Light-Front Simulations of True

Hank Lamm with Rich Lebed 17 May 2018 LIGHTCONE 2018

Hank Lamm Light-Front True Muonium 17 May, 2018 1 / 18 ...but mν implies this isn’t the end of the story

Who ordered that?

Within the , universality is broken only by the Higgs interaction

Hank Lamm Light-Front True Muonium 17 May, 2018 2 / 18 Who ordered that?

Within the Standard Model, lepton universality is broken only by the Higgs interaction

...but mν implies this isn’t the end of the story

Hank Lamm Light-Front True Muonium 17 May, 2018 2 / 18 What’s the deal with physics?123

mu·on prob·lem: (n) the curious observation that discrepancies exist in muon sector

2.9σ ~~ ~~~ 7σ ~~~ 4σ ~~ ~~ ~~~

1G. Bennett et al. “Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL”. In: Phys. Rev. D73 (2006), p. 072003. arXiv: hep-ex/0602035 [hep-ex]. 2A. Antognini et al. “ Structure from the Measurement of 2S − 2P Transition Frequencies of Muonic Hydrogen”. In: Science 339 (2013), pp. 417–420. 3R. Pohl et al. “Laser spectroscopy of muonic deuterium”. In: Science 353.6300 (2016), pp. 669–673.

Hank Lamm Light-Front True Muonium 17 May, 2018 3 / 18 The ultimate discriminator: true muonium

Hank Lamm Light-Front True Muonium 17 May, 2018 4 / 18 Nearly purely leptonic, nearly purely QED ...but many channels suggested456

Wait? I can bind ?

Proposed in 1961, still undetected

4S. J. Brodsky and R. F. Lebed. “Production of the Smallest QED : True Muonium (µ+µ−)”. In: Phys. Rev. Lett. 102 (2009), p. 213401. arXiv: 0904.2225 [hep-ph]. 5 + − Y. Ji and H. Lamm. “Discovering True Muonium in KL → (µ µ )γ”. In: (2017). arXiv: 1706.04986 [hep-ph]. 6Y. Ji and H. Lamm. “Discovering True Muonium in η, η0 → (µ+µ−)γ”. In: in prep. (2018).

Hank Lamm Light-Front True Muonium 17 May, 2018 5 / 18 ...but many channels suggested456

Wait? I can bind muons?

Proposed in 1961, still undetected Nearly purely leptonic, nearly purely QED bound state

4S. J. Brodsky and R. F. Lebed. “Production of the Smallest QED Atom: True Muonium (µ+µ−)”. In: Phys. Rev. Lett. 102 (2009), p. 213401. arXiv: 0904.2225 [hep-ph]. 5 + − Y. Ji and H. Lamm. “Discovering True Muonium in KL → (µ µ )γ”. In: (2017). arXiv: 1706.04986 [hep-ph]. 6Y. Ji and H. Lamm. “Discovering True Muonium in η, η0 → (µ+µ−)γ”. In: in prep. (2018).

Hank Lamm Light-Front True Muonium 17 May, 2018 5 / 18 Wait? I can bind muons?

Proposed in 1961, still undetected Nearly purely leptonic, nearly purely QED bound state ...but many channels suggested456

4S. J. Brodsky and R. F. Lebed. “Production of the Smallest QED Atom: True Muonium (µ+µ−)”. In: Phys. Rev. Lett. 102 (2009), p. 213401. arXiv: 0904.2225 [hep-ph]. 5 + − Y. Ji and H. Lamm. “Discovering True Muonium in KL → (µ µ )γ”. In: (2017). arXiv: 1706.04986 [hep-ph]. 6Y. Ji and H. Lamm. “Discovering True Muonium in η, η0 → (µ+µ−)γ”. In: in prep. (2018).

