Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://qfthep.sinp.msu.ru/talks2015/1435297199_SRSamara.pdf Äàòà èçìåíåíèÿ: Fri Jun 26 08:39:59 2015 Äàòà èíäåêñèðîâàíèÿ: Sat Apr 9 23:23:26 2016 Êîäèðîâêà:

Multi-Higgs models. Perspectives for identication of wide set of models in future experiments at colliders in the SM-like scenario
Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia; Novosibirsk State University, Novosibirsk, 630090, Russia

I. F. Ginzburg


BASICS
1. Higgs boson
h

with mass 125 GeV is discovered at LHC

2. Its properties are close to those in minimal SM (SM)

SM-like scenario is realized

This scenario does not ruled out extended Higgs sector, containing new neutral and charged scalars. Higgs mechanism of EWSB can be realized in both well known minimal model (SM) and with more complex non-minimal Higgs sector.


Non-minimal models for EWSB
1. Models in which non-zero v.e.v. is formed by Higgs doublets like in SM only. Other elds have no independent v.e.v.'s. 2. Models with alternative explanations or (and) additional mechanisms with additional v.e.v.'s for some other elds scalars, triplets, etc., little Higgs, orbifold, radion,...

!


I discuss only models of the rst group
(n fundamental weak isodoublets, p1 real weak isosinglets S1)

nH D M + p2(H S2M ) + p1(H S1M )
p2

complex weak isosinglets

S2

and

(since 1973) at some values of parameters can explain CP violation, FCNC, etc gives Dark Matter (Inert doublet Model IDM) (without CP violation in Higgs sector and FCNC) realizes Higgs sector of MSSM
"

2HDM

Examples


2H DM + 1(H S2M ) 3H D M

realizes Higgs sector of nMSSM

gives Dark Matter (IDM) with CP violation and possible FCNC gives asymmetric Dark Matter 6H DM is used for some symmetry problems

#


The non-minimal models contain new scalar particles new Higgs ± bosons, neutral ha with masses Ma and widths a, just as charged Hb b with masses M± and widths b . ± Necessary step in the discovery of such model is observation of these additional Higgses.

$


Lesson
In the general form these models are determined by huge number of constants. For example, 2HDM contains two elds with identical quantum numbers. Its description in terms of original elds or in terms of their linear superpositions are equivalent; this statement verbalizes the reparameterization (RPa) freedom of the model. This freedom means that the standard description of model contains irrelevant parameters like gauge xing. All parameters of model can be expressed via measurable parameters observables. The minimal set of observables for 2HDM contains 4 masses of scalars M±, M1-3, v.e.v. of Higgs eld v = 246 GeV, two of three couplings g(W +W -ha), 3 triple Higgs couplings g(H +H -ha) and one quartic coupling g(H +H -H +H -)
%


We dene relative couplings
P P = ga , , a P gS M

(P = W, Z, t, b, , ...)
+- Hb Hb ha

The models with charged Higgs bosons contain vertices ± and Hb W ha. For them, we dene relative couplings
± ± g (Hb W ha) Hb W ; a = MW /v +- g (Hb Hb ha) ±b = . a 2 /v 2M±

The neutrals ha generally have no denite CP parity. Couplings V and a ±b are real due to Hermiticity of Lagrangian, while other couplings a are generally complex. The Re(f ) and I m(f ) are responsible for the a a interaction of fermion f with CP-even and CP-odd components of ha respectively.
&


Conditions for CP conservation

In the CP conserving case some of In this case we have
(a)

a

ha

are scalars, others are pseudoscalars.
(c)

a

V = 0 , a

(b)


a

±b = 0 , a

f = a


a

f a

for each fermion

f.

(In the 2HDM with CP conservation we have h3 = A (pseudoscalar) and V = 0, ± = 0, I m(f ,1) = 0, Re(f ) = 0. In this model the 3 3 2 3 relationship (c) for fermions follows from the (a) for gauge bosons.)
'


Some of them are known in CP conserving 2HDM with some denite forms of Yukawa interaction. All discussed Sum rules allow CP violation and arbitrary form of Yukawa interaction Sum rules for couplings of neutral Higgses ha to vector bosons a V (real due to Hermiticity of Hamiltonian) describe the fact that the masses of gauge bosons are given by Higgs mechanism of EWSB:

Sum rules

·



a

( V )2 = 1 , a

(V = W, Z ) (H S2M ) + p1(H S1M )


valid for any nH D M + p2 mo del. (One can be W = Z or W = Z ). a a a a


Sum rules for couplings (generally complex!)


·

a

f

of neutrals to separate fermion

f

a

(f )2 = 1 a

valid for nH D M + p2(H S2M ) + p1(H S1M ) mo del, when Higgs singlets don't interact with fermions.




To prove this SR, we write general Yukawa interaction for given f ¯ fermion (before EWSB) Lf = gj f 0f . Simple reparameterization j Y
¯ 0 term to the form Lf = g1f f 1 f . In this form Yukawa term coincides Y with that of 2H DM I or 2H DM I I , where such sum rules were proven earlier. The relations between couplings a for dierent fermions f vary for f dierent forms of Yukawa interaction. 0 = N g f g f 0 1 1 jj j j

(N normalization factor) transforms this Yukawa




·

Sum rules for couplings H ±W ha of neutral Higgs boson ha to charged Higgs boson H ± and vector boson W ± (generally complex)
V |2 + |H ± W |2 = 1 |a a

valid for 2H DM + p2(H S2M ) + p1(H S1M ) model (e.g. nMSSM). These sum rules were proven for 2HDM by me and K. Kanishev (Phys. Rev. D, July 2015). This proof is naturally spread for models with additional Higgs singlets.

