Charm CP Violation and the electric dipole moment of the neutron

Transcription

1 and the electric dipole moment of the neutron Thomas Mannel (with N. Uraltsev, arxiv: and arxiv: ) Theoretische Physik I Universität Siegen Seminar at TUM,

2 Contents Introduction 1 Introduction General Relevance of Charm 2 The Standard Model Prediction New Physics? 3 Loop-less

3 General Relevance of Charm General Relevance of Charm Strong interactions QCD laboratory Intermediate case between heavy and light quarks Interesting Spectroscopy Strong decay modes Weak Interactions interactions Complementary to measurements for b quarks Mixing and CP violation Possible Window to Physics beyond the Standard Model

4 General Relevance of Charm Looking up: Investigate the up-type quarks Flavour Physics of charm: Compared to B and K : The roles of up and down quarks are interchanged Complementarity to top quark (flavour) physics Up-type Flavour tests are mandatory for a full test of our understanding of Flavour Physics

5 Charm is unique... General Relevance of Charm FCNC s are suppressed in the SM by GIM For bottom and strange: GIM CKM Factor 1 16π 2 m 2 t m 2 u M 2 W GIM is weakened by the large Top mass For charm (and top): GIM CKM Factor 1 16π 2 m 2 b m2 d M 2 W GIM is MUCH more efficient

6 General Relevance of Charm Up-type FCNC s have a very small SM pollution Relative Strength of New Physics (NP) in Up vs. Down-Type FCNC s might be different Cleaner (but not neccessary larger) signals of new physics: ( ) NP Signal ( ) NP Signal SM noise up-type > SM noise down-type Top plays a special role No Top Hadrons Flavour Phenomenology less rich Strong interactions perturbative Charm: Novel access to flavour dynamics

7 The Charm of the world General Relevance of Charm Many Experiments have done / can do charm physics: CLEO-c (finished) BaBar (finished) LHC, in particular LHCb BESS III in Beijing BELLE and BELLE II COMPASS (to some extend) possibly PANDA

8 The Standard Model Prediction New Physics?

9 The Standard Model Prediction New Physics? Recent LHC Measurement: Difference of time-integrated CP asymmetries for D K + K and D π + π : a CP = A CP (D 0 K + K ) A CP (D 0 π + π ) = (0.82 ± 0.21 ± 0.11)% World Average for this quantity: a CP = (0.68 ± 0.18)% This is a surprise! The SM tends to have a smaller value

10 The Standard Model Prediction New Physics? dir a CP A CP A CP A CP A CP A Γ A Γ A Γ BaBar Belle Prelim. LHCb CDF Prelim. LHCb BaBar Prelim. Belle Prelim ind a CP

11 The SM prediction... The Standard Model Prediction New Physics? Sources of CP violation in the Standardmodel Strong CP violation: θ term L strong CP = θ α s 8π Gµν,a Ga µν will be ignored in what follows CKM CP violation: CKM matrix, unique source = Im V csv us V cd V ud = Im (V cb V cd) (V ub V ud) Any CP violation in the SM is proportional to! is proportional to sin γ in the standard parametrization CP violating observables by interference effects

12 The Standard Model Prediction New Physics? Effective (four fermion) weak interaction H eff = G F 2 { V cs V us [ ( cu)( ss) ( cu)( dd) ] V cbv ub [ ( cu)( dd) ( cu)( bb) ]} = G F [ ] sin θ C cos θ C o1 + r SM e iγ o 2 2 Strong CKM Suppr.: r SM = Vcb V ub V csv us Matrix Elements: m (i) f = D 0 o i f Amplitude A(D 0 f ) = G [ ] F sin θ C cos θ C m (1) f + r SM e iγ m (2) f 2

13 The Standard Model Prediction New Physics? CP Asymmetry: interference between the two contributions in the amplitude: A CP (D 0 m (2) f f ) = 2r SM sin δ f sin γ m (1) f Assuming U Spin: A CP (D 0 K + K ) = A CP (D 0 π + π ) a CP 2A CP (D 0 K + K m (2) f ) = 4r SM sin δ f sin γ m (1) f

14 The Standard Model Prediction New Physics? Let: sin δ f sin γ 1 Expectation: m (2) f m (1) f a CP = m (2) f m (1) f D 0 ( cd)( du) K + K D 0 ( cs)( su) K + K should be (significantly?) less than unity... Can the hadronic effects be such that the this ratio is largish?

