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True Muonium on the Light Front

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True Muonium on the Light Front True muonium on the light front Hank Lamm LIGHTCONE2015 in collaboration with Richard Lebed Hank Lamm True Muonium LIGHTCONE2015 1 / 17 Outline 1 True Muonium, (µ+µ−) 2 Light-Front Hamiltonians 3 TMSWIFT 4 In-Progress Theoretical Improvements 5 Conclusions Hank Lamm True Muonium LIGHTCONE2015 2 / 17 Nearly purely leptonic, nearly purely QED bound state τTM ≈ 1 ps τµ = 2:2 µs (compare to τπ0 ≈ 10 as) Never detected, but many channels suggested [Brodsky, Lebed PRL 2009] Many BSM scenarios can be cleanly explored! [Lamm PRD 2015] Arguably a better QED analogy of Quarkonium Wait? I can bind muons? Proposed in 1971 Hank Lamm True Muonium LIGHTCONE2015 3 / 17 τTM ≈ 1 ps τµ = 2:2 µs (compare to τπ0 ≈ 10 as) Never detected, but many channels suggested [Brodsky, Lebed PRL 2009] Many BSM scenarios can be cleanly explored! [Lamm PRD 2015] Arguably a better QED analogy of Quarkonium Wait? I can bind muons? Proposed in 1971 Nearly purely leptonic, nearly purely QED bound state Hank Lamm True Muonium LIGHTCONE2015 3 / 17 Never detected, but many channels suggested [Brodsky, Lebed PRL 2009] Many BSM scenarios can be cleanly explored! [Lamm PRD 2015] Arguably a better QED analogy of Quarkonium Wait? I can bind muons? Proposed in 1971 Nearly purely leptonic, nearly purely QED bound state τTM ≈ 1 ps τµ = 2:2 µs (compare to τπ0 ≈ 10 as) Hank Lamm True Muonium LIGHTCONE2015 3 / 17 Many BSM scenarios can be cleanly explored! [Lamm PRD 2015] Arguably a better QED analogy of Quarkonium Wait? I can bind muons? Proposed in 1971 Nearly purely leptonic, nearly purely QED bound state τTM ≈ 1 ps τµ = 2:2 µs (compare to τπ0 ≈ 10 as) Never detected, but many channels suggested [Brodsky, Lebed PRL 2009] Hank Lamm True Muonium LIGHTCONE2015 3 / 17 Arguably a better QED analogy of Quarkonium Wait? I can bind muons? Proposed in 1971 Nearly purely leptonic, nearly purely QED bound state τTM ≈ 1 ps τµ = 2:2 µs (compare to τπ0 ≈ 10 as) Never detected, but many channels suggested [Brodsky, Lebed PRL 2009] Many BSM scenarios can be cleanly explored! [Lamm PRD 2015] Hank Lamm True Muonium LIGHTCONE2015 3 / 17 Wait? I can bind muons? Proposed in 1971 Nearly purely leptonic, nearly purely QED bound state τTM ≈ 1 ps τµ = 2:2 µs (compare to τπ0 ≈ 10 as) Never detected, but many channels suggested [Brodsky, Lebed PRL 2009] Many BSM scenarios can be cleanly explored! [Lamm PRD 2015] Arguably a better QED analogy of Quarkonium Hank Lamm True Muonium LIGHTCONE2015 3 / 17 Both could observe (µ+µ−) DIRAC has \possibility" of measuring Lamb shift Future muon facility at Fermilab should be considered Future experimental efforts to detect exist DIRAC Experiment at CERN HPS Experiment at JLab Hank Lamm True Muonium LIGHTCONE2015 4 / 17 DIRAC has \possibility" of measuring Lamb shift Future muon facility at Fermilab should be considered Future experimental efforts to detect exist DIRAC Experiment at CERN HPS Experiment at JLab Both could observe (µ+µ−) Hank Lamm True Muonium LIGHTCONE2015 4 / 17 Future muon facility at Fermilab should be considered Future experimental efforts to detect exist DIRAC Experiment at CERN HPS Experiment at JLab Both could observe (µ+µ−) DIRAC has \possibility" of measuring Lamb shift Hank Lamm True Muonium LIGHTCONE2015 4 / 17 Future experimental efforts to detect exist DIRAC Experiment at CERN HPS Experiment at JLab Both could observe (µ+µ−) DIRAC has \possibility" of measuring Lamb shift Future muon facility at Fermilab should be considered Hank Lamm True Muonium LIGHTCONE2015 4 / 17 24 years spent developing LF techniques to solve 3+1 bound states Development of DLCQ for 3+1 [Tang et al. PRD 1991] First numerical computation of e¯eγ model of Ps [Kaluza et al. PRD 1992] Partial 1=r2 counterterms implemented [Krautg¨artneret al. PRD 1992] Instability in singlet state of Yukawa [Glazek et. al PRD 1993] Hyperfine split w/o annihilation in T-D equation [Kaluza et al. PRD 1993] First attempt at QCD bound states [W¨olzDiss. 1995] Ps with jγi and Full Coulomb counterterms [Trittmann Diss. 1997] Flow Equations for Ps [Gubankova et al. hep-th/9809143] Flow Equations for Glueballs [Gubankova et al. PRD 2000] AdS/QCD wavefunctions [Brodsky et al. PRL 2006] BLFQ Positronium [Wiecki et al. PRD 2015] (See Vary talk Friday) Hank Lamm True Muonium LIGHTCONE2015 5 / 17 Potential V given be vertex, seagull, and fork diagrams calculable from LCPT. Infinite tower of Fock states!Must truncate Divergences appear at x ! 0; 1 and k? ! 