Producing Exotic hadrons at the EIC

Producing Exotic hadrons at the EIC

Alessandro PilloniSnowmass, RF7 working group, September 16th, 2020

An Electron Ion Collider @BNL

A. Pilloni – Producing Exotic Hadrons at the EIC 2

3

Timeline

A. Pilloni – Producing Exotic Hadrons at the EIC

J. Yeck, May 2020

0,01

0,1

1

10

100

0 40 80 120Center of Mass Energy [GeV]

Spin and Flavor Structure of the Nucleon and Nuclei

QCD at Extreme Parton Densities-

Saturation

Tomography (p/A)

100

10

1

Peak

Lu

min

osi

ty [c

m-2

s-1]

An

nu

al In

tegr

ated

Lu

min

osi

ty [f

b-1

]

1034

1033

1032

EICOptimization for high Ecm

Internal Landscape of the Nucleus

EICOptimization for low Ecm

150

EIC Luminosity vs. Energy


F. Willeke, May 2020

4

5

Original EIC white book

A. Pilloni – Spectroscopy at EIC

Spectroscopy working group


• Exclusive production of XYZ• Polarization observables in XYZ• Semi-inclusive production of XYZ• Potential access to heavy hybrids• Production of XYZ in cold nuclear

matter, multiplicity studies

Contributing to the EIC Yellow Report,http://www.eicug.org/web/content/yellow-report-initiative

J. Stevens, convener

Exclusive (quasi-real) photoproduction


< 𝜆𝒬𝜆𝑁′ |𝑇|𝜆𝛾𝜆𝑁 >= ∑

𝑉,ℰ

𝑒𝑓𝑉𝑚𝑉

𝒯𝜆𝑉=𝜆𝛾,𝜆𝒬

𝛼1⋯𝛼𝑗 𝒫𝛼1⋯𝛼𝑗;𝛽1⋯𝛽𝑗ℬ

𝜆𝑁𝜆𝑁′

𝛽1⋯𝛽𝑗

• XYZ have so far not been seen in photoproduction: independent confirmation• Not affected by 3-body dynamics: determination of resonant nature• Experiments with high luminosity in the appropriate energy range are promising• We study near-threshold (LE) and high energies (HE)• Couplings extracted from data as much as possible, not relying on the nature of XYZ

M. Albaladejo et al. [JPAC], 2008.01001




𝑉,ℰ




𝜆𝑁𝜆𝑁′

𝛽1⋯𝛽𝑗

VMD is used to couple the incoming photonto a vector quarkonium V





𝑉,ℰ




𝜆𝑁𝜆𝑁′

𝛽1⋯𝛽𝑗

Top vertex from measured 𝒬 → 𝑉ℰ decay width





𝑉,ℰ




𝜆𝑁𝜆𝑁′

𝛽1⋯𝛽𝑗

Bottom vertex from standard photoproduction pheno,exponential form factors to further suppress large t


From threshold to high energy


• Fixed-spin exchanges expected to hold from threshold to moderate energies (LE):Contain full 𝑠 dependence

• 𝑡 channel grows as 𝑠 𝑗, exceeding unitarity bound:Reggeized tower of particles with arbitrary spin at HE

4𝑝(𝑡)𝑞(𝑡)

𝑠0

𝑗−𝑀

𝒩𝜇𝜇′𝑗

𝑑𝜇𝜇′𝑗

(𝜃𝑡)

𝜉𝜇𝜇(𝑡)

(𝑠, 𝑡)

1

𝑡 − 𝑚ℰ2 ⟶ −𝛼′Γ(𝑗 − 𝛼(𝑡))[

1 + 𝜏𝑒−𝑖𝜋𝛼(𝑡)

2]

𝑠

𝑠0

𝛼(𝑡)−𝑀

Holds at LE, fixed spin Holds at HE, resummationof leading 𝑠 power

𝑍 photoproduction


• The 𝑍𝑠 are charged charmoniumlike 1+− states close to open flavor thresholds• Focus on 𝑍𝑐 3900 + → 𝐽/𝜓 𝜋+, 𝑍𝑏 10610 +, 𝑍𝑏

