Физика антипротонов низких Физика антипротонов низких энергий и антивеществаэнергий и антивещества

О.Д.ДалькаровО.Д.Далькаров

Физический институт Физический институт им.П.Н.Лебедева РАНим.П.Н.Лебедева РАН

План докладаПлан доклада

1.BbarB Thresholds1.BbarB Thresholdsa. Baryon electromagnetic form-factor in the time-like regiona. Baryon electromagnetic form-factor in the time-like region (theory and experiment)(theory and experiment)

b. e+e- annihilation near NbarN thresholdb. e+e- annihilation near NbarN threshold (theory and experiment)(theory and experiment) 2.Low energy antiprotons as a new probe of nuclear matter2.Low energy antiprotons as a new probe of nuclear matter (theory and experiment)(theory and experiment)

3.Ultracould antihydrogen – hydrogen systems3.Ultracould antihydrogen – hydrogen systems (theory and proposals)(theory and proposals)

Cross-sections and nucleon Cross-sections and nucleon electromagnetic form-factorelectromagnetic form-factor

From the Lorenz-invariance and charge conservation:From the Lorenz-invariance and charge conservation: <p<p22 | j| j (0)|p (0)|p11 >=u(p >=u(p22 )[F )[F11 (q (q22 ) ) +iF +iF2 2 (q (q 22)) q q ]u(p ]u(p11 ) ) It is more convenient to introduceIt is more convenient to introduce GGEE = F = F11 – q – q22/4m/4m22 F F22 ; G ; GMM = F = F11 + F + F22

Taking into account isotopic spinTaking into account isotopic spin GGPP = G = GSS + G + GVV ; G ; Gnn = G = GSS - G - GVV

In the time-like region (qIn the time-like region (q22 < -4m < -4m22 ): ): dd /d /d(pbarp→e+e-)= (pbarp→e+e-)= 22//8Ek {|G8Ek {|GMM | |22(1+ cos(1+ cos22) – 4m) – 4m22/q/q22|G|GE E ||22 sin sin22} } Near NbarN threshold ( qNear NbarN threshold ( q22 - 4m - 4m22 ) ) GGEE (-4m (-4m22 ) = G ) = GMM (-4m (-4m22 ) = G ) = G and soand so k/m k/m ( pbarp → e+e- ) = ( pbarp → e+e- ) = 22/2m/2m2 2 |G ||G |22

Experimental dataExperimental data

Proton time-like FF (low qProton time-like FF (low q22 ) )

Proton electromagnetic form-factorProton electromagnetic form-factor ( q ( q22 < -4m < -4m22 ) )

G = GG = G0 0 | | (0) | (0) | (0) ( ``enhancement factor``)(0) ( ``enhancement factor``)

increasis very fast at small kincreasis very fast at small k GG00 corresponds to singularities very far from corresponds to singularities very far from

threshold ( VDM )threshold ( VDM ) O.D.Dalkarov. JETP Lett. 28(1978)183O.D.Dalkarov. JETP Lett. 28(1978)183

(0) = 1/ f (-k) ( f(k) is Yost function )(0) = 1/ f (-k) ( f(k) is Yost function ) For S-waveFor S-wave f (k) = exp(if (k) = exp(i(k) / (k) / (k (k22) , ) , where where (k) is complex phase shift (k) is complex phase shift ThereforeTherefore | | (0)| = exp (-Im (0)| = exp (-Im(k)) / l(k)) / l(k(k22)l)l At small k: At small k: (k) (k) a att k k

Analytical behaviour Analytical behaviour

HenceHence G = GG = G0 0 exp(-Ima exp(-Imattk) / lk) / l (k(k22)l)l

For small k < 1/ Im aFor small k < 1/ Im att

G = C ( 1 – ImaG = C ( 1 – Imattk + bkk + bk22…)…)

a. Linear behaviour of G at small ka. Linear behaviour of G at small k

b. Connection with pbarp low energy data:b. Connection with pbarp low energy data: ImaImatt could be extracted from pbarp atomic data ( width of could be extracted from pbarp atomic data ( width of 33SS11

protonium state: protonium state: Im a = - 0.8 fm ) Im a = - 0.8 fm ) Electromagnetic nucleon form-factor near the NbarN threshold is Electromagnetic nucleon form-factor near the NbarN threshold is

strongly influenced by NbarN initial state interaction strongly influenced by NbarN initial state interaction

