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How to ‘see’ the invisible at collider?

Rohini Godbole

Centre for High Energy Physics,

Indian Institute of Science, Bangalore – 560012, India

E-mail: rohini@iisc.ac.in

Rohini Godbole is a Professor at the Centre for High Energy Physics at the Indian Institute of Science.

She got her PhD from Stony Brook University, USA. She has been working for the last four decades

on theoretical Elementary Particle Physics, specialising in different aspects of particle

phenomenology. She has authored more than 250 research papers and several graduate level text

books. She is a fellow of the Indian Science Academies and the World Academy of Sciences. She was

awarded Padma Shri by Govt. of India in 2019. She was awarded R.D. Birla award of IPA in 2018

She has co-edited a book 'Lilavati's Daughters: Women Scientists of India', and 'A Girls' Guide to a

Life in Science’. She has worked for over two decades in many arenas to increase, both, the proportion

of women’s participation in science and its efficacy.

Abstract

First I describe, very briefly, the current state of affairs in particle physics. This is done with a view to put in context some of

my work related to proposals to study decay of the Higgs boson into final states that leave no evidence in the detector, the so

called 'invisible decay', at the Large Hadron Collider (LHC) as well as the next generation electron-positron colliders that are

currently under planning. This discussion will be done in a model independent way. Such a decay, if observed, will be a sure signal of Beyond the Standard Model (BSM) physics. Hence I will also discuss the framework of a specific model for BSM,

viz. Supersymmetry, wherein the strength of the invisible decay is related to the amount of Dark Matter (DM) that is observed

in the universe and also to the expected cross-section in the experiments that have been constructed to detect the relic DM in

the universe. These two studies then can be used together to evaluate the region of the parameter space of SUSY models that

can be probed at the LHC in its current and future runs.

Introduction1

With the discovery of the spin-zero Higgs-like boson H in

2012 [1] at the CERN LHC, the entire particle content of the

Standard Model (SM), the quantum gauge field theoretical description of the fundamental particles and interactions

among them, based on a gauge group SU(3)C x SU(2)L x

U(1)Y, has been experimentally observed. All measurements

of the properties of H, to date, are compatible with H being the

SM Higgs boson [2]. This discovery was the last element

needed to confirm to us the correctness of our currently

accepted description of ElectroWeak (EW) interactions as a

gauge theory [3] based on the gauge group SU(2)L x U(1)Y

where the EW symmetry is broken spontaneously using the

Higgs mechanism [4].

The mt - MW plot shown in Fig. 1 shows that the observed mass

of the Higgs boson verifies the correctness of the SM at the loop level. Since the fits use predictions of the SM including

radiative corrections, the large overlap of the green regions

with the blue regions not only tells us that the SM works

extremely well at loop level, but also that the space allowed in

this plot for physics (particles and/or interactions) outside the

1 This article is based on the talk given at R.D. Birla Award - 2018

presentation.

SM, the so called BSM, is very limited too. The plot in the

Fig. 1 (bottom) shows a recent compilation in which we see

that the couplings of the Higgs to various SM particles relative

to the predication of SM, extracted from the measured rates

are consistent with 1, the expectation for the SM.

This discovery of the Higgs was a very important step as it

closed an important chapter in the story of the SM, confirming

the mass generation mechanism. However, this is certainly not

the last chapter. The SM framework is indeed capable of

addressing issues of cosmology and the early universe.

However, there still remain a lot of observations such 1) as the

Dark Matter or 2) observation of the Matter-Antimatter

asymmetry in the Universe or 3) the closeness of MH to MW, MZ etc. The SM provides only qualitative explanations such

as in the case of Matter-Antimatter asymmetry or none at all

such as in the case of DM. Much before the 'direct' observation

of the Higgs boson, the good overlap between the grey and

green areas in the top panel of Fig. 1, for a finite mass of the

Higgs, had already convinced the particle physicists about the

basic consistency of the SM. Hence the community had been

thinking for the past few decades about physics (particles and

interactions) possibilities beyond the SM, most of them on

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Figure 1: The top panel in the figure shows regions of the MW

and mt plane allowed by direct measurements along with the

region allowed by fits to the EW precision data from the LEP,

obtained without using the experimental measurements on

MW; mt, MH (grey shaded region) and the one where

experimental information on MH is used (blue region). The

light and dark region correspond the regions enclosed by 68%

and 95% c.l. contours. This plot is taken from

http://gfitter.desy.de/Standard_Model/ The bottom panel shows a recent compilation [5] of the Higgs couplings relative

to their SM values and also upper limits on branching ratio of

the Higgs into invisible, BSM or undetermined modes,

extracted from measurements of decays into various final

states.

