Baryon Electric Dipole Moments from Strong CP Violation

Transcription

1 Baryon Electric Dipole Moments from Strong CP Violation Feng-Kun Guo Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn IHEP, Beijing, April 11, 2013 Ottnad, Kubis, Meißner, Guo, PLB687(2010)42; Guo, Meißner, JHEP07(2012)097 F. K. Guo (Uni. Bonn) Baryon EDMs / 25

2 ... it may be that the next exciting thing to come along will be the discovery of a neutron or atomic or electron electric dipole moment. These electric dipole moments... seem to me to offer one of the most exciting possibilities for progress in particle physics. Steven Weinberg (1992) F. K. Guo (Uni. Bonn) Baryon EDMs / 25

3 Outline 1 Introduction 2 Baryon EDMs in chiral perturbation theory 3 Finite volume corrections 4 Summary F. K. Guo (Uni. Bonn) Baryon EDMs / 25

4 Introduction Electric dipole moment (EDM) EDM measures the polarity of a charged system, d = i q i r i For a hadron or any elementary particle at rest, d = d S S Hamiltonian for a dipole interacting with an electric field P and T(CP) violation H edm = d E = d S E S F. K. Guo (Uni. Bonn) Baryon EDMs / 25

5 Introduction Electric dipole moment (EDM) EDM measures the polarity of a charged system, d = i q i r i For a hadron or any elementary particle at rest, d = d S S Hamiltonian for a dipole interacting with an electric field P and T(CP) violation H edm = d E = d S E S F. K. Guo (Uni. Bonn) Baryon EDMs / 25

6 Introduction Neutron and proton EDMs In the Standard Model, no EDM at the first order of weak interaction d n (SM) ecm see e.g., Donoghue et al, Dynamics of the Standard Model, Ch.IX Sensitive to physics beyond the Standard Model: some new physics models predictions are orders-of-magnitude larger Current experimental upper limit d p < ecm calculated from the limit on the EDM of the 199 Hg atom Griffith et al (2009) d n < ecm ultracold neutron experiment Baker et al (2006) d Λ < ecm Λ pπ decays Pondrom et al (1981) F. K. Guo (Uni. Bonn) Baryon EDMs / 25

7 Introduction Neutron and proton EDMs In the Standard Model, no EDM at the first order of weak interaction d n (SM) ecm see e.g., Donoghue et al, Dynamics of the Standard Model, Ch.IX Sensitive to physics beyond the Standard Model: some new physics models predictions are orders-of-magnitude larger Current experimental upper limit d p < ecm calculated from the limit on the EDM of the 199 Hg atom Griffith et al (2009) d n < ecm ultracold neutron experiment Baker et al (2006) d Λ < ecm Λ pπ decays Pondrom et al (1981) F. K. Guo (Uni. Bonn) Baryon EDMs / 25

8 Introduction Neutron and proton EDMs In the Standard Model, no EDM at the first order of weak interaction d n (SM) ecm see e.g., Donoghue et al, Dynamics of the Standard Model, Ch.IX Sensitive to physics beyond the Standard Model: some new physics models predictions are orders-of-magnitude larger Current experimental upper limit d p < ecm calculated from the limit on the EDM of the 199 Hg atom Griffith et al (2009) d n < ecm ultracold neutron experiment Baker et al (2006) d Λ < ecm Λ pπ decays Pondrom et al (1981) F. K. Guo (Uni. Bonn) Baryon EDMs / 25

9 Introduction History of the neutron EDM measurements c Andreas Knecht F. K. Guo (Uni. Bonn) Baryon EDMs / 25

10 Introduction Current and near future experiments Neutron EDM nedm Ultracold neutron experiment Goal for 2012&2013 data: ecm (95% CL) n2edm (2015?) with a sensitivity goal of ecm with a sensitivity goal of ecm TRIUMF neutron EDM (2018?): ecm... R. Brock et al, arxiv: [hep-ex]; EDMs of charged particles (proton, deutron and other light nuclei) Storage ring experiment Goal: ecm Strorage ring EDM BNL (?), Fermilab (?) JEDI Jülich (?) F. K. Guo (Uni. Bonn) Baryon EDMs / 25

