Neutron Electric Dipole Moment from flavor changing Higgs couplings

Transcription

1 oment from flavor changing Higgs couplings January 24, 2017 CP-Violation in the Universe: The SM has not enough! nedm tiny but important: Control SM extensions!

2 Outline hat is an EDM? CPV in SM NEDM in SM NEDM beyon SM NEDM from colore scalar flavor changing coupling NEDM from flavor changing Higgs coupling Results an Conclusion

3 hat is an Electric ipole moment? L eff = L 4 +L 5 +L L 5EDMf = i 2 ψ f σ µν γ 5 F µν ψ f Non-relativistic limit;- interaction between EM fiel an spin: S E µ S B Magnetic interaction conserve P, T-sym, EDM violate P an T-sym. i.e. NEDM violates CP-sym (-assuming CPT-sym) Present experimental boun n /e < cm (corresp to in Bohr Magnetons)

4 How to measure n? Slow neutrons (velocity v n < 7 m/s) in paralell- an antiparallell Ban E- fiels. Larmor precession of neutron spin S Measure frequences ν Electric ipole moment h ν = 2µ n B ± 2 n E n = h ν 4E Challenge: Keep constant B uring experiment Ref: Baker et al, Nucl. Instr. Meth. A736 (2014) 184. arxiv:

5 Energy scales 1 TeV?? SUSY, STRINGS, EXTRA DIMENSIONS...??? M ~80GeV w m b ~5GeV SU(3) x SU(3) L R Λ χ SU(3) V QCD + E u,,s,c,b,t,... HQET c, b QCD u,, s χ QM + HL χ QM CPT + HLCPT K, η, π, B, D,... quarks mesons Figure: Energy levels in particle (flavor) physics Quantum fluctuations (loop effects) at high scales penetrate own to haronic scales 1 GeV

6 2014: 50 year annivers. of CP-violation! s, b u, c, t, s c, s, b u, s ū, c, t s, b ū, s, b c Figure: Fig.1 : K K, B B an D D mixing in SM Ï Ù Ù ¼ Õ Ï Ø Ø Õ Figure: CP-cons an CP-viol quark iagrams, ( Penguin iagram ) Difference of K L π + π an K L π 0 π 0 ( ǫ /ǫ- effect). Later CP-violation in B-ecays... Further?

7 NEDM in SM -small but non-zero γ γ, s, b, s, b u, c, t u, c, t u, c, t u, c, t Figure: Loop iagrams for giving zero EDM SM estimates from 1980 s ( 1990s) NEDM-interaction not in SM Lagrangian. Must be loop generate. Must contain Imaginary parts of CKM. Must be non-iagonal! -cannot be one-loop iagram. BUT: 2-loop zero if summe!

8 , s, b γ u, c, t u, c, t Figure: Typical iagram for EDM of -quark to lowest orer n /e α s 4π (G F) 2 Im(V ub V tbv t V u) F(m q, M ) Valence quark approximation: n = u, (Recent lattice calculation : n = u s ) Result (Czarnecki an Krause 1997): n /e cm

9 NEDM in SM- Pole mechanism Pole iagram mechanism (Orsay group, 1980 s) γ n Σ( ) Σ( 1 2 ) n Figure: EDM from pole iagram Nee quark moel at baryonic level..or other assumptions... n /e ( ) cm ;- epen on proucts of three (moel ep.) haronic matrix elements

10 NEDM as two loop The same pole iagrams at quark level as two loop iagrams. Also, b in loop. NB! : two-fol GIM cancellations ue to unitary CKM matrix ( Relics of SD effects). (JOE an I.Picek, Nucl Phys.B 1983) γ s s u u, c, t G u u Figure: Pole iagram at quark level 2-loop iagr. More iagrams of same orer! Result (eff. Lagrangian. Only one haronic matrix element!) : n /e cm

11 NEDM from chiral loop SM: Consiere Diagrams at haronic level with chiral loop (Khriplovich an Zhitnitsky, 1982) γ π + n Σ n Figure: Haronic iagram for NEDM. One of the blobs is a Penguin interaction, an one -exchange. n /e ( )cm ;- ep on har. matrix uncertainty. Anyway: SM preicts nedm 0

12 Other mechanisms for NEDM Mechanisms beyon the SM - often bigger than in SM (more complex phases) Examples: LR-symmetric moel(s) (many authors... in 1980 s... Recent: Maiezza an Nemevšek (2014) SUSY (many authors...) Barr-Zee mechanism (many authors), Still within SM: U(1) gluonic anomaly (θ term. Axions?)

