

r(1450)

K*(1410)w(1420)f(1680)

r(770)

K*(892)w(782)f(1020)

n=n+L-1

3S1=1--1S0=0

3P2=2++

1P1=1++

1P1=1+-3P0=0

3S =1--1S0=0-+

Amsler et al., Phys. Rept. 389 (2004) 61

COMPASS

Light-quark meson spectrum (cont.)

a2(1320)

K2*(1430)

f2(1270)

f2'(1525)

a1(1260)

K1af1(1285)

f1(1420)

a0(1450)

K0*(1430)

f0(1370)

f0(1710)

b1(1235)

K1bh1(1170)

h1(1380)

a2(1700)

K2*(1980)

f2(2010)

f2(1950)

a1(1640)

p(1300)K(1460)h(1295)h(1440)

r(1450)

K*(1410)w(1420)f(1680)

p(1800)

r(770)

K*(892)w(782)f(1020)

r3(1690)

K*3(1780)

w3(1670)f3(1850)

K2(1820)

p2(1670)

K2(1770)

h2(1645)h2(1870)

r(1700)

K*(1680)w(1650)

n=n+L-1

3S1=1--1S0=0

3P2=2++

1P1=1++

1P1=1+-3P0=0

1D2=2-+ 3D1=1

3D2=2--3D3=3

K(1830)

h(1760)

13 1 1

1 13P2=2++

2P1=1++

3S =1--1S0=0-+

“Light meson frontier”:

Many missing and disputedstates in mass regionm ≈ 2 GeV/c2

Identification of higherexcitations becomesexceedingly difficult

Wider states + higher statedensityMore overlap and mixing

COMPASS

Light-quark meson spectrum (cont.)

a2(1320)

K2*(1430)

f2(1270)

f2'(1525)

a1(1260)

K1af1(1285)

f1(1420)

a0(1450)

K0*(1430)

f0(1370)

f0(1710)

b1(1235)

K1bh1(1170)

h1(1380)

a2(1700)

K2*(1980)

f2(2010)

f2(1950)

a1(1640)

p(1300)K(1460)h(1295)h(1440)

r(1450)

K*(1410)w(1420)f(1680)

p(1800)

r(770)

K*(892)w(782)f(1020)

r3(1690)

K*3(1780)

w3(1670)f3(1850)

K2(1820)

p2(1670)

K2(1770)

h2(1645)h2(1870)

r(1700)

K*(1680)w(1650)

n=n+L-1

3S1=1--1S0=0

3P2=2++

1P1=1++

1P1=1+-3P0=0

1D2=2-+ 3D1=1

3D2=2--3D3=3

K(1830)

h(1760)

13 1 1

1 13P2=2++

2P1=1++

3S =1--1S0=0-+

“Light meson frontier”:

Many missing and disputedstates in mass regionm ≈ 2 GeV/c2

Identification of higherexcitations becomesexceedingly difficult

Wider states + higher statedensityMore overlap and mixing

COMPASS

Beyond the Constituent Quark Model

QCD: Gluonic d.o.f. should manifest themselves in hadron spectra

Hybrids |qqg〉Resonances with excited glue

Definition of “excited glue” model dependent

Angular momentum of glue component =⇒ all JPC possibleLightest predicted hybrid: spin-exotic JPC = 1−+

Mass 1.3 to 2.2 GeV/c2

Experimental candidates π1(1400, 1600, 2000) controversial

Glueballs |gg〉Bound states consisting purely of gluonsLightest predicted glueball: ordinary JPC = 0++

Will strongly mix with nearby conventional JPC = 0++ statesMass 1.5 to 2.0 GeV/c2

Experimental candidate f0(1500); glueball interpretation disputed

COMPASS

QCD in the confinement regime: αs = O(1)QCD Lagrangian not calculable using perturbation theory

General ab-initio method: Lattice Gauge Theory

Simulation of QCD Lagrangian on finite discreet space-time latticeusing Monte Carlo techniques (computationally very expensive)Challenge: extrapolation to physical point

Heavier u and d quarks than in reality=⇒ extrapolation to physical quark masses

Extrapolation to infinite volumeExtrapolation to zero lattice spacing

Rotational symmetry broken due to cubic lattice

Tremendous progress in past yearsFiner lattices =⇒ spin-identified spectraLarger operator bases =⇒ extraction of many excited statesAccess to gluonic content of calculated states

COMPASS

Light-Meson Spectrum in Lattice QCDState-of-the-art light-meson spectrum Dudek, PR D84 (2011) 074023

Resonance widths and decay modes still very difficult11 Boris Grube, TU München Hadron Spectroscopy at and related experiments

COMPASS

Finding states beyond the CQM is difficult

Physical mesons = linear superpositions of allallowed basis states: |qq〉, |qqg〉, |gg〉, |q2q2〉, . . .