11 Introduction Current and near future experiments Neutron EDM nedm Ultracold neutron experiment Goal for 2012&2013 data: ecm (95% CL) n2edm (2015?) with a sensitivity goal of ecm with a sensitivity goal of ecm TRIUMF neutron EDM (2018?): ecm... R. Brock et al, arxiv: [hep-ex]; EDMs of charged particles (proton, deutron and other light nuclei) Storage ring experiment Goal: ecm Strorage ring EDM BNL (?), Fermilab (?) JEDI Jülich (?) F. K. Guo (Uni. Bonn) Baryon EDMs / 25

12 Introduction History of the neutron EDM measurements F. K. Guo (Uni. Bonn) Baryon EDMs / 25

13 Introduction Theta-term in QCD & Strong CP problem Nothing forbids a θ-term in the QCD Lagrangian L QCD = 1 4 Ga µνg a,µν + q(i D M q )q + θ Here, G a,µν = 1 2 ε µναβ G a αβ The contribution of the θ-term to the neutron EDM d n θ ecm Crewther et al (1979) g2 32π 2 Ga a,µν µν G Strong CP problem: θ 10 10, why is it so small? F. K. Guo (Uni. Bonn) Baryon EDMs / 25

14 Introduction Theta-term in QCD & Strong CP problem Nothing forbids a θ-term in the QCD Lagrangian L QCD = 1 4 Ga µνg a,µν + q(i D M q )q + θ g2 32π 2 Ga a,µν µν G Here, G a,µν = 1 2 ε µναβ G a αβ The contribution of the θ-term to the neutron EDM d n θ ecm Crewther et al (1979) π γ π γ n p n p Strong CP problem: θ 10 10, why is it so small? F. K. Guo (Uni. Bonn) Baryon EDMs / 25

15 Introduction Theta-term in QCD & Strong CP problem Generally, M q is complex and non-diagonal in the Standard Model. We will encounter a U A (1) transformation exp(iα) exp[i(ϕ R ϕ L )/2] M q e iϕ L M q e iϕ R, q L e iϕ L q L, q R e iϕ R q R arg(detm q ) arg(detm q ) + 2N f α For massless quarks Classically, µ J µ 5 = 0 Quantum U A (1) anomaly: µ J µ 5 = N f g 2 θ θ 2N f α G a 16π 2 µν G a,µν One cannot solve the strong CP problem by simply imposing CP on QCD The measurable quantity is not θ but θ 0 = θ + arg(detm q ) F. K. Guo (Uni. Bonn) Baryon EDMs / 25

16 Introduction Theta-term in QCD & Strong CP problem Generally, M q is complex and non-diagonal in the Standard Model. We will encounter a U A (1) transformation exp(iα) exp[i(ϕ R ϕ L )/2] M q e iϕ L M q e iϕ R, q L e iϕ L q L, q R e iϕ R q R arg(detm q ) arg(detm q ) + 2N f α For massless quarks Classically, µ J µ 5 = 0 Quantum U A (1) anomaly: µ J µ 5 = N f g 2 θ θ 2N f α G a 16π 2 µν G a,µν One cannot solve the strong CP problem by simply imposing CP on QCD The measurable quantity is not θ but θ 0 = θ + arg(detm q ) F. K. Guo (Uni. Bonn) Baryon EDMs / 25

17 Introduction Theta-term in QCD & Strong CP problem Generally, M q is complex and non-diagonal in the Standard Model. We will encounter a U A (1) transformation exp(iα) exp[i(ϕ R ϕ L )/2] M q e iϕ L M q e iϕ R, q L e iϕ L q L, q R e iϕ R q R arg(detm q ) arg(detm q ) + 2N f α For massless quarks Classically, µ J µ 5 = 0 Quantum U A (1) anomaly: µ J µ 5 = N f g 2 θ θ 2N f α G a 16π 2 µν G a,µν One cannot solve the strong CP problem by simply imposing CP on QCD The measurable quantity is not θ but θ 0 = θ + arg(detm q ) F. K. Guo (Uni. Bonn) Baryon EDMs / 25

