The Non-Relativistic Potential The functional form of the potential is chosen to reproduce the known asymptotic properties of the strong interaction. At small distances asymptotic freedom, the potential is • coulomb-like: 4 ( r ) α V ( r ) s ⎯ → ⎯→ ⎯ − r 0 3 r At large distances confinement : • V ( r ) kr ⎯ r ⎯ ⎯ → → ∞ Diego Be(oni Hadron Physics 23
The Non-Relativistic Potential II 4 π ( ) α µ = s 2 2 µ ( 11 n ) ln( ) − f 3 2 Λ n f = number of flavours Λ ~ 0.2 GeV QCD scale parameter k string constant (~ 1 GeV/fm) Diego Be(oni Hadron Physics 24
The Spin-Dependent Potential H V V V = + + SD LS SS T � � ( L S ) dV dV ⋅ ⎛ ⎞ spin-orbit V 3 V S = − ⎜ ⎟ LS 2 2 m r dr dr (fine structure) ⎝ ⎠ c � � ( ) 2 S S ⋅ spin-spin 2 V 1 2 V ( r ) = ∇ (hyperfine structure) SS V 2 3 m c � � [ ] ( )( ) 2 2 2 3 S r S r S 1 dV d V ˆ ˆ ⎛ ⎞ ⋅ ⋅ − tensor V V V ⎜ − ⎟ T 2 2 12 m r dr dr ⎝ ⎠ c V S and V V are the scalar and vector components of the non-relativistic potential Diego Be(oni Hadron Physics 25
The Spin-Dependent Potential II • The Coulomb-like part of V(r) corresponds to one-gluon exchange and contributes only to the vector part of the potential V V . The scalar part is due to the linear confining potential. This could in principle contribute to both V S and V V , but the fit to the χ cJ masses suggests that the V V contribution is small. • The charmonium mass spectrum can be computed also within the framework of Lattice QCD (LQCD), which is essentially QCD applied to a discreet 4-dimensional space with given spacing a . • Non Relativistic QCD (NRQCD) provides another framework for the calculation of the heavy quarkonium spectrum. In NRQCD the various dynamical scales m, mv, mv 2 in the production and decay processes are well separated. Diego Be(oni Hadron Physics 26
Effective Field Theories (EFT) A non-relativistic bound state is characterized by at least three scales: – mass m ( hard ) – momentum transfer mv ( soft ) – kinetic energy of the q q pair in the CMS E ∼ p 2 /m ∼ mv 2 ( ultrasoft ) Hierarchy of scales ⇒ substitute QCD with simpler, but equivalent, Effective Field Theory (EFT) , i.e. a quantum field theory with the following properties: It contains the relevant degrees of freedom to describe • phenomena which occur in a certain limited range of energies and momenta. It contains an intrinsic energy scale Λ that sets the limit of • appicability of the EFT. Diego Be(oni Hadron Physics 27
Effective Field Theories (EFT) Heavy Quark Effective Theory (HQET) describes systems • with one heavy quark (q Q , Q q ), characterized by scales m and Λ QCD . Integrate m out and build expansion in Λ QCD /m . Non Relativistic QCD (NRQCD) describes bound states of • two heavy quarks (Q Q ). Integrate out only m and leaves lower scales as dynamical degrees of freedom. Diego Be(oni Hadron Physics 28
Lattice QCD (LQCD) The interac5on is discre5zed on a 3 (Space) + 1 (Time) dim. Labce e.g. ∂ t φ → [ φ (t+a) - φ (t-a)]/2a. Con5nuum results obtained by a → 0. LQCD formulated in Euclidean space-5me. LQCD is a first principles approach : only parameters inherent to QCD, i.e. α s and the quark masses. These n f +1 parameters are fixed by matching n f +1 low-energy quan55es to their experimental values. Observables are calculated Q Q (Mesons) taking their expectation values in the path integral approach ⇒ take average of all possible “configurations” of gauge fields. Glueballs Diego Be(oni Hadron Physics 29