′ 10650 + → Υ(𝑛𝑆) 𝜋+

• The pion is exchanged in the 𝑡-channel• Sizeable cross sections especially at LE

𝑋 photoproduction


• Focus on the famous 1++ 𝑋 3872 → 𝐽/𝜓 𝜌, 𝜔• Studying also 𝑋 6900 → 𝐽/𝜓 𝐽/𝜓 (assumed 0++)• 𝛚 and 𝛒 exchanges give main contributions:

need to assume the existence of a OZI-suppressed 𝑋 6900 → 𝐽/𝜓 𝜔• Extremely suppressed cross sections at HE: LE most promising

𝑌 (vector) photoproduction


𝑅𝜓′ =𝑔2(𝜓′ → 𝛾𝑔𝑔)

𝑔2(𝜓 → 𝛾𝑔𝑔)∼ 0.55 𝑔2(𝜓 → 𝛾𝑔𝑔) =

6𝑚𝜓ℬ(𝜓 → 𝛾𝑔𝑔)Γ𝜓

PS(𝜓 → 𝛾𝑔𝑔)

How to rescale from 𝐽/𝜓 to 𝜓′ ?

• Focus on the 1−− 𝑌 4260 → 𝐽/𝜓 𝜋+𝜋− , check with 𝜓′ → 𝐽/𝜓 𝜋+𝜋−

• Diffractive production, dominated by Pomeron (2-gluon) exchange• Good candidates for EIC: diffractive production increases with energy!• We have 𝛾𝜓-pomeron coupling from our analyses 1606.08912, 1907.09393



• Focus on the 1−− 𝑌 4260 → 𝐽/𝜓 𝜋+𝜋− , check with 𝜓′ → 𝐽/𝜓 𝜋+𝜋−

• Diffractive production, dominated by Pomeron (2-gluon) exchange• Good candidates for EIC: diffractive production increases with energy!• We have 𝛾𝜓-pomeron coupling from our analyses 1606.08912, 1907.09393

How to rescale from 𝐽/𝜓 to 𝑌(4260) ?

𝑅𝑌 =𝑒𝑓𝜓

𝑚𝜓

𝑔2(𝑌 → 𝜓𝜋𝜋)

𝑔2(𝜓 → 𝛾𝑔𝑔)

𝑔2(𝜓′ → 𝜓𝑔𝑔)

𝑔2(𝜓′ → 𝜓𝜋𝜋)

We assume VMD and 𝑔2 𝑌 → 𝜓𝜋𝜋 = 𝑔2 𝑌 → 𝜓𝑔𝑔 × 𝑔2(𝑔𝑔 → 𝜋𝜋) (Novikov & Shifman)

Caveat : 𝐵𝑅(𝑌 → 𝜓𝜋𝜋) only known times the leptonic width Γ𝑒𝑒𝑌



Existing data allow to put a 95% upper limiton the ratio of 𝜓′/𝑌(4260) yields

Assuming previous formula, one gets:Γ𝑒𝑒𝑌 = 930 𝑒𝑉

(cfr. hep-ex/0603024, 2002.05641)

𝐵𝑅 𝑌 → 𝐽/𝜓𝜋𝜋 = 0.96%𝑅𝑌 = 0.84

Data from H1hep-ex/971112

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Primakoff X photoproduction


Using measurement of Γ(X → 𝛾𝛾∗) from Belle, one can get predictions for Primakoff

Makes use of the ion beam, enhancement of cross sections as 𝑍2

14

Diffractive semi-inclusive 𝑍𝑐 ph.


