Deeply Virtual Electroproduction of Mesons and Photons with Jlab at 12 GeV

Transcription

1 Deeply Virtual Electroproduction of Mesons and Photons with Jlab at GeV e ƒ Γ e ƒι Ι Ι±Ι ΙΚΚΚ ~~ p H,E,H,E p

2 / Theoretical Formalism and Motivations / Experimental aspect : Simulations for some key channels 3/ Sensitivities of observables to GPDs 4/ Conclusions

3 Structure of nucleons The structure of the nucleon has been studied in a very limited fashion mostly in inclusive reactions Many questions of fundamental nature remain regarding the quark-quark and quark-gluon interaction in the nucleon Exclusive processes allow access to the Generalized Parton Distributions which are a manifestation of the confinement of QCD The GPDs reflect the full complexity of the internal quark-gluon structure in the nucleon They can be measured using electron, photon and mesons as probes in controlled interactions Theory support for this program is broad and growing fast

4 OFPD formalism ) Ji, Radyushkin, Collins, Frankfurt, Strikman (96-97) q (= R t ) At leading order in PQCD : q ; L R - 0 L! 0 p x + ) 4 x ; H E(x t) ~H ~ E(x t) ( ; ) x ; R p + 6 H E(x t) ~H ~ E(x t)? R H q (x t) N (p 0 ) + N (p) + E q (x t) N (p 0 )i + N (p) M N +( 5 ; ) ~H q (x t) N (p 0 ) + 5 N (p) + E ~ q (x t) N + (p 0 ) 5 m N N (p) H ~ HE ~ E : Off-Forward Parton Distributions function of 3 variables : x t ) Q >> t << ) 0 L! L ( ; ): M H, E ) 0 (0 ; ): M ~ H, ~ E ) Factorization for L part, L = T / Q

5 0 N DIS R x Link with DIS : - f (x) g (x) C A / Im 0 B N R DVCS - H E(x t) ~H ~ E(x t) H q (x 0 0) = q(x) f (x) = R X q R C N A e q q(x)! =0 ~H q (x 0 0) = q(x) g (x) = X q e q q(x)! Z + ; Z + ; SUM RULES for the OFPD s : Z + dx H q (x t) = F q (t) dx E q (x t) = F q (t) Z + dx H ~ q (x t) = g q (t) dx E ~ q (x t) = h q (t) A A Z + dx x (H q (x t =0)+ E q (x t =0)) = J quark ; ; = J q + J g J quark = + L q ; ;

6 Pion cloud «D-term term» Φ(z) (z) DDs J q Trans. Mom.. of partons k F, (t), G (t) A,PS GPDs <x 0 > t=0 <x > <x - > q(x), = =q(x) R(t),R(t) A V

7 GPDs probe the nucleon at amplitude level DIS : DES : x x x+ξ x-ξ p p p p q(x)~<p Φ(x) (x)φ(x) p (x) p > H(x,ξ)~<p )~<p Φ(x (x-ξ)φ(x+ (x+ξ) p > x>ξ= ξ=: x+ξ x-ξ p p x<ξ= ξ=: x+ξ x-ξ p p 0 z 0 z

8 H q (x,ξ,t,q,q ) but only ξ=, t and Q accessible experimentally ξ= x B t=(p-p ) -x B / Q =(e-e ) γ ξ x Β x t ~~ H,E,H,E γ,μ,... p p x = x B! dσ dq dx B dt A ~ H q (x,ξ,t,q ) dx +B E(x,ξ,t,Q q ) dx +. - x-ξ+iε - x-ξ+iε x : mute variable Deconvolution needed!

