Deeply Virtual Exclusive Processes with Charm
DDecember 11, 2018 20:24 WSPC - Proceedings Trim Size: 9in x 6in charm˙exc˙2 DEEPLY VIRTUAL EXCLUSIVE PROCESSES WITHCHARM
S. LIUTI University of Virginia - Physics Department382, McCormick Rd., Charlottesville, Virginia 22904 - USA E-mail: [email protected]
G.R. GOLDSTEIN Department of Physics and AstronomyTufts University, Medford, MA 02155 - USA. E-mail: [email protected]
We propose to investigate a largely unexplored sector that is unique to the for-mulation of hard exclusive processes in terms of GPDs, namely the electropro-duction of strange and charmed mesons in the kinematical ranges of JeffersonLab’s 12 GeV upgrade, and of the proposed Electron Ion Collider (EIC). Inthis contribution we focus on charmed meson production that is unique to theEIC. Exclusive strange and charmed meson production provides new insightsin the connection of the quark/gluon degrees of freedom with the meson-baryondescription, both in the unpolarized and polarized sectors. However, as partic-ularly evident in polarized scattering, the underlying mechanisms are still farfrom being fully understood. We present an approach in terms of generalizedparton distributions. As an application, we show that through exclusive elec-troproduction of pseudoscalar charmed mesons one can uniquely single out thenon-perturbative charmed component in the nucleon structure function.
1. Introduction
Many experiments have been conducted to determine the charm contentof the proton. Different types of hadronic reactions allow us in principle toaccess the charm quark distributions in a varied set of kinematical ranges,from hadron scattering at the Tevatron to inclusive and semi-inclusive lep-toproduction at colliders (HERA) and in various fixed target experiments.Two main competing interpretations can be given on the way charmgets excited. Either c − ¯ c pairs are produced through a Perturbative QCD(PQCD) mechanism such as gluon-gluon or photon-gluon fusion, when thescale of the probe, Q ≥ m c , m c being the charm quark mass, or such a r X i v : . [ h e p - ph ] S e p ecember 11, 2018 20:24 WSPC - Proceedings Trim Size: 9in x 6in charm˙exc˙2 pairs exist in the nucleon as a so-called ”Intrinsic Charm” (IC) component,with a non-negligible probability density at Q = m c , due to some under-lying non-perturbative mechanism. Predictions from the two mechanismsat Q > m c , could differ in an observable way. The problem of disentan-gling them lies, however, unsolved to date. Figure 1 illustrates the ratherlarge impact of non-perturbative charm contributions on the state of theart PDF parametrizations (dot-dashed curves) compared to the radiativelygenerated ones (shaded area) (Ref.1). Fig. 1. Illustration of the status of present studies of the charmed quarks parton dis-tribution. The arrow, and the visibly smaller error band, indicate the region in Bjorken x were most experiments are concentrated. The dashed and dot-dashed curves wereobtained including different models of IC at the scale µ = 100 GeV (adapted from 1). It has now become particularly pressing to study the heavy quark com-ponents of the nucleon because of the advent of the LHC. The heavy quarkcomponents will be key in the study of QCD matrix elements in the un-precedented multi-TeV CM energy regimes accessible at the LHC. At thesame time, as the LHC opens new horizons for studies of physics beyondthe Standard Model, many “candidate theories” will provide similar sig-natures of a departure from SM predictions. For these types of precisionmeasurements it will be necessary to provide accurately determined QCDinputs.The analyses in Ref.2 have shown how the inclusion of IC could modifythe outcome of global PDF analyses. However, the situation is not clear-cut. PDF analyses do not provide direct evidence that IC exists, but can ecember 11, 2018 20:24 WSPC - Proceedings Trim Size: 9in x 6in charm˙exc˙2 be considered as indications in that direction.In this contribution we make the point that in order to substantiatethese findings it is important to identify new observables that would allowus to extend the studies to parton distribution size observables such asin Deeply Virtual Meson Production (DVMP), and to spin correlations.We present preliminary results involving the following electroproductionexclusive processes (Fig.2):(1) γ ∗ p → J/ψ p (cid:48) ,(2) γ ∗ p → D D p (cid:48) ,(3) γ ∗ p → D Λ c ,(4) γ ∗ p → η C p (cid:48) .As we explain on what follows, these processes necessitate: i) high lumi-nosity because they are exclusive; ii) high enough Q , in order to producethe various charmed mesons, and iii) a wide kinematical range in Bjorken x (see discussion relative to Fig.1). Their ideal realization would be at anElectron Ion Collider (EIC) that could guarantee high luminosity conditionsalso at relatively large x . Fig. 2. Deeply Virtual Charmed Meson Production (DVCMP). All produced mesonsare unique probes of the IC charm content. ecember 11, 2018 20:24 WSPC - Proceedings Trim Size: 9in x 6in charm˙exc˙2
2. Windows into Heavy Flavor Production at the EIC