The b b Spectrum from LQCD G.S. Bali, K. Sc hilling and A.Wachte r, PRD56 (1997) 2566 G .S. Ba li, K. Sc hilling a nd A.Wac hte r, he p-ph/9611226 2 10.8 =6.0 e=0.495 b e=0.40 =6.2 b 10.6 1.5 fit 10.4 1 V 0 (r)/GeV 10.2 0.5 10 0 9.8 9.6 -0.5 9.4 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 r/fm 9.2 n 1 S 0 n 3 S 1 n 1 P 1 n 3 P 0 n 3 P 1 n 3 P 2 The static potential derived from LQCD confirms the Coulomb + Confinement Ansatz Diego Be(oni Hadron Physics 30
Q Q Potential from LQCD 4 m ps + m s 3 In the quenched approximation Π u sea quarks are neglected. 2 2 m ps Excited Gluon [V(r)-V(r 0 )]r 0 1 4 α + s V ( ) r r + 0 = − σ Σ g One-Gluon-Exchange 3 r -1 quenched -2 G . Ba li e t a l., h e p -la t/000301 2 κ = 0.1575 SESAM a nd T L χ -3 0.5 1 1.5 2 2.5 3 r/r 0 Diego Be(oni Hadron Physics 31
Glueballs • Glueballs are the excitation of the QCD vacuum – Comparably easy to calculate – Lots of improvements in the last decade – Mainly due to • anisotropic lattices • improved actions Diego Bettoni Hadron Physics 32 Morningstar und Peardon, PRD60 (1999) 034509 Morningstar und Peardon, PRD56 (1997) 4043
Hadrons are very complicated • Quarkmodels usually account for q q states q q qq + • Other color neutral (q q )(q q ) (q )(q ) q q configurations with same + quantum numbers can (and will mix) (q q )g q (q )g + • Decoupling only possible for gg – narrow states – vanishing leading q q term Diego Bettoni Hadron Physics 33
Definition of Hadron Configurations SU(3) c symmetry tells us that (3i+n)q (3j+n) q (k)g is colour neutral i=1, j=n=k=0 baryon i=j=k=0, n=1 meson i=j=n=0, k>1 glueball i=j=0, n=1, k>1 meson hybrid i=1, j=n=0, k>1 baryon hybrid i=n=1, j=k=0 pentaquark i=j=k=0, n=2 four-quark i=j=k=0, n=3 or i=j=1, n=k=0 baryonium Diego Bettoni Hadron Physics 34
Classification (Close and Lipkin) Exotics of the first kind External quantum numbers unambiguously incompatible with assignment to baryons or mesons B=1 - baryonlike – Q>2, Q<-1, S<-3, S>0, I>3/2, .... B=0 - mesonlike – |Q|>1, I>1, |S|>2, |C|>2, |S-C|>1, .... Diego Bettoni Hadron Physics 35
Classification (Close and Lipkin) Exotics of the second kind Combination of quantum numbers not allowed for leading Fock-term Only possible for B=0 – J PC = 0 -- , 0 +- ,1 -+ , 2 +- , ... – cannot be formed by any unexcited q q -System Diego Bettoni Hadron Physics 36
Classification (Close and Lipkin) Exotics of the third kind – Crypto-Exotics Internal exotic structure – like gluonic excitations – like N-quarks but no model free signature approach: – overpopulation of hadron multiplets – unexpected masses and decay properties – a well understood conventional meson picture is mandatory Diego Bettoni Hadron Physics 37