18 Introduction Lattice calculations Calulations from several groups. For a review, see Shintani, talk at ConfinmentX (2012) From lattice to reality Finite lattice spacing: a 0 Finite volume: V Quark masses: normally M lattice π > Mπ physical, chiral extrapolation Our purpose: to calculate baryon EDMs in U(3) CHPT chiral extrapolation and finite volume corrections F. K. Guo (Uni. Bonn) Baryon EDMs / 25

19 Introduction Lattice calculations Calulations from several groups. For a review, see Shintani, talk at ConfinmentX (2012) From lattice to reality Finite lattice spacing: a 0 Finite volume: V Quark masses: normally M lattice π > Mπ physical, chiral extrapolation Our purpose: to calculate baryon EDMs in U(3) CHPT chiral extrapolation and finite volume corrections F. K. Guo (Uni. Bonn) Baryon EDMs / 25

20 Baryon EDMs in CHPT Baryon electromagnetic form factors [ B(p ) Jem B(p) ν = ū(p ) γ ν ( F 1 q 2 ) if ( 2 q 2 ) σ µν q µ 2m B +i ( γ ν q 2 γ 5 2m B q ν ) ( γ 5 FA q 2 ) F ( 3 q 2 ) ] σ µν q µ γ 5 u(p) 2m B F 1,2 (q 2 ): Dirac and Pauli form factors, preserve P and CP F A (q 2 ): anapole form factor, P-violating F 3 (q 2 ): electric dipole form factor (EDFF), P- and CP-violating The EDM is related to F 3 (0) d B = F 3,B(0) 2m B F. K. Guo (Uni. Bonn) Baryon EDMs / 25

21 Baryon EDMs in CHPT CHPT in a nut shell Chiral perturbation theory (CHPT) is the low-energy effective theory of QCD Weinberg (1979), Gasser & Leutwyler, (1984,1985) CHPT has the same symmetries as QCD Chiral symmetry is broken both spontaneously and explicitly a double-expansion in both small momentum and light quark masses, p Λ χ M π Λ χ 1 Mπ 2 = B 0 (m u + m d ) + O(m 2 q) Framework for extrapolation from unphysical to physical quark masses Construct the most general effective Lagrangian up to a certain order more and more parameters: low-energy constants (LECs) Nonrenormalizable, but can be renormalized to a given order Calculations of d n(p) in CHPT: Crewther, Di Vecchia, Veneziano, Witten (1979); Pich, de Rafael (1991); Borasoy (2000); Narison (2008), Hockings, van Kolck (2005); Mereghetti et al (2011);... F. K. Guo (Uni. Bonn) Baryon EDMs / 25

22 Baryon EDMs in CHPT CHPT in a nut shell Chiral perturbation theory (CHPT) is the low-energy effective theory of QCD Weinberg (1979), Gasser & Leutwyler, (1984,1985) CHPT has the same symmetries as QCD Chiral symmetry is broken both spontaneously and explicitly a double-expansion in both small momentum and light quark masses, p Λ χ M π Λ χ 1 Mπ 2 = B 0 (m u + m d ) + O(m 2 q) Framework for extrapolation from unphysical to physical quark masses Construct the most general effective Lagrangian up to a certain order more and more parameters: low-energy constants (LECs) Nonrenormalizable, but can be renormalized to a given order Calculations of d n(p) in CHPT: Crewther, Di Vecchia, Veneziano, Witten (1979); Pich, de Rafael (1991); Borasoy (2000); Narison (2008), Hockings, van Kolck (2005); Mereghetti et al (2011);... F. K. Guo (Uni. Bonn) Baryon EDMs / 25

23 Baryon EDMs in CHPT CHPT in a nut shell Chiral perturbation theory (CHPT) is the low-energy effective theory of QCD Weinberg (1979), Gasser & Leutwyler, (1984,1985) CHPT has the same symmetries as QCD Chiral symmetry is broken both spontaneously and explicitly a double-expansion in both small momentum and light quark masses, p Λ χ M π Λ χ 1 Mπ 2 = B 0 (m u + m d ) + O(m 2 q) Framework for extrapolation from unphysical to physical quark masses Construct the most general effective Lagrangian up to a certain order more and more parameters: low-energy constants (LECs) Nonrenormalizable, but can be renormalized to a given order Calculations of d n(p) in CHPT: Crewther, Di Vecchia, Veneziano, Witten (1979); Pich, de Rafael (1991); Borasoy (2000); Narison (2008), Hockings, van Kolck (2005); Mereghetti et al (2011);... F. K. Guo (Uni. Bonn) Baryon EDMs / 25

