Multi-charmed hadron production in heavy-ion collisions and...

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MinJung Kweon Inha University June 11, 2020 Multi-charmed hadron production in heavy-ion collisions and future measurements

Transcript of Multi-charmed hadron production in heavy-ion collisions and...

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MinJung KweonInha University

June 11, 2020

Multi-charmed hadron production in heavy-ion collisions and future measurements

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Charmed hadrons

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− Charmed hadrons 1) Charmonium states : Bound states made up of a charm and an anti-charm quarks - the 1S scalar ηc and vector J/ψ, three 1P states χc (scalar, vector, and tensor), and the 2S vector state ψ’ 2) Charmed baryons and mesons : D, D*, Ds, Ds*, Λc(2286), Λc(2595), Λc(2625), Σc(2455), Σc(2520), Ξc(2470). Ξc(2578), Ξc(2645), Ωc(2695), Ωc(2770). 3) Doubly charmed hadrons, exotic hadrons Ξcc, Tcc, X(3872)

4 March 26th 2019 Yukawa Institute for Theoretical Physics

Hadron Interactions and Polarization from Lattice QCD, Quark Model, and Heavy Ion Collisions

− Charmed hadrons 1) Charmonium states : Bound states made up of a charm and an anti-charm quarks - the 1S scalar ηc and vector J/ψ, three 1P states χc (scalar, vector, and tensor), and the 2S vector state ψ’ 2) Charmed baryons and mesons : D, D*, Ds, Ds*, Λc(2286), Λc(2595), Λc(2625), Σc(2455), Σc(2520), Ξc(2470). Ξc(2578), Ξc(2645), Ωc(2695), Ωc(2770). 3) Doubly charmed hadrons, exotic hadrons Ξcc, Tcc, X(3872)

4 March 26th 2019 Yukawa Institute for Theoretical Physics

Hadron Interactions and Polarization from Lattice QCD, Quark Model, and Heavy Ion Collisions

Sungtae Cho’s slide

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!4

Hadron Quark content Mass MeV/c2 cτ μmBc+ bc 6275 153Λc+ udc 2286 60Σc++ , Σc+ , Σc0 uuc, udc, ddc 2454 strong decayΞc0 dsc 2471 33Ξc+ usc 2468 132Ωc0 ssc 2695 80Ξcc++ ucc 3621 77Ξcc+ dcc 3519 ** 10 **Ωcc+ scc Not measured Not measuredΩccc++ ccc Not measured Not measured

Multi-HF hadrons

c=0

c=1

c=2

c=3

** SELEX measurement: notably short lifetime, large ΔM w.r.t. Ξcc++

The quark model predicts the existence of states with multiple heavy quarks• numerous states with C=1 have been discovered• 3 weakly decaying qqq states with C=2 are expected (Ξcc++, Ξcc+, Ωcc++)• 1 state with C=3

Multi-charmed hadrons

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Multi-heavy flavour hadrons measured at the LHC

• LHCb measurements in pp collisions at 13 TeV (1.7 fb-1)• Very rare signal

- Integrated luminosity: 1.7 fb-1

- Ξcc++ ➝ Λc+K-π+π+ , Λc+ ➝ pK-π+ (raw signal ~300)- Ξcc++ ➝ Ξc+π+ , Ξc+ ➝ pK-π+ (raw signal ~90)

• Mass = 3621 MeV/c2• Lifetime = 0.256 ps (~77μm)• Weakly decaying particle• [B(Ξcc++ ➝ Λc+K-π+π+) x B(Λc+ ➝ pK-π+)]/[B(Ξcc++ ➝ Ξc+π+) x B(Ξc+ ➝ pK-π+)] = 0.035

Existing measurements at LHCMulti-HF hadrons

Ξcc

Bc

• First measurements at Tevatron (then at LHC by LHCb)• Heaviest ground-state b-flavoured meson• Production rates about 3 orders of magnitude smaller than other B mesons (bq)

- Integrated luminosity used >1 fb-1

• Decay modes- Semi-leptonic: Bc+ ➝ J/ψ l+ν-- Bc+ ➝ ψ(2S) π+

- b-spectator type: Bc+ ➝ Bs0 π+

- Bc+ ➝ J/ψ Ds , Bc+ ➝ J/ψ Ds* , Bc+ ➝ J/ψ π+ , Bc+ ➝ J/ψ π+ π- π+ , Bc+ ➝ J/ψ 3π+ 2π- , Bc+ ➝ J/ψ K+ K- π+ , Bc+ ➝ J/ψ K+

• Mass = 6274 MeV/c2, lifetime = 0.5 ps (~150μm)• Excited state measured by ATLAS: Bc(2S) ➝ J/ψ π, mass=6842 MeV/c2, 5(19) fb-1 of pp at

7(8) TeV ➞ info about the strong interaction potential!5

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Multi-HF hadronsProduction in vacuum-like fragmentation processes expected to be negligible in AA

Pure coalescence particles

Coalescence process sensitive to the relative momentum between the HQ pair• pp collisions: relative momentum is uncontrolled and likely suppresses coalescence • HI collisions:

- rapidity density of heavy quarks produced is high (O(100) for charm and O(10) for beauty in central PbPb)- Deconfined QGP medium lasts ~10 fm/c during which time c quarks can diffuse in the QGP interacting

with light quarks and gluons- Charm participate in the collective flow of the QGP: relative momentum of charm quark pair can be of the

order of the QGP temperature ➞ coalescence probability of a charm enhanced if the T of the QGP is not too high

Rates expected in HI collisions significantly enhanced with respect to pp collisions

Another signature of deconfinement… but a SPECTACULAR one!

!6

Why multi-heavy flavour hadrons in heavy-ion collisions

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Multi-charmed hadron production in heavy-ion collisionsPRODUCTION OF MULTICHARMED HADRONS … PHYSICAL REVIEW C 101, 024902 (2020)

in Sec. IV. Section V is devoted to conclusions. We showthe equivalence of the transverse momentum distribution ofa four-quark hadron on alternative relative coordinates inthe Appendix. In the paper we use sometimes the simplifiednotation for the X (3872) meson: X4 for the X (3872) mesonin a four-quark state, and X2 for the X (3872) meson in atwo-quark state.

II. PRODUCTION OF MULTICHARMED HADRONSFROM THE QUARK-GLUON PLASMA

We evaluate yields of multicharmed hadrons, !cc, !∗cc,

"scc, "∗scc, "ccc baryons, as well as X (3872) and Tcc mesons

produced in relativistic heavy ion collisions using both thestatistical and coalescence model in midrapidity. The sta-tistical hadronization model assuming hadron production inthermal and chemical equilibrium at chemical freeze-out hasbeen very successful in explaining the production yields ofhadrons in heavy ion collisions [32]. In applying the statisticalhadronization model here for the estimation of the produc-tion yields of multicharmed hadrons we introduce additionalcharm quark fugacities γc in order to take into account charmquarks which are not in equilibrium in a quark-gluon plasmaphase due to their heavier masses compared to availabletemperatures in a system. The yields are then given as

N stath = VH

gh

2π2

! ∞

0

p2d pγ −n

c eEh/TH ± 1, (1)

where gh is the degeneracy factor of a hadron of species h,n is the number of charm quarks in the hadron, VH and THare the hadronization volume and temperature, respectively.Eh =

√m2

h + p2 in Eq. (1) is the energy of the hadron ofmass mh. Here we consider that the multicharmed hadrons areproduced at the same chemical freeze-out point as in the sta-tistical hadronization model analysis, i.e., at the hadronizationtemperature and volume TH = 162 MeV and VH = 2100 fm3

at RHIC [33] and TH = 156 MeV and VH = 5380 fm3 at LHC[34], respectively. We use the total numbers of charm quarkpairs in the unit rapidity region available from the initial hardcollisions, 4.1 at RHIC and 11 at LHC [35], which leads to thecharm quark fugacity factors γc = 22 at RHIC and 39 at LHC[19]. All charm quarks produced at the initial hard collisionsare assumed to be conserved and fully distributed to charmedhadrons including D, D∗, Ds mesons, and %c after chemicalfreeze-out [17–19].