Hank Lamm Light-Front True Muonium 17 May, 2018 5 / 18 DIRAC, HPS are existing fixed targets LEMAM is proposed µ+µ− collider Proposed e+e− collider at BINP REDTOP is a proposed η/η0 factory

Difficult, but it’s what we pay experimentalists for

Hank Lamm Light-Front True Muonium 17 May, 2018 6 / 18 LEMAM is proposed µ+µ− collider Proposed e+e− collider at BINP REDTOP is a proposed η/η0 factory

Difficult, but it’s what we pay experimentalists for

DIRAC, HPS are existing fixed targets

Hank Lamm Light-Front True Muonium 17 May, 2018 6 / 18 Proposed e+e− collider at BINP REDTOP is a proposed η/η0 factory

Difficult, but it’s what we pay experimentalists for

DIRAC, HPS are existing fixed targets LEMAM is proposed µ+µ− collider

Hank Lamm Light-Front True Muonium 17 May, 2018 6 / 18 REDTOP is a proposed η/η0 factory

Difficult, but it’s what we pay experimentalists for

DIRAC, HPS are existing fixed targets LEMAM is proposed µ+µ− collider Proposed e+e− collider at BINP

Hank Lamm Light-Front True Muonium 17 May, 2018 6 / 18 Difficult, but it’s what we pay experimentalists for

DIRAC, HPS are existing fixed targets LEMAM is proposed µ+µ− collider Proposed e+e− collider at BINP REDTOP is a proposed η/η0 factory

Hank Lamm Light-Front True Muonium 17 May, 2018 6 / 18 − + 2 HLC = P P = M Acting on a state with this gives Z X 0 2 0 0 0 0 0 dxjd k⊥,jhxi, k⊥,i; λi |HLC | xj, k⊥,j; λj, iψ(xj, k⊥,j; λj) = 0 D λj 2 M ψ(xi, k⊥,i; λi) (2)

How can we construct a LF model for true muonium?

Fock state expansion with partons Z X + 2 |Ψi ≡ [dµn] |µni hµn|Ψ; M,P , P⊥,S ,Sz; h n X Z ≡ [dµn] |µni Ψn|h(µ) , (1) n

Hank Lamm Light-Front True Muonium 17 May, 2018 7 / 18 Acting on a state with this gives Z X 0 2 0 0 0 0 0 dxjd k⊥,jhxi, k⊥,i; λi |HLC | xj, k⊥,j; λj, iψ(xj, k⊥,j; λj) = 0 D λj 2 M ψ(xi, k⊥,i; λi) (2)

How can we construct a LF model for true muonium?

Fock state expansion with partons Z X + 2 |Ψi ≡ [dµn] |µni hµn|Ψ; M,P , P⊥,S ,Sz; h n X Z ≡ [dµn] |µni Ψn|h(µ) , (1) n

− + 2 HLC = P P = M

Hank Lamm Light-Front True Muonium 17 May, 2018 7 / 18 How can we construct a LF model for true muonium?

Fock state expansion with partons Z X + 2 |Ψi ≡ [dµn] |µni hµn|Ψ; M,P , P⊥,S ,Sz; h n X Z ≡ [dµn] |µni Ψn|h(µ) , (1) n

− + 2 HLC = P P = M Acting on a state with this gives Z X 0 2 0 0 0 0 0 dxjd k⊥,jhxi, k⊥,i; λi |HLC | xj, k⊥,j; λj, iψ(xj, k⊥,j; λj) = 0 D λj 2 M ψ(xi, k⊥,i; λi) (2)

Hank Lamm Light-Front True Muonium 17 May, 2018 7 / 18 Hamiltonian operator have sparse structure7

+ Gauge fixing required for defining HLC . Standard choice is A = 0

HLC = T + V + S + C + F (3)

Sector n 0 1 2 3 4 |γi 0 • VV FF |ee¯i 1 V • S V · |µµ¯i 2 VS • · V |ee¯ γi 3 FV · • S |µµ¯ γi 4 F · V S • The Hamiltonian matrix for two-flavor QED, where n labels Fock states. The vertex, seagull and fork interactions are denoted by V, S, F respectively.

7U. Trittmann and H.-C. Pauli. “ at strong couplings”. In: (1997). arXiv: hep-th/9704215 [hep-th].

Hank Lamm Light-Front True Muonium 17 May, 2018 8 / 18 Method of iterated resolvents “include” effects of missing states in effective interaction Consider a two sector HLC operator:   HPP HPQ HLC = (4) HQP HQQ A generic Q state can be rewritten as −1 Qˆ|Ψi = Qˆ(ω − HLC ) QHˆ LC Pˆ|Ψi (5) With this, we write an effective Hamiltonian without Q states eff −1 H (ω)LC = PHˆ LC Pˆ + PHˆ LC Qˆ(ω − HLC ) QHˆ LC Pˆ (6) 0 0 Replace ω by f(x , k⊥, x, k⊥) to remove divergences

Use effective interactions, or you’ll have a bad time8

IF we truncate Fock space, we have model wavefunctions (Yay) but breaks gauge invariance (Boo)

8See Xingbo Zhao’s talk on earlier today!