Experimental Measurements Spectroscopy of QCD bound states. Precision measurement • of particle spectra to be compared with theory calculations. Identification of the relevant degrees of freedom. – light quarks, c c , b b – D meson – baryon Search for new forms of hadronic matter: hybrids, • glueballs, multiquark states ... Hadrons in nuclear matter. Origin of mass. • Hypernuclei. • Study of nucleon structure. • – Form Factors – PDF, GDA, TMD Spin physics. • Diego Be(oni Hadron Physics 38
Experimental Techniques e + e - collisions + low hadronic background direct formation + high discovery potential two-photon production - direct formation limited to vector initial state radiation (ISR) states - limited mass and width resolution B meson decay for non vector states (BaBar, Belle(2), BESIII, CLEO(-c), LEP) - high hadronic background + high discovery potential p p annihiliation + direct formation for all (non-exotic) (LEAR, Fermilab E760/E835, P ANDA) states + excellent mass and width resolution for all states Hadroproduction Electroproduction (CDF, D0, Compass, LHC) (HERA, JLAB12) Diego Be(oni Hadron Physics 39
Hadron Production in e + e - Annihilation Direct Forma5on In e + e - annihilations direct formation is possible only for states with the quantum numbers of the photon J PC =1 -- : J/ ψ , ψʹ and ψ (3770). Diego Be(oni Hadron Spectroscopy 40
Hadron Production in e + e - Annihilation Two-Photon Produc5on Direct Forma5on J-even states can be produced in e + e - annihilations at higher energies through γγ collisions. The ( c c ) state is usually identified by its hadronic decays. The cross section for this process scales linearly with the γγ partial width of the ( c c ) state. Diego Be(oni Hadron Spectroscopy 41
Hadron Production in e + e - Annihilation Two-Photon Produc5on Direct Forma5on • 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 = σ (e + e - → hadrons)/ σ (e + e - → µ + µ - ). • Can be used to search for new vector states. Diego Be(oni Hadron Spectroscopy 42 Ini5al State Radia5on
Hadron Production in e + e - Annihilation e + e - annihila5on provides a very favourable environment for the study of hadron spectroscopy Two-Photon Produc5on Direct Forma5on Diego Be(oni Hadron Spectroscopy 43 Ini5al State Radia5on B-meson decay Double Charmonium
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. Diego Be(oni Hadron Physics 44
Experimental Method The cross section for the process: p p → R → final state is given by the Breit-Wigner formula: 2 2 J 1 B B + π Γ in out R σ = BW 2 2 4 k 2 ( ) E M / 4 − + Γ R R The production rate ν is a convolution of the BW cross section and the beam energy distribution function f(E, Δ E): L dEf ( E , E ) BW E ( ) { } ν = ε Δ σ + σ ∫ 0 b The resonance mass M R , total width Γ 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 . Diego Be(oni Hadron Physics 45
Example: χ c1 and χ c2 scans in Fermilab E835 χ 1 χ 2 Diego Be(oni Hadron Physics 46
Hybrids and Glueballs in p p Annihilation n n g s s g/c c g p p p Production H H G _ _ _ p p p all J PC available M M M p p p Formation G H H _ _ _ p p p only selected J PC Gluon rich process creates gluonic excitation in a direct way – c c requires the quarks to annihilate (no rearrangement) – yield comparable to charmonium production – even at low momenta large exotic content has been proven – Exotic quantum numbers can only be achieved in production mode Diego Be(oni Hadron Physics 47
