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Probing gluonic structure of the proton
with J/y exclusive photoproduction
“First measurements of near-threshold J/ψ exclusive photoproduction
off the proton” PRL 123, 072001 (Aug 2019)
The experiment
• GlueX detector
• J/y identification
• Normalization and systematic uncertainties
• Results: total/differential cross-sections
What can we learn about the gluonic content of the proton at high x?
(from more general to more model dependent theoretical interpretations)
• Factorization
• Perturbative methods
• Proton gluonic form factors
Outlook
Will not talk about LHCb pentaquarks
gp → J/yp
2
“First measurements of near-threshold J/ψ exclusive photoproduction
off the proton” PRL 123, 072001 (Aug 2019)
Probing gluonic structure of the proton
with J/y exclusive photoproduction
gp → J/yp
3
Hall D Apparatus
• Photon beam from coherent Bremsstrahlung
off thin diamond
• Photon energy tagged by scattered electron:
0.2% resolution
• Beam collimated at 75m, <35 mrad
• Intensity: ~ 2 107 - 5 107 g/sec above J/y
threshold (8.2 GeV) – total ~68 pb-1 in 2016-
2017 runs (25% of total statistics up to date)
• Photons are linearly polarized (~ 40% at
peak); polarization not used – runs with perp.
polarization planes mixed, also using
amorphous radiators
• Hermetic detector: 1 – 120° polar and full azimuthal acceptance
• Tracking: sp/p ~ 1 – 5%
• Calorimetry: sE/E ~ 6%/√ E + 2%
2T-solenoid, LH target
Tracking (FDC,CDC) , Calorimetry (BCAL,FCAL) , Timing (TOF,SC)
FDC
CDC
FCAL
TOF BCAL
SC
4
GlueX spectrometer
Near-threshold J/y photoproduction
p
e+
e-
Exclusive reaction gp → J/yp → e+e-p
5
• Electrons separated from pions by E/p – energy deposition in the calorimeters over
measured momentum (pions >103 times more than electrons)
6
e+e- invariant mass spectrum
• Tagged photon beam (0.2% energy resolution) and exclusivity of the reaction:
• Kinematic fit (constrained mostly by the recoil proton): 13 MeV mass
resolution; no radiative tail
• BH(1.2 – 2.5 GeV) used for normalization
• Pion contamination ~50% in the continuum (using E/p fits to estimate it)
electron/pion separation
7
Results: total cross-section
8
• Yields (NJ/y and NBH) extracted
from fits of M(e+e-) and E/p in
bins of energy
• sBH calculated using analytical
and numerical calculation of
e.m. tree level diagrams
• Syst. errors of individual data
points assigned to max
deviation when varying fitting
methods
• Errors dominated by statistics
• 27% overall normalization
error, however not so
important for studying gluonic
distributions
9
Results: total cross-section
• Published results (stat. errors): 25%
of statistics accumulated up to date
• Preliminary results (STAT. ERRORS
ONLY SHOWN!) based on 70% of data
Factorization in hard exclusive meson electro-production
10
• Factorization theorem for hard exclusive meson electro-production
– requires large virtuality for heavy mesons : Q2 >> M2
– two soft pieces: GPD and F (light-cone wave function of the meson)
g* g*
M M F
F
GPD GPD
g* g*
M M F F
GPD GPD
Collins, Frankfurt, and Strikman, Phys.Rev. D56 (1997)
Radyushkin, Phys. Rev. D56 (1997)
11
• In contrast, in heavy meson photo-production (Q2=0)
– the heavy quark mass provides the hard scale: M >> Lqcd
Idea dates back: Shifman, Vainstaen, and Zakharov, Phys.Lett. B65 (1976)
– allows non-relativistic treatment of charmonium WF (studied by