24 Baryon EDMs in CHPT SU(3) CHPT at O ( p 2) Leading order Lagrangian for SU(N f ) mesonic CHPT L (2) SU(3) = F2 4 Tr[ µ U µ U ] + F2 4 Tr[ χu + Uχ ] Here µ U = µ U + il µ U iur µ, χ = 2B 0 (s + ip) External sources: l µ,r µ,s,p Quark masses can be included by s = M q = diag(m u,m d,m s ) ( ) The Goldstone bosons are included in U = exp i 2 F φ φ = 1 2 π η 8 π + K + π 1 2 π η 8 K 0 K K η 8 F. K. Guo (Uni. Bonn) Baryon EDMs / 25

25 Baryon EDMs in CHPT U(3) CHPT at O ( p 2) When the θ-term is absent, L QCD has a U L (3) U R (3) symmetry. Treating θ as an external field, θ(x) U(1) θ(x) N f (ϕ R ϕ L ) θ(x) = θ 0 gives QCD. Nine Goldstone bosons: (π,k,η 8,η 0 ) are collected in Ũ(x) Ũ(x) U(1) e iϕ R Ũ(x)e iϕ L lndetũ(x) lndetũ(x) + in f (ϕ R ϕ L ) θ(x) = θ(x) ilndetũ(x) is chirally invariant The most general Lagrangian up to O ( p 2) Gasser, Leutwyler (1985) L (2) U(3) = V 0 + V 1 Tr [ µ Ũ µ Ũ ] + V 2 Tr [ χ Ũ + χũ ] + iv 3 Tr [ χ Ũ χũ ] +V 4 Tr [ Ũ µ Ũ ] Tr [ Ũ µ Ũ ] + V 5 Tr [ µ θ µ θ ] V 0,...,5 are functions of θ(x) F. K. Guo (Uni. Bonn) Baryon EDMs / 25

26 Baryon EDMs in CHPT U(3) CHPT at O ( p 2) When the θ-term is absent, L QCD has a U L (3) U R (3) symmetry. Treating θ as an external field, θ(x) U(1) θ(x) N f (ϕ R ϕ L ) θ(x) = θ 0 gives QCD. Nine Goldstone bosons: (π,k,η 8,η 0 ) are collected in Ũ(x) Ũ(x) U(1) e iϕ R Ũ(x)e iϕ L lndetũ(x) lndetũ(x) + in f (ϕ R ϕ L ) θ(x) = θ(x) ilndetũ(x) is chirally invariant The most general Lagrangian up to O ( p 2) Gasser, Leutwyler (1985) L (2) U(3) = V 0 + V 1 Tr [ µ Ũ µ Ũ ] + V 2 Tr [ χ Ũ + χũ ] + iv 3 Tr [ χ Ũ χũ ] +V 4 Tr [ Ũ µ Ũ ] Tr [ Ũ µ Ũ ] + V 5 Tr [ µ θ µ θ ] V 0,...,5 are functions of θ(x) F. K. Guo (Uni. Bonn) Baryon EDMs / 25

27 Baryon EDMs in CHPT U(3) CHPT at O ( p 2) Ũ = U 0 U U 0 where U 0 describes the vacuum and ( 2 η 0 U = exp i +i 2 φ ) 3 F }{{ 0 F }}{{} U(1) SU(3) Vacuum alignment: U 0 = diag ( e iϕ u,e iϕ d,e iϕ s) is determined by minimizing the potential energy density V 0 V 2 Tr [ χ U 0 + χu 0] iv3 Tr [ χ U 0 χu ] 0 For θ 0 = 0, the vacuum solution is trivial U 0 = 1. Expanding V i s around θ 0 = θ 0 i ln detu 0, parameters determined by normalization of the kinetic terms, η η mixing,... Herrera-Siklódy et al, (1998) F. K. Guo (Uni. Bonn) Baryon EDMs / 25

