Overview of Conventional Charmonium Diego Bettoni INFN, Ferrara, Italy.

Overview of Conventional Charmonium

Diego BettoniINFN, Ferrara, Italy

Charmonium Spectroscopy

Outline

• Introduction• Experimental techniques• Overview of conventional charmonium states• Future opportunities• Conclusions and outlook

Introduction


11 November 1974


Measurement of the J/ Total Width - I

The cross section for the process a+bRc+d is given by the

Breit-Wigner formula:

where k, s1 and s2 are the CMS momentum and spins of a and b;

J, MR and are the resonance spin and mass and total width, E is the

CMS energy, ab and cd are the partial widths for Rab and Rcd.

If G(E) is the beam distribution function, the measured cross section is:

4)()12)(12(

12)( 22

221

R

cdabBW

MEkssJE

0 )()()( EdEEGEE BW


The area under the resonance is given by:

where peak is the value of the Breit-Wigner cross section at E=MR.

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

0 2

)( peakdEEA


Heavy quarkonia are non relativistic bound statesmultiscale systems:

2vmvmm QQQ

GeVmGeVm

m

cb

QCDQ

5.15

The mass scale is perturbative:

The system is non relativistic: 3.01.0 22 cb vv

The structure of separated energyscales makes quarkonium an ideal probe of (de)confinement.Quarkonia probe the perturbative,non perturbative and transitionregimes.


Charmonium Spectrum I

All 8 states below open charm thresholdare well established experimentally,although some precision measurementsstill needed (e.g. c(2S), hc)

The region above threshold still to beunderstood:- 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 VSS component of quark potential model


Charmonium Spectrum II

Experimental Techniques


Experimental Techniquese+e- collisionsdirect formation

two-photon productioninitial 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

pp annihiliation(LEAR, Fermilab E760/E835, PANDA)

- 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)


Direct Formation

In e+e- annihilations direct formation is possibleonly for states with the quantum numbers of thephoton JPC=1--: J/, and (3770).

All other states can be produced inthe radiative decays of the vectorstates. For example:

XSee )2(

Crystal Ball inclusive photon spectrum

The precision in the measurement of massesand widths is limited by the detector resolution.


Two-photon Production e+e-e+e-+(cc)

C-even charmonium states can be produced in e+e- annihilations at higherenergies through collisions. The (cc)state is usually identified by its hadronicdecays. The cross section for this processscales linearly with the partial width ofthe (cc) state.

ccLdcceeee i 5

22

212222

,128 qqFMMs

MMJcc

Limititations: knowledge of hadronic branching ratios andform 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 cc state.s = cm energy of system two-photon partial widthq1,q2 photon 4-momentaF = Form Factor describingevolution of cross section.

cc


Initial State Radiation (ISR)

•Like in direct formation, only JPC=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.

cc


B-Meson Decay

J/,,(3770), c,c,c0,c1,D(*),D(*),X(3872)

K,KS,KL,K*(890),K(1270)...

Charmonium states can be produced at the B-factories in the decaysof 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-factoriesfor charmonium studies.

Charmonium 16Diego Bettoni

Double Charmonium

Discovered by Belle in e+e- J/ + X

Enhances discovery potential of B-factories: states which so far areunobserved might be discovered in the recoil spectra of J/ and c.


pp AnnihilationIn pp collisions the coherent annihilation of the 3 quarks inthe 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 andwidths is very accurate because itdepends only on the beam parameters,not on the experimental detectorresolution, which determines only thesensitivity to a given final state.


Experimental Method

4/412

22

2

2RR

RoutinBW ME

BBk

J

The cross section for the process: pp R final stateis given by the Breit-Wigner formula:

The production rate is a convolution of theBW cross section and the beam energy distribution function f(E,E):

bBW EEEdEfL )(),(0

The resonance mass MR, total width R and product of branching ratiosinto the initial and final state BinBout can be extracted by measuring theformation rate for that resonance as a function of the cm energy E.


Beam Energy and Width Measurement

In pp 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.

2)1(2 pcm mE21

1

p

beam

mE Lf

2232

12

LL

ff

EE

cm

cm

The beam revolution frequency f canbe measured to 1 part in 107 from thebeam current Schottky noise. In orderto 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


Direct Measurement of the J/ and widths


• 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


• 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


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

Angular Distribution for pp → ψ(2S) → e+e-


*2* cos1

cos

ddN

11

1

0CC C0, C1 = helicity

amplitudes

E835-I (2391 events) E835-II (4453 events)

= 0.59 0.24 = 0.71 0.18

Combined result: 04.015.067.0 03.012.044.01

0 CC


The cJ(13PJ) 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 pp experiments (R704, E760, E835). •c1 width measured only by E760, most precise measurement of c0 width by E835.