Hoodbhoy, Phys. Rev. D56 (1997) )
– factorization demonstrated explicitly in NLO calculations:
Factorization in exclusive heavy meson photo-production
Ivanov, Schaefer, Szymanowski, Krasnikov, EPJ C34 (2004)
12
Conclusions for the factorization of J/y photoproduction:
• In LO: Cg strongly peaks at |X| ~ x probing Fg(x,x), Cq= 0
• NLO corrections significant, strong dependence on the factorization scale
• Using a GPD model (A.Freund et al.,(2002)) to compapre to data
• Despite some agreement with the data they conclude: the NLO corrections are
not under theoretical control
Factorization in exclusive heavy meson photo-production
Ivanov, Schaefer, Szymanowski, Krasnikov, EPJ C34 (2004)
ds
/dt (t
=0
)
W, GeV W, GeV
13
Factorization in exclusive heavy meson photo-production at
small x
Jones, Martin, Ryskin, Teubner, EPJC 76 (2016)
Flett, Jones, Martin, Ryskin, Teubner, arXiv:1908.08398 (Aug 2019)
• Heavy meson photo-production at small x (to use LHCb ultraperipherial J/y
production):
– GPD F(x,x) related to PDF(x+x) at small x (Shuvaev transform)
– new factorization scale reduces the effects of small x (log1/x terms)
– most importantly: avoid double counting between NLO and PDF
evolution contributions by applying cut on loop momentum |l2| > Q02 where Q0 is
input scale for the GPD evolution:
14
Factorization in exclusive heavy meson photo-production at
small x
Jones, Martin, Ryskin, Teubner, EPJC 76 (2016)
Flett, Jones, Martin, Ryskin, Teubner, arXiv:1908.08398 (Aug 2019)
Q0 correction reduces the NLO contribution and the scale dependence significantly
Before Q0 correction After Q0 correction
Can similar corrections be applied for threshold energies and high x?
Misha Ryskin:” Yes, it can and (from my viewpoint) this Should be done. The problem is
that for x close to 1 the subtraction must be calculated more precisely taking care about
the log(1-x); i.e. resumming the (\alpha_s\ln(1-x))^n terms.”
J/y-nucleon cross-section
15
Kharzeev, CERN-TH/95-342,arXiv:nucl-th/9601029 (1996),
Kharzeev et al. EPJ C9 (1999):
Heavy J/y sets the hard scale:
allowing to use the same apparatus as for DIS for the calculations of
forward yN -> yN : Operator Product Expansion (OPE) (where the Willson
coefficients are process independent) and dispersive relations that relate
the cross-section to the partonic structure of the proton:
in first approximation total cross-section:
(l – nucleon energy in J/y rest frame). The Im and Re parts of forward
elastic amplitude are calculated from optical theorem and dispersion
integral with one subtraction MyN(l = 0):
16
• Assuming VMD:
J/y photoproduction differential cross-section – using VMD
Kharzeev et al. EPJ C9 (1999):
W, GeV
PDF MRS H
Re
Im
ds
/dt (t
=0
)
g(x) ~ (1-x)4
W, GeV
J/y photoproduction total cross-section – using t-dependence
17
• Total cross-section calculated using exponential t-dependence
parametrization (from data) with slope depending on energy:
• Dima Kharzeev: “Normalization uncertainty is a factor of 2-3”.
Kharzeev et al. EPJ C (1999):
W, GeV
B (
slo
pe
), G
eV
-2
J/y photoproduction cross-section – assuming factorization
18
• Near threshold cross-section is very sensitive to gPDF(x→1)
• In case of two-gluon exchange model in LO:
• Factorization of (g→Q𝑄 )x(Q𝑄 p→ Q𝑄 p)x(Q𝑄 →J/y) assumed
Sibirtsev et al. JP G30 (2004)
GlueX data
27% norm.