Selected Hot Topics Heavy Quarkonium The X, Y, Z States Open Charm Baryons Electromagne5c Form Factors
Heavy quarkonia are non rela5vis5c bound states mul5scale systems: 2 m m v m v >> >> Q Q Q 2 2 v 0 . 1 v 0 . 3 The system is non rela5vis5c: ≈ ≈ b c The mass scale is perturba5ve: m >> Λ Q QCD m 5 GeV m 1 . 5 GeV ≈ ≈ b c The structure of separated energy scales makes quarkonium an ideal probe of (de)confinement. Quarkonia probe the perturba5ve, non perturba5ve and transi5on regimes. Diego Be(oni Hadron Physics 49
Charmonium Spectrum I All 8 states below open charm threshold are well established experimentally, although some precision measurements still needed (e.g. η 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 Diego Be(oni Hadron Physics 50
Charmonium Spectrum II Diego Be(oni Hadron Physics 51
New Quarkonium States Below Open Flavor Threshold Diego Be(oni Hadron Physics 52
The η c (2 1 S 0 ) Belle PDG 2016 M( η c ʹ ) = 3639.2 ± 1.2 MeV/c 2 Γ ( ηʹ c ) = 11.3 +3.2 -2.9 MeV Δ M hf (2S) c c ≡ M( ψ (2S)) - M( η c (2S)) = 46.9 ± 1.3 MeV Diego Be(oni Hadron Physics 53
The h c ( 1 P 1 ) • Quantum numbers J PC =1 +- . • The mass is predicted to be within a few MeV of the center of gravity of the χ c ( 3 P 0,1,2 ) states M ( ) 3 M ( ) 5 M ( ) χ + χ + χ 0 1 2 M = cog 9 • The width is expected to be small Γ (h c ) ≤ 1 MeV. • The dominant decay mode is expected to be η c + γ , which should account for ≈ 50 % of the total width. • It can also decay to J/ ψ : J/ ψ + π 0 violates isospin J/ ψ + π + π - suppressed by phase space and angular momentum barrier Diego Be(oni Hadron Physics 54
The h c ( 1 P 1 ) 0 e e ' h ( )( ) + − → ψ → π → γγ γη The ψ ' decay mode is isospin viola5ng c c 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 sta5s5c, was also done by BES − 0.10 ± 0.13 ± 0.18MeV/ c 2 Diego Be(oni Hadron Physics 55 Center of gravity of P-states
Jingzhi Zhang – Charm 2013 Diego Be(oni Hadron Physics 56
X(3823) B à χ c1 γK Measured mass and width consistent with predicted values for ψ 2 (1D) ( 1 D 2 ) M = 3823.1 ± 1.8 ± 0.7 MeV/c 2 Γ < 24 MeV 711 fb -1 3.8 σ V. Bhardwaj et al.(Belle Collab.), Phys. Rev. Lett. 111 , 032001 Diego Be(oni Hadron Physics 57
Bottomonium Specroscopy Agreement with theore5cal predic5ons be(er because of: higher b quark mass • lower value of α s . • dominance of Coulomb term • in the poten5al Diego Be(oni Hadron Physics 58
The η b ( 1 S 0 ) Bottomonium State The ϒ (1 3 S 1 ) state of bo(omonium was discovered in 1977 . The ground state spin-singlet partner, η b (1 1 S 0 ), has been found only recently by the BaBar Collabora5on by studing Υ (3S) → γ η b (1S) [PRL101,071801,2008] Then confirmed in Υ (2S) → γ η b (1S) [PRL103, 161801,2009] and by CLEO [PRD8,031104,2010] The observa5on of the η b is an important valida5on of Labce QCD predic5ons Mass of the η b (1S): • Peak in γ energy spectrum at • Corresponds to η b mass 9391.1±3.1 MeV/ c 2 • The hyperfine ( Υ (1S)- η b (1S) ) mass splibng is 69.9 ± 3.1 MeV/ C 2 Diego Be(oni Hadron Physics 59