15 New Physics Introduction The Standard Model Prediction New Physics? Assume: The effect is indeed due to new physics Assume: The SM contribution to is small For simplicity we completely neglect it Pick some dim-6 operators with complex couplings, which induce additional CP violation O 1 = em c c iσ αβ F αβ γ 5 u, O 3 = [ cγ µ u]([ sγ µ s] + [ dγ µ d]), O 2 = g s m c c iσ αβ G αβ γ 5 u, O 4 = ( cγ µ (1+γ 5 )u) ( dγ µ (1 γ 5 )d) and define L np = G F sin θ C cos θ C c k O k, 2 k

16 The Standard Model Prediction New Physics? Estimate the matrix elements O 3 is the SM operator, with an arbitrary coefficient π + π O k D f π f D π + (0)M 2 D O 4 can be estimated in naive factorization π + π O 4 D f π f D π + (0)M 2 D 1 N c 2m 2 π (m u +m d )m c. O 3 estimated form the ratio of partonic rates π + π O 2 D 4πg s 3 fπ f D π + (0)M 2 D. O 2 estimated from the ratio of partonic rates π + π O 2 D 8 2πeq d f π f D π + (0)M 2 D

17 The Standard Model Prediction New Physics? Summary on the Coefficients Taking these operators as the single source of CPV, we can estimated the imaginary parts of the coefficients, up to the state strong phase δ FSI Im c sin δ FSI, Im c , sin δ FSI Im c sin δ FSI, Im c sin δ FSI, Fixing these numbers and operators, one may investigate the impact on the neutron EDM

18 Loop-less Electric Dipole Moment of the Neutron

19 Loop-less in the SM Electric dipole moments in classical physics d = d 3 r ρ( r) r Energy: U = d E Quantum Field theory: States are characterized by momentum p and Spin J: d must be proportional to J U = d J E d mud be parity odd: P Violation (and also T Violation) CP violation

20 EDM s of elementary particles Loop-less Electromagnetic interaction with EDM: (Flavour diagonal) L EDM = d 2 ψiσ µν γ 5 ψ F µν SM Scenario without Strong CP: d must be proportional to! Thus we have two W exchanges:

21 Loop-less However, sum of all the two-loop diagrams vanishes for quark edm s need another (gluon) loop Shabalin 78 Result for d quark (similar for the up qark) d d = e m [ ] dα s GF 2 m2 c ln 2 mb 2 ln M2 W e cm 108π 5 mc 2 mb 2 Khiplovich 86, Czarnecki, Krause 97 Naive composition of the Neutron edm: d N = 4 3 d d 1 3 d u e cm This is too small, neutron is a composite object.

22 Loop-less Composite Objects: Neutron EDM There are long distance effects: Penguin Operators: d s transitions (with CPV) H Pen G F 2 α s 3π ( sγ µ T a d)( qγ µ T a q) q Long distance strangeness t: (Gavela et al., 82, Khriplovich et al, 82) Estimates much larger than the EDM s of the constituents Still there is a loop suppression in the penguins

23 Loop-less Loop-less EDM s Uraltsev, M Systematic Study: Start from the effective Hamiltonian H W for weak interactions below M W : H W is bi-linear in the CKM elements: CP violation will be second order in H W L 2 = i G2 F d 4 x T {H W (x)h W (0)} 4 In the nucleon top and bottom are irrelevant: At tree level this means to leave them out. H W = J µj µ, J µ = V cs cγ µ s+v cd cγ µ d+v us ūγ µ s+v ud ūγ µ d with Γ µ = γ µ (1 γ 5 )

24 Loop-less This looks almost like the two-generation case, however, the remaining 2 2 matrix V ij is not unitary, not all phases can be removed. In particular: = ImV csv cd V udv us 0 L 2 contains 256 terms, 64 are flavour neutral. Only two combinations proportional to (or its complex conjugate) These have q and q for each flavor.