28 Baryon EDMs in CHPT U(3) baryon CHPT up to NLO 1 2 Σ Λ Σ + p Baryon octet B = Σ 1 2 Σ Λ Ξ Ξ Λ Up to NLO, about 10 parameters in the Lagrangian Borasoy (2000) itr [ Bγ µ [D µ,b] ] mtr[ BB] D 2 Tr[ Bγ µ γ 5 {u µ,b} ] F 2 Tr[ Bγ µ γ 5 [u µ,b] ] + w 0 2 Tr[ Bγ µ γ 5 B ] Tr[u µ ] + b D Tr [ B{ χ +,B} ] + b F Tr [ B[ χ +,B] ] ( +b 0 Tr[ BB]Tr[ χ + ] + i w θ 6 ) w 13 η 0 Tr [ Bσ µν { γ 5 F + F µν,b }] 0 6 ( +4A w 10 η 0 Tr[ BB] + i w 14 F θ 6 ) 0 + w 14 η 0 Tr [ Bσ µν [ γ 5 F + 0 F µν,b ]], 0 Only two combinations up to NLO in total 8 baryon EDMs: [w 13,w r 13 (µ)] and [w 14,w r 14 (µ),w 0,w 10,b 0] F. K. Guo (Uni. Bonn) Baryon EDMs / 25 n

29 Baryon EDMs in CHPT Feynman diagrams up to NLO η 0 (a) (b) (c) (d) (e) (f) Loops are regularized using the method of infrared regularization: Lorentz covariant, well-defined power counting Becher, Leutwyler (1999) Divergences are absorbed into the renormalization of w 13 and w 14 F. K. Guo (Uni. Bonn) Baryon EDMs / 25

30 Baryon EDMs in CHPT d n = d p γ Loops are different d n = d p n {π,p} n π (K + ) p(σ ) p {K +,Σ } {π 0,p} {π +,n} γ {K 0,Σ + } {K +,Λ} {K +,Σ 0 } π + (K +, K + ) {η 8,p} p n(σ 0, Λ) {η 0,p} F. K. Guo (Uni. Bonn) Baryon EDMs / 25

31 Baryon EDMs in CHPT Pion mass dependence of d n(p) dn loop e Θ0 fm Π M Π GeV Lattice data: Shintani et al (2008); Shintani, talk given at Confinement X (2012) Grey bands: LO loop results Two parameter combinations can be fixed to the two data points at M π = 530 MeV dp loop eθ0 fm F. K. Guo (Uni. Bonn) Baryon EDMs / 25

32 Baryon EDMs in CHPT Pion mass dependence of d n(p) dn loop e Θ0 fm Π M Π GeV Lattice data: Shintani et al (2008); Shintani, talk given at Confinement X (2012) Grey bands: LO loop results Two parameter combinations can be fixed to the two data points at M π = 530 MeV dp loop eθ0 fm F. K. Guo (Uni. Bonn) Baryon EDMs / 25

33 Baryon EDMs in CHPT Predictions Predictions at physical M π in units of θ 0 ecm d n = 2.9 ± 0.9, d p = 1.1 ± 1.1 d Λ = 2.5 ± 0.4, d Σ + = 0.7 ± 1.1 d Σ 0 = 0.7 ± 0.4, d Σ = 2.2 ± 0.5 d Ξ 0 = 3.4 ± 0.9, d Ξ = 0.6 ± 0.5 Upper limit of θ 0 : θ F. K. Guo (Uni. Bonn) Baryon EDMs / 25

34 Baryon EDMs in CHPT Predictions Predictions at physical M π in units of θ 0 ecm d n = 2.9 ± 0.9, d p = 1.1 ± 1.1 d Λ = 2.5 ± 0.4, d Σ + = 0.7 ± 1.1 d Σ 0 = 0.7 ± 0.4, d Σ = 2.2 ± 0.5 d Ξ 0 = 3.4 ± 0.9, d Ξ = 0.6 ± 0.5 Upper limit of θ 0 : θ F. K. Guo (Uni. Bonn) Baryon EDMs / 25