If the target fragments are separated from the beam ones, one can invoke Regge factorization

= Im

Quark-Regge duality allows to replace the intermediate hadrons with Pomeron , prediction reliable for 𝑥𝐵 ∼ 1, 𝑡 ≪ 𝑊𝛾𝑝

2

𝜋𝜋 𝜋

16

Semi-inclusive 𝑋 production


For large 𝑄2 one can invoke NRQCD factorizationto describe quarkonium(-like) production

Perturbative partonic matrix element, calculable

Nonperturbative transition matrix element 𝑄 𝑄 → 𝐻

fitted from data

X. Yao

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Semi-inclusive 𝑋 production


One can assume the same NRQCD factorization for exotics, independent of their internal structure

Artoisenet and Braaten, PRD81, 114018 from Tevatron data

If one consider the first term only, it leads to

X. Yao

Joint Physics Analysis Center


Exclusive reactions:2008.01001

Inclusive reactions:in progress

Code available onhttps://github.com/dwinney/jpacPhoto

Contact : [email protected]

BACKUP

23

Another 𝑋?

A. Guskov


COMPASS claimed the existence of a statedegenerate with the 𝑋(3872), but with 𝐶 = 1

Large photoproduction cross sectionA. Guskov

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Exclusive 𝑃𝑐 photoproduction


At Jlab12 measurements of direct 𝑃𝑐production are being performed

Using VMD, BR 𝑃𝑐 → 𝐽/𝜓 𝑝 ∼ 1%

25

Polarized 𝑃𝑐 photoproduction


∼ 𝑠𝛼(𝑢)

• s channel resonances significant at low energies: u channel dominates at high energies

• Main background from N(*) trajectories

• Estimated 𝑃𝑐 coupling upper bound of same order of magnitude as 𝑁(∗) coupling• Reggeization suppresses 𝑃𝑐 due to larger mass (smaller trajectory intercept)• We estimate that the 𝑃𝑐 trajectories will hardly be visible at the EIC• 𝑃𝑏 searches still possible: 𝑠 channel at higher energies!

Cao et al., Phys.Rev. D 101, 074010 (2020)E. Paryev, arXiv:2007.01172 [nucl-th] (2020)

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Diffractive semi-inclusive 𝑍𝑐 ph.


Very large cross sections obtained, checking the validity of approximations in this range

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Production of other exotics


Other cross sections have been estimated, generally quite largeGuo et al. EPJC74, 9, 3063

Guo et al. CTP, 61, 354

Estimates can be given using MC generators, using coalescence model and assuming a molecular nature for

the exotics

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Comparison: EIC vs. others

Flexibility in the production mechanism Flexibility in energy (no Λ𝑏) Less clean environment

Too late (?) for charm physics

Larger luminosity (4.5 × 1032 cm−2s−1 at LHCb)Lower cross sections Better efficiencies for neutrals (?)

Polarized electron & ion beams

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Multiscale system


𝑚𝑄 ≫ 𝑚𝑄𝑣 ≫ 𝑚𝑄𝑣2𝑚𝑏 ∼ 5 GeV,𝑚𝑐 ∼ 1.5 GeV

𝑣𝑏2 ∼ 0.1, 𝑣𝑐

2 ∼ 0.3

Systematically integrateout the heavy scale,

𝑚𝑄 ≫ Λ𝑄𝐶𝐷 Full QCD NRQCD pNRQCD

Factorization (to be proved)of universal LDMEs

Good description of many production channels,some known puzzles (polarizations)

30A. Pilloni – Producing Exotic Hadrons at the EIC

Esposito, AP, Polosa, Phys.Rept.

HadSpec, PRD

The spectrum of hadron excitations is incredibly rich

Several new observations beyond the minimal quark content

QCD spectrum

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𝑄 𝑄

𝑉 𝑟 = −𝐶𝐹𝛼𝑠

𝑟+ 𝜎𝑟

(Cornell potential)

Effective theories(HQET, NRQCD, pNRQCD...)

