Femtoscopy in pp and pa collisions at TeV energies Laura Fabbietti, Technische Universität München http://www.denseandstrange.ph.tum.de Vale Andi Bernie Oton Dimitar 1
Outline The Hyperon-Nucleon and Hyperon-Hyperon interaction: what is known? Femtoscopy in pp and ppb collisions at the LHC as complementary measurement to scattering data p : NLO vs LO : Exclusion plot for scattering length and effective range p : First experimental evidence of the two body attractive interaction in S=-2 pk + and pk - : Unique check of momentum dependence of the interaction Outlook For More info about the analysis method and fitting framework check out 1) CATS paper: (D.L.Mihaylov et al. Eur.Phys.J. C78 (2018) no.5,394) 2) ALICE RUN1 Femtoscopy paper: arxive:1805.12455 3) Dimitar Mihaylov Poster Baryon-baryon femtoscopy in pp and p-a collisions 2
Experimental Methods I http://eaae-astronomy.org/blog/?cat=254 (2017) 19 F Λ (K -, π) (K - stop, π + ) Hypernuclei can be produced Binding Energy of to nucleus = 28 MeV 6 H Λ Updated from: O. Hashimoto and H. Tamura, Prog. Part. Nucl. Phys. 57 (2006) (π, K + ) (e,e K + ) Nothing is known about - hypernuclei - Hypernuclei shows a shallow attractive interaction 3 Even -hypernuclei exists
Experimental Methods I http://eaae-astronomy.org/blog/?cat=254 Hypernuclei can be produced Binding Energy of to nucleus = 28 MeV Scarce information on - hypernuclei - Hypernuclei shows a shallow attractive interaction 4 Even -hypernuclei exists
Experimental Methods I http://eaae-astronomy.org/blog/?cat=254 Courtesy H. Tamura, Bormio Winter Meeting 2018 Kiso event New analysis! α e 8Li p Hypernuclei can be produced Binding Energy of to nucleus = 28 MeV 8Be α p d Scarce information on - hypernuclei - Hypernuclei shows a shallow attractive interaction Even -hypernuclei exists The first clear Ξ hypernucleus = - K. Nakazawa et al. PTEP 2015, 033D02 5
Experimental Methods I http://eaae-astronomy.org/blog/?cat=254 Nagara event p n Λ Hypernuclei can be produced Binding Energy of to nucleus = 28 MeV 6 ΛΛ He -> 5 ΛHe + p + π α Scarce information on - hypernuclei - Hypernuclei shows a shallow attractive interaction 4-5 -hypernuclei events ΔB ΛΛ = 0.67±0.17 MeV H. Takahashi et al., PRL 87 (2001) 212502 Λ-Λ is weakly attractive 6
Scattering Data and Interaction Parameters Scattering experiments -> Extraction fo the differential cross section d d d d Expansion in partial waves: l = phase shifts Scattering Length a 0 = 1 lim k 0 k tan 0(k). l =0#$>#s$wave only!! 7
Nuclear Collisions 8
Particle Production 9
Particle Propagation 10
The Correlation Function The correlation function: Experimentally obtained as: Given by:! " = % & ', & ) % & ' % & ),! " = +, -'./(" ), 234/5 (" ) " 1! " = 6 7 8, " 9(8, " ) : <8 Source " = & ' & ) 2 and & ' + & ) = 0 Relative Wave Function
The Correlation Function The correlation function: Experimentally obtained as: Given by:! " = % & ', & ) % & ' % & ),! " = +, -'./(" ), 234/5 (" ) " 1! " = 6 7 8, " 9(8, " ) : <8 Source " = & ' & ) 2 and & ' + & ) = 0 Relative Wave Function Assumption of a common source with Gaussian shape for the p-p, p-λ, p-ξ, Λ Λ and pk Correlation Function
