Ab Initio Calculations of Charge Symmetry Breaking in Light Hypernuclei

Ab Initio Calculations of Charge Symmetry Breaking in Light Hypernuclei Daniel Gazda Nuclear Physics Institute Prague, Czech Republic Together with: A. Gal (HU Jerusalem)

Outline Introduction Charge symmetry in hadron physics Charge symmetry breaking in light (hyper)nuclei Methodology Results Ab initio hypernuclear calculations Ab initio calculations of 4 Λ He 4 Λ H Conclusions & Outlook

Introduction

Introduction Charge symmetry in hadron physics invariance of the strong interaction under the interchange of up and down quarks (protons and neutrons) broken in QCD by the up and down light quark mass differences and their QED interactions should break down at (m u m d )/M 10 3 Charge symmetry breaking in nuclear physics manifest in pp and nn scattering lengths, well understood 3 He 3 H: E CSB SI 70 kev 10 3 E Charge symmetry breaking in hypernuclear physics poor pλ and no nλ scattering data highly suppressed in 3 Λ H 4 Λ He 4 ΛH energy level splittings, BCSB Λ 200 kev 10 2 B Λ 2

Charge symmetry breaking in A=4 mirror hypernuclei 3 H+Λ 0 3 He+Λ 1 + 1.067±0.08 1.09±0.02 0 + 2.157±0.077 4 Λ H 1 + 0 + B Λ (MeV) 0.984±0.05 2.39±0.05 4 Λ He 1.406±0.003 B Λ = -0.083±0.094 B Λ = +0.233±0.092 Recently reaffirmed by: J-PARC E13 observation of 4 Λ He(1+ exc. 0 + g.s.) γ-ray transition [Yamamoto et al., PRL 115, 222501 (2015)] MAMI-A1 determination of B Λ ( 4 Λ H) [Esser et al., PRL 114, 232501 (2015)] 3

Charge symmetry breaking in A=4 mirror hypernuclei Until recently, no microscopic calculation was able to consistently reproduce the large value of B Λ. NY model B Λ (kev) NSC97 e 75 [Nogga et al., PRL 88, 172501 (2002)] NSC97 f 100 [Haidenbauer et al., LNP 724, 113 (2007)] LO χeft 10 ± 30 [Gazda, Gal, NPA 954, 161 (2016)] NLO χeft 46 [Nogga, NPA 914, 140 (2013)] LO χeft+λ-σ 0 mixing 180±130 [Gazda, Gal, PRL 116, 122501 (2016)] exp. 233 ± 92 Residual CSB increased Coulomb repulsive energy in 4 Λ He Σ hyperon mass differences in intermediate NΣ states 4

Electromagnetic Λ Σ 0 mixing Physical Λ and Σ 0 hyperons have mixed isospin composition in terms of the SU(3) pure-isospin Λ (I=0) and Σ (I=1) hyperons: with mixing angle: Λ phys. = Λ cos α Σ sin α Σ 0 phys. = Λ sin α + Σ cos α tan α = Σ δm Λ M Σ M Λ proportional to electromagnetic mass matrix element, related to isospin-breaking mass differences within the baryon octet: Σ δm Λ = 1 3 [(M Σ 0 M Σ +) (M n M p )] = 1.14(05) MeV [Dalitz, von Hippel, Phys. Lett. 10, 153 (1964)] Recent LQCD calculation Σ δm Λ = 0.52(23) MeV [R. Hosley et al., PRD 91, 074512 (2015)] no QED effects, baryon mass differences are not reproduced 5

Electromagnetic Λ Σ 0 mixing Direct πλλ coupling is forbidden by isospin conservation Λ Σ 0 mixing results in effective πλλ coupling, giving rise to CSB NΛ interaction: Λ N π 0 V CSB NΛ = g πλλτ N3 [σ Λ σ N + T(r)S(ˆr, σ Λ, σ N )]Y(r) Σ 0 δm g πλλ = 2 Σ0 δm Λ M Σ 0 M Λ g πλσ Λ N contributions from heavier shorter-range isovector meson exchanges, e.g. ρ (replaced by contact terms in χeft) expected B Λ ( 4 Λ He 4 ΛH) 170 kev [Gazda, Gal, NPA 954, 161 (2016)] 6

Electromagnetic Λ Σ 0 mixing For NY interaction models with explicit NΣ NΛ coupling, the electromagnetic Λ Σ 0 mixing relates matrix elements of VNΛ CSB with V NΣ NΛ: Σ 0 Λ N δm V NΣ NΛ NΛ V CSB NΛ NΛ = 2 Σ0 δm Λ M Σ 0 M Λ τ N3 1 3 NΣ V NΣ NΛ NΛ [Gal, PLB 744, 352 (2015)] Λ N The first microscopic model which generates large B Λ (0 + g.s.) 200 kev in A = 4 hypernuclei! [Gazda, Gal, PRL 116, 122501 (2016)] 7