9 H - = H q (x,ξ,t) is real but amplitude is complex q (x,ξ,t) x-ξ+iε dx Differential cross section H - q (x,ξ,t) x-ξ dx Real part (charge asymmetry) +iπ=δ(x-ξ) H q (x,ξ,t) dx H q (ξ,ξ,t) Imaginary part (spin asymmetries)

10 Need High Energy Beam Large Q range Large x range B Need Luminosity Small cross sections ( with Q ) Need Resolution Identify exclusive reactions Need Large Acceptance Need t-coverage (extrapolation to t=0) Need χ-coverage (DVCS, VM decay,...) Measure different channels & variables (x B,Q,t,...) simultaneously

11 Experimental Program Identify L part (mesons) T part (Compton) (because of factorization) (not dominant at low Q ) (dominant at low Q ) Make sure we are in the Bjorken regime Mesons: L~/Q 6, L/T~Q, ±/, 0 /, x B dep., Compton: T~/Q 4 Separate H, E from H ~, ~ E Vector mesons ± ΜΙΗΙ ϑ ΙΚΚΚ ΙΚΚΚ Pseudo-scalar mesons ΜΙΗΙ ϑ ΙΚΚΚ ΙΚΚΚ ƒ

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13 Separate flavors H q,e q ~,H q ~,E q ± Ω=ΟΛΠH u +/3H d Ω=ΟΛΠH u -/3H d ± ΜΙΗΙϑ Ι ΜΙΗΙϑ Ι= Ι=ƒΛpΙ=ƒΛn, Need X-sections and spin observables (beam asymmetries, target, recoil polar.) (K,ιΦ=> Broad program to complete, several reactions/channels/observables to measure

14 Investigate, in a systematic fashion, the x B,Q and t dependences of a series of exclusive reactions e p e p ƒ e N (± ΜΙΗΙϑ Ι Φ e N ( ΜΙΗΙϑ Ι Φ e α ( ΜΙΗΙϑ Φ e (ιιπφ K In the kinematical regions : W>.5 GeV, Q >.5 GeV,.00<x B <.7 (essentially an unexplored domain) 3 key channels : e p e p ±= Η ϑ e p e n Η e p e p ƒ

15 GPD s in vector meson production

16 E665 ZEUS Q =6 GeV Q =9 GeV NMC ƒ* Q =7 GeV GLUON EXC. ± p p Q ξxg ( ) ζ 6 x W Brodsky et al. 994 Frankfurt et al. 996 GLUON CTEQ3L DISTR.

17 Vanderhaeghen, Guichon, Guidal : PRL 80(998) 5064 QUARK EXC. ƒ* ± p p

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19 γ * + p ρ 0 L + p σ L ( µb ) Cornell data Q in GeV

20 GPD s in pseudo-scalar meson production

21 eη p e Η nη Η contributions for ====production : + ƒ * L + ƒ * L + PV : PS : p PV : ~ H α=q(x) G A (t) n Spin distribution of quarks in nucleon Εαq(x)) PS : H ~ ~ H ~ Meson cloud,, pion distribution ~ E ~ E ~ ~ E (x) G P (t) t-m

22 Mankiewicz,, Piller & Radyushkin (998) : t=t min PS PV t=.4 PS PV x. B PS+PV PV CEBAF

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25 GPD s in photon production

26 l + p l + γ p d σ / dq lab dx B dω M (nb/gev sr) COMPASS Q =.5 GeV, x B = 0.3 HERMES JLab ELFE γ JLab BH 0 - E µ = 00 GeV E e = 7 GeV E e = GeV E e = 6 GeV Θ lab (deg)

27 dσ/dq /dx/dt/dφ, nb GeV/c -4 str t, (GeV/c)

28 Single spin asymmetries beam helicity asymmetry in DVCS transverse spin asymmetry

29 (σ -σ )/(σ +σ ) φ, degree -

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32 GPDs modelling Most simplistic toy ansatz : H q (x,,t)~q(x)f (t) ~ H q (x,,t)~αq(x)g A (t) (Vanderhaeghen, Guichon, Guidal) With q and αq of (MRS( MRS) Satisfies relations with DIS and first sum rules With dependence : (Radyushkin) H q (x,,t)~ dϒ d Εxϑϒϑ ΦF q ( ΙϒΙt) With : F q ( Ιϒ,t)~q b (ϒ) χε Ιϒ) F (t) x> = =: x< : p p p p 0 z 0 z