13 γ L R g Figure: Typical iagram for EDM of -quark in SUSY For SUSY: Cancellations among contributions neee γ f f Figure: EDM for a fermion f within the Barr-Zee mechanism In aition einberg operator......an of course the QCD θ-term...(axions?)

14 Recent example: CPV in D-ecays? CP-violation in D PP within SM?? ū c, s, b G s, s, u ū Figure: Fig.12: D PP with Penguin mechanism in SM Small CKM factor an m 2 b << m2 t a CP -Saga. New Physics (2011) (Now 0?)

15 NP for D PP c u s, ū Φ8 s, ū Figure: Fig. 13: D PP with c u coupling New Physics?. Assumption by Altmannshofer et al: L eff = G(c u)ū L t A Φ A c R + X L t A R Φ A + h.c., Asymmetry,assuming max CPV phase Φ f,an strong phase δ f is a CP MΦ 2 m 2 K G(c u) X Assuming New Physics ;- shoul check NEDM

16 NEDM from EDM of -quark (New type iagr.) EDM of light (u, ) quarks (ith Svjetlana Fajfer) : c γ Φ c u Figure: NEDM from 2-loop iagram with c u coupling (M Φ 0.4 to 2 TeV). Expression for loop calculation (M Φ 0.4 to 2 TeV) connecte to parameters in a CP for D PP. Obtain: ( n /e) Φ 2 loop ( ) cm,

17 Flavor changing Higgs coupling? u, H u, q γ Figure: One loop iagrams with FC Higgs coupling. Quaratic in(y l,r )s FC coupling for fermions: f 1 f 2 + H in quark an lepton cases: ( f 1 an f 2 has same el. charge!). Example: b H coupling: L eff = Y R ( b) b L H R + Y L ( b) b R H L + h.c. Note: Not SU(2) L U(1) Y invariant alone (-incomplete). Y L (b ) = Y R ( b) an Y L (b ) = Y R ( b) Similar for other quarks, an for leptons (say e µ H). Note: SM has f 1 f 2 + H at one loop, BUT: Small!!

18 FC Higgs stuie by various authors: Guoelis, Lebeev an Park, Phys Lett B (2012) Blankenburg, Ellis an Isiori, Phys Lett B (2012) Harnik,Kopp an Zupan, JHEP (2012) Greljo, Kamenik an Kopp, JHEP (2014) Gorbahn an Haisch, JHEP (2014). Bouns on such FC Yukawa s from various processes, K K - an D D-, an B B-mixing, (Tree-level an one-loop box iagrams) In leptonic sector µ eγ an τ µγ (up to 2-loop) Bouns on Y s of orer 10 3 to This stuy : nedm from FC Higgs extene to two loop!

19 Two loop iagr. for EDM from FC Higgs u t H t t Figure: Three iagrams with FC Higgs coupling for EDMs of a -quark. Soft photon emission from one of the charge particles is assume to be ae. Left iagram gives contributions suppresse by m u, /M. Crosse iagrams in the center or to the right, give contributions not suppresse by light quark masses. The iagram to the right is the complex conjugate of the iagram in the center. H b b H t t NB! : Only one FC Yukawa an tth-coupling. t-quark in loop ominates!

20 b t H γ t γ b H t t b H t t γ b H t t γ Figure: Fig. 17: Four iagrams for an EDM of a quark obtaine by aing a soft photon to the iagram to the right of Fig. 3. The left iagram is the same as in Fig. 1, with obvious particle replacements. For the first three iagrams, there are also corresponing iagrams where the -boson is replace by an unphysical Higgs-boson within Feynman gauge. The first two iagrams are finite. The thir an fourth are log. ivergent NB : First orer in Y s. Big SM H-coupling to t-quark!

21 EDM for the -quark (ê i = charge of γ emitting part.) ( e ) i = ê i F S i Im[Y R ( b) Vt V tb ] ( ) F = g3 1 2 ( ) M 2 16π 2 = 2M2 1 2 v 3 16π cm, v 246 GeV. (Conversion: 1/(200 MeV) = cm ) Recall Y R ( b) < from other authors (B B -mixing,). Some terms log. ivergent ln(λ 2 ), some S i finite of orer one. Interaction of unphysical Higgs fiel φ for t transitions L φt = g M V t φ (m P L m t P R )t + h.c., an similar for t b transitions Terms with top quark ominate! m 2 t >> m 2 b u small!