Amplitudes determined by QCD interactions

Resonance classification in quarkonia, hybrids,glueballs, tetraquarks, etc. assumes dominanceof one basis state

In general “configuration mixing”Disentanglement of contributions difficult

Special case: “exotic” mesons

Have quantum numbers forbidden for |qq〉Discovery =⇒ unambiguous proof for meson states beyond CQM

Especially attractive:“spin-exotic” states with JPC = 0−−, 0+−, 1−+, 2+−, 3−+, . . .

COMPASS

Search for spin-exotic mesons in pion diffractionScalar mesons in central productionBaryon spectroscopy in proton diffraction

Outline

COMPASS

Production of Hadrons in Diffractive DissociationBNL E852, VES, COMPASS

π´beam

Target Recoil

X´π´beam

Target Recoil

π´beam

Target Recoil

π´beam

Target Recoil

π´π+

Soft scattering of beam hadron off nuclear target (remains intact)Beam particle is excited into intermediate state XX decays into n-body final state

High√

s, low t′: Pomeron exchange dominantRich spectrum: large number of overlapping and interfering XGoal: use kinematic distribution of final-state particles to

Disentangle all resonances XDetermine their mass, width, and quantum numbers

Method: partial-wave analysis (PWA)

COMPASS

π´beam

Target Recoil

X´π´beam

Target Recoil

π´beam

Target Recoil

π´beam

Target Recoil

π´π+

High√

COMPASS

π´beam

Target Recoil

X´π´beam

Target Recoil

π´beam

Target Recoil

π´beam

Target Recoil

π´π+

High√

COMPASS

Diffractive Dissociation of π− into π−π+π− Final StateBNL E852, VES, COMPASS

π´beam

Target Recoil

X´[JPCMǫ]

Isobar

π´beam

Target Recoil

π´beam

Target Recoil

π´beam

Target

Recoil

Bachelorπ´

π´beam

Target

Recoil

Bachelorπ´

Isobar model: X− decay is chain of successive two-body decays

“Wave”: unique combination of isobar and quantum numbersFull wave specification (in reflectivity basis): JPC Mε[isobar]L

Fit model: σ(mX , τ) = σ0

∣∣∣∑waves Twave(mX) Awave(mX , τ)∣∣∣2

Calculable decay amplitudes Awave(mX , τ)

Transition amplitudes Twave(mX) determined frommulti-dimensional fit to final-state kinematic distributions taking intoaccount interference effects

COMPASS

Diffractive Dissociation of π− into π−π+π− Final StateBNL E852, VES, COMPASS

π´beam

Target Recoil

X´[JPCMǫ]

Isobar

π´beam

Target Recoil

π´beam

Target Recoil

π´beam

Target

Recoil

Bachelorπ´

π´beam

Target

Recoil

Bachelorπ´

Isobar model: X− decay is chain of successive two-body decays

“Wave”: unique combination of isobar and quantum numbersFull wave specification (in reflectivity basis): JPC Mε[isobar]L

Fit model: σ(mX , τ) = σ0

∣∣∣∑waves Twave(mX) Awave(mX , τ)∣∣∣2

Calculable decay amplitudes Awave(mX , τ)

Transition amplitudes Twave(mX) determined frommulti-dimensional fit to final-state kinematic distributions taking intoaccount interference effects

COMPASS

PWA of π− p→ π−π+π− pslowCOMPASS

π´beam

ptarget pslow

X´[JPCMǫ]

Isobar

π´beam

ptarget pslow

π´beam

ptarget pslow

π´beam

ptarget

Bachelorπ´

π´beam

ptarget

Bachelorπ´

190 GeV/c negative hadron beam: 97 % π−, 2 % K−, 1 % p

Liquid hydrogen target

Recoil proton pslow measured by RPD

Kinematic range 0.1 < t′ < 1.0 (GeV/c)2

COMPASS

PWA of π− p→ π−π+π− pslow

World’s largest diffractive 3π data set: ≈50 M exclusive events

Challenging analysisNeeds precise understanding of apparatusModel deficiencies become visible

π−π+π− invariant mass distribution Dalitz plot for π2(1670) region

COMPASS

π−π+π− invariant mass distribution

Dalitz plot for π2(1670) region

COMPASS

π−π+π− invariant mass distribution Dalitz plot for π2(1670) region

COMPASS

π−π+π− invariant mass spectrum

1++ 0+ [ρπ]S: a1(1260)