33 l + p l + p + ρ 0 L E µ = 00 GeV, Q =.5 GeV (nb / GeV sr ) x B = 0. x B = 0.3 x B = 0.5 lab lab lab d σ / dk e dωe dωm lab Θ M (deg) Θ M lab (deg) lab Θ M (deg)

34 SSA = (σ - σ ) / (σ +σ ) e - + p e - + p + γ E e = 6 GeV Q =.5 GeV x B = 0.35 t = GeV b val =.0, b sea =.0 b val =.0, b sea =.0 b val = 0.5, b sea = 0.5 b val =.0, b sea =.0 ξ indep Φ (deg)

35 «D-term» (Polyakov et al.) H(x, Ιt)~(H DD (x, )+D(x, ))F(t) p p Contributes only to the unpolarized GPDs ( H, E, i.e. only vector mesons ) Contributes only to isoscalar channel (i.e., only neutral vector mesons) Contributes only for - <x< It is purely real

36 H(x,ξ, ) 4 ξ = 0.3 Τ = x

37 dσ L /dt (µb/gev ) 0 dσ L /dt (µb/gev ) t (GeV ) 0 3 -t (GeV ) dσ L /dt (µb/gev ) 0 dσ L /dt (µb/gev ) t (GeV ) 0 3 -t (GeV )

38 Theoretical Motivations : Access to fundamental quantities of the structure of the nucleon : GPDs (f (x), g (x), F (t), G (t), χ(z), pion cloud, ) A Experimental program : L/T separations feasible up to (CLAS35): ± Μ, + : Q ~ 6 GeV Unseparated cross sections : ± Μ, +,ƒ : Q ~ 8 GeV Beam & Target asymmetries : ƒ, + : Q ~ 4-5 GeV

39 Look for signatures of scaling regime : Scaling of d L,T /dt ±/, + / 0, 0 / = Εx B, t dependences) «Stability» of asymmetries When scaling regime reached : Sensitivity of observables to GPDs models Model-independent deconvolution procedure needs to be worked out particular goal : J q +/- α J q If no scaling regime reached : Understand preasymptotic effects Higher twists, k effects,

40 JLab at GeV With appropriate equipment Can measure the Generalized Parton Distributions And provide Fundamentally new insight in the Nature of Elementary Matter

41 BACKUP TRANSPARENCIES

42 - Ν (H(x, Ι Ιt=0)+ t=0)+e(x, (x,,t=0))xdx=j /=J quark +Jgluon J =/ απηα ΗαL z quark quark απ ΠΜΒ e Η=p p e + p+ ±= gives access to αlz

43 SCALING Cross sections estimates : - Vanderhaeghen, Guichon & Guidal Guidal (998) - PS PV Vector mesons : ~ unpolarized. OFPDs PS mesons : ~ polarized OFPDs

44 Existing data Bebek (78) PS+PV PV Leading order calculation - Vanderhaeghen, Guichon & Guidal (999) -

45 DEEP INELASTIC (INCLUSIVE) ( e f, f ( ) ) ƒ ( ) e q ' Q Ζ( e ϑe) x B Q Ζ ( pq. ) (, τ ) E e ' e ' d Af Q xbf B Q x (, ) Η (, B ) dq dx B A A g Bjorken scaling (Q > GeV ) ; pointlike objects f x f : spin / objects B ' ( xb ) Η B g ( x ' B / momentum carried by quarks ( f( x) Ζ e q q( x)) q Bjorken Sum Rule : ( g ( x) g ( xdx )) g p n B ϑ B BΖ 6 g /4 spin carried by quarks ) ( g( x) Ζ e q αq( x)) q A V

