Theoretical study of the 3H(p, e+, e−)4He reaction and the search for the particle X17

M. Viviani

INFN, Sezione di Pisa & Department of Physics, University of Pisa Pisa (Italy)

INT 20-2b - Beyond-the-Standard-Model Physics with Nucleons and Nuclei

Zoom meeting July 13 - August 7, 2020 Seattle, WA, USA

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 1 / 34 Outline

1 Introduction 2 Theoretical study of the A = 4 reactions

3 Transition amplitudes and the EM charge & current operators

4 The 3H(p, e+e−)4He process

5 The X17 boson “anomaly” (in progress)

6 Conclusions

Collaborators R. Schiavilla Jefferson Lab. & ODU, Norfolk (VA, USA) M. Piarulli & S. Pastore GWU, St.Louis (MS, USA) L. Girlanda University of Salento & INFN-Lecce, Lecce (Italy) A. Gnech, A. Kievsky, & L.E. Marcucci - INFN-Pisa & Pisa University, Pisa (Italy) A. Baroni LANL (NM, USA)

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 2 / 34 The X17 boson hypothesis

The ATOMKI experiments [Krasznahorkay et al., PRL 116, 042501 (2016)]: “Observation of Anomalous Internal Pair Creation in 8Be: A Possible Indication of a Light, Neutral Boson” [Krasznahorkay et al., arXiv:1910.10459v1 (23 October 2019)]: “New evidence supporting the existence of the hypothetic X17 particle”

Reaction mX ∆mX (stat) ∆mX (syst) τ Evidence [MeV] [MeV] [MeV] [sec] 7Li(p, e+e−)8Be 16.70 0.35 0.50 10−14 > 5σ 3H(p, e+e−)4He 16.84 0.16 0.20 > 7.2σ

Measurements of the e+e− angular Previous “anomalies” found in IPC correlation in the internal pair conversion (IPC) nuclear transition [De Boer et al., Phy. Lett. B388, 235 (1996); J. Phys. G 27 L29 (2001)]: IKF Frankfurt: 9 MeV Boson? [Vitéz et al., Acta Physica Polonica B 39, 483 (2008)] [de Boer & Fields, Int. J. mod. Phys. E 20, 1787 image from [Feng et al., (2011)] arXiv:1608.03591] − M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 3 / 34 The 8Be experiment

[Krasznahorkay et al., PRL 116, 042501 (2016)]

Angular distribution of the e−e+ pair

[Tanedo, www.particlebites.com/?p=3970 (Aug. 25, 2016)] “The Delirium over Beryllium” for a nice introduction to the experiment and the possible explanations [Feng et al., PRL 117, 071803 (2016)]: “Protophobic Fifth-Force Interpretation of the Observed Anomaly in 8Be Nuclear Transitions” [Pastore et al., PRC 90, 024321 (2014)] “Quantum Monte Carlo calculations of electromagnetic transitions in 8Be with meson-exchange currents derived from chiral effective field theory” [Zhang & Miller, arXiv:1703.04588] “Can nuclear physics explain the anomaly observed in the internal pair production in the Beryllium-8 nucleus?” − M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 4 / 34 The 4He experiment

[Krasznahorkay et al., arXiv:1910.10459v1], [Firak et al., EPJ Web Conf. 232, 04005 (2020)] [Frankenthal, https://www.particlebites.com/?p=6696 (Jan. 4, 2020)] “The Delirium over Helium” for an update of the precedent particlebites.com report cerncourier.com/a/rekindled-atomki-anomaly-merits-closer-scrutiny/

Angular distribution of the e−e+ pair

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 5 / 34 Following these announcements...

[Wong, arXiv:2001.04864] “Open string QED meson description of the X17 particle and dark matter” [Tursunov, arXiv:2001.08995] “Evidence of quantum phase transition . . . X17 boson” [Koch, arXiv:2003.05722] “X17: A new force, or evidence for a hard γ + γ process?” [Chen, arXiv:2006.01018] “Is the X17 composed of four bare quarks?” [Feng, Tait, & Verhaaren, arXiv:2006.01151] “Dynamical Evidence For a Fifth Force Explanation of the ATOMKI Nuclear Anomalies” [Du et al., J.Phys.Conf.Ser. 1506, 012004 (2020)] “Decay of neutron with participation of the light vector boson X17” actively searched by a number of experiments BelleII, MEG, PADME, HPS, LHCb, . . .

Most of the speculations based on “resonance saturation” Assumed mechanism p + 3H (4He)∗ 4He + X, followed by the decay→X e+e→− → Motivation of this work: solve accurately the A = 4 nuclear dynamics include the contribution of all relevant waves treat the X17 interaction within the χPT framework warning: very preliminary results!