QCD factorization for exclusive meson electroproduction was proven ini-tially in Ref.3. Factorization arguments can be extended to the productionof charmed mesons, thus allowing us to write the various contributionsto the cross section, originating from the amplitudes for different beamand target spin configurations, as a convolution over the longitudinal mo-mentum fraction X of the hard scattering process with the quark-protonamplitudes. Using the approach in Ref.4 (see Section 3), we can describethe exclusive production of pseudoscalar charmed mesons mainly in termsof chiral-odd Generalized Parton Distributions (GPDs) for the u, d and c quarks, F qT ≡ { H T E T , (cid:101) H T , (cid:101) E T } , with q = u, d, c . a These by definitiondo not couple to gluons, or they evolve perturbatively similarly to the fla-vor non singlet distributions, Refs.5–7. All GPDs involved in pseudoscalarcharmed mesons electroproduction are therefore of the ”intrinsic” kind sincethey cannot evolve from gluons. By finding observables that can isolate thecharmed GPDs, one can therefore uniquely gauge the size of the IC contri-bution.A somewhat similar perspective was presented in Ref.8 where it wasshown that the IC content of the proton can be studied by measuring asym-metries in inclusive heavy quark jet production, ep → e (cid:48) QX ( Q ). In fact,IC does not contribute at all to azimuthal asymmetries of the cos (2 φ ) form σ TT σ T + (cid:15)σ L . Hence the reduction at high x Bj of large asymmetry from theirperturbative gluon model signals the intrinsic charm contribution. This,however is dependent on their model and requires measuring an asymme-try that is reduced from the gluon contribution. While these studies presentyet another opportunity for studying the multifaceted and still elusive con-nections between semi-inclusive and exclusive processes, our approach is amore stringent test for IC since the suggested exclusive production processesoccur solely via the IC channel.The hard scattering amplitudes for the four processes above are re-spectively (1) γ ∗ c (¯ c ) → J/ψ c (¯ c ), (2) γ ∗ c → D u , (3) γ ∗ ¯ c → D (¯ u ) and γ ∗ u → D c , (4) γ ∗ c (¯ c ) → η C c (¯ c ) (Fig.2). All of these involve the charmmass scale in some way, along with a heavy meson distribution amplitude.For D and ¯ D creation in the beam direction, the distribution or wavefunc-tion will be of the same order for each. The J/ Ψ will be more difficultto produce in the hard process, aside from its sizable diffractive produc- a A small contribution from the chiral even GPD is in principle also present, that wedisregard here. ecember 11, 2018 20:24 WSPC - Proceedings Trim Size: 9in x 6in charm˙exc˙2 tion, which occurs through the virtual photon dissociation into c ¯ c . Thepair scatter diffractively and recombine as the J/ Ψ. The diffractive scatter-ing is implemented through two gluon exchange, so that the overall processwould involve gluon-nucleon GPDs rather than intrinsic charm, at least inthe diffractive region.Amplitudes (1) and (4) could be smaller than (2) and (3) for severalreasons. From the GPD perspective, the soft contribution is given only bythe charm GPD, F c that, based on the constraint from inclusive scattering– giving the forward limit of GPDs– we expect to be a few per cent ofthe light quarks’ GPDs. Moreover process (4) requires the detection ofan η c meson, which seems to be a forbidding task even in a future EIC.Process (2) does not seem the best way to access GPDs because of theexotic D p final hadronic configuration. Finally, process (3) can occur inthe two configurations described in Fig.1c and Fig.1d. By assuming SU (4)symmetry, these are proportional to linear combinations of the non-singletGPDs H c , H u and H d . So the mechanism involving IC is dominated byscattering off the light flavor quarks, at least before symmetry breakingis implemented. However, by detecting different baryons in the final state,that is considering the reactions: γ ∗ p → D Λ + c ⇒ (cid:0) F uT − F dT + F cT (cid:1) / √ γ ∗ p → D Σ + c ⇒ (cid:0) F dT − F cT (cid:1) / √ γ ∗ n → D − Σ ++ c ⇒ F dT − F cT ,one can extract the charmed GPDs, F cT .We related the GPDs that involve charmed quarks or charmed hadronsto their uncharmed counterparts through flavor SU(4). In the GPDs involv-ing open charm production, process (3), there are the off-diagonal ampli-tudes for N → u ( d ) : c → Λ + C , Σ + C (Σ ++ C ). The spin hadrons belong tothe 20-plet. To simplify the determination of the SU(4) Clebsch-Gordon co-efficients, notice that the n & p are in the same relation to these 3 charmedbaryons as the strange set Λ , Σ , and Σ + , which corresponds to replacing cby s and vice versa. This result can be seen as a rotation in the SU(4) spaceof the usual baryon octet with no s, one s, two s (the non-charm subset ofthe 20) to the non-strange no c, one c and two c octet (the non-strange sub-set of the 20). The same correspondence applies to the meson 15-plet. The 4X 4 matrix can have s & c entries reversed. Now there is strong breaking ofthe SU(4) symmetry. There are many ans¨atze for such symmetry breaking,e.g. Ref. 9. Obviously, symmetry breaking must suppress the production ofcharm. Phase space does enter, but other effects may be significant. This is ecember 11, 2018 20:24 WSPC - Proceedings Trim Size: 9in x 6in charm˙exc˙2 being studied.