We also consider yields of the !cc, !∗cc, "scc, "∗

scc, "ccc,X (3872), and Tcc in the coalescence model which successfullyexplains the enhanced production of the baryon compared tothe meson in the intermediate transverse momentum region[12–15]. The yield of the multicharmed hadron in the coales-cence model becomes for s-wave constituents [19]

Ncoalh = ghVc

(4π )3/2

"ωc

#3i mi

$3/2

(1 + 2Tc/ωc)2

3%

i=1

Ni(4π )3/2

giVc(miωc)3/2. (2)

where gi is the color and spin degeneracy of the quark, 2 × 3.Following Ref. [19] we consider that hadron productions bycoalescence occur at temperature Tc = 166 MeV and volumeVc = 1790 (3530) fm3 at RHIC (LHC). The thermodynamicvariables with a subscript c here refer to the freeze-out

TABLE I. The !cc, !∗cc, "scc, "∗

scc, "ccc, Tcc, and X (3872) yieldsat midrapidity in both the statistical and coalescence model expectedat RHIC in

√sNN = 200 GeV Au+Au collisions and at LHC in√

sNN = 2.76 TeV Pb+Pb collisions.

RHIC LHC

Stat. Coal. Stat. Coal.

!cc 1.0 × 10−2 1.3 × 10−3 2.8 × 10−2 4.9 × 10−3

!∗cc 6.4 × 10−3 9.0 × 10−4 1.8 × 10−2 3.3 × 10−3

"scc 2.8 × 10−3 2.5 × 10−4 8.0 × 10−3 9.0 × 10−4

"∗scc 1.5 × 10−3 1.6 × 10−4 4.3 × 10−3 6.0 × 10−4

"ccc 1.1 × 10−4 1.1 × 10−6 4.0 × 10−4 5.3 × 10−6

Tcc 8.9 × 10−4 5.3 × 10−5 2.7 × 10−3 1.3 × 10−4

X2 5.7 × 10−4 5.6 × 10−4 1.7 × 10−3 1.7 × 10−3

X4 5.7 × 10−4 5.3 × 10−5 1.7 × 10−3 1.3 × 10−4

conditions at the moment of hadronization by quark coales-cence. Although the hadronization conditions are differentin the statistical and coalescence model, we use the termhadronization point to refer to both cases depending on themodel used. In Eq. (2) mi is the mass of constituent quarks;the masses of light, strange, and charm quarks are 350, 500,and 1500 MeV, respectively. In general, the thermal mass ofquarks is different in different literature, and it seems reason-able to choose the light quark mass value between 300 and350 MeV. As a different constituent quark mass will inevitablylead to a different ωc value within our prescription, we findthat it is necessary to study systematically the thermal massdependence on the yield or transverse momentum distribution,but we leave it as a future study. For the number of quarksin a system, Ni, in Eq. (2) we adopt that the number oflight quarks available at hadronization is 302 (593), that ofstrange quarks 176 (347), and that of charm quark pairs 4.1(11) at RHIC (LHC). Finally, by taking the charm quarkoscillator frequencies for the Wigner function, ωc = 244 MeVfor RHIC and 278 MeV for LHC, we evaluate the productionyields of the !cc, "scc, "ccc baryons, Tcc and X (3872) mesons,and show the results in Table I.

We show two yields for the X (3872) meson, one for theX (3872) in a two-quark state, the X2, and the other for theX (3872) meson in a four-quark state, the X4 [19]. We consideronly a four-quark state for the Tcc when evaluating the yieldof the Tcc in the coalescence model.

In the statistical hadronization model 3621.4 MeV for themass of the !cc [23], 3648.0 MeV for the !∗

cc, 3679.0 MeVfor the "scc, 3765.0 MeV for the "∗

scc, 4761.0 MeV for the"ccc, [36], 3871.6 MeV for the X (3872) [37], and 3797 MeVfor the Tcc [19] are adopted. The mass of multicharmed hadrontaken here is very close to that obtained in the recent analysis[38]. When evaluating yields of the !cc and "scc, we haveassumed the exclusive decay of a spin 3/2 baryon to a spin1/2 baryon, similar to decay modes of !∗ and ' baryons [37]as summarized in Table II. We expect that the "scc decays tothe baryon with one charm quark like the !c without decayingto the !cc. The "ccc is expected to decay to either the !cc orthe "scc, but the yield of the "ccc is much smaller comparedto those of the !cc and "scc, and therefore we neglect thecontribution of the "ccc decay to the yield of the !cc and "scc.

024902-3

S. Cho and SH Lee, PRC 101, 024902 (2020)

The yields in the coalescence model are smaller than those in stat. model reflecting the suppression effect in the quark coalescence process

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pT spectra of multi-charmed hadrons from coal. model

S. Cho and SH Lee, PRC 101, 024902 (2020)

PRODUCTION OF MULTICHARMED HADRONS … PHYSICAL REVIEW C 101, 024902 (2020)

FIG. 3. Transverse momentum distributions (2π pT )−1dN/d pT

of multicharmed hadrons, "cc, "∗cc, #scc, #∗

scc, #ccc baryons, and aX (3872) meson in a four-quark state X4 at RHIC (a) and at LHC (b).

momenta whereas that at LHC deviates from measurementswithin errors at high transverse momenta.

D. Transverse momentum distributionsof multicharmed hadrons

Now we evaluate transverse momentum distributions of"cc, "∗

cc, #scc, #∗scc, #ccc baryons, X (3872), and Tcc mesons

produced by quark recombination using Eqs. (9)–(13) and(20)–(22). In the calculation we use light quark mass ml =ml̄ = 300 MeV, charm quark mass mc = mc̄ = 1500 MeV,and the volume 1790 fm3 for RHIC and 3530 fm3 for LHC.

We show in Fig. 3 transverse momentum distributions(2π pT )−1dN/d pT of multicharmed hadrons, "cc, "∗

cc, #scc,#∗

scc, #ccc baryons, and the X (3872) meson in a four-quarkstate, X4, at both RHIC

√sNN = 200 GeV and LHC

√sNN =

2.76 TeV. Here we have taken into account feed-down con-tributions for transverse momentum distributions of the "ccand #scc baryon from their spin 3/2 hadrons, "∗

cc and #∗scc

baryons, respectively. However, we assume that transversemomentum distributions of the daughter hadrons, "cc and#scc baryons, are almost same as those of "∗

cc and #∗scc

baryons after the "∗cc and #∗

scc baryon decays to the "cc and

FIG. 4. Transverse momentum distributions of the X (3872) ina four-quark state, X4, and the Tcc meson for

√sNN = 200 GeV at

RHIC. In the inset dN/d pT of the X4 and Tcc in unit of 10−5 GeV−1

are shown.

#scc baryon, respectively since "cc and #scc baryons are muchheavier than the other daughter hadron in the decay process.

As we see in Fig. 3, all transverse momentum distributionsof charmed hadrons at LHC are larger than those at RHICdue to the larger number of charm and light quarks availableat LHC compared to that at RHIC. It has been found thatthe yield of a hadron with more quarks is suppressed sincethe probability to combine more quarks to form a multiquarkhadron decreases as the number of quarks within a hadron isincreased [17–19]. Therefore it is expected that the transversemomentum distribution of normal hadrons composed of threequarks, "cc, "∗

cc, #scc, and #∗scc baryons is larger than that

of four-quark hadrons, X (3872) mesons at both RHIC andLHC. We find that transverse momentum distributions of the"cc and "∗

cc baryon is larger than that of the X4 meson byan order of magnitude at both RHIC and LHC as expectedbut the transverse momentum distribution of the X4 meson islarger than that of the #ccc baryon by two orders of magnitudeat both RHIC and LHC. The effect from the much smallerabundance of charm quarks in the system compared to thatof light quarks by a factor of hundreds at RHIC and LHCoverwhelms the meaningful contribution from the larger pos-sibility for forming a hadron composed of three charm quarkscompared to the relatively smaller possibility for forming ahadron with four quarks, leading to the smaller transversemomentum distribution of the #ccc baryon compared to thatof the X (3872) meson.

We have also obtained the transverse momentum distribu-tion of the Tcc meson, similar to that of the four-quark X (3872)meson. Since the same transverse momentum distributions ofcharm quarks at RHIC and LHC, Eq. (23), are introduced, thedifference of the transverse momentum distribution betweenthe Tcc and the X4 is originated from the light quark/antiquarkdistributions, or the nonzero baryon chemical potential. Weshow in Fig. 4 the transverse momentum distributions of X4and Tcc mesons at RHIC. As expected the transverse momen-tum distribution of the Tcc is slightly smaller than that of theX4 due to the smaller number of antilight quarks caused by

024902-9

PRODUCTION OF MULTICHARMED HADRONS … PHYSICAL REVIEW C 101, 024902 (2020)

FIG. 3. Transverse momentum distributions (2π pT )−1dN/d pT

of multicharmed hadrons, "cc, "∗cc, #scc, #∗

scc, #ccc baryons, and aX (3872) meson in a four-quark state X4 at RHIC (a) and at LHC (b).

momenta whereas that at LHC deviates from measurementswithin errors at high transverse momenta.