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 6 / 34 Theoretical study of the A = 4 reactions

0.002 0.008 0.02 3 p- He polarization observable Ay Ecm=266 keV Ecm = 431 keV Ecm = 666 keV 0,6 0.0015 0.006 0.015 E =4 MeV E =5.54 MeV Ep=2.25 MeV p p y

A 0,5 0.001 0.004 0.01 George 2001 Fisher 2006 Alley 1993 Fisher 2006 Alley-2 1993 I-N3LO/N-N2LO 0.0005 0.002 0.005 0,4 AV18/UIX AV18/IL7

Vlow-k

0 0 0 y 0,3 A 0.05 0.06 0.04 Ecm = 1.33 MeV Ecm = 1.66 MeV Ecm = 2.0 MeV 0.05 0.04 0,2 0.03 0.04 y

A 0.03 0.02 0.03 0,1 0.02 0.02 0.01 0.01 0.01 0 0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150 180 0 0 0 θ θ θ 0 30 60 90 120 150 180 0 30 60 90 120 150 180 0 30 60 90 120 150 180 [c.m.] [deg] [c.m.] [deg] [c.m.] [deg] θ θ θ cm [deg] cm [deg] cm [deg] A = 4: p 3He & n 3H scattering A = 3 − −

Numerical techniques for A = 4 for scattering Faddeev-Yakubovsky methods [Lazauskas & Carbonell, 2004], [Deltuva & Fonseca, 2007] Expansion on a basis: NCSM [Quaglioni, Navratil & Roth, 2010], Gaussians [Aoyama et al., 2011], R-matrix [Descouvemont & Baye], HH [Kievsky, MV, et al., 2008], . . .

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 7 / 34 HH expansion

Example: n3He → p3H + n3He process

N (AB),± 1 GL(η, qAByp) FL(η, qAByp) Ω = Y (yˆ ) ⊗ [φ ⊗ φ ] f (yp) ± i LSJJz L p A B S L r N JJz  qAByp qAByp  permX.=1h i

(nh) (nh) (nh),− (nh,pt) (pt),+ (nh,nh) (nh,+) Ψ = a Φ +Ω − S ′ ′ Ω ′ ′ − S ′ ′ Ω ′ ′ LSJJz LS,[K ] n,[K ] LSJJz LS,L S L S JJz LS,L S L S nX,[K ] XL′S′ XL′S′

Φn,K ] HH states – essentially, homegeneous polynomials of degree K ′ ′ (AB,A B ) ′ ′ = S-matrix SLS,L S ′ ′ (nh) (AB,A B ) a and ′ ′ computed using the Kohn variational principle LS,[K ] SLS,L S For a review, see [J. Phys. G: Nucl. Part. Phys. 35, 063101 (2008) ]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 8 / 34 Interactions NN interaction Jülich (up to N4LO) [Epelbaum, Krebs, & Meissner, 2014], [ Reinert, See, for example [Epelbaum, 2010], [Machleidt Krebs, & Epelbaum, 2017] & Entem, 2011] Idaho (up to N4LO) [Entem, Machleidt, & Nosyk, 2017] N3LO + ∆ dof’s (Norfolk VIa,. . .) [Piarulli et al., 2018] LEC’s fitted to the NN database or πN database. Cutoff Λ= 450 600 MeV − 3N interaction N2LO [Epelbaum et al, 2002] two LECS cD and cE : fitted to reproduce B(3H) and some other observable 3N force at N3LO & N4LO [Krebs et al., 2012-2013] +∆ dof’s [Baroni et al., 2018], [Krebs et al., 2018] +13 new LEC’s N3LO [Girlanda et al., 2019–. . .] − M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 9 / 34 Benchmark test of 4N scattering calculations

N3LO500 potential – 3He(n, n)3He elastic scattering

3 3 3 3 He(n,n) He elastic scattering at E =1 MeV 3 3 He(n,n) He elastic scattering at E =3.5 MeV n He(n,n) He elastic scattering at En=2 MeV n 500 0.8 600 0.8 600 0.8 0.7 0.7 A 0.7 A Seagrave (1960) Jany (1988) E =0.944 MeV Seagrave (1960) Jany (1988) y0 Seagrave (1960) y0 n 500 500 400 AGS 0.6 Jany (1988) E =1 MeV AGS 0.6 AGS 0.6 FY n FY FY Jany (1988) E =1.053 MeV 0.5 0.5 HH 0.5 n 400 HH 400 HH 300 0.4 0.4 0.4 Ay0 [mb/sr] [mb/sr] [mb/sr] 0.3 300 0.3 300 0.3 Ω Ω Ω /d /d /d 0.2 σ 0.2 200 0.2 σ σ d d d 200 200 0.1 0.1 0.1 0 0 100 0 100 100 -0.1 -0.1 -0.1 0 0 0.5 0 0.5 A A Ayy A yy A A 0.5 0y 0.5 0y 0.5 0y yy

