Overview of Conventional Charmonium Diego Bettoni INFN, Ferrara, Italy

Outline Introduction Experimental techniques Overview of conventional charmonium states Future opportunities Conclusions and outlook Charmonium Spectroscopy

Introduction

11 November 1974 Charmonium Spectroscopy

Measurement of the J/ Total Width - I The cross section for the process a+b  R  c+d is given by the Breit-Wigner formula: where k, s 1 and s 2 are the CMS momentum and spins of a and b; J, M R and  are the resonance spin and mass and total width, E is the CMS energy,  ab and  cd are the partial widths for R  ab and R  cd. If G(E) is the beam distribution function, the measured cross section is:

Charmonium Spectroscopy The area under the resonance is given by: where  peak is the value of the Breit-Wigner cross section at E=M R. The area under the resonance is thus independent of the form of G(E): if G(E) is unknown, then the value of the resonance width  can be obtained from the measured area (indirect determination of  ). This is how the J/  and  total widths were determined at SLAC. On the other hand, if G(E) is known, than  can be determined directly from the analysis of the shape of the measured excitation function (i.e. the measured cross section as a function of the CMS energy). Measurement of the J/ Total Width - II

Charmonium Spectroscopy Heavy quarkonia are non relativistic bound states multiscale systems: The mass scale is perturbative: The system is non relativistic: The structure of separated energy scales makes quarkonium an ideal probe of (de)confinement. Quarkonia probe the perturbative, non perturbative and transition regimes.

Charmonium Spectrum I Charmonium Spectroscopy All 8 states below open charm threshold are well established experimentally, although some precision measurements still needed (e.g.  c (2S), h c ) The region above threshold still to be understood: -find missing states (e.g. D-wave) -understand nature of newly discovered states (e.g. X Y Z) Hyperfine splitting of quarkonium states gives access to V SS component of quark potential model

Charmonium Spectrum II Charmonium Spectroscopy

Experimental Techniques

e + e - collisions direct formation two-photon production initial state radiation (ISR) B meson decay (BaBar, Belle(2), BESIII, CLEO(-c), LEP) + low hadronic background + high discovery potential - direct formation limited to vector states - limited mass and width resolution for non vector states p p annihiliation (LEAR, Fermilab E760/E835, P ANDA) - high hadronic background + high discovery potential + direct formation for all (non-exotic) states + excellent mass and width resolution for all states Hadroproduction (CDF, D0, Compass, LHC) Electroproduction (HERA,JLAB12) Charmonium Spectroscopy

Direct Formation In e + e - annihilations direct formation is possible only for states with the quantum numbers of the photon J PC =1 -- : J/ ,  and  (3770). All other states can be produced in the radiative decays of the vector states. For example: Crystal Ball inclusive photon spectrum The precision in the measurement of masses and widths is limited by the detector resolution.

Charmonium Spectroscopy Two-photon Production e + e - e + e - +(c c ) C-even charmonium states can be produced in e + e - annihilations at higher energies through  collisions. The ( c c ) state is usually identified by its hadronic decays. The cross section for this process scales linearly with the  partial width of the ( c c ) state. Limititations: knowledge of hadronic branching ratios and form factors used to extract the  partial width. L = Luminosity function  = e.g. 4-momenta of out going leptons. J,M,  = spin, mass,total width of c c state. s = cm energy of  system   two-photon partial width q 1,q 2 photon 4-momenta F = Form Factor describing evolution of cross section. cccc

Charmonium Spectroscopy Initial State Radiation (ISR) Like in direct formation, only J PC =1 – states can be formed in ISR. This process allows a large mass range to be explored. Useful for the measurement of R =  (e + e -  hadrons)/  (e + e -  +  - ). Can be used to search for new vector states. cccc

Charmonium Spectroscopy B-Meson Decay J / , ,  (3770),  c,  c,  c0,  c1,D (*),D (*),X(3872) K ,K S,K L,K*(890),K(1270)... Charmonium states can be produced at the B-factories in the decays of the B-meson. The large data samples available make this a promising approach. States of any quantum numbers can be produced.  c and X(3872) discoveries illustrate the capabilities of the B-factories for charmonium studies.

Diego BettoniCharmonium16 Double Charmonium Discovered by Belle in e + e -  J/ + X Enhances discovery potential of B-factories: states which so far are unobserved might be discovered in the recoil spectra of J/ and  c.