22 νe? γ e ln(λ 2 ) u νe e γ ln(m 2 ) u Figure: Fig.18. QED correction to beta-ecay within Fermi-theory. -an with -exchange Ol example with cut-off: Non-renormalizable Fermi theory

23 There are terms m 2 t an even m 4 t for unphys Higgs terms. Logarithmic ivergence parametrize in terms of for Λ 1 to 3 TeV. Total contribution from Fig. 17 : C Λ ln( Λ2 M 2 ) to 8 ( e ) Fig.17 = ( C Λ ) F Im[Y R ( b) V t V tb ] Log. iv. easy to fol into next subloop. Finite terms more complicate. En up with integrals over one feynman parameter,- numerically.

24 Numerical integration S 1 = u C 0 C 0 (x) = 1 0 x [ (1 3x) u 2 (1 x)] (u 1)(1 x) H C 1 H ln(c 1 H ) + {ln C 1 C 0 H C 0 H ln(c 0 H )}. u x(1 x), C 1 C 1 (x) = 1+x(u 1). x(1 x) Mass ratios: u m2 t M 2, H M2 H M 2 ; S 2 = u(1+ u 2 ) 2(u 1) 1 0 ilog(z) = x(1 2x) { ilog( C 1 H ) + ilog(c 0 H )}, z 1 ln(t) t (1 t) = Li 2(1 z)

25 Diagrams 3,4 are log. ivergent in left subloop Log(r 2, x, y, masses) Λ = x (1 x) 0 y (ln(λ 2 ) 32 ) ln(r), R Q x(1 x)r 2 ; Q m 2 b + x(m 2 m 2 b) + y(m 2 H m 2 b). r 2 = loop momentum square for other sub-loop. Log(r 2, x, y, masses) Λ [ C Λ x (1 x) 0 y L Z (r 2, x, y, masses)) ], C Λ = ln( Λ2 ) + 1 M to 7.7 for Λ = 1 Tev to 3 TeV [ L Z (r 2, x, y, masses) = ln r 2 + ] Q ln(m 2 x(1 x) ).

26 Fin(r 2, x, y, masses) = i 16π x (1 x 0 ( r 2 ) p(x) y Q (1 x)r 2, p(x) is a secon orer polynomial in x. Fol into: J = r (r 2 M 2 )(r2 m 2 t) 2 Func(r2, x, y, masses), For Log- ivergent term x, y integration trivial. In general y-integration easy. Left with complicate integration over remaining Feynman parameter x.

27 S 3 = u 2(H b) 1 where the functions K are in general given by 0 x x (K(1, u; B 1 ) K(1, u; B 0 )) K(A, a; B) a (A a) ln(b) + a 2 (A a)(b a) ln(b a ) ( ) A 2 ilog( B ( ) A 2 A a A ) + [ 1] ilog( B A a a ) B 0 B 0 (x) b+x(u b) x(1 x) ; B 1 B 1 (x) H + x(u H) x(1 x). where b m2 b, u m2 M 2 t, an H M2 M 2 H M 2

28 S φ 3Z = u2 (H b) 1 where the Z-function is in general given by: 0 x x(1 x)[z(1, u; B 1 ) Z(1, u; B 0 )] Z(C, A; B) (A2 AB) C A ( ln(b) A + ln( B A ) ) (B A) + C(C B) (C A) 2 {1 B 2 [ln(b C)]2 + ilog( B C ) ln(c) ln(b C)} + [BC A(2C A)] (C A) 2 { 1 B 2 [ln(b A)]2 + ilog( B A ) ln(a) ln(b A)}

29 Only one FC Yukawa coupling -an H-coupling Big H coupling compensates for loop suppression H, u, u q q H, u, u q q, u, u (a) (b) (c) q q H Figure: Fig. 19. The three classes of with FC Higgs coupling. The (b) iagrams are zero (-or proportional to very small current quark masses) ue to chirality, an the (c) iagrams are complex conjugates of the (a) iagrams. Here q = s, b an q = u, c, t (with GIM-cancellations) for EDM of a -quark, an q = c, t an q =, s, b (with GIM) for EDM of a u-quark. Soft photon emission from charge particles shoul be ae

