A glimpse of gluons through deeply virtual Compton scattering

Transcription

1 A glimpse of gluons through deeply virtual Compton scattering M. Defurne On behalf of the DVCS Hall A collaboration CEA Saclay - IRFU/SPhN June 1 st 017 June 1 st / 7

2 The nucleon: a formidable lab for QCD The nucleon is a dynamical object made of quarks and gluons. This dynamics is ruled by the strong interaction. A perturbative approach from first principles to unravel this dynamics is impossible due to the large size of the strong coupling constant. Although non-perturbative approaches (DSE, lattice QCD) starts making progress, the experimental approach remains more convenient to get complex information about this dynamics. June 1 st 017 / 7

3 A set of distributions encoding the nucleon structure June 1 st / 7

4 The deep exclusive processes By measuring the cross section of deep exclusive processes, we get insights about the GPDs. e e 1 The electron interacts with the proton by exchanging a hard virtual photon. The proton emits a particle (γ, π 0, ρ,...) p p The link between these diagrams and the GPDs is guaranted by the factorization. June 1 st / 7

5 Factorization and GPDs Twist Twist 3 Hard kernel Hard kernel Nucleon medium Nucleon medium Hard kernel Nucleon medium GPD H, E,... The amplitudes at twist-(n + 1) are suppressed by a factor 1 Q with respect to the twist-n amplitudes, with Q the virtuality of the photon. June 1 st / 7

6 DVCS and GPDs k q k x+ ξ x-ξ H, H ~ (x, ξ, t) E, E ~ (x, ξ, t) p p q Q = q = (k k ). x B = Q p q x longitudinal momentum fraction carried by the active quark. x B x B ξ transfer. the longitudinal momentum t = (p p ) squared momentum transfer to the nucleon. The GPDs enter the DVCS amplitude through a complex integral. This integral is called a Compton form factor (CFF). H(ξ, t) = 1 1 ( H(x, ξ, t) 1 ξ x iɛ 1 ξ + x iɛ ) dx. June 1 st / 7

7 Photon electroproduction and GPDs Experimentally we measure the cross section of the process ep epγ. d 4 σ(λ, ±e) dq dx B dtdφ = d [ σ 0 π T BH dq dx B e 6 + with λ the helicity of the electron. ] T DVCS I, June 1 st / 7

8 A parameterization of cross section We can partially unfold the contributions, studying the φ-dependence. T BH = { T DVCS e 6 = y Q c0 DVCS + I = e 6 n=0 cbh n cos(nφ) xb ty (1 + ɛ ) P 1 (φ)p (φ) n=1 { e 6 x B y 3 c0 I + P 1 (φ)p (φ)t KNOWN! [ ] } cn DVCS cos(nφ) + λs1 DVCS sin(nφ) 3 n=1 [ ] } cn I cos(nφ) + λsn I sin(nφ). Defurne On behalf of the DVCS Hall A collaboration GPDs (CEA through Saclay DVCS - IRFU/SPhN) June 1 st / 7

9 A parameterization of cross section The CFFs are encapsulated in c n and s n, offering a parameterization of the cross section. In the leading twist approximation for unpolarized target: c DVCS 0 C DVCS (F, F ) = 4(1 x B )HH + (1) c I 1 Re CI (F) = F 1 ReH + ξ(f 1 + F ) Re H t 4M F ReE, s I 1 Im CI (F) = F 1 ImH + ξ(f 1 + F ) Im H t 4M F ImE, By studying the φ-dependence of the observables, we can extract the CFFs. However there are too many CFFs to extract them all... We have to make some assumptions. Mueller D., Belitsky A.V., Phys.Rev.D.8 (010) June 1 st / 7

10 A fit global to disentangle all the CFFs A lot of data have been collected in different kinematical regions. Kumericki and Muller performed a global fit of CFFs at leading-twist and leading-order (KM10a). σ LU σ UL sinφ Im sinφ Im { F 1 H + ξ(f 1 + F ) H { F 1 H + ξ(f1 + F ) t } 4M F E ( H + x B E ), () t } 4M F Ẽ, the imaginary part of CFFs are given by beam or target spin asymmetries. the real parts are built using dispersion relations with the imaginary parts. This fit was able to reproduce all the DVCS observables collected in the other facilities and CLAS. What about the Hall A experiments in 004 and 010? June 1 st / 7

