Charmed hypernuclei, nuclear-bound heavy-flavor hadrons · 2018-07-10 · Charmed hypernuclei, nuclear-bound heavy-flavor hadrons Gastão Krein Instituto de Física Teórica, São

Charmed hypernuclei, nuclear-bound heavy-flavor hadrons

Gastão KreinInstituto de Física Teórica, São Paulo

Motivation for charm in nuclei— Overwhelming evidence QCD is the fundamental theory

of the strong interaction

— Yet, we are very far of understanding how it actually works

— Lattice QCD has had remarkable progress with masses of ground-state quark-antiquark and three valence quark hadrons

— Yet beyond that, our ignorance is profound

Prominent nonperturbative QCD phenomenaVital role of gluons: Color confinement, mass generation— origin proton mass: probed with quarkonium-nucleon— chiral symmetry restoration: D-mesin nuclei, charm hypernuclei— X,Y,Z: what are they?

This talk, concentrate on:

— charmed hypernuclei

— heavy quarkonia in nuclei

Not covered:— D-mesic nuclei— phi-meson in nuclei

P. Gubler, talk at this conference

Recent reviews:— Nuclear-bound quarkonia and heavy-flavor hadrons

GK, A.W. Thomas & K. Tsushima Prog. Part. Nucl. Phys. 100, 161 (2018)

— Heavy hadrons in nuclear matter A. Hosaka, T. Hyodo, K. Sudoh, Y. Yamaguchi & S. Yasui Prog. Part. Nucl. Phys. 96, 88 (2017)

— Right after discovery of charm, suggestion (Tyapkin) possible existence of charm hypernuclei

— Binding energies calculated, using meson-exchange models, SU(4) flavor symmetry for couplings (Dover & Kahanna, Iwao, Gibson et al.)

— One (inconclusive) experimental evidence

Charmed hypernuclei

⇤(uds) ! ⇤+c (udc)

A primary vertex

B vertex decay of a supernucleus

C decay of D0 — signal of pair productioncc̄

Fermilab — Emulsion experiment (1976)

Interesting because

— opportunity to learn about medium effects on diquark correlations, as the masses of u and d quarks are affected by the medium

— few-nucleon charmed states have the potential of having a rich spectroscopy similar to the X,Y,Z hadrons

— opportunity to learn about the interactions of charmed baryons with nucleons

Production at FAIR, J-PARC(future Super-B, EIC)

Antiproton beam, production of charmed hadrons in the Hadron Hall at J-PARC

@ FAIRB⇤+

cZ

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⇤+c

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⇤̄�c

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Chances of a charmed hadron meeting one or two nucleons not much smaller than of two antinucleons and one antiyperon meeting to form an antihypernucleus

Coalescence at the LHC— heavy-ion collisions

Most recent theory (spectrum)— QMC model

— No SU(4) uncertainties; mean meson fields couple directly to the light quarks in the nucleons and hyperons

— No free parameters, all fixed by normal nuclear matter and normal nuclei

Effective masses - nuclear matter

Single-particle energies

Production at PANDA energies*

*Shyam & Tsushima, PLB 770, 236 (2018)

Difficulty for detection— Many decay channels

While a few in strange hyperon decays

A lot in charm hyperon decays

continues …

Nonmesonic weak decay (NMWD)

C. Conti, C.E. Fontoura, A.P. Galeao, GK, F. KrmpoticJ Phys G 45, 01501 (2018)

L: weak vertex+

R: strong vertex

In nuclear medium

⇤+c

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⇤+c + n ! ⇤+ p

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Model

Nuclear structure — Independent particle shell model*— relativistic mean fields (NL3, Ring et al)

Decay — Pion and Kaon exchange

Recoil of nucleus— Fully relativistic

*Ramos et al, Parreño et al

Matrix element of NMWD

Decay rates Free-space decay rate

~1/2 free-space decay rate


100 200 300 400 500

TΛ [MeV]