2−+ 0+ [ f2π]S: π2(1670) 2++ 1+ [ρπ]D: a2(1320)

COMPASS

π−π+π− invariant mass spectrum 1++ 0+ [ρπ]S: a1(1260)

2−+ 0+ [ f2π]S: π2(1670) 2++ 1+ [ρπ]D: a2(1320)

COMPASS

2−+ 0+ [ f2π]S: π2(1670)

2++ 1+ [ρπ]D: a2(1320)

COMPASS

2−+ 0+ [ f2π]S: π2(1670) 2++ 1+ [ρπ]D: a2(1320)

COMPASS

2−+ 0+ [ f2π]S: π2(1670) 2++ 1+ [ρπ]D: a2(1320)

COMPASS

Data described by model consisting of 52 waves+ incoherent isotropic backgroundIsobars:

(ππ)S−wavef0(980)ρ(770)f2(1270)f0(1500)ρ3(1690)

Spin-exotic 1−+ 1+ [ρπ]P

1−+ 1+ [ρπ]P− 1++ 0+ [ρπ]S

1++ 0+ [ρπ]S: a1(1260)

Structure around 1.1 GeV/c2

unstable w.r.t. fit modelEnhancement around1.6 GeV/c2

Phase motion w.r.t. to tail ofa1(1260)Phase locked w.r.t. π2(1670)Ongoing analysis

COMPASS

Spin-exotic 1−+ 1+ [ρπ]P 1−+ 1+ [ρπ]P− 1++ 0+ [ρπ]S

1++ 0+ [ρπ]S: a1(1260) Structure around 1.1 GeV/c2

COMPASS

Spin-exotic 1−+ 1+ [ρπ]P 1−+ 1+ [ρπ]P− 2−+ 0+ [ f2π]S

2−+ 0+ [ f2π]S: π2(1670) Structure around 1.1 GeV/c2

COMPASS

Spin-Exotic 1−+ 1+ [ρπ]P WaveComparison with BNL E852 and VES

COMPASS

190 GeV/c π beamp target50 · 106 events0.1 < t′ < 1.0 (GeV/c)2

Rank-2 fit with 53 waves

BNL E852 PR D73 (2006) 072001

18 GeV/c π beam2.6 · 106 events0.1 < t′ < 0.5 (GeV/c)2

Rank-1 fit with 21/36 waves

COMPASS

BNL E852 PR D73 (2006) 072001

COMPASS

BNL E852 PR D73 (2006) 072001

COMPASS

VES NP A675 (2000) 155

36.6 GeV/c π beamBe target9 · 106 events“Infinite”-rank fit with 44waves

COMPASS

PWA of π− Pb → π−π+π− Pb at low t′COMPASS

π´beam

X´π´beam

π´beam

π´π+

π−π+π− production in Primakoff reaction

Very small momentum transfer: t′ < 0.001 (GeV/c)2

Photoproduction in Coulomb field of heavy target nucleus (Pb)For M = 1 waves diffractive contribution kinematicallysuppressedNo intensity in 1.6 GeV/c2 region in spin-exotic 1−+ wave

COMPASS

PWA of π− Pb → π−π+π− Pb at low t′COMPASS

π´beam

X´π´beam

π´beam

π´π+

COMPASS

Photoproduction of Spin-Exotic 1−+ 1+ [ρπ]P WaveComparison with CLAS g12

COMPASS Primakoff

π´beam

X´π´beam

π´beam

π´π+

CLAS g12 C. Bookwalter, arXiv:1108.6112

γbeam

X+γbeam

γbeam

π´π+

Tagged photon beam3.6 < Eγ < 5.5 GeVp target502 000 events

COMPASS

COMPASS Primakoff

π´beam

X´π´beam

π´beam

π´π+

γbeam

X+γbeam

γbeam

π´π+

COMPASS

COMPASS Primakoff

π´beam

X´π´beam

π´beam

π´π+

1000 1200 1400 1600 1800 2000M(π+π+π−) (GeV/c2)

1−+1εP-wave [Y=ρ(770)] total intensity

1−+1+

1−+1−

COMPASS

PWA of π− p→ π−π+π− pslowSummary

Understanding of spin-exotic 1−+ wave is work in progress

COMPASS: intensity in ρπ and η′π channelsSimilar to BNL E852 and VESResonance interpretation still unclearAs CLAS: no signal in photoproduction

