FLIGHT OF THE WARPED PENGUINS. In collaboration with Csaba Csáki, Yuval Grossman, and Yuhsin Tsai. Pheno 2011, 10 May 2011

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1 FLIGHT OF THE WARPED PENGUINS Phys. Rev. D83, arxiv: Cornell University In collaboration with Csaba Csáki, Yuval Grossman, and Yuhsin Tsai Pheno 2011, 10 May / Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 1/13 13

2 Warped Penguins UV finite 5D loops Anarchic flavor in Randall-Sundrum Defying anarchy in µ eγ Remarks on current work 2 / Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 2/13 13

3 Finiteness: naïve dimensional analysis 4D Naïve: d 4 k F γ µ F B log(λ) Really log divergent? No, finite. Here s why: Gauge invariance: q µ M µ = 0. Lorentz invariance: d 4 k /k = 0. k2n Indeed, M 4D Λ 2. Suspect that M 5D Λ 1 compactification shouldn t affect UV 5D bulk, i.e. d 4 k d 5 k Turns out to be correct, but brane fields make this very subtle. See our paper for the gory details 3 / Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 3/13 13

4 Lepton Flavor Violation Crimpin our free-wheeling model-building ways Br (µ eγ) SM = 0 Current bound: Br (µ eγ) < MEGA, LAMPF Later this year from MEG: Br (µ eγ) < / Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 4/13 13

5 Anarchic Flavor in RS Fermion Gauge Boson Y (4D) ij = f i Y ij f j f i = 1 2c i 1 (R/R ) 1 2c i Anarchy: Y ij are all O(Y ) with arbitrary phase. 5 / Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 5/13 13

6 Lepton Flavor Violation Controlled by two dominant parameters Flavor is dominantly controlled by: Y and M KK Y µ e Y Y M loop ( 1 M KK ( 1 M KK ) 2 f L Y 3 f E ) 2 Y 2 m 6 / Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 6/13 13

7 Lepton Flavor Violation Two dominant parmeters µ e e Z, Z Fermion µ e Gauge Boson Ti Z, Z e ( )2 ( ) 1 1 M tree M KK Y If we increase Y, must maintain SM mass spectrum push fermion profiles to UV Less overlap with the FCNC part of the Z 7 / Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 7/13 13

8 Complementary tree- and loop-level bounds Possible tension between tree- and loop-level processes Tree-level bound: ( ) 2 ( ) 3 TeV 2 < 0.5, 1.6 (Custodial) M KK Y Penguin bound: 2 ay + b ( ) 2 3 TeV M KK What the heck is this? Can test anarchic flavor ansatz. 8 / Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 8/13 13

9 Operator analysis of µ eγ Match to 4D EFT: R 2 e 16π 2 v ( 2 f Li akl Y ik Y kl Y ) lj + b ij Y L(0) ij f Ej i σ µν E (0) j F µν (0) Y ij is a spurion of U(3) 3 lepton flavor Indices on a ij and b ij encode bulk mass dependence Flavor structure a ij Y ik Y kl Y lj gives a generic contribution Depends only on Y and M KK New: b ij Y ij is aligned up to structure of b ij f i Y ij f j m ij, so this term is almost diagonal in the mass basis This depends on the particular flavor structure of the anarchic Y 9 / Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 9/13 13

10 Leading order diagrams H ± H ± L µ E i Z E e L j E e E µ L e L e ν N Y E Y N Y N Y E Y E Y E Z Y E Three coefficients (a H, a Z, b) with arbitrary relative signs Defined ay 3 = k,l a kly ik Y kl Y lj and by = k,l (U L) ik b kl Y kl (U R ) lj So, just calculate these: (many details in paper) We use 5D position/momentum space no cutoff ambiguity. 10 / Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 10/13 13

11 Representative Bounds: b = 0 Y * (Left of this ruled out) ( ) 2 ( ) 3 TeV 2 M KK Y < 0.5, 1.6 Generic Custodial a H a Z µ eγ, average ay 2 + b ( 3TeV M KK ) 2 < For M KK = 3 TeV, b = 0 a =.001 and generic 3.7 Y 4 a =.016 and custodial 1 Y M KK (TeV) 11 / 13 KK bound Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 11/13

12 Representative Bounds: b 0 Y * (Left of this ruled out) ( ) 2 ( ) 3 TeV 2 M KK Y < 0.5, 1.6 Favorable b µ eγ, b = b 1σ (Above this ruled out) µ eγ, average ay 2 + b ( 3TeV M KK ) 2 <.015 µ eγ, b = + b 1σ M KK (TeV) 12 / Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 12/13 13

13 Further directions and conclusions µ eγ in a warped extra dimension: Finite at one-loop, suspect perturbative Near tension between loop- and tree-level bounds on Y, M KK Sensitive to specific structure of anarchic matrices Open questions: b sγ penguin and heavy flavor structure in progress with M. Blanke, B. Shakya, Y. Tsai Two-loop contribution and perturbativity Effect of loop-level brane-localized terms Thanks! 13 / Flip Tanedo pt267@cornell.edu Warped Penguins: the Empire Strikes Back 13/13 13