Studying two- and three-body hadronsystems at the LHC
Laura Fabbietti, Technische Universität München

Laura Fabbietti CLUSHIQ22

Residual strong interaction among hadrons

Non perturbative QCD → Q ~1 GeV, R ~ 1 fm
→ Effective theories with hadrons as degrees of freedom constrained to experimental data

Laura Fabbietti CLUSHIQ222

Residual strong interaction among hadrons

Non perturbative QCD → Q ~1 GeV, R ~ 1 fm
→ Effective theories with hadrons as degrees of freedom constrained to experimental data
New results:→ Understanding of the interaction starting from quark and gluons

Laura Fabbietti CLUSHIQ223

Residual strong interaction among hadrons

Non perturbative QCD → Q ~1 GeV, R ~ 1 fm
→ Effective theories with hadrons as degrees of freedom constrained to experimental data
New results:→ Understanding of the interaction starting from quark and gluons→ New experimental methods to investigate three-body systems

Laura Fabbietti CLUSHIQ224

Residual strong interaction among hadrons

Non perturbative QCD → Q ~1 GeV, R ~ 1 fm
→ Effective theories with hadrons as degrees of freedom constrained to experimental data
New results:→ Understanding of the interaction starting from quark and gluons→ New experimental methods to investigate three-body systems→ First studies of the strong interaction for the charm sector
Laura Fabbietti CLUSHIQ225

Residual strong interaction from lattice

T. Hatsuda, K. Sasaki et al.
HAL QCD Coll. PLB 792 (2019)
HAL QCD Coll. NPA 998 (2020)
HAL QCD Coll. PRD 99 (2019)

a = 0.085 fm
L = 8.1 fm
m⇡ = 146 MeV/c2mK = 525 MeV/c2

Laura Fabbietti CLUSHIQ226

Residual strong interaction from latticeLocal potentials for the nucleon-Xinteractions

T. Hatsuda, K. Sasaki et al.
HAL QCD Coll. PLB 792 (2019)
HAL QCD Coll. NPA 998 (2020)
HAL QCD Coll. PRD 99 (2019)

a = 0.085 fm
L = 8.1 fm
m⇡ = 146 MeV/c2
mK = 525 MeV/c2

Laura Fabbietti CLUSHIQ22

HAL QCD Coll. NPA 998 (2020)

7

Residual strong interaction from lattice
Local potentials for the nucleon-Xinteractions

T. Hatsuda, K. Sasaki et al.
HAL QCD Coll. PLB 792 (2019)
HAL QCD Coll. NPA 998 (2020)
HAL QCD Coll. PRD 99 (2019)

a = 0.085 fm
L = 8.1 fm
m⇡ = 146 MeV/c2
HAL QCD Coll. NPA 998 (2020)mK = 525 MeV/c2
S=0NN

S = -1
NL, NSS = -2
LL, LS, SS, NX

S = -3
LX, SX, NW

S = -4
XX, LW, SW

S = -5XW

S = -6
WWBetter S/N of LQCD
Experimental data
Laura Fabbietti CLUSHIQ228

pp collisions at the LHC

Laura Fabbietti ICHEP2022, Bologna

9pp collisions at the LHC

Laura Fabbietti ICHEP2022, Bologna

10Particle production and propagation
Pair reference framepa*parpbpb*⇤k =Laura Fabbietti ICHEP2022, Bologna|~p⇤a2p~⇤b |11

The Koonin-Pratt formalism

S. E. Koonin et al. PLB 70 (1977)

Pair reference frame
pa*parpb

C 𝑘∗

𝑁"#$% 𝑘 ∗∗=𝜁 𝑘 %= 'S 𝑟
𝑁$&'%( 𝑘 ∗ψ 𝑘 ∗ , 𝑟⃑)d* 𝑟pb*⇤k =|~p⇤a2p~⇤b |Emission source
Two-particle wave function

Laura Fabbietti ICHEP2022, Bologna

12The Koonin-Pratt formalism

S. E. Koonin et al. PLB 70 (1977)

Pair reference frame
pa*parpbC 𝑘∗𝑁"#$% 𝑘 ∗∗=𝜁 𝑘 %= 'S 𝑟
𝑁$&'%( 𝑘 ∗ψ 𝑘 ∗ , 𝑟⃑)d* 𝑟pb*⇤k =|~p⇤a2p~⇤b |Emission source
Two-particle wave function

