Quantum Monte Carlo calculations of Neutrino-Nucleus Interactions - PowerPoint PPT Presentation

Quantum Monte Carlo calculations of Neutrino-Nucleus Interactions PONDD Physics Opportunities in the Near DUNE Detector Hall Alessandro Lovato In collaboration with: C. Barbieri, O. Benhar, J. Carlson, S. Gandolfi, W. Leidemann, G. Orlandini, M. Piarulli, N. Rocco, and R. Schiavilla

The Physics case Neutrino-oscillation and 0 νββ experiments Multi-messenger era for nuclear astrophysics • Accurately measure neutrino-oscillation • Gravitational waves have been detected! parameters • Supernovae neutrinos will be detected by the • Determine whether the neutrino is a Majorana current and next generation neutrino experiments or a Dirac particle • Need for including nuclear dynamics; mean- • Nuclear dynamics determines the structure and field models inadequate to describe neutrino- the cooling of neutron stars nucleus interaction

The basic model • In the low-energy regime, quark and gluons are confined inside hadrons. Nucleons can treated as point-like particles interacting through the Hamiltonian p 2 X X X i H = v ij + V ijk + . . . 2 m + i i<j i<j<k • E ff ective field theories are the link between QCD and nuclear observables. They exploit the separation between the “hard” (M~nucleon mass) and “soft” (Q ~ exchanged momentum) scales 2N Force 3N Force LO ( Q/ Λ χ ) 0 NLO ( Q/ Λ χ ) 2 NNLO Courtesy of M. Savage ( Q/ Λ χ ) 3 +...

Nuclear (phenomenological) Hamiltonian The Argonne v 18 is a finite, local, configuration-space potential controlled by ~4300 np and pp scattering data below 350 MeV of the Nijmegen database N N N N N N π π ∆ N N N N N N Three-nucleon interactions e ff ectively include the lowest nucleon excitation, the ∆ (1232) resonance, end other nuclear e ff ects π π π π π π π ∆ π ∆ ∆ ∆ π π π ∆ π π π π π

Nuclear electroweak currents The nuclear electromagnetic current is constrained by the Hamiltonian through the continuity equation r · J EM + i [ H, J 0 EM ] = 0 • The above equation implies that involves • They are essential for low-momentum and J EM two-nucleon contributions. low-energy transfer transitions. 4 π 3 π π 9 B ∆ 7 Li p 9 Li 3 H 2 1 8 Li 8 B µ ( µ N ) 2 H 6 Li 0 GFMC(IA) 9 C GFMC(TOT) 9 Be 7 Be ρ , ω π π EXPT -1 3 He n -2 -3 S. Pastore at al., PRC 87, 035503 (2013)

Quantum Monte Carlo • Di ff usion Monte Carlo methods use an imaginary-time projection technique to enhance the ground-state component of a starting trial wave function. τ →∞ e − ( H − E 0 ) τ | Ψ T i = lim X c n e − ( E n − E 0 ) τ | Ψ n i = c 0 | Ψ 0 i lim τ →∞ n • Suitable to solve of A ≤ 12 nuclei with ~1% accuracy -20 1 + 4 + 7/2 − 2 + 2 + 0 + 2 + 0 + 0 + 5/2 − 0 + -30 3 + 0 + 1 + 4 He 2 + 5/2 − 1 + 6 He 4 + 8 He 7/2 + 2 + 7/2 − 4 + 6 Li 3 + 5/2 + 1 + 1/2 − 5/2 − -40 2 + 1 + 3 + 7/2 − 3/2 − 1/2 − 3 + 2 + 1 + 7/2 − 3/2 − 7 Li 2 + 4 + 3/2 − 2 + 3 + -50 9 Li 3 + Energy (MeV) 1 + 3/2 + 4 + 8 Li 2 + 1 + 3,2 + 5/2 + 2 + 0 + 1 + Argonne v 18 0 + 1/2 − 3 + -60 8 Be 2 + 5/2 − 2 + 2 + 1/2 + 1 + with Illinois-7 0 + 3/2 − 1 + -70 3 + GFMC Calculations 10 Be 9 Be 10 B 24 November 2012 -80 0 + AV18 -90 AV18 0 + +IL7 Expt. 12 C -100 J. Carlson et al. RMP 87, 1067 (2015)