Spin-exotic 1−+ also claimed in channelsf1(1285)π (E852, VES)b1(1235)π (E852, VES, Crystal Barrel)COMPASS will analyze these channels as well

Significant contributions fromnon-resonant Deck-like processes

Inclusion into fit model

Exploit t′-dependence ofpartial-wave amplitudes

PWA in narrow mπ−π+π−

and t′ bins

π´beam Isobarπ´beam

π´beam

Target Recoil

π´beam π´

Target Recoil

Improvements of wave set and isobar parameterization

COMPASS

and t′ bins

π´beam

Target Recoil

π´beam π´

Target Recoil

COMPASS

and t′ bins

π´beam

Target Recoil

π´beam π´

Target Recoil

COMPASS

Central ProductionCOMPASS, CERN Omega (WA76, WA91, WA102)

pbeam pfast

ptarget pslow

pbeam pfast

ptarget pslow

pbeam pfast

ptarget pslow

[JǫM]

ptarget

π+ π0 K+ K0S η

π´ π0 K´ K0S η

Search for glueball candidates

Glueballs: mesonic states with no valence quarksLattice QCD simulations predict lightest glueballs to be scalars

Glueball would appear as supernumerous stateStrong mixing with conventional scalar mesons expectedDifficult to disentangle

Pomeron-Pomeron fusion well-suited to search for glueballsIsoscalar mesons produced at central rapiditiesScalar mesons dominant in this channelGluon-rich environment

COMPASS

K+K− Central Productionpbeam pfast

ptarget pslow

pbeam pfast

ptarget pslow

pbeam pfast

ptarget pslow

[JǫM]

ptarget

Suppression of diffractive background by cut p(pfast) > 140 GeV/c

pfastK− invariant mass Rapidity in CM frame

COMPASS

K+K− Central Productionpbeam pfast

ptarget pslow

pbeam pfast

ptarget pslow

pbeam pfast

ptarget pslow

[JǫM]

ptarget

Suppression of diffractive background by cut p(pfast) > 140 GeV/c

pfastK− invariant mass K+K− invariant mass

COMPASS

Fit of K+K− Mass Dependence

Fit model:Relativistic Breit-Wignerresonances

S−0 : f0(1370), f0(1500),f0(1710)

D−0 : f2(1270), f2′(1525)

Exponentially dampedcoherent background terms

COMPASS

Fit of K+K− Mass DependenceComparison with WA102

COMPASS WA102 PL B453 (1999) 305

450 GeV/c p beamFit of wave intensities only

COMPASS

Fit of K+K− Mass DependenceComparison with WA102

COMPASS WA102 PL B453 (1999) 305

450 GeV/c p beamFit of wave intensities only

COMPASS

PWA of p p→ pfast K+K− pslow

Summary

Clean K+K− central-production samplePWA result similar to WA102Mass dependence can be described by model with three S−0 andtwo D−0 Breit-Wigner resonances

Extracted Breit-Wigner parameters mostly comparable to PDGvalues

Surprisingly strong signal for f0(1370)f0(1370) resonance required by observed phase motion

Work in progress

Simplistic fit modelAngular information of the two proton scattering planes not takeninto accountMass dependence parametrized by sum of relativistic Breit-Wigners

Goal: combined analysis including K0SK0

S, π+π−, π0π0, and ηη

COMPASS

Baryon Spectroscopy

Search for

“Missing” states

Gluonic excitations (hybrids)

Worldwide experimental program

ELSA, JLab, MAMI, J-PARCExcitation of baryon resonances using low-energy pion andphoton beams

E.g. γ + N → N + π, ππ, πππ, η, πη, πω, ηη, . . .

“Complete experiment”Polarized beam and target + measurement of recoil polarization8 carefully selected double/single-spin observablesWell-defined quantum numbers of initial and final stateUnambiguous determination of scattering amplitude

COMPASS

Baryon Spectroscopy

Search for

“Missing” states

Gluonic excitations (hybrids)

Worldwide experimental program

ELSA, JLab, MAMI, J-PARCExcitation of baryon resonances using low-energy pion andphoton beams

E.g. γ + N → N + π, ππ, πππ, η, πη, πω, ηη, . . .