0.4 0.4 0.4 0.4 0.4 0.2 0.3 0.3 0.3

0.2 0.2 0.3 0.2 0.3

0.1 0.1 0.1 0.1 0 0 0.2 0 0.2

-0.1 -0.1 -0.1

-0.2 0 -0.2 0.1 -0.2 0.1 0 30 60 90 120 150 180 0 30 60 90 120 150 180 0 30 60 90 120 150 180 0 30 60 90 120 150 180 0 30 60 90 120 150 180 0 30 60 90 120 150 180 θ [deg] θ [deg] θ [deg] θ [deg] θ [deg] θ [deg]

AGS= Deltuva & Fonseca – FY= Lazauskas & Carbonell – HH= present work

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 10 / 34 Benchmark test of 4N scattering calculations (2)

3 3 H(p,p) H elastic scattering

400 E =2.5 MeV E =3.5 MeV p p Ep=4.15 MeV AGS 300 HH FY

[mb/sr] 200 Ω /d σ d 100

0 E =2.5 MeV Ep=4.15 MeV p Ep=3.5 MeV A y0 0.6 AGS HH FY 0.4

0.2

0 0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150 180 θ θ θ c.m. [deg] c.m. [deg] c.m. [deg]

AGS= Deltuva & Fonseca – FY= Lazauskas & Carbonell – HH= present work

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 11 / 34 n + 3He elastic scattering

See [MV at al., ArXiv:2003.14059 ]

Cyan band N3LO500 - N3LO600 NN potential Blue band N3LO500/N2LO500 - N3LO600/N2LO600 NN+3N potential

E =1 MeV E =3.15 MeV 600 n E =2 MeV n 0.8 n E =1 MeV E =2 MeV E =3.5 MeV Esterline (2013) n n n NN Jany (1988) NN Seagrave (1960) Seagrave (1969) NN+3N NN+3N 0.6 Jany (1988) 0.944 MeV Seagrave (1960) 400 Jany (1988) 1 MeV Jany (1988) 1.053 MeV

[mb/sr] 0.4 A Ω y0 /d σ

d 200 0.2

0 0 0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150 180 θ θ θ 0 30 60 90 120 150 0 30 60 90 120 150 0 30 60 90 120 150 180 c.m. [deg] c.m. [deg] c.m. [deg] θ θ θ c.m. [deg] c.m. [deg] c.m. [deg]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 12 / 34 p + 3He elastic scattering (1)

Cyan band N3LO500 - N3LO600 NN potential Blue band N3LO500/N2LO500 - N3LO600/N2LO600 NN+3N potential

E =5.54 MeV Ep=2.25 MeV p 400 0.25 400 NN Famularo Fisher NN+3N 0.5 Fisher 0.2 Knudson 300

300 [mb/sr] A

[mb/sr] NN A y0

y0 Ω 0.4

Ω NN+3N /d

/d 0.15 σ σ d 200 0.3

d 200 0.1 0.2 100 100 0.05 0.1

0 0.100 0.200 0.200 0.08 Daniels Daniels 0.15 0.15 0.05 A0y Ayy A0y Ayy 0.10 0.10 0.04 0.00 0.05 0.05

-0.05 0.00 0.00 0.00

0.10 -0.10 -0.050.20 -0.050.2

0.10 0.15 Daniels 0.1 0.05 Axx Axz Axx Axz 0.05 0.10 0.00 0.0 0.00 0.05

-0.05 -0.1 -0.05 0.00

-0.05 -0.2 -0.10 -0.10 0 45 90 135 180 0 45 90 135 180 0 45 90 135 180 0 45 90 135 180 θ θ θ θ c.m. [deg] c.m. [deg] c.m. [deg] c.m. [deg] − M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 13 / 34 p + 3He elastic scattering (2) NN potentials up to N4LO [Entem, Machleidt, & Nosyk, 2017] Order VNN W3N 0 LO − Theoretical error estimated using the 1 NLO − 2 N2LO N2LO method proposed by [Epelbaum, Kreb, & ∗ 3 N3LO N2LO (N3LO c from table IX of EMN17) Meissner, 2014] ∗∗ i 4 N4LO N2LO (N4LO ci from table IX of EMN17) X max Q X X Q2 X X ∆ i = [ | i − i−1|, | i−1 − i−2|,...] 3 cD, cE fitted to B( H) and tritium GTME by [Marcucci with Q = mπ/Λ et al., 2018]