D. Transverse momentum distributionsof multicharmed hadrons

Now we evaluate transverse momentum distributions of"cc, "∗

cc, #scc, #∗scc, #ccc baryons, X (3872), and Tcc mesons

produced by quark recombination using Eqs. (9)–(13) and(20)–(22). In the calculation we use light quark mass ml =ml̄ = 300 MeV, charm quark mass mc = mc̄ = 1500 MeV,and the volume 1790 fm3 for RHIC and 3530 fm3 for LHC.

We show in Fig. 3 transverse momentum distributions(2π pT )−1dN/d pT of multicharmed hadrons, "cc, "∗

cc, #scc,#∗

scc, #ccc baryons, and the X (3872) meson in a four-quarkstate, X4, at both RHIC

√sNN = 200 GeV and LHC

√sNN =

2.76 TeV. Here we have taken into account feed-down con-tributions for transverse momentum distributions of the "ccand #scc baryon from their spin 3/2 hadrons, "∗

cc and #∗scc

baryons, respectively. However, we assume that transversemomentum distributions of the daughter hadrons, "cc and#scc baryons, are almost same as those of "∗

cc and #∗scc

baryons after the "∗cc and #∗

scc baryon decays to the "cc and

FIG. 4. Transverse momentum distributions of the X (3872) ina four-quark state, X4, and the Tcc meson for

√sNN = 200 GeV at

RHIC. In the inset dN/d pT of the X4 and Tcc in unit of 10−5 GeV−1

are shown.

#scc baryon, respectively since "cc and #scc baryons are muchheavier than the other daughter hadron in the decay process.

As we see in Fig. 3, all transverse momentum distributionsof charmed hadrons at LHC are larger than those at RHICdue to the larger number of charm and light quarks availableat LHC compared to that at RHIC. It has been found thatthe yield of a hadron with more quarks is suppressed sincethe probability to combine more quarks to form a multiquarkhadron decreases as the number of quarks within a hadron isincreased [17–19]. Therefore it is expected that the transversemomentum distribution of normal hadrons composed of threequarks, "cc, "∗

cc, #scc, and #∗scc baryons is larger than that

of four-quark hadrons, X (3872) mesons at both RHIC andLHC. We find that transverse momentum distributions of the"cc and "∗

cc baryon is larger than that of the X4 meson byan order of magnitude at both RHIC and LHC as expectedbut the transverse momentum distribution of the X4 meson islarger than that of the #ccc baryon by two orders of magnitudeat both RHIC and LHC. The effect from the much smallerabundance of charm quarks in the system compared to thatof light quarks by a factor of hundreds at RHIC and LHCoverwhelms the meaningful contribution from the larger pos-sibility for forming a hadron composed of three charm quarkscompared to the relatively smaller possibility for forming ahadron with four quarks, leading to the smaller transversemomentum distribution of the #ccc baryon compared to thatof the X (3872) meson.

We have also obtained the transverse momentum distribu-tion of the Tcc meson, similar to that of the four-quark X (3872)meson. Since the same transverse momentum distributions ofcharm quarks at RHIC and LHC, Eq. (23), are introduced, thedifference of the transverse momentum distribution betweenthe Tcc and the X4 is originated from the light quark/antiquarkdistributions, or the nonzero baryon chemical potential. Weshow in Fig. 4 the transverse momentum distributions of X4and Tcc mesons at RHIC. As expected the transverse momen-tum distribution of the Tcc is slightly smaller than that of theX4 due to the smaller number of antilight quarks caused by

024902-9

PRODUCTION OF MULTICHARMED HADRONS … PHYSICAL REVIEW C 101, 024902 (2020)

FIG. 3. Transverse momentum distributions (2π pT )−1dN/d pT

of multicharmed hadrons, "cc, "∗cc, #scc, #∗

scc, #ccc baryons, and aX (3872) meson in a four-quark state X4 at RHIC (a) and at LHC (b).

momenta whereas that at LHC deviates from measurementswithin errors at high transverse momenta.

D. Transverse momentum distributionsof multicharmed hadrons

Now we evaluate transverse momentum distributions of"cc, "∗

cc, #scc, #∗scc, #ccc baryons, X (3872), and Tcc mesons

produced by quark recombination using Eqs. (9)–(13) and(20)–(22). In the calculation we use light quark mass ml =ml̄ = 300 MeV, charm quark mass mc = mc̄ = 1500 MeV,and the volume 1790 fm3 for RHIC and 3530 fm3 for LHC.

We show in Fig. 3 transverse momentum distributions(2π pT )−1dN/d pT of multicharmed hadrons, "cc, "∗

cc, #scc,#∗

scc, #ccc baryons, and the X (3872) meson in a four-quarkstate, X4, at both RHIC

√sNN = 200 GeV and LHC

√sNN =

2.76 TeV. Here we have taken into account feed-down con-tributions for transverse momentum distributions of the "ccand #scc baryon from their spin 3/2 hadrons, "∗

cc and #∗scc

baryons, respectively. However, we assume that transversemomentum distributions of the daughter hadrons, "cc and#scc baryons, are almost same as those of "∗

cc and #∗scc

baryons after the "∗cc and #∗

scc baryon decays to the "cc and

FIG. 4. Transverse momentum distributions of the X (3872) ina four-quark state, X4, and the Tcc meson for

√sNN = 200 GeV at

RHIC. In the inset dN/d pT of the X4 and Tcc in unit of 10−5 GeV−1

are shown.

#scc baryon, respectively since "cc and #scc baryons are muchheavier than the other daughter hadron in the decay process.

As we see in Fig. 3, all transverse momentum distributionsof charmed hadrons at LHC are larger than those at RHICdue to the larger number of charm and light quarks availableat LHC compared to that at RHIC. It has been found thatthe yield of a hadron with more quarks is suppressed sincethe probability to combine more quarks to form a multiquarkhadron decreases as the number of quarks within a hadron isincreased [17–19]. Therefore it is expected that the transversemomentum distribution of normal hadrons composed of threequarks, "cc, "∗

cc, #scc, and #∗scc baryons is larger than that

of four-quark hadrons, X (3872) mesons at both RHIC andLHC. We find that transverse momentum distributions of the"cc and "∗

cc baryon is larger than that of the X4 meson byan order of magnitude at both RHIC and LHC as expectedbut the transverse momentum distribution of the X4 meson islarger than that of the #ccc baryon by two orders of magnitudeat both RHIC and LHC. The effect from the much smallerabundance of charm quarks in the system compared to thatof light quarks by a factor of hundreds at RHIC and LHCoverwhelms the meaningful contribution from the larger pos-sibility for forming a hadron composed of three charm quarkscompared to the relatively smaller possibility for forming ahadron with four quarks, leading to the smaller transversemomentum distribution of the #ccc baryon compared to thatof the X (3872) meson.

We have also obtained the transverse momentum distribu-tion of the Tcc meson, similar to that of the four-quark X (3872)meson. Since the same transverse momentum distributions ofcharm quarks at RHIC and LHC, Eq. (23), are introduced, thedifference of the transverse momentum distribution betweenthe Tcc and the X4 is originated from the light quark/antiquarkdistributions, or the nonzero baryon chemical potential. Weshow in Fig. 4 the transverse momentum distributions of X4and Tcc mesons at RHIC. As expected the transverse momen-tum distribution of the Tcc is slightly smaller than that of theX4 due to the smaller number of antilight quarks caused by

024902-9

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Baryon to meson ratio

Λc/D0

• Remarkable similarities of baryon to meson ratio in the charm sector with light flavor results in pp and p-Pb collisions.

