Les Rencontres de Physique

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1 Anreas Crivellin ITP Bern Chirally enhance self-energies energies in the MSSM Les Rencontres e Physique e la Vallée Aosta 011 Effective Higgs Vertices in the generic MSSM. Anreas Crivellin, arxiv: [hep-ph] Raiative Flavor-Violation in the MSSM Raiative Flavor Violation in the MSSM Anreas Crivellin, Lars Hofer, Doinik Scherer an Ulrich Nierste, arxiv:1103.xxxx [hep-ph]

2 Outline: The SUSY flavor-proble Self-energies energies an the origin of chiral enhanceent Renoralization an tan(β) resuation. Flavor-changing neutral Higgs vertices Raiative flavor-violation in the MSSM

3 Quark asses Top quark is very heavy. v Botto quark rather light, but Y b can be big at large tan(β) All other quark asses are very sall sensitive to raiative corrections t u c s b 3

4 CKM atrix is the only source of flavor an CP violation in the SM. No tree-level FCNCs. Off-iagonal CKM eleents are sall Flavor-violation violation is suppresse in the SM. CKM atrix V V V u us ub V = V V V CKM c cs cb V V V t ts tb 4

5 SUSY flavor (CP) proble The squark ass atrices are not necessarily iagonal (an real) in the sae basis as the quark ass atrices. Especially the trilinear A-ters can inuce angerously large flavor-ixing i (an coplex phases) since they on t necessarily posses the suppression of the SM. The MSSM possesses two Higgs-oublets: Flavour- changing charge an (loop-inuce) neutral Higgs interactions. Possible solutions: -MFV D Abrosio, Giuice, Isiori, Struia hep-ph/ ph/ effective SUSY Barbieri et at hep - Raiative flavour violation Barbieri et at hep-ph/ ph/

6 heritian: q M % LL,RR Squark ass atrix M M Δ = q % qlr % LL q% qlr % q % Δ MRR W M W = M q % q% (D) q% q% involves only bilinear ters (in the ecoupling liit) The chirality-changing changing eleents are proportional to a vev Δ = v LR ij ( β) ( ( 0) ) μtan Yi δ ij+ Aij ( β ) u LR ( u( 0) u cot + ) ij = vu μ Yi δij Aij Δ + tan ( ) β = v v u 6

7 Mass insertion approxiation (L.J. Hall, V.A. Kostelecky an S. Raby, Nucl. Phys. B 67 (1986) 415.) Useful to visualize flavor-changes in the squark sector q q AB Δ ij = u, off-iagonal eleent of the squark ass atrix i, j flavor inices 1,,3 A,B chiralitys L,R % B q i Δ i qab fi % A q f 7

8 SQCD self-energy: energy: ( ) qlr fi Σ i 0 = qlr * Σ fi =αs WW g% fs i+ 3,s B 0 g%, q% 3 π ( ) Finite it an proportional to at least one power of Σ =α WW Δ WW C, s, 3π ecoupling liit s qlr Δ fi ( ) qlr q q* qlr q q* fi s g% fs js jl lt it 0 g% q% q% t 8

9 Decoposition of the self-energy energy Decopose the self-energy Σ =Σ +Σ LR LR LR ii ii A ii Y into a holoorphic part proportional to an A-ter Σ LR = * q * fi A v α s gwfs Wjs AjlWlt Wit C0 g, q, s q 3π π % % % % non-holoorphic part proportional to a Yukawa ( ) LR j fi Y = vuμαs WW g fs js Y WW jt it C0 g, q, s 3 π LR Σ i ii Y Define iensionless quantity ( ) q Σ * * % % % % ε = i vy which is iensionless an inepenent of a Yukawa coupling u i t t 9

10 Renoralization I All corrections are finite; counter-ter not necessary. Minial renoralization schee is siplest. Mass renoralization i ( 0) LR = v Y +Σii i = vy +Σ + v tan Y ε Y ( ) ( ) i 0 qlr i( 0) iia β i ( 0) i i = Σ qlr iia ( β) ( + ε ) v 1 tan tan(β) is autoatically resue to all orers i 10

11 Renoralization II Corrections to the CKM atrix: ( 0) V = U V U CKM u L* CKM L fi jf jk ki qlr Σ1 1 qlr 1 1 Σ Σ q q q3 q LR 1 Σ1 1 U = Σ 1 Σ q q q3 qrl qrl 1 qrl Σ3 Σ1 1 qrl Σ31 + Σ3 1 q 3 q q 3 q3 qlr 1 13 ql qrl qlr 1 3 iportant two-loop corrections A.C. Jennifer Girrbach

12 Chiral enhanceent qlr LR 1 Δfi v A ( 0) ij fi tan ( β) Yi ij 50 MSUSY 50 MSUSY Σ = δ + For the botto quark only the ter proportional to tan(β) is iportant. tan(β) enhanceent Blazek, Raby, Pokorski, hep-ph/ ph/ For the light quarks also the part proportional to the A-ter is relevant. 1 ( ) Σ = v tan ( β) Y 50 LR b 0 33 Y b O tan ( β) 50 LR Σ = O ( 1 ) A M A SUSY LR 1 Σ = O() 1 A M A 11 SUSY 1