“Complete experiment”Polarized beam and target + measurement of recoil polarization8 carefully selected double/single-spin observablesWell-defined quantum numbers of initial and final stateUnambiguous determination of scattering amplitude

COMPASS

Baryon Spectroscopy in Proton Diffraction

ptarget pslow

X+pbeam

ptarget pslow

ph1...hn

Large data set with 190 GeV/c positive hadron beam on liquidhydrogen target in kinematic range 0.1 < t′ < 1.0 (GeV/c)2

Diffractive dissociation of beam p into various final states:pπ0, pη, pη′, pω

pπ+π−, pπ0π0, pK+K−, pK0SK0

S, pηη

Unpolarized beam and target; recoil polarization not measuredJP quantum numbers of initial state not fixedQuantization axis = beam direction (Gottfried-Jackson frame)JP Mε of intermediate state X deducible from kinematic distributionof final-state particles

COMPASS

ptarget pslow

X+pbeam

ptarget pslow

ph1...hn

S, pηη

COMPASS

ptarget pslow

X+pbeam

ptarget pslow

ph1...hn

S, pηη

COMPASS

pp→ pπ0 pslowpπ0 invariant mass

cos θGJ of π0 vs. mpπ0 φTY of π0 vs. mpπ0

COMPASS

pp→ pπ0 pslowpπ0 invariant mass

cos θGJ of π0 vs. mpπ0 φTY of π0 vs. mpπ0

COMPASS

pp→ pπ+π− pslowpπ+π− invariant mass pπ+ subsystem

pπ− subsystem π+π− subsystem

COMPASS

pp→ pπ+π− pslowpπ+π− invariant mass pπ+ subsystem

pπ− subsystem π+π− subsystem

COMPASS

Summary

Large data sets from p diffractionpπ0: 8.8 · 106 eventspη: 440 000 eventspπ+π−: more than 50 · 106 events. . .

Interesting structures visible in kinematic distributions

Pp data complementary to γp and πp dataWill start with PWA of two-body final states

Acceptance correction in preparationImplementation of PWA model started

Three-body final states require more work on PWA model

COMPASS

Summary

COMPASS

Summary

COMPASS

Outline

COMPASS

Conclusions and OutlookCOMPASS has acquired large data sets for many reactions

Diffractive dissociation of p, π−, and K− on various targetsCentral production with p and π− beams on proton targetπ−γ and K−γ Primakoff reactions on heavy targets

Main focus: search for mesonic states beyond the CQM

Huge diffractive π−π+π− data set: precision spectroscopy oflight-quark isovector sectorSpin-exotic JPC = 1−+ signals observed in π− diffraction

π−η and π−η′ channelsπ−π+π− and π−π0π0 final statesResonance interpretation still unclear

Study of scalar mesons in central production of ππ, KK, and ηηFurther analyses

π− diffraction into π−ηη, π−π+π−π+π−, (ππKK)−, . . .K− diffraction into K−π+π−

Radiative couplings of a2(1320) and π2(1670)

COMPASS

Running and upcoming experiments

BESIII

Belle II

GlueX, CLAS12

COMPASS

Backup slides IBackup Slides II

Outline

4 Backup slides IIntroductionSearch for spin-exotic mesons in π− diffraction

π−π+π− final stateη′π− final state

PWA of π−η and π−η′ from final statesPWA of π−π+π−π+π− decay channel

5 Backup Slides IISearch for scalar glueballs in central production

PWA of π+π− system

COMPASS

IntroductionSearch for spin-exotic mesons in π− diffractionPWA of π−η and π−η′ from final states

The COMPASS Experiment at the CERN SPSExperimental Setup NIM A 577, 455 (2007)

COMPASS

Fixed-target experiment

Two-stage spectrometer

Large acceptance over widekinematic range

Electromagnetic and hadroniccalorimeters

Beam and final-state particle ID(CEDARs, RICH)

The COMPASS Experiment at the CERN SPSExperimental Setup NIM A 577, 455 (2007)

COMPASS

Fixed-target experiment

Two-stage spectrometer

Large acceptance over widekinematic range

Electromagnetic and hadroniccalorimeters

Beam and final-state particle ID(CEDARs, RICH)

Hadron spectroscopy 2008-09, 2012

190 GeV/c secondary hadron beamsh− beam: 97 % π−, 2 % K−, 1 % ph+ beam: 75 % p, 24 % π+, 1 % K+

Various targets: `H2, Ni, Pb, W> 1 PByte of data per year

Meson Production in Diffractive Dissociation

Reaction similar to diffraction of light by black disk

Relevant kinematic variable is squared four-momentum transfert = (pbeam − pX)

