Vector-like fermions: a reviewbenasque.org/2017lhc/talks_contr/232_FAguila.pdf · There is a large number of papers on the subject: • H. Fritzsch, M. Gell-Mann and P. Minkowski,

Vector-likefermions:areviewFranciscodelÁguilaandJoséSan<ago

Outline

• Introduction: personal historical view

• Grand Unified Theories, Majorana masses, Little Higgs models, SUSY

• Extendedspectrum

• Decoupling:wellbehaved(decoupling)butflavourviola<on,although model dependent predictions (changing prejudices)

• Indirecteffects

• Directeffects

• Fermionmassesandmixings

• LHC searches (today’s talks)

Thereisalargenumberofpapersonthesubject:

• H. Fritzsch, M. Gell-Mann and P. Minkowski, Phys. Lett. 59B (1975) 256 (SO(10) H. Georgi) Light (now, heavy then ~ 10’s of GeV) mirror, anomaly free

• M.J. Bowick and P. Ramond, Phys. Lett. 103B (1981) 338 (E6 F. Gursey, P. Ramond and P. Sikivie) Heavy (up to the GUT scale) vector-like

• F. del Aguila and M,J. Bowick, Phys. Lett. l19B (1982) 144 Phenomenology

• P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B 258 (1985) 46 SUSY motivation (at the TeV scale in E6 representations)

• G.C. Branco and L. Lavoura, Nucl. Phys. B 278 (1986) 738 Phenomenology

• F. del Aguila, L. Ametller, G.L. Kane and J. Vidal, Nucl. Phys. B 334 (1990) 1 Reach of hadron colliders

• F.J. Botella, G.C. Branco, M. Nebot, M.N. Rebelo and J.I. Silva-Marcos, arXiv:1610.03018 [hep-ph] Model building

• J.A. Aguilar-Saavedra, R. Benbrik, S. Heinemeyer and M. Pérez-Victoria, [arXiv:1306.0572 [hep-ph]] Review

• ATLAS and CMS limits. Specific talks this week, and especially today

Large μ

μ = M

Small μ

LSM + LT

LSM = qLi6DqL + tRi6DtR � �t(qL�tR + tR�†qL) + . . .

LT = T (i 6D �M)T � �T (qL�TR + TR�†qL)

F. del Aguila, M. Perez-Victoria and J. Santiago [hep-ph/0007316]

L(0l)6 = ↵(1)

�qO(1)�q + ↵(3)

�qO(3)�q + ↵u�Ou� + h.c.

LSM + L(0l)6

Heavy vector-like quark of charge 2/3

EOM (no TL interaction): TL =1M

(��T �†qL), TR =i 6DM2

(��T �†qL)

use t EOM to write the dimension 6 effective Lagrangian in the Warsaw basis

★

★

↵(1)�q = �↵(3)

�q =|�T |2

4M2, ↵u� = 2�t↵

(1)�q

O(1)�q = i�†Dµ� q�µq, O(3)

�q = i�†�aDµ� q�µ�aq, Ou� = �†�q�t

fdp header will be provided by the publisher 3

χ2

MH [GeV] a)

SMNeW

1

B150

155

160

165

170

175

125 200 400 600 800

χ2

MH [GeV] b)

SMNe

W1

B150

155

160

165

170

175

130 200 250 400 600 800

Fig. 1 a) From top to bottom, minimum χ2 as a function of the Higgs mass for the SM fit, and the fits includingbesides a heavy neutrino singlet Ne coupled to the first lepton family, a vector triplet of hyperchage one W1, and aneutral vector singlet B (see [4, 9, 11] for conventions). b) The same but assuming that the SM Higgs is found to havea massMH = 130± 10 GeV orMH = 250± 10 GeV (blue bands).

of the hadronic cross section observed at LEP 2 can be explained by four-fermion operators involvingelectrons and quarks, like O(1,3)

lq , etcetera. Parity violation in Møller scattering can be improved by O(1)ll

orOee, for example. On the other hand, the relatively large value of theW mass can be accounted byO(3)φ

and OWB . While the large forward-backward bottom asymmetry results in an asymmetric α(1)φd interval,

although we assume universality. At any rate, the size and asymmetry of the intervals get reduced when alldata are considered.

3 Implications on the Higgs mass

In the previous fits to dimension six operators the SM parameters are fixed to their best value in the fit tothe SM alone, except for the Higgs massMH which is left free. This, in general, prefers to be next to itsdirect lower limit of 114 GeV [1, 2, 13]. In the left figure we show the χ2 dependence on MH in the fitto the SM alone with all SM parameters free (upper black solid line). As it is apparent, if the SM Higgsis found to be relatively heavy, further physics has to cancel its one-loop contributions to the differentelectroweak precision observables, in order to restore the excellent agreement with the data. In particular,it has to balance the negative quantum correction to the ρ = M2

W /M2Z cos2 θW parameter [14]. This can

be done at tree level increasing the numerator or decreasing the denominator, yielding in both cases therequired positive contribution. The former can be effectively achieved reducing the SM contribution to theFermi constant Gµ by mixing the electron neutrino with a sterile heavy neutrino Ne [9, 15], and the lattermixing the Z0 boson with heavier extra vector bosons [11, 16]. 1 In the left figure we show the effect ofboth possibilities. The second upper line (blue dashed) corresponds to the heavy neutrino addition, whichcan not completely account for a heavy Higgs but improves the global fit. Whereas there are two gaugeboson additions balancing the heavy Higgs corrections to EWPD, named B andW1 in [11], respectively(bottom green dotted-dashed and second bottom red solid lines in the figure). In these three fits the onlySM parameters left free, besides the Higgs mass, are the strong coupling constant and the top mass. Thelarge χ2 values on the ordinate reminds the large number (212) of data included in the fits. Finally, in theright figure we plot the same as in the left one but replacing the present large collider bounds [13] by twoguesses of the Higgs mass eventually measured at CERN [17].

1 Note that in the operator basis chosen here corrections toGµ can be encoded either inO(3)φl orO

(1,3)ll . While, direct corrections

to the ρ parameter are accounted byO(3)φ , allowing for largeMH values for negative α(3)

φ (see Table 1).

Copyright line will be provided by the publisher

F. del Aguila and J. de Blas, [arXiv:1105.6103 [hep-ph]]

L. Lavoura and J.P Silva, Phys. Rev. D 47 (1993) 2046

v

Figure 1:

M <

Lifetimes

I I I I I I I I T s T(Q+qbZ) "'

I t J -1 I G M "' I g /2n

I so 3 I (M in GeV) sec sec

I I I I I I I I

- _I_

-18 10 sec < T < 1 sec

TABLE 2 (continued)

-48-

Usual SU(S) representations containing these ll.I"' 0 '!."'" r k.s

(Used in super-symmetrYl_ and

45F + 45F

representations

------other representation

Difficult to embed

Other characteristics I

I I I I I I I I I I

, I I I

--- of neutr al to charged dec ays

I large I I I I I

imply exotics I I I I I I I I I I I I

Singlets

Doublets

Triplets

Other Multiplets

TABLE 2

LH and RH Masses parts (M large)

u No

t-- -- - constraint

D

u

D

----- Particles 0 D in the

same , multiplet u 0 are nearly degenerate

u 0

in mass

D u D 0

!!0 M r-----D

0

u

-47-

Non-diagonal couplings with normal generations. We indicate only the mixing angles suppressing the gauge and Yukawa couplings.

Higgs Gauge RL LR L R (q is a doublet) (q is a singlet:

I : I I 2 mixing I n I n n

QTq {no mixing Q I Q q I if no other : " I I I I=O multi- I I I z,w I plets H I H I I I

I I I I I

2 I I n m1.x1.ng (no mixing I I in NC if no I n n I Q other I=O Q

-r-q Q l q ; q I I multiplets) I I ------1 z,w H I H

I l 2 mixing I I n

I I I I QT I I n ql Q q Q q : I I

I I z,w I HI I H I

1- - - - - -_I Negligible I ------1-------I

Negligible I Negligible I I I

Negligible Negligible .

, , , , "''"" '"'''''1!"" "'""" 1111"1' 1' I II f'l I II '•IIU1•1• '""" r '"' ''"" "' <' "''" """' ' 0 "" " 11 " ''" '' I'" "'" •r'l '"'""''I!"'"""'' O•I•W•I '"I"'" 0 ""

0 r•r "''''" "

0 " ..,,o

0 " '"' """ "'

0

" ' '"

F. del Aguila and M.J. Bowick, Nucl. Phys. B 224 (1983) 107

Singlets

Doublets

Triplets

Other Multiplets

TABLE 1

LH and RH parts

N

-----E

N

E

- ----E

Ec N N , E E

1-----E .

Masses (M large)

No constraint

Particles in the same multiplet are nearly degenerate in mass

LiM"'m EO M

-45-

Non-diagonal couplings with normal generations. We indicate only the mixing angles ( n"-m/M) suppressing the gauge and Yukawa couplings.

Higgs Gauge RL LR U is a doublet) U is a singlet' L R '

L Tl £ (N will be in L £ (N will be in ( general a self I general a self-conjugate I conjugate, z,w Major ana H Major ana spinor) spinor) ----- -,--- - - - -- - -r- -- -L Tl 2 ..

Tl i £ Tl L £ L £ I (no mixing : I ' I if no other I z,w I I I llii=O multi- H I H 1 plets) I 2 ' I Tl mJ.xl.ng I

(no mixing I j in NC if no I L Tl £ Tl I L £ other lii=O L ; £ multiplets) I I I

I I ------1 z,w I H H I J 2 mixing Tl I I I I I I

Tl I

I Tl L £ I L £ L £ I I I :

I I z,w I I H H

- -_I Negligible I 1---- 1------.L.------I I Negligible I Negligible

I I

Negligible Negligible .