Charmonium Spectroscopy p p Annihilation In p p collisions the coherent annihilation of the 3 quarks in the p with the 3 antiquarks in the p makes it possible to form directly states with all non-exotic quantum numbers. The measurement of masses and widths is very accurate because it depends only on the beam parameters, not on the experimental detector resolution, which determines only the sensitivity to a given final state.

Charmonium Spectroscopy Experimental Method The cross section for the process: p p  R  final state is given by the Breit-Wigner formula: The production rate is a convolution of the BW cross section and the beam energy distribution function f(E,  E): The resonance mass M R, total width  R and product of branching ratios into the initial and final state B in B out can be extracted by measuring the formation rate for that resonance as a function of the cm energy E.

Charmonium Spectroscopy Beam Energy and Width Measurement In p p annihilation the precision in the measurement of mass and width is determined by the precision in the measurement of the beam energy and beam energy width, respectively. The beam revolution frequency f can be measured to 1 part in 10 7 from the beam current Schottky noise. In order to measure the orbit length L to the required precision (better than 1 mm) it is necessary to calibrate using the known mass of a resonance, e.g. the  for which  M = 12 keV.  is a machine parameter which can be measured to ~ 10 %  machine slip factor

Overview of Charmonium

Charmonium Spectroscopy Direct Measurement of the J/  and  widths

Charmonium Spectroscopy Beam width is inversely proportional to slip factor . Positive correlation between slip factor and resonance width. Slip factor can be measured from synchrotron frequency with 10 % accuracy. Corresponding systematic uncertainty on resonance width is 16 %.  (2S) Scan at Constant Orbit

Charmonium Spectroscopy Need better accuracy on . E760 achieved 6 % accuracy with double-scan technique In E835/2000. –Combine scan at constant orbit with scan at constant B. –higher luminosity. –accurate beam spectra. For measurement at constant B negative correlation between slip factor and resonance width.  (2S) Scan at Constant B

Charmonium Spectroscopy By combining the two stacks resonance width and slip factor can be determined simultaneously.

Charmonium Spectroscopy

Angular Distribution for p p → ψ(2S) → e + e - Charmonium Spectroscopy C 0, C 1 = helicity amplitudes E835-I (2391 events)E835-II (4453 events) = 0.59  0.24 = 0.71  0.18 Combined result:

Charmonium Spectroscopy The  cJ (1 3 P J ) States  c0 First observed by the early e + e - experiments, which measured radiative decay widths, directly for  c1 and  c2, indirectly for  c0. Radiative decay important for relativistic corrections and coupled channel effects. Precision measurements of masses and widths in p p experiments (R704, E760, E835).  c1 width measured only by E760, most precise measurement of  c0 width by E835. Mass (MeV/c 2 )Width (MeV) 0   0.9 1   0.14 2  

Charmonium Spectroscopy Measurements of  c1 and  c2 in E835  c1  c2

Charmonium Spectroscopy  c1 and  c2 masses and widths  c1E835E760 M(MeV/c 2 )    0.09  0.02  (MeV)0.876    0.11  0.08 B( p p)  (J/  )(eV)21.5  0.5  0.6   1.5  2.2  c2E835E760 M(MeV/c 2 )    0.13  0.02  (MeV)1.915    0.17  0.07 B( p p)  (J/  )(eV)27.0  1.5  0.8   1.5  2.0 11 22

Charmonium Spectroscopy Fine Structure Splittings

Charmonium Spectroscopy Resonant Interfering (helicity 0) Non-Interfering (helicity 1) PRL 91, (2003) E835 Interference Measurement of the  c0 Parameters

Charmonium Spectroscopy E835 p p   c   M(  c ) MeV/c 2  (  c ) MeV B in B out  10 8 B in  (  c  )  10 3 keV  (  c  ) keV B(  c  )  10 4

New Quarkonium States Below Open Flavor Threshold Charmonium Spectroscopy

The  c (2 1 S 0 ) Belle PDG 2014 M(  c ) =  1.2 MeV/c 2  (  c ) = MeV  M hf (2S) c c  M(  (2S)) - M(  c (2S)) = 46.9  1.3 MeV

