Real and virtual Compton scattering experiments at MAMI and Jefferson Lab. S. Širca, U. of Ljubljana, Slovenia Bled 8-14 July 2013

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1 Real and virtual Compton scattering experiments at MAMI and Jefferson Lab S. Širca, U. of Ljubljana, Slovenia Bled 8-14 July

2 Reminder: polarizability of atoms and molecules Neutral atom in external field E F = mω 2 x = e 0 E R p = e 0 x = e2 0 mω 2 E α atom ε 0 E α atom m 3 O(R 3 ) x 10 6 nm for E = 10 kv/cm E α proton < α atom x unmeasurably small for macroscopic E 2

3 Polarizability of proton A = ɛ 2ω e ikx A = ɛ 2ω eik x M T = e2 0 M ɛɛ + α ω 2 ɛɛ + β ω 2 (ɛ ˆk )(ɛ ˆk) Thomson α = α + e2 0 3M r 2 β = β para + β dia Nucleons have spin there are also (four) spin polarizabilities 3

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5 Measuring (static) nucleon polarizabilities straightforward: γ + p γ + p tag scattered electron, bremsstrahlung γ is almost real E e - E e - E 0 decades of experiments with MeV real-photons at Saskatoon (SAL), Brookhaven (LEGS), Mainz (A2), Bonn (TAPS) good precision for proton, poor for neutron 5

6 Proton static polarizabilities β (10-4 fm 3 ) Zieger MacGibbon global average 0 TAPS Sum Rule -2 Federspiel α (10-4 fm 3 ) α p = (12.0 ± 0.6) 10 4 fm 3 β p = ( ) α p + β p = (13.6 ± 1.0) Baldin s sum rule 6

7 Generalized polarizabilities nucleon exposed to static uniform electric field E electric polarization P i (r) = 4πα ij (r)e j is generated which is related to the density of the induced electric dipole moments α ij (r) = α L (r ) r i r j +α T (r ) (δ ij r i r j ) + 3 r i r j δ ij r 3 r [α L (r ) α T (r )] r 2 dr L vov, Scherer et al. AIP Conf Proc 768 (2005) 110 PRC 64 (2001)

8 Mapping out generalized polarizabilities map electric, magnetic,... polarizabilities as functions of Q 2 i.e. α E α E (Q 2 ), β M β M (Q 2 ), etc. need virtual photons: electro-production of photon (!) e + p e + p + γ electron-scattering with final photon identified by missing-mass technique there is plenty of background e γ e e p e p e = e + e + p p p p p B ethe-h eitler V CS Born V CS non-born 8

9 Theoretical tools to analyze VCS extractions of polarizabilities via cross-section calculations ( fits ) Low-energy theorem, LET (or LEX ) Guichon++ NPA 591 (1995) 606 Vanderhaeghen PLB 402 (1997) 243 yields VCS response (or structure) functions P LL P TT /ε and P LT linear combinations of polarizabilities works only below the pion production threshold Dispersion-relations analysis ( DR ) Pasquini++ EPJA 11 (2001) 185 Drechsel++ Phys Rep 378 (2003) 99 yields structure functions as well as polarizabilities α(q 2 ) and β(q 2 ) 9

10 Low-Energy Expansion (LEX) expansion to first power of outgoing photon momentum in CM d 5 σ = d 5 σ BH+B + ( Φq cm ) [ v LL (P LL P ) ] TT + v LT P LT + O ε d 5 σ = d 5 σ /dk lab dω lab dω γcm ( other options) ( ) q cm 2 d 5 σ BH+B contains no polarizability effect and is exactly calculable assuming that the proton elastic FFs are well known extract only linear combinations of generalized polarizabilities i.e. only two (combinations of) structure functions at one ε P LL P TT ε P LT = 4m p α Gp E = 2m p α (Q 2) ( α E Q 2) + [spin flipgps] qcm 2 Q 2 Gp E (Q 2) β M ( Q 2) + [spin flipgps] need additional assumptions on spin-flip GPs to extract α E and β M 10

11 Dispersion Relations (DR) dispersive integrals for non-born amplitudes πn part given by MAID γ N πn multipoles γ* γ π spin GPs are fixed scalar GPs have an unconstrained part and must be parameterized, typically in dipole forms, e.g. N α E (Q 2 ) α πn E (Q2 ) = α E(0) α πn E [ ] (0) Q2 Λ 2 α Λ 2 α and Λ 2 β extracted from experimental data 11