30 The relevant Higgs--coupling is then given by L H = g M 2 H ( )µ (+) µ For -boson in Feynman gauge, must a unphys. Higgs. Relevant Higgs--φ coupling L φh = g { } H(i µ φ ( ) ) (i µ H)φ ( ) ) µ (+) + h.c. 2 Derivative coupling implies momentum epenent vertex which create logarithmic ivercences. Nee as before the relevant φ--t coupling L φt = g M V t φ ( ) (m P L m t P R )t + h.c

31 EDMs for u, -quarks generate by FC Higgs γ u, H q q γ u, u, H q q u, γ u, H q q u, Figure: Fig. 20: Emission of a soft photon from (a)-type iagrams from previous Fig. There is also a iagram with emission from the in center of the iagram, an in aition aitional graphs with the replace by an unphysical Higgs NB! : First orer in FC Y couplings. Big H-couplings. Consier all quarks in loops.

32 EDM of -quark for γ-emission from q = s, b (Left iagram, finite!): ( /e) q = 2 ê s F Im{Y R ( s)[λ u (f(s, u) f(s, c)) +λ t (f(s, t) f(s, c))]} +2 ê b F Im{Y R ( b)[ξ u (f(b, u) f(b, c)) +ξ t (f(b, t) f(b, c))]} λ q = V qv qs, ξ q = V qv qb, q = u, c, t The f(q, q) s are finite integrals of orer one. ( Also with unphys Higgs φ inclue). GIM-cancellation among light quarks only: terms almost kille! But (c t)-case survives! ( c-quark term neee) f (b; t c) f(b, t) f(b, c) 0.34 Dominating term (NB! u small also in this case) ( /e) q 2 ê b F Im{Y R ( b)v t V tb} f (b; t c)

33 For the u-quark the EDMs are suppresse by a factor of orer 10 3 compare to the-quark EDM. The two next iagrams have the same GIM an CKM structure as the left. BUT: they have ivergent terms when φ. Total contribution from Fig. 20 : ( e ) Fig.20 (3.46 C Λ 9.35) F Im[Y R ( b) V t V tb ] For the u-quark the EDM is suppresse by a factor of orer 10 3 compare to the-quark EDM.

34 Result/Conclusion for nedm for FC Higgs ( e ) Tot = (4.83 C Λ 7.70) F Im[Y R ( b) V t V tb] Using experimental boun on nedm ; ForΛ 1 to 3 TeV [ Vt Im Y R ( b) V ] tb Vt V (2.0 to 3.2) tb to be compare to prev. authors (from B B -mixing): Y R ( b) Y R ( b) Boun Scale with this boun { YR (b ) n /e N Λ Im Y R (b ) Boun [ YR ( b) Y R (b ) Vt V ]} tb Vt V cm tb where N Λ = 0.31 (ln(λ 2 /m 2 ) 1.59).

35 Figure: The quantity N Λ as a function of cut-off Lamba (in TeV)

36 b t H H t b t Figure: Fig.20.The ivergent effective -loop vertex correction iagram relevant for iagrams of section III (left), an the (finite) effective vertex correction relevant for iagrams in section IV (right). FCH hypothesis extene to two loop case for EDM. ivergent sub-loops right-hane current) imply non-renorm. Only effective theory;- incomplete. Nee at the en SU(2) L U(1) Y symmetric Lagrangian. FC Higgs effective Lagrangian nees aitional couplings an (probably) aitional higher mass states.

37 Foun boun for the imaginary part of Y R ( b) of the same orer of magnitue as previously by other authors. (Note: Not coherent relative signs from the ifferent iagrams) Turne aroun, using the boun for Y R ( b) foun in previous papers, - a value for nedm not too far below the experimental boun cannot be exclue. However, effective theory, imply unprecise preictions.

38 u u H c, t γ Figure: Diagrams with FC Higgs coupling

39 Technical remark May often use effective propagator in soft el.-magn. fiel F µν : S eff (p, F) = ( eq 4 ) (2mσ F+{γ p,σ F}) (p 2 m 2 ) 2 Similarly for emission from a : (D 1 (k, F)) αβ = ( e 4 ) 3 i { g µα g νβ g µβ g να} F µν (k 2 M 2 )2 (1) Many loop iagrams suppresse because of chirality (P L P R = 0), or symmetric momentum integration: 4 p (4π) 4 f(p 2 ; masses) p µ = 0