2 < 0; more practical t′ ≡ |t| − |t|min > 0“Intermediate-t′” region: diffraction pattern of Pb nucleus“High-t′” region: scattering on individual nucleons in nucleus

t′ ∈ [0, 0.1] (GeV/c)2

COMPASS

t′ ∈ [0, 0.1] (GeV/c)2

COMPASS

t′ ∈ [0, 0.1] (GeV/c)2 t′ ∈ [0.1, 1] (GeV/c)2

COMPASS

Gottfried-Jackson Coordinate System

COMPASS

Canonical vs. Helicity Coordinate System

COMPASS

Partial-Wave Analysis Formalism

Cross section parameterization in mass-independent PWA

σ(τ; mX) = σ0 ∑ε=±1

∑r=1

∣∣∣∣∣waves

Trεi (mX) Aε

i (τ)

∣∣∣∣∣2

ε, i: quantum numbers of partial wave (JPC Mε[isobar]L)Trε

i : complex production amplitudes; fit parametersAε

i : complex decay amplitudesτ: phase space coordinates

Spin-density matrix

ρεij =

∑r=1

Trεi Trε

j∗ σ(τ; mX) = σ0 ∑

ε=±1

∑i,j

ρεij(mX) Aε

i (τ) Aε∗j (τ)

Diagonal elements ρii: intensitiesOff-diagonal elements ρii, i 6= j: interference terms

COMPASS

Two-body decay amplitude in helicity formalism

Decay X(w, J, λ)→ 1(J1, λ1) [L, S] 2(J2, λ2)

AhelX =

√2L + 1 ∑

λ1,λ2

(J1 λ1 J2−λ2|S δ) (L 0 S δ|J δ)

D J∗λδ(θ, φ, 0) FL(q)∆(w) A1 A2

δ = λ1 − λ2D J∗

λδ(θ, φ, 0) — Wigner D-function describes rotational propertiesof helicity statesθ, φ — polar angles of decay daughter 1 in X rest frame (GJ orhelicity frame)FL(q) — Blatt-Weisskopf barrier factor∆(w) — amplitude that describes resonance shape of XA1,2 — decay amplitudes of (unstable) daughter particles 1 and 2

COMPASS

Two-body decay amplitude in canonical formalism

Decay X(w, J, M)→ 1(J1, M1) [L, S] 2(J2, M2)

AcanX =

√2J + 1 ∑

(J1 M1 J2 M2|S MS) ∑ML

(L ML S MS|J M)√4π

2L + 1YL

ML(θ, φ) FL(q)∆(w) A1 A2

(θ, φ) — Spherical harmonic describes rotational property of|L ML〉 stateθ, φ — polar angles of decay daughter 1 in X rest frame (reachedby simple boost, no rotations)FL(q) — Blatt-Weisskopf barrier factor∆(w) — amplitude that describes resonance shape of XA1,2 — decay amplitudes of (unstable) daughter particles 1 and 2

COMPASS

Extended maximum-likelihood method

Likelihood L to observe N events distributed according toσ(τ; mX) and acceptance Acc(τ; mX)

N!e−N

]︸︷︷︸

Poisson likelihood

∏i=1

σ(τi; mX)Acc(τi)∫dΦn(τ) σ(τ; mX)Acc(τ; mX)

︸︷︷︸

Likelihood of event n

with N ∝∫

dΦn(τ) σ(τ; mX)Acc(τ; mX)

N!e−N

∏i=1

σ(τi; mX)

L ∝ e−∫

dΦn(τ) σ(τ;mX)Acc(τ;mX)N

∏i=1

σ(τi; mX)

COMPASS

Extended maximum-likelihood method (cont.)

Insert parameterization of cross section for σ(τi; mX)

L ∝ e−∫

dΦn(τ) σ(τ;mX)Acc(τ;mX)N

∏i=1

∑r=1

∣∣∣∣∣ ∑waves

Trwave(mX) Awave(τi; mX)

∣∣∣∣∣2

Make expression less unwieldy by taking logarithm

lnL =N

∑i=1

∑r=1

∣∣∣∣∣ ∑waves

Trwave(mX) Awave(τi; mX)

∣∣∣∣∣2

−∫

dΦn(τ) σ(τ; mX)Acc(τ; mX)︸︷︷︸Normalization integral

Normalization integral estimated using phase space Monte Carlo

COMPASS

2++ 2+ [ρπ]D: a2(1320)

4++ 1+ [ f2π]F: a4(2040)

0−+ 0+ [ f0(980)π]S: π(1800) 4++ 1+ [ρπ]G: a4(2040)

COMPASS

2++ 2+ [ρπ]D: a2(1320) 4++ 1+ [ f2π]F: a4(2040)