0.000

0.002

0.004

0.006

0.008

0.010

0.012

S(T Λ

) x

1011

no recoil

nonrel. recoil

rel. recoil

Effect of nuclear recoilSpectrum of emitted strange hyperon


few-nucleon bound states⇤+c

<latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit><latexit sha1_base64="q79nshUesI/6sFkmSIzGuIRJFHM=">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</latexit>

Several model calculations— potential model— meson-exchange model— constituent quark model

- Bando & Bando PLB 109, 1604 (1982)- Gibson, Bhamathi, Dover & Lehman PRC 27, 2085 (1983)- Liu & Oka PRD 85, 014015 (2012)- Huang, Ping & Wang PRC 87, 034002 (2013)- Gal, Garcilazo, Valcarce & Caramès PRD 90, 014019 (2014)- Garcilazo, Valcarce & Caramès PRC 92, 024006 (2015)- Maeda, Oka, Yokota, Hiyama & Liu, PTEP 2016, 023D2 (2016)- Ohtani, Araki & Oka, PRC 96, 055208 (2017)

few-nucleon bound states⇤+c


Several model calculations— potential model— meson-exchange model— constituent quark model

- Bando & Bando PLB 109, 1604 (1982)- Gibson, Bhamathi, Dover & Lehman PRC 27, 2085 (1983)- Liu & Oka PRD 85, 014015 (2012)- Huang, Ping & Wang PRC 87, 034002 (2013)- Gal, Garcilazo, Valcarce & Caramès PRD 90, 014019 (2014)- Garcilazo, Valcarce & Caramès PRC 92, 024006 (2015)- Maeda, Oka, Yokota, Hiyama & Liu, PTEP 2016, 023D2 (2016)- Ohtani, Araki & Oka, PRC 96, 055208 (2017)

⇤+c


-nucleon interactionCrucial input:

-nucleon from lattice QCD⇤+c


HAL collab. NPA 971, 113 (2018)

Charmed hypernuclei HAL collab. NPA 971, 113 (2018)

J. Haidenbauer and G.K, arXiv:1711.06470

Extrapolation to physical pion masses

Chiral EFT

— one-pion exchange

— contact terms

— Lippmann-Schwinger eq, coupled channels⇤cN

⇡�! ⌃cN<latexit sha1_base64="b1raW/84gvyqFEVmez/y9M2SltE=">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</latexit><latexit sha1_base64="b1raW/84gvyqFEVmez/y9M2SltE=">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</latexit><latexit sha1_base64="b1raW/84gvyqFEVmez/y9M2SltE=">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</latexit><latexit sha1_base64="b1raW/84gvyqFEVmez/y9M2SltE=">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</latexit>

J. Haidenbauer and G.K, arXiv:1711.06470

Red bands, extrapolation to m⇡ = 138 MeV<latexit sha1_base64="o3pto93eTrdFtOJyTiddAR5ShJA=">AAACS3icbVDLSgMxFM3Ud31VXboJFkFESqYuLIhQdONGULAP6Awlk97WYJIZk4xQhvk/N27c+RNuXCjiwrRW8HUgcDj33nNvTpQIbiwhj15hanpmdm5+obi4tLyyWlpbb5o41QwaLBaxbkfUgOAKGpZbAe1EA5WRgFZ0fTKqt25BGx6rSztMIJR0oHifM2qd1C1FQQQDrjK4UVRrOtzNi1kwtu3oQRRmpFIjDnukQsgPkstukHB8hP39Gg4OcRZoic+gmefFAFTvm2G3VP4awn+JPyFlNMF5t/QQ9GKWSlCWCWpMxyeJDTOqLWcCnH9qIKHsmg6g46iiEkyYjY/O8bZTergfa/eUxWP1+0RGpTFDGblOSe2V+V0bif/VOqnt18KMqyS1oNjnon4qsI3xKFjc4xqYFUNHKNPc3YrZFdWUWRd/0YXg//7yX9KsVnxS8S+q5frxJI55tIm20A7y0QGqo1N0jhqIoTv0hF7Qq3fvPXtv3vtna8GbzGygHyjMfABts67k</latexit><latexit sha1_base64="o3pto93eTrdFtOJyTiddAR5ShJA=">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</latexit><latexit sha1_base64="o3pto93eTrdFtOJyTiddAR5ShJA=">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</latexit><latexit sha1_base64="o3pto93eTrdFtOJyTiddAR5ShJA=">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</latexit>