13 Flavour-changing corrections Σ q qlr fi ( ) ax f,i V CKM fi V : A M CKM q cb 3 SUSY V : A M 10 CKM q 1 ub 13 SUSY V : A M 10 CKM q 1 us 1 SUSY Flavor-changing g A-ter can easily lea to orer one correction. A.C., Ulrich Nierste, hep-ph/ ph/

14 Higgs vertices in the EFT I H H u μy i μ new i Y i i i i H A fi LL Δ fi H u μy f i μy H u RR Δ fi i f i f i f 14

15 Higgs vertices in the EFT II ( ( Y δ + ) ε + E ) fi L eff a b a* Y = Qf L i fi E ε fi bah + Hu ir Non-holoorphic corrections Holoorphic corrections E fi E Σ fi = LR fi A Σ LR fi Y v u ( ) i Y δ + E fi = v + vu E fi fi fi Y E The quark ass atrix is no longer iagonal in the sae basis as the Yukawa coupling = Flavour-changing neutral Higgs couplings v u 15

16 Effective Yukawa couplings Final result: Y = 1 δ Σ% LR ( ) eff ij i ij ij Y v with Σ Σ 0 3 LR LR Σ Y Σ33 Y Σ % = U Σ U Σ Σ 0 Σ q3 LR LR Σ33 Y Σ LR 33 Y LR Σ31 Σ3 0 3 q3 LR LR Y LR 33 Y LR Σ1 Σ13 LR L* LR R LR LR LR jk Y jf jk Y ki fiy 1 3 Diagraatic explanation in the full theory: 16

17 Higgs vertices in the full theory Σ 0 H k H 0 k LR 3 A 3 0 H k 0 H k A q 3 v q LR v 3 Y Σ3 A v q Σ LR 3 3 A q 3 q Σ qlr 3 q q 3 q 3 3 q 3 vy Cancellation incoplete since vy 3 LR Part proportional to Σ 33Y is left over. A-ters generate flavor-changing Higgs couplings 17

18 Raiative flavor-violationviolation SU()³ flavor-syetry in the MSSM superpotential: CKM atrix is the unit atrix. syetry in ( 0) VCKM = q 1 Y = v q 0 0 q Only the thir generation Yukawa coupling is ifferent fro zero. 3 All other eleents are generate raiatively using the trilinear A-ters! 18

19 Features of the oel Aitional flavor syetries in the superpotential. Explains sall asses an ixing angles via a loop- suppression. Deviations fro MFV if the thir generation is involve. Solves the SUSY CP proble via a anatory phase alignent. (Phase of μ enters only at two loops) Borzuati, Farrar, Polonsky, Thoas The SUSY flavor proble reuces qlr qlr to the eleents δ, δ 3 31 Can explain the B s ixing phase 19

20 CKM generation in the own-sector:! LR 13 b ub Σ =V! LR 3 b cb Σ =V Constraints fro b sγ. Chirally Chirally enhance corrections ust be taken into account. A.C., Ulrich Nierste 009 δ LR, δ LR 31 3 less constraine since they contribute to C7,C8. LR δ μ 3 can explain the CP b ( β ) phase in B s ixing. b ( β) (not possible in MFV) ( β) can explain the CP μ tan = 0.1TeV μ tan = 0TeV μ tan = 0.1TeV b 0

21 Higgs effects: B s μμ Constructive contribution ue to Σ =V LR 3 b cb ε b = ε b = 0.01 ε b = ε b = 0.01 tan Β H 1

22 Higgs effects: B s ixing Contribution only if V Σ RL R 3 3 = 0 b ue to Pecci-Quinn syetry ( β ) tan = 11 ( β ) tan = 14 ( β) tan = 17 ( β) tan = 0 I V V R R Re V R

23 CKM generation in the up-sector:! ulr * 13 t t Σ = V! ulr * 3 t cb Σ =V Constraints fro Kaon ixing. ulr ulr δ31, δ3 unconstraine fro FCNC processes. ulr δ 31 can inuce a sizable right-hane hane W coupling. A.C. 009 M M = 00GeV M = 400GeV M = = 400GeV 800GeV 3

24 BR K L ΠΝΝ M 00 GeV M 400 GeV M 600 GeV Effects in K πνν M 800 GeV SM value q in GeV Verifiable preictions for NA6 BR K Π ΝΝ M 00 GeV M 400 GeV M 600 GeV M 800 GeV SM value q in GeV 4

25 Conclusions The MSSM possesses any new sources of flavor an CP violation Self-energies energies can be chirally enhance an of orer one. Flavour-conserving non-holoorphic corrections inuce flavour-changing neutral Higgs couplings proportional to A- ters. Self-energies energies have physical effects. Raiative flavor-violation violation in the MSSM is a interesting solution to the SUSY CP an SUSY flavor proble. Constraints fro b sγ an Kaon ixing are satisfie for SUSY asses O(1TeV). Large effects in K πνν are possible. B s ixing phase can be explaine. 5