Vector-like quarks at. the TeV scale

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1 Dopustne uporabe logotipa v vertikalnih in horizontalnih pozicijah at Univerza v Ljubljani the TeV scale Univerza v Ljubljani Universitas Labacensis Jožef Stefan Institute Department of Theoretical Physics Advisor: prof. dr. Svjetlana Fajfer Coadvisor: dr. Jernej Kamenik Samo v primeru horizontalnih formatov Univerza v Ljubljani Ljubljana,

2 Particle Content Electroweak Unification The CKM Mechanism

3 Particle Content of the Standard left handed up and down quarks observed to interact via W bosons Particle Content Electroweak Unification The CKM Mechanism u L and d L form a doublet of an ( SU(2) ) L ul group: q L = u R and d R are invariant, they don t interact through W s SU(2) singlets d L

4 gauge group SU(3) C SU(2) L U(1) Y Nobel Prize in 1979 for the GSW theory of electroweak unification SU(2) L U(1) Y spontaneously broken to U(1) EM via Higgs mechanism Particle Content Electroweak Unification The CKM Mechanism

5 The CKM Mechanism in 1963 Nicola Cabbibo introduced a mixing angle between 1 st and 2 nd generation quarks weak interactions between quarks of different generations physical states (mass states) are superpositions of weak (flavour) eigenstates Particle Content Electroweak Unification The CKM Mechanism (ū L, c L, t L ) L mass = Yu ij i j q L φu R Y ij d q L i φd j R + h.c. 2 v Y u u R c R t R diagonalization: v 2 Y u = L um u R u

6 The CKM Mechanism weak interactions in the SM: neutral current u i charged current u i Particle Content Electroweak Unification The CKM Mechanism δij Z 0 Vij CKM W + u j d j

7 The CKM Mechanism weak interactions in the SM: neutral current u i charged current u i Particle Content Electroweak Unification The CKM Mechanism δij Z 0 Vij CKM W + u j d j L u, L d unitary no flavour changing neutral currents (FCNC s)! L u L d = V CKM nonunitarity of CKM matrix new physics!

8 for New Physics flavour hierarchy = distribution of fermion masses hierarchy/naturalness problem (Higgs mass) m 2 h = m2 h,0 + 3λ 16π 2 Λ 2 h need new physics at the TeV scale B.Dobrescu, LHC European School of High Energy Physics

9 introduce New Physics by adding new particles minimal way but applicable to numerous models focus on vector-like (= non-chiral) quarks under SU(2) BOTH chiralities singlets, or both doublets, etc.

10 introduce New Physics by adding new particles minimal way but applicable to numerous models focus on vector-like (= non-chiral) quarks under SU(2) BOTH chiralities singlets, or both doublets, etc. have them in models with extra dimensions Little Higgs model some Grand Unified Theories theories of strong EWSB with partial compositeness, etc.

11 introduce New Physics by adding new particles minimal way but applicable to numerous models focus on vector-like (= non-chiral) quarks under SU(2) BOTH chiralities singlets, or both doublets, etc. have them in models with extra dimensions Little Higgs model some Grand Unified Theories theories of strong EWSB with partial compositeness, etc. mix with SM quarks and modify couplings indirect way to observe them powerful tool:

12 Example: (within SM) Fermi s theory of weak interaction get four-quark point interaction, dim 6 at low energies W is not dynamical W propagator = ( 1 k 2 Mw 2 g µν kµkν M 2 w ) 1 M 2 w +...

13 SM valid up to a scale Λ L eff = L SM + C i Λ 2 O i +... integrate out heavy degrees of freedom, obtain higher dim operators impose SM symmetries, no dim 5 (1/Λ term) because of Lepton and Barion number conservation all information on heavy degrees of freedom inside Wilson coefficients C i C i enter analytical expressions of our observables

14 Vector-like singlet T (charge 2/3) singlet B (charge -1/3) doublet Q = (U,D) triplets in colour ( quarks ) couple them to all three generations analyse the implications one by one

15 L T = T (i /D M T )T [Y u i q L i φt + Mt i T u R i + h.c.] analogy: Dirac Lagrangian L = ψ(i / m)ψ Dirac mass terms possible because of non-chiral nature of T s Field Mass Field SM symmetry allows coupling to up quarks through Yukawa (and also Dirac) terms enlarged Yukawa/mass matrices new diagonalization process CKM matrix modified! additional rotation of states effects in gauge sector

16 L eff = L SM + C i Λ 2 O i +... in this case, the O i s represent for quark-gauge boson interactions, and for interactions of quarks with the Higgs boson

17 new gauge operators + modified CKM check weak couplings!