!


Our subsequent discussion is based on assumption that LHC data tell us that: 1) One Higgs boson h has mass Mh 126 GeV 2) Its couplings to gauge bosons V and fermions f are close to the SM expectations, P = |1 - |P |2| 1, . (P = V , f ) exp The realization of SM-like scenario don't shoot the doors for realization of non-minimal Higgs models. It is clear that successful experiments reduce P and, consequently, the region of the allowed parameters of each non-minimal model.
"

the SM-like scenario is realized:


No doubts that the SM-like scenario in the non-minimal model can occur if additional Higgs bosons are very heavy and are coupled only weakly with usual matter (decoupling limit). 15 years ago we (I.F.G., M. Krawczyk, P.Osland) found that, at nite (even high) precision of future experiments at LHC and at the planned linear e+e- collider even the simplest non-minimal model 2HDM with the special choice of the Yukawa interaction 2HDM-II (as in MSSM) allows several possible windows signicantly diering from the decoupling limit and implementing the SM-like scenario. Naturally, such windows exist in other models as well. These very windows are studied now by many authors.
#


Consequences from SR's in the SM-like scenario
Discov ered H ig g s boson - h1, other neutrals - ha with a 2. 1) |V |2 < V 1 . a ± W± 2) |W H |2 1 (a 2), |1 H |2 1 . a

3) The SR's for couplings to given fermions saturated by dierent ways, for example:
a) b) c) (bI ) |t | < 1 a

f



a2

f (a )2 0

can be (1a) (1b) .(1c)

for all

ha , |t | |1/b | 1 , a a ha
1

|t | |b | 1; (bI I ) a a |t 2 | |t 1 | > 1 , t 2 it 1 a a a a

for some

and

ha2

$


Prop erties of neutral Higgses

ha

For deniteness Ma > 150 GeV, |f | < 40 for f = t, a invisible interactions with dark matter particles can be added. b We compare with would be Higgs of SM with the same mass, wM . S · Decay channels and total width. The detection of ha via ha W W, Z Z is highly improbable. b At Ma < 350 GeV we have a wM (Ma). The same is valid at S Ma > 350 GeV in the case I-t for coupling to t. The main decay channel is ha b¯ with huge background the detection of each ha b is a dicult problem. At Ma > 350 GeV in the case II-t for coupling to t contribution of t¯ t b decay is enhanced so that one can be a wM (Ma). In this case one S can hope to see ha in t¯ mode. t
&


Production of heavy Higgs through a gauge vertex
was until recently assumed to ensure the best signal/background ratio and the least inaccuracy in the measurement of its parameters: W fusion at the LHC, e+e- Z ha and e+e- ha at the ILC, and ¯ e W -ha, W +H -ha at the PLC (photon collider). In view of our SR's the experiments on the search for additional Higgs bosons at the LHC and linear collider in such processes cannot be successful, their cross sections are typically one order of value lower then those calculated for wbSM, having the same mass.
'


The

a

gg

[ ] (wb) t )|2 + |I m(t )|2 (O/E )(4M 2/M 2 ) . (g g ha) = S M (g g h|Ma) |Re(a a t a

is saturated by contribution of t-quark loop.

Gluon fusion

ratio of two well known loop integrals, dened for CPodd and CP-even Higgs bosons respectively at Ma = 300 GeV we wb have (O/E )(r) 2.7. In the case a (gg ha) S M (gg h(ma)). In the case b the (gg ha) > (gg hwb (Ma)). sM
(O/E )(r)




At Ma < 350 GeV for Yukawa sector similar to Model I one can hope to observe ha as the narrow peak in the production of ¯ pairs: bb Benchmark example for CP-even h2 with M2 = 300 GeV. ( At this mass (wb) = 8.4 GeV, B RSwb)(h b¯) 0.0008, b S M ,tot M (wb) S M (h g g ) 3.4 MeV.
|t | = |b | = 6, |V | = 0.2 . In this case 2 2 2 (h2 b¯) = |b |2 · 7 MeV 250 MeV, b 2 + W - (Z Z )) = |V |2 · 8.4 GeV 340 MeV, (h2 W 2 t |2 · 3.4 MeV 120 MeV. (h2 g g ) = |2 It gives 2 0.7 GeV with B R(h2 b¯) 0.36. b ( The cross section (gg ha ¯ ) |t |2Swb)(gg bb a M h|Ma)B R(h2 b¯). b The possible CP odd admixture in h2 increases result.

Let






At Ma1 > 350 GeV, Ma2 > 350 GeV. Either two separated enhancements in t¯ production or even one enhancement (at |Ma1 - Ma2 | a1 + a2 ). t


In the description of widths ha , ha Z new information about vertices H +H -ha should be added. The knowledge of all masses and couplings a don't limit values of these vertices. V

!


(models

Using of charged Higgs

2H DM + p2(H S2M ) + p1(H S1M )).

We assume that masses M± are not extremely large and their observation has good signature. · The partial width (H + W +h1 is small, while at M± > MW + Ma the partial width (H + W +ha is relatively large for a 2. · The pro duction of Higgs b oson h1 in asso ciation with H ±W is hardly observable. · The search for Higgs b osons ha can b e successful in the following channels: q1q2 H +ha, q q W H ±ha at LHC, ¯ ¯ e H -ha, e+e- H ±W ha at ILC, H ±W ha at PLC. Certainly, ILC and PLC have advantages due to much better background conditions.
"