The h b ( 1 P 1 ) Bottomonium State Diego Be(oni Hadron Physics 60
Diego Be(oni Hadron Physics 61
Evidence for Υ (3S) → π 0 h b (1P) 10721 ± 2806 events Sta5s5cal significance 3.1 σ 2 M ( ) ( h 9902 2 1 ) MeV / c = ± ± b ( ) 0 4 B ( 3 S ) h B ( h ) ( 4 . 3 1 . 1 0 . 9 ) 10 − Υ → π × → γη = ± ± × b b b Diego Be(oni Hadron Physics 62
h b → γη b at Belle BR (h b → γη b ) = (49.8 ± 6.8 +10.9 -5.2 ) % Diego Be(oni Hadron Physics 63
The Y(1D) CLEO ( 3 S ) ( 1 3 ) ( 1 S ) + π − D Υ → γγ Υ → γγπ Υ J ( ) ( 3 2 M 1 D 10164 . 5 0 . 8 0 . 5 ) MeV / c = ± ± 2 Diego Be(oni Hadron Physics 64
The χ b (3P) χ b (3P) → Υ (1S) + γ χ b (3P) → Υ (2S) + γ χ b (3P) M( χ b (3P)) = 10.539 ± 0.004 (stat) ± 0.008 (syst) GeV/c 2 Diego Be(oni Hadron Physics 65
The XYZ States Diego Be(oni Hadron Physics 66
The XYZ States Diego Be(oni Hadron Physics 67
The X(3872) Discovery New state discovered by Belle in the hadronic decays of the B-meson: B ± → K ± (J/ ψπ + π - ), J/ ψ→ µ + µ - or e + e - M = 3872.0 ± 0.6 ± 0.5 MeV Γ < 2.3 MeV (90 % C.L.) X ( 3872 ) ( ) Γ → γχ c 1 0 . 89 ( 90 % C . L .) < ( ) X ( 3872 ) + − J / Γ → π π ψ Diego Be(oni Hadron Physics 68
The X(3872) Confirmation BaBar CDF D0 Diego Be(oni Hadron Physics 69
The X(3872) at LHCb Confirmed from analysis of angular correla5ons in B + → X(3872)K + → π + π - J/Ψ, J/Ψ→μ + μ - arXiv:1504.06339v1 J PC = 1 ++ Diego Be(oni Hadron Physics 70
The X(3872) at BES III ISR ψ ’ signal is used for rate, mass, and mass resolution calibration. N( ψ ’)=1242 ; Mass=3685.96 ± 0.05 MeV; σ M =1.84 ± 0.06 MeV BESIII preliminary N(X(3872))=15.0 ± 3.9 5.3 σ M(X(3872)) = 3872.1 ± 0.8 ± 0.3 MeV [PDG: 3871.68 ± 0.17 MeV] C. Yuan – Charm 2013 Diego Be(oni Hadron Physics 71
What is the X(3872) ? • Mass: Very close to D 0 D *0 threshold • Width: Very narrow, < 1.2 MeV • Small binding energy implies huge separation ∼ 5 fm • J PC =1 ++ [LHCb] • Production – in p p/pp collison – rate similar to charmonia – In B decays – KX similar to c c, K*X smaller than c c – Y(4260) à γ +X(3872) [BESIII] • Decay BR: open charm ~ 50%, charmonium~O(%) • Nature (very likely exotic) – Loosely D 0 D *0 bound state (like deuteron?)? – Mixture of excited χ c1 and D 0 D *0 bound state? – Many other possibilities (if it is not χ ’ c1 , where is χ ’ c1 ?) . Diego Be(oni Hadron Physics 72
Y(4260) Discovered by BaBar in ISR events: e + e - → γ ISR π + π - J/ ψ J PC = 1 -- Confirmed by CLEO, CLEO III, Belle, BESIII 2 M 4250 9 MeV / c = ± From PDG: 108 12 MeV Γ = ± Weak coupling consistent with hybrid meson. Shows up as very small maximum near the deep minimum between conventional charmonium states ψ (4160) and ψ (4415) Diego Be(oni Hadron Physics 73
Z + (4430), Z 1 + (4050), Z 2 + (4250) Z + (4430) →ψ (2S) π + Z 1 + (4050) →χ c1 π + , Z 2 + (4250) →χ c1 π + Not confirmed by BaBar that also studied Not confirmed by BaBar which did not the J/ ψπ - K + and J/ ψπ - K 0 s channels. find evidence of a signal in the exo5c The J/ ψπ K final state was also studied by χ c1 π + channel. Belle, who did not find any evidence of Z. Belle confirmed the Z in a Dalitz reanalysis. Diego Be(oni Hadron Physics 74