... '""''"""""'"'""''''"''"'""'"'"' """" '""'''''"'""'"'"""'"'"' .,.,, .• ,,,.,,.,,., ' '"'' ,.,,,,,.,.,.,,, .. , ... ,. ......... .

Lifetimes

M < "\v,z

T ,; T(L+R. ev ) "' T e

m M "' [ G2

2 3] -l T

I I I I I I I

"\v,z < M

I T " -r(L+R.,Z) "'

I

: ts Mrl "' I

< 20 )3 I 10-20 < 100 ) M in GeV sec I M in GeV

I I I I I I I

_I_

-16 10 sec < T < 1 sec

TABLE 1 (continued)

sec

-46-

Usual SU(5) representations containing these 6J>o leptons

1-------

5F +SF (used in super-symmetry) and __ 45F __

other

representation::

24F, other

representations

other

representations

Difficult to embed

Other characteristics I

I I I I I I I I I J No sequential

character or I associated nea rly 1 massless neutr inc

or conserved I quantum number --- - -.., 1 ratio of neutr al

to charge deca ys I large I j

I in general I

imply exotics I I I I I I I I I I I

' I

Effective Lagrangian

basis of local operators (no redundant) -systematic use of equations of motion-

accidental symmetries are not fulfiled by higher order operators -lepton number, ...-

⇒⇣E

⇤

⌘dimOi�4⇠ ✏ dimOi ⇠ 4 +

log ✏

log(E/⇤)

engineering dimension upper limit

Le↵ = LSM +X

dimOi>4

ci

⇤dimOi�4Oi

finite number of independent operators

⇣2 =

log 0.01

log

100 GeV1 TeV

⌘

Table 2: Values of Φab for the different possibilities of mixing between heavy fields.

U bR Db

R

⎛

⎜

⎜

⎝

XU

D

⎞

⎟

⎟

⎠

b

R

⎛

⎜

⎜

⎝

UD

Y

⎞

⎟

⎟

⎠

b

R

(

UD

)a

L

φ φ σI

2 φ σI

2 φ

(

XU

)a

L

φ − σI

2 φ −

(

D

Y

)a

L

− φ − σI

2 φ

Llh contains the Yukawa couplings mixing SM and new vector-like quarks. In Table 3 we

collect these terms for each type of multiplet in Table 1. We use primes for these Yukawacouplings and include V in the definition of some of them in order to simplify the finalexpressions. As we pointed out only one chirality of each type of vector-like multiplet

mixes. Because Llh is linear in heavy fields, it can be written

Llh = QaL

δLlh

δQaL

+ QaR

δLlh

δQaR

+ h.c., (2.4)

where δLlh

δQa can be read from Table 3.

In order to find the effective Lagrangian describing the physics below the scale Λ, weintegrate out the heavy modes for a generic addition of vector-like multiplets. Note that,unlike chiral fermions [11], vector-like quarks decouple when their mass is sent to infinity.

For our purposes it is sufficient to perform the integration at tree level, which can becarried out imposing the equations of motion of the heavy modes. There is no need to

consider each kind of exotic quark separately, as Llh has essentially the same form in allcases (see Ref. [1], however, for a particular example). The requirement that the action

be stationary under variations of the heavy fields QaL,R gives two coupled equations of

motion (with no sum in a):

iDQaL − MaQ

aR − λabΦabQ

bR +

δLlh

δQaL

= 0 , (2.5)

iDQaR − MaQ

aL − λ†

abΦ†abQ

bL +

δLlh

δQaR

= 0 , (2.6)

where we have used Eqs. (2.3) and (2.4). These equations can be solved iteratively. The

solution to order 1/M2 is

QaR =

iD

M2a

δLlh

δQaR

+1

Ma

δLlh

δQaL

−1

MaMb

λabΦabδLlh

δQbL

, (2.7)

4

Table 3: Yukawa terms mixing light (qiL, ui

R, diR) and heavy (Qa

L,R) quarks. The hermitian

conjugate terms must be added. The index I in the Pauli matrices corresponds to the (+, 0,−)

basis of isospin, as it does in the vector-like triplets. The superscript m = 1, . . . , 7 in λ′(m) labels

the different type of multiplet addition. δLlh

δQaL,R

can be read directly from Llh which is linear in

QaL,R.

Q(m) −Llh

U λ′(1)aj VjiUa

Rφ†qiL

D λ′(2)ai Da

Rφ† qiL

(

UD

)

λ′(3u)ai

(

UD

)a

L

φuiR + λ′(3d)

ai

(

UD

)a

L

φdiR

(

X

U

)

λ′(4)ai

(

X

U

)a

L

φuiR

(

D

Y

)

λ′(5)ai

(

D

Y

)a

L

φdiR

⎛

⎜

⎜

⎝

X

UD

⎞

⎟

⎟

⎠

λ′(6)aj Vji

⎛

⎜

⎜

⎝

X

UD

⎞

⎟

⎟

⎠

a

R I

φ† σI

2 qiL

⎛

⎜

⎜

⎝

U

DY

⎞

⎟

⎟

⎠

λ′(7)aj Vji

⎛

⎜

⎜

⎝

U

DY

⎞

⎟

⎟

⎠

a

R I

φ† σI

2 qiL

QaL =

iD

M2a

δLlh

δQaL

+1

Ma

δLlh

δQaR

−1

MaMb

λ†abΦ

†ab

δLlh

δQbR

. (2.8)

Inserting these expressions in the original Lagrangian in Eq.(2.1) we obtain, to order1/M2,

L4 = Ll, (2.9)

1

Λ2L6 =

δLlh

δQaL

iD

M2a

δLlh

δQaL

+δLlh

δQaR

iD

M2a

δLlh

δQaR

−(

δLlh

δQaR

1

MaMb

λabΦabδLlh

δQbL

+ h.c.

)

. (2.10)

We have set δLlh

δQaL

δLlh

δQaR

= 0 since for each a one of the two factors vanishes. Diagrammaticallythese dimension 6 corrections follow from the Feynman diagrams in Fig. 1. The addition

of the first two diagrams generates the operators with a covariant derivative, whereas thelast diagram generates the operators in parentheses in Eq. (2.10).

In order to use the results of Ref. [1] we have to write L6 in terms of the operatorsof Ref. [3]. The covariant derivative in Eq.(2.10) acts on δLlh

δQa , which is the product of the

5

F. del Aguila, M. Perez-Victoria and "J. Santiago, [hep-ph/0007316]

Equations of motion and field redefinitions

Relevant (dimension < 4), marginal (dimension = 4) and irrelevant (dimension > 4) operators, which it is convenient to bring to a canonical form without redundancies:

• Necessary to make a meaningful comparison between different (phenomenological) analyses.

• Although there are subsets more suitable for given data subsets.

As in the case of lepton number violation, just discussed, new physics may originate at a rather large order but its effects in general do manifest at the lowest possible order after quantum corrections are taken into account.

LSM = qLi6DqL + tRi6DtR � �t(qL�tR + tR�†qL) + . . .

i6DqL � �t�tR = 0

qL EOM: O(1)

�q = �†� qL i 6D qL �t (Ou� = �†� qL � tR)

Se↵ =Z

d

4x Le↵

Le↵ = LSM +X

dimOi>4

ci

⇤dimOi�4Oi =

1X

n=0

Ln

�LSM

�'† � @µ�LSM

�@µ'† = 0

Lm =1

⇤m

⇣· · · + f(', @µ')

⇣�LSM

�'† � @µ�LSM

�@µ'†

⌘⌘

↵(1)�q

⇣(O(1)

�q = �†� qL i 6D qL) �t (Ou� = �†� qL � tR)⌘

Any combination of terms which allows for the factorization of an equation of motion of a light field φ can be removed because it has no contribution to the S-matrix

This follows from the observation that the field redefinition

cancels such a combination without modifying L =mX

n=0

Ln

'† ! '† � 1⇤m

f(', @µ')

Z[J ] =

Z

D' exp

n

i

Z

dx [L('(x), @µ'(x)) + J(x)'(x)]

o

C. Arzt, hep-ph/9304230

Table 4: Coefficients αmx resulting from the integration of an arbitrary number of each type of vector-like quarks.

The superscript m = 1, . . . , 7 in λ′(m) labels the different type of multiplet addition.

Q(m) (α(1)φq

)ij

Λ2

(α(3)φq

)ij

Λ2(αφu)ij

Λ2(αφd)ij

Λ2(αφφ)ij

Λ2(αuφ)ij

Λ2(αdφ)ij

Λ2

U 14V †

ik

λ′(1)†ka

λ′(1)al

M2a

Vlj −(α(1)

φq)ij

Λ2 − − − 2(α(1)

φq)ik

Λ2 V †kjλ

uj −

D − 14

λ′(2)†ia

λ′(2)aj

M2a

(α(1)φq

)ij

Λ2 − − − − −2(α

(1)φq

)ij

Λ2 λdj

(

U

D

)

− − − 12

λ′(3u)†ia

λ′(3u)aj

M2a

12

λ′(3d)†ia

λ′(3d)aj

M2a

−λ′(3u)†ia

λ′(3d)aj

M2a

−V †ikλu

k(αφu)kj

Λ2 λdi

(αφd)ij

Λ2

(

X

U

)

− − 12

λ′(4)†ia

λ′(4)aj

M2a

− − V †ikλu

k(αφu)kj

Λ2 −

(

D

Y

)

− − − − 12

λ′(5)†ia

λ′(5)aj

M2a

− − −λdi

(αφd)ij

Λ2

⎛

⎝

X

U

D

⎞

⎠

316V †

ik

λ′(6)†ka

λ′(6)al

M2a

Vlj13

(α(1)φq

)ij

Λ2 − − − 23

(α(1)φq

)ik

Λ2 V †kjλ

uj

43

(α(1)φq

)ij

Λ2 λdj

⎛

⎝

U

D

Y

⎞

⎠ − 316V †

ik

λ′(7)†ka

λ′(7)al

M2a

Vlj − 13

(α(1)φq

)ij

Λ2 − − − − 43

(α(1)φq

)ik

Λ2 V †kjλ

uj − 2

3

(α(1)φq

)ij

Λ2 λdj

8

p

(a) (b) (c)

