Can we measure the Higgs boson’s quantum numbers?

D.J. Miller

University of Glasgow

22nd November 2007

Introduction

The Higgs boson’s Spin

The Higgs boson’s CP

CP Violating Higgs bosons

Conclusions

Outline:

Are secrets of the universe just about to be reveal ed?

The invisible force which explains the nature of life, the universe and everything was first predicted by an Edinburgh scientist.

Now, a team of Glasgow University physicists are preparing to discover if he was right.

"The exciting thing is that we have no idea what we will find," say Parkes. "It could be the Higgs boson, or it could be something else entirely .”

At dinner parties, Dr Parkes is often too embarrasse d to admit what he does for a living.

There is even a plucky band of space boffins … [led] by an English ex-pop star. You couldn’t make it up. Physicist Brian Cox, an expert on the forces created by the Big Bang and science adviser on Sunshine, played keyboards for Nineties rock group D:Ream.

This is just a tiny part of an equation which stretches to 36 lines. Scientists say it explains everything in the universe.The only trouble is that one of its key ingredients, the Higgs particle represented by the letter H, has never been found. CERN hope their particle machine will find the missing clue.

Brian says: “It explains everything in physics from why is the sky blue to why chemistry works.”

They are just one of the things Brian and his colleagues hope to find in a £2BILLION project to blast, pulverise and smash the atom in a recreation of the forces unleashed by the Big Bang….

Almost right!(missed gW)

1. Introduction

If the Higgs boson exists, it is almost certain that the LHC will see it within 10fb-1 or so:

Notice that heavier Higgs bosons are dominated by leptons.

(or Tevatron)

I have a question for the experimenters about CMS’s figures (I know this is the wrong audience….)

How can we reconcile these plots?

CMS Also produce a “required luminosity” plot:

This reflects the Higgs decay branching ratios:

For low Higgs mass, the Higgs predominantly decays to b-quarks

For higher Higgs mass, the Higgs predominantly decays to gauge bosons.

The leptons is more significant than because it is so clean.

Electroweak precision data:

We have good indications that the Higgs boson will be reasonably light:

triviality

vacuum stability

[Numbers from Terry Wyatt’s talk at EPS 07]

(95% conf.)

Folding in LEP limit gives (95% conf.)

Imagine we discover a “Higgs-like” resonance at the LHC.

How do we know that it is the Higgs boson?

We need to measure:

Higgs CP and spin

The Higgs is a pretty weird object – we have never seen a fundamental scalar before.

Also should ensure it is not a pseudoscalar, or a mixture of scalar and pseudoscalar.

Higgs couplings to fermions and gauge bosons

Must be proportional to the particle masses

Higgs self couplings

In principle allows us to reconstruct the Higgs potential (out of reach of the LHC)

The first 2 are intimately linked since CP and spin restrict the form of the couplings.

In this talk, I will concentrate on the first requirement: Higgs CP and spin

I consider a reasonably heavy Higgs boson, 150 - 200 GeV, and look at its decay

All the information on the Higgs spin and CP is contained in this vertex

Our approach: Write down the most general vertex for a particle of a particular spin and CP coupling to ZZ and see how it differs from the SM Higgs.

HZ

Z

In principle, there are lot of other production mechanisms, decays and couplings one could exploit.

For example,

Production at LHC:

(W boson fusion)

Production at ILC:

Decays:

[see arXiv:0708.0458 for references]

2. Higgs boson spin(or lack thereof)

Let’s start with an example: distinguishing the SM state from an axial vector

SM coupling:

General axial-vector coupling:

“constants” could be (dimensionless) functions

of momenta

Z momenta:

Notice that the 0- terms always contain a momentum dependence, unlike the SM.

Examine the dependence of the cross-section on the virtuality of the off-shell Z boson:

This β comes from phase space , not the Higgs properties.

⇒ At threshold (β → 0) dependence on β is linear.

β is the Z*/Z three-momentum in the H rest frame, in units of the Higgs mass MH.

By contrast, for the axial-vector, the cross-section is

[helicityamplitudes]

⇒ At threshold (β → 0) have β3 rise.

For even normality, only spin 0 and spin 2 give ΓH ∼ β

O(1) is caused by gµ β1 gν β2 term in coupling. (I will come back to this.)

This is reflected for almost all spin choices: normality

For odd normality, only spin 1 shows Γ ∼ β

The time only 1+ has a linear dependence.

If we set the dangerous terms to zero ,

and

(Even normality only)

Higher spins (≥ 3) always show a steeper dependence on β

Even normality:

Odd normality:

So, an observation of a β dependence near threshold rules allows only 0+, 1- or 2+

dependence

dependence

dependence

Ruling out the dangerous terms:

If we see or then 1- (in fact any odd spin) is ruled out generally by Yang’s theorem

Alternatively use angular correlations of the leptons

SM has

By contrast 0- has so no term

And the offending spin-2 term causes all so contains terms such as

which are absent in the SM.

3. CP Quantum Numbers

You may have noticed in the above that we also had 0-, so we can use the same ideas to check the CP of the Higgs.

A CP odd term must take the form which leads to

CP odd

SM

here included ΓZfor both Z’s

Alternatively (or above the ZZ threshold), one can use angulardistributions again.

This provides a very clear distinction between 0+ and 0- states.

Standard Model

CP odd

Note that and simultaneously CP violation

But or CP is conserved

The most general vertex for a spinless particle coupling to a Z boson is

SM coupling(CP even) CP even CP odd

The SM is given by a=1, b=c=0.

a can always be chosen to be real, but b and c can be complex.