ATHIC 2018 Pengyao CuiStrangeness production in jets and the UE

Results of Pb-Pb collisions 10

⚫ The different media affect seen at low V0 𝑝T in comparison with PYTHIA

⚫ The ratio in jets is far below the inclusive one in Pb–Pb collisions

⚫ The ratio in jets is similar to that in pp collisions

𝒑𝐓𝐣𝐞𝐭,𝐜𝐡 > 𝟏𝟎 𝐆𝐞𝐕/𝒄 𝒑𝐓

𝐣𝐞𝐭,𝐜𝐡 > 𝟐𝟎 𝐆𝐞𝐕/𝒄

• Peak is originated from a competition between two particle production mechanisms: a fragmentation dominates at large transverse momenta (power law) and a coalescence prevails at lower transverse momenta (exponential)

2) The transverse momentum spectra and

16 March 26th 2019 Yukawa Institute for Theoretical Physics

Hadron Interactions and Polarization from Lattice QCD, Quark Model, and Heavy Ion Collisions

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Ratio of charmed hadrons

S. Cho and SH Lee, PRC 101, 024902 (2020)

PRODUCTION OF MULTICHARMED HADRONS … PHYSICAL REVIEW C 101, 024902 (2020)

FIG. 6. Transverse momentum distribution ratios (a) between the X (3872) and the !c, (b) between the "cc and the !c, (c) between the#ccc and the !c, and (d) between the #scc and the !c at both RHIC

√sNN = 200 GeV and LHC

√sNN = 2.76 TeV.

B. Transverse momentum distribution ratios betweena multicharmed hadron and a !c

We compare the transverse momentum distribution of mul-ticharmed hadrons with that of the singly charmed hadron, the!c. For the !c transverse momentum distribution we have in-cluded the contribution of the !c production by fragmentationas well as feed-down contributions from $c(2455), $c(2520),!c(2595), and !c(2625) baryons. We show in Fig. 6 fourtransverse momentum distribution ratios, (a) between theX (3872) and the !c, (b) between the "cc and the !c,(c) between the #ccc and the !c, and (d) between the #scc andthe !c for both RHIC,

√sNN = 200 GeV and LHC,

√sNN =

2.76 TeV.As we see in Fig. 6, the ratio is much smaller than unity,

again reflecting the small possibility to coalesce more charmquarks to form a multicharmed hadron. Since the numberof charm quarks is smaller than that of light quarks by anorder of 2, the ratio between the X (3872) and the !c isalso smaller than that between the X (3872) and the "cc bythe same order. Nevertheless we still see peaks appearing inthe intermediate transverse momentum region, but at lowertransverse momentum about 4 GeV.

We have argued that the peak can appear for the ratio in-volving both light quarks in thermal equilibrium with an expo-nential transverse momentum distribution and charm quarkswith a power law type transverse momentum distribution in

addition to an exponential transverse momentum distribution.We have also found that the peak appears in the ratio involvingpure light quarks with the same kind but different numbers inthe numerator and the denominator, e.g., qq̄/q.

We further argue that a peak appears in the ratio involvingcharm and light quarks, especially when a remaining charmquark is in the numerator and a light quark remains in thedenominator, e.g., c/q. As shown in Fig. 5 the peak appearsin ratios c/s (b) and c/q (c), except the peak in the ratio qq̄/q(a). No peak appears for the ratio q/c (d), s/q (e), and qq̄/s(f). We see that all the ratios shown in Fig. 6 involve at leastone charm quark in the numerator and one light quark in thedenominator, q̄c̄/q (a), c/q (b), cc/qq (c), and cs/qq (d), andtherefore we find that the peak always appears in the ratiobetween a multicharm hadron and a !c.

Transverse momentum distribution ratios shown inFigs. 6(a), 6(b), and 6(d) look very similar in both shape andmagnitude, ∼10−3; three ratios represent cc̄qq̄/cqq, ccq/cqq,and ccs/cqq, respectively. If we neglect spectator quarks wesee ratios c̄q̄/q, c/q, and cs/qq. The inclusion of one morelight quark in the numerator, cc̄qq̄, not only suppresses morethe ratio cc̄qq̄/cqq to ∼10−4, it also broadens the peak inFig. 6(a) compared to the other two ratios. The same expo-nential transverse momentum distribution and 200 MeV massdifference between light and strange quarks give the similarratios c/q and cs/qq as shown in Figs. 6(b) and 6(d).

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PRODUCTION OF MULTICHARMED HADRONS … PHYSICAL REVIEW C 101, 024902 (2020)

FIG. 6. Transverse momentum distribution ratios (a) between the X (3872) and the !c, (b) between the "cc and the !c, (c) between the#ccc and the !c, and (d) between the #scc and the !c at both RHIC

√sNN = 200 GeV and LHC

√sNN = 2.76 TeV.

B. Transverse momentum distribution ratios betweena multicharmed hadron and a !c

We compare the transverse momentum distribution of mul-ticharmed hadrons with that of the singly charmed hadron, the!c. For the !c transverse momentum distribution we have in-cluded the contribution of the !c production by fragmentationas well as feed-down contributions from $c(2455), $c(2520),!c(2595), and !c(2625) baryons. We show in Fig. 6 fourtransverse momentum distribution ratios, (a) between theX (3872) and the !c, (b) between the "cc and the !c,(c) between the #ccc and the !c, and (d) between the #scc andthe !c for both RHIC,

√sNN = 200 GeV and LHC,

√sNN =

2.76 TeV.As we see in Fig. 6, the ratio is much smaller than unity,

again reflecting the small possibility to coalesce more charmquarks to form a multicharmed hadron. Since the numberof charm quarks is smaller than that of light quarks by anorder of 2, the ratio between the X (3872) and the !c isalso smaller than that between the X (3872) and the "cc bythe same order. Nevertheless we still see peaks appearing inthe intermediate transverse momentum region, but at lowertransverse momentum about 4 GeV.

We have argued that the peak can appear for the ratio in-volving both light quarks in thermal equilibrium with an expo-nential transverse momentum distribution and charm quarkswith a power law type transverse momentum distribution in

addition to an exponential transverse momentum distribution.We have also found that the peak appears in the ratio involvingpure light quarks with the same kind but different numbers inthe numerator and the denominator, e.g., qq̄/q.

We further argue that a peak appears in the ratio involvingcharm and light quarks, especially when a remaining charmquark is in the numerator and a light quark remains in thedenominator, e.g., c/q. As shown in Fig. 5 the peak appearsin ratios c/s (b) and c/q (c), except the peak in the ratio qq̄/q(a). No peak appears for the ratio q/c (d), s/q (e), and qq̄/s(f). We see that all the ratios shown in Fig. 6 involve at leastone charm quark in the numerator and one light quark in thedenominator, q̄c̄/q (a), c/q (b), cc/qq (c), and cs/qq (d), andtherefore we find that the peak always appears in the ratiobetween a multicharm hadron and a !c.

Transverse momentum distribution ratios shown inFigs. 6(a), 6(b), and 6(d) look very similar in both shape andmagnitude, ∼10−3; three ratios represent cc̄qq̄/cqq, ccq/cqq,and ccs/cqq, respectively. If we neglect spectator quarks wesee ratios c̄q̄/q, c/q, and cs/qq. The inclusion of one morelight quark in the numerator, cc̄qq̄, not only suppresses morethe ratio cc̄qq̄/cqq to ∼10−4, it also broadens the peak inFig. 6(a) compared to the other two ratios. The same expo-nential transverse momentum distribution and 200 MeV massdifference between light and strange quarks give the similarratios c/q and cs/qq as shown in Figs. 6(b) and 6(d).

024902-13

• In addition to the hadronization mechanism, peak can appear involving light quarks in thermal equilibrium with an exponential transverse momentum distribution and charm quarks with a power law type transverse momentum distribution in addition to an exponential transverse momentum distribution

PRODUCTION OF MULTICHARMED HADRONS … PHYSICAL REVIEW C 101, 024902 (2020)

FIG. 6. Transverse momentum distribution ratios (a) between the X (3872) and the !c, (b) between the "cc and the !c, (c) between the#ccc and the !c, and (d) between the #scc and the !c at both RHIC

√sNN = 200 GeV and LHC

√sNN = 2.76 TeV.

B. Transverse momentum distribution ratios betweena multicharmed hadron and a !c

We compare the transverse momentum distribution of mul-ticharmed hadrons with that of the singly charmed hadron, the!c. For the !c transverse momentum distribution we have in-cluded the contribution of the !c production by fragmentationas well as feed-down contributions from $c(2455), $c(2520),!c(2595), and !c(2625) baryons. We show in Fig. 6 fourtransverse momentum distribution ratios, (a) between theX (3872) and the !c, (b) between the "cc and the !c,(c) between the #ccc and the !c, and (d) between the #scc andthe !c for both RHIC,

√sNN = 200 GeV and LHC,

√sNN =

2.76 TeV.As we see in Fig. 6, the ratio is much smaller than unity,

again reflecting the small possibility to coalesce more charmquarks to form a multicharmed hadron. Since the numberof charm quarks is smaller than that of light quarks by anorder of 2, the ratio between the X (3872) and the !c isalso smaller than that between the X (3872) and the "cc bythe same order. Nevertheless we still see peaks appearing inthe intermediate transverse momentum region, but at lowertransverse momentum about 4 GeV.