Figure 1: Diagrams contributing to dimension 6 operators in the effective Lagrangian. Light

(heavy) quarks are depicted by a single (double) line.

scalar and a light quark multiplet (see Table 3). Using the (covariant) Leibniz rule we

obtain terms in which the covariant derivative acts either on the scalar field or on the lightquark. Whereas the former give—after a simple Fierz reordering of the representation

indices—operators in the catalogue of [3], the latter have to be transformed using theequations of motion of L4. The result takes the form (see Ref. [3] for notation)

L6 = (α(1)φq )ij(φ

†iDµφ)(qiLγµqj

L) + (α(3)φq )ij(φ

†σIiDµφ)(qiLγµσIqj

L)

+(αφu)ij(φ†iDµφ)(ui

RγµujR) + (αφd)ij(φ

†iDµφ)(diRγµdj

R)

+(αφφ)ij(φT ϵiDµφ)(ui

RγµdjR) + (αuφ)ij(φ

†φ)(qiLφuj

R)

+(αdφ)ij(φ†φ)(qi

LφdjR) + h.c. . (2.11)

Note that vector-like quarks generate only these 7 operators. In particular, operators of

magnetic-moment type or with stress-energy tensors do not appear at this order. Four-fermion operators are not generated either, although one should keep in mind that they

may arise from other kinds of new physics. Each vector-like quark gives and independentcontribution to one of the first two terms in Eq. (2.10), which is diagonal in the heavy

quark flavour, a. The term in parentheses in this equation—which contributes only toOuφ and Odφ—requires the cooperative participation of two different types of vector-likemultiplets. Thus, the coefficients in Eq. (2.11) can be written

αx =!

m

αmx +

!

m<n

αmnx , (2.12)

where αmx is the diagonal contribution of the vector-like multiplets Q(m) and αmn

x is the

combined contribution of multiplets Q(m) and Q(n). Note that αmnx = 0 unless x = uφ, dφ,

and only one of the two quarks is a doublet. The contributions αmx and αmn

x are collectedin Table 4 and Table 5, respectively.

3. Corrections to quark couplings

Upon SSB, the 7 operators in L6 give v2

Λ2 corrections to the SM Lagrangian. In the masseigenstate basis these corrections read:

LZ = −g

2 cos θW

"

uiLXuL

ij γµujL + ui

RXuRij γµuj

R

6

p

(a) (b) (c)






L6 = (α(1)φq )ij(φ


L) + (α(3)φq )ij(φ


L)




R)



†φ)(qiLφuj

R)


LφdjR) + h.c. . (2.11)





αx =!

m

αmx +

!

m<n

αmnx , (2.12)


x is the







LZ = −g

2 cos θW

"

uiLXuL

ij γµujL + ui

RXuRij γµuj

R

6

−diLXdL

ij γµdjL − di

RXdRij γµdj

R − 2 sin2 θW JµEM

!

Zµ,

LW = −g√2(ui

LW Lijγ

µdjL + ui

RW Rij γ

µdjR)W+

µ + h.c., (3.1)

LH = −1√2(ui

LY uiju

jR + di

LY dijd

jR)H + h.c.,

with

XuLij = δij −

v2

Λ2Vik(α

(1)φq − α(3)

φq )klV†lj,

XuRij = −

v2

Λ2(αφu)ij ,

XdLij = δij +

v2

Λ2(α(1)

φq + α(3)φq )ij,

XdRij =

v2

Λ2(αφd)ij , (3.2)

W Lij = Vik(δkj +

v2

Λ2(α(3)

φq )kj),

W Rij = −

1

2

v2

Λ2(αφφ)ij,

Y uij = δijλ

uj −

v2

Λ2

"

Vik(αuφ)kj +1

4δij [Vik(αuφ)kj + (αuφ)

†ikV

†kj]#

,

Y dij = δijλ

dj −

v2

Λ2

"

(αdφ)ij +1

4δij(αdφ + α†

dφ)ij

#

,

where we have introduced the unitary matrix

V = V +v2

Λ2(V Ad

L − AuLV ). (3.3)

Au,dL are the antihermitian matrices which, together with Au,d

R , diagonalize the correctedmass terms:

(AuL)ij =

1

2(1 −

1

2δij)

λui (V αuφ)

†ij + (−1)δij (V αuφ)ijλu

j

(λui )2 − (−1)δij (λu

j )2, (3.4)

(AdL)ij =

1

2(1 −

1

2δij)

λdi (αdφ)†ij + (−1)δij (αdφ)ijλd

j

(λdi )2 − (−1)δij (λd

j )2. (3.5)

L6 in Eq. (2.11) does not generate any other trilinear coupling. A possible derivativecoupling to the Higgs is forbidden in these models because the corresponding coefficients

αx are always hermitian (see Ref. [1]). With Eq. (3.2) and Tables 4 and 5 we can answerphenomenological questions on quark mixing in processes with a vector boson or a Higgs.

4. Relations and Bounds

As can be readily observed from Eq. (3.2), this effective Lagrangian gives mixing effects

which are forbidden in the SM. In general:

7

−diLXdL

ij γµdjL − di

RXdRij γµdj

R − 2 sin2 θW JµEM

!

Zµ,

LW = −g√2(ui

LW Lijγ

µdjL + ui

RW Rij γ

µdjR)W+

µ + h.c., (3.1)

LH = −1√2(ui

LY uiju

jR + di

LY dijd

jR)H + h.c.,

with

XuLij = δij −

v2

Λ2Vik(α

(1)φq − α(3)

φq )klV†lj,

XuRij = −

v2

Λ2(αφu)ij ,

XdLij = δij +

v2

Λ2(α(1)

φq + α(3)φq )ij,

XdRij =

v2

Λ2(αφd)ij , (3.2)

W Lij = Vik(δkj +

v2

Λ2(α(3)

φq )kj),

W Rij = −

1

2

v2

Λ2(αφφ)ij,

Y uij = δijλ

uj −

v2

Λ2

"

Vik(αuφ)kj +1

4δij [Vik(αuφ)kj + (αuφ)

†ikV

†kj]#

,

Y dij = δijλ

dj −

v2

Λ2

"

(αdφ)ij +1

4δij(αdφ + α†

dφ)ij

#

,

where we have introduced the unitary matrix

V = V +v2

Λ2(V Ad

L − AuLV ). (3.3)

Au,dL are the antihermitian matrices which, together with Au,d

R , diagonalize the correctedmass terms:

(AuL)ij =

1

2(1 −

1

2δij)

λui (V αuφ)

†ij + (−1)δij (V αuφ)ijλu

j

(λui )2 − (−1)δij (λu

j )2, (3.4)

(AdL)ij =

1

2(1 −

1

2δij)

λdi (αdφ)†ij + (−1)δij (αdφ)ijλd

j

(λdi )2 − (−1)δij (λd

j )2. (3.5)

L6 in Eq. (2.11) does not generate any other trilinear coupling. A possible derivativecoupling to the Higgs is forbidden in these models because the corresponding coefficients

αx are always hermitian (see Ref. [1]). With Eq. (3.2) and Tables 4 and 5 we can answerphenomenological questions on quark mixing in processes with a vector boson or a Higgs.

4. Relations and Bounds

As can be readily observed from Eq. (3.2), this effective Lagrangian gives mixing effects

which are forbidden in the SM. In general:

7

p

(a) (b) (c)






L6 = (α(1)φq )ij(φ


L) + (α(3)φq )ij(φ


L)




R)



†φ)(qiLφuj

R)


LφdjR) + h.c. . (2.11)





αx =!

m

αmx +

!

m<n

αmnx , (2.12)


x is the







LZ = −g

2 cos θW

"

uiLXuL

ij γµujL + ui

RXuRij γµuj

R

6

SU(2)L ⇥ SU(2)c

�b

✓TB

◆

L

�bR + �t

✓TB

◆

L

�tR + �0t

✓XT 0

◆

L

�tR

↵�u

⇤2 = � 12

�2t

M216

+ 12

�02t

M276

↵�d

⇤2 = 12

�2b

M216

!

!

!

ZµtR�µtR

ZµbR�µbR

WµtR�µbR

0

0

0

!

!

![2 1

6, 2 7

6] =

✓TB

◆,

✓XT 0

◆�

8><

>:

8><

>:

�t = �0t

M 16= M 7

6

�b = 0

A. Atre, M. Carena, T. Han and J. Santiago [arXiv:0806.3966 [hep-ph]]

BR, XR ! WtR

TL + T 0L ! HtR

TR � T 0R ! ZtR

9>=

>;

↵��

⇤2 = ��t�b

M216

Table 5: Coefficients αmnx resulting from the integration of an arbitrary number of vector-

like quarks of each type due to the mixing between vector-like multiplets. The superscript

m = 1, . . . , 7 in λ′(m) labels the different type of multiplet addition.

Q(m), Q(n) (αmnuφ )ij

Λ2

(αmndφ )ij

Λ2

U,

(

U

D

)

V †ik

λ′(1)†ka

λabλ′(3u)bj

MaMb−

U,

(

X

U

)

V †ik

λ′(1)†ka

λabλ′(4)bj

MaMb−

D,

(

U

D

)

−λ′(2)†ia

λabλ′(3d)bj

MaMb

D,

(

D

Y

)

−λ′(2)†ia

λabλ′(5)bj

MaMb

(

U

D

)

,

⎛

⎝

X

U

D

⎞

⎠

14V †

ik

λ′(6)†ka

λabλ′(3u)bj

MaMb

12V †

ik

λ′(6)†ka

λabλ′(3d)bj

MaMb

(

U

D

)

,

⎛

⎝

U

D

Y

⎞

⎠

12V †

ik

λ′(7)†ka

λabλ′(3u)bj

MaMb

14V †

ik

λ′(7)†ka

λabλ′(3d)bj

MaMb

(

X

U

)

,

⎛

⎝

X

U

D

⎞

⎠ − 14V †

ik

λ′(6)†ka

λabλ′(4)bj

MaMb−

(

D

Y

)

,

⎛

⎝

U

D

Y

⎞

⎠ − − 14V †

ik

λ′(7)†ka

λabλ′(5)bj

MaMb

• There are flavour changing neutral currents (FCNC) in the gauge interactions attree level, as the GIM mechanism [12] does not apply: XuL

ij , XdLij = δij .

