Recent developments in Electromagnetic Hadron Form Factors

Transcription

1 Recent developments in Electromagnetic Hadron Form Factors (JOH7RPDVL*XVWDIVVRQ '$31,$63K16DFOD\ :KDW are Form Factors? :K\ to measure? +RZ to measure? :KDWLVQHZ" Consequences, Conclusions

2 6SRNHSHUVR QV &K 3HUGULVDW 93XQMDEL 0-RQHV (%UDVK

3 Hadron Electromagnetic Form factors Characterize the internal structure of a particle ( point-like) FFs are real in space-like region (scattering) and imaginary in time-like region (annihilation). Elastic form factors contain information on the hadron ground state. In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors. Neutron and proton form factors are different. Deuteron: 2 structure functions, but 3 form factors. Playground for theory and experiment.

4 027,9$7,216 In the traditional view, the atom s nucleus appears as a cluster of nucleons - protons and neutrons. A deeper view reveals quarks and gluons inside the nucleons. CEBAF s continuous, energetic beams of probing electrons let physicists examine how the two view fit together. Ultimately, the process of bridging the views will yield a complete understanding of nuclear matter. Istitutional plan (2000)

5 Dipole Approximation G D =1/(1+Q 2 /0.71 GeV 2 ) 2 Classical approach Nucleon FF (in the Breit system) are Fourier transform of the charge or magnetic distribution. The dipole approximation corresponds to an exponential density distribution. 0 exp(-r/r 0 ), r 02 = (0.24 fm) 2, <r 2 > ~(0.81 fm) 2 m 2 D =0.71 GeV2

6 Dipole Approximation and pqcd Dimensional scaling F n (Q 2 )= C n [1/( 1+Q 2 /m n ) n-1 ], m n =nβ 2, <quark momentum squared> n is the number of constituent quarks Setting β 2 =(0.471±.010) GeV ILWWLQJSLRQ GDWD pion: F π (Q 2 )= C π [1/ (1+Q 2 /0.471 GeV 2 ) 1 ], nucleon: F 1 (Q 2 )= C 1 [1/( 1+Q 2 /0.71 GeV 2 ) 2 ], deuteron: F G (Q 2 )= C G [1/( 1+Q 2 /1.41GeV 2 ) 5 ]

7 The Pauli and Dirac Form Factors The electromagnetic current in terms of the Pauli and Dirac FFs: Related to the Sachs FFs : Normalization: F 1p (0)=1, F 2p p Normalization: G Ep (0)=1, G Mp p =2.79

8 Proton Form Factors 2YHUDSHULRGRIWLPHODVWLQJDWOHDVW \HDUV0DQKDVSX]]OHGRYHUDQGVRXJKWDQ XQGHUVWDQGLQJRIWKHFRPSRVLWLRQRIPDWWHU«F1 F2 Q 2 =1 GeV 2

9 The Rosenbluth separation Elastic HS cross section (1- H[FKDQJH point-like particle: σ Mott /LQHDULW\RIWKHUHGXFHGFURVVVHFWLRQ

10 The Rosenbluth data (SLAC) /$QGLYDKLV HWDO3K\V5HY'

11 Proton Form Factors...before One photon-exchange /$QGLYDKLV HWDO3K\V5HY' Dipole approximation: G D =1/(1+Q 2 /0.71 GeV 2 ) 2 5RVHQEOXWK VHSDUDWLRQ3RODUL]DWLRQREVHUYDEOHV

12 The polarization method (1968) The polarization induces a term in the cross section proportional to G E G M Polarized beam and target or polarized beam and recoil proton polarization

13 Proton polarimeter Inclusive reaction p+c 1 Charged particle+x Analyzing powers: Figure of merit, efficiency, uncertainties:

14 The experimental set-up(jlab-e99007) -Trigger on proton: background, target walls and pion electroproduction -The solid angle is defined by the proton