1 ! Regularization integrals via D/Renormalization Using HLC it is possible to construct eigenvalue problem ! X m2 + k2 M 2 − i ?i (x ; k ; h ) x i ?i i i i Z X 0 2 0 0 0 0 0 = dxjd k?jhxi; k?i; hi jV j xj; k?j; hji (xj; k?;j; hj) D hj (1) Hank Lamm True Muonium LIGHTCONE2015 6 / 17 Infinite tower of Fock states!Must truncate Divergences appear at x ! 0; 1 and k? ! 1 ! Regularization integrals via D/Renormalization Using HLC it is possible to construct eigenvalue problem ! X m2 + k2 M 2 − i ?i (x ; k ; h ) x i ?i i i i Z X 0 2 0 0 0 0 0 = dxjd k?jhxi; k?i; hi jV j xj; k?j; hji (xj; k?;j; hj) D hj (1) Potential V given be vertex, seagull, and fork diagrams calculable from LCPT. Hank Lamm True Muonium LIGHTCONE2015 6 / 17 Divergences appear at x ! 0; 1 and k? ! 1 ! Regularization integrals via D/Renormalization Using HLC it is possible to construct eigenvalue problem ! X m2 + k2 M 2 − i ?i (x ; k ; h ) x i ?i i i i Z X 0 2 0 0 0 0 0 = dxjd k?jhxi; k?i; hi jV j xj; k?j; hji (xj; k?;j; hj) D hj (1) Potential V given be vertex, seagull, and fork diagrams calculable from LCPT. Infinite tower of Fock states!Must truncate Hank Lamm True Muonium LIGHTCONE2015 6 / 17 Using HLC it is possible to construct eigenvalue problem ! X m2 + k2 M 2 − i ?i (x ; k ; h ) x i ?i i i i Z X 0 2 0 0 0 0 0 = dxjd k?jhxi; k?i; hi jV j xj; k?j; hji (xj; k?;j; hj) D hj (1) Potential V given be vertex, seagull, and fork diagrams calculable from LCPT. Infinite tower of Fock states!Must truncate Divergences appear at x ! 0; 1 and k? ! 1 ! Regularization integrals via D/Renormalization Hank Lamm True Muonium LIGHTCONE2015 6 / 17 Using method of iterated resolvents we \include" effects of higher Fock states in an effective interaction [H.C. Pauli hep-th/9608035] The Fock space will have an energy squared operator: HPP HPQ HLC = (2) HQP HQQ We write a generic state jΨi with Q component as a function of P component and a resolvent −1 Q^jΨi = Q^(! − HLC ) QH^ LC P^jΨi (3) With this, we write an effective Hamiltonian without Q states eff −1 H (!)LC = PH^ LC P^ + PH^ LC Q^(! − HLC ) QH^ LC P^ (4) Fock State can be truncated by Method of Iterated Resolvents IF we can truncate Fock space, we have model wavefunctions (Yay) but breaks gauge invariance (Boo) Hank Lamm True Muonium LIGHTCONE2015 7 / 17 The Fock space will have an energy squared operator: HPP HPQ HLC = (2) HQP HQQ We write a generic state jΨi with Q component as a function of P component and a resolvent −1 Q^jΨi = Q^(! − HLC ) QH^ LC P^jΨi (3) With this, we write an effective Hamiltonian without Q states eff −1 H (!)LC = PH^ LC P^ + PH^ LC Q^(! − HLC ) QH^ LC P^ (4) Fock State can be truncated by Method of Iterated Resolvents IF we can truncate Fock space, we have model wavefunctions (Yay) but breaks gauge invariance (Boo) Using method of iterated resolvents we \include" effects of higher Fock states in an effective interaction [H.C. Pauli hep-th/9608035] Hank Lamm True Muonium LIGHTCONE2015 7 / 17 We write a generic state jΨi with Q component as a function of P component and a resolvent −1 Q^jΨi = Q^(! − HLC ) QH^ LC P^jΨi (3) With this, we write an effective Hamiltonian without Q states eff −1 H (!)LC = PH^ LC P^ + PH^ LC Q^(! − HLC ) QH^ LC P^ (4) Fock State can be truncated by Method of Iterated Resolvents IF we can truncate Fock space, we have model wavefunctions (Yay) but breaks gauge invariance (Boo) Using method of iterated resolvents we \include" effects of higher Fock states in an effective interaction [H.C. Pauli hep-th/9608035] The Fock space will have an energy squared operator: HPP HPQ HLC = (2) HQP HQQ Hank Lamm True Muonium LIGHTCONE2015 7 / 17 With this, we write an effective Hamiltonian without Q states eff −1 H (!)LC = PH^ LC P^ + PH^ LC Q^(! − HLC ) QH^ LC P^ (4) Fock State can be truncated by Method of Iterated Resolvents IF we can truncate Fock space, we have model wavefunctions (Yay) but breaks gauge invariance (Boo) Using method of iterated resolvents we \include" effects of higher Fock states in an effective interaction [H.C. Pauli hep-th/9608035] The Fock space will have an energy squared operator: HPP HPQ HLC = (2) HQP HQQ We write a generic state jΨi with Q component as a function of P component and a resolvent −1 Q^jΨi = Q^(! − HLC ) QH^ LC P^jΨi (3) Hank Lamm True Muonium LIGHTCONE2015 7 / 17 Fock State can be truncated by Method of Iterated Resolvents IF we can truncate Fock space, we have model wavefunctions (Yay) but breaks gauge invariance (Boo) Using method of iterated resolvents we \include" effects of higher Fock states in an effective interaction [H.C.
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