Schrödinger Equation:V(r) →ψ k ∗ , r⃑"relative wave function for the pair
Laura Fabbietti ICHEP2022, Bologna

13

Correlation function and potentials
Interacting potential

Correlation function
C(k*)

V(r *) (MeV)

Source parametrisation

Repulsive
01

Attractive0

Gaussian source
S(r) = (4⇡r02 ) 3/2 · exp

0.5

Schrödinger✓r2
4r02◆11.5Attractive

Repulsive

2r (fm)50equation**

100

150

200

k* (MeV/c )Two-particle wavefunction Ψ(k ∗ , r)**CATS (Correlation Analysis Tool using the Schödinger equation)
D. Mihaylov et al. EPJC 78 (2018)

C𝑘∗= 'S 𝑟Emission source∗ψ 𝑘 , 𝑟⃑)*d 𝑟

Two-particle wave function>1 if the interaction is attractive= 1 if there is no interaction<1 if the interaction is repulsive

Laura Fabbietti ICHEP2022, Bologna

14

Source model
ALICE Coll., PLB, 811 (2020)

C k∗ = . S r

ψ k ∗ , r⃑,d- r

pp Correlation: AV18 +Coulomb potentials
used to calculateψ k ∗ , r⃑

pppΛpΞpΣ0pΩ-

One universal source for all hadrons with strong
resonance decays considered for each pair ofinterest

Laura Fabbietti ICHEP2022, Bologna

15

NLO13: J.Haidenbauer et al. NPA 915 (2013)
NLO19: J.Haidenbauer et al. EPJ.A 56 (2020)|S|=1: Lp Interaction in scattering data

CLAS Coll. PRL 127 (2021)

Uncertainties ~20-25% at low plabCusppΛ scattering data from 80ies→ Low-statistics scattering at low momentum→ ΣN-LN coupling is experimentally not seen

Kaonproton

ElectronhyperonpΛ scattering in CLAS (2021)→ Improved statistics at large momenta
Laura Fabbietti ICHEP2022, Bologna

16

|S|=1: Lp Interaction and ΣN coupling

NLO13: J.Haidenbauer et al. NPA 915 (2013)
NLO19: J.Haidenbauer et al. EPJ.A 56 (2020)

ALICE PLB 833 (2022) 137272

CLAS Coll. PRL 127 (2021)

Uncertainties ~20-25% at low plabCusp

nσ = 3.9pΛ Correlation function measured by ALICE→ SN-LN cusp visible for the first time
→ 30 times more precise at low momentum
Laura Fabbietti ICHEP2022, Bologna→ Challenges NLO1917

|S|=2 sector: pΞ- interaction and first test of LQCD
Lattice QCD potentials from HAL
QCD collaboration available
Local potentials for the nucleon-Xinteractions
reff = 1.4, 0.85 fm

𝐶 𝑘∗ = . 𝑆 𝒓𝑑-𝑟

HAL QCD Coll. NPA 998 (2020)

Laura Fabbietti ICHEP2022, Bologna

18

|S|=2 sector: pΞ- interaction and first test of LQCD
Lattice QCD potentials from HAL
QCD collaboration available

ALICE Coll. Nature 588 (2020)
3.5Local potentials for the nucleon-Xinteractions

ALICE data pp s!! = 13 TeVCoulomb

3-Coulomb + p-Ξ HAL QCD-Coulomb + p-Ω

C (k *)

2.5-Coulomb + p-Ω

21.5
10100

200300k * (MeV/c )HAL QCD Coll. NPA 998 (2020)

Observation of a strong attractive interaction beyondCoulomb in agreement with lattice predictions
Laura Fabbietti ICHEP2022, Bologna

19p–Ω- correlation function in pp at 13 TeV
ALICE Coll. Nature 588, 232–238 (2020)

7

ALICE data-Enhancement above Coulomb→ Observation of the strong interaction•Attraction in 5S2 results in the prediction of abound state (B.E. = 1.54 MeV)•

Missing potential of the 3S1 channel→ Test of two cases:•Inelastic channels dominated byabsorption•
Neglecting inelastic channels•