Methodology

Ab initio hypernuclear calculations Given a Hamiltonian solve the eigenvalue problem of A nucleons [ ˆp 2 i 2m + ˆV BB (i, j) + ] ˆV BBB (i, j, k) Ψ = E Ψ i A i<j A i<j<k A realistic interparticle interactions controllable approximations Ab initio no-core shell model Hamiltonian is diagonalized in a finite A-particle harmonic oscillator basis Ψ(r 1,..., r A ) = n (r 1,..., r A ) n N tot φ HO (dimensions up to 10 10 with 10 14 nonzero matrix elements) all particles are active (no core) NCSM results converge to exact results, N tot 8

Input V NN, V NNN and V NY potentials Potentials derived from chiral EFT long-range part (π, K, η-exchange) predicted by χpt short-range part parametrized by contact interactions, LECs fitted to experimental data NN+NNN interaction chiral N 3 LO NN potential [Entem, Machleidt, PRC 68, 041001 (2003)] chiral N 2 LO NNN potential [Navrátil, FBS 41, 14 (2007)] NY interaction chiral LO potential [Polinder et al., NPA 779, 244 (2006)] ΛN ΣN mixing explicitly taken into account: ( ) ( ) V ΛN ΛN V ΛN ΣN 0 0 V NY = + V ΣN ΛN V ΣN ΣN 0 m Σ m Λ supplemented by V CSB NΛ 9

Results

Charge symmetry breaking in 4 Λ He 4 Λ H hypernuclei 300 200 0 + g.s. without V CSB 1 + ex. without V CSB B Λ CSB (kev) 100 0 100 200 550 600 650 700 Λ EFT (MeV) Fig. 1: Cutoff momentum Λ EFT dependence of the difference B CSB Λ = B Λ ( 4 Λ He) B Λ( 4 Λ H) of Λ separation energies in 4 Λ He and 4 ΛH in ab initio NCSM calculations without VCSB ΛN generated by ΛN ΣN conversion from LO chiral NY interactions. 10

Charge symmetry breaking in 4 Λ He 4 Λ H hypernuclei 300 200 0 + g.s. without V CSB 1 + ex. without V CSB 0 + g.s. with V CSB 1 + ex. with V CSB B Λ CSB (kev) 100 0 100 200 550 600 650 700 Λ EFT (MeV) Fig. 1: Cutoff momentum Λ EFT dependence of the difference B CSB Λ = B Λ ( 4 Λ He) B Λ( 4 Λ H) of Λ separation energies in 4 Λ He and 4 ΛH in ab initio NCSM calculations without and with VΛN CSB generated by ΛN ΣN conversion from LO chiral NY interactions. 10

Charge symmetry breaking in 4 Λ He 4 Λ H hypernuclei 500 without V CSB E x CSB (kev) 400 300 200 100 Exp. 0 550 600 650 700 Λ EFT (MeV) Fig. 2: Cutoff momentum (Λ EFT ) dependence of the difference Ex CSB of the excitation energies E x(0 + g.s. 1 + ) in 4 Λ He and 4 ΛH in ab initio NCSM calculations without VCSB ΛN generated by ΛN ΣN conversion from LO chiral NY interactions. 11

Charge symmetry breaking in 4 Λ He 4 Λ H hypernuclei 500 without V CSB with V CSB E x CSB (kev) 400 300 200 100 Exp. 0 550 600 650 700 Λ EFT (MeV) Fig. 2: Cutoff momentum (Λ EFT ) dependence of the difference Ex CSB of the excitation energies E x(0 + g.s. 1 + ) in 4 Λ He and 4 ΛH in ab initio NCSM calculations without and with VΛN CSB generated by ΛN ΣN conversion from LO chiral NY interactions. 11

Conclusions & Outlook

Conclusions Ab initio calculations of light hypernuclei Electromagnetic Λ Σ 0 conversion is able to produce sizeable value of CSB in A=4 mirror hypernuclei. Within a model based on chiral LO NY ΛN ΣN interactions it is possible to resolve the CSB puzzle in the ground states of 4 Λ He and 4 Λ H. [Gazda, Gal, PRL 116, 122501 (2016); NPA 954, 161 (2016)] Outlook Sizeable cutoff dependence need to study NLO V NY. p-shell hypernuclei 12

Thank you! 12

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