400 0.6 0.20 σ Ω d /d [mb/sr] Ay0 A0y 0.15 300 LO NLO 0.4 N2LO 0.10 200 N3LO N4LO 0.05 0.2 100 0.00

0.200 0 -0.05 Ayy Axx Axz 0.15 0.20 0.1 0.15 0.10 0.10 0.0 0.05 0.05 -0.1 0.00 0.00

-0.05 -0.05 -0.2 0 45 90 135 180 0 45 90 135 180 0 45 90 135 180 θ θ θ c.m. [deg] c.m. [deg] c.m. [deg]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 14 / 34 p + 3He elastic scattering (2) NN potentials up to N4LO [Entem, Machleidt, & Nosyk, 2017] Order VNN W3N 0 LO − Theoretical error estimated using the 1 NLO − 2 N2LO N2LO method proposed by [Epelbaum, Kreb, & ∗ 3 N3LO N2LO (N3LO c from table IX of EMN17) Meissner, 2014] ∗∗ i 4 N4LO N2LO (N4LO ci from table IX of EMN17) X max Q X X Q2 X X ∆ i = [ | i − i−1|, | i−1 − i−2|,...] 3 cD, cE fitted to B( H) and tritium GTME by [Marcucci with Q = mπ/Λ et al., 2018]

400 0.6 0.20 σ Ω d /d [mb/sr] Ay0 A0y 0.15 300 NLO 0.4 0.10 200 0.05 0.2 100 0.00

0.200 0 -0.05 Ayy Axx Axz 0.15 0.20 0.1 0.15 0.10 0.10 0.0 0.05 0.05 -0.1 0.00 0.00

-0.05 -0.05 -0.2 0 45 90 135 180 0 45 90 135 180 0 45 90 135 180 θ θ θ c.m. [deg] c.m. [deg] c.m. [deg]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 14 / 34 p + 3He elastic scattering (2) NN potentials up to N4LO [Entem, Machleidt, & Nosyk, 2017] Order VNN W3N 0 LO − Theoretical error estimated using the 1 NLO − 2 N2LO N2LO method proposed by [Epelbaum, Kreb, & ∗ 3 N3LO N2LO (N3LO c from table IX of EMN17) Meissner, 2014] ∗∗ i 4 N4LO N2LO (N4LO ci from table IX of EMN17) X max Q X X Q2 X X ∆ i = [ | i − i−1|, | i−1 − i−2|,...] 3 cD, cE fitted to B( H) and tritium GTME by [Marcucci with Q = mπ/Λ et al., 2018]

400 0.6 0.20 σ Ω d /d [mb/sr] Ay0 A0y 0.15 300 NLO N2LO 0.4 0.10 200 0.05 0.2 100 0.00

0.200 0 -0.05 Ayy Axx Axz 0.15 0.20 0.1 0.15 0.10 0.10 0.0 0.05 0.05 -0.1 0.00 0.00

-0.05 -0.05 -0.2 0 45 90 135 180 0 45 90 135 180 0 45 90 135 180 θ θ θ c.m. [deg] c.m. [deg] c.m. [deg]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 14 / 34 p + 3He elastic scattering (2) NN potentials up to N4LO [Entem, Machleidt, & Nosyk, 2017] Order VNN W3N 0 LO − Theoretical error estimated using the 1 NLO − 2 N2LO N2LO method proposed by [Epelbaum, Kreb, & ∗ 3 N3LO N2LO (N3LO c from table IX of EMN17) Meissner, 2014] ∗∗ i 4 N4LO N2LO (N4LO ci from table IX of EMN17) X max Q X X Q2 X X ∆ i = [ | i − i−1|, | i−1 − i−2|,...] 3 cD, cE fitted to B( H) and tritium GTME by [Marcucci with Q = mπ/Λ et al., 2018]

400 0.6 0.20 σ Ω d /d [mb/sr] Ay0 A0y 0.15 300 NLO N2LO 0.4 N3LO 0.10 200 0.05 0.2 100 0.00

0.200 0 -0.05 Ayy Axx Axz 0.15 0.20 0.1 0.15 0.10 0.10 0.0 0.05 0.05 -0.1 0.00 0.00