Coupled channels model forCoupled channels model for NbarN – e+e- reaction NbarN – e+e- reaction

Potential matrix has a formPotential matrix has a form VVNbarNNbarN (OBEP) V (OBEP) Vannann V VNbarN-e+e-NbarN-e+e-

VVannann < < > 0> 0 VVe+e--NbarNe+e--NbarN 0 e+e- 0 e+e- For S-matrix: S = ( 1 – iK ) ( 1 + iK )For S-matrix: S = ( 1 – iK ) ( 1 + iK ) Since VSince VNbarN-e+e-NbarN-e+e- ~ ~ (r), potential matrix and boundary condition were changed (r), potential matrix and boundary condition were changed VVNbarN NbarN V Vann ann 0 K 0 Kijij (r=0) = K (r=0) = Kijij

00

VVannann 0 0 0 0 1 0 0 0 0 1 0 0 0 K0 0 0 K ijij

00 = C = C00 k kii k kjj 0 0 0 0 0 0 1 0 01 0 0 Here CHere C00 = (1/3 = (1/3 /2m) G/2m) G00 O.D.Dalkarov, K.V.Protasov. Phys.Lett.B280 (1992) 11O.D.Dalkarov, K.V.Protasov. Phys.Lett.B280 (1992) 11 O.D.Dalkarov and K.V. Protasov. Nucl.Phys.A504 (1989) 845 O.D.Dalkarov and K.V. Protasov. Nucl.Phys.A504 (1989) 845

NbarN model without cut-off parametrsNbarN model without cut-off parametrs O.D.Dalkarov and A.Yu.Voronin. Eur.Phys.J. A25 (2005) 429 O.D.Dalkarov and A.Yu.Voronin. Eur.Phys.J. A25 (2005) 429

theory

YbarY thresholdsYbarY thresholds barbar thresholdthreshold Experiment: important P – wave contamination in all of Experiment: important P – wave contamination in all of

observables observables ( reaction and differential pbarp → ( reaction and differential pbarp → barbar cross-sections, cross-sections,

polarization ) at low relative momenta of polarization ) at low relative momenta of and and bar bar Theory: coupled channel modelTheory: coupled channel model Existance of Existance of barbar nearthreshold nearthreshold quasinuclear states quasinuclear states J.Carbonell, O.D.Dalkarov and K.V.Protasov.J.Carbonell, O.D.Dalkarov and K.V.Protasov. Phys.Lett.B 306 (1993)407 Phys.Lett.B 306 (1993)407 O.D.Dalkarov, P.A.Khakhulin and A.Yu.VoroninO.D.Dalkarov, P.A.Khakhulin and A.Yu.Voronin Nucl.Phys.A833 (2010) 104Nucl.Phys.A833 (2010) 104

Electromagnetic formfactor of Electromagnetic formfactor of lambda-hyperonlambda-hyperon

PEP-2, BaBar collaborationPEP-2, BaBar collaboration

EM formfactor of Lambda-EM formfactor of Lambda-HyperonHyperon

Others thresholdsOthers thresholds

O.D.Dalkarov, P.A.Khahulin and A.Yu.Voronin. Nucl.Phys. A833 (2010) 104O.D.Dalkarov, P.A.Khahulin and A.Yu.Voronin. Nucl.Phys. A833 (2010) 104

Possibility to extract Im aPossibility to extract Im a from the slope parameter from the slope parameter It`s necessary to measure e+e- (pbarp)→ DbarD cross-sectionsIt`s necessary to measure e+e- (pbarp)→ DbarD cross-sections for the relative momenta k < 200 MeV/cfor the relative momenta k < 200 MeV/c