11 The experimental setup We want to study ep epγ: The accelerator provided: 80% longitudinally polarized electron beam on a 15 cm-long LH target, with a maximal beam current of 00 µa (I<4 µa), up to 6 GeV (now 1 GeV). June 1 st / 7

12 The experimental setup We want to study ep epγ: In the Hall A, The scattered electron is detected by a High Resolution Spectrometer (HRS): We measure accurately xb and Q. The photon is detected by an electromagnetic calorimeter: The 4-momenta of the scattered electron and the photon gives t and φ. M. Defurne On behalf of the DVCS Hall A collaboration GPDs (CEA through Saclay DVCS - IRFU/SPhN) June 1st / 7

13 N M X <M cut = N ep epγ + N acc + N π0 1γ + N SIDIS N SIDIS cannot be subtracted and we need to cut low enough in missing mass to have: N SIDIS << N ep eγp The fraction of exclusive events lost with the cut is corrected through the Monte-Carlo simulation. Number of events φ (deg) June 1 st / 7

14 Here are the results for the 004 experiment! June 1 st / 7

15 Here are the results for the 004 experiment! June 1 st / 7

16 Kinematical power corrections needed for all bins! June 1 st / 7

17 Rosenbluth separation The φ-dependence is not enough to disentangle the contributions. Using the beam energy dependence, we can add constrains on the model (separation of DVCS and interference contribution) Setting E (GeV) Q (GeV ) x B W (GeV) 004-Kin Kin Kin Setting E (GeV) Q (GeV ) x B W (GeV) 010-Kin1 (3.355 ; 5.55) Kin (4.455 ; 5.55) Kin3 (4.455 ; 5.55) June 1 st / 7

18 M. Defurne Is there On behalf or not of the kinematical DVCS Hall A collaboration power GPDs corrections? (CEA through Saclay DVCS - IRFU/SPhN) June 1 st / 7 Before final results, let s compare While analyzing the 010 data, a new fit including the previous results has been produced Q =1.95 GeV, t=-0.18 GeV, E=5.55 GeV 0.1 Q =1.99 GeV, t=-0.3 GeV, E=5.55 GeV 0.16 Q =1.99 GeV, t=-0.8 GeV, E=5.55 GeV Φ (deg) Φ (deg) Φ (deg) Q =1.99 GeV, t=-0.33 GeV, E=5.55 GeV Bethe-Heitler KM15 predictions Prediction Φ (deg) Fit of the cross section 4 d σ 4 (nb.gev ) dq dx B dtdφ

19 Where do the kinematical power corrections come from? Belitsky, Muller and Ji decomposed the DVCS amplitude in helicity amplitude, using the lab frame as reference frame. In the BMJ formalism, the cross section is parametrized by a set of CFFs: { F µν H µν, E µν, H } µν, Ẽµν (3) where µ (ν) is the helicity of the virtual (real) photon. Therefore we can distinguish three cases: F ++ are the helicity-conserved CFFs. They are the regular leading-twist CFFs which describes diagram for which virtual and real photon have the same helicity. F 0+ are the longitudinal-to-transverse helicity flip CFFs. They are twist-3 CFFs related to the contribution of the longitudinal polarization of the virtual photon. F + are the transverse-to-transverse helicity flip CFFs. At leading-order, these CFFs are twist-4. But at NLO order, these CFFs involves the twist- gluon transversity GPDs. June 1 st / 7

20 Where do the kinematical power corrections come from? In the BMP formalism, the reference frame is taken such as both photons have purely longitudinal momentum. This choice makes easier the inclusion of kinematically suppressed terms (in t/q or M /Q ). In the BMP formalism, the cross section is parametrized by a set of CFFs: } F µν {H µν, E µν, H µν, Ẽ µν (4) where µ (ν) is the helicity of the virtual (real) photon. Therefore we can distinguish three cases: F ++ are the helicity-conserved CFFs. They are twist- CFFs. F 0+ are the longitudinal-to-transverse helicity flip CFFs. They are twist-3 CFFs. F + are the transverse-to-transverse helicity flip CFFs. At LO, these CFFs are twist-4. At NLO, these CFFs involves the gluon transversity GPDs. June 1 st / 7