46 p e DEEP INELASTIC ƒ e ƒι Ι Ι±Ι ΙΚΚΚ Final state constrained : = p (EXCLUSIVE) New generation of machines : - high energy - high duty cycle + spectrometers : - large acceptance - high resolution e e ƒι Ι Ι±Ι ΙΚΚΚ ƒ t x ~~ p H,E,H,E p accessible now! Ζ xx B ϑ B d dq dx B dt ( ah ( x,, t) Η be( x,, t) ~ ~ Η ch ( x,, t) Η de ( x,, t))

47 OFPDs parametrisation Vanderhaeghen, Guichon, Guidal (998) H ( x,, t) Ζ q( x) F ( t) ~ G ( t) H ( x,, t) Ζ αq( x) With q and αq of (MRS( MRS) Satisfies relations with DIS and first sum rules Dependence in A g A x+ x- p p - 0 -} qq _ qq } qq x 0 z 0 z

48 LEARN ABOUT PREASYMPTOTIC EFFECTS Leading Order : Jakob, Kroll, Raulfs (996) Musatov, Radyushkin (997) + k dependence («Fermi motion» of quarks in hadron) Sum. Leading Order : Soft. «Soft» contribution : L.O. L.O.+ k Stefanis, Schroers, Kim (999)

49 ƒ L * ϑο FACTORISATION «HARD«HARD»-«SOFT» - Collins,, Frankfurt & Strikman (997) - t T H o o =Ι± z p- M x p + p ~ ~ H,E,H,E p Q >> t << M 4 χ( z) Ζ ( ϑie4 s ) dz 9 Q z H L Scaling dx Η ϑ x ϑ Η i x Η ϑ i Η ƒ Η α x,, t) N N Η E( x,, t) Ni N Η Η P MP Valid for all mesons Factorization for longitudinal photons only ( d dt Ζ 6 ( s ϑ M ) M Q 6

50 T H AT LEADING ORDER ƒ L * T H = Wave functions : o Ε±=Φ=Ω o Ε =Φ=Ω ϑ Η p Λ ± Ζ p ± ƒ pλ ƒ Ζ p ƒ ϑ Η 5 ƒ 5 Trδ ƒ ƒ Η ϑ T H ƒ Η ƒ 5 δ δ ϑ ϑ Trδ ƒ ƒ ϑ ƒ ƒ Η Η ƒ 5 ƒ ƒ ϑ H,E 5 ϑ ƒ H ~, E ~ By selecting the meson, one selects the OFPDs : ϑ ϑ ƒ Ε kλ Η qλ Φ ƒ non-polarised polarised o Ε =Φ o Ε±=Φ L

51 ) ( 6 M s dt d ϑ Ζ M Scaling Scaling χ ϑ Ζ z z dz Q ie s ) ( 9 4 ) 4 ( ϑ ϑ Η Η Η ϑ i x i x dx α Η Η Η Η Η N MP Ni t x E N P N t x H ),, ( ),, ( ƒ M z -( (-z) z) ) ( 6 ) ( z z f z ϑ Ζ χ ) ( * 0 ƒ ƒ Wave functions Wave functions : χ=== χ=== χ=== χ=== χ=== χ=== χ=== χ===(z) (z) z 0 (from from ) Ζ f from from Η Η ) ( ) ( 6 ) ( z z f z ϑ Ζ χ ± ± Ζ 0.53 ± f from from ϑ Η e e 0 ± ) (

52 χ (z) Pion wave function deduced from F 0 * ( Q «Leading order pqcd» diagram : Η ϑ Η ϑ 0 e e e e : ƒ * ƒ ƒ ƒ -(-z)p zp χ ) p F ( Q ) Ζ Q 0 * ƒ ƒ f 5 3 ASY C-Z χ===(z) ASY 0 χ===(z) C-Z z Jakob, Kroll, Raulfs (996) Musatov, Radyushkin (997) 0 z