Hank Lamm Light-Front True Muonium 17 May, 2018 9 / 18 Consider a two sector HLC operator:   HPP HPQ HLC = (4) HQP HQQ A generic Q state can be rewritten as −1 Qˆ|Ψi = Qˆ(ω − HLC ) QHˆ LC Pˆ|Ψi (5) With this, we write an effective Hamiltonian without Q states eff −1 H (ω)LC = PHˆ LC Pˆ + PHˆ LC Qˆ(ω − HLC ) QHˆ LC Pˆ (6) 0 0 Replace ω by f(x , k⊥, x, k⊥) to remove divergences

Use effective interactions, or you’ll have a bad time8

IF we truncate Fock space, we have model wavefunctions (Yay) but breaks gauge invariance (Boo) Method of iterated resolvents “include” effects of missing states in effective interaction

8See Xingbo Zhao’s talk on positronium earlier today!

Hank Lamm Light-Front True Muonium 17 May, 2018 9 / 18 A generic Q state can be rewritten as −1 Qˆ|Ψi = Qˆ(ω − HLC ) QHˆ LC Pˆ|Ψi (5) With this, we write an effective Hamiltonian without Q states eff −1 H (ω)LC = PHˆ LC Pˆ + PHˆ LC Qˆ(ω − HLC ) QHˆ LC Pˆ (6) 0 0 Replace ω by f(x , k⊥, x, k⊥) to remove divergences

Use effective interactions, or you’ll have a bad time8

IF we truncate Fock space, we have model wavefunctions (Yay) but breaks gauge invariance (Boo) Method of iterated resolvents “include” effects of missing states in effective interaction Consider a two sector HLC operator:   HPP HPQ HLC = (4) HQP HQQ

8See Xingbo Zhao’s talk on positronium earlier today!

Hank Lamm Light-Front True Muonium 17 May, 2018 9 / 18 With this, we write an effective Hamiltonian without Q states eff −1 H (ω)LC = PHˆ LC Pˆ + PHˆ LC Qˆ(ω − HLC ) QHˆ LC Pˆ (6) 0 0 Replace ω by f(x , k⊥, x, k⊥) to remove divergences

Use effective interactions, or you’ll have a bad time8

IF we truncate Fock space, we have model wavefunctions (Yay) but breaks gauge invariance (Boo) Method of iterated resolvents “include” effects of missing states in effective interaction Consider a two sector HLC operator:   HPP HPQ HLC = (4) HQP HQQ A generic Q state can be rewritten as −1 Qˆ|Ψi = Qˆ(ω − HLC ) QHˆ LC Pˆ|Ψi (5)

8See Xingbo Zhao’s talk on positronium earlier today!

Hank Lamm Light-Front True Muonium 17 May, 2018 9 / 18 0 0 Replace ω by f(x , k⊥, x, k⊥) to remove divergences

Use effective interactions, or you’ll have a bad time8

IF we truncate Fock space, we have model wavefunctions (Yay) but breaks gauge invariance (Boo) Method of iterated resolvents “include” effects of missing states in effective interaction Consider a two sector HLC operator:   HPP HPQ HLC = (4) HQP HQQ A generic Q state can be rewritten as −1 Qˆ|Ψi = Qˆ(ω − HLC ) QHˆ LC Pˆ|Ψi (5) With this, we write an effective Hamiltonian without Q states eff −1 H (ω)LC = PHˆ LC Pˆ + PHˆ LC Qˆ(ω − HLC ) QHˆ LC Pˆ (6)

8See Xingbo Zhao’s talk on positronium earlier today!

Hank Lamm Light-Front True Muonium 17 May, 2018 9 / 18 Use effective interactions, or you’ll have a bad time8

IF we truncate Fock space, we have model wavefunctions (Yay) but breaks gauge invariance (Boo) Method of iterated resolvents “include” effects of missing states in effective interaction Consider a two sector HLC operator:   HPP HPQ HLC = (4) HQP HQQ A generic Q state can be rewritten as −1 Qˆ|Ψi = Qˆ(ω − HLC ) QHˆ LC Pˆ|Ψi (5) With this, we write an effective Hamiltonian without Q states eff −1 H (ω)LC = PHˆ LC Pˆ + PHˆ LC Qˆ(ω − HLC ) QHˆ LC Pˆ (6) 0 0 Replace ω by f(x , k⊥, x, k⊥) to remove divergences 8See Xingbo Zhao’s talk on positronium earlier today!