21 BMP... BMJ... which difference? But let s stay at leading-order. The BMP CFFs are not the same as the BMJ CFFs. The BMP CFFs are more complex terms. As an example, H ++, we have: H ++ = T 0 H, (5) H ++ = T 0 H + t Q [ 1 T 0 T 1 ξd ξ T ] H + t Q ξ ξ T (H + E). (6) We can go from BMP to BMJ CFFs by making the following replacement: F ++ = F ++ + χ [F ++ + F + ] χ 0 F 0+, (7) F + = F + + χ [F ++ + F + ] χ 0 F 0+, (8) F 0+ = (1 + χ)f 0+ + χ 0 [F ++ + F + ], (9) with: χ 0 t /Q and χ t /Q. The leading-twist assumption gives different results between BMP and BMJ. June 1 st / 7

22 Differences in the LT-LO assumption: BMJ Assuming leading-twist and LO in BMJ, we have F + = 0 and F 0+ = 0. It is important when regarding the DVCS amplitude. We have: c VCS 0,unp { } c1,unp VCS s1,unp VCS c VCS,unp which reduces to: = y + y + ɛ y C VCS 1 + ɛ unp (F ±+, F±+) y ɛ y 4 C VCS 1 + ɛ unp (F 0+, F0+), = 4 1 y ɛ y ɛ { y λy 1 + ɛ } { } Re Im (10) C VCS ( unp F0+ F ++, F + ),(11) = 8 1 y ɛ y 4 Re C VCS 1 + ɛ unp (F +, F++). (1) 0,unp = y + y + ɛ y 1 + ɛ C VCS unp (F ++, F++) (13) c VCS The DVCS amplitude is φ-independent with a single beam-energy dependence. June 1 st / 7

23 Differences in the LT-LO assumption: BMP Assuming leading-twist and LO in BMP, we have F + = 0 and F 0+ = 0. It is important when regarding the DVCS amplitude. c VCS 0,unp { } c1,unp VCS s1,unp VCS c VCS,unp F ++ = ( 1 + χ ) F++, (14) χ F + = F ++, (15) F 0+ = χ 0 F ++, (16) = y + y + ɛ y C VCS 1 + ɛ unp (F ±+, F±+) y ɛ y 4 C VCS 1 + ɛ unp (F 0+, F0+), = 4 1 y ɛ y ɛ { y λy 1 + ɛ } { } Re Im (17) C VCS ( unp F0+ F ++, F + ),(18) = 8 1 y ɛ y 4 Re C VCS 1 + ɛ unp (F +, F++). (19) The DVCS amplitude is no longer φ-independent with multiple beam-energy dependences. June 1 st 017 / 7

24 chi0(1.5,0.36,-x) A complicated Rosenbluth separation By changing the beam energy, we also change the polarization of the virtual photon. χ Q = 1.5 GeV Q = 1.75 GeV Q =.3 GeV Q = 4 GeV t (GeV) We must take them into account. Let s fit the real and imaginary parts of H ++ E ++ H ++ Ẽ ++ : simultaneously on unpolarized and polarized cross sections, simultaneously on the two beam energies, simultaneously for the three Q -values (but I neglect the Q-evolution), June 1 st / 7

25 A glimpse of gluons through DVCS 4 nb/gev 0. 4 d σ 4 σ Fit LT/LO Fit HT KM nb/gev Φ (deg) Φ (deg) Figure: Q =1.75 GeV, -t=0.3 GeV. E=4.445 GeV (left) and E=5.55 GeV (right) LT/LO: H ++, E ++, H ++, Ẽ ++. HT: H ++, H ++, H 0+, H 0+. NLO: H ++, H ++, H +, H +. Equally good fit between the HT and NLO scenario. M. Defurne et al., Hall A collaboration, arxiv: June 1 st / 7