• There are right-handed (RH) neutral currents not proportional to JµEM : XuR

ij , XdRij =

0.

• The left-handed (LH) charged currents are not described by a unitary CKM matrix:W L

ikWL †kj , W L †

ik W Lkj = δij .

• There are RH charged currents: W Rij = 0

• There are FCNC mediated by the Higgs boson: Y u,dij =

√2δij

mu,dj

v.

At this point it is important to remember that, whereas the couplings among the five

lightest quarks are known with good precision, the couplings involving the top are only

9

Accidental symmetries Lepton number is an accidental symmetry of the (minimal) Standard Model because all renormalizable couplings among the electroweak quark and lepton doublets and singlets and invariant under the gauge symmetry group SU(3)XSU(2)XU(1) do also preserve baryon and lepton number.

However, already at next order there exists one dimension 5 operator with non-vanishing lepton number equal to 2:S. Weinberg, Phys. Rev. Lett. 43 (1979) 1566"A. Santamaría’s talk

see-saw I, III see-saw IIP. Minkowski ‘77; M. Gell-Mann, P. Ramond and R. Slansky ‘79; T. Yanagida ‘79; "R.N. Mohapatra and G. Senjanovic ’80; J. Schechter and J.W.F. Valle ‘80

10 14. Neutrino mixing

violating effects will be strongly suppressed. In particular, we get A(l′l)CP = 0, unless all

three ∆m2ij = 0, (ij) = (32), (21), (13).

If the number of massive neutrinos n is equal to the number of neutrino flavours,n = 3, one has as a consequence of the unitarity of the neutrino mixing matrix:!

l′=e,µ,τ P (νl → νl′) = 1, l = e, µ, τ ,!

l=e,µ,τ P (νl → νl′) = 1, l′ = e, µ, τ .Similar “probability conservation” equations hold for P (νl → νl′). If, however, thenumber of light massive neutrinos is bigger than the number of flavour neutrinos asa consequence, e.g., of a flavour neutrino - sterile neutrino mixing, we would have!

l′=e,µ,τ P (νl → νl′) = 1 − P (νl → νsL), l = e, µ, τ , where we have assumed theexistence of just one sterile neutrino. Obviously, in this case

!

l′=e,µ,τ P (νl → νl′) < 1 ifP (νl → νsL) = 0. The former inequality is used in the searches for oscillations betweenactive and sterile neutrinos.

Consider next neutrino oscillations in the case of one neutrino mass squared difference“dominance”: suppose that |∆m2

j1| ≪ |∆m2n1|, j = 2, ..., (n − 1), |∆m2

n1|L/(2p) !1 and

|∆m2j1|L/(2p) ≪ 1, so that exp[i(∆m2

j1 L/(2p)] ∼= 1, j = 2, ..., (n − 1). Under theseconditions we obtain from Eq. (14.13) and Eq. (14.14), keeping only the oscillating termsinvolving ∆m2

n1:

P (νl(l′) → νl′(l))∼= P (νl(l′) → νl′(l))

∼= δll′ − 2|Uln|2"

δll′ − |Ul′n|2#

(1 − cos∆m2

n1

2pL) . (14.20)

It follows from the neutrino oscillation data (Sections 14.4 and 14.5) that in the caseof 3-neutrino mixing, one of the two independent neutrino mass squared differences, say∆m2

21, is much smaller in absolute value than the second one, ∆m231: |∆m2

21| ≪ |∆m231|.

The data imply:

|∆m221| ∼= 7.5 × 10−5 eV2 ,

|∆m231| ∼= 2.5 × 10−3 eV2 ,

|∆m221|/|∆m2

31| ∼= 0.03 . (14.21)

Neglecting the effects due to ∆m221 we get from Eq. (14.20) by setting n = 3 and choosing,

e.g., i) l = l′ = e and ii) l = e(µ), l′ = µ(e) [60]:

P (νe → νe) = P (νe → νe) ∼= 1 − 2|Ue3|2$

1 − |Ue3|2%

&

1 − cos∆m2

31

2pL

'

, (14.22)

P (νµ(e) → νe(µ)) ∼= 2 |Uµ3|2 |Ue3|2&

1 − cos∆m2

31

2pL

'

=|Uµ3|2

1 − |Ue3|2P 2ν

$

|Ue3|2, m231

%

, (14.23)

August 29, 2014 14:37

atmospheric neutrinos

L5 = (α5)ij(liL)cφ∗φ†ljL + h.c., (5)

L6 =!

(α(1)φl )ij

"

φ†iDµφ# "

liLγµljL

#

+ (α(3)φl )ij

"

φ†iσaDµφ#"

liLσaγµljL

#

+$

αeφ

%

ij

"

φ†φ#"

liLφejR

#

+ (α(1)ll )ijkl

1

2

"

liLγµljL

#"

lkLγµllL

#

+ h.c.

&

+ α(1)φ

"

φ†φ#"

(Dµφ)† Dµφ#

+ α(3)φ

"

φ†Dµφ#"

(Dµφ)†φ#

+ αφ1

3

"

φ†φ#3

,

(6)

where we choose the basis of Buchmuller and Wyler to express the result 16. lL stands for anylepton doublet, eR for any lepton singlet, and φ is the SM Higgs doublet. In Table 1 we collectthe explicit expressions of the coefficients in terms of the original parameters for each type ofsee-saw (see Fig. 2 and the table caption for definitions).

Only the dimension 6 operators can give deviations from the SM predictions for the elec-troweak precision data (EWPD). The operators of dimension 4 only redefine SM parameters.The one of dimension 5 gives tiny masses to the light neutrinos, and contributes to neutrinolessdouble β decay. An important difference is that the coefficient α5 involves LN-violating prod-ucts of two λ’s or of µ and λ, while the other coefficients depend on λ∗λ or |µ|2. Therefore,it is possible to have large cancellations in α5 together with sizeable coefficients of dimension

six14,15. Type I and III fermions generate the operators O(1,3)φl , which correct the gauge fermion

couplings. Type II scalars, on the other hand, generate 4-lepton operators and the operator O(3)φ ,

which breaks custodial symmetry and modifies the SM relation between the gauge boson masses.EWPD are sensitive to all these effects and put limits on the see-saw parameters.

There are two classes of processes, depending on whether they involve neutral currentsviolating lepton flavour (LF) or not. The first class puts more stringent limits 17,18, but onlyon the combinations of coefficients entering off-diagonal elements. The second class is measuredmainly at LEP19 and constrains the combinations in the diagonal entries 20. The LF violatinglimits are satisfied in types I and III if N and Σ mainly mix with only one charged leptonfamily. In Table 2 we collect the bounds from EWPD on the N and Σ mixings with the SMleptons VℓN,ℓΣ

20, and in Table 3 their product including the LF violating bounds17,18. These

Table 2: Upper limit at 90 % confidence level (CL) on the absolute value of the mixings. The first three columnsare obtained by coupling each new lepton with only one SM family. The last one corresponds to the case of leptonuniversality: three new lepton multiplets mixing with only one charged-lepton family each, all of them with the

same mixing angle. All numbers are computed assuming MH ≥ 114.4 GeV.

Coupling Only with e Only with µ Only with τ Universal'

'

'

'

VℓN =v(λ†

N )lN√2MN

'

'

'

'

< 0.055 0.057 0.079 0.038

'

'

'

'

VℓΣ = −v(λ†Σ)lΣ

2√

2MΣ

'

'

'

'

< 0.019 0.017 0.027 0.016

values update and extend previous bounds on diagonal entries for N 21,22 (see also 23.) Theirdependence on the model parameters entering in the operator coefficients in Table 1 is explicit inthe first column of Table 2. All low energy effects are proportional to this mixing, and the sameholds for the gauge and Higgs couplings between the new and the SM leptons, responsible of theheavy lepton decay (and N production if there is no extra NP). An interesting by-product of anon-negligible mixing of the electron or muon with a heavy N is that the fit to EWPD prefers aHiggs mass MH higher than in the SM, in better agreement with the present direct limit. Thisis so because their contributions to the most significative observables partially cancel24, so that

coupling λ∆ needs not be very small because it is only one of the factors entering in the LNviolating expression for ν masses (see Table 1). In fact, this process is LN conserving as we can

Table 1: Coefficients of the operators up to dimension 6 arising from the integration of the heavy fields involved ineach see-saw model. The parameters λ3 and λ5 are the coefficients of the scalar potential terms −(φ†φ)(∆†∆) and−(∆†Ti∆)(φ†σiφ), respectively, and (λe)jj the diagonalised SM charged-lepton Yukawa couplings. The remaining

parameters are defined in the caption of Fig. 2.

