Magnetic Properties of Light Nuclei from Lattice QCD

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1 Magneic Properies of Ligh Nuclei from Laice QCD INT-Program 16-1 Nuclear Physics from Laice QCD B C Tiburzi 18 May 216 My work funded by Done in collaboraion wih Nuclear Physics Laice QCD =

2 Magneic Momens of Ligh Nuclei Beane, e al. (NPLQCD), Phys.Rev. Le.113, 214. Firs Compuaion: m u = m d =(m s ) phys m 8 MeV

3 Grand Overview Elecroweak Ineracions: Nucleons and Nuclei Laice QCD coninues o sharpen our knowledge of The Sandard Model (e.g. CKM exracion, K > π π ) Nucleons and ligh nuclei presen challenge opporuniy QCD relevan for high-precision low-energy experimens Nuclear Physics from QCD EW Reacions BSM Physics Magneic properies of ligh nuclei

4 Quark Ineracions o Nuclear Physics Texbook: gauge heories defined in perurbaion heory QCD: shor disance perurbaive, long disance non-perurbaive q (D/ + m q ) q G µ G µ Many Technicaliies M N NN(k) Ken Wilson b (D) Non-perurbaive definiion of asympoically free gauge heories One sep: Z Anoher sep: [DA µ ] e S YM(A µ ) 1 N cfg X {A µ } Srong ineracion observables e S YM(A µ ) sa. evaluaion Quarks: L a sys. approx. U µ (x) =e igaa µ(x) 2 SU(3) 1 Quark elecroweak ineracions D/ (U µ )+m q forunaely perurbaive J µ = q µ q

5 Paricle Physics (B=) vs. Nuclear Physics (B>) Pion Correlaion Funcion X hqq()qq()i e m Signal Noise^2 {A µ } X {A µ } hqq()qq()qq()qq()i e 2m Signal/Noise cons.12 d log G ()/d

6 Paricle Physics (B=) vs. Nuclear Physics (B>) Pion Correlaion Funcion X hqq()qq()i e m Signal Noise^2 Nucleon Correlaion Funcion X hqqq()qqq()i e M Signal Noise^2 d log G ()/d {A µ } X {A µ } {A µ } X {A µ } hqq()qq()qq()qq()i e 2m Baryons are saisically noisy Signal/Noise hqqq()qqq()qqq()qqq()i e 3m e (M 3 2 m ) d log GN ()/d Signal/Noise cons Scales exponenially wih B in asympoic ime limi mass_pro eff mass

7 Nuclear mπ =8 and 45 MeV d log G3 He ()/d Beane, Chang, Cohen, Demold, Lin, Luu, Orginos, Parreño, Savage, Walker-Loud PRD87 (213) Orginos, Parreño, Savage, Beane, Chang, Demold PRD92 (215) Specrum e.g. mπ = 8 G3 He() X hqqqqqqqqq()qqqqqqqqq()i {A µ } E (Ep +2En) = E [MeV]

8 Nuclear mπ =8 and 45 MeV d log G3 He ()/d Beane, Chang, Cohen, Demold, Lin, Luu, Orginos, Parreño, Savage, Walker-Loud PRD87 (213) Orginos, Parreño, Savage, Beane, Chang, Demold PRD92 (215) Naure and properies of hese saes? X hqqqqqqqqq()[q µ q]( )qqqqqqqqq()i {A µ } Specrum Ground sae requires, & 1 Nuclear Marix Elemens from QCD? e.g. mπ = 8 G3 He() X hqqqqqqqqq()qqqqqqqqq()i {A µ } 1, 1 h 3 He J µ 3 Hei E (Ep +2En) = E [MeV]... no ye aemped Curren echnology >2 Beer sources Greaer saisics

9 Nuclear mπ =8? Specrum responds o exernal fields: e.g. uniform magneic fields d log G3 He ()/d ~B X hqqqqqqqqq()qqqqqqqqq()i ~B {A µ } G3 He() ~B = Compue specrum as a funcion of applied field I). In weak enough fields, can uilize same sources II). Need roughly same saisics for each field srengh III). Requires fiing he field-srengh dependence IV). Limied number of properies for a given ype of field Pracical Soluion: Laice QCD + Classical Fields Beane, e al. PRL:113 (214) Beane, e al. PRL:115 (215) Chang, e al. PRD:92 (215) Demold, e al. PRL:116 (216)

10 Gauge links: Magneic Field on a Periodic Laice U µ (x) =e igg µ(x) 2 SU(3) U e.m. µ (x) =e iqa µ(x) 2 U(1) Seek uniform B-field U µ (x) =e iqx 2B µ1 N 1 qb x 2 x 1 N 1 U 1 (x)u 2 (x + î)u 2 (x + î + ĵ)u 1 (x + ĵ) =eiqf 12 = e iqb

11 Gauge links: Magneic Field on a Periodic Laice U µ (x) =e igg µ(x) 2 SU(3) U e.m. µ (x) =e iqa µ(x) 2 U(1) Seek uniform B-field U µ (x) =e iqx 2B µ1 N 1 qb(1 N) qb(1 N) qb(1 N) qb(1 N) qb(1 N) qb(1 N) qb qb qb qb qb qb qb qb qb qb qb qb qb qb qb qb qb qb x 2 qb qb qb qb qb qb qb qb qb qb qb qb x 1 N 1 U 1 (x)u 2 (x + î)u 2 (x + î + ĵ)u 1 (x + ĵ) =eiqf 12 = e iqb