uncertainty
J/y total cross-section – 2g vs 3g exchange
GlueX errors: quadratic sums of statistical and
systematic ones
SLAC data:
Cornell data: gBe→J/yX 19
GlueX data falls
toward threshold less
steeply than 2g
exchange model
Brodsky et al.PLB498 (2001):
s(Eg) depending on number
of hard-gluons exchanged
using dimensional scaling
J/y differential cross-section – t-dependence
20
gluonic form factor
(dipole form in analogy
with the e.-m. FF):
Frankfurt and Strikman
PRD66 (2002)
Gluex t-slope: 1.67 ± 0.39
(t-dependence not given by the models discussed so far)
Proton gluonic FF: “..these are nothing but the gravitational form factors 𝐴𝑔, 𝐵𝑔, 𝐶𝑔, 𝐶 𝑔”
21
Y. Hatta, A. Rajan, and D.-L. Yang, PRD100 (2019):
𝐴𝑔, 𝐵𝑔, 𝐶𝑔 were recently calculated on lattice: Shanahan and Detmold, PRD99 (2019)
Red – maximal contribution from gluons, favored by GlueX data
Blue – no gluonic contribution
<Eg >= 9.5 GeV
J/y cross-section – non-perturbative (holographic)
calculations
Proton Gluonic Form Factors: A,B,C (lattice calculations)
Fits in dipole form:
Shanahan and Detmold, PRD99 (2019)
12GeV CEBAF – unique opportunity (correct energy, high intensity, polarized
beams) to study the J/y photoproduction right above the threshold
GlueX published first measurements of J/y exclusive photoproduction off the
proton; the uncertainties in the absolute normalization not so important for the
studies of the gluonic distributions
Results with much higher statistics are expected to come soon also from the other
halls
The heavy charmonium sets the hard scale, allowing to use the same methods as
in DIS to relate the measured cross-sections to the partonic (gluonic) structure of
the proton
Factorization for J/y exclusive photoproduction demonstrated explicitly in NLO,
however QCD “fine tuning” has been done only for small x
Many open questions remain:
• Can we apply the methods used in the small-x studies to the near threshold
high-x region; if yes, who can do it?
• If the factorization works for the high-x region what is the object we can
study: gGPD(X,x), what is the behavior at |X|~x? Since gGPD is more
complicated object than gPDF, is this an advantage or disadvatage?
• What is the relation b/n different theoretical approaches, can we use VMD
(and corresponding factorization), is the two-gluon exchange model valid
near threshold?
• What can we learn from the t-dependence of the differential cross-sections:
gGPD(t), gravitational form-factors?
Outlook
23
Back-ups
24
gp → J/yp → e+e-p reconstruction methods (leptons tagged)
s = 7.5 MeV s = 12.8 MeV
s = 18.1 MeV s = 83.8 MeV
gp → pMx
25
reconstruction
• If LHCb pentaquarks exist they should be seen in s-channel photoproduction
(free of rescattering effects in the final state):
g
p p
Pc
J/y
𝑐𝑐 J/y(VMD)
LHCb Pc related to gp ->Pc->J/yp
LHCb pentaquarks and J/y photo-production
• V.Kubarovsky and M.B.Voloshin, PRD 92.031502 (2015).
• M.Karliner and J.Rosner, arXiv: PLB 752, 329 (2016).
• A.Blin, C.Fernandez-Ramirez, A.Jackura, V.Mathieu, V.Mokeev,
A.Pilloni, and A.Szczepaniak, PRD 94,034002 (2016).
Pc(4312)
26
Main uncertainty
Br(Pc->J/yp)
Pc(4457)
Pc(4440)
J/y cross-section: model-dependent upper limits
27
Assuming:
• all Pc independent JP = 3/2-
• s-channel model:
s(gp → Pc→ J/yp) ≈ 0.35 mb Br2(Pc → J/yp) (2J+1)
• JPAC model for t-channel:
Pomeron and tensor part
extracted at high energies
Upper limits at 90% confidence level
Lower limits on Br(Pc → J/yp) from data?
28
<
(model dependent 2-4%) GlueX
at the level of
X. Cao, J-P. Dai arXiv:1904.06015