Hank Lamm Light-Front True Muonium 17 May, 2018 9 / 18 TMSWIFT: Two- Hamiltonian Solver

µµ ↑ ↑ component of state 6 for Jz=0 µµ ↑ ↓ component of state 6 for Jz=0

9.0x10-4

-8 1.0x10 7.2x10-4

-9 7.8x10 5.4x10-4

-9 5.2x10 3.6x10-4

2.6x10-9 1.8x10-4 3.88 3.88 0.0x100 2.91 0.0x100 2.91 0.1 0.1 0.3 1.94 k⊥ 0.3 1.94 k⊥ 0.5 0.5 0.7 0.97 0.7 0.97 x 0.9 0 x 0.9 0

ee ↑ ↑ component of state 6 for Jz=0 ee ↑ ↓ component of state 6 for Jz=0

7.5x10-3

-3 1.0x10 6.0x10-3

-4 7.5x10 4.5x10-3

-4 5.0x10 3.0x10-3

2.5x10-4 1.5x10-3 3.96 3.96 0.0x100 2.97 0.0x100 2.97 0.1 0.1 0.3 1.98 k⊥ 0.3 1.98 k⊥ 0.5 0.5 0.7 0.99 0.7 0.99 x 0.9 0 x 0.9 0

ττ ↑ ↑ component of state 6 for Jz=0 ττ ↑ ↓ component of state 6 for Jz=0

-11 1.4x10 1.2x10-7

-11 1.1x10 1.0x10-7

-12 8.1x10 7.5x10-8

-12 5.4x10 5.0x10-8

2.7x10-12 4.75 2.5x10-8 4.75 3.8 3.8 0.0x100 2.85 0.0x100 2.85 0.1 0.1 0.3 1.9 k⊥ 0.3 1.9 k⊥ 0.5 0.5 0.7 0.95 0.7 0.95 x 0.9 0 x 0.9 0

Hank Lamm Light-Front True Muonium 17 May, 2018 10 / 18 0 0 1 lim δG2(x, k ; x , k ) = → δ(r) (7) 0 ⊥ ⊥ 0 2 k⊥→∞ (k⊥) M2

3.91

3.9

3.89

3.88

3.87

3.86 1 10 100 Λµ 2 3 0 1 0 9 M for (top) 1 S1 , (bottom) 1 S0 as function of Λµ.(◦) are from ,() remove δG2.

Regularization improves singlet state Λ dependence

Remove remaining uncancelled divergence in h↑↓ |Heff | ↓↑i

9U. Trittmann and H.-C. Pauli. “Quantum electrodynamics at strong couplings”. In: (1997). arXiv: hep-th/9704215 [hep-th]. Hank Lamm Light-Front True Muonium 17 May, 2018 11 / 18 M2

3.91

3.9

3.89

3.88

3.87

3.86 1 10 100 Λµ 2 3 0 1 0 9 M for (top) 1 S1 , (bottom) 1 S0 as function of Λµ.(◦) are from ,() remove δG2.

Regularization improves singlet state Λ dependence

Remove remaining uncancelled divergence in h↑↓ |Heff | ↓↑i

0 0 1 lim δG2(x, k ; x , k ) = → δ(r) (7) 0 ⊥ ⊥ 0 2 k⊥→∞ (k⊥)

9U. Trittmann and H.-C. Pauli. “Quantum electrodynamics at strong couplings”. In: (1997). arXiv: hep-th/9704215 [hep-th]. Hank Lamm Light-Front True Muonium 17 May, 2018 11 / 18 Regularization improves singlet state Λ dependence

Remove remaining uncancelled divergence in h↑↓ |Heff | ↓↑i

0 0 1 lim δG2(x, k ; x , k ) = → δ(r) (7) 0 ⊥ ⊥ 0 2 k⊥→∞ (k⊥) M2

3.91

3.9

3.89

3.88

3.87

3.86 1 10 100 Λµ 2 3 0 1 0 9 M for (top) 1 S1 , (bottom) 1 S0 as function of Λµ.(◦) are from ,() remove δG2.

