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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

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“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

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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

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GlueX spectrometer

Near-threshold J/y photoproduction

p

e+

e-

Exclusive reaction gp → J/yp → e+e-p

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• Electrons separated from pions by E/p – energy deposition in the calorimeters over

measured momentum (pions >103 times more than electrons)

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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

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Results: total cross-section

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• 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

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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

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• 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)

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• 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)

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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

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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:

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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

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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):

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• 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

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• 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

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• 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

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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”

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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

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Back-ups

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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

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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)

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Main uncertainty

Br(Pc->J/yp)

Pc(4457)

Pc(4440)

J/y cross-section: model-dependent upper limits

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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?

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<

(model dependent 2-4%) GlueX

at the level of

X. Cao, J-P. Dai arXiv:1904.06015