0−+ 0+ [ f0(980)π]S: π(1800) 4++ 1+ [ρπ]G: a4(2040)

COMPASS

2++ 2+ [ρπ]D: a2(1320) 4++ 1+ [ f2π]F: a4(2040)

0−+ 0+ [ f0(980)π]S: π(1800)

4++ 1+ [ρπ]G: a4(2040)

COMPASS

2++ 2+ [ρπ]D: a2(1320) 4++ 1+ [ f2π]F: a4(2040)

0−+ 0+ [ f0(980)π]S: π(1800) 4++ 1+ [ρπ]G: a4(2040)

COMPASS

π−π+π− Final StateAcceptance (p Target)

π−π+π− mass

)2 System (GeV/c+π -π -πMass of 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

1COMPASS 2008

p+π-π-π →p -π2/c2 < t' < 1.0 Gev2/c20.1 GeV

preliminary

π+π− mass

)2 Subsystem (GeV/c+π -πMass of 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

1COMPASS 2008

preliminary

COMPASS

π−π+π− Final StateAcceptance (p Target)

Gottfried-Jackson frame: cos θGJ

GJθcos -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

1COMPASS 2008

preliminary

Gottfried-Jackson frame: ϕTY

-150 -100 -50 0 50 100 150

1COMPASS 2008

preliminary

Helicity frame: cos θHF

HFθcos -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

1COMPASS 2008

preliminary

Helicity frame: ϕHF

-150 -100 -50 0 50 100 150

1COMPASS 2008

preliminary

COMPASS

PWA of π− Pb → π−π+π− Pb at low t′ (Pilot Run)

π´beam

X´π´beam

π´beam

π´π+

Consistent with CLAS result

COMPASS

PWA of π− Pb → π−π+π− Pb at low t′ (Pilot Run)

π´beam

X´π´beam

π´beam

π´π+

Consistent with CLAS result

COMPASS

PWA of π− p→ π− η pslow and π− η′ pslow

Selection of exclusive events with 3 charged tracks + 2 photons

η reconstructed from η → π+π−π0

η′ reconstructed via π+π−η decay with η → γγ

γγ invariant mass distribution

COMPASS

Selection of exclusive events with 3 charged tracks + 2 photons

η reconstructed from η → π+π−π0

η′ reconstructed via π+π−η decay with η → γγ

γγ invariant mass distribution π+π−η invariant mass distribution

COMPASS

PWA of π− p→ π− η pslow and π− η′ pslowπ−η invariant mass distribution

π−η: dominant a2(1320)

π−η′: dominant broad structure around 1.7 GeV/c2 and a2(1320)close to thresholdBulk of data described by 3 partial waves

1−+ 1+, 2++ 1+, and 4++ 1+

COMPASS

PWA of π− p→ π− η pslow and π− η′ pslowπ−η invariant mass distribution π−η′ invariant mass distribution

π−η: dominant a2(1320)

π−η′: dominant broad structure around 1.7 GeV/c2 and a2(1320)close to thresholdBulk of data described by 3 partial waves

1−+ 1+, 2++ 1+, and 4++ 1+

COMPASS

PWA of π− p→ π− η pslow and π− η′ pslowa2(1320) in 2++ 1+ Partial Wave

π−η final state π−η′ final state

η-η′ mixing together with OZI rule

Partial-wave amplitudes for spin J related by mixing angle φ,phase space, and barrier factors (q = breakup momentum)

Tπη′J (m)

TπηJ (m)

= tan φ

[qπη′(m)

qπη(m)

]J+1/2

COMPASS

η-η′ mixing together with OZI rule

Partial-wave amplitudes for spin J related by mixing angle φ,phase space, and barrier factors (q = breakup momentum)

Tπη′J (m)

TπηJ (m)

= tan φ

[qπη′(m)

qπη(m)

]J+1/2

COMPASS

π−η scaled, π−η′

COMPASS

2++ 1+

4++ 1+

Phase: 4++ 1+− 2++ 1+

Very similar even-spin waves

Expected for nn resonances(OZI rule)

Similar physical content alsoin non-resonant high-massregion

COMPASS

2++ 1+ 4++ 1+

Phase: 4++ 1+− 2++ 1+

Very similar even-spin waves

Expected for nn resonances(OZI rule)