⇤cN⇡�! ⌃cN

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very small effect

Charmed hypernuclei — physical pion masses

— No bound state

— , perhaps bound

— certainly bound to large nuclei

N⇤+c

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NN⇤+c

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While experimental data not available, lattice QCD only hope to make real progress

Nuclear-bound quarkonium— origin of proton mass

Trace anomaly

Take mq = 0 & mQ = ∞

�SQCD

��

= �Z

d

4xT

µµ (x) = 0

From classical Lagrangian:

Quantum theory

— this is the trace anomaly— no scale invariance— trace of is nonzeroTµ⌫

The entire mass

comes from gluons

Contribution from quark masses

small

Why is this interesting ?

Because

contributes to thresholdquarkonium-nucleon scattering

Quarkonium-nucleon

Quarkonium:

Experiments— JLab

Definite results still this year (?)

© CERN / LHCb Collaboration

Renewed interest— LHCb pentaquark

ATHENNA* collaboration JLab @ 12 GeV

*A J/Ψ THreshold Electroproduction on the Nucleon and Nuclei Analysis

Hall A — E12-12-006K. Hafidi, Z.-E. Meziani, N. Sparveris, Z. W. Zhao

Hall C — E-12-16-007 (Pentaquarks)Z.-E. Meziani, S. Joosten, et al.

— Chances of a quarkonium meeting one or two nucleons

not much smaller than of two antinucleons and one

antihyperon meeting to form an antihypernucleus

Coalescence at the LHC— heavy-ion collisions

Antiproton annihilation on deuteron, re-scattering on spectator nucleon

@ FAIR

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Quarkonium-nucleon scattering

Forward amplitude

: color polarizability (property of the quarkonium)

Measure scattering length:

Bound from trace anomaly:

Quarkonium in nuclei:

— scattering amplitude is enhanced

— formation of a new exotic nuclear state

— adds a new flavor axis in the nuclear e.o.s.

Low-momentum quarkonium in a nucleus

— Quarkonium interacts with light quarks in nucleons by exchanging gluons with wavelengths

� ⇠ rN

— Size of quarkonium

� � 2 rJ/

rJ/ ⇠ 0.35 fm

Quarkonium behaves as a small color dipole

immersed in a uniform gluon field

hTNi ⇠3

5

k2F2mN

⇠ 20MeV ⌧ ⇤QCD

rN ⇠qhr2chi ' 0.88 fm ⇠ ⇤�1

QCD

Embbeding quakonium-nucleon into aNonrelativistic nuclear many-body problem

quarkonium-nucleon

G.K., A.W. Thomas & K. Tsushima,PPNP 100, 161 (2018)

Hartree-Fock equation— for quarkonium in a nucleus

quarkonium-nucleus potential

nuclear density functional

Neglecting back reaction of quarkonium on nucleons, take density from a model or experiment

Need quarkonium-nucleon potential

From the forward amplitude:

No repulsionfrom Pauli principle

J/Ψ in nuclei— nuclear potentials

Nuclear density from QMC model:P.A.M. Guichon et al.

Quarkonium in nuclei— use scattering length only

aJ/ N = �0.18 fm

aJ/ N = �0.36 fm

Models

NPLQCD

Can one do better?