aesthetic grounds but which also had ideas/constructs built in

which were capable of answering these big questions of our

field. This is indicated in Fig. 2 taken from [6].

Supersymmetry [7] has been the favoured option for the BSM

among all these big ideas, because this theory is a natural

extension of the symmetry ideas which have formed the basis

of the 20th century fundamental physics and has within itself

enough theoretical structures to 'naturally' provide solutions to

all of the big problems mentioned above. Unfortunately in the

seven and a half year since the discovery of the Higgs boson at the LHC, the experiments have confirmed the predictions of

the SM in different sectors with high accuracy but have not

yet found any evidence for any of the big ideas listed in the

Fig. 2. This has led to a time of great introspection in the field

of particle physics and the community is pondering over the

next steps that the field should take. Since the paths indicated

by symmetry/aesthetic considerations have not yielded any

fruit, the consensus is that the community should be guided

more than ever by experiments. Understanding the DM is on

the top of the list of observational puzzles that lack solutions

in the framework of the SM. I want to describe some of my

work in this context. In the next section I will mention a few facts about the DM and also point out one way suggested by

us to look for the evidence for this DM candidate, 'invisible' in

the detector, by a study of the Higgs physics. I will then

summarise results of our explorations of how a particular

BSM model (viz. SUSY) can be investigated in

complementary ways at the LHC through the 'invisible' decays

of the Higgs or otherwise, as well as in experiments set up for

direct detection (DD) of the DM. I will then conclude.

Figure 2: Big questions in particle physics and score card of

the big ideas to answer them [6].

DM and Invisible decay of the Higgs Boson

Existence of DM is now confirmed through a series of

cosmological and astrophysical measurements [8]. One of the

first evidence for DM in the Universe came from observed rotational speeds of galaxies away from the centre, higher than

expected from the luminous mass known to be present in the

galaxy. These indicated existence of matter which would

provide additional gravitational force to sustain the observed

rotational speeds. Fig. 3 shows one of the astronomical

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evidences of the DM and also the summary of information

available from the CMB measurements by PLANCK [11] as

presented in [10]. DM plays an important role in structure

formation and hence CMB data is able to provide us

information about it.

In the early stages of the evolution (and expansion) of the

universe, when all the particles masses are negligible with

respect to the temperature, the number of different particle

species are in equilibrium with the photon bath. Fig. 4 shows

two possible 2→2 interaction diagrams that are allowed with

the DM particle (the electrically neutral particle which is

stable on cosmological scale) and X a SM particle, which is

essentially massless and in equilibrium with the photon bath.

When the interaction →XX is in equilibrium, the DM

particles are constantly being replenished. As the Universe

expands, though, it becomes increasingly harder for a DM

particle to find a partner to annihilate with and the forward

reaction shuts off. At this point, the DM number density

remains frozen in time.

Figure 3: The Top panel shows rotation curve [9] of spiral

galaxy Messier 33 (yellow and blue points with error bars),

and a predicted one from distribution of the visible matter

(gray line). The discrepancy between the two curves can be

accounted for by adding a dark matter halo surrounding the

galaxy. The bottom panel shows the determination of the energy budget of the Universe, taken from [10], obtained

using the data on Cosmic Microwave Background (CMB)

measurements by PLANCK [11].

The relic density of a particular type of DM particle is thus

determined by its mass and the strength of its interaction with

various SM particles. Thus a specific BSM model will then

have specific prediction for DM relic energy density. The

controlling factor is the size of annihilation cross-section and

the DM particle mass. It can be shown that for DM particles

with Electro- Weak strength cross-section and with ~O (GeV)

masses, can give rise to relic density of the right order of

magnitude. In fact it can be shown that 's, where the annihilation indicated in the top panel of Fig. 4 is provided

through an exchange of a Z boson, can only provide 0.5% of

the total energy density of the universe. Hence the SM does

not contain a good DM candidate. Thus an understanding of

the observed DM density thus necessarily requires physics

beyond the SM.