Similar physical content alsoin non-resonant high-massregion

COMPASS

2++ 1+ Spin-exotic 1−+ 1+

Phase: 2++ 1+− 1−+ 1+Completely differentintensity of 1−+ wave

Suppression in πη channelpredicted for intermediate|qqg〉 state

Different phase motion in1.6 GeV/c2 region

COMPASS

Summary

Found significant intensity in spin-exotic 1−+ wave in πη and πη′

2++ and 4++ waves very similar in both channels

1−+ wave enhanced in πη′

First mass-dependent fits describe data in terms of Breit-Wignerresonances and backgrounds

a2(1320) and a4(2040) resonance parameters consistent in bothchannelsDescription of 1−+ wave by Breit-Wigner requires large interferingbackground and additional 2++ resonance

Resonance interpretation of 1−+ wave requiresBetter understanding of resonance structure of 2++ and 4++ wavesInclusion of non-resonant contributions from double-Reggeprocesses in high-mass region

Final goal: combined analysis of both channels56 Boris Grube, TU München Hadron Spectroscopy at and related experiments

COMPASS

Summary

COMPASS

Summary

COMPASS

Summary

COMPASS

Non-resonant contributions

π´beam π´

ptarget pslow

π´beam

ptarget pslow

Summary

COMPASS

η′π− Final Statecos θGJ vs. η′π− Invariant Mass

COMPASS

PWA of π− Pb → π−π+π−π+π− Pb

π´beam

X´π´beam

π´beam

π´π+

First mass-dependent PWA of this reaction

Light-meson frontier: access to mesonic states in 2 GeV/c2 regionLittle information from previous experiments

Data from pilot run

Pb targetRecoil not measuredKinematic range t′ < 5 · 10−3 (GeV/c)2

COMPASS

Fit model

Complicated isobar structureLarge number of possible wavesData exhibit no dominant waves

Exploration of model space using evolutionary algorithm basedon goodness-of-fit criterion

284 waves testedAlso provides estimate for systematic uncertainty from fit model

Best model: 31 waves + incoherent isotropic backgroundIsobars

(2π)0 isobars: (ππ)S−wave, ρ(770)(3π)± isobars: a1(1260), a2(1320)(4π)0 isobars: f2(1270), f1(1285), f0(1370, 1500), and ρ′(1450, 1700)

Only few information available for (4π)0 isobars

COMPASS

Proof of Principle: First mass-dependent five-body PWA

Spin-density sub-matrix of 10 waves described using 7 resonances+ background termsRather simplistic fit model

Parameterization by sum of relativistic constant-width Breit-WignersMixing and coupled-channel effects neglectedMulti-peripheral processes (Deck-effect) not taken into account

Good description of data

Work in progress

Much more data on tapeProton target, kinematic range 0.1 < t′ < 1 (GeV/c)2

Improvement of fit modelsAnalysis of (4π)0 subsystem

COMPASS

Proof of Principle: First mass-dependent five-body PWA

Spin-density sub-matrix of 10 waves described using 7 resonances+ background termsRather simplistic fit model

Parameterization by sum of relativistic constant-width Breit-WignersMixing and coupled-channel effects neglectedMulti-peripheral processes (Deck-effect) not taken into account

Good description of data

Work in progress

Much more data on tapeProton target, kinematic range 0.1 < t′ < 1 (GeV/c)2

Improvement of fit modelsAnalysis of (4π)0 subsystem

COMPASS

Search for scalar glueballs in central production

PWA of p p→ pfast π+π− pslowpbeam pfast

ptarget pslow

pbeam pfast

ptarget pslow

pbeam pfast

ptarget pslow

[JǫM]

ptarget

Suppression of diffractive background with m(pfastπ±) > 1.5 GeV/c2

pfastπ+ invariant mass pfastπ

− invariant mass

COMPASS

PWA of p p→ pfast π+π− pslow

pbeam pfast

ptarget pslow

pbeam pfast

ptarget pslow

pbeam pfast

ptarget pslow

[JǫM]

ptarget

Selected central events

xF distribution π+π− invariant mass

COMPASS

Work in progress

Analysis similar to WA102 experimentComparable results

Simplistic fit modelAngular information of the two proton scattering planes not takeninto account

8 different mathematically ambiguous solutionsAdditional constraints needed to select physical solution

Next steps

Fit of mass dependence

Analysis of K+K− final state

Data for K0SK0

S, π0π0, and ηη final states on tape

COMPASS

Work in progress

Analysis similar to WA102 experimentComparable results

Simplistic fit modelAngular information of the two proton scattering planes not takeninto account

8 different mathematically ambiguous solutionsAdditional constraints needed to select physical solution

Next steps

Fit of mass dependence

Analysis of K+K− final state

Data for K0SK0

S, π0π0, and ηη final states on tape

COMPASS

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