Coefficient Type I Type II Type III

α4 − 2 |µ∆|2

M2∆

−

(α5)ij

Λ12

(λTN )ia(λN )aj

MNa−2µ∆(λ∆)ij

M2∆

18

(λTΣ)ia(λΣ)aj

MΣa

(α(1)φl )ij

Λ214

(λ†N )ia(λN )aj

M2Na

− 316

(λ†Σ)ia(λΣ)aj

M2Σa

(α(3)φl )ij

Λ2 −(α

(1)φl )ij

Λ2 − 13

(α(1)φl )ij

Λ2

(α(1)ll )ijkl

Λ2 − 2(λ∆)jl(λ

†∆)ki

M2∆

−αφ

Λ2 − −6(λ3 + λ5)|µ∆|2

M4∆

−

α(1)φ

Λ2 − 4 |µ∆|2

M4∆

−

α(3)φ

Λ2 − 4 |µ∆|2

M4∆

−

(αeφ)ij

Λ2 − 43

(α(1)φl )ij

Λ2 (λe)jj

conventionally assign LN equal to 2 to ∆−−. There are other processes that do violate LN, e.g.when one of the doubly-charged ∆ in Fig. 2–(II) decays into WW . Then, what does violateLN is the corresponding ∆WW vertex, which is proportional to the coupling of the only LNviolating term in the fundamental Lagrangian φ†(σ · ∆)†φ, with total LN equal to 2. In theexamples in Fig. 1–(I, III) LN is violated in the decay (mass) of the heavy neutral fermion.

In conclusion, all the three mechanisms produce same-sign dilepton signals, but only thelast two are observable at LHC 7,8,9,10,11,12,13 in minimal models. Heavy neutrino singlets inparticular non-minimal scenarios could also be observed, as described in Section 3.

In the following we first review the experimental constraints on the parameters entering thethree see-saw mechanisms, and then the LHC reach for the corresponding see-saw messengers.Complementary reviews on this subject have been presented by other speakers at this Conference(see F. Bonnet, T. Hambye and J. Kersten in these Proceedings).

2 Electroweak precision data limits on see-saw messengers

The low energy effects of the see-saw messengers can be described by the effective Lagrangian

Leff = L4 +1

ΛL5 +

1

Λ2L6 + . . . , (3)

where Λ is the cut-off scale, in our case of the order of the see-saw messenger masses M , and thedifferent terms contain gauge-invariant operators of the corresponding dimension. The non-zeroterms up to dimension 6 are 14,15

L4 = LSM + α4

!

φ†φ"2

, (4)

The PMNS matrixis unitary to a very good approximation

Modify the SM gauge couplings to neutrinos

F. del Aguila, J.A. Aguilar-Saavedra, J. de Blas and M. Zralek, "[arXiv:0710.2923 [hep-ph]]

—-

3

FIG. 1: Example diagrams giving rise to h ! ⌧µ (left), ⌧ !µ� (center) and (g � 2)µ (right) at leading order in v and v�after symetry breaking, i.e. after the external H and � fieldsare replaced by their vevs.

with V = Z,Z 0, S = ', a, h, and , 0 = µ, ⌧, L,E. Aftersymmetry breaking, ' can mix with h via a quartic term�|�|2|H|2. While this mixing does not a↵ect the CP-odd components, the CP-even mass matrix has to bediagonalized by

'! ' cos↵� h sin↵ , h ! h cos↵+ ' sin↵ , (9)

where sin↵ ' 2�vv�/m2

'. The mixing has three impor-tant e↵ects: (i) it reduces all couplings of h to SM statesby a factor of cos↵. Given the good agreement of Higgsrate measurements at the LHC [78–80] with the SM pre-dictions, the size of the mixing is constrained. Using themeasured combined signal yield relative to the SM ex-pectation of µ = 1.09± 0.11, we find sin↵ . 0.36 at the2� level (see e.g. also [81]). (ii) it induces Higgs likecouplings of ' to all SM particles proportional to sin↵.Searches for ' ! WW/ZZ lead to constraints on sin↵of the order of ⇠ 0.3 for ' masses in the few hundredGeV range [81–83]. (iii) it leads to non-standard flavorviolating couplings of h

�hµ⌧(⌧µ) ' sin↵

2vv�MEML

YLE�µL(E)

�⌧E(L)

. (10)

Note that the flavor violating Higgs couplings scale asv2v2�/(m

2

SM2), with M = ME ,ML and mS = mh (mS =

m�) if m� ⌧ mh (mh ⌧ m�). The two powers of v� arerequired to compensate the change in the Lµ�L⌧ chargeby two units going from ⌧ ! µ. An example diagramshowing the leading order in v and v� in the unbrokenphase is shown in Fig. 1.

Phenomenology. Using the flavor violating Higgs cou-plings in Eq. (10), the h ! ⌧µ branching ratio is given(at leading order in v and v�) by

BR(h ! ⌧µ) ' mh

2⇡�h

v2v2�M2

EM2

L

sin2 ↵

⇥ �Y 2

LE�2

µL�2

⌧E + Y 2

LE�2

⌧L�2

µE

�, (11)

with the total Higgs width �h ' �SM

h cos2 ↵ and �SM

h ⇠4.1MeV [84]. We find that for couplings of O(1) and v�of the order of the electroweak scale, one can reach %level branching ratios with vector-like lepton masses inthe few TeV range.

Also the flavor conserving Higgs decay h ! µµ is mod-ified significantly. We find

BR(h ! µµ)

BR(h ! µµ)SM

'��1 +

v

mµtan↵

2vv�MEML

YLE�µL�µE

��2

,

(12)For a % level h ! ⌧µ rate, we generically expect O(1)corrections to the h ! µµ decay. The current bound ofBR(h ! µµ) < 1.6⇥10�3 [85] already starts to constrainparts of the relevant parameter space.Compared to h ! ⌧µ, the flavor violating tau de-

cay ⌧ ! µ� shows a di↵erent decoupling with the NPscales. The dominant contributions to ⌧ ! µ� comefrom loops of vector-like leptons together with the scalar' and pseudoscalar a. As ⌧ ! µ� violates Lµ � L⌧ bytwo units, the ' and a loops cancel up to terms of or-der �m2/M2 = (m2

' �m2

a)/M2 where M is the generic

mass of the vector-like leptons. The middle diagram inFig. 1 shows an example diagram corresponding to therelevant contribution in the unbroken phase. We find thefollowing ⌧ ! µ� branching ratio

BR(⌧ ! µ�)

BR(⌧ ! µ⌫⌫)' 3↵

e

8⇡

v6�m4

m2

⌧M4

EM4

L

��2⌧L�

2

µE + �2⌧E�2

µL

�

⇥YEL + YLE

✓ME

ML+

ML

ME

◆�2

, (13)

where we used the ⌧ ! µ⌫⌫ branching ratio as conve-nient normalization. Due to the suppression by the smallmass di↵erence �m2, the constraint from BR(⌧ ! µ�) <4.4⇥10�8 [86, 87], can be easily satisfied in regions of pa-rameter space that lead to a percent level BR(h ! ⌧µ).This is illustrated in the left plot of Fig. 2. We fixsin↵ = 0.2 for �m2 = 0.1v2� and �m2 = v2� and scanthe couplings YEL, YLE ,�µL,�µE ,�⌧L,�⌧L in the range0.5 � 2. We also scan 1 TeV < ME = ML < 3 TeV and0.1v < v� < 2v.For the corrections to the flavor conserving observable

(g � 2)µ, the suppression by �m2/M2 is absent. Thedominant contributions arise again from loops of vector-like leptons with ' and a. However, in contrast to ⌧ !µ�, the ' and a loops add up constructively. An examplediagram at leading order in v is shown in Fig. 1. We find

�aµ ' 1

8⇡2

mµv

MEMLYLE�µL�µE . (14)

For vector-like lepton massesM in the few TeV range andO(1) couplings, this is in the right ball park to explain thediscrepancy in Eq. (3). The center plot of Fig. 2 showsthe regions of parameter space in the �µE vs. �⌧E = �⌧Lplane where both the h ! ⌧µ signal and the (g � 2)µdiscrepancy can be explained simultaneously. In the plotwe set ME = ML = 1 TeV, YLE = YEL = 2, tan↵ = 0.2and consider the 3 scenarios: (a) �µL = �µE and v� = v;(b) �µL = 0.1�µE and v� = 0.1v; (c) �µL = 0.1�µE andv� = 3v.

An additional important constraint in the discussedsetup comes from the flavor violating tau decay ⌧ ! 3µ

2

E821 [43] and is given by [44] aexpµ = (116 592 091 ±54 ± 33) ⇥ 10�11, where the first error is statistical andthe second systematic. The SM prediction is [45–53]aSMµ = (116 591 855±59)⇥10�11, where almost the entireuncertainty is due to hadronic e↵ects. This amounts to adiscrepancy between the SM and experimental values of

�aµ = aexpµ � aSMµ = (236± 87)⇥ 10�11 , (3)

i.e. a 2.7� deviation3. Possible NP explanations be-sides supersymmetry (see for example Ref. [54] for a re-view) include leptoquarks [55, 56], additional fermions[57], new scalar contributions in two-Higgs-doublet mod-els (2HDM) [11, 58], also within the lepton-specific2HDM [59–62], and very light Z 0 bosons [63–70], in par-ticular the Z 0 gauge boson related to gauging Lµ � L⌧ .

The abelian Lµ�L⌧ symmetry is interesting in general:not only is it an anomaly-free global symmetry within theSM [71–73], it also leads to a good zeroth-order approx-imation for neutrino mixing with a quasi-degenerate ⌫µ,⌫⌧ mass spectrum, predicting a maximal atmospheric andvanishing reactor neutrino mixing angle [74–76]. Break-ing of Lµ�L⌧ is mandatory for a realistic neutrino sector,and such a breaking can also induce charged LFV pro-cesses, such as ⌧ ! 3µ [68, 77] and h ! µ⌧ [8].

In this Letter we extend the basic Lµ � L⌧ modelby including vector-like leptons which are neutral underLµ�L⌧ . We find that in this framework the h ! ⌧µ sig-nal can be naturally explained without violating boundsfrom ⌧ ! µ�. At the same time one can account for theAMM of the muon and for LFUV in rare B decays.