18 new gauge operators + modified CKM check weak couplings! neutral current u i Xij Z 0 u j charged current u i Wij W + d j

19 new gauge operators + modified CKM check weak couplings! neutral current u i Xij Z 0 Higgs u i Yij H u j charged current u j u i d j Wij W + (X, Y ) ij δ ij + v 2 terms, MT 2 W CKM + v 2 terms MT 2

20 non-diagonal Higgs coupling because bare mass term present going to mass basis doesn t diagonalize the 3 3 Yukawa matrices T u i H would uniquely signal vector-like nature of T

21 non-diagonal Higgs coupling because bare mass term present going to mass basis doesn t diagonalize the 3 3 Yukawa matrices T u i H would uniquely signal vector-like nature of T Other possibilities adding a B instead of T gives FCNC s in DOWN sector a Q gives Right Handed charged currents and RH FCNC s

22 Where to look... direct bounds from t decays within SM branching ratios of t u i Z /γ : O(10 13 ) LHC with 100fb 1 sensitive to O(10 5 ) Br s detection would be a clear sign of New Physics

23 Where to look... direct bounds from t decays within SM branching ratios of t u i Z /γ : O(10 13 ) LHC with 100fb 1 sensitive to O(10 5 ) Br s detection would be a clear sign of New Physics meson decays ( F = 1)

24 Where to look... direct bounds from t decays within SM branching ratios of t u i Z /γ : O(10 13 ) LHC with 100fb 1 sensitive to O(10 5 ) Br s detection would be a clear sign of New Physics meson decays ( F = 1) meson mixing ( F = 2) loop processes are sensitive to particle masses in loops also sensitive to couplings (CKM elements!)

25 Where to look... direct bounds from t decays within SM branching ratios of t u i Z /γ : O(10 13 ) LHC with 100fb 1 sensitive to O(10 5 ) Br s detection would be a clear sign of New Physics meson decays ( F = 1) meson mixing ( F = 2) loop processes are sensitive to particle masses in loops also sensitive to couplings (CKM elements!) direct search for new particles collider (LHC)

26 Meson Mixing meson = q q pair neutral mesons can turn into their antiparticles K 0 K 0, D 0 D 0, B 0 B 0 in the SM achieved through box diagrams Figure: Box diagrams contributing to K 0 K 0 mixing in the SM

27 now have at tree level as well, but v 4 /M 4 T suppressed box has v 2 /M 2 T contribution F = 1 Figure: tree-level diagram contributing to K 0 K 0 mixing in NP framework largest effect: FCNC for semileptonic decays only one of two vertices modified Figure: q i decaying to q j and a charged lepton pair via a Z boson

28 get analytical expressions for branching ratios of the processes of interest SM plus terms with Wilson coefficients Br(C ij ) experimental limits on these Br s put bounds on C s Fox et al.,deciphering top flavor violation at the LHC with B factories, involving 3rd generation Wilson coefficients treated one by one, the others set to zero top FCNC decays still give very weak constraints best bound from B 0 B 0 mixing

29 the aim is to find an absolute lower bound on the physical masses of the vector-like quarks coupling to all three generations enables a wider range of processes branching ratios for decay to 3rd generation get relaxed mass can be lower than from former analyses include also the direct search for heavy particles investigate limits from electroweak precision observables do the analysis for all the cases T, B, Q

30 Conclusions SM works well but has unanswered questions SM is the low energy limit of a more general theory need new physics first step possible new particles that emerge from higher energy domain indirect effects can be already visible at relatively low energies, through interactions within the SM investigation of present limits constrains the new physics scale

31 Thank you for your attention