-0.05 -0.05 -0.2 0 45 90 135 180 0 45 90 135 180 0 45 90 135 180 θ θ θ c.m. [deg] c.m. [deg] c.m. [deg]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 14 / 34 p + 3He elastic scattering (2) NN potentials up to N4LO [Entem, Machleidt, & Nosyk, 2017] Order VNN W3N 0 LO − Theoretical error estimated using the 1 NLO − 2 N2LO N2LO method proposed by [Epelbaum, Kreb, & ∗ 3 N3LO N2LO (N3LO c from table IX of EMN17) Meissner, 2014] ∗∗ i 4 N4LO N2LO (N4LO ci from table IX of EMN17) X max Q X X Q2 X X ∆ i = [ | i − i−1|, | i−1 − i−2|,...] 3 cD, cE fitted to B( H) and tritium GTME by [Marcucci with Q = mπ/Λ et al., 2018]

400 0.6 0.20 σ Ω d /d [mb/sr] Ay0 A0y 0.15 300 NLO N2LO 0.4 N3LO 0.10 200 N4LO 0.05 0.2 100 0.00

0.200 0 -0.05 Ayy Axx Axz 0.15 0.20 0.1 0.15 0.10 0.10 0.0 0.05 0.05 -0.1 0.00 0.00

-0.05 -0.05 -0.2 0 45 90 135 180 0 45 90 135 180 0 45 90 135 180 θ θ θ c.m. [deg] c.m. [deg] c.m. [deg]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 14 / 34 p + 3H phase-shifts and the excited states of 4He

180 1 S R-matrix 3 150 0 N3LO500 P0 N3LO600 120 N3LO500/N2LO500 N3LO600/N2LO600

[deg] 90 H 3 p+

δ 60

30 0 C.M. energies measured 3 3 P P 1 2 3 60 from the p + H threshold [deg] H 3 p+

δ 30

0 0 1 2 3 0 1 2 3 Tr [MeV] Tr [MeV]

1 3 1 S0 P0 P1 Interaction ER (MeV) Γ (MeV) ER (MeV) Γ (MeV) ER (MeV) Γ (MeV) N3LO500 0.13 0.56 0.89 0.46 1.7 8.2 N3LO600 0.13 0.59 1.05 0.57 1.7 8.6 N3LO500/N2LO500 0.12 0.48 0.90 0.46 1.8 8.6 N3LO500/N2LO500 0.13 0.99 0.98 0.54 1.8 8.7 R-matrix 0.39 0.50 1.20 0.84 6.13 12.7 3 3 P1 P2 Interaction ER (MeV) Γ (MeV) ER (MeV) Γ (MeV) N3LO500 1.0 4.7 1.4 3.1 N3LO600 1.0 4.8 1.5 3.3 N3LO500/N2LO500 1.3 4.7 1.4 2.7 N3LO600/N2LO600 1.3 4.4 1.7 2.9 R-matrix 4.43 6.10 2.02 2.01

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 15 / 34 Calculation of transition amplitudes

Initial/final wave functions + transition operators (currents & charges)

(nh) L 1 1 (nh) Ψ = 4πi YLM (pˆ)( , m1, , m3 SSz )(LMSSz JJz )Ψ m1,m3 2 2 | | LSJJz LSJJXz

Multipole expansion of the transition operators (γ emission)

† (nh) LSJ Ψ4 ρ (q) Ψ C , J 0 h | | LSJJz i ∼ J ≥ ∗ † (nh) LSJ LSJ Ψ4 ǫˆ J (q) Ψ (E + λM ) , J 1 h | q,λ · | LSJJz i ∼ J J ≥ A 1 + τz (i) ρ(q) = eiq·ri + 2 · · · Xi=1 A 1 + τz (i) p J(q) = [ i , eiq·ri ]+ 2 2m · · · Xi=1

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 16 / 34 EM charge and currents transition operators

EM charge & current from χEFT [Park et al, 1993], [Kolling et al, 2009], [Pastore et al, 2009] Including the ∆ d.o.f. [Schiavilla et al., 2018]

Diagrams in standard χEFT Diagrams with the inclusion of the ∆ d.o.f. up to N2LO

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 17 / 34 Selection rules

Parity of Ψ =+, parity of Ψ =( )L 4 LSJ −

2S+1 state LJ charge multipoles current multipoles + 1 000 0 S0 C0 − 3 − 0 P0 + 3 3 − −LS1 1 S1, D1, M1 − 1 3 −LS1 LS1 1 P1, P1, C1 E1 + 1 3 LS2 LS2 2 D2, D2, C2 E2 2− 3P , 3F , MLS2 2 2 − 2