The basic model of nuclear Physics + Realistic nuclear interactions Nuclear ab-initio methods -20 1 1 + 4 + 7/2 − 2 + 2 + 0 + 2 + 0 + 0 + 12 Be 5/2 − 12 C GT- ν 0 + -30 3 + 0.8 0 + 1 + 4 He 2 + GT-AA 5/2 − 1 + 6 He 4 + 8 He 2 + 7/2 + F- ν 7/2 − 4 + 6 Li 3 + 5/2 + 1 + 0.6 1/2 − 5/2 − T- ν -40 2 + 1 + 7/2 − 3 + 3/2 − 1/2 − F-NN 3 + 2 + 1 + 7/2 − 3/2 − 7 Li GT- ππ 2 + 4 + 0.4 3/2 − 2 + 3 + -50 9 Li GT- π N 3 + Energy (MeV) 1 + 3/2 + 4 + 8 Li 2 + T- ππ 1 + 5/2 + 3,2 + -1 ] 2 + 0 + 0.2 T- π N 1 + 0 + C(r) [fm Argonne v 18 1/2 − 3 + -60 8 Be 2 + 5/2 − 2 + 2 + 1/2 + with Illinois-7 1 + 0 0 + 3/2 − 1 + -70 3 + GFMC Calculations 9 Be 10 Be -0.2 10 B 24 November 2012 -80 -0.4 0 + AV18 -90 AV18 -0.6 0 + S. Pastore et al. PRC 97, 014606 (2018) +IL7 Expt. J. Carlson et al. RMP 87, 1067 (2015) 12 C -100 -0.8 0 2 4 6 0 2 4 6 r [fm] r [fm] 2.8 -2 -2 PNM 2.4 � � -4 -4 PSR J0348+0432 2.0 -6 -6 PSR J1614-2230 � N + � NN (II) E/A (MeV) � � 1.6 M [M 0 ] -8 -8 Exp 1.2 -10 -10 � N + � NN (I) LO � NLO 0.8 -12 -12 N 2 LO E τ τ (b) R 0 = 1.2 fm -14 -14 0.4 � N N 2 LO E1 13 D. Lonardoni et al. PRL 120, 122502 (2018) D. Lonardoni et al. PRL 114, 092301 (2015) R [km] r (fm) -16 -16 0.0 3 H 3 H 3 He 3 He 4 He 4 He 6 He 6 He 6 Li 6 Li 12 C 12 C 16 O 16 O 11 12 13 14 15 R [km]

Lepton-nucleus scattering Schematic representation of the inclusive cross section as a function of the energy loss. Courtesy of Saori Pastore

Lepton-nucleus scattering The inclusive cross section of the process in which a lepton scatters o ff a nucleus can be written in terms of five response functions ` 0 | Ψ f i d σ / [ v 00 R 00 + v zz R zz � v 0 z R 0 z γ , Z, W ± dE ` 0 d Ω ` + v xx R xx ⌥ v xy R xy ] • In the electromagnetic case only the longitudinal and the transverse response functions contribute | Ψ 0 i ` • The response functions contain all the information on target structure and dynamics X h Ψ 0 | J † R αβ ( ω , q ) = α ( q ) | Ψ f ih Ψ f | J β ( q ) | Ψ 0 i δ ( ω � E f + E 0 ) f • They account for initial state correlations, final state correlations and two-body currents + =

Lepton-nucleus scattering • At low momentum transfer the space resolution of the lepton becomes much larger than the average NN separation distance ( ∼ 1.5 fm). • In this regime the interaction involves many nucleons long-range correlations ← λ ∼ q − 1 → c f X | Ψ f i = 1 p, 1 h | Ψ 1 p 1 h i d • The giant dipole resonance is a manifestation of long-range correlations + −

Lepton-nucleus scattering • At (very) large momentum transfer, scattering o ff a nuclear target reduces to the sum of scattering processes involving bound nucleons short-range correlations. | Ψ f i ' | p 1 i ⌦ | Ψ f i A − 1 | Ψ f i ' | p 1 , p 2 i ⌦ | Ψ f i A − 2 • Relativistic e ff ects play a major role and need to be accounted for along with nuclear correlations (Non trivial interplay between them) • Resonance production and deep inelastic scattering also need to be accounted for