Charmonium Spectroscopy Chengping Shen – PIC 2013

Charmonium Spectroscopy Chengping Shen – PIC 2013

Charmonium Spectroscopy Quantum numbers J PC =1 +-. The mass is predicted to be within a few MeV of the center of gravity of the  c ( 3 P 0,1,2 ) states The width is expected to be small  (h c )  1 MeV. The dominant decay mode is expected to be  c + , which should account for  50 % of the total width. It can also decay to J/  : J/  +  0 violates isospin J/  +  +  - suppressed by phase space and angular momentum barrier The h c ( 1 P 1 )

Charmonium Spectroscopy E760 J/  0 E835 J/  0 E835  c    E835-I E835-II E760

The h c ( 1 P 1 ) The  ' decay mode is isospin violating The CLEO experiment was able to find it with a significance of 13 σ in ψ’ decay by means of an exclusive analysis. The width and the BF ψ’→π 0 h c were not measured. A similar analysis, with higher statistic, was also done by BES Center of gravity of P-states Charmonium Spectroscopy

Jingzhi Zhang – Charm 2013

Charmonium Spectroscopy X(3823) B  χ c1 γK M = ± 1.8 ± 0.7 MeV/c 2  < 24 MeV 711 fb  V. Bhardwaj et al.(Belle Collab.), Phys. Rev. Lett. 111, Measured mass and width consistent with predicted values for  2 (1D) ( 3 D 2 )

 c2 (2P) (formerly Z(3930)) Charmonium Spectroscopy e + e - → e + e - D D M = ± 2.6 MeV/c 2  = 24 ± 6 MeV S. Uehara et al.(Belle Collab.), Phys. Rev. Lett. 96, (2006)

Future Opportunities

The Future BES III at BEPC Belle 2 LHC P ANDA at FAIR Charmonium Spectroscopy

BEPCII/BESIII

BESIII Detector Charmonium Spectroscopy 1.3 × 10 9 J/ψ 0.5 × 10 9 ψ(2S) ψ(3770) 4.23, 4.26, 4.36 GeV

Charmonium Spectroscopy

GSI Helmholtz Center and FAIR D.BettoniPANDA at FAIR50 p-Linac HESR SIS18 SIS100 CR/RESR Antiprotons Production Target

D.BettoniPANDA at FAIR51 High luminosity mode High resolution mode N stored = p dp/p ~ 3×10 -5 (electron cooling) Lumin. = cm -2 s -1 N stored = p Lumin. = 2 x cm -2 s -1 dp/p ~ (stochastic cooling) Production rate 2x10 7 /sec P beam = GeV/c Internal Target 4×10 15 cm -2 High-Energy Storage Ring Modularized Start Version (MSV0-3) L ~ cm -2 s -1 Δp/p ~ 5 × 10 -5

P ANDA Spectrometer Charmonium Spectroscopy

D.Bettoni PANDA at FAIR53

D.BettoniPANDA at FAIR54

D.BettoniPANDA at FAIR55

Charmonium Spectroscopy P ANDA Physics Program ArXiV: HADRON SPECTROSCOPY – CHARMONIUM – GLUONIC EXCITATIONS – OPEN CHARM – (MULTI)STRANGE BARYONS NUCLEON STRUCTURE – ELECTROMAGNETIC FORM FACTORS – TMDs – GPDs, TDAs HYPERNUCLEAR PHYSICS HADRONS IN THE NUCLEAR MEDIUM

Charmonium Spectroscopy Sensitivity to h c Width Measurement signal efficiency  =0.24 each point corresponds to 5 days of data taking

p p → h c (2P) Charmonium Spectroscopy m = 3934 – 3956 GeV/c 2  = 87 MeV  = 4.5 nb (3.9  10 3 /day)  b = 43 mb p p = 15 GeV/c

pp → 3F4pp → 3F4 Charmonium Spectroscopy

Summary and Outlook Heavy Quarkonium is an invaluable tool for a deeper understanding of the strong interaction and QCD. Exciting new experimental results achieved over the past two decades thanks to many experiments at hadron machines and e + e - colliders. – Quarkonium states below threshold – X, Y, Z states reveal new sector of QCD spectrum – Open charm states Progress in theory – Lattice QCD – Effective Field Theories For the near and medium term future first rate results are expected from – LHC – e + e - colliders (BES III, Belle2). – JLAB 12 GeV (CLAS12 and GlueX) –P ANDA at FAIR Complementary approaches Charmonium Spectroscopy