Longitudinal component We impose that q J(q)= ωρ(q) (nuclear EM current conservation) · Verified only if the operators J and ρ are consistently constructed with H [Buchmann et al, 1985], [Riska, 1989], [Schiavilla et al, 1990] Automatically verified using V and J, ρ constructed using an EFT, but . . . different orders, different cutoff functions...work in progress! “Norfolk” potentials and currents (including the ∆ dof) constructed to (partially) solve this problem [Piarulli et al., 2018], [Baroni et al., 2018], [Schiavilla et al., 2018]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 18 / 34 3H(p,γ)4He EM capture

Calculation of the astrophysical factor S1+3(E) Dominated by the E transition 1− 0+ 1 → Use of the continuity equation ∇ Jˆ + i[H0, ρˆ] to write E1 f d i (Siegert) Preliminary result – NVIa+3N interaction· – No sensivity to∼h interactions/MEC| | i

Figure adapted from [Dubovichenko et al., 2018]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 19 / 34 3He(n,γ)4He EM capture

n(3He,γ)4He at thermal energies Dominated by the S-wave M transition 1+ 0+ 1 → Experimental value σ = 55 3 µb [Wervelman et al., 1991] nh ± Very sensitive to interaction/MEC

LO contribution very small: J Ψ 3 contains no spatially symmetric components LO n+ He → only contribution from the “small” components of Ψ4He Current: [Schiavilla et al., 2018] (three unknown LECs fixed by reproducing the light nuclei magnetic moments) Very preliminary calculations!

AV18/UIX N3LO500/N2LO500 N3LO600/N2LO600 NVIa+3N (with ∆ dof) σnh [µb] σnh [µb] σnh [µb] σnh [µb] LO 15.3 9.0 12.5 15.3 N3LO 54.5 86.6 78.0 66.9 Expt. 55 3 ±

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 20 / 34 The 3H(p, e+e−)4He pair production

“Standard” EM process

6 2 ′ d σ α kk ′ 2 = δ(E0 ǫ ǫ (p q) /2M4) vi Ri (q,ω) dǫdkdˆ ǫ′dkˆ′ 8π3 Q4v − − − − Xi

′ ′ 2 2 2 E0 = Ep + B4 B3 20 MeV, q = k + k , ω = ǫ + ǫ , Q = ω q > 0 “time-like” − ≈ ′ ′ ′ − cos θee = kˆ kˆ , i = L, T , TT , TT , LT , LT ·

Q4 v = (ǫǫ′ + k k ′ m2) R (q,ω)= Ψ ρ(q)† Ψ(nh) 2 CLSJ 2 L q4 · − e L |h 4| | m1,m3 i| ∼ | J | m ,m X1 3 XLSJ

′ ′ ′ ′ ′ After integrating the δ over ǫ and numerically over ǫ (pr = ǫ (k p cos θ + k cos θee)/k ) −

d4σ α2 ǫmax kk ′ 1 = dǫ v R 3 4 i i ˆ ˆ′ 8π Q v 1 + pr /M dkdk me " 4 i # ′ Z X ǫ ≈E0−ǫ − M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 21 / 34 q dependence

A 1 + τ (j) + z iq·rj π Ψ4 ;(0 ) e Ψ 3 ;(J ) h He | 2 | p+ H i Xj=1 Behaviour at q 0 → A 1+τz (j) = 2 q = k + k ′ 0: lepton pair emitted j=1 2 back-to-back| |→ Peiq·rj = 1 + iq r + 1 (iq r )2 + · j 2 · j · · · Q2 = ω2 E2 finite Jπ = 0+: first contributing order q2 ≈ 0 4 π − v = Q (ǫǫ′ + k k ′ m2) 1/q2 J = 1 : first contribution order q L q4 · − e → Jπ = 2+: first contribution order q2 A carefull calculation of the RMEs is needed: RMEs qn, n > 0 . . . ∼ 0.04 From a helicity argument, the amplitude + + for the trnsition 0 0 should vanish 000 |C0 | → 0.03 L=0,S=0,J=0 2 -1/2 for q 0 Fit with y=a x (a=2.7902 fm ) → L=1,S=0,J=1 ] L=1,S=1,J=1 3/2 L=2,S=0,J=2 2 -1/2 | [fm 0.02 Fit with y=a x (a=0.56789 fm )

LSJ 101 J |C |

|C 1

0.01

111 x |C1 | 10 201 x |C2 | 10 0 0 0.05 0.1 -1 q [fm ]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 22 / 34 Calculation of the 3H(p, e+e−)4He cross section (1)