Im a = - 0.44 fm**3Im a = - 0.44 fm**3

Quasinuclear vector NbarN state Quasinuclear vector NbarN state

11. e+e- - 6pions . e+e- - 6pions

(DCI, ORSAY)(DCI, ORSAY)

2. e+e- - mh 2. e+e- - mh

total cross-sectiontotal cross-section

Green function for compositeGreen function for composite two-body system two-body system

G(r,r`), where r is relative coordinateG(r,r`), where r is relative coordinate +-----------------------++-----------------------+ VV11 G(r,r`) V G(r,r`) V22

M ~ < VM ~ < V22 |G(r,r`)|V |G(r,r`)|V11 > > Case of G(0,r) for V = - Case of G(0,r) for V = - /r (E.Schrodinger) /r (E.Schrodinger) Let`s propose: 1. r = r` =0Let`s propose: 1. r = r` =0 2. G(r,r`) has a pole corresponded to bound state2. G(r,r`) has a pole corresponded to bound state

→→ Using usual representationUsing usual representation

G(r,r`)G(r,r`) =- =- ( (rr) ) *(r') / ( l *(r') / ( l b b l + E +l + E + i i) + ) + dk dk kk(r)(r)kk**(r') / (k(r') / (k22 /2m-E-i /2m-E-i))

where where bb is the binding energy of two-body composite system is the binding energy of two-body composite system

e+

e-

FinallyFinally

G(0,0) = - lG(0,0) = - l(0)l(0)l22 /( l /( lbbl + E + il + E + i ) + ) + dk l dk l kk(0)l(0)l22 / (k / (k22/2m – E – i/2m – E – i) )

++ - + ++ - + -----------*----------------------------------|-----------------------------*----------------------------------|------------------ pole continuumpole continuum

Exact compensation of these two terms is possibleExact compensation of these two terms is possible

Result: nullification of reaction amplitude due to existance of Green function`s Result: nullification of reaction amplitude due to existance of Green function`s zerozero

O.D.Dalkarov and V G Ksenzov. Pis`ma v ZhETP. 30 (1979) 74O.D.Dalkarov and V G Ksenzov. Pis`ma v ZhETP. 30 (1979) 74 Pis`ma v ZhETP. 31 (1980) 425Pis`ma v ZhETP. 31 (1980) 425

Realistic coupled channels Realistic coupled channels calculationscalculations

NbarN: V(OBEP) → NRD potentialNbarN: V(OBEP) → NRD potential NbarN – nNbarN – n : V : VNbarNhNbarNh → → exp(-2mr)/r exp(-2mr)/r e+e- -- NbarN: Ve+e- -- NbarN: Ve+e-e+e- → V → V00 (r) ~ proton electromagnetic form-factor near NbarN threshold (r) ~ proton electromagnetic form-factor near NbarN threshold Resulting amplitude:Resulting amplitude: M(e+e- - nM(e+e- - n ) = M ) = M thth + M + M bgbg

MMbgbg was normalized at s = 4 GeV was normalized at s = 4 GeV22

Varying parameters:Varying parameters: 1. Cut-off radius for 1. Cut-off radius for 3333SS11 - state - state G = (-1)G = (-1)L+S+TL+S+T =+1, T = 1 =+1, T = 1 2. Relative phase: M = M 2. Relative phase: M = M thth + M + M bgbg

From the best agreement with experiment: r =0.5fm, From the best agreement with experiment: r =0.5fm, = - = - /4 /4

RESULT: quasinuclear 2 RESULT: quasinuclear 2 3333 S S11 - state - state J J PCPC = 1 = 1 - -- - , M = 1800 MeV and , M = 1800 MeV and = 15 MeV = 15 MeV

O.D.Dalkarov and K.V.Protasov. Nucl.Phys.A504(1989)845O.D.Dalkarov and K.V.Protasov. Nucl.Phys.A504(1989)845

““Qusinuclear model”. O.D.Dalkarov, V.B.Mandelzweig and Qusinuclear model”. O.D.Dalkarov, V.B.Mandelzweig and I.S.Shapiro.I.S.Shapiro. Nucl.Phys.B21(1970) 88Nucl.Phys.B21(1970) 88