12 (Generalized) proton polarizabilities Results so far P LL -P TT /ε (GeV -2 ) P LT (GeV -2 ) RCS Bates MAMI JLab ChPT o(p 3 ) (ε = 0.645) DR (if one dipole) example Λ α = 0.7 GeV JLab RCS Bates MAMI JLab DR (if one dipole) example Λ β = 0.63 GeV LEX analysis direct DR fit JLab Q 2 (GeV 2 ) 12

13 (Generalized) proton polarizabilities Status Approved... up and running at Mainz 13

14 Wide-angle (real) Compton scattering (WACS) at 8 and 10 GeV NPS Collaboration proposal to JLab PAC40 (June 2013) D. J. Hamilton (U of Glasgow), S. Širca, B. Wojtsekhowski (JLab) Physics motivation Applicability of pqcd scaling (?) Handbag mechanism and GPDs Advances in soft collinear effective theory (SCET) Connection to elastic e-p scattering and DVCS Connection to 6 GeV results 14

15 WACS: physics motivation Compton scattering on proton in the wide-angle regime (s, t, u M 2 ) is a powerful and under-utilized probe of nucleon structure Elegantly simple: involves only real γ and ground-state proton in both initial and final state physics involved is similar to elastic e-p scattering or DVCS: EM response of the nucleon without complications from other hadrons It is, however, one of the least understood fundamental processes in the several-gev regime 15

16 WACS: reaction mechanism Many proposed over the years: Relat. constituent quark models pqcd (two-gluon exchange) Handbag mechanism (GPDs) Soft collinear effective theory WACS poses just as many questions: Does large t ensure dominance of short-distance physics? What factorization scheme is valid? Is it true that the WACS reaction proceeds through interaction of γ with individual q? What information on the structure of proton can be extracted from measurement of WACS FFs? Given the fact that pqcd is not expected to be valid at this kinematic scale, why are the scaling predictions so close to the observed values? P q q P xp q xp + t P q q q P P xp xp + t P 16

17 Factorization schemes in RCS Hard scale : s, t, and u large compared to m p or, equivalently, the transverse momentum transfer, p, is large the transition amplitude is expected to become factorized as a convolution of a perturbative hard scattering amplitude, which involves the coupling of the external photon to the active quarks, with an overlap of initial and final soft (nonperturbative) wave-functions, which describes the coupling of the active quarks to the proton: T if (s, t) = Ψ f K(s, t) Ψ i, where K(s, t) is the perturbative hard scattering amplitude and the Ψ s are the soft wave functions. Different factorization schemes for RCS are distinguished by the number of active constituents participating in the hard scattering subprocess. The handbag mechanism involves only one active constituent. The pqcd mechanism involves three. In any given kinematic regime, both mechanisms may contribute. At sufficiently high energy, the pqcd mechanism is expected to dominate, but the anticipated point of onset of this regime is not known. 17

18 Handbag mechanism and GPDs γp γp ep ep R V (t) = a e 2 a 1 1 dx x Ha (x, 0, t) F 1 (t) = a e a 1 1 dx H a (x, 0, t) R A (t) = a e 2 a 1 1 dx x sign(x) Ĥa (x, 0, t) G A (t) = a 1 1 dx sign(x) Ĥ a (x, 0, t) R T (t) = a 1 ea 2 1 dx x Ea (x, 0, t) F 2 (t) = a e a 1 1 dx E a (x, 0, t) e a is the charge of the active quark ξ = 0 (momentum absorbed by the quark is purely transverse) V, A, T form-factors for RCS Dirac, axial, Pauli form-factors for e-p x 1 moments of GPDs x 0 moments studying WACS form-factors can lead to constraints on GPDs at large t and x, which differ from EM form-factors due to 1/x and e 2 a Diehl, Kroll, arxiv:

19 RCS form-factors via GPDs Diehl/Kroll, arxiv: t 2 R V 10 2 dσ dt (γp γp) [pb/gev 2 ] t 2 R A 10 1 s = GeV t 2 R T t [GeV] 10 0 s = 20 GeV cos θ 19