We have argued that the peak can appear for the ratio in-volving both light quarks in thermal equilibrium with an expo-nential transverse momentum distribution and charm quarkswith a power law type transverse momentum distribution in

addition to an exponential transverse momentum distribution.We have also found that the peak appears in the ratio involvingpure light quarks with the same kind but different numbers inthe numerator and the denominator, e.g., qq̄/q.

We further argue that a peak appears in the ratio involvingcharm and light quarks, especially when a remaining charmquark is in the numerator and a light quark remains in thedenominator, e.g., c/q. As shown in Fig. 5 the peak appearsin ratios c/s (b) and c/q (c), except the peak in the ratio qq̄/q(a). No peak appears for the ratio q/c (d), s/q (e), and qq̄/s(f). We see that all the ratios shown in Fig. 6 involve at leastone charm quark in the numerator and one light quark in thedenominator, q̄c̄/q (a), c/q (b), cc/qq (c), and cs/qq (d), andtherefore we find that the peak always appears in the ratiobetween a multicharm hadron and a !c.

Transverse momentum distribution ratios shown inFigs. 6(a), 6(b), and 6(d) look very similar in both shape andmagnitude, ∼10−3; three ratios represent cc̄qq̄/cqq, ccq/cqq,and ccs/cqq, respectively. If we neglect spectator quarks wesee ratios c̄q̄/q, c/q, and cs/qq. The inclusion of one morelight quark in the numerator, cc̄qq̄, not only suppresses morethe ratio cc̄qq̄/cqq to ∼10−4, it also broadens the peak inFig. 6(a) compared to the other two ratios. The same expo-nential transverse momentum distribution and 200 MeV massdifference between light and strange quarks give the similarratios c/q and cs/qq as shown in Figs. 6(b) and 6(d).

024902-13

PRODUCTION OF MULTICHARMED HADRONS … PHYSICAL REVIEW C 101, 024902 (2020)

FIG. 8. The transverse momentum distribution ratio between the!ccc and the X (3872) in a two-quark state, ccc/cc̄.

quark contents in two ratios, q̄q̄/q for the p̄/π and cc/c̄ forthe !ccc/X2.

As expected from the transverse momentum distributionratio between the X (3872) and various charmed hadrons, thetransverse momentum distribution of the X (3872) meson ina two-quark state is quite different from that of the X (3872)meson in a four-quark state. Therefore, we consider that wecan identify whether the X (3872) meson is composed of fourquarks or two quarks by measuring the transverse momentumdistribution ratio between the X (3872) and various charmedbaryons. We also show transverse momentum distributions,dNX (3872)/d pT of both the X (3872) in a four-quark stateand that in a two-quark state in Fig. 9. Recently, transversemomentum spectra of the X (3872) cross section for Pb-Pband Kr-Kr collisions at

√s = 5 TeV have been predicted in

the statistical hadronization model [46]. We hope that we cancompare directly the transverse momentum distribution of theX (3872) yield obtained here to that measured in relativisticheavy ion collision experiments as well as that obtained in the

FIG. 9. Transverse momentum distributions of both the X (3872)in a four-quark state X4 and that in a two-quark state X2 for

√sNN =

200 GeV at RHIC and√

sNN = 2.76 TeV at LHC.

statistical hadronization model in the near future, and that wecan identify the quark structure of the X (3872) meson.

V. CONCLUSION

We have studied the production of multicharmed hadronsby recombination in relativistic heavy ion collisions by focus-ing on the production of #cc, #∗

cc, !scc, !∗scc, !ccc baryons

and X (3872) mesons. We first pay attention to the yield inheavy ion collisions, and have estimated that of multicharmedhadrons mentioned above at chemical freeze-out in both thestatistical and coalescence model. We have also discussed thevarious yield ratio between multicharmed hadrons.

Second, we focus on the transverse momentum distributionin heavy ion collisions, and have evaluated that of multi-charmed hadrons, the #cc, #∗

cc, !scc, !∗scc, !ccc baryon, and

the X(3872) meson at midrapidity in the coalescence model.We have also obtained transverse momentum distributionratios between multicharmed hadrons, especially transversemomentum distribution ratios related to the X (3872) meson, ameson/baryon ratio similar to a usual baryon/meson ratio, inorder to investigate whether there exists enhanced productionfor a four-quark hadron compared to a normal hadron atintermediate transverse momentum region due to some rea-sons, e.g., hadron production mechanisms or transverse mo-mentum distributions of constituent quarks. We have furtherevaluated transverse momentum distribution ratios betweenmulticharmed hadrons and a singly charmed baryon, the $c.Last, we have discussed the transverse momentum distributionof the X (3872) in a four-quark state, X4, and that of theX (3872) in a two-quark state, X2.

We find that yields decrease with increasing number ofcharm and light quarks in multicharmed hadrons in boththe statistical and coalescence models as expected. However,when the X (3872) is considered to be a normal meson com-posed of a charm and an anticharm quark, X2, the yield in thecoalescence model is almost the same as that in the statisticalmodel. It is interesting to notice that the yield of the X4 iscomparable to that of the !scc in the coalescence model whenthe feed-down contribution of the !∗

scc to the !scc is not takeninto account; the effect of including two more light quarks ofthe constituent mass 350 MeV is comparable to that of addingone more strange quark of the mass 500 MeV.

The yield of multicharmed hadrons in the quark coales-cence model is found to be smaller than that in the statis-tical model, reflecting the suppression effects in the quarkcoalescence process. Among the yield ratio between charmedhadrons we find that yield ratios involving the !ccc, or!ccc/#cc, !ccc/!scc, and !ccc/X4 at LHC, are always largerthan those at RHIC in both the statistical and coalescencemodels. For other ratios without the !ccc ratios at RHIC arecomparable to or larger than those at LHC.

Transverse momentum distributions of charmed hadronsat LHC are found to be larger than those at RHIC due tothe larger number of charm and light quarks available atLHC compared to that at RHIC. We find that the transversemomentum distribution of the X4 meson is larger than that ofthe !ccc baryon by two orders of magnitude at both RHICand LHC. The effect from the much smaller abundance of

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Multi-HF hadrons• Statistical coalescence between uncorrelated heavy quarks in thermal equilibrium at the hadronization point

[Beccattini, PRL 95 022301 (2005)]- Up to 2-3 orders of magnitude higher Ωccc/Nccbar w.r.t. models based on QCD hard scattering - Significant enhancement of ratios of MHF baryons over singly HF hadrons, especially Ξbc/B and Ωccc/D

Hadron Yield in central Pb-Pb (full phase space) Expected enhancement w.r.t. pp

Ξcc , Ωcc 0.02-0.38 1-10Ξbc , Ωbc , Bc 3x10-4 - 0.02 >10 for Ξbc

Ξbb , Ωbb 2.6x10-6 - 7x10-5 -Ωccc 10-3 - 0.03 100-1000

Production yields calculated using different approaches

• Probe kinetic equilibration/thermalization of charm in the QGP

!7

PRODUCTION OF MULTICHARMED HADRONS … PHYSICAL REVIEW C 101, 024902 (2020)

in Sec. IV. Section V is devoted to conclusions. We showthe equivalence of the transverse momentum distribution ofa four-quark hadron on alternative relative coordinates inthe Appendix. In the paper we use sometimes the simplifiednotation for the X (3872) meson: X4 for the X (3872) mesonin a four-quark state, and X2 for the X (3872) meson in atwo-quark state.