12 Gauge links: Magneic Field on a Periodic Laice U µ (x) =e igg µ(x) 2 SU(3) U e.m. µ (x) =e iqa µ(x) 2 U(1) Seek uniform B-field U µ (x) =e iqx 2B µ1 e +iqx 1BN µ2 x2,n 1 N 1 qb qb qb qb qb qb qb qb qb qb qb qb qb Flux quanizaion qb qb qb qb qb(1 N 2 ) qb = 2 N 2 n N = 32 We choose: qb qb qb qb qb qb n =+3, 6, +12 x 2 qb qb qb qb qb qb qb qb qb qb qb qb x 1 N 1 U 1 (x)u 2 (x + î)u 2 (x + î + ĵ)u 1 (x + ĵ) =eiqf 12 = e iqb

13 Magneic Momens of Oce Baryons Compue Zeeman Effec using Laice QCD + Uniform Magneic fields E(B,J z ) Proon m & MeV G E" E# Φ =- Φ = Unis! µ p =2.56(9)(52) [LaM] [LaM] = ea Φ = a =.145(2) fm Δ µ p =1.77(6)(36)(19) [NM] [NM] = e 2M N

14 Magneic Momens of Oce Baryons E" E# Compue Zeeman Effec using Laice QCD + Uniform Magneic fields E(B,J z ) Proon m & MeV G Φ =- Φ = µ p =1.77(6)(36)(19) [NM] [NM] = Ruler Mass Rule (Walker-Loud, LHPC) M N (m ) = 8 MeV + m 1, 6 MeV e 2M N Φ = Δ [nnm] = e 2M N (m )

15 Magneic Momens of Oce Baryons E" E# Compue Zeeman Effec using Laice QCD + Uniform Magneic fields E(B,J z ) Proon m & MeV G Φ =- Φ = Φ = µ p =1.77(6)(36)(19) [NM] [NM] = Naural nucleon magneons [nnm] = µ p =3.87(1)(62) [nnm] e 2M N e 2M N (m ) Δ Dirac par is shor-disance & guaraneed o O(a 2 2 QCD) µ p =2.87(1)(62) [nnm] µ exp p = [NM]

16 Magneic Momens of Oce Baryons Compue Zeeman Effec using Laice QCD + Uniform Magneic fields δμ [ ] π ~ Naural baryon magneons [nbm] = e 2M B (m ) Anomalous magneic momens. µ B [nbm] = µ B [nbm] Q B -.5 Σ + - -Ξ -Σ - -Ξ - U(3) F Q! U(1)U U(1) D+S SU(2) U spin d s U-spin SU(2)! U d s

17 Magneic Momens of Oce Baryons Compue Zeeman Effec using Laice QCD + Uniform Magneic fields δμ [ ] Preliminary π ~ π ~ Naural baryon magneons [nbm] = e 2M B (m ) Anomalous magneic momens. µ B [nbm] = µ B [nbm] Q B -.5 Σ + - -Ξ -Σ - -Ξ - U(3) F Q! U(1)U U(1) D+S SU(2) U spin U(2) I U(1) S Q! U(1)B U(1) I3 U(1) S m 45 MeV [Acually more complicaed, our sea quarks are neural]

18 Magneic Momens of Oce Baryons Compue Zeeman Effec using Laice QCD + Uniform Magneic fields δμ [ ] Preliminary π ~ π ~ Naural baryon magneons [nbm] = e 2M B (m ) Anomalous magneic momens. µ B [nbm] = µ B [nbm] Q B -.5 Σ + - -Ξ -Σ - -Ξ - U(3) F Q! U(1)U U(1) D+S SU(2) U spin U(2) I U(1) S Q! U(1)B U(1) I3 U(1) S m 45 MeV [Acually more complicaed, our sea quarks are neural]

19 Magneic Momens of Ligh Nuclei Compue Zeeman Effec using Laice QCD + Uniform Magneic fields.15 3 He m 8 MeV [nnm] = e 2M N (m ) E" E# Δ Φ = Φ = Φ = µ3 He = 2.33(3)(11) [nnm] µ exp 3 He μ [ ] = [NM] π ~ Beane, e al. (NPLQCD), Phys.Rev. Le.113,

20 Magneic Momens of Ligh Nuclei Compue Zeeman Effec using Laice QCD + Uniform Magneic fields 1..8 π ~ [nnm] = e 2M N (m ) μ [ ] π ~ 3 -( + ) - -( - ) μ [ ] Beane, e al. (NPLQCD), Phys.Rev. Le.113,

21 Firs Nuclear Reacion from QCD Dominan M1 Low Energy n + p! d + + d! n + p Magneically Coupled Channels I = J =1 I 3 = j z = µ 1 Two-body conribuion isolaed & compares favorably wih EFT(π) phenomenology L 1 Beane, e al. (NPLQCD), Phys.Rev. Le.115, 215.

22 Exreme Magneic Environmens Beyond Linear: Magneic Polarizabiliies Chang, e al. (NPLQCD), Phys.Rev. D92, 215. E "+# (B) = p M 2 +(2n + 1) QB 1 2 M B 2 + Landau idenificaion dominaes uncerainies Ed(B)m=+1 Uniary NN Ineracions? a NN (B)!1? B [1 19 G] Demold, e al. (NPLQCD), Phys.Rev. Le.116, 216.

23 Fuure Direcions Magneic Srucure of Nuclei + Move beyond exploraory sudies: remove sysemaics, lower pion mass, beer rea Landau levels, sea quarks, Elecric Srucure of Nuclei Elecric polarizabiliies? EDMs of ligh nuclei from θ-erm?, BSM sources? Nuclei in oher classical fields Graviaional?, Weak? Nuclear Physics from QCD EW Reacions BSM Physics