LSJ −1 3/2 RMEs XJ at q = 0.1 fm in units of fm EP = 0.90 MeV PRELIMINARY Calculation using the N3LO500/N2LO500 + χEFT current by [Pastore et al., 2009]

3 3 RMEs 10 p + H wave IA IA+MEC VERY PRELIMINARY!! 000 × 1 C0 S0 23.2 23.3 Only J 2 waves included | 101| 1 ≤ C1 P1 16.3 16.4 | 111| 3 0.01 C1 P1 0.59 2.59 | 202| 1 PRELIMINARY C2 D2 0.44 0.44 4 2 | 212| 3 d σ/dΩdΩ’ [µb/sr ] C2 D2 0.00 0.01 0.001 | 011| 3 M S1 0.27 0.75 1 All multipoles | 211| 3 C0+E1 M D1 0.02 0.02 | 1 | 0.0001 E101 1P 17.4 24.1 1 1 C0 | 111| 3 LO current, all multipoles E1 P1 0.37 1.44 | 202| 1 1e-05 E2 D2 0.63 0.65 | 202| 3 E2 D2 0.00 0.00 | 112| 3 1e-06 M P 2.50 2.68 0 30 60 90 120 150 180 2 2 θ [deg] | | ee M312 3F 0.00 0.00 | 2 | 2

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 23 / 34 Calculation of the 3H(p, e+e−)4He cross section (2)

0.01

PRELIMINARY

4 2 d σ/dΩdΩ’ [µb/sr ] 0.001 Calculation using the N3LO500/N2LO500 + All multipoles χEFT current by [Pastore et al., 2009] C0+E1 0.0001

C0 Multipole angular distribution as reported in LO current, all multipoles [Tanedo, 1e-05 www.particlebites.com/?p=3970]

1e-06 0 30 60 90 120 150 180 θ ee [deg]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 24 / 34 Dependence on the energy of the RMEs

Calculation using the N3LO500/N2LO500 + χEFT current by [Pastore et al., 2009]

VERY PRELIMINARY!!

0.08 3 n+ He th.

101 E1 0.06

000 C ] 0 3/2

0.04 PRELIMINARY Re(RME) [fm

0.02

ATOMKI expt.

0 0 0.5 1 1.5 2 ECM [MeV]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 25 / 34 Assuming the transition mediated by a massive particle

4 2 ′ ′ d σ α ǫmax kk 1 ǫmax kk 1 = dǫ  v R  +C dǫ  v R  ′ 3 4 i i i i dkdˆ kˆ 8π Zm Q v 1 + pr /M X Zm 2 2 2 4 1 + pr /M X e 4 i ǫ′ −ǫ e (Q − MR ) + Mi v 4 i   =E0    ǫ

0.01

] 0.001 2 PRELIMINARY b/sr µ ’ [ Ω d Ω /d σ 4 d 0.0001

1e-05 0 30 60 90 120 150 180 θ ee [deg]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 26 / 34 What we “know” (1)

[Feng, Tait, & Verhaaren, arXiv:2006.01151] (AN)∗ AN + X: ~J∗ = ~L ~JX and Π∗ =( )LΠX → ⊗ − 4 8Be experiment He experiment

pseudoscalar particle: JX = 0, ΠX = scalar particle: JX = 0, ΠX =+ − 8Be: L = 1 OK! 8 + + Be: transition 1 0 : NO 4 ∗ → He (0+): NO ∗ 4He (0−): L = 0 OK! No ruled out Γ(8Be)/Γ(4He) 1: but from the experiments → ≪ vector boson (JX = 1, ΠX = ) Γ(8Be)/Γ(4He) 1 − ∼ axial boson (JX = 1, ΠX =+) Also unlikely due to the experimental bounds on the observation of “axion-like-particle” (ALP) − M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 27 / 34 What we know (2)

[Feng et al., 2016] [Kozaczuk, Morrissey, & Stroberg, 2016] light axial vector (in this case no problems with the NA48 bound) µ 5 µ 5 = Xµ guu¯γ γ u + g d¯γ γ d LI d h i

“Protophobia?” No evidence in the π0 decay studied by the NA48 experiment [Batley et al., 2015] A way out: the particle X does not couple with protons

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 28 / 34 EFT approach

Interaction between X17 and the SM particles (example: X17 is an axial-vector boson)

µ 5 µ 5 µ 5 = Xµ(x) guu¯(x)γ γ u(x)+ g d¯(x)γ γ d(x)+ gee¯(x)γ γ e(x)+ LI d · · · h i

q = u, d, e quarks and electron fields, Xµ axial field of particle X17, gi coupling constants