The Correlation Function The correlation function: Experimentally obtained as: Given by:! " = % & ', & ) % & ' % & ),! " = +, -'./(" ), 234/5 (" ) " 1! " = 6 7 8, " 9(8, " ) : <8 Strong constraint Source " = & ' & ) 2 and & ' + & ) = 0 Relative Wave Function Assumption of a common source with Gaussian shape for the p-p, p-λ, p-ξ, Λ Λ and pk Correlation Function
The Correlation Function (D.L.Mihaylov, V.M.S, O.W.Arnold, L.Fabbietti, B.Hohlweger, A.M.Mathis, Eur.Phys.J. C78 (2018) no.5,394) The correlation function: Experimentally obtained as: Given by:! " = % & ', & ) % & ' % & ),! " = +, -'./(" ), 234/5 (" ) " 1! " = 6 7 8, " 9(8, " ) : <8 Strong constraint Source " = & ' & ) 2 and & ' + & ) = 0 Relative Wave Function Assumption of a common source with Gaussian shape for the p-p, p-λ, p-ξ, Λ Λ and pk Correlation Function CATS: Different Interacting potential translated into Predictions for the correlations function
Modeling the Correlation Function C k = N C '()*+,-* k 1 + λ 1*-2,-* C 1*-2,-* k 1 + λ,6 C,6 (k ) 1 CATS Correlation Analysis Tool Using the Schrödinger Equation Numerical Solver Analytical source distribution Distributions from transport models Solution of the two particle Schrödinger Equation Ø Can incorporate any strong interaction potential, Coulomb interaction and effects of quantum statistics SOURCE WAVE FUNCTION Analytical Model Lednický Gaussian source distribution Based on the effective Range expansion Ø The interaction is modeled using the scattering length (f 0 ) and the effective range (d 0 ) p-p, p-x and p-l (NLO) Correlation function Used to fit the p-l (LO) and L-L Correlation function (D.L.Mihaylov, V.M.S, O.W.Arnold, L.Fabbietti, B.Hohlweger, A.M.Mathis, Eur.Phys.J. C78 (2018) no.5,394) 15
Small Source -> Repulsive Core Pdf for a Gaussian Source Function (R G = 1.5 fm) Typical short range nuclear potential for pp Small Radii provided by pp Collisions at the LHC ( r ~ 1.2 fm) 16 p+nb at 3.5 GeV HADES coll. Phys.Rev. C94 (2016) no.2, 025201 (r~2 fm)
The ALICE Data Set! " # " $ We measure p-p, p-λ, Λ-Λ, p-ξ, pk Proton and Pion identification with TPC and TOF Reconstruction of hyperons Λ pπ (BR ~ 64%) Ξ Λ π (BR ~ 100%) Datasets: pp 7 TeV: 3.4 10 8 Events pp 13 TeV: 10 10 8 Events p-pb 5.02 TeV: 6.0 10 8 Events 17
Proton-Λ : Scattering vs Femtoscopy Data? Exp LO NLO LO: H. Polinder, J.H., U. Meiβner, NPA 779 (2006) 244 NLO: J.Haidenbauer., N.Kaiser, et al., NPA 915 (2013) 24 18
Proton-Λ : Scattering vs Femtoscopy Data? C(k*) 2 1.8 1.6 ALICE pp r 0 = 1.144 ± s pλ pλ pairs = 7 TeV 0.019 +0.069-0.012 Syst. uncertainties fm Femtoscopic fit (NLO params.) C(k*)> 1: Attractive interaction Exp LO NLO 1.4 1.2 Femtoscopic fit (LO params.) Nucl. Phys. A915 (2013) 24. 1 LO: H. Polinder, J.H., U. Meiβner, NPA 779 (2006) 244 NLO: J.Haidenbauer., N.Kaiser, et al., NPA 915 (2013) 24 arxive:1805.12455 RUN1 data: 250 Mevts Combination of spin singlet and triplet * Extension to the low momentum regime * Statistics not sufficient to test different models 0.8 0 0.05 0.1 0.15 0.2 k* (GeV/c) C(k*) <1: Repulsive interaction 19
Proton-Λ : Scattering vs Femtoscopy Data? Exp LO LO: H. Polinder, J.H., U. Meiβner, NPA 779 ALI-PREL-144801 ALI-PREL-144813 RUN2 data: 1000 Mevts for p+p and 500 MeVt for p+pb * Extension to the low momentum regime * Statistics sufficient to test different models Under the assumption of a Gaussian source smaller scattering lengths are favoured a 1 S 0 = 1.91fm d 1 S 0 =1.40fm a 1 S 0 = 2.91fm d 1 S 0 =2.78fm 20 a 3 S 1 = 1.23fm d 3 S 1 =2.13fm a 3 S 1 = 1.54fm d 3 S 1 =2.72fm