II. PRODUCTION OF MULTICHARMED HADRONSFROM THE QUARK-GLUON PLASMA

We evaluate yields of multicharmed hadrons, !cc, !∗cc,

"scc, "∗scc, "ccc baryons, as well as X (3872) and Tcc mesons

produced in relativistic heavy ion collisions using both thestatistical and coalescence model in midrapidity. The sta-tistical hadronization model assuming hadron production inthermal and chemical equilibrium at chemical freeze-out hasbeen very successful in explaining the production yields ofhadrons in heavy ion collisions [32]. In applying the statisticalhadronization model here for the estimation of the produc-tion yields of multicharmed hadrons we introduce additionalcharm quark fugacities γc in order to take into account charmquarks which are not in equilibrium in a quark-gluon plasmaphase due to their heavier masses compared to availabletemperatures in a system. The yields are then given as

N stath = VH

gh

2π2

! ∞

0

p2d pγ −n

c eEh/TH ± 1, (1)

where gh is the degeneracy factor of a hadron of species h,n is the number of charm quarks in the hadron, VH and THare the hadronization volume and temperature, respectively.Eh =

√m2

h + p2 in Eq. (1) is the energy of the hadron ofmass mh. Here we consider that the multicharmed hadrons areproduced at the same chemical freeze-out point as in the sta-tistical hadronization model analysis, i.e., at the hadronizationtemperature and volume TH = 162 MeV and VH = 2100 fm3

at RHIC [33] and TH = 156 MeV and VH = 5380 fm3 at LHC[34], respectively. We use the total numbers of charm quarkpairs in the unit rapidity region available from the initial hardcollisions, 4.1 at RHIC and 11 at LHC [35], which leads to thecharm quark fugacity factors γc = 22 at RHIC and 39 at LHC[19]. All charm quarks produced at the initial hard collisionsare assumed to be conserved and fully distributed to charmedhadrons including D, D∗, Ds mesons, and %c after chemicalfreeze-out [17–19].

We also consider yields of the !cc, !∗cc, "scc, "∗

scc, "ccc,X (3872), and Tcc in the coalescence model which successfullyexplains the enhanced production of the baryon compared tothe meson in the intermediate transverse momentum region[12–15]. The yield of the multicharmed hadron in the coales-cence model becomes for s-wave constituents [19]

Ncoalh = ghVc

(4π )3/2

"ωc

#3i mi

$3/2

(1 + 2Tc/ωc)2

3%

i=1

Ni(4π )3/2

giVc(miωc)3/2. (2)

where gi is the color and spin degeneracy of the quark, 2 × 3.Following Ref. [19] we consider that hadron productions bycoalescence occur at temperature Tc = 166 MeV and volumeVc = 1790 (3530) fm3 at RHIC (LHC). The thermodynamicvariables with a subscript c here refer to the freeze-out

TABLE I. The !cc, !∗cc, "scc, "∗

scc, "ccc, Tcc, and X (3872) yieldsat midrapidity in both the statistical and coalescence model expectedat RHIC in

√sNN = 200 GeV Au+Au collisions and at LHC in√

sNN = 2.76 TeV Pb+Pb collisions.

RHIC LHC

Stat. Coal. Stat. Coal.

!cc 1.0 × 10−2 1.3 × 10−3 2.8 × 10−2 4.9 × 10−3

!∗cc 6.4 × 10−3 9.0 × 10−4 1.8 × 10−2 3.3 × 10−3

"scc 2.8 × 10−3 2.5 × 10−4 8.0 × 10−3 9.0 × 10−4

"∗scc 1.5 × 10−3 1.6 × 10−4 4.3 × 10−3 6.0 × 10−4

"ccc 1.1 × 10−4 1.1 × 10−6 4.0 × 10−4 5.3 × 10−6

Tcc 8.9 × 10−4 5.3 × 10−5 2.7 × 10−3 1.3 × 10−4

X2 5.7 × 10−4 5.6 × 10−4 1.7 × 10−3 1.7 × 10−3

X4 5.7 × 10−4 5.3 × 10−5 1.7 × 10−3 1.3 × 10−4

conditions at the moment of hadronization by quark coales-cence. Although the hadronization conditions are differentin the statistical and coalescence model, we use the termhadronization point to refer to both cases depending on themodel used. In Eq. (2) mi is the mass of constituent quarks;the masses of light, strange, and charm quarks are 350, 500,and 1500 MeV, respectively. In general, the thermal mass ofquarks is different in different literature, and it seems reason-able to choose the light quark mass value between 300 and350 MeV. As a different constituent quark mass will inevitablylead to a different ωc value within our prescription, we findthat it is necessary to study systematically the thermal massdependence on the yield or transverse momentum distribution,but we leave it as a future study. For the number of quarksin a system, Ni, in Eq. (2) we adopt that the number oflight quarks available at hadronization is 302 (593), that ofstrange quarks 176 (347), and that of charm quark pairs 4.1(11) at RHIC (LHC). Finally, by taking the charm quarkoscillator frequencies for the Wigner function, ωc = 244 MeVfor RHIC and 278 MeV for LHC, we evaluate the productionyields of the !cc, "scc, "ccc baryons, Tcc and X (3872) mesons,and show the results in Table I.

We show two yields for the X (3872) meson, one for theX (3872) in a two-quark state, the X2, and the other for theX (3872) meson in a four-quark state, the X4 [19]. We consideronly a four-quark state for the Tcc when evaluating the yieldof the Tcc in the coalescence model.

In the statistical hadronization model 3621.4 MeV for themass of the !cc [23], 3648.0 MeV for the !∗

cc, 3679.0 MeVfor the "scc, 3765.0 MeV for the "∗

scc, 4761.0 MeV for the"ccc, [36], 3871.6 MeV for the X (3872) [37], and 3797 MeVfor the Tcc [19] are adopted. The mass of multicharmed hadrontaken here is very close to that obtained in the recent analysis[38]. When evaluating yields of the !cc and "scc, we haveassumed the exclusive decay of a spin 3/2 baryon to a spin1/2 baryon, similar to decay modes of !∗ and ' baryons [37]as summarized in Table II. We expect that the "scc decays tothe baryon with one charm quark like the !c without decayingto the !cc. The "ccc is expected to decay to either the !cc orthe "scc, but the yield of the "ccc is much smaller comparedto those of the !cc and "scc, and therefore we neglect thecontribution of the "ccc decay to the yield of the !cc and "scc.

024902-3

S. Cho and SH Lee, PRC 101, 024902 (2020)

Multi-heavy flavour hadron yields in various models

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Multi-HF hadrons• Sudden coalescence at hadronization temperature [He, Liu,

Zhuang, PLB 746 (2015) 59-63 and Zhao, He, Zhuang, PLB 771 (2017) 349-353]- Coalescence probability defined by the Wigner function

(obtaining wave function solving non-rel. Schrodinger eq.) - Diquark potential = 1/2 quark-antiquark potential = 1/2

Cornell potential

Production yields calculated using different approaches

HadronYield in central PbPb

Cross section per binary coll.

pp cross section Enhancement

Ξcc 0.03 513 nb 62 nb 8

Ωccc 5x10-4 9 nb 0.1-0.2 nb 90-45

• Probe kinetic equilibration/thermalization of charm in the QGP • Interesting 3-body problem: wave func. from 2+1- or 3-body Schrodinger equation

!8

ΩcccΞcc

ΩcccΞcc

Multi-heavy flavour hadron yields in various models

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Multi-HF hadronsModel Collision system Ξcc yield per event

Statistical hadronization 0-5% PbPb @5.5 TeV 0.02-0.38

Sudden coalescence at hadronization temperature 0-5% PbPb @2.76 TeV 0.03

Dynamical evolution of diquark states in the medium 0-10% PbPb @2.76 TeV 0.0125-0.02

Model Collision system Ωccc yield per event

Statistical hadronization 0-5% PbPb @5.5 TeV 10-3 - 0.03

Sudden coalescence at hadronization temperature 0-5% PbPb @2.76 TeV 5x10-4

Yao, Muller, PRD 97 0744003 (2018)

Zhao, He, Zhuang, PLB 771 (2017) 349-353

Beccattini, PRL 95 022301 (2005)

Beccattini, PRL 95 022301 (2005)

He, Liu, Zhuang, PLB 746 (2015) 59-63

Ξcc and Ωccc yields per event obtained from different models similar within a factor 2

!11

Multi-heavy flavour hadron yields in various models

A. Festanti’s slide (ALICE Physics week, 2019)

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B.R.5% x 0.5

5%6.35%70%

0.0055%

B.R.5% x 0.5

5%2.2 ± 0.8%

70%0.0019%

B.R.5%

2.2%9%

0.0099%

Multi-HF hadrons

B.R.5%5%5%

67.8%63.9%

0.0054%Ωccc decays suggested in JHEP08(2011)144, assumption: BR=5%

B.R.5%

6.35%0.32%

B.R.