<latexit sha1_base64="wnLvSs9vVDQ4SOet/Eh6fyoJs+o=">ACAHicdVDLSgNBEJyNrxhfq14EL4NB8CBhN4omt6AXjxFcE0himJ10kiGzs8vMrBDW9eKvePGg4tXP8ObfOHkIPgsaiqpurv8iDOlHefdyszMzs0vZBdzS8srq2v2+salCmNJwaMhD2XdJwo4E+BpjnUIwk8DnU/MHpyK9dg1QsFBd6GErID3BuowSbaS2vXVzlbhOmjRlgE8g3Y+ipiSix6Ft51CsVxyDsr4N3ELzh5NEW1b81OyGNAxCacqJUw3Ui3UqI1IxySHPNWEFE6ID0oGoIAGoVjL+IMW7RungbihNCY3H6teJhARKDQPfdAZE9VPbyT+5TVi3S21EiaiWIOgk0XdmGMd4lEcuMkUM2HhAqmbkV0z6RhGoTWs6E8Pkp/p94xUK54J4f5itH0zSyaBvtoD3komNUQWeoijxE0S26R4/oybqzHqxn62XSmrGmM5voG6zXDwSQls4=</latexit> <latexit sha1_base64="wnLvSs9vVDQ4SOet/Eh6fyoJs+o=">ACAHicdVDLSgNBEJyNrxhfq14EL4NB8CBhN4omt6AXjxFcE0himJ10kiGzs8vMrBDW9eKvePGg4tXP8ObfOHkIPgsaiqpurv8iDOlHefdyszMzs0vZBdzS8srq2v2+salCmNJwaMhD2XdJwo4E+BpjnUIwk8DnU/MHpyK9dg1QsFBd6GErID3BuowSbaS2vXVzlbhOmjRlgE8g3Y+ipiSix6Ft51CsVxyDsr4N3ELzh5NEW1b81OyGNAxCacqJUw3Ui3UqI1IxySHPNWEFE6ID0oGoIAGoVjL+IMW7RungbihNCY3H6teJhARKDQPfdAZE9VPbyT+5TVi3S21EiaiWIOgk0XdmGMd4lEcuMkUM2HhAqmbkV0z6RhGoTWs6E8Pkp/p94xUK54J4f5itH0zSyaBvtoD3komNUQWeoijxE0S26R4/oybqzHqxn62XSmrGmM5voG6zXDwSQls4=</latexit> <latexit sha1_base64="wnLvSs9vVDQ4SOet/Eh6fyoJs+o=">ACAHicdVDLSgNBEJyNrxhfq14EL4NB8CBhN4omt6AXjxFcE0himJ10kiGzs8vMrBDW9eKvePGg4tXP8ObfOHkIPgsaiqpurv8iDOlHefdyszMzs0vZBdzS8srq2v2+salCmNJwaMhD2XdJwo4E+BpjnUIwk8DnU/MHpyK9dg1QsFBd6GErID3BuowSbaS2vXVzlbhOmjRlgE8g3Y+ipiSix6Ft51CsVxyDsr4N3ELzh5NEW1b81OyGNAxCacqJUw3Ui3UqI1IxySHPNWEFE6ID0oGoIAGoVjL+IMW7RungbihNCY3H6teJhARKDQPfdAZE9VPbyT+5TVi3S21EiaiWIOgk0XdmGMd4lEcuMkUM2HhAqmbkV0z6RhGoTWs6E8Pkp/p94xUK54J4f5itH0zSyaBvtoD3komNUQWeoijxE0S26R4/oybqzHqxn62XSmrGmM5voG6zXDwSQls4=</latexit> <latexit sha1_base64="wnLvSs9vVDQ4SOet/Eh6fyoJs+o=">ACAHicdVDLSgNBEJyNrxhfq14EL4NB8CBhN4omt6AXjxFcE0himJ10kiGzs8vMrBDW9eKvePGg4tXP8ObfOHkIPgsaiqpurv8iDOlHefdyszMzs0vZBdzS8srq2v2+salCmNJwaMhD2XdJwo4E+BpjnUIwk8DnU/MHpyK9dg1QsFBd6GErID3BuowSbaS2vXVzlbhOmjRlgE8g3Y+ipiSix6Ft51CsVxyDsr4N3ELzh5NEW1b81OyGNAxCacqJUw3Ui3UqI1IxySHPNWEFE6ID0oGoIAGoVjL+IMW7RungbihNCY3H6teJhARKDQPfdAZE9VPbyT+5TVi3S21EiaiWIOgk0XdmGMd4lEcuMkUM2HhAqmbkV0z6RhGoTWs6E8Pkp/p94xUK54J4f5itH0zSyaBvtoD3komNUQWeoijxE0S26R4/oybqzHqxn62XSmrGmM5voG6zXDwSQls4=</latexit> Moderate momentum-transfer regime • At moderate momentum transfer, the inclusive cross section can be written in terms of the response functions X h Ψ 0 | J † R αβ ( ω , q ) = α ( q ) | Ψ f ih Ψ f | J β ( q ) | Ψ 0 i δ ( ω � E f + E 0 ) f • Both initial and final states are eigenstates of the nuclear Hamiltonian H | Ψ 0 i = E 0 | Ψ 0 i H | Ψ f i = E f | Ψ f i • As for the electron scattering on 12 C | 10 Be , pp i | 12 C ∗ i , | 11 B , p i , | 11 C , n i , | 10 B , pn i , | 10 B , pp i . . . • Relativistic corrections are included in the current operators and in the nucleon form factors

Integral transform techniques • The integral transform of the response function are generally defined as Z E αβ ( σ , q ) ≡ d ω K ( σ , ω ) R αβ ( ω , q ) • Using the completeness of the final states, they can be expressed in terms of ground-state expectation values E αβ ( σ , q ) = h Ψ 0 | J † α ( q ) K ( σ , H � E 0 ) J β ( q ) | Ψ 0 i K