20 Handbag mechanism and GPDs (cont d) The t = 0 limit of the GPDs yields the PDFs: H a (x, 0, 0) = q a (x), Ĥ a (x, 0, 0) = q a (x), E a (x, 0, 0) = 2Ja (x) x q a (x) total ang.mom. of quark flavor a (not directly measurable in DIS) Relation of RCS helicity amps to the FFs: M µ +,µ+(s, t) = 2πα [ T µ +,µ+(s, t)(r V (t) + R A (t)) + T µ,µ (s, t)(r V (t) R A (t)) ] t [ M µ,µ+(s, t) = 2πα Tµ m +,µ+(s, t) + T µ,µ (s, t) ] R T (t) R V ±R A describe response of proton to emission/re-absorption of quarks with helicity in the same/opposite direction wrt. proton helicity, and R T is directly related to proton helicity-flip amplitude. the spin-averaged cross-section factorizes into a product of Klein-Nishina (hard scattering from a single quark) and a sum of form-factors depending only on t: dσ /dt dσ KN /dt = f V [ R 2 V (t) + t ] 4m (t) + (1 f 2R2 T V )R 2 (t) A 20

21 Soft collinear effective theory (SCET) Kivel, Vanderhaeghen, JHEP 1304 (2013) Importance of WACS in understanding 2γ (TPE) effects in elastic e-p scattering Due to universality considerations, the FF describing TPE at high Q 2 can be determined from WACS cross-sections Try to extend the measurements of R(t) to higher s and t check validity of factorization in both WACS and TPE in elastic e-p scattering learn more about the soft physics describing the proton structure in the 12 GeV regime 21

22 Elastic e-p vs. WACS in SCET Kivel/Vanderhaeghen, arxiv: Factorization of TPE in elastic e-p scattering: Factorization of TPE in WACS: soft spect. soft spect. hard spect. 22

23 The JLab 6-GeV real Compton (RCS) era Experiment E (Hall A, 2002) Measured spin-averaged cross-sect over a broad kinematic range (6.8 < s < 11 GeV 2, 2 < t < 7 GeV 2 ) and polarization transfer K LL, K LT at s = 6.9 GeV 2, t = 4 GeV 2 Danagoulian++ PRL 98 (2007) Hamilton++ PRL 94 (2005) Experiment E (Hall C, 2008) Measured polarization observables K LL, K T T and P N at s = 8.0 GeV 2, t = 2.1 GeV 2 (to be submitted) 23

24 RCS 6-GeV highlights Factor of 1000 improvement (L γp ) over the last Cornell experiment Huge improvement in precision of cross-section measurements and first measurement of polarization observables in this kin. regime Danagoulian++ PRL 98 (2007)

25 RCS 6-GeV highlights (cont d) Factor of 1000 improvement (L γp ) over the last Cornell experiment Huge improvement in precision of cross-section measurements and first measurement of polarization observables in this kin. regime Evidence for factorization of the reaction mechanism and dominance of the handbag mechanism Danagoulian++ PRL 98 (2007)

26 RCS 6-GeV highlights (cont d) Factor of 1000 improvement (L γp ) over the last Cornell experiment Huge improvement in precision of cross-section measurements and first measurement of polarization observables in this kin. regime Evidence for factorization of the reaction mechanism and dominance of the handbag mechanism As in elastic e-p, polarization obs. in RCS added insight: strongly favor leading-quark mechanism (x 1) NB: some points did not satisfy the wide-angle condition (s, t, u M 2 ) due to small value of u Danagoulian++ PRL 98 (2007)

27 Real Compton scattering: the JLab 12-GeV era Proposal PR Measure 13 kinematic points Determine scaling power n at fixed θ cm and therefore dominant reaction mechanism Most important features Wide-angle condition (s, t, u M 2 ) satisfied in all settings Broad range in t extract RCS form-factor R(t) evidence for factorization constraints on GPDs at high x constraints on 2γ effects in e-p elastic scatt. at high Q < s < 21.0 GeV < t < 12.0 GeV < u < 15.3 GeV 2 27

28 WACS at 12 GeV: expected results dσ/dt [nb/gev 2 ] e-05 *1/10 *1/100 E s=4.8 s=6.8 s=8.9 s=10.9 s=10.9 Diehl/Kroll (DK) Kivel/Vanderhaeghen (KV) s=15.9 DK KV s=19.6 DK KV 1e-06 1e t [GeV 2 ] 28

29 WACS at 12 GeV: expected results 3 E s=8.9 E s=10.9 sqrt(σ DK /σ Klein-Nishina ) / F 1 (t) sqrt(σ KV /σ Klein-Nishina ) / F 1 (t) this proposal s=15.9 this proposal s= R(t)/F 1 (t) t [GeV 2 ] 29

30 JLab (Hall C) Status BUT... deferred by PAC40 30