The Model. We consider a gauged Lµ�L⌧ model sup-plemented with one generation of heavy vector-like lep-tons. The Lµ�L⌧ symmetry amounts to assigning charge+1 to muons (and muon neutrinos), charge �1 to taus(and tau neutrinos) while keeping electrons (and electronneutrinos) uncharged. We choose the vector-like leptonsto be neutral under Lµ � L⌧ . If one aims at an expla-nation of the b ! sµµ anomalies, one can in additionintroduce vector-like quarks with appropriate Lµ � L⌧charges, as shown in Ref. [27].

The Lµ � L⌧ symmetry is broken spontaneously in ascalar sector. Besides the SM Higgs doublet H, it con-tains a SM singlet scalar �

1

that carries Lµ � L⌧ charge�1 and a second SM singlet scalar �

2

also charged underLµ � L⌧ . For reasons which will become clear later, weassume that the Z 0 mass originates to a good approxima-tion from only one of the scalars, �

2

. Assuming negligiblemixing among the scalars and no couplings of �

2

with thevector-like leptons, muons and taus (which can be eas-ily achieved by an appropriate charge assignment), theonly role of �

2

is to provide the Z 0 mass, mZ0 , whichwe will therefore treat as independent parameter. The

3 Less conservative estimates lead to discrepancies up to 3.6�

only scalar that is relevant for the charged lepton phe-nomenology is then �

1

for which we drop the subscriptin the following: �

1

! �.The vector-like leptons L and E (with the quantum

numbers of the SM lepton doublets and the lepton sin-glets, respectively) have vector-like mass terms

LM = �MLLLLR �MEELER + h.c. . (4)

The Yukawa couplings of the vector-like leptons to theHiggs doublet are given by

LY = �YLELLHER � YELLRHEL + h.c. . (5)

The vector-like leptons can also couple to muons, tausand the SM singlet �

L� = ��µLµLLR�⇤ � �⌧L⌧LLR�

��µEµREL�⇤ � �⌧E ⌧REL� + h.c. . (6)

The masses ML and ME , the Yukawa couplings YLE andYEL, as well as the couplings �i can in principle be com-plex. For simplicity, we will assume them to be real inthe following4.

The Higgs doublet H and the scalar � acquire vac-uum expectation values v ⇡ 174 GeV and v�. In thebroken phase we parameterize the neutral components ofthe Higgs and the scalar as H0 = v + (h+ iG0)/

p2 and

� = v� + ('+ ia)/p2 , where ' (a) is the CP-even (CP-

odd) component of the scalar, h will become the maincomponent of the 125 GeV Higgs and G0 provides thelongitudinal component of the SM Z boson. If � was theonly source of Lµ�L⌧ breaking, a would become the lon-gitudinal component of the Z 0. However, provided that �gives only a subdominant contribution of the Z 0 mass, aremains a physical degree of freedom and is a mass eigen-state, to a good approximation. Due to Lµ�L⌧ breaking,the masses of ' and a can be split m2

' �m2

a = O(v2�).In the broken phase, we obtain a 4⇥4 mass matrix for

the vector-like leptons, the muon and the tau

0

B@

LL

EL

µL

⌧L

1

CA

T 0

B@

ML vYLE 0 0vYEL ME v��µE v��⌧Ev��µL 0 vYµ 0v��⌧L 0 0 vY⌧

1

CA

0

B@

LR

ER

µR

⌧R

1

CA . (7)

Rotating to lepton mass eigenstates will a↵ect the cou-plings of leptons to the Z, the Z 0, the (pseudo) scalar (a)' and the Higgs h. We parameterize the couplings as

L � ��V L 0( L�

↵ 0L) + �V R

0( R�↵ 0

R)�V↵

+��S 0( L

0R) + �S

0 ( R 0L)�S , (8)

4 Note that the couplings �i are absent for electrons, as electronsare not charged under Lµ � L⌧ . However, for electrons onecould consider mixing with the vector-like leptons originatingfrom Yukawa couplings to the SM Higgs doublet, or from vector-like mass terms. We assume such terms to be absent, motivatedby the tiny electron mass. This could for example be enforcedby a global flavor symmetry under which electrons are charged.

2


�aµ = aexpµ � aSMµ = (236± 87)⇥ 10�11 , (3)






1


2


2


2


2




1


1








��µEµREL�⇤ � �⌧E ⌧REL� + h.c. . (6)



p2 and



' �m2



0

B@

LL

EL

µL

⌧L

1

CA

T 0

B@


1

CA

0

B@

LR

ER

µR

⌧R

1

CA . (7)


L � ��V L 0( L�

↵ 0L) + �V R

0( R�↵ 0

R)�V↵

+��S 0( L

0R) + �S

0 ( R 0L)�S , (8)


2


�aµ = aexpµ � aSMµ = (236± 87)⇥ 10�11 , (3)






1


2


2


2


2




1


1








��µEµREL�⇤ � �⌧E ⌧REL� + h.c. . (6)



p2 and



' �m2



0

B@

LL

EL

µL

⌧L

1

CA

T 0

B@


1

CA

0

B@

LR

ER

µR

⌧R

1

CA . (7)


L � ��V L 0( L�

↵ 0L) + �V R

0( R�↵ 0

R)�V↵

+��S 0( L

0R) + �S

0 ( R 0L)�S , (8)


W. Altmannshofer, M. Carena and A. Crivellin, [arXiv:1604.08221 [hep-ph]]

⌧ ! µ�h ! ⌧µ (g � 2)µ

Lµ � L⌧

Flavor changing top couplings

3 (2) stands for t (c)

J.A. Aguilar-Saavedra, [arXiv:0904.2387 [hep-ph]]

Warsaw basis

B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, [arXiv:1008.4884 [hep-ph]]


W. Buchmüller and D. Wyler, Nucl. Phys. B268 (1986) 621

Operator basis 1986 2010

No fermions 16 15

2 fermions 35 19

4 fermions 29 25

Dimension 6 80 59

Gauge-invariant dimension 6 operators constructed with the Standard Model fields, up to redundancies which are taking care using equations of motion for fermions and gauge and Higgs bosons, integration by parts, Pauli (SU(2)) and Gell-Mann (SU(3)) matrix properties and Fierz transformations

Ignoring flavor indices and assuming that there are not light right-handed neutrinos (and that baryon number is conserved)

Pauli (τ) and Gell-Mann (λ) matrices: Fierz rearrangements:

572 independent gauge-invariant four-fermion operators involving one or two top quarks (taking into account different fermion chiralities, colour contractions and flavour combinations) -out of the 25 different types of independent four-fermion operators-.


Three-body top decays and single and pair top production

two orderings

TABLE 1 Relevant lagrangian terms for vector-like fermion production and decay

New vector-like

fermion Dominant production terms

D

U

E

"~QCD = -- i gs A a~, 1) Ta Y ~* D

'Y~QCD = ig*Aat,(UT~7 ~'U + I)T'~Y I'D)

~"gQC D = - ig, A a~,UT a yt' U

£,°v+ z = eA~,J~M - eSw Zt, J~M; C w

Ja~ = E r i e

+ Z - - eAp.JEM

g2 ZI,( NytH,¢ Ey~'E 2 p. _ _ _ 2SWJEM ) + 2c w

+ ~ - W~+ Nf~'E + h.c.: J~M = E-/~/:"

Dominant decay terms

D

U

E

gz - , .1; _ m f \ - - D E - t t d c i ~ 7 D R) + h.c. 2Cw z~ ac, v ~ MQ

_ _ D 1 _ D I ~

dRjYU MQ DR]

g2 Z~,ULTI, Q ULi_ IfUFt -ULi] +h.c . + 2c w

g2 mti _ ".l; . ] 2~'w Z~eL'V~MTEI" - t t~'77' EO + h.c.

,~ ( g2 __ ,*lj = \ 7 W~+ NR YP" ML eRj

g2 -- D]j _ Dlj \

2Cw Zt, E R y ~ ' ~ ep, j - l l E t f ' eR , ] + h.c.

F. del Aguila, L. Ametller, G.L. Kane and J. Vidal, Nucl. Phys. B 334 (1990) 1

VLQs have a quite rich phenomenology

| 34Searches for new physics in the top quark sector at the LHC

Nuno Castro, Granada, 11/05/2017

Vector-like quarks: where do we stand?

| 39

● Single production is more complicate (and interesting…) from the phenomenology point of view

● Can dominate for high VLQ masses:

Phys. Rev. D 88, 094010 (2013)

Phys. Rev. D 88, 094010 (2013)

Searches for new physics in the top quark sector at the LHC


M. Chala and J. Santiago, [arXiv:1305.1940 [hep-ph]]

and BH. As we now show, the latter ensures a clean triggerand a very simple reconstruction algorithm.

The process we are interested in is therefore

pp ! G! ! BH!bþ !BHb ! Hb !b ! 4b; (14)

where the heavy gluon is produced via a Drell-Yan–likeprocess through its coupling to the SM light quarks. Due tothe large masses we can probe at the LHC, all four b quarksin the final state are very hard. We show in Fig. 4 (left) thepT distribution of the four b quarks at the partonic level,for a heavy gluon mass MG! ¼ 2:5 TeV, together with thepT distribution of the hardest b quark for the irreducible4b QCD background (distributions are normalized to unitarea). All four b jets are quite hard with the pT of the twoleading jets well above 300 and 200 GeV, respectively.This allows for a very clean trigger of the signal events andalso for the possibility of hard cuts on the pT of the leadingb jets, an important ingredient to bring the irreduciblebackground down to manageable levels.

One important feature is that, due to the relatively largemass of BH, the Higgs boson tends to be quite boosted andits decay products relatively aligned. We show in Fig. 4(right) the "R separation between the two b quarks thatreconstruct the Higgs, at the partonic level, for two differ-ent values ofMG! (recall that we haveMBH

¼ MG!=2). Wefind that less than 35% of the events have "R< 0:4 forMG! ¼ 2:5 TeV. This number goes up to 60% for MG! ¼4 TeV. Thus, it is clear that for larger heavy gluon masses,the use of boosted techniques [47,48] is likely to enhancethe sensitivity. However, we have decided to restrictourselves to traditional techniques because the use of oneless b-tag would force us to consider new backgroundprocesses that are difficult to estimate with other meansthan data-driven methods.