Fit of the pp, Λp and ΛΛ Correlation Function RUN2 ~ 1000 MeVts Gaussian source and Argonne ν18 potential describes the p-p correlation function Source size of the pp (7 TeV) system r0=1.14 fm (ALICE Coll. arxiv:1805.12455) Source size of the pp (13 TeV) system r0=1.19 fm Source size of the p-pb (5.02 TeV) system r0=1.44 fm 21
t, 0 itlength, is convenient to introduce scattering a0, defined by condition that u(a0 ) = 0 for kr 1, i.e. by condition that u(a0 ) = 0 for kr 1, i.e. u(a0 ) = sin(ka0 + 0 ) = sin(ka0 ) cos 0 + cos(ka0 ) sin 0 ) cos cos(ka 0 + 0 ) = sin(ka0= 0 ) sin ) 0+ cos(kr )] sin 0 + [cot sin(ka sin [ka cot + 1] The Exclusion Plot 0 0 0 0 0 0 ot 0 sin(ka )] sin 0 [ka Scattering Parameters, Effective range= defines the range of the interaction 0 ) + cos(kr 0 cot 0 + 1] 1 leads to scattering length a0 = lim tan 0 (k). 1 k 0 lk =0#$>#s$wave only!! ength a0 = lim tan 0 (k). k 0 k From this result, we find the scattering cross section ATTRACTIVE find the scattering crossrepulsive section 4 2 (ka0 )2 k 0 4 2 2 sin 0 (k) = 4 a tot 0 (kak0 )2 k 0 4 2 1 + (ka )2 2 2 k 0 n 0 (k) 4 a0 k 2 1 + (ka0 )2 i.e. a0 characterizes e ective size of target. e ective size of target. charachterizes the#effective size#of#the#target The#scattering#length# Au + Au p s = 200 GeV BOUND STATE Comparison of the correlation function obtained with specific scattering parameters ( via Lednicky model) to experimental data p+p at 7, 13 TeV and p+pb at 5 TeV considered for this global exclusion plot 22
Potentials 23
Non Physical Region and STAR parameters Lednicky model breaks down for small radii, large effective ranges and negative scattering parameters It shows although at most 10% deviation from CATS in the region of positive scattering parameters 24
H-dibaryon Binding Energies ( 1!"" = ( 1 %" &' 2&' 1+,' Femto sign convention! Rept.Prog.Phys. 80 (2017) no.5, 056001 Phys.Rev.Lett. 120 (2018) 212001 25
H-dibaryon Binding Energies ( 1!"" = ( 1 %" &' 2&' 1+,' Femto sign convention! Rept.Prog.Phys. 80 (2017) no.5, 056001 Phys.Rev.Lett. 120 (2018) 212001 26
H-dibaryon Binding Energies ( 1!"" = ( 1 %" &' 2&' 1+,' Femto sign convention! Rept.Prog.Phys. 80 (2017) no.5, 056001 Phys.Rev.Lett. 120 (2018) 212001 Preliminary Point from Hal-QCD calculation (priv. comm. T. Hatsuda) 27
proton- Correlation Function Preliminarycalculations by the HAL QCD Collaboration Taking the strong interaction into account creates a significantly different Correlation function than Coulomb only Decay mode Ξ ± Λ + ' ( + ' Run2 p-pb, ca. 250 Million Events C(k*) r 0 =1.2 fm r 0 =0.85 fm Strong+Coulomb Coulomb 120 100 80 60 3 10 p-p (2017) - X : 509051 m = 1322.5MeV/c 2 X s = 2.1MeV/c 2 X Purity = 92.0 % s = 13 TeV 40 0 / 50 100 150 k (MeV) 50 100 150 k (MeV) arxiv:1702.06241, Nuclear Physics A 967 (2017) 856 859 1.29 1.3 1.31 1.32 1.33 1.34 (GeV/c 2 ) IM pl CATS (D.L.Mihaylov et al. Eur.Phys.J. C78 (2018) no.5,394) 20 0 28
proton- Correlation Function First observation of strong attractive interaction in p-ξ ALI-PREL-144825 29