Invisibly decaying Higgs boson, and the LHC

Let me discuss a particular case where the mass and the

interaction of are such that the annihilation process where

the mediator in the bottom panel of Fig. 4 is a Higgs boson,

can play an important part in giving rise to the right relic

density of the DM particles . This also implies that the if M

< MH/2 then the Higgs boson can also decay into a pair of .

First question one may ask then is whether the experimental data obtained on the Higgs boson production and decay can be

used to constrain the occurrence of such 'invisible' decays for

the observed Higgs. Existence of such an additional decay

mode will alter the total expected width of the Higgs and

hence decrease the branching ratios of the Higgs into the SM

particles. The latter have been measured accurately as

indicated in the bottom panel of Fig. 1. Indeed a simultaneous

fit to all the observed signals and the couplings of the Higgs

with all the SM particles, while allowing for an invisible decay

mode, restricts the branching ratio in to the 'invisible' channel

to about 30% as seen in the bottom panel of Fig. 1.

Figure 4: The top panel indicates representative DM

annihilation and scattering processes. The bottom panel

indicates annihilation of a pair of DM particles through the

exchange of a mediator.

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However, this is only a roundabout way of looking for these

'invisible' decays of the Higgs. Since the particles do not

leave a signal in the detector, it will be impossible to look for

the signal of a Higgs boson, unless it is produced in association

with something else, where the something else leaves tracks

in the detector. This was the philosophy of our study proposed

in [12] wherein we looked at production of an invisibly

decaying Higgs boson in association with a vector boson, as

indicated in the top panel of Fig. 5. The Higgs boson decays

invisibly and leave no tracks, but the Z does decay into a l+l-

pair which do. Since the two colliding protons at the LHC are

moving in directions opposite to each other, the component of the initial state momentum transverse to the beam direction,

the so called transverse momentum, is zero. Conservation of

three momentum then tells us that the transverse momentum

of the leptons produced in the decay of the Z will in fact seem

to have a nonzero value as the Higgs decay products are not

seen in the detector. The event where a H is produced in

association with Z, with H decaying invisibly and Z decaying

into two leptons, will be characterised by a missing transverse

momentum and energetic lepton pair coming from the Z

decay. One can then use this feature to separate the signal from

the background. We simulated the signal as well as various

Figure 5: The Top panel indicates the processes leading to

production of a Higgs boson in association with a vector

boson V = W/Z. The Bottom panel indicates production of the

Higgs boson in the vector boson fusion channel.

background processes and investigated different kinematic

variables. Fig. 6 shows comparison of calculated signal and

the dominant background, after all the cuts which got rid of

most of the backgrounds. Even then the signal is overwhelmed by the background. However, high accuracy is possible for

both, the prediction and measurement, of the SM backgrounds

at the LHC. Thus one can just analyse dilepton + missing

transverse momentum events and look for excess over the SM

prediction. Absence or presence of an excess over the SM

prediction in the spectrum of Fig. 6 can then be converted into

information on the product of the HZ production cross-section

times the branching ratio of the Higgs into this invisible

channel. We had estimated the reach of a LHC run with beam

energy of 7000 GeV, for this product and then on the invisible

branching ratio assuming the SM value of the V H production cross section, the assumption being well justified

theoretically.

Around the same time feasibility of using production of a

Higgs boson along with two forward-backward jets, via vector boson fusion process indicated in the bottom panel of Fig. 5,

to look for the invisible Higgs was investigated [13]. In this

case the characteristic kinematic properties of the two jets are

useful but the SM backgrounds are a little larger than our case.