µ 5 µ 5 gu + gd µ 5 µ 5 gu gd µ 5 µ 5 guu¯γ γ u + g d¯γ γ d = u¯γ γ u + d¯γ γ d + − u¯γ γ u d¯γ γ d d 2 2 −     gu + gd µ 5 gu gd µ 5 u(x) = q¯γ γ q + − q¯γ γ τz q q(x)= 2 2 d(x)  

Due to the UA(1) anomaly, it is not possible to introduce isoscalar axial currents in SU(2) space go to SU(3) [See, for example, Scherer & Schindler, 2004] → 5 5 5 5 5 N u¯γµγ u + d¯γµγ d N Nu¯γµγ u + d¯γµγ d 2¯sγµγ s N h | | i→h − | i Valid in the hypothesis that the content of the strange quark in the nucleon vanishes [Ellis, Nagata & Olive, 2018]

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 29 / 34 SU(3) χEFT

u(x) q(x)= d(x) See, for example, [Scherer, 1986], s(x) [Bernard, Kaiser, & Meissner, 1995], etc   1 0 0 5 5 5 5 1 u¯γµγ u + d¯γµγ d 2¯sγµγ s = √3q¯γµγ λ8q λ8 = 0 1 0 − √3 0 0 2 −   1 0 0 5 5 5 u¯γµγ u d¯γµγ d = q¯γµγ λ3q λ3 = 0 1 0 − 0− 0 0   can be rewritten as LI

µ 5 µ 5 = q¯(x)γ γ aµ(x)q(x)+ gee¯(x)γ γ Xµ(x)e(x) LI (i) with aµ(x)= λi aµ (x) and

(3) gu gd (8) gu + gd a = − Xµ(x) a = √3 Xµ(x) µ 2 µ 2

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 30 / 34 SU(3) χEFT Lagrangian

F µ 5 D µ 5 µ = Tr B¯(iγµDµ M)B B¯γ γ [uµ, B]+ B¯γ γ uµ, B + b B¯[u , [uµ, B]] + L − − 2 2 1 · · · h i 0 0 p B = 0 0 n + strange baryon part 0 0 0   uµ = 3 3 matrix of meson fields, F, D, b , . . . LECs (F + D = g ) × 1 A

A gu + gd J(5)(q) = (3F D) σ eiq·ri + RMEs at q = 0.1 fm−1 in units of fm3/2 − 2 i · · · i=1 EP = 0.90 MeV – PRELIMINARY X gu +gd Divided by (3F D) 2 Now we have to consider also the longitudinal − component C, L, E, M multipoles → RMEs 103 p + 3H wave IA × E011 3S 0.21 2S+1 | 1 | 1 state LJ C, L E M E211 3D 0.03 + 1 | 1 | 1 0 S0 M101 1P 0.29 − 3 − − − 1 1 0 P0 OK | 111| 3 − − M D1 1.21 1+ 3S , 3D , OK OK | 1 | 1 1 − 1− 1P , 3P , OK 1 1 − − − M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 31 / 34 Conclusions and perspectives

Current studies in A = 3, 4 scattering Accurate 3NF interactions Promising fit of p d scattering with the subleading contact 3NF as a way to solve − the Ay “puzzle”

Sensitivity study of 4N observables to cD and cE and to the cutoff EM and weak transitions p d capture S-factor at BBN energies: tension with new LUNA data [Mossa et al., − 2020] ν + 3H 3He + e− and the relic neutrino background (PTOLEMY expt.) → New calculation of the “hep” S-factor using the updated axial current of [Baroni et al., 2018] 3H(p,γ)4He, 3He(n,γ)4He, d(d,γ)4He, 4He(e, e′p)3H, . . .

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 32 / 34 The 3H(p, e+e−)4He experiment and the ATOMKI “anomaly” VERY PRELIMINARY results for the reaction 3H(p, e+e−)4He − Contribution of the 1 wave very significative at Ep = 0.90 MeV it would be interesting to repeat the experiment for different proton beam energies and a more sophisticated experimental setup program:

Using the estimates for gu and gd from [Kozaczuk, Morrissey, & Stroberg, 2016], see if the 4He data is compatible with 8Be data Perform accurate studies using EFT for scalar, pseudoscalar, vector, axial, tensor, etc X17 particles Estimate the theoretical uncertainties (Bayesian method) Hopefully, more results at the next year BSM program!

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 33 / 34 Thank you for your attention!

− M. Viviani (INFN-Pisa) 3H(p, e+e )4He process July 29, 2020 34 / 34