9U. Trittmann and H.-C. Pauli. “Quantum electrodynamics at strong couplings”. In: (1997). arXiv: hep-th/9704215 [hep-th]. Hank Lamm Light-Front True Muonium 17 May, 2018 11 / 18 n nn





Rotational invariance is made worse for regularization Renormalization effects seen in positronium Discrepancy comes from excluding high momentum states

All the bound states!

Units of mµ for me = 1/2mµ, α = 0.3, Λe = 1/2Λµ,Λµ = mµα/2 M2 4 M2 1 0.995 3.98 0.99

3.96 0.985

0.98 3.94 0.975

3.92 0.97

0.965 3.9 0.96

3.88 0.955 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Jz Jz

2S+1 Jz Spectroscopic notation LJ

Hank Lamm Light-Front True Muonium 17 May, 2018 12 / 18 n nn

Renormalization effects seen in positronium Discrepancy comes from excluding high momentum electron states

All the bound states!

Units of mµ for me = 1/2mµ, α = 0.3, Λe = 1/2Λµ,Λµ = mµα/2 M2 4 M2 1 0.995 3.98 0.99

3.96 0.985

0.98 3.94 0.975

3.92 0.97

0.965 3.9  0.96

3.88 0.955 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Jz Jz

2S+1 Jz Spectroscopic notation LJ Rotational invariance is made worse for regularization

Hank Lamm Light-Front True Muonium 17 May, 2018 12 / 18 Discrepancy comes from excluding high momentum electron states

All the bound states!

Units of mµ for me = 1/2mµ, α = 0.3, Λe = 1/2Λµ,Λµ = mµα/2 M2 4 M2 1 0.995 3.98 0.99 3.96 0.985 n 0.98 3.94 0.975 nn

3.92 0.97

0.965 3.9  0.96

3.88 0.955 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Jz Jz

2S+1 Jz Spectroscopic notation LJ Rotational invariance is made worse for regularization Renormalization effects seen in positronium

Hank Lamm Light-Front True Muonium 17 May, 2018 12 / 18 All the bound states!

Units of mµ for me = 1/2mµ, α = 0.3, Λe = 1/2Λµ,Λµ = mµα/2 M2 4 M2 1 0.995 3.98 0.99 3.96 0.985 n 0.98 3.94 0.975 nn

3.92 0.97

0.965 3.9  0.96

3.88 0.955 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Jz Jz

2S+1 Jz Spectroscopic notation LJ Rotational invariance is made worse for regularization Renormalization effects seen in positronium Discrepancy comes from excluding high momentum electron states

Hank Lamm Light-Front True Muonium 17 May, 2018 12 / 18 Effects of lepton loop consistent with instant form

-3 Mesonix 2.0x10 TMSWIFT IF 1.5x10-3

1.0x10-3

-4 2 5.0x10 M ∆ 0.0x10+0

-5.0x10-4

-1.0x10-3

-1.5x10-3 0.2 0.4 0.6 0.8 1

me

2 2 2 2 3 0 Eigenvalue shifts ∆M ≡ Mµµ − M0 (in units of mµ) for 1 S1 . The dashed line IF is the instant-form prediction, using the non-relativistic wave function, while the light-front (LF) points are obtained by taking α = 0.3 Hank Lamm Light-Front True Muonium 17 May, 2018 13 / 18 N, Λ limits appear regulated

2 Extract M and fi from finite-size and finite-cutoff through Pad´e expansion 2 b c 2 MΛ + N + N 2 M (N, Λ) = d e 1 + N + N 2 2 M (N,Λµ) of Triplet State for α=0.2

3.96195

3.9619

3.96185

3.9618

3.96175

3.9617

3.96165 6 8 13 10 15 12 17 19 Λ 14 21 µ 16 23 N 18 25 20 27

Hank Lamm Light-Front True Muonium 17 May, 2018 14 / 18 2 10 Results for the M (α) and fV,P (α)