KbarK and D*barD* thresholdsKbarK and D*barD* thresholds

Low-energy antiprotons as a newLow-energy antiprotons as a new probe of nuclear reaction probe of nuclear reaction

mechanismmechanism

For the validity of the Glauber approach:For the validity of the Glauber approach: a) rectilinearness of the hadron trajectory a) rectilinearness of the hadron trajectory

in a nucleus (eikonal apprpximation);in a nucleus (eikonal apprpximation); b) the possibility to neglect the motion of b) the possibility to neglect the motion of

nucleons in the nucleus during the flight nucleons in the nucleus during the flight time of the hadron through a nucleus time of the hadron through a nucleus

(adiabatic approximation)(adiabatic approximation)

In the case of protons beam:In the case of protons beam: the validity or invalidity of conditions a) and b) is made the validity or invalidity of conditions a) and b) is made

simultaneously.simultaneously.. In the case of antiprotons beam:. In the case of antiprotons beam: low-energy pbarN scattering is strongly forward directed, low-energy pbarN scattering is strongly forward directed,

moreover, the slope of the cone increases when energy moreover, the slope of the cone increases when energy decreases.decreases.

The specific feature of pbarN scattering can ensure the The specific feature of pbarN scattering can ensure the validity of condition (a) in the case when there no reason validity of condition (a) in the case when there no reason for validity of condition (b) i.e. this gives for validity of condition (b) i.e. this gives unique unique possibility to judge independently on the applicability of possibility to judge independently on the applicability of the adiabatic approximation.the adiabatic approximation.

Condition (b): many effectsCondition (b): many effects which are at first glance not which are at first glance not connected with each other (e.g., rescattering of connected with each other (e.g., rescattering of intranuclear nucleons and off-mass- shell effects in the intranuclear nucleons and off-mass- shell effects in the hadron-nucleon amplitude ) almost completely cancel hadron-nucleon amplitude ) almost completely cancel each othereach other

O.D.Dalkarov, V.M.Kolybasov and V.G.Ksenzov. O.D.Dalkarov, V.M.Kolybasov and V.G.Ksenzov. Nucl.Phys. A397(1983) 49Nucl.Phys. A397(1983) 4988

O.D.Dalkarov and V.G.Ksenzov. Yad.Phys.32(1980) 1439O.D.Dalkarov and V.G.Ksenzov. Yad.Phys.32(1980) 1439 “ “Frozen” nucleons Frozen” nucleons

Antiproton-nucleus interaction at low energyAntiproton-nucleus interaction at low energy O.D.Dalkarov and V.A.Karmanov.O.D.Dalkarov and V.A.Karmanov. Nucl.Phys. A478(1988) 635Nucl.Phys. A478(1988) 635

Glauber approach in the theory of Glauber approach in the theory of low energy Pbar-nucleus scatteringlow energy Pbar-nucleus scattering

1. q-dependence of f1. q-dependence of fpbarppbarp(q) – from experimental angular (q) – from experimental angular distributionsdistributions

2. nuclear transition densities – from electron scattering 2. nuclear transition densities – from electron scattering datadata

3. only one fitting parameter:3. only one fitting parameter: = Re f= Re fpbarppbarp(0)/Im f(0)/Im fpbarppbarp(0)(0)

O.D.Dalkarov and V.A.Karmanov. Nucl.Phys. A445 (1985) O.D.Dalkarov and V.A.Karmanov. Nucl.Phys. A445 (1985) 579579; Nucl.Phys. A478 (1988) 635; Nucl.Phys. A478 (1988) 635

Resume: Low energy pbar - nucleus scattering is a new Resume: Low energy pbar - nucleus scattering is a new unique tool for penetrating into the nuclear many body unique tool for penetrating into the nuclear many body problemproblem

ULTRACOLD HYDROGEN-ULTRACOLD HYDROGEN-ANTIHYDROGEN SYSTEMANTIHYDROGEN SYSTEM

CPT symmetryCPT symmetry Novel branch of antiAtomic PhysicsNovel branch of antiAtomic Physics Crossroad of atomic, nuclear, elementary particle physicsCrossroad of atomic, nuclear, elementary particle physics

CERN Programme for Matter-Antimatter InteractionCERN Programme for Matter-Antimatter Interaction

O.D.Dalkarov, J.Carbonell and A.Yu.Voronin.O.D.Dalkarov, J.Carbonell and A.Yu.Voronin.