5%2.2 ± 0.8%

0.11%

Possible decay channels

!12

Ξcc decays: BR from 1703.09086 (authors claim ~1%<BR<~10%)

Branching ratio of possible decay channels of Ξcc and Ωccc

A. Festanti’s slide (ALICE Physics week, 2019)

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Multi-HF hadrons

!13

• Heavy-ion data taking in LHC Run4 or beyond Long Shutdown 4 might enable the measurement of multi-charm baryons

• Lighter beams might also be considered: need to evaluate the impact of potential increased luminosity vs. reduced cross section

Estimate A-scaling for different processes:• Hard processes as charm production: σ ~ A2 , dN/dy ~ A4/3• Double charm hadrons production: σ ~ A7/3 , dN/dy ~ A5/3 = A4/3 x A1/3

with A1/3 ~ charm to light q density• Triple charm hadrons production: σ ~ A8/3 , dN/dy ~ A6/3 = A4/3 x A2/3

with A2/3 ~ (charm to light q density)2

Thanks to F. Antinori

Estimate A-scaling for different processes

A. Festanti’s slide (ALICE Physics week, 2019)

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Multi-HF hadrons

!14

Estimate of the gain in statistics for different processes vs. collision system

Ar-Ar Kr-Kr Xe-Xe Pb-PbA 40 78 129 208

Lint/month (nb-1) 3180 218 38 4.9σhad (b) 2.6 4.06 5.67 7.8

evts/month 8300 x 109 890 x 109 220 x 109 38 x 109

Gain for c 24 6.2 3 1Gain for cc 14 4.5 2.6 1

Gain for ccc 8 3.2 2.2 1

Thanks to F. Antinori

Achievable Lint after LS3 (upper limit) [J. Jowett et al., HL-LHC Yellow Report,1812.06772]

Estimate of the gain in statistics for different systems

A. Festanti’s slide (ALICE Physics week, 2019)

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Multi-HF hadrons

!15

Rate = (yield/event) x B.R. x (single track eff.)Nprongs x acceptance x (sel. efficiency)

Assuming:• yield/event (at mid rapidity) = 5x10-4-0.03(Ωccc), 0.0125-0.38(Ξcc)• Branching ratio from slide 12• Single track efficiency = 98%• Number of central events = 1010 (considering 3 months of PbPb data taking as in the Yellow

Report)

Central PbPb Ξcc Ωccc

Rate(no acc/eff effects considered) 1.2x10-5 - 10-3 8x10-9 - 2.6x10-6

Total yield(no acc/eff effects considered) 1.2x106 - 108 800 - 2.6x105

Estimate of the total “visible” yields of Ξcc and Ωccc

• Ξcc total yield might be larger of a factor from 2.6 to 14 considering Xe-Xe or Ar-Ar respectively• Ωccc total yield might be larger of a factor from 2.2 to 8 considering Xe-Xe or Ar-Ar respectively

Estimate of the total visible yields of Ξcc and Ωccc

1011

A. Festanti’s slide (ALICE Physics week, 2019)

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We have a plan…

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ALICE upgrade timeline

ALICE with LS2 upgrades

+ ITS3, FoCal, fixed target, … next-generation experiment

HL-LHCALICE upgrades time line

(Run 3 extension)

3

Phase II upgrades ATLAS/CMS

major ALICE upgrades

Pb-Pb in Run 3+4: ℒ = 13 nb-1

NB: next-generation experiment could start in ~10 years, similar time line to current upgrades!

4

After LS3 and LS4

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After LS3 (Run 4)

Physics motivation

• Heavy-flavour (charm, bottom): focus on low transverse momenta→ production yields, flow, in jets, vs event shape, …• Exclusive reconstruction of D, Ds, B, Bs,!c,!b, "c, #c decay channels• Analysis of non-prompt signals 

• Low-mass di-leptons: First high-statistics signals for di-leptons at LHC

• New ideas:• c-deuteron, c-triton • Strangeness tracker (“Kick-off” meeting)

5

7"

Table 1: Geometrical parameters of the upgraded ITS.

Beam pipe inner/outer radius (mm) 16.0/16.5

IB Layer parameters Layer 0 Layer 1 Layer 2

Radial position (mm) 18.0 24.0 30.0

Length (sensitive area) (mm) 270 270 270

Pseudo-rapidity coveragea ±2.5 ±2.3 ±2.0

Active area (cm2) 305 408 508

Pixel sensors dimensions (mm2) 140⇥56.5 140⇥75.5 140⇥94

Number of pixel sensors / layer 4

Pixel size (µm2) O(30⇥30)a The pseudorapidity coverage of the detector layers refers to tracks originating from

a collision at the nominal interaction point (z = 0).

3.3 System Integration272

The requirement to locate the first layer at a minimal distance from the beam pipe drives the273

design of the mechanical support structure. The integration scheme is similar to the one adopted274

for the ITS2, with the detector mechanically decoupled from the beam pipe and completely275

supported by an extractable barrel (service barrel) which is fixed to the cage, as shown in Fig. 10.276

Figure 10: Layout of the ITS3 Inner Barrel. Two end-wheels provide precise position andfixation of the detector relative to the beam pipe.

The End-Wheels at the barrel extremities provide accurate positioning and fixation of the detec-277

tor with respect to the beam pipe. The End-Wheels also provide a path for the services to exit278

12

DRAFT

Geometrical"Parameters"of"ITS3""

Beampipe####### IR###16#mm ΔR##0.5mm#

~14cm

Beam"pipe"thickness:"500µm"(0.14%"X0)"

Sensor"thickness:""20"−"40µm"(0.03"L"0.05%"X0)"

Pipe:"r"≈"16mm","ΔR"="0.5mm"

L0:"r"≈"18mm","L1:"r"≈"24mm."L2:"r"≈"30"mm"

L.&Musa&(CERN)&–&ALICE&Physics&Week,&23&Oct&2018&

6"

Silicon&Genesis:&20&micron&thick&wafer&Can we exploit flexible nature of thin silicon ? &

Chipworks:&30µmNthick&RFNSOI&CMOS&

UltraLthin"chip"(<50"um):"flexible"with"good"stability"

van"den"Ende"DA"et"al."Mechanical&and&electrical&properQes&of&ultraNthin&chips&and&flexible&electronics&assemblies&during&bending.""Mircoelectron"reliab"(2014),"hcp://dx.doi.org/10.1016/j.microrel.2014.07.125""

distribution of polishing stresses (Fig. 13). The silicon materialdirectly under the bump experiences a tensile stress, which inextreme cases incurs micro cracks originating in the silicon in thisregion. An example is shown in Fig. 15, where polarized lightmicroscopy analysis of the weakest 50 lm polished chip (12 MPafailure stress, see Fig. 11) reveals polishing damage at the bumplocations. In Fig. 15C the position of the crack can be seen withrespect to the bending setup, showing the failure occurred insidethe inner two loading supports, in the constant stress regime. Evi-dently the damage on the bump positions at the backside of thechips leads to a severely reduced stress at failure.

The strength of the plasma treated chips is shown in Fig. 12. Themean chip strength quadruples and minimum chip strengthincreases by a factor 10 compared to the background chips fromFig. 10. The plasma treatment etches away the surface layer andthis reduces the subsurface grinding damage in the chip, however,the Weibull modulus remains comparable to the background chips.This similar Weibull modulus may indicate that the plasma treat-ment is not fully effective in eliminating all the grinding inducedsubsurface damage at the bump sites, although the surface andedges of the chips are strengthened by the plasma etching treat-ment, leading to a higher CDS.

In Table 3 all the properties of the different tested chips aresummarized. For application purposes, the reliability of ultra-thinchips in flexible electronics devices can be characterized by theminimum die strength (MDS), the strength at which 1% of the dieshas failed [7]. The MDS is calculated from the fitted Weibull mod-ulus of the chips and presented along with the correspondingbending radius for this characteristic die strength.

The minimum bending radius that can be achieved by theplasma treated IZM28 dies is around 4.7 mm while that of theground and polished dies is 33 mm. In the case of the polished diesthe higher bending radius is partly caused by the higher diethickness and partly by the higher bump thickness. For the plasmatreated dies a minimum bending radius of 4.7 mm is perfectlysuitable for many applications of flexible electronics.

5.3.2 STM8 microcontroller diesFailure distributions of microcontroller dies are shown in

Fig. 16. The microcontrollers are comparable in backside strengthto the IZM chips and have a high flexural strength, even having ahigher Weibull modulus to the IZM28 test chips (2.8 comparedto 2.64). This is possibly related to the bump configurations, whichdiffer between both chips. The IZM28 chips have a small number ofbumps with a large pitch, whereas the STM8L dies have a muchsmaller pitch, leading to a more even stress distribution acrossthe back surface during polishing. In contrast, the front side ofthe die is somewhat weaker than the test chips (CDS is 960 MPacompared to 1207 MPa). This is to be expected, because the micro-controllers involve more complex processing, leading to moreintricate patterns with a larger variety of different materials and

more possibilities for developing residual stresses in the activelayers.