26 4 4 Separation of DVCS and interference Despite an equally good fit, slight differences appear when separating the interference and DVCS term. nb/gev nb/gev NLO-DVCS HT-DVCS NLO-Interference HT-Interference Φ (deg) Φ (deg) In the HT scenario, the beam helicity dependent cross section is not a pure interference term, as it is usually assumed in most phenomenological analyses. M. Defurne et al., Hall A collaboration, arxiv: June 1 st / 7

27 Conclusion High statistcal precision data are essential to get the 3D picture of the nucleon. Kinematical power corrections must be taken into account. It seems that there is higher-twist and/or Next-to-Leading order contributions in the JLab-6GeV data. We can hope these contributions could disappear at 1 GeV although gluons and 3-parton correlations can teach us so much about confinement. A rich program concerning DVCS at JLab with two Rosenbluth separation experiments in Hall B and Hall C And cannot wait to see the first results from Hall A at 1 GeV. June 1 st / 7

28 Thank you! June 1 st / 7

29 The experimental setup We want to study ep epγ: Hall A Hadron Detector DAQ Electronics Pion Rejector S Rear FPP Chambers Carbon Analyzer Front FPP Chambers S1 Gas Cherenkov VDC m-drive/martz/graphics/3dart/halla/newfolder/elecarm.ai jm 8/11/00 VDC support frame S0 Aerogel Cherenkov The High Resolution spectrometer detects and characterizes the scattered electron: δp 4 and solid angle ' 6 msr. p '.10 It allows an accurate measurement of Q and xb. Scintillators and Čerenkov detector were part of the trigger. M. Defurne On behalf of the DVCS Hall A collaboration GPDs (CEA through Saclay DVCS - IRFU/SPhN) June 1st / 7

30 N M X <M cut [noframenumbering] = N ep epγ + N acc + N π0 1γ + N SIDIS Accidentals are time-independent. Estimated by studying events outside of the coincidence window. Accidentals are mostly located around φ = 0. We require a missing mass higher than 0.5 GeV to reduce the statistical uncertainty from the subtraction. Number of events ) Mep->eγX (GeV June 1 st / 7

31 N M X <M cut = N ep epγ + N acc + N π0 1γ + N SIDIS Pion rest frame Direction of the boost Direction of the boost Laboratory frame The kinetic energy of the π 0 is shared between the two photons depending on their direction with respect to the π 0 momentum. We just need to evaluate the phase space of decay contributing to the contamination. Principle: For each detected π 0, generate a large number of decays to estimate the contamination. Detect the two photons. Detect only one of the two photons. Considered as exclusive photon events. June 1 st / 7

32 N M X <M cut = N ep epγ + N acc + N π0 1γ + N SIDIS Direction of the boost Direction of the boost The kinetic energy of the π 0 is shared between the two photons depending on their direction with respect to the π 0 momentum. We just need to evaluate the phase space of decay contributing to the contamination. Pion rest frame Laboratory frame Advantage: No need for a parameterization of π 0 cross section. Drawback: Depends on the ability to detect the photons. June 1 st / 7

33 The calorimeter resolution: A crucial effect The events of a specific t and φ bins are located in a specific area of the calorimeter. Figure: Left: φ-distribution of the events as a function of the photon position in the calorimeter. Right: t-distribution of the events as a function of the photon position in the calorimeter. June 1 st / 7

34 The calorimeter resolution: A crucial effect From one edge of the calorimeter to the other, the energy resolution is not the same (φ = 0 in red et φ = 180 in blue) M (GeV ) ep e γ X µ (GeV ) σ (GeV ) Beam-side (red) side (blue) sum (red+blue) Table: Mean value µ and standard deviation σ of a gaussian fitted on the squared missing mass distributions. Assuming a uniform resolution and calibration, we would have induced a -15% shift of the cross section at 0 and +5% at Defurne On behalf of the DVCS Hall A collaboration GPDs (CEA through Saclay DVCS - IRFU/SPhN) June 1 st / 7

35 ep eγx The calorimeter resolution: A crucial effect I have developed a calibration/smearing/fit method for the Monte-Carlo calorimeter q x q x q y q z gaus(µ, σ) q y q z, E E which reproduces locally the resolution M (GeV ) June 1 st / 7