Mass (MeV/c2) Width (MeV)

0 3415.19 0.34

10.2 0.9

1 3510.59 0.12

0.88 0.14

2 3556.26 0.11

2.00 0.18

1++

0++

2++


Measurements of c1 and c2 in E835

c1

c2


c1 and c2 masses and widths

c1 E835 E760

M(MeV/c2) 3510.719 0.051 0.019

3510.60 0.09 0.02

(MeV) 0.876 0.045 0.026 0.87 0.11 0.08

B(pp)(J/)(eV) 21.5 0.5 0.6 0.6 21.4 1.5 2.2

c2 E835 E760

M(MeV/c2) 3556.173 0.123 0.020

3556.22 0.13 0.02

(MeV) 1.915 0.188 0.013 1.96 0.17 0.07

B(pp)(J/)(eV) 27.0 1.5 0.8 0.7 27.7 1.5 2.01 2


Fine Structure Splittings

210

21

20110

21221

/10.039.3525

002.0477.0

/6.02.95)()(

/15.045.45)()(

cMeVM

MM

cMeVMMM

cMeVMMM

cog

cc

cc

22110

22110

/06.006.1072

510

/09.080.3412

52

cMeVMMh

cMeVMMh

T

LS


00pp22

),( BA iiR BeAeix

Azxdzd

2/0

0

MEx CM

*cosz

ResonantInterfering(helicity 0)

Non-Interfering(helicity 1)

PRL 91, 091801 (2003)E835 Interference Measurement of the c0 Parameters


E835 pp c

M(c) MeV/c2

(c) MeV

BinBout108

Bin(c)103 keV(c) keV

B(c)104

0.24.20 7.77.6

0.11.21.2984

0.24.22 8.37.3

4.06.4 3.11.1

9.11.10.10.18.3

95.050.032.087.1


New Quarkonium States Below Open Flavor Threshold


The c(21S0)

Belle

PDG 2014M(c) = 3639.2 1.2 MeV/c2

(c) = 11.3 +3.2-2.9 MeV

Mhf(2S)cc M((2S)) - M(c(2S)) = 46.9 1.3 MeV


Chengping Shen – PIC 2013


• Quantum numbers JPC=1+-.• The mass is predicted to be within a few MeV of the center of gravity of the

c(3P0,1,2) states

• The width is expected to be small (hc) 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 hc(1P1)

9)(M5)(M3)(MM 210

cog


The hc(1P1)

E760J/0

E835J/0

MeVhcMeVhM

c

c

1)(/2.02.08.3525)( 2

E835 c

E835-IE835-IIE760


The hc(1P1)))((' 0

cchee 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’→π0hc were not measured.

A similar analysis, with higher statistic, was also done by BES

Center of gravity of P-states

0.100.130.18MeV/c2


Jingzhi Zhang – Charm 2013


X(3823)

B χc1γK

M = 3823.1 ± 1.8 ± 0.7 MeV/c2 < 24 MeV711 fb-1 3.8

V. Bhardwaj et al.(Belle Collab.), Phys. Rev. Lett. 111, 032001

Measured mass andwidth consistentwith predicted valuesfor 2(1D) (3D2)


c2 (2P) (formerly Z(3930))

e+e- → e+e- DD

M = 3927.2 ± 2.6 MeV/c2 = 24 ± 6 MeV

S. Uehara et al.(Belle Collab.), Phys. Rev. Lett. 96, (2006) 082003

Future Opportunities


The Future• BES III at BEPC • Belle 2• LHC• PANDA at FAIR


BEPCII/BESIII


BESIII Detector

1.3 × 109 J/ψ0.5 × 109 ψ(2S)ψ(3770)4.23, 4.26, 4.36 GeV

PANDA at FAIR 50

GSI Helmholtz Center and FAIR

D.Bettoni

p-Linac

HESR

SIS18SIS100

CR/RESR

AntiprotonsProduction Target

PANDA at FAIR 51D.Bettoni

High luminosity mode

High resolution mode

Nstored = 1010 pdp/p ~ 3×10-5 (electron cooling)Lumin. = 1031 cm-2 s-1

Nstored = 1011 pLumin. = 2 x 1032 cm-2 s-1 dp/p ~ 10-4 (stochastic cooling)

Production rate 2x107/sec

Pbeam = 1.5 - 15 GeV/c

Internal Target 4×1015 cm-2

High-Energy Storage Ring

Modularized Start Version (MSV0-3)L ~ 1031cm-2s-1 Δp/p ~ 5 × 10-5


PANDA Spectrometer

53D.Bettoni PANDA at FAIR


PANDA Physics Program

ArXiV:0903.3905

• 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


Sensitivity to hc Width Measurement

signal efficiency =0.24

each point correspondsto 5 days of data taking


pp → hc(2P)

m = 3934 – 3956 GeV/c2

= 87 MeV = 4.5 nb (3.9 103/day)b = 43 mb pp = 15 GeV/c


pp → 3F4


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)– PANDA at FAIR

• Complementary approaches

Overview of Conventional Charmonium Diego Bettoni INFN, Ferrara, Italy.

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