Integrate out heavy DOF↓

Quarkonium orthodoxy & exotic

approximate heavy quark spin symmetry (HQSS)

A. Pilloni - Producing Exotic Hadrons at the EIC

spectrum, decay & production rates

A host of unexpected resonances have appeared

Hardly reconciled with usual charmonium interpretation

Esposito, AP, Polosa, Phys.Rept. 668

Bottomonium exotic sector notequally well explored

• Discovered in 𝐵 → 𝐾 𝑋 → 𝐾 𝐽/𝜓 𝜋𝜋

• Quantum numbers 1++

• Very close to 𝐷𝐷∗ threshold

• Too narrow for an above-treshold charmonium

• Isospin violation too big Γ 𝑋→𝐽/𝜓 𝜔

Γ 𝑋→𝐽/𝜓 𝜌~0.8 ± 0.3

• Mass prediction not compatible with 𝜒𝑐1(2𝑃)

𝑀 = 3871.68 ± 0.17 MeV𝑀𝑋 − 𝑀𝐷𝐷∗ = −3 ± 192 keVΓ < 1.2 MeV @90%

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𝑋(3872)


Sizeable prompt production at hadron colliders, ∼ 5% of 𝜓(2𝑆)

𝜎𝑃𝑅 × 𝐵(𝑋 → 𝐽/𝜓𝜋𝜋) = (1.06

𝑒+𝑒− → 𝑍𝑐 3900 +𝜋− → 𝐽/𝜓 𝜋+𝜋− and → 𝐷𝐷∗ +𝜋−

𝑀 = 3888.7 ± 3.4 MeV, Γ = 35 ± 7 MeV

𝑒+𝑒− → 𝑍𝑐′ 4020 +𝜋− → ℎ𝑐 𝜋+𝜋− and → 𝐷∗0𝐷∗+𝜋−

𝑀 = 4023.9 ± 2.4 MeV, Γ = 10 ± 6 MeV

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Charged 𝑍 states: 𝑍𝑐 3900 , 𝑍𝑐′(4020)

Two states 𝐽𝑃𝐶 = 1+− appear

slightly above 𝐷(∗)𝐷∗ thresholds

Charged quarkonium-like resonances have been found, 4q needed


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Pentaquarks!LHCb, PRL 115, 072001LHCb, PRL 117, 082003

Quantum numbers

𝐽𝑃 =3

2

−

,5

2

+

or3

2

+

,5

2

−

or5

2

+

,3

2

−

Two states seen in Λ𝑏 → 𝐽/𝜓 𝑝 𝐾−,evidence in Λ𝑏 → 𝐽/𝜓 𝑝 𝜋−

𝑀1 = 4380 ± 8 ± 29 MeVΓ1 = 205 ± 18 ± 86 MeV

𝑀2 = 4449.8 ± 1.7 ± 2.5 MeVΓ2 = 39 ± 5 ± 19 MeV


LHCb, PRL 122, 222001 Higher statistics analysis revealed a two-

peak structure of the narrow state,plus a new lighter one

Quantum numbers still unknown

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Models

MoleculeBound or virtual state generated by long-range exchange forces

MultiquarkSeveral (cluster)

of valence quarks

HybridsContaining gluonicdegrees of freedom

𝑱/𝝍𝝅𝝅

𝝅HadroquarkoniumHeavy core interacting with a light cloud via Van der Waals forces

Rescattering effectsStructures generated by

cross-channel rescattering, very process-dependent

Compact

Extended


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Hybrid production

Suprisingly, no calculationfor heavy hybrid productionhas been carried out so far

The only example for B decaysis Petrov et al. PRD58, 034013

Room for improvement and inclusion of the large number of gluons at small x

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Doubly heavy

Lots of attention recently on tetraquark and baryons with two heavy quarks, driven by LHCb and lattice results

Quigg and Eicthen, PRL119, 202002 Esposito, AP et al. PRD88, 054029

Karliner and Rosner, PRD90, 094007 Karliner and Rosner, PRL119, 202001

Francis et al. PRL118, 142001

MC code available, GENXICC2.0, which implements the heavy diquark in PythiaNRQCD approach in 𝑒+𝑒− collisions in Chen et al. JHEP1412, 018

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Producing Exotic hadrons at the EIC