Andreas Crivellin Effective Field Theory, Higgs-quark couplings and Dark Matter Direct Detection in the MSSM

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1 Andreas Crivellin Effective Field Theory, Higgs-quark couplings and Dark Matter Direct Detection in the MSSM Supported by a Marie Curie Intra-European Fellowship of the European Community's 7th Framework Programme under the contract number (PIEF-GA ).

2 Outline: Introduction: Effective Filed Theories Matching Running / Mixing Effective Higgs vertices in the MSSM Resummation of chirally enhanced corrections 2-loop SQCD calculation Loop effects in Dark Matter direct detection Dark Matter scattering in the natural MSSM Higgs contributions Squark contributions Conclusions 2

3 Introduction: Effective field theory approach 3

4 Why EFT methods: Properly connect physics at different scales via Matching of the high energy theory Running, Mixing and threshold correction Calculation of the low-energy observables Separation of UV and IR physics important for QCD processes (modular approach) Beyond the Standard Model the EFT can be used to correlate different experiments Can be easily extended to account for DM, righthanded neutrinos, 4

5 EFT for Low Energy Processes (Flavour, DM direct detection, etc.) Matching at the high scale Λ (electroweak or new physics scale) on the effective operators Determination of the Wilson coefficients Calculation of the anomalous dimension Renormalization group evolution to the low scale Calculation of the matrix elements Determination of the observables 5

6 Full Theory and Effective Theory Full theory: Contains all fields of the UV complete theory as dynamical degrees of freedom. Effective theory: Only contains the light particles as dynamical fields. Matching scale: Scale of some (heavy) particles at which the full and the effective theory are compared. Threshold correction: Difference between the coefficient of an operator in the effective and in the full theory.

7 Evolution of Wilson coefficients Running: Scale dependence of a Wilson coefficient in the effective theory (most times induced by QCD effects). Mixing: Scale dependence in the case of a matrix valued evolution for the Wilson coefficients Anomalous dimension: Divergent part of the loop diagrams generating running and mixing Renormalization Group Evolution: Solution to the differential equation for the running/mixing Resummation of large logs e.g. α n s log n µ µ high log

8 Matching Example: Fermi Theory Full Theory EFT p p g + µν m p µ ν 2 W 2 2 mw g m 1 + O µν 2 4 W mw

9 Example: b sγ matching Wilson Coefficients C, C,

10 Example: b sγ running and mixing mixing O O running O Evolution to the low scale

11 Higher dimensional operators beyond the SM NP at the scale Λ>v must be invariant under the SM gauge group The heavy degrees of freedom can be integrated out T. Appelquist, J. Carazzone The resulting effective operators must be Lorentz invariant, respect the SM gauge group and are suppressed by powers of 1/Λ. B. Grzadkowski et al., arxiv: W. Buchmüller, D. Wyler, Nucl.Phys. B268 (1986)

12 Operator classification L L 1/ C Q 1/ C Q O 1/ Dim 5: 1 operator, the Weinberg operator j m k T n T jk mn p r p r ( ) ( ) ( l l ) Qνν = ε ε ϕ ϕ Cl = ϕ l C ϕ Dim 6: 59 operators 30 four-fermion operators 4 pure field-strength tensor operators 3 SM-scalar-doublet operators 8 Higgs-field-strength operators 3 Higgs-fermion operators 8 magnetic operators 8 Higgs-fermion-derivative Q Q ϕ = ( ϕϕ ) = ϕ ϕlϕe ϕe i j 3 ( ) = + Λ + Λ + Λ (4) (5) (5) 2 (6) (6) 3 SM SM k k k k k k ( γ )( µ µ γ ) Q = l l e e le p r s t eb i µν j Q = f G G G G A A Q G G G µν ϕ µν = ϕ ϕ Q =lσ e ϕb µν Q ( ) µ = ϕ D ϕl γ l 1 ϕ l µ i j ABC Aν Bρ Cµ µ ν ρ 12

13 General procedure Perform EW symmetry breaking Derive the Feynman rules Calculate the Feynman diagrams Perform the matching (integrate out W,Z, t and h) RGE evolution to the low scale Calculation of decay width, cross sections, etc. 13