25 Loop-less Left: close the charm loop, conventional penguin Right diagram: Integrate out highly virtual charm: ig 2 F 2 V csv cd V udv us d 4 x T{( dγ µ c)(ūγ µ d)(0) ( cγ ν s)( sγ ν u)(x)} + h.c. Charm Propagator c(0) c(x) }{{} ( ) 1 m c i /D 0x

26 Loop-less ( Expansion of the charm propagator: 1/m c expansion ) 1 m c i /D 0x = 1 δ 4 (x)+ 1 δ 4 (x)i /D+ 1 δ 4 (x)(i /D) 2 + m c mc 2 mc 3 Left handed currents of the SM: only 1/m 2 c, 1/m 4 c... Thus in a 1/m c expansion: L CPV O 2mc 2 uds 2 = i G2 F O uds = (ūγ µ d)( dγ µ i /DΓ ν s)( sγ ν u) h.c. No loops, no 1/(16π 2 ) supressions However, a local dim-10 operator appears...

27 Loop-less The covariant derivative contains a photon: O α uds = (ūγ µ d)( dγ µ iγ α Γ ν s)( sγ ν u) (s d) from this we get the overall electromagnetic current relevant for EDM s [ ] L α = ie G2 F 2 mc 2 3 Oα uds + i d 4 x T{O uds (0)Jem(x)} α The matrix element between neutron states yields n(p + q) L α n(p) q 0 = d n q ν ū(p + q)iσ αν γ 5 u(p)

28 Loop-less How to estimate the matrix elememts Local piece n(p + q) O α uds n(p) = 2iK uds q ν n(p + q)iσ αν γ 5 n(p) Estimating K uds is difficult: Naive estimate by dimensions: K uds κµ 5 hadr κ 0.3 for the suppression of strangeness µ 0.5 GeV, but this probably overestimates qq (250 MeV) 3 yet q(id) 2 q (650 MeV) 2 qq hence we write a factor of µ 3 q = (250 MeV) 3 for each qq pair, remaining dimensions from µ hadr 500 MeV Thus form the local term we get d n = 32 3 eg2 F K mc 2 uds = e cm κ ( µ q 0.25 GeV ) ( ) GeV µ hadr

29 Loop-less Non-local term: Estimate with a single intermediate Ñ state Coupling ρñ from Ñ nγ: ρ Ñ 0.34 GeV 1 d n 32e G2 F κµ 6 ρñ m qµ c 2 hadr e cm κ MÑ M n Consistent with other (as well crude) estimates

30 Loop-less Summary on the neutron EDM in the SM The loop-less estimate is (order of magnitude) d n = e cm Short distance loops will be parametrically small by loop factors 1/(16π 2 ) The EDM s of the constituents do not play any role Strong CP remains a problem: d n e cm θ Given the current experimental bound: d n e cm (90%CL)

31 Loop-less 1/m c suppression is present in the OPE, however, this is mild p/m c 0.5 Similar Effects in B decays: Intrinsic charm (Bigi et al. 2003, Zwicky et al. 2005, M. et al, 2010 V A Structure yields an additional factor of p/m c The loop-less contribution may as well be the dominant one! There are issues conceding the mass dependence, chiral limit, the limit m s m d etc. SM minimizes the EDM of the neutron

32 Loop-less Insert the new physics operators discussed in the part on charm CPV These will generate contributions to the neutron EDM Some of the operators contain right handed quarks: This can lift the helicity suppression

33 Loop-less Estimates for the additional effects: O 1 = e m c c i(σf)γ 5 u: d n 10 4 d (SM) n O 2 = g s m c c i(σg)γ 5 u: d n 30d (SM) n (right handed c) O 3 = [ cγ µ u]([ sγ µ s] + [ dγ µ d]): O 4 = ( cγ µ (1+γ 5 )u) ( dγ µ (1 γ 5 )d): d n 10d (SM) n d n 50d (SM) n The current experimental limits are safe w/r to charm CPV

34 Loop-less Some comments on other work One may try to accommodate the observed charm CPV in a model Effective TH analysis and impact on charm CPV on ɛ /ɛ (Isidori et al. 2012) Supersymmetric models (Giudice et al. 2012) Models (like SUSY) imply effects in other places.

35 Outlook Introduction Loop-less The current hints to CP violation in charm are certainly very interesting It is not (yet?) clear, if this can be accommodated in the SM If these effects are found also in other chair decays, this may become the first hint to NP Any new CPV has an impact on the neutron EDM... but the experimental limits are yet far too high to be in conflict with the observed charm CPV There is a good motivation to improve the limits on the neutron EDM