Using the MDS values from Fig. 16, the 20 lm thick microcon-troller dies are calculated to have at least a minimum bendingradius of 2.4 mm when the back side is stressed but when the frontside is stressed the minimum achievable bending radius at 1% fail-ure is much higher: 8.5 mm.

5.4 Bending of bonded chips

5.4.1 IZM28 test chip mechanical resultsWhen thin dies are bonded to foil assemblies several factors

influence the bendability compared to stand alone dies, such asthe bonding process and the increase in stack thickness. The flipchip ACA bonded die in Fig. 17 has an experimentally observedminimum radius of 2.4 mm when the backside of the die is tensilestressed. The neutral plane in the assembly is calculated at 16.7 lmfrom the die surface (Eq. (5)) resulting in a calculated maximumbending stress in the die of 1460 MPa. Typically the bendingstrength of the bonded dies was found to be lower than the standalone dies. By comparing the results of the unbonded (Fig. 12) withthose of a bonded chip (Fig. 18) it can be seen that the character-istic bending strength of the bonded dies is much less than thestand-alone dies. This could be related to the residual stresses inthe assembly caused by the relatively high curing temperature,which leads to stresses from thermal shrinkage of the adhesiveand substrate [29] and CTE differences between the silicon dieand the organic substrate [30,31]. These residual stresses are also

Table 3Chip properties including MDS and corresponding minimum bending radius of tested dies.

Die type Front/back side Ground/polished/plasma Bumps Die thickness (lm) CDS (MPa) Weibull modulus MDS (MPa) rmin (mm)

Blank Front Ground No 15–20 1263 7.42 691 2.46Blank Back Ground No 15–20 575 5.48 221 7.72IZM28 Front Ground Yes 15–20 1032 9.44 636 2.70IZM28 Back Ground Yes 15–20 494 2.04 52 32.7Blank Back Polished No 25–35 1044 4.17 334 7.72IZM28 Back Polished Yes 25–35 482 2.98 107 24.3Blank Back Plasma Yes 18–22 2340 12.6 679 2.50IZM28 Front Plasma Yes 18–22 1207 2.64 833 2.05IZM28 Back Plasma Yes 18–22 2139 3.74 362 4.72

Fig. 16. Probability of failure for ground and plasma treated microcontroller chips.Front side strength distributions of 20 lm thick chips (blue, x) and backsidestrength distributions of 20 lm thick chips (black, h) and 50 lm thick chips (black,s). (For interpretation of the references to color in this figure legend, the reader isreferred to the web version of this article.)

8 D.A. van den Ende et al. / Microelectronics Reliability xxx (2014) xxx–xxx

Please cite this article in press as: van den Ende DA et al. Mechanical and electrical properties of ultra-thin chips and flexible electronics assemblies duringbending. Microelectron Reliab (2014), http://dx.doi.org/10.1016/j.microrel.2014.07.125

UltraLthin"curved"silicon"chips""

L.&Musa&(CERN)&–&ALICE&Physics&Week,&23&Oct&2018&R&D"with"IZM"ALPIDE"started""

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20

After LS4 (Run 5)

19"

A"new"experiment"based"on"a"“allLsilicon”"detector"

~100cm

~360cm

Tracker:""~10"tracking"barrel"layers"(blue,"yellow"and"green)"based"on"CMOS"sensors""Hadron"ID:"TOF"with"outer"silicon"layers"(orange)"Electron"ID:"preLshower"(outermost"blue"layer)"

SpaBal#resoluBon# •  Innermost#3#layers:#σ"~"1µm"•  Outer#layers:#σ"~"5µm"

Time#Measurement Outermost#layer#integrates#high#precision#Bme#measurement###(σt"<"30ps)"

Preliminary#studies

MagneBc#Field •  B#=#0.5#or#1#T

Extended"rapidity"coverage:"up"to"8"rapidity"units"+"FoCal"

L.&Musa&(CERN)&–&ALICE&Physics&Week,&23&Oct&2018&

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21

After LS4 (Run 5): LS4+HI experimentLS4+ HI experiment

• Impact parameter resolution <10μm for pT~1 GeV/c and <100μm down to pT~0.1 GeV/c• Unique tracking and vertexing capabilities combined with high-luminosity capabilities

➞ high precision HF measurements ➞ open window on measurements currently out-of-reach

!19

[arXiv:1902.01211]

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Into the unknown

R&D started!

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Extra Slides

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24

Doubly charmed baryon and mesons

4

: Recent measurements of a doubly charmed baryon in 2017

− Tcc (ccqq) mesons S. Cho et al. (EXHIC Collaboration), Phys. Rev. C 84, 064910 (2011) S. Cho et al. (EXHIC Collaboration), Prog. Part. Nucl. Phys. 95, 279 (2017) J. Hong, S. Cho, T. Song, and S-H. Lee, Phys. Rev. C 98, 014913 (2018)

− X(3872) mesons J. Beringer et al. (PDG), Phys. Rev. D86, 010001 (2012) : The first measurement in 2003 S.K. Choi et al. [Belle Collaboration], Phys. Rev. Lett. 90, 242001 (2003) 6 March 26th 2019

Yukawa Institute for Theoretical Physics Hadron Interactions and Polarization from Lattice QCD,

Quark Model, and Heavy Ion Collisions

− Charmed hadrons 1) Charmonium states : Bound states made up of a charm and an anti-charm quarks - the 1S scalar ηc and vector J/ψ, three 1P states χc (scalar, vector, and tensor), and the 2S vector state ψ’ 2) Charmed baryons and mesons : D, D*, Ds, Ds*, Λc(2286), Λc(2595), Λc(2625), Σc(2455), Σc(2520), Ξc(2470). Ξc(2578), Ξc(2645), Ωc(2695), Ωc(2770). 3) Doubly charmed hadrons, exotic hadrons Ξcc, Tcc, X(3872)

4 March 26th 2019 Yukawa Institute for Theoretical Physics

Hadron Interactions and Polarization from Lattice QCD, Quark Model, and Heavy Ion Collisions

Sungtae Cho’s slide

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25

Multi-HF hadronsLight quark mass different in vacuum (originating from chiral condensate, broken symmetry) and when chiral symmetry is restored ➞ mass decreases with increasing temperature: mq=0.3 GeV at T=0 and 0.1 GeV at Tc

Chiral symmetry restoration on the coalescence hyper surface:• Ξcc mass: 3.58 GeV ➞ 2.79 GeV• Ξcc <radius>: 0.41 fm ➞ 0.49 fm• Distance between 2 c quarks and between cc pair and q:

<rcc>=0.44 fm, <rcc-q>=0.53 fm ➞ <rcc>=0.46 fm, <rcc-q>=0.97 fm

More from the Ξcc …

Chiral symmetry broken: Ξcc is a 3-quark state ccqChiral symmetry restored: Ξcc is a quark-diquark state➞ production yield sensitive to coalescence happening between a 3-quark state and a diquark-quark state➞ variation from 0.03 to 0.04 (cross section per binary collision from 513 nb to 667 nb)

• Role of chiral symmetry restoration • Sensitivity to light quark spectrum and medium properties

!9

[Zhao, He, Zhuang, PLB 771 (2017) 349-353]

Chiral symmetry

broken

Chiral symmetry restored

Role of chiral symmetry restoration

A. Festanti’s slide (ALICE Physics week, 2019)

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Multi-HF hadrons• Dynamical in-medium evolution considering formation, diffusion and dissociation of bound diquarks within the QGP

[Yao, Muller, PRD 97 0744003 (2018)]- Incomplete equilibration of the HQ spectrum - Boltzmann equations to describe charm and diquark dynamical evolution- Diquark potential from pNRQCD- Diquarks hadronize into charged baryons by absorbing an up or down quark from the medium- Melting temperature above which diquark cannot form (250 MeV) ➞ reduction of the expected yield (0.02 ➞ 0.0125)

Production yields calculated using different approaches

• Probe diquark states in the QGP • Compare melting temperature obtained from diquark free energy calculated with Lattice QCD

- Different multi-HF states ➞ different melting temperatures of heavy diquarks (cc, cb, bb) • New thermometer?

Medium expansion ➞ decreasing temperature

Decreasing HF density➞ reduce recombination probability

Reduced color screening➞ reduce dissociation probabilityvs.

From sequential-suppression to a sequential-formation thermometer to probe hadronisation/diquark formation starting at different temperatures?

!10

Yao, Muller, PRD 97 0744003 (2018)

A. Festanti’s slide (ALICE Physics week, 2019)