14 (Effective) Higgs-quark vertices in the MSSM 14

15 Loop corrections to Higgs quark couplings Before After electroweak symmetry breaking H d H u d A µy d di d f d i d f d LR H H fi A Γ d v d d d Σ = Γ f d i f d i Σ = Γ d LR H H fi Y Γ d v d u d d One-to-one correspondence between Higgs-quark couplings and chirality changing self-energies. (In the decoupling limit) f u i f u i 15

16 SQCD self-energy: iσ 0 = ( ) q LR fi q LR 2 * 2 2 Σ fi = αs m gɶ W fs W i+ 3,s B 0 m gɶ,m qɶ 3 π Finite and proportional to at least one power of 2 Σ = α m W W W W C m,m,m 3 ( ) q LR q q* q LR q q* fi s g fs js jl l 3.t i 3,t 0 g q q + + s t π ɶ ɶ ɶ ɶ decoupling limit ( ) q LR fi s

17 Decomposition of the self-energy Decompose the self-energy d LR d LR d LR Σ ii = Σ ii A + Σ i i Y into a holomorphic part proportional to an A-term 2 Σ = v α mɶw W A W W C m ɶ,m ɶ,m s ɶ 3 π non-holomorphic part proportional to a Yukawa ( ) d LR d d* q d d* fi A d s g fs js jl lt it 0 g q q 2 = µα 3 π ( ) g q q Σ d LR d d* d d d* fi Y ɶ ɶ ɶ ɶ j vu s mgwfs Wjs Y WjtWit C0 m, m, m s t t Define dimensionless quantity ε = Σ v Y d d LR i ii Y u d i which is independent of a Yukawa coupling

18 Chargino self-energy: χɶ ± iσ 0 ± = ( ) d LR fi χɶ di df uɶ s 1 6 LR u RL u RR d LL 2 2 d d 33 s 33 t 33 0 u u 16π s,t= 1 ( ) ( 2 ) u * Y V V C, m ɶ,mɶ ± χɶ d3 CKM 0 * 3 Σ = µ Y V f 3 2 3f µ s 6 ( ) ( 2 2 ) d LL 2 Vs f 3 m qɶ,, 2 2g2 sin β MWM2 C0 µ M s s= 1 t

19 Renormalization I All corrections are finite; counter-term not necessary. Minimal renormalization scheme is simplest. Mass renormalization m di ( 0) d LR d d ii i = v Y + Σ = v Y + Σ + v tan Y ε d ( ) ( ) i 0 q LR di ( 0) d ii A d β d i Y d ( 0) i = d m d i Σ q LR ii A ( ( ) d + β ε ) v 1 tan i tan(β) is automatically resummed to all orders

20 Renormalization II Flavour-changing corrections important two-loop corrections A.C. Jennifer Girrbach q LR Σ Σ 2 2mq mq U q LR q LR mq q LR 2 q L 1 Σ q RL 12 1 q LR = Σ21 Σ 2 23 mq 2mq mq 1 Σ Σ 1 Σ m q q RL q RL q RL q RL 31 + Σ32 mq mq mq Σ 1

21 Renormalization III Renormalization of the CKM matrix: ( 0 ) V = U u L V U d L Decomposition of the rotation matrices q L U = U q L q L Corrections independent of the CKM matrix CKM dependent corrections U u L CKM ɶ VU CKM ɶ u L V = U CKM V V d L CKM ( ) U CKM ( 0) Vɶ = + U d L CKM 0 13,23 13,23 1 ε FC

22 Effective gaugino and higgsino vertices No enhanced genuine vertex corrections. Calculate d εd, εfc, Σ q LR,Σ q LR ii Y ii CKM i Determine the bare Yukawas and bare CKM matrix Insert the bare quantities for the vertices. U fi Apply rotations q L, R to the external quark fields. Similar procedure for leptons (up-quarks) i