3. Pseudoscalar Charmed Mesons Electroproduction andChiral Odd GPDs
The next step is to provide a model for charmed GPDs that could guideexperimenters for future simulations and possible extractions of F cT fromdata. Our approach is similar to Refs.10,11, where a Regge improved quark-diquark model was devised to provide a parametrization of the chiral even,unpolarized GPDs H q and E q , q = u, d that is quantitatively constrained bythe nucleon form factors data, and from deep inelastic scattering structurefunctions data through (cid:90) − ζ dXH q ( X, ζ, t ) = F q ( t ) (cid:90) − ζ dXE q ( X, ζ, t ) = F q ( t ) F q ( X, , Q ) ≡ q ( X, Q )where we introduced the kinematical variables X = k + /P + , ζ = ∆ + /P + ,and t = ∆ , P being the proton momentum, k the struck quark momentum,and ∆ the momentum transfer between the initial and final proton. F q are the quark contributions to the nucleon Dirac and Pauli form factors,and q ( X ) is the quark parton distribution at a given scale, Q (for a reviewof GPDs see Ref.12).In order to constrain charmed GPD, H c (¯ c ) T , we used the same set ofnon-perturbative models of IC that were used in Ref.2. These were foundto be consistent with present DIS data, posing an upper limit on the intrin-sic charm content measured by the momentum fraction (cid:104) x (cid:105) c +¯ c ≤ abinitio evaluations are available (see however, Ref.13). We therefore took asan upper limit the recent experimental extraction of the strangeness axialform factor G sA ( t ) [14]. This predicts negative values of G sA in the range0 . ≤ − t ≤ , that are consistent with recent findings of ∆ s . Ini-tial results based on these estimates are shown in Fig.3. We have chiral oddGPDs for these pseudoscalar processes, just as we introduced for the π & η ,Ref.15. The logic followed the observation that transverse virtual photonswere significant, while the chiral even contributions, severely limited by theC-parity odd t − channel, were small, in principle. Once the dominant be-haviour is established as due to transversity ( H T ( X, ζ, t )), the admixture ofgluons at leading twist is forbidden. So focusing on charmed pseudoscalarsprovides access to purely intrinsic charm rather than photon-gluon fusion. ecember 11, 2018 20:24 WSPC - Proceedings Trim Size: 9in x 6in charm˙exc˙2 π o η c s= 600 GeV Q = 5 GeV x = 0.1 -t GeV σ T + ε σ L -4 -3 -2 -1 -0.8 -0.6 -0.4 -0.2 0 Fig. 3. Comparison of π o and η c cross sections. Although η c is hard to detect, therange between the two lines gives an estimate of where the cross sections for the otherprocesses will lie.
4. Conclusions
The emergence of the EIC as a top priority of the nuclear physics commu-nity presents a unique opportunity to explore the non-perturbative sea andgluonic structure of the nucleon and nuclei. Here we presented a connectionbetween intrinsic and open charm and transverse spatial distributions ofthe nucleon’s sea structure through electroproduction and GPDs.In particular the issue of whether perturbative gluons produce c ¯ c pairs,or intrinsic, non-perturbative charm mechanisms are present in the nu-cleon, still remains unsettled. One possibility that we studied is that variousasymmetries for exclusive charm production providing e.g. the azimuthaldependence for the D or D ∗ meson, the cos (2 φ ) term in the unpolarizeddifferential cross section, may provide that discrimination.The proposed EIC presents a unique opportunity to test the distinctionbetween intrinsic charm and competing models by exploiting its kinematicreach in x and the final state variables ( z , and P T ) in semi-inclusive DIS, and t in exclusive proccesses. The various design scenarios range from E e /E P =10 / −
250 GeV, E e /E P = 3 − / − ecember 11, 2018 20:24 WSPC - Proceedings Trim Size: 9in x 6in charm˙exc˙2 ranging from few × cm − s − to few × cm − s − , and to a recentlyproposed medium energy collider E e /E P = 3 − / −
60 GeV (Ref.16).Another feature of exclusive charm production is that the producedcharmed hyperon can carry significant polarization through a mechanismsimilar to strange hyperons. The Λ c hyperon’s polarization is determinedby its weak decay products and is known to provide favorable polariza-tion analysis (Ref.17). Utilizing polarized electron and proton beams in theproposed kinematic regime would allow the disentangling of the multiplemechanisms as well. We are studying these multiple spin correlation observ-ables to see what their impact can be in both LHC and EIC kinematicalregimes (Ref.18). Acknowledgements
The authors appreciate the work of the organizers of Exclusives 2010.We also thank our colleague L. Gamberg for initial participation in thisproject.This work is partially supported by the U.S. Department of Energygrants DE-FG02-01ER4120 (S.L.), and DE-FG02-92ER40702 (G.R.G.).
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