53 e Η p e Η pη( ±, ) (E98 (E98-07) Identification of : ƒ Η p pη ±, ) L ( L L By analysis of (±, )( decay angular distribution : ±==, === + SCHC : ƒ=== L L L Lever arm at CEBAF (6 GeV) 3 4

54 (MRS) xs(x)=x(u+d+s) -mer- xu (x) v xd (x) v xαu (x) v xαd (x) v

55 H q (x,ξ,t,q,q ) but only ξ, t and Q accessible experimentally ξ= x B t=(p-p ) -x B / Q =(e-e ) γ ξ x t ~~ H,E,H,E γ,μ,... p p dσ dq dx B dt A ~ H q (x,ξ,t,q ) x-ξ+iε - - +C H q (x,ξ,t,q ) x-ξ+iε dx +B E(x,ξ,t,Q q ) x-ξ+iε dx+d E(x,ξ,t,Q q ) x-ξ+iε dx ~ ~ dx - - x : mute variable Deconvolution needed!

56 Elastic Form Factors F () t = e q H q ( ξ, x, t) dx q F () t = e q E q ( ξ, x, t) dx q Wide Angle Compton Scattering R V () t e = q H q ( ξ, x, t) d x x q R A () t e = q E q ( ξ, x, t) d x x q Resonance Form Factors ( N ) G * ( 3) M () t = eq H q M ( ξ, x, t) dx q ( 3) H q M E ( 3)q = = E q p q E n G * ( 3) E () t = eq H q E ( ξ, x, t) dx q G * ( 3) C () t = eq H q C ( ξ, x, t) dx q

57 Exclusive reactions at higher momentum transfers. (Generalized Parton Distributions) hard perturbative kernel soft physics H q ( x, ξ, t) H q, ( x, ξ, t)... High W (> GeV), High Q, Low t ρωπηk,,,, meson production virtual Compton scattering Connection to DIS H q ( x, 00, ) qx ( ) q + q H q ( x, 00, ) q( x) q q DIS High t baryon and meson form-factors H q ( x, ξ, t) GM, G E, A, C H q ( x, ξ, t) GA... Wide angle Compton scattering H q ( x, ξ, t) -- R x... Paul Stoler, TJNAF GeV

58 Proton Dirac Form Factor F () t F D t~5 GeV Theory: A. Radyushkin Data: SLAC t (GeV ) Soft wave function: Ψ( x, k ) Φ( x)e k xxλ = Generalized Parton Distribution: H q ( ξ, x, t) f ( x)e xt 4xλ = Form Factor: F () t = e q H q ( ξ, x, t) dx q 0 Transverse momentum: λ 0.7 GeV k u ( 90 MeV) k d ( 50 MeV) Add hard correlations: H q ( ξ, x, t) = f ( x) e xt 4xλ ( α s π) n + c n n t n exponential (soft) power law (hard)

59 Modeling Parton Spin-Flip Distributions - k q (x) p p µg E GM k q ( x) = x( x)f q ( x) k q ( x) = x ( x)f q ( x) k q ( x) = ( x)f q ( x) JLab 99 Theory: A. Afanasev G E p Q p = F M F G M = F + F F () t = e q H q ( ξ, x', t) dx q F () t = e q E q ( ξ, x', t) dx q H q ( ξ, x', t) = e q f q ( x' )g soft ( x', t) E q ( ξ, x, t) = e q k q ( x' )g soft ( x', t) g soft ( x', t) = ( x' )t exp πxλ k x =x-

60 Transverse Momentum and Spin Distributions J q () t = -- [ A q () t + B q ()] t q A q () t = xh ( ξ, x, t) dx B q () t = xe q ( ξ, x, t) dx helicity non-flip helicity flip DIS: Exclusive: H q ( ξ, x, 0) = e q f q ( x) H q ( ξ, x, t) = e q f q ( x, t) x k t k H q, E q, H q, Ẽ q GPD Paul Stoler, TJNAF GeV