Lepton flavour violation in RS models

Transcription

1 Lepton flavour violation in RS models P. Moch with M. Beneke and J. Rohrwild Theoretische Physik 1 Uni Siegen Outline: Introduction Strategy and formalism Results P. Moch (Uni Siegen LVF in RS PSI, Oktober /12

2 General Theory Overview Five dimensional Anti de Sitter spacetime with compact extra dimension ( 2 ds 2 1 = (η µνdx µ dx ν d 2 z kz ε T k TeV MPl 4d z [1/k, 1/T] Geometric solution of the gauge gravity hierarchy problem [Randall, Sundrum (1999] Natural mechanism for generation of flavour hierarchies [Grossman et al. (2000, Gherghetta et al. (2000, Huber et al. (2000 ] Compact fifth dimension quantises the 5th component of the momenta Kaluza-Klein towers for all bulk fields typical KK mass scale m KK 2.45T P. Moch (Uni Siegen LVF in RS PSI, Oktober /12

3 Models & Particle Content Minimal RS: only SM fields (promoted to 5D + Higgs localised near IR branes Custodial protected RS: extended gauge group SU(3 c SU(2 L SU(2 R U(1 X Z 2 custodial symmetry only broken by UV brane boundary conditions extended fermion sector (but no unique choice for fermion reps. ξ i 1L = ( χ ν i L (, + 1 χ l i L (, + 0 l ν i L (+, + 0 l l i L (+, + 1 ξ i 2R = ν R (+, + 0 ξ3r i = T3R i T4R i = λ i R (, + 1 Ñ i R (, + 0 L i R (, + 1 λ i R (, + 1 N i R (, + 0 E i R (+, + 1. Models where the Higgs leaks into the bulk (Bulk Higgs with KK Higgs modes P. Moch (Uni Siegen LVF in RS PSI, Oktober /12

4 Model Constraints Direct production: m KK > 2.45 TeV Higgs decay: m KK 4.9 (10 TeV for the minimal (custodial protected model [Hahn, Hörner, Malm, Neubert, Novotny, Schmell (2014] Gluon FCNCs: m KK 32 TeV for a fully anarchic Yukawa [Csaki, Falkowski, Weiler (2008] Electroweak precision observables S and T : 4.9 (10 TeV for the minimal (custodial protected model [B. Duling; S. Casagrande, F. Goertz, U. Haisch, M. Neubert, T. Pfoh] Direct production off KK excitations at the LHC not likely P. Moch (Uni Siegen LVF in RS PSI, Oktober /12

5 Lepton Transitions (g 2 µ and d e pure loop-induced effects in RS; flavour diagonal [M.Beneke, P. Dey, J. Rohrwild (2012] µ eγ pure loop-induced effects in RS; LFV [Agashe et al. (2006; Csaki et al. (2010] µ 3e tree + loop induced effects [Grojean et al. (2003; Csaki et al. (2010] µ e in nuclei tree dominated effects; [Chang & Ng (2005; Csaki et al. (2010] P. Moch (Uni Siegen LVF in RS PSI, Oktober /12

6 Strategy: Effective Field Theory Distinct hierarchy of scales k m KK }{{} UV v m l }{{} IR Strategy: integrate out the bulk by matching onto an SU(3 SU(2 U(1 Y invariant Lagrangian at a scale m KK µ v: L RS L eff = L SM + 1 m 2 KK C io i i [ M.Beneke, P. Dey J, Rohrwild],(2012 Relevant dim. six operators include C io i a B,ij L iφσ µνe jb µν + a W,ij L iτ a Φσ µνe j W a,µν i +b LE, ij ( L iγ µ L i(ē jγ µe j + c 1,i (Ē iγ µe i(φ id µ Φ + c 2,i ( L iγ µl i(φ id µ Φ + c 3,i ( L iγ µ τ a L i(φ iτ a D µφ +h ij (Φ Φ( L iφe j + b LτL,ij ( L iγ µτ a L i( L jγ µ τ a L j + b LL,ij ( L iγ µl i( L jγ µ L j + b EE,ij (Ē iγ µe i(ē jγ µ E j +... Dipole Operators Tree Operators P. Moch (Uni Siegen LVF in RS PSI, Oktober /12

7 EFT after EWSB ( Φ 1 φ + 2 (v + H + ig E i V ijp Rψ j, L i U ijp L ( νj ψ j Set of Diagrams contributing to radiative LFV (a (b (c1 (c2 (d1 (d2 (e1 (e2 (f1 (f2 similar set for µ eee [Crivelin et al., 2014] TASK: determine the Wilson coefficients P. Moch (Uni Siegen LVF in RS PSI, Oktober /12

8 5d Formalism Work in a five dimensional QFT no KK sums; vertices and propagators are 5D [Randall, Schwartz, 2001] Use mixed coordinate-momentum representation for propagators in the unbroken theory [Randall, Schwartz, 2001] propagators depend on 4D momentum and start/end coordinate in the 5th dimension L(p, x, y = P LF + L (p, x, y/pp R P RF L (p, x, y/pp L }{{} contains zero mode SM field Exact solution in the unbroken phase: + P Ld + F L (p, x, yp L + P Rd F + L (p, x, yp L }{{} mass term F L (p, x, y = ( ( ik 4 x 5/2 y 5/2 θ(x y K p ( c 1 Ic 1 (py I p 2 k 2 c 1 2 k ( p Ic 1 Kc 1 T ( ( p I c 1 2 T ( p T Kc 1 2 ( K p c 1 Ic 1 2 k ( p K c 1 (px K 2 c 1 I 2 T c 1 (px + (x y 2 ( p k (py P. Moch (Uni Siegen LVF in RS PSI, Oktober /12

9 EFT Matching: Diagram Classes Tree level diagrams: four fermion etc. Higgs contribution to dipole operator: strong dependence on Higgs and 5D parameters localisation (bulk Higgs vs. brane Higgs. Gauge contribution to dipole operator: numerically computed to one permille precision[rohrwild, Moch, 2014]. RS contribution UV insensitive P. Moch (Uni Siegen LVF in RS PSI, Oktober /12

10 LVF Minimal RS Model No significant reduction of the possibe range due to experimental d e constraint M KK > 5 TeV constraint due experimental limits Exclusion range of future Mu2e experiment up to M KK of 20 TeV [M. Beneke, P. Moch, J. Rohrwild, (2015 ] P. Moch (Uni Siegen LVF in RS PSI, Oktober /12

11 LVF Custodial Protected RS model M KK > 20 TeV due to experimental constraints [M. Beneke, P. Moch, J. Rohrwild, (2015 ] P. Moch (Uni Siegen LVF in RS PSI, Oktober /12

12 Conclusion Complete 5D computation of all dominant Wilson coefficients contributing to LVF First time fully 5D computation of the Higgs KK contribution M KK > 5 (20 TeV from the LVF for the minimal (custodial RS model Potential reach of future LVF experiment up too KK masses of 20 TeV 5D Wilson coefficients adaptable for further projects, for example B X s γ [P. Moch, J. Rohrwild Nucl.Phys. B902 (2016] EFT programs usable for different models [T. Feldmann, C. Luhn, P. Moch (2016] P. Moch (Uni Siegen LVF in RS PSI, Oktober /12