23 Chiral enhancement q LR d LR 1 fi v A d ( ) d( 0) Σfi = tan β Yi δ ij + 50 MSUSY 50 M d ij SUSY For the bottom quark only the term proportional to tan(β) is important. tan(β) enhancement Blazek, Raby, Pokorski, hep-ph/ For the light quarks also the part proportional to the A-term is relevant. 1 Σ = v tan β Y m 100 d LR ( ) b( 0) 33 Y d b tan ( β) O 100 d LR d Σ = O ( 1), A M 22 A 22 SUSY d LR d 1 Σ = O ( 1), A M A 11 SUSY

24 Higgs vertices in the EFT I H d H u µy d i new d i Y d i di di di H d d A fi d LL fi H u µy d f H u Y d i d RR µ fi d i d f di d f di d f

25 Higgs vertices in the EFT II (( d d ) d Y δ + E E ) L = Q ε H + H d eff a b a* Y f L i fi fi ba d fi u i R Non-holomorphic corrections E = Σ v d d LR fi fi Y u Holomorphic corrections E = Σ v d d LR fi fi A d ( ) i E m = v Y δ + + v E d d d d fi d fi fi u fi The quark mass matrix is no longer diagonal in the same basis as the Yukawa coupling Flavor-changing neutral Higgs couplings

26 Σ ɶ = U Σ Effective Yukawa couplings Final result: U Y d LR d L* d LR d R jk Y jf jk Y ki 1 = δ Σ ɶ ( d LR m ) d eff ij di ij ij Y vd with d LR d LR Σ22 Y Σ d LR 33 Y d LR 0 Σ12 Σ13 md m 2 d3 d LR d LR Σ d LR 22 Y Σ d LR 33 Y d LR Σfi Y Σ21 0 Σ 23 md m 2 q3 d LR d LR Σ33 Y Σ d LR 33 Y d LR Σ31 Σ32 0 md m 3 q3 Diagrammatic explanation in the full theory:

27 Higgs vertices in the full theory Σ H 0 k d LR 32 vv Y q 2 3 d 0 H k Y d A d 32 0 H k Σ 0 H k d LR 32 A A q 23 Σ d LR 32 A Σ q 23 LR A q d 2 3 d 3 q 2 d 2 v d d 3 q 3 q 2 qd 3 2 v Y d d 3 m d 3 d3 Cancellation incomplete since vdy md3 d LR Part proportional to Σ33Y is left over. A-terms generate flavor-changing Higgs couplings

28 NLO Calculation 28

29 NLO calculation of the quark self-energies NLO calculation is important for: Computation of effective Higgs-quark vertices. Determination of the Yukawa couplings of the MSSM superpotential (needed for the study of Yukawa unification in GUTs). NLO calculation of FCNC processes in the MSSM at large tan(β). Reduction of the matching scale dependence 29

30 NLO calculation NLO calculation includes analytic results and tan(β) resummation in the generic MSSM. 2 at order b α s Examples of 2-loop diagrams 30

31 NLO results NLO LO Relative importance of the 2-loop corrections approximately 9% 31

32 Extension to the NMSSM A.C., Youichi Yamada, arxiv:

33 NMSSM Additional gauge singlet Superfield S The mu term of the MSSM superpotnential is generated by the vacuum expectation value of the scalar component of this singlet µ λv S = Extended Higgs sector Higgs mass can be generated with less fine tuning The mostly singlet does not couple to SM fermions at tree-level and can be very light 33

34 Gluino contribution S dd λ Γ = Σ µ eff LR dd 34

35 Chargino contribution + 35

36 k k Solution with Dyson series + µ + µ eff 2 2 eff Odd power of = + µ eff + µ eff µ eff +... k k k k k k µ * µ eff + µ eff µ eff µ eff +... = k k k k k k k k µ λs One replaced by eff λs + λ µ µ + k k k k k k k 2 1 µ eff = λs + k µ eff k µ * 2 S eff eff... ( ) eff 2 µ + eff µ 2 2 eff

37 Effective field theory approach to Dark Matter A.C., F. d Eramo, M. Procura, arxiv: A.C., M. Hoferichter, M. Procura arxiv: A.C., U. Haisch, arxiv:1408:

38 Direct/inderect Detection and LHC searches Same couplings and particles, but at different energy scales LHC and direct detection mainly sensitive to quark couplings 38

39 Spin independent scattering SI N cross section Up to Dim 7 (at the direct detection scale) m m σ + πc f 2 N VV N N SS N S N C 12 4 qq fv C q qq f q gg Q π q= u, d q= u, d, s Λ Λ 2 L O eff X X X S gg = C O αs = G G 3 χχ µν Λ µν f N m N : nucleon couplings : nucleon mass m SS q Oqq = χχqq Λ 3 VV 1 µ Oqq = χγ χqγ q 2 µ Λ The Wilson coefficients C X must be connected to UV physics 39

40 Scalar quark content of the nucleon Tradiational approach: SU(3) chiral pertubation Better: SU(2) chiral pertubation theory and f s from lattice our result SU( 3) with fs n f u n f d SU( 3) 40

41 EFT for Dark Matter We assume that DM is: A SM singlet (other choices are also possible) A Dirac fermion (biggest number of operators) Interactions of DM with the SM arise through messengers at a high scale Λ Construct operators which are invariant under the SM gauge group This scale Λ must be connected to the direct detection scale via running, mixing and threshold effects. 41

42 Operators dim T µν 5 O, S, P M = χσ χ Bµν OHH = χχh H OHH = χγ χh H Λ Λ Λ T O M P O HH S O HH : : : Matching: Tree-level contribution to direct detection Affects only spin dependent direct detection Enters only via matching corrections C C S gg SS qq 1 Λ = 12π m Λ = m 2 2 h ( 5) ( 4) ( µ ) h 0 C C S HH S HH Mixing turns out to be small 1 Λ C U U C b t b 12π m 0 h ( ) ( ) n f 3C α F s Λ U µ, Λ = ln. πβ α µ 2 SS S qq ( µ 0 ) = m, m + 2,m 1 2 HH 0 s ( ) 42

43 VV 1 µ Oqq = χγ χ qγ q 2 µ Λ VA 1 µ 5 Oqq = χγ χ qγ q 2 µ γ Λ i O = χγ χφ D φ Λ V µ φφ D 2 µ Operators dim-6 No QCD effects VA O qq EW-mixing of into V O HHD V V α N VA µ Cφφ D µ Cφφ D Ctt t b π Λ ( ) ( ) t c = Λ ( Λ)ln ( ) Matching contributions VV VV 1 V VV VV 1 V Cuu Cuu + CHHD, Cdd Cdd CHHD 2 2 Bounds on previously unconstrained operators 43

44 Experimental constraints C VA = qq 1 XENON1T supercdms LUX LHC relic density 44

45 Operators dim-7 Field strength tensors especially interesting 1 1 OB = χχ B B, O = χχw W Λ Λ Mixing into µν µν 2 µν W 2 µν O O S φ φ qq 1 = Λ Y = Λ 3 q 3 χχφφ φφ χχqφq Contributions to direct detection after EW symmetry breaking and integrating out the Higgs. 45

46 Constraints on C WW Interesting interplay between direct detection and LHC searches

47 Dark Matter Direct Detection and LHC searches in the MSSM A.C., M. Hoferichter, M. Procura and L. C. Tunstall, Light stops, blind spots, and isospin violation in the MSSM, arxiv: [hep-ph]. 47

48 Naturalness and MSSM spectra Standard model like Higgs discovered Lepton sector unimportant for direct detection 2 nd Higgs light? Light stops (and sbottoms)? 48

49 SM Higgs only 49

50 SM and heavy Higgs Blind spot: Different contributions cancel Cheung et al. Huang & Wagner 50

51 Light Stop 51

52 Stop and heavy Higgs 52

53 Conclusions Effective Field Theories simplify the calculations and allow for a consistent treatment of QCD effects. EFTs can be used to explore systematically physics beyond the SM Effective Higgs-quark vertices in the (N)MSSM can be determined by a matching on a 2HDM (+singlet), allowing for a resummation of tan(beta) enhanced effects. Interesting loop effects in DM direct detection: new constraints on operators The natural MSSM posses blind spots and is a prime example for the interplay between different searches 53