2 1 1 2 3 3 α M (1 S0) fV (1 S0) M (1 S1) fP (1 S1) CHFS,LF CHFS,ET 0.01 3.99989993(3) 4.18(10) × 10−5 3.99989996(3) 3.893(6) × 10−5 0.76(77) 0.5834 0.02 3.9995997(2) 1.1(4) × 10−4 3.9996002(2) 1.088(7) × 10−4 0.79(42) 0.5837 0.03 3.9990987(4) 2.05(9) × 10−4 3.999101(2) 1.93(6) × 10−4 0.74(34) 0.5841 0.04 3.998397(4) 3.15(5) × 10−4 3.998404(5) 3.07(7) × 10−4 0.76(56) 0.5847 0.05 3.9974914(4) 4.466(2) × 10−4 3.9975098(3) 3.95(2) × 10−4 0.74(2) 0.5855 0.07 3.995068(3) 7.404(7) × 10−4 3.9951351(8) 5.908(5) × 10−4 0.7(4) 0.5877 0.1 3.98987(6) 1.273(2) × 10−3 3.990137(3) 9.16(3) × 10−4 0.67(2) 0.5922 0.2 3.9576(6) 3.9(2) × 10−3 3.9614(5) 1.9(2) × 10−3 0.6(2) 0.6204 0.3 3.8996(6) 1.02(3) × 10−2 3.91538(4) 2.39(2) × 10−3 0.49(2) 0.6735 Z 2 dx d k⊥ h J J i fV (P ) = ψ (k⊥, x, ↑↓) ∓ ψ (k⊥, x, ↓↑) px(1 − x) (2π)3 Jz =0 Jz =0

0.8 Dirac-Coulomb O(α7) TMSWIFT 0.75

0.7

2 0.65 M

0.6

0.55

0.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 α

10H. Lamm and R. Lebed. “High Resolution Nonperturbative Light-Front Simulations of the True Muonium Atom”. In: Phys. Rev. D94.1 (2016), p. 016004. arXiv: 1606.06358 [hep-ph].

Hank Lamm Light-Front True Muonium 17 May, 2018 15 / 18 Only minor issues with α-dependence

2 2 P β Fit parameters of M (α) = β Nβα . The perturbative predictions are 1 N2 = − 4 ,N4s ≈ −0.328,N4t ≈ 0.255

En α N0 N2 N4 N5 1 1 S0 [0.01,0.3] 1.99999998(2) -0.2500(2) -0.37(5) -0.04(21) [0.01,0.1] 1.999999990(2) -0.25004(2) -0.35(2) 0.08(10) 3 1 S1 [0.01,0.3] 1.99999998(2) -0.24990(8) 0.39(3) -0.78(8) [0.01,0.1] 1.999999979(6) -0.24993(5) 0.38(3) -0.60(26)

β Fit parameters of fi(α) = Nα . The perturbative prediction is β = 3/2.

fi α N β fV [0.01,0.3] 0.0412(9) 1.510(7) [0.01,0.1] 0.0411(3) 1.509(3) fP [0.01,0.3] 0.022(3) 1.37(4) [0.01,0.1] 0.0240(8) 1.394(10)

Hank Lamm Light-Front True Muonium 17 May, 2018 16 / 18 Studying Ψ(µ) = aµ−κ can guide phenomenology

104 0.01 0.07 0.3 102 Use to build models of 100 -3.59 µ -2 -2

↑ ↓ 10 Without Counterterm ↑ ↑

Ψ With Counterterm ↑ ↑ -3.93 Without Counterterm ↑ ↓ µ With Counterterm ↑ ↓ 10-4 -2.5

-6 -3.99 10 µ

κ -3 10-8 10-3 10-2 10-1 100 101 µ -3.5

Strongly-coupled QED seems to in- -4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 dicate that κ → 3.5 for dominant α term, and κ → 2.5 for subdominant term.

Hank Lamm Light-Front True Muonium 17 May, 2018 17 / 18 Leptonic loops, masses, decay rates, and wavefunctions computed TMSWIFT allows for renormalization implementations and new Fock states

True muonium has pushed LF an inch further up the hill

True muonium presents novel LF testing ground

Hank Lamm Light-Front True Muonium 17 May, 2018 18 / 18 TMSWIFT allows for renormalization implementations and new Fock states

True muonium has pushed LF an inch further up the hill

True muonium presents novel LF testing ground Leptonic loops, masses, decay rates, and wavefunctions computed

Hank Lamm Light-Front True Muonium 17 May, 2018 18 / 18 True muonium has pushed LF an inch further up the hill

True muonium presents novel LF testing ground Leptonic loops, masses, decay rates, and wavefunctions computed TMSWIFT allows for renormalization implementations and new Fock states

Hank Lamm Light-Front True Muonium 17 May, 2018 18 / 18