Data more precise than lattice calculations•

So far, no indication of a bound state

pp s!! = 13 TeV p-Ω

Coulomb

6•

Coulomb + HAL-QCD elastic
Coulomb + HAL-QCD elastic + inelastic

4

1.2C (k *)C (k *)

5

3

10.8

2100

150
200
k * (MeV/c )25010100k * (MeV/ c )200300Laura Fabbietti ICHEP2022, Bologna

20

|S| = 3: Λ-Ξ– interaction – with femtoscopy
ALICE Coll., arXiv:2204.10258, accepted by PLB•

Unknown contribution from coupled channels
in Lattice QCD calculations→ Coupling ΛΞ–ΣΞ sizable in HAL QCD
calculation→ No sensitivity yet (“No coupling” 0.64 nσ
vs. „Coupling“ 1.43 nσ)•𝐩𝛀

No NΩ cusp visible→ Hint to negligible NΩ-ΛΞ coupling( )Laura Fabbietti ICHEP2022, Bologna* N. Ishii et al.. EPJ Web of Conferences 175, 05013 (2018)21

p-p-p correlation functionp-p-L correlation function

ALICE Coll., arXiv:2206.03344, accepted by EPJA

ALICE Coll., arXiv:2206.03344, accepted by EPJA

C (Q 3)C (Q 3)p-p-p and p-p-L Correlation functions

ALICE
pp s = 13 TeV

4.5
430
25

High Mult. (0−0.17% INEL)

3.5
20

p−p−p⊕p−p−p Data3p−p−p Two-particle correlations,2.5p−p−Λ Two-particle correlations,

15projector method2p−p−Λ⊕p−p−Λ Data
projector method

101.5
15

0.5
0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Q 3 (GeV/c )00.1

Laura Fabbietti ICHEP2022, Bologna

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Q 3 (GeV/c )22

Cumulants
Genuine three-particle correlations isolated using the Kubo’s cumulant expansion method:
R. Kubo, J. Phys. Soc. Jpn. 177 (1962)

Genuine three-body Measured
three-bodycorrelations
correlation

Two-body correlations

In terms of correlation functions:𝑐! 𝑄! = 𝐶 𝑄! − 𝐶"# 𝑄! − 𝐶#! 𝑄! − 𝐶!" 𝑄! + 2
Projector method

Event mixing method

R. Del Grande et al. EPJC 82 (2022) 244
Laura Fabbietti ICHEP2022, Bologna

23

p-p-p Cumulants

Cumulant
c 3 (Q 3)

ALICE Coll., arXiv:2206.03344, accepted by EPJA

4

Statistical significance→ 𝑛4 = 6.7 for Q3 < 0.4 GeV/cp−p−p genuine cumulant, flat feed-downp−p−p genuine cumulant, flat feed-down

2Conclusion→ Genuine three-body effect in the p-p-p system

0Possible interpretations→ Pauli blocking at the three-particle level→ Long range Coulomb interaction effects→ Three-body strong interaction−2ALICEpp s = 13 TeVHigh Mult. (0−0.17% INEL)−4−60.1

0.2

0.3

0.40.50.6

0.70.8Q 3 (GeV/c )Test with mixed-charge particles, cumulant negligible

Laura Fabbietti ICHEP2022, Bologna

24

p-p-L Cumulants

Cumulant
ALICE Coll., arXiv:2206.03344, accepted by EPJA

Statistical significance→ 𝑛4 = 0.8 for Q3 < 0.4 GeV/cConclusion→ No significant deviation from the null hypothesis
A factor 500 in statistics from the Run 3 data taking→ Non-zero cumulant can be directly linked to thethree-body strong interaction→ Important measurement for neutron stars

Laura Fabbietti ICHEP2022, Bologna

25

Scattering parameters for pd and kd
kd scattering parameters from:• From Haidenbauer: [a = - 0.470 fm, r= - 1.75fm ] based on potential describing K+-d low-energy
cross sections T. Takaki Phys. Rev. C 81, 055204 (2010),• From Hyodo [a = - 0.540 fm, r= 0.0 fm ] Starting from Chiral model KN scattering lengths : K. Aoki
and D. Jido, PTEP 2019, 013D01 (2019)

Pd scattering parameters from: experiments and calculations listed in the table below

S = 3/2

Laura Fabbietti ICHEP2022, Bologna

26

Comparison of model and data
• Source size:

7 8- 𝑟566= 1.41=:.:>
9:.:< fm.