35 Finite volume corrections Introduction Lattice calculations are performed in a finite volume momentum is quantized q = n 2π L The continuum Lagrangian can still be used Gasser, Leutwyler (1987,1988) Loop integrals become summations i d 4 k (2π) 4 1 (k 2 m 2 1 )[(k + q)2 m 2 2 ] i Finite volume corrections: dk 0 L 3 2π n δ L [Q] Q(L) Q( ) 1 (k 2 m 2 1 )[(k + q)2 m 2 2 ] F. K. Guo (Uni. Bonn) Baryon EDMs / 25

36 Finite volume corrections Introduction Lattice calculations are performed in a finite volume momentum is quantized q = n 2π L The continuum Lagrangian can still be used Gasser, Leutwyler (1987,1988) Loop integrals become summations i d 4 k 1 (2π) 4 (k 2 m 2 1 )[(k + q)2 m 2 2 ] i Finite volume corrections: dk 0 L 3 2π n δ L [Q] Q(L) Q( ) 1 (k 2 m 2 1 )[(k + q)2 m 2 2 ] F. K. Guo (Uni. Bonn) Baryon EDMs / 25

37 Finite volume corrections Results for d n Finite volume corrections to d n at LO O Connell,Savage (2006); Guo, Meißner (2012) [ ] δ L d LO M 2 n = πeθ 0 4π 2 F [ (D + F)(bD π 2 + b F )K 0 (LM π n ) (D F)(b D b F )K 0 (LM K n ) n 0 K 0 (z): modified Bessel function of the second kind NLO results Upper lines: NLO Lower lines: LO F. K. Guo (Uni. Bonn) Baryon EDMs / 25

38 Finite volume corrections Results for d n Finite volume corrections to d n at LO O Connell,Savage (2006); Guo, Meißner (2012) [ ] δ L d LO M 2 n = πeθ 0 4π 2 F [ (D + F)(bD π 2 + b F )K 0 (LM π n ) (D F)(b D b F )K 0 (LM K n ) n 0 K 0 (z): modified Bessel function of the second kind NLO results Upper lines: NLO Lower lines: LO F. K. Guo (Uni. Bonn) Baryon EDMs / 25

39 Summary Neutron and proton EDMs: P and CP violating, sensitive to new physics, under intense experimental investigations Many lattice calculations: at unphysical pion masses and in a box CHPT: chiral extrapolation and finite volume corrections d n = ( 2.9 ± 0.9) θ 0 ecm, d p = (1.1 ± 1.1) θ 0 ecm Omitted but very interesting Parameterizing new physics in EFT: chiral properties de Vries, Timmermans, Mereghetti, van Kolck (2011),... Light nuclei EDMs de Vries et al (2011), Bsaisou et al (2012) Recent review: Electric Dipole Moments of Nucleons, Nuclei, and Atoms: The Standard Model and Beyond, Engel, Ramsey-Musolf, van Kolck, arxiv: [nucl-th] F. K. Guo (Uni. Bonn) Baryon EDMs / 25

40 Summary Neutron and proton EDMs: P and CP violating, sensitive to new physics, under intense experimental investigations Many lattice calculations: at unphysical pion masses and in a box CHPT: chiral extrapolation and finite volume corrections d n = ( 2.9 ± 0.9) θ 0 ecm, d p = (1.1 ± 1.1) θ 0 ecm Omitted but very interesting Parameterizing new physics in EFT: chiral properties de Vries, Timmermans, Mereghetti, van Kolck (2011),... Light nuclei EDMs de Vries et al (2011), Bsaisou et al (2012) Recent review: Electric Dipole Moments of Nucleons, Nuclei, and Atoms: The Standard Model and Beyond, Engel, Ramsey-Musolf, van Kolck, arxiv: [nucl-th] F. K. Guo (Uni. Bonn) Baryon EDMs / 25

41 Advertisement Coupled-channel effects in radiative charmonium transitions Time: 10:00am, next Tuesday F. K. Guo (Uni. Bonn) Baryon EDMs / 25