proton- Correlation Function First observation of strong attractive interaction in p-ξ modeled with preliminary QCD strong potential by the HAL QCD collaboration (Hatsuda et al., NPA967 (2017) 856, PoS Lattice2016 (2017) 116)! " = 1 8! '() *() +! *() '(, + 3 8! '() *(, +!*(, '(, Coulomb-only hypothesis excluded at around 3 ALI-PREL-144825 Estimate of the average interaction in pure neutron matter predicts a repulsive interaction though!! 30
Proton- K Correlation Function The analysis has also been extended to Meson-Baryon pairs Collaboration TUM-Univ. Trieste Studying the strong interaction for Analyzer Dr. Ramona Lea -> meson-baryon with femtoscopy in pp collisions with ALICE K " n channel opening First Experimental data that resolve the opening of the charged conjugate channel in the momentum space -> Unique Data set to constraint the SHAPE of the K-p potential -> Complementary to Kaonic atoms -> Next step K - d 31 Blue Histo -> Hyodo: private communication
Summary Femtoscopy in pp and ppb colliding systems at the LHC is a suitable technique to analyse nucleon-hyperon and hyperonhyperon correlations and test interaction models Technique successfully extended to proton-kaon interaction Factor 100 in statistics is expected in RUN3 (Phys.Rev. C94 (2016) no.2, 025201) HADES: p+nb at 3.5-4 GeV: probably the only way to measure p correlation 0 32
Average Interaction Estimation of the average nucleon- interaction at 0 (Potential from Hatsuda et al., NPA967 (2017) 856, PoS Lattice2016 (2017) 116) <VIS> (MeV) I=0 I=1 S=0-103±25 180±97 S=1-32±10 12±14 Errors due to different integration times 33
Consequences for Neutron Stars (Potential from Hatsuda et al., NPA967 (2017) 856, PoS Lattice2016 (2017) 116) ρ (fm -3 ) p-x-, n-x 0 (I=0,1) n-x-, p-x 0 (I=1) ρ 0 0.43+15-9 MeV 53+30-20 MeV 34
Consequences for Neutron Stars (Potential from Hatsuda et al., NPA967 (2017) 856, PoS Lattice2016 (2017) 116) ρ (fm -3 ) p-x-, n-x 0 (I=0,1) n-x-, p-x 0 (I=1) ρ 0 0.43+15-9 MeV 53+30-20 MeV (Weissborn et al., NPA881 (2012) 62-77) RMF models: EOS of neutron-rich matter with hyperon content -> constraint to average interactions at saturation density U NN ( 0 ),U N ( 0 ),U N ( 0 ),U N ( 0 ), 35
Consequences for Neutron Stars (Potential from Hatsuda et al., NPA967 (2017) 856, PoS Lattice2016 (2017) 116) ρ (fm -3 ) p-x-, n-x 0 (I=0,1) n-x-, p-x 0 (I=1) ρ 0 0.43+15-9 MeV 53+30-20 MeV (Weissborn et al., NPA881 (2012) 62-77) RMF models: EOS of neutron-rich matter with hyperon content -> constraint to average interactions at saturation density U NN ( 0 ),U N ( 0 ),U N ( 0 ),U N ( 0 ), Repulsive interaction Production of X pushed to higher densities stiffer EoS, higher masses 36
Proton-Λ : Scattering vs Femtoscopy Data? Exp LO NLO C(k*) 2 1.8 1.6 1.4 1.2 1 ALICE pp s = 7 TeV +0.069 r 0 = 1.144 ± 0.019 fm -0.012 pλ pλ pairs Syst. uncertainties Femtoscopic fit (NLO params.) Femtoscopic fit (LO params.) Nucl. Phys. A915 (2013) 24. 0.8 0 0.05 0.1 0.15 0.2 k* (GeV/c) A factor 100 in statistics is expected in RUN3 Differential studies in k* and emission angles -> partially disentangle spin single and triplet? LO: H. Polinder, J.H., U. Meiβner, NPA 779 (2006) 244 NLO: J.Haidenbauer., N.Kaiser, et al., NPA 915 (2013) 24 37 ALI-PREL-144801 ALI-PREL-144813