IV. EXPERIMENTAL ANALYSIS

In this section we describe a very simple experimentalanalysis that takes advantage of the kinematical featuresdiscussed in the previous section to disentangle the signalfrom the background. In our simulations we have usedMADGRAPH V4 [49] and ALPGEN V2.13 [50] for parton levelsignal and background generation, respectively. We haveset the factorization and renormalization scales to thedefault values and used the CTEQ6L1 PDFs [51]. Wehave used PYTHIA V6 [52] for parton showering and hadro-nization and DELPHES V1.9 [53] for fast detector simulation.Jets are reconstructed using the anti-kt algorithm withR ¼ 0:4, and we are assuming a value of 0.7 for theb-tagging efficiency. Jets and charged leptons used in ouranalysis are defined to have pj

T > 20 GeV. Charged lep-tons are also required to be well isolated from jets with"RðljÞ> 0:4. We have considered two different configu-rations for the LHC parameters with benchmark valuesffiffiffis

p ¼ 8 TeV and an integrated luminosity of 20 fb&1

(LHC8) andffiffiffis

p ¼ 14 TeV with an integrated luminosityof 100 fb&1 (LHC14).

FIG. 3. Hb !b production cross section in the benchmark model,Eqs. (11) and (12), with gc ¼ 3, as a function of MG! . MF inEq. (11) has been chosen such that the lightest fermionicresonance has a mass MG!=2.

[GeV]T

p0 200 400 600 800 10000

0.05

0.1

0.15

0.2

Background

4b

3b

2b 1b

)H

,b’H

R(b∆0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.05

0.1

0.15

0.2

0.25

0.3

0.35 = 4 TeVG*M

= 2.5 TeVG*M

FIG. 4. Left: Parton level pT distribution of the 4 b quarks in the signal (denoted in decreasing order of pT by b1;2;3;4) and of thehardest b quark in the irreducible 4b background. Right: "R separation between the two b quarks from the Higgs decay at the partoniclevel for two different values of the heavy gluon mass. The mass of the heavy bottom is in both casesMBH

¼ MG!=2. All distributionsare normalized to unit area.

Hb !b PRODUCTION IN COMPOSITE HIGGS MODELS PHYSICAL REVIEW D 88, 035010 (2013)

035010-5

and BH. As we now show, the latter ensures a clean triggerand a very simple reconstruction algorithm.

The process we are interested in is therefore

pp ! G! ! BH!bþ !BHb ! Hb !b ! 4b; (14)

where the heavy gluon is produced via a Drell-Yan–likeprocess through its coupling to the SM light quarks. Due tothe large masses we can probe at the LHC, all four b quarksin the final state are very hard. We show in Fig. 4 (left) thepT distribution of the four b quarks at the partonic level,for a heavy gluon mass MG! ¼ 2:5 TeV, together with thepT distribution of the hardest b quark for the irreducible4b QCD background (distributions are normalized to unitarea). All four b jets are quite hard with the pT of the twoleading jets well above 300 and 200 GeV, respectively.This allows for a very clean trigger of the signal events andalso for the possibility of hard cuts on the pT of the leadingb jets, an important ingredient to bring the irreduciblebackground down to manageable levels.

One important feature is that, due to the relatively largemass of BH, the Higgs boson tends to be quite boosted andits decay products relatively aligned. We show in Fig. 4(right) the "R separation between the two b quarks thatreconstruct the Higgs, at the partonic level, for two differ-ent values ofMG! (recall that we haveMBH

¼ MG!=2). Wefind that less than 35% of the events have "R< 0:4 forMG! ¼ 2:5 TeV. This number goes up to 60% for MG! ¼4 TeV. Thus, it is clear that for larger heavy gluon masses,the use of boosted techniques [47,48] is likely to enhancethe sensitivity. However, we have decided to restrictourselves to traditional techniques because the use of oneless b-tag would force us to consider new backgroundprocesses that are difficult to estimate with other meansthan data-driven methods.

IV. EXPERIMENTAL ANALYSIS

In this section we describe a very simple experimentalanalysis that takes advantage of the kinematical featuresdiscussed in the previous section to disentangle the signalfrom the background. In our simulations we have usedMADGRAPH V4 [49] and ALPGEN V2.13 [50] for parton levelsignal and background generation, respectively. We haveset the factorization and renormalization scales to thedefault values and used the CTEQ6L1 PDFs [51]. Wehave used PYTHIA V6 [52] for parton showering and hadro-nization and DELPHES V1.9 [53] for fast detector simulation.Jets are reconstructed using the anti-kt algorithm withR ¼ 0:4, and we are assuming a value of 0.7 for theb-tagging efficiency. Jets and charged leptons used in ouranalysis are defined to have pj

T > 20 GeV. Charged lep-tons are also required to be well isolated from jets with"RðljÞ> 0:4. We have considered two different configu-rations for the LHC parameters with benchmark valuesffiffiffis

p ¼ 8 TeV and an integrated luminosity of 20 fb&1

(LHC8) andffiffiffis

p ¼ 14 TeV with an integrated luminosityof 100 fb&1 (LHC14).

FIG. 3. Hb !b production cross section in the benchmark model,Eqs. (11) and (12), with gc ¼ 3, as a function of MG! . MF inEq. (11) has been chosen such that the lightest fermionicresonance has a mass MG!=2.

[GeV]T

p0 200 400 600 800 10000

0.05

0.1

0.15

0.2

Background

4b

3b

2b 1b

)H

,b’H

R(b∆0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.05

0.1

0.15

0.2

0.25

0.3

0.35 = 4 TeVG*M

= 2.5 TeVG*M

FIG. 4. Left: Parton level pT distribution of the 4 b quarks in the signal (denoted in decreasing order of pT by b1;2;3;4) and of thehardest b quark in the irreducible 4b background. Right: "R separation between the two b quarks from the Higgs decay at the partoniclevel for two different values of the heavy gluon mass. The mass of the heavy bottom is in both casesMBH

¼ MG!=2. All distributionsare normalized to unit area.

Hb !b PRODUCTION IN COMPOSITE HIGGS MODELS PHYSICAL REVIEW D 88, 035010 (2013)

035010-5

I2 ki del Aguila et al. / Higgs production

TABLE 7a Frac t ion of (vector-l ike) QQ) decays into final s tates wi th at most one neutr ino. {' s tands for c and ~t. We take an average for the b ranch ing rat io into W, Z and H (see text) and assume that H a lways decays into

qq. For each mode wc give in parentheses the fraction of events with at least one Higgs

D e c a y mode (Frac t ion of events Signal fract ion wi th a Higgs)

qTq[{{¢ 3 × 10 -4 ( ) q ~ { f { v 4 × 10 . 3 ( ) qqq£q {'{ 0.03 (0.33 ) qYqqq[v 0.17 (0.33) q q q q q q 0.59 (0.55)

quark singlets, whereas the difference with the ( ~ ) doublet is simply that in this case both U and D contributions have to be summed up, due to the assumed degeneracy of their masses, resulting in cross sections a factor of two larger than those of the singlet cases (table 7b). This may not be enough to distinguish between singlet and doublet vector-like quarks in hadron colliders. The best way to distinguish between them and a sequential quark is provided by the ratio

f? j j j j /dv j j j j - ~6 (0 ) , (3.2)

for a vector-like (sequential) quark.

TABLE 7b Tota l cross sect ions (in pb) for the signals wi th at least one lepton, and for different col l iders and

i l lustrat ive vector-l ike quark masses

qC t E?E• qq {?d v qYqqZqt@ qqqq t ~ v 1 U 1 U 1 U u)

Teva t ron MQ = 150 GeV 2 X 10 -3 0.03 0.2 1.3

U N K MQ = 300 GeV 2 × 10 3 0.03 0.2 1.2

L H C MQ = 700 GeV 3 × I0 4 4 × I0 -3 0.03 0.2

SSC MQ = 700 GeV 4 × 10 3 0.05 0.4 2.4

I2 ki del Aguila et al. / Higgs production

TABLE 7a Frac t ion of (vector-l ike) QQ) decays into final s tates wi th at most one neutr ino. {' s tands for c and ~t. We take an average for the b ranch ing rat io into W, Z and H (see text) and assume that H a lways decays into

qq. For each mode wc give in parentheses the fraction of events with at least one Higgs

D e c a y mode (Frac t ion of events Signal fract ion wi th a Higgs)

qTq[{{¢ 3 × 10 -4 ( ) q ~ { f { v 4 × 10 . 3 ( ) qqq£q {'{ 0.03 (0.33 ) qYqqq[v 0.17 (0.33) q q q q q q 0.59 (0.55)

quark singlets, whereas the difference with the ( ~ ) doublet is simply that in this case both U and D contributions have to be summed up, due to the assumed degeneracy of their masses, resulting in cross sections a factor of two larger than those of the singlet cases (table 7b). This may not be enough to distinguish between singlet and doublet vector-like quarks in hadron colliders. The best way to distinguish between them and a sequential quark is provided by the ratio

f? j j j j /dv j j j j - ~6 (0 ) , (3.2)

for a vector-like (sequential) quark.

