Haunting For the Higgs Chia-Nan Yeh

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Haunting For the Higgs

Chia-Nan Yeh National Taiwan University

(Dated: January 19, 2015)

I. BACKGROUND INFORMATION In order to make the later discussion more clear. I will talk about some relative information and usual definition in experimental particle physics.

A. Jet

Quarks, gluons and anti-quarks are the constituents of protons, neutrons and other hadrons. It is a fasci- nating aspect of the physics of our world that when one of these particles is kicked out of the hadron that con- tains it, flying out with high motion-energy, it is never observed macroscopically. Instead, a high-energy quark (or gluon or anti-quark) is transformed into a spray of hadrons (particles made from quarks, antiquarks and gluons). And This spray is called a jet. This feature, which makes quarks behave so differently from charged leptons, neutrinos, photons and the like, is a consequence of the fact that quarks and gluons are affected by the strong nuclear force, while the other known particles are not.

Most forces between two particles become weaker with distance. However, due to the anti-screening effect, the longer the distance is, the stronger the interaction is. For example, when a neutron breaks, you would have a proton, plus (