Z - (4430) at LHCb B 0 → K + ψ (2S)π - M = 4475 ± 7 +15 -25 MeV Γ = 172 ± 13 +37 -34 MeV J P = 0 + Diego Be(oni Hadron Physics 75
Z b (10610) and Z b (10650) + (10650) - Z b + (10610) and Z b - Discovered by Belle in 2011 in π + π - transi5ons from Υ (5S) . - Both decay to Υ (nS) π + and h b (nP ) π + . 5 σ evidence for neutral isospin partner of Z b + (10610). - Minimal quark content b b u d The Z b + (10610) and Z b + (10650) lie very close to the BB* and B*B* thresholds, respectively. Molecular states ? Diego Be(oni Hadron Physics 76
Z c + (3900) Y(4260) →π + π - J/ ψ , J/ ψ→ l + l - 1477 events – 525 pb-1 σ = (62.9 ± 1.9 ± 3.7) pb consistent with Y(4260) produc5on A structure observed in the M = 3899.0 ± 3.6 ± 4.9 MeV J/ ψπ ± mass spectrum Γ = 46 ± 10 ± 20 MeV 307 ± 48 events Minimal quark content b b u d >8 σ Z c (3900) ± Diego Be(oni Hadron Physics 77
Z c + (3900) C. Yuan – Charm 2013 CLEOc data at 4.17 GeV: Belle with ISR: 1304.0121 1304.3036 Belle M = 3894.5 ± 6.6 ± 4.5 MeV M = 3885 ± 5 ± 1 MeV Γ = 63 ± 24 ± 26 MeV Γ = 34 ± 12 ± 4 MeV 159 ± 49 events 81 ± 20 events >5.2 σ 6.1 σ Diego Be(oni Hadron Physics 78
0 (3900) in e + e - → π 0 π 0 J/ ψ Z c Diego Be(oni Hadron Physics H. Peng – ICHEP2014 79
e + e - → π Z c (4020) à π + π - h c (1P) Ecm=4.36 GeV Ecm=4.26 GeV BESIII preliminary N= 64 ± 19 N= 56 ± 17 Simultaneous fit to 4.26/4.36 GeV data and 16 η c decay modes . 6.4 σ M(Z c (4020)) = 4021.8 ± 1.0 ± 2.5 MeV; Γ (Z c (4020)) = 5.7 ± 3.4 ± 1.1 MeV C. Yuan – Charm 2013 Diego Be(oni Hadron Physics 80
e + e - → π Z c (4025) à π - (D* D *) + +c.c. Fit to π ± recoil mass yields 401 ± 47 Z c (4025) events. >10 σ M(Z c (4025)) = 4026.3 ± 2.6 ± 3.7 MeV; BESIII: 1308.2760 Γ (Z c (4025)) = 24.8 ± 5.6 ± 7.7 MeV Diego Be(oni Hadron Physics 81
The LHCb Pentaquark Λ 0 b → P + c K - J/ψpK - M = 4449.8±1.7±2.5 MeV Γ = 39±5±19 MeV M = 4380±8±29 MeV Γ =205±18±86 MeV Diego Be(oni Hadron Physics 82
Eric Braaten – Charm 2013 Diego Be(oni Hadron Physics 83
Eric Braaten – Charm 2013 Diego Be(oni Hadron Physics 84
Open Charm Interest of charm • Strong interactions – QCD laboratory – Intermediate case between heavy and light quarks – Interesting spectroscopy – Strong decay modes • Weak interactions – Complementary to measurements with b quarks – Mixing and CP violation – Possible window to physics beyond the Standard Model Diego Be(oni Hadron Physics 85
Charm Meson Spectroscopy • Ground states (D, D * ) and two of the 1P states D 1 (2420) and D 2 * (2460) experimentally well established since they are narrow. • Broad L=1 states D 0 * (2400) and D 1 ’(2430) found by BaBar and Belle in exclusive B decays • Babar found 4 new states decaying to D π and D * π . Diego Be(oni Hadron Physics 86
D mesons at LHCb Diego Be(oni Hadron Physics 87
D s States For the states c( u/d ) theory and experiment were in agreement. The quark model describes the spectrum of heavy-light systems and it was expected to be able to predict unobserved excited D S (c s ) mesons with good accuracy D S2 D S1 D S * D S Diego Be(oni Hadron Physics 88 B. Aubert et al., PRD74, 032007 (2006).