TABLE 7b Tota l cross sect ions (in pb) for the signals wi th at least one lepton, and for different col l iders and

i l lustrat ive vector-l ike quark masses

qC t E?E• qq {?d v qYqqZqt@ qqqq t ~ v 1 U 1 U 1 U u)

Teva t ron MQ = 150 GeV 2 X 10 -3 0.03 0.2 1.3

U N K MQ = 300 GeV 2 × 10 3 0.03 0.2 1.2

L H C MQ = 700 GeV 3 × I0 4 4 × I0 -3 0.03 0.2

SSC MQ = 700 GeV 4 × 10 3 0.05 0.4 2.4

Vector-like quarks: what next?

| 43

● With more data we will have new opportunities for discovery (or

to improve on exclusion limits…):

[arXiv:0907.3155]

This is an old study on the discovery reach of 500 GeV VLQs

→ the message is still valid: different channels are required for a

discovery (and to identify the nature of the discovered VLQ)



TABLE 1 Relevant lagrangian terms for vector-like fermion production and decay

New vector-like

fermion Dominant production terms

D

U

E

"~QCD = -- i gs A a~, 1) Ta Y ~* D

'Y~QCD = ig*Aat,(UT~7 ~'U + I)T'~Y I'D)

~"gQC D = - ig, A a~,UT a yt' U

£,°v+ z = eA~,J~M - eSw Zt, J~M; C w

Ja~ = E r i e

+ Z - - eAp.JEM

g2 ZI,( NytH,¢ Ey~'E 2 p. _ _ _ 2SWJEM ) + 2c w

+ ~ - W~+ Nf~'E + h.c.: J~M = E-/~/:"

Dominant decay terms

D

U

E

gz - , .1; _ m f \ - - D E - t t d c i ~ 7 D R) + h.c. 2Cw z~ ac, v ~ MQ

_ _ D 1 _ D I ~

dRjYU MQ DR]

g2 Z~,ULTI, Q ULi_ IfUFt -ULi] +h.c . + 2c w

g2 mti _ ".l; . ] 2~'w Z~eL'V~MTEI" - t t~'77' EO + h.c.

,~ ( g2 __ ,*lj = \ 7 W~+ NR YP" ML eRj

g2 -- D]j _ Dlj \

2Cw Zt, E R y ~ ' ~ ep, j - l l E t f ' eR , ] + h.c.

BR, XR ! WtR

TL + T 0L ! HtR

TR � T 0R ! ZtR

9>=

>;

A. Atre, M. Carena, T. Han and J. Santiago "B. [arXiv:0806.3966 [hep-ph]]

8><

>:

8><

>:

�t = �0t

M 16= M 7

6

�b = 0[2 1

6, 2 7

6] =

✓TB

◆,

✓XT 0

◆�

1

1 IntroductionThe discovery of a Higgs boson at the CERN LHC [1, 2] has completed a long search for thefinal missing piece of the standard model (SM). The Higgs boson mass however lies in anenergy regime where it causes the so-called hierarchy problem due to quadratic divergencesin the quantum-loop corrections. Extensions of the SM predict new heavy particles to cancelthese quantum-loop corrections. We focus on heavy fermionic partners of the SM top quark aspredicted in composite Higgs theories [3, 4], with an exotic electric charge of +5/3 in units ofthe elementary positive charge, referred to as X5/3.

We present a search for events where the X5/3 is pair produced with its anti-particle via thestrong interaction. Each X5/3 then decays into a top quark and a W boson (tW) with 100%branching fraction as shown in Fig. 1. We require one of the W bosons to decay into leptons(an electron or muon and a neutrino), while the other three W bosons decay hadronically. Theeffect of chirality is taken into account by considering two coupling scenarios separately: al-lowing purely left-handed (LH) or right-handed (RH) X5/3 coupling to W bosons. For heavyX5/3, the spin correlations can affect the kinematical distributions of the decay products in asignificant way, resulting in differences in signal efficiencies [5]. In this search, differences insignal efficiencies are small when searching for LH or RH X5/3 with the same selection criteria.

q

q

g

5/3X

5/3X

+W

t

−W

t

g

g

g

5/3X

5/3X

+W

t

−W

t

Figure 1: Leading order Feynman diagrams for the production and decay of pairs of X5/3particles.

Previous searches for X5/3 were performed by both ATLAS and CMS experiments. Using thedata collected at

ps = 8 TeV, CMS results excluded masses below 800 GeV [6] in the same-

sign dilepton final state. Similar exclusion limits were also set by the ATLAS experiment againusing data collected at

ps = 8 TeV in both the same-sign dilepton [7] and the single lepton [8]

final states. This search uses proton-proton (pp) collision data corresponding to an integratedluminosity of 35.9 fb�1, collected by the CMS experiment at a center-of-mass energy of 13 TeVin 2016.

2 The CMS detectorThe central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diame-ter, providing a magnetic field of 3.8 T. Within the superconducting solenoid volume are a sili-con pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass andscintillator hadron calorimeter, each composed of a barrel and two endcap sections. Forwardcalorimeters extend the pseudorapidity coverage provided by the barrel and endcap detectors.Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke out-side the solenoid. The first level of the CMS trigger system, composed of custom hardware

X5/3 masses with right-handed (left-handed) couplings below 1.32 (1.30) TeV are excluded at 95% confidence level

Under the assumption of strong pair production of vector-like quarks and 100% !branching fractions to bW, an observed (expected) lower limit of 1295 (1275) !GeV at 95% CL is set on the T2/3(Y-4/3) quark mass

CMS Collaboration, CMS PAS B2G-17-003

CMS Collaboration, CMS PAS B2G-17-008

M. Chala, [arXiv:1705.03013 [hep-ph]]

0.0 0.2 0.4 0.6 0.8 1.0

BR(T ! Wb)

0.0

0.2

0.4

0.6

0.8

1.0

BR

(T!

Ht)

M = 700 GeV

mS = 100 GeV

BR(T ! St) = 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

BR(T ! Wb)

0.00.10.20.30.40.50.60.70.80.9

BR

(T!

Ht)

M = 700 GeV

mS = 100 GeV

BR(T ! St) = 0.1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

BR(T ! Wb)

0.00.10.20.30.40.50.60.70.8

BR

(T!

Ht)

M = 700 GeV

mS = 100 GeV

BR(T ! St) = 0.2

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

BR(T ! Wb)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

BR

(T!

Ht)

M = 700 GeV

mS = 100 GeV

BR(T ! St) = 0.3

Figure 6: Excluded regions in the space of branching ratios for M = 700 GeV and mS =100 GeV. The gray area results from a combined statistical analysis of all signal regions oftab. 2. In the green area, the St+X events are disregarded. The red region is excluded bythe analysis of ref. [35]. Likewise, the blue region is excluded by the analysis of ref. [34].

of how constraining current searches are if T decays also into some elusive channel (forexample into very soft final state particles). In other words, it reflects departures fromeq. 3.1 by an amount of BR(T ! St). Clearly, in the limit in which BR(T ! St) = 0, thisregion coincides with the gray one. In the limit BR(T ! St) = 1, this region is empty.The red region enclosed by the dashed red line represents the area excluded by searchesfor Ht + X at 13 TeV of c.m.e., as explained in section 3.2. Finally, the blue regionenclosed by the dashed blue line represents the area excluded by searches for Wb + X at13 TeV of c.m.e., as explained in section 3.3. Let us discuss these results case by case.

M = 700 GeV: All combinations of branching ratios are excluded, independently onthe value of BR(T ! St). Note that we do not show results for values of this rate largerthan 0.3. The reason is that, according to the plot in the right panel of fig. 5, such

15

Ht + X Wb + X Zt + X CMSc.m.e. [TeV] 8 8 13 13

HtHt, HtWb, WbWb ZtZt, ZtHt, StStChannels HtZt ZtWb, StHt,

StZt, StWbNb 81 27.6 6.5 9.6, 0.16Nd 84 30 7 14, 1Ns 22 15 8 13, 5

Table 2: Experimental analyses considered in this work and channels for which e�ciencieshave been estimated. The number of observed and expected SM events in each signalregion are also shown. Any signal leading to more than Ns events in at least one analysisis excluded, although stronger bounds are obtained if the di↵erent analyses are combinedinto a shape analysis. See the text for details.

that values of M as large as 1100 GeV are excluded for BR(T ! St) = 1. Much lighterresonances are still allowed if the branching ratio is smaller. In that case, however, decaysinto SM particles are also present. Consequently both standard and exotic T decays haveto be considered at once. We address this point in the next section.

5 Final results

At this stage, the number of signal events passing the cuts of the analyses reported intab. 2 can be computed for arbitrary branching ratios of a heavy top T into Zt, Ht, Wbot St. We recall that St stands for an invisible S, while the BR(T ! St, S ! bb) isincluded in BR(T ! Ht). The number of expected and observed events for each analysisare also written in the table. Given this information, bounds combining all these searchescan be obtained by using the CLs method as described in section 3.1. These are shown infigs. 6, 7, 8 and 9 for di↵erent values of M and di↵erent choices of BR(T ! St). Giventhe small dependence of searches for St + St on the value of mS (see the right panel offig. 5), we have fixed mS = 100 GeV in all plots. We have also assumed

BR(T ! Ht) + BR(T ! Wb) + BR(T ! Zt) + BR(T ! St) = 1 . (5.1)

The di↵erent colors have the following meanings. The gray area enclosed by the solidblack line shows the region excluded after combining all the (statistically independent)signal regions presented in tab. 2. In the green one, enclosed by the dashed green line, wedo the same, but neglecting the events resulting from T ! St. This region gives an idea

14

Vector-like quarks: what next?

| 44

● But there is also a lot to do beyond that (and already with 100/fb):

● More data will allow us to have more elaborate analysis

● Advanced MVA techniques

● Continue to explore (and improve) the use of boosted objects and top/W/Z/H tagging

● And also to be more advanced in our assumptions

(actually some of this work already started in run-1…)

● Present limits relaxing the S BR(VLQ→ SM) =1 assumption

● Test the chirality of the VLQ couplings

● Coupling to light generations

● Alternative production mechanisms



Further conclusions

• Rare processes

• Much richer phenomenology when lower is the new physics scale

• Complementary to production

( ⇠ m0

M ! m02

M2 )

( E ⇠ M )

Thanks for your attention

Documents

Vector-like fermions: a reviewbenasque.org/2017lhc/talks_contr/232_FAguila.pdf · There is a large number of papers on the subject: • H. Fritzsch, M. Gell-Mann and P. Minkowski,