Table 1: Estimated reach for the invisible branching ratio of

the Higgs at the LHC with different energies and luminosities

[14]

Process 8 TeV

20 /fb

14 TeV

30 /fb

14 TeV

100 /fb

VBH 0.34 0.32 0.17

Z (→l+l-) h 0.58 0.32 0.18

Z(b��)h(substructure) - - 0.5

Z(b��)h(b-jet cluster) - - 0.55

In a later publication [14] we estimated the LHC reach for the

full beam energy, using both the above methods and also

improved cuts for the background. Here we already used

knowledge about the observed signal. In the Table I estimated

reach for the LHC with different energies and luminosities are

summarised. The current results from ATLAS and CMS have

Figure 6: Comparison of the expected signal (dashed

histogram), assuming 100% branching ratio for the H into

invisible decay products with the dominant ZZ background

(solid histogram) where one Z decays invisibly into a pair

[12].

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reported an upper limit on the invisible branching ratio of the

Higgs of 25% and 36% respectively [15]. Unfortunately, even

though the methods we suggested have been found useful and

in fact used at the LHC for directly searching for an invisibly

decaying Higgs, nature has not obliged us with a positive

signal for such a decay mode.

Complementary ways of probing the invisible Higgs

using colliders and DD experiments

Figure 7: The top panel shows the distribution of the PMSSM

parameter space, with mass of the thermal DM particle, M0

< 65 GeV, where the LHC constraints on Sparticle searches are implemented such that the relic is at most equal to the

PLANCK value, with respect to the invisible branching ratio

of the Higgs and the DD detections cross-sections. Both the

current and future experimental reaches are shown. The

bottom panel shows the expected scaled DD cross-sections as

a function of the DM mass along with the invisible branching

ratio of the Higgs on the right axis. Both the plots are from

[15].

The discussion in the above section was almost model

independent. In this part I will give a flavour of the results of

our exploration [15] of theoretically predicted values of the

invisible branching ratio of the Higgs, the expected relic

density as well as expected values of the DD cross-sections, in

the framework of the Phenomenological Supersymmetric

Standard Model (PMSSM). Due to certain symmetries that the SUSY theories possess, the lightest supersymmetric particle

0 ≅ is a perfect candidate for the DM particle, with EW

couplings with the SM particles as well as the Higgs. The mass

and the couplings of the are determined completely by the

PMSSM model parameters. The absence of any signal for

production of SUSY particles at the LHC, means that some

regions of this parameter space are already ruled out. The plot

in the top panel of Fig. 7 shows the distributions of all the LHC

allowed points in the parameter space with respect to invisible

branching ratio and the reach of the various current and future

DD experiments. We have restricted the scan to a region

where M < MH/2. Further we ensure that the theoretically

computed relic density is ≤ 0.1220 as given by the PLANCK

[17] measurement. The cross-section for the observed Higgs

boson into various final states also constrains the parameter

space further. Only the blue coloured regions are still allowed by all the current constraints and will be probed by future DD

experiments. The horizontal lines indicate capability of the

LHC and future electron-positron linear colliders, for the

invisible branching ratio of the Higgs. Thus we see that the

regions of SUSY parameter space, where the DM particle has

mass smaller than 65 GeV, will be completely probed by these

different experiments. However, the cosmological

considerations used while computing the relic density assume

that the DM was in thermal equilibrium with radiation. If the

cosmology is non-canonical and the DM is non-thermal, then

as one can see from the plot in the bottom panel, a light DM

candidate will be still allowed even after the future DD experiments have taken place. In this case the couplings will

be such that at low values of the DM masses, the currently

planned DD experiments will have no sensitivity. Thus in this

case the invisible branching ratio of the Higgs might be the

only probe for a light DM.

Conclusions

Observation of the Higgs boson has proved the correctness of

the SM. However, need for BSM physics is indicated by a

number of observational puzzles which have no explanation

in the SM. Understanding the character of the DM in the

universe is a problem in need of solution. Searches for the

'invisible' decay of the Higgs at the LHC and at the future e+e- colliders and the experiments looking for the DM via its direct

detection are complementary ways of looking for the DM. In

the framework of the PMSSM the parameter space where

M < MH/2 will be completely probed by these experiments

for a thermal DM. However, such is not the case for

nonstandard cosmology and hence non thermal DM. Even in

this situation the invisible decay of the Higgs bosons offers

possible experimental probes of this parameter space of the

PMSSM.

Acknowledgement

This work is supported by the Department of Science and

Technology, India under Grant No. SR/S2/JCB-64/2007.

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