Quarkonium-nucleon*Lattice

Chiral EFT

J.T. Castellà, GKPRD (2018), arXiv: 1803.05412

Degrees of freedom & Scales & Power counting

DOF: nucleons, quarkonia, pions

terms of the effective Lagrangian organized in powers of

EN , E� ⇠ m⇡ ⌧ ⇤� ⇠ 1GeVScales:

Power counting:(~ Weinberg for NN)

m⇡

⇤�

Loops: dimensional regularization

Nucleon-pion

Quarkonium-nucleon EFT— QNEFT

Quarkonium

Quarkonium-Pion

cd0 = �4⇡2↵�

b1

cdi = �4⇡2↵�

b2

cm = �12⇡2↵�

b

Chromopolarizability

Quarkonium-Nucleon

Low-energy quarkonium-nucleon dynamics

Quarkonium-nucleon dynamics, e.g bound to nucleus occurs at energies

E�N ⇠k2�N2µ�N

<m2

⇡

⇤�⌧ m⇡

Integrate out the pion

Quarkonium-nucleon potential— pQNEFT

Integrate out the pion

Matching

Renormalization of couplings + van der Waals

C0 = c0 + 4m2⇡dm +

9g2Am2⇡c0

64⇡2F 2

✓log

m2⇡

⌫2+

2

3

◆+

3g2Am3⇡

64⇡F 2(5cdi � 3cm)

D1 = d1 +g2Am⇡

256⇡F 2(23cdi � 5cm)

Dj = dj for j = 2, 3 and 4

Long-distance part of QN potential— vdW force

No free parameters here:— trace anomaly— chiral physics

First, model-independent derivation of a quarkonium-nucleon van der Waals force

For :

V (r) =3g2Am

4⇡ (cdi + cm)

128⇡2F 2

e�2m⇡r

r2

r � 1

2m⇡

To extrapolate lattice data to physical quark masses, need:

mN = m̂N � 4c1m2⇡ � 3g2Am

3⇡

32⇡F 2

m� = m̂� � F 2cmm2⇡

Unknown contact couplings— get them from lattice QCD

Lattice: [27] Yokokawa et al PRD 74, 034504 (2006) [28] Liu et al PoS (LATTICE) 2008, 112 (2008) [29] Kanaway & Sasaki PoS (LATTICE) 2010, 156 (2010)

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Comparing long distance partwith HAL lattice potential

Kanaway & Sasaki, PRD 82, 091501 (2010)

⌘c �NvdW force

Lattice:T. Kawanay & S. Sasaki, Pos (Lattice) 2010, 156 (2010)

J/ �NvdW force

Lattice:T. Kawanay & S. Sasaki, Pos (Lattice) 2010, 156 (2010)

Fits of the polarizabilites

Are there quarkonium-nucleonbound states at this order in pQNEFT?

Scattering amplitude (s-wave)

a0 =

µ�N

2⇡

c0 + 4dmm2

⇡ +

9g2Am2⇡c0

64⇡2F 2

✓log

m2⇡

⌫2+

2

3

◆+

3g2A64⇡F 2

m3⇡ (5cdi � 3cm)

�

A =

2⇡

µ�N

1

p cot � � ip=

2⇡

µ�N

1

� 1a0

+

12r0p

2+ . . .

r0 =8⇡

µ�Nc20

(d1 + d2) +

g2A256⇡F 2

m⇡ (23cdi � 5cm)

�

No quarkonium-nucleon bound states within the applicability of the present calculation:

|p�N | m⇡

YES, for sufficiently large nuclei

Are there quarkonium-nucleusbound states at this order in pQNEFT?

Qualitativeagreement with

No quarkonium-nucleon bound states

Bound states

Lattice HAL

Perspectives

Charmed hypernuclei— experiments: LHC (existing data), future FAIR, J-PARC, … — theory: lattice crucial for progress

Quarkonium-nucleon— experiments: JLab data (2018?) LHC (existing data), PANDA (2025)— theory: EFT, lattice

Funding

Documents

Charmed hypernuclei, nuclear-bound heavy-flavor hadrons · 2018-07-10 · Charmed hypernuclei, nuclear-bound heavy-flavor hadrons Gastão Krein Instituto de Física Teórica, São