?8- 𝑟566= 1.08=:.:<
9:.:< fm• Remarks:- Kd data are well

reproduced- for pd theLednicky formula
does not work!

Laura Fabbietti ICHEP2022, Bologna

27

—First measurement of D-p residual strong interaction
Small compared to other interactions (scattering lengths light-light ~ 7-8 fm, light-strange ~ 1.5 fm)
Many models predict repulsive interaction
Possible bound state formation (Yamaguchi et al)
ALICE Coll. PRD 106 (2022) 5, 052010

Interval of scattering
length for isospin I=0 at
68% CL indicates either
attractive interaction withor without the formationof a bound state
J. Haidenbauer et al, EPJA 33 (2007) 107—117
J. Hofmann and M. Lutz, NPA 763 (2005) 90—139

Fontura et al, PRC 87 (2013) 025206
Yamaguchi et al, PRD 84 (2011) 014032
Laura Fabbietti ICHEP2022, Bologna

ALICE Preliminarypp, s = 13 TeV, high. mult. (0−0.17%)
π+D+ ⊕ π−D−1.2

1.1

genuine CFCoulomb
Coulomb + Lednicky−Lyuboshits (stat. unc.)
Coulomb + Lednicky−Lyuboshits (tot. unc.)

1.2

ALICE Preliminarypp, s = 13 TeV, High-mult. (0−0.17%)
Data
68% CL
95% CL

0.5

ModelsX.Y. Guo
Z.H. Guo-1
Z.H. Guo-2
B.L. Huang Fit-u2
L. Liu1.0

0.9

Double-Gaussian source

0.8+ 0.09
r eff
1 = 0.97− 0.07 fm+ 0.36eff
r 2 = 2.52− 0.20 fm

0π+D− ⊕ π−D+

1.1

1.0

D+-p-

1.3

aπD(I=21) fm

D+-p+

1.3

C (k *)C (k *)First measurement of D-K and D-p residual strong interaction

204060ALI−PREL−506604

80 100 120 140 160 180 200
k * (MeV/c )0.9

Simultaneous fit
Coulomb + Lednicky−Lyuboshits

0.0+0.01

0.80aπD(I=21) = -0.03±0.04(stat)±0.02(sys.)(source sys.) fm

aπD(I=32) = -0.06±0.03(stat)±0.02(sys.)(source sys.) fm

−0.01
+0.01
−0.03

20406080 100 120 140 160 180 200
k * (MeV/c )Double-Gaussian source
+0.09
+0.36
eff
r eff
1 = 0.97 −0.07 fm, r 2 = 2.52−0.20 fm−0.2
ALI−PREL−513658

0.0

0.20.40.63aπD(I=2) fm

Simultenous fits of D-p and D-K correlations allow todetermine the I= ½ and I= 3/2 scattering parameters. For
I=1/2 the results agree with theoretical predictions

Laura Fabbietti ICHEP2022, Bologna

31

D*D correlation and link to molecular states
LHCb Coll. Nature Phys. (2022)

C D0D*+ALICE3 LoI https://cds.cern.ch/record/2803563

876543ALICE 3 upgrade projection|y | < 41 fm (pp)
2 fm
3 fm
5 fm (Pb−Pb)
Lint:- pp = 18 fb−1- 0−10% Pb−Pb = 35 nb−1

2= P
T@@(J = 1+, I= 0): molecular state LHCb coll. Nature Comm. 13 3351 (2022)
The scattering length of the D*+D0 pair should experience an inversionof sign at threshold
This translates into an inversion of the correlation function from pp toPb-Pb collisions at the LHC Y. Kamiya and A. Ohnishi EPJA 58 (2022) 7,131

Laura Fabbietti ICHEP2022, Bologna

100 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
k * (GeV/c )32Summary•••••Several two-body residual strong interaction have been measured with good precision and first test oflattice have been made possible
The implication of the new findings on hyperon-nucleon interactions for the physics of neutron star could
be importantThree-body interactions can be investigated at the LHCFirst measurements of the residual strong interaction in the charm sector
Implications for the study of molecular states containing charm quarks

Laura Fabbietti CLUSHIQ22