D s States The discovery of the new D SJ states has brought into ques5on poten5al models Two new states D S (2317) and D S (2460) were discovered in e + e − → c c events, then observed in B decays by Babar, Belle and CLEO D S (2317) D S (2460) CLEO D S2 D S1 D S (2460) D S (2317) D S * The iden5fica5on of these states as the D S 0 + and 1 + c s states is difficult within the poten5al model Diego Be(oni Hadron Physics 89
D s States The discovery of the new D SJ states con5nued … D S (2860) D S (2860) D S (2710) D S2 D S1 D S (2460) D S (2710) D S (2317) D S * D S Belle Collab, PRL 100 (08) 092001 Diego Be(oni Hadron Physics 90
D s States The assignment of the q.n. to the D S (2710) was possible thanks to an analysis performed by BaBar studying DK , D*K final states. D SJ (3040) In the same analysis another broad D S (2860) structure in the D*K distribu5on D SJ (3040) D S (2710) D S2 D S1 D S (2460) D S (2317) D S * D S There is a problem for the poten5al models in describing excited states Diego Be(oni Hadron Physics 91
Strange and Charmed Hyperons Diego Be(oni Hadron Physics 92
Strange and Charmed Baryons Diego Be(oni Hadron Physics 93
Hypernuclear Physics Hypernuclei, systems where one (or more) nucleon is replaced by one (or more) hyperon(s) (Y), allow access to a whole set of nuclear states containing an extra degree of freedom: strangeness. • Probe of nuclear structure and its possible modifications due to the hyperon. • Test and define shell model parameters. • Description in term of quantum field theories and EFT. • Study of the YN and YY forces (single and double hypernuclei). • Weak decays ( Λ→π N suppressed, but Λ N → NN and ΛΛ→ NN allowed ⇒ four-baryon weak interaction) • Hyperatoms • Experimentally: in 50 years of study 35 single, 6 double hypernuclei established Diego Be(oni Hadron Physics 94
Product Pro ction of Double Hyp ypern rnucl clei 2. Kaons _ Slowing down trigger and capture _ Ξ p of Ξ - in secondary Ξ - capture: 3 GeV/c target Ξ - p → ΛΛ Ξ - ΛΛ + 28 MeV nucleus 1300 Hz 5600 / day Ξ - (dss) p(uud) → Λ (uds) Λ (uds) γ 1. Hyperon- 8000 / month antihyperon Λ production γ at threshold Λ +28MeV 3. γ -spectroscopy 80 / month with Ge-detectors D.Be(oni PANDA at FAIR 95
Introduction p 0 p j µ J µ k k ʹ κ ⎡ ( ) ( ) ⎤ 2 2 µ µ µ ν J e F q F q i q = γ + σ 1 2 ⎢ ν ⎥ 2 M ⎣ ⎦ p p F ( 0 ) 1 F ( 0 ) 1 = = 1 2 n n F ( 0 ) 0 F ( 0 ) 1 = = 1 2 Dirac and Pauli Form Factors Diego Be(oni Hadron Physics 96
Sachs Form Factors 2 q κ G F F ≡ + E 1 2 2 4 M G F F ≡ + κ M 1 2 • G E and G M are Fourier transforms of nucleon charge and magnetization density distributions (in the Breit Frame). • Spacelike form factors are real, timelike are complex. • The analytic structure of the timelike form factors is connected by dispersion relations to the spacelike regime. • By definition they do not interfere in the expression of the cross section, therefore, in the timelike case, only polarization observables allow to get the relative phase. Diego Be(oni Hadron Physics 97
e e N N + − + → + p e + e - 2 > s = Q 0 θ * p 2 2 4 C 2 m ⎡ ⎤ α πβ 2 2 N G ( s ) G ( s ) σ = + ⎢ ⎥ M E 3 s s ⎣ ⎦ 2 2 d C 4 m ⎡ ⎤ σ α β 2 2 2 * 2 * N G ( s ) ( 1 cos ) G ( s ) sin = + θ + θ ⎢ ⎥ M E d 4 s s Ω ⎣ ⎦ Diego Be(oni Hadron Physics 98
C is the Coulomb correction factor, taking into account the QED coulomb interaction. Important at threshold. 1 2 M πα C = y N = y − 1 e s β − 1 C σ finite ⎯ ⎯ 4 ⎯ ⎯ → 2 s M → β N 2 3 2 π α ( ) 2 2 4 M G ( 4 M ) 0 . 1 nb σ = ≈ s ( GeV ) N E N 2 4 M N There is no Coulomb correction in the neutron case. Diego Be(oni Hadron Physics 99
Form Factor Properties • At threshold G E =G M by definition, if F 1 and F 2 are analytic functions with a continuous behaviour through threshold. G E (4m p 2 ) = G M (4m p 2 ) • Timelike G E and G M are the analytical continuation of non spin flip and, respectively, spin flip spacelike form factors. Since timelike form factors are complex functions, this continuity requirement imposes theoretical constraints. • Two-photon contribution can be measured from asymmetry in angular distribution. Diego Be(oni Hadron Physics 100
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