4. CP violating Higgs couplings

since it may just be that the Z couples to the CP even or CP odd part

This vertex manifestly doesn’t satisfy the expected Ward identities:

i.e. and

In principle, one could make the extra terms in the vertex satisfy these identities by rewriting them as, for example

A note on gauge invariance

Notice that this term still breaks the Ward identities, but this is not surprising since the Ward identities are broken also for the SM.

This is because electroweak symmetry is already broken. The Ward identities only need to hold in the limit

The above vertex is equivalent to the original vertex with a redefinition of a and bsince extra terms like will vanish when contracted with conserved currents.

The total rate

The most obvious expectation is to have a SM like coupling plus an extra CP violating part, i.e and c small

This will boost (or shrink) the total rate for

Can we distinguish the extra couplings via that total width to Z’s?

m1 and m2 are the virtualities of the Z-bosons, which must be integrated over

Examine the total number of events observed in leptonsas according to the ATLAS TDR study [Hohlfeld, ATL-PHYS-2001-004].

Initial cuts: Two leptons with

Two additional leptons with

All four leptons with rapidity

Compare signal with background in a small window around mH and usual lepton identification and reconstruction efficiency applied.

Additionally: For mH = 150 GeV,

+ impact parameter and isolation cuts

For mH = 200 GeV,

+ pT of hardest Z

Notice that there were no K factors in the ATLAS study.

For the production this may enhance the rate by up to a factor 2

For the decay, NLO changes the rate by about 5%

The ATLAS study found:

For and

signal: 67.6 events background: 8.92 events

For and

signal: 54 events background: 7 events

The number of signal events will be increased or decreased by our altered coupling,but the backgrounds will stay the same.

We assumed that the effect of the cuts on the signal is the same as the SM.

We only allowed the HZZ coupling to change.

In principle, the same physics that changes the HZZ coupling may change the HWW coupling. Although this wouldn’t effect the HZZ width, it would effect the HZZ branching ratio.

Set b=0 for simplicity

Scale up to

NSSM is the number of signal events in the SM, and we calculated the number with an

altered coupling NS. If the number of background events is NB, then we expect a typical fluctuation of the SM total events to be

Then the significance of any deviation is

Deviation from the SM (with b=0)

>5σ <3σ 3-5σ

It is impossible to tell whether the difference arises from an overall factor (e.g. bigger a) or a new term in the coupling. So the total rate is not a lot of use.

Also, we can’t measure the phase of c.

Threshold behaviour

Previously we saw how the threshold behaviour could distinguish a CP even and CP odd state. Can we do the same with a CP-violating vertex?

Only one term (the square of the CP-even part) has a linear dependence on β (this comes from the phase space)

However, this term will dominate the threshold dependence as long as .

So the threshold is not much use for distinguishing a CP mixed vertex – it will just look like the CP even case.

This is good for telling a pure CP even state from a pure CP odd state, but cannot distinguish a mixed CP state.

Angle distributions

These were very good at distinguishing the CP odd and CP even states. Can we use these to distinguish a vertex which simultaneous contains both CP even and CP odd contributions?

distribution:

SM

CP odd

Mixed CP

SM

CP odd

Mixed CP

Notice there is an asymmetry for the CP mixed state for both angular distributions

⇒ we can construct asymmetries too

distribution

Asymmetries

We can construct asymmetries which vanish when CP is conserved:

e.g. the most obvious observable to use for an asymmetry is

vanishes if a=0 or c=0so truly tests to see if

both are present

x and γb are kinematic factors

suppressed by factor

So we can already anticipate that this might be small.

This is the perfect theoretical asymmetry

It includes no backgrounds.

We still need to figure out how well this can be measured.

Calculate significance using number of events from ATLAS TDR study.

The backgrounds will not contribute to the numerator of the asymmetry (since they conserve CP) but will contribute to the normalisation.

Also background fluctuations may mimic an asymmetry.

Statistical fluctuation

Significance

Since backgrounds don’t contaminate the asymmetry itself (only the normalisation) we can use event sample before the additional cuts outlined earlier.

Not very good significance

We can see why this is by examining an analytic expression for the angular distributions

poor significance caused by η

some other terms have no such supression

For example, probes ℜe(c)

Provides bigger asymmetries…

Alternatively

…and better exclusion

Complicated asymmetries which pick up multiple contributions do best.

e.g. probes ℜe(c)

Evidence (3σ) of CP violation for

Discovery (5σ) of CP violation for

Evidence (3σ) of CP violation for

Discovery (5σ) of CP violation for

(x) denotes a dependence which may be suppressed if b and/or c are small

e.g.

For completeness, we examined 6 different observables and constructed asymmetries from them:

Dependences:

It is important to probe the structure of Higgs vertices at the LHC, since it gives us insight into the CP and spin of the Higgs boson.

We have investigated the HZZ vertex in leptons .

The spin is nicely determined by examining the threshold behaviour (if ) or angular distributions of the leptons.

The CP can be similarly determined if the Higgs is a pure CP odd or CP even state.

The total rate does not probe CP violation (but is still interesting)

Asymmetries constructed from angles of the leptons must be used to definitively study CP violating vertices.

Many asymmetries are small due to vector-axial interference, but can construct some which have reasonable sensitivity to new couplings.

Can potentially provide exclusion limits on these couplings at the LHC.

5 Summary and Conclusions