Antiproton-Hydrogen annihilation at sub-kelvin Antiproton-Hydrogen annihilation at sub-kelvin tenperatures.tenperatures.

Phys.Rev. A57(1998)4335Phys.Rev. A57(1998)4335LPSC Grenoble France

J.Carbonell, K.ProtasovLebedev Physical Institute Moscow

O.Dalkarov, A.Yu.Voronin

-8 -7.5 -7 -6.5 -6 -5.5 -5

0

1

2

3

4

5

6

7

8

9

10

ann103 a.u.2

Quantum

Semiclassical

1/v

1/v2/3

Log10(E) a.u.

Hydrogen- Antihydrogen annihilation cross-section.

First Quantum Study of H-H molecule

E(HH)=-3-i1.5 meV

Gravitational effectGravitational effectAntihydrogenAntihydrogen bouncing on a surface bouncing on a surface

Mgz

V(z) z

0 0 4 0

0

0 4 4

4

140 0

2 2 /

2 2 2 2

Lifetime is determined by gravitational force and 2 .

Numbers: 5.17 10 a.u. 6.2 0.1

n n MC l

l

MC Mg MC

Mg MC

l m s

Quantum reflection from Casimir-Polder potential and gravitational states4

4 /)( zCzV

“ “GBar” Collaboration GBar” Collaboration ( CERN, ILL, FIAN ) ( CERN, ILL, FIAN )

Gravitational states of neutronsGravitational states of neutrons V.V.Nesvizhevsky et. al. Phys.Rev. D75 V.V.Nesvizhevsky et. al. Phys.Rev. D75

075006 (2007)075006 (2007)

barbar((bar) and bar) and barbar thresholdsthresholds

barbar barbar barbar DbarD DbarD ------------l----------l----------l---------------------------------------l----------------------l----------l----------l---------------------------------------l---------------------- 2.2 2.3 2.4 GeV2.2 2.3 2.4 GeV

Pure isospin statesPure isospin states T = 0 T = 0 barbar + + barbar T = 1 T = 1 barbar + + barbar pbard→ ppbard→ pSS + KbarKn + KbarKn (n = 2-4) (n = 2-4) Study of Study of -meson spectrum ( 2m-meson spectrum ( 2m - 2m- 2m = 150 MeV )= 150 MeV )

Exotic states ( Exotic states ( barbar, T = 2, Q = 2 ), T = 2, Q = 2 ) pbard→ ppbard→ pSS + + ++ + K + K++KK------

Baryon-Antibaryon PhysicsBaryon-Antibaryon Physics Laboratoire de Physique Corpusculaire,Laboratoire de Physique Corpusculaire, Blaise Pascal UniversiteBlaise Pascal Universite Dr. H.FornvieilleDr. H.Fornvieille Lebedev Physical InstituteLebedev Physical Institute O.D.Dalkarov, V.A.KarmanovO.D.Dalkarov, V.A.Karmanov Preparation of new experiments (electromagnetic Preparation of new experiments (electromagnetic

baryon form factor in the time-like region, baryon-baryon form factor in the time-like region, baryon-antibaryon and charmonium states,…)antibaryon and charmonium states,…)

FAIR (Facility for Antiproton and Ion Reseach, FAIR (Facility for Antiproton and Ion Reseach, Darmstadt, Germany)Darmstadt, Germany)

PANDA CollaborationPANDA Collaboration

СПАСИБО ЗА ВНИМАНИЕСПАСИБО ЗА ВНИМАНИЕ