15 The polarization method (exp) The simultaneous measurement of 3 W and 3 O reduces the systematic errors!!

16 The HALL A at JLAB

17 The HALL A-calorimeter (OHFWURQ GHWHFWLRQ Assembled a 1.35 x 2.55 m2 calorimeter 17 rows and 9 columns of 15x15 leadglass blocks

18 Focal plane polarimeter

19 Azymuthal distribution Q 2 =5.6 GeV/c 2

20 7+(5(68/76 Linear deviation from dipole G Ep G Mp -ODE (( 6SRNHSHUVRQV &K3HUGULVDW93XQMDEL0-RQHV(%UDVK 0-RQHVHWTO3K\V5HY/HWW 2*D\RX HWDO3K\V5HY/HWW

21 Scaling? pqcd: F 1 1/Q 4, F 2 1/Q 6 F 1 / F 2 Q 2

22 Models, models, models... Skyrme Models (Soliton) Vector Dominance Models (G-K, IJL ) Perturbative QCD (Relativistic) Constituent Quark Model Di-quark models SkPD

23 Comparison with theory

24 Issues When pqcd starts to apply? Simultaneous description of the four nucleon form factors......in the space-like and in the time-like regions Consequences for the light ions description

25 The proton magnetic form factor The new results induce 3% global effect Radiative corrections on σ(ep) up to 30%! (%UDVKHWDO3K\V5HY&

26 The nucleon form factors proton neutron

27 The deuteron (S=1)

28 The deuteron &URVVVHFWLRQ B(Q 2 ) A(Q 2 )

29 The deuteron 3RODUL]DWLRQREVHUYDEOHV -ODE ( 6SRNHSHUVRQV %%HLVH6 R[ '$EERWWHWTO3K\V5HY/HWW

30 The IA deuteron structure: S=1, T=0 1) The nucleon form factors: 2) The S X and D Z deuteron wave function

31 G En from the deuteron G En > G Ep starting from 2 GeV 2 (7*DQG035HNDOR(XURSK\V/HWW

32 The IA deuteron structure (7*DQG035HNDOR(XURSK\V/HWW

33 The reaction d(e,e n)p - A x - The Impulse Approximation - The deuteron structure - Kinematics: proton spectator - Polarization observables

34 Select the quasi-elastic Kinematics The reaction d(e,e n)p - A x Large dependence of the asymmetry on Gen! Polarized electron beam, polarized target or neutron polarimeter

35 The neutron electric form factor Polarization method Nuclear effects *DOVWHU SDUDPHWUL]DWLRQ

36 Jlab E approved 07/2001 scheduled 2005 When G E p =0? 6SRNHSHUVRQV&K3HUGULVDW 93XQMDEL0-RQHV(%UDVK /DERUDWRULHVSHRSOH Hall A => Hall C New polarimeter New calorimeter G e p IV: up to 12 GeV 2, after the upgrade of Cebaf

37 3RODULPHWU\ DW*H9 3RPPH SRODULPHWHU -,15/+(V\QFKURSKDVRWURQ

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39 Time-like and space-like regions Form factors are UHDOLQWKHVSDFHOLNHUHJLRQ and FRPSOH[LQWKHWLPHOLNHUHJLRQ. 6FDWWHULQJ $QQLKLODWLRQ _ e - + h => e - + h _ e + + e - => h + h

40 Time-like and space-like regions T-L G M 2 Asymptotic properties from the Phragmèn-Lindelöf theorem (7*DQG035HNDOR3K\V/HWW%

41 Possible corrections 2- H[FKDQJH" Radiative corrections? P-violating terms? Complete calculations in progress Estimations give effects of the order of few percent

42 Conclusions New precise results on proton electric form factor Recoil polarization method Polarimetry Jlab polarized electron beam The electric and the magnetic distributions of the proton are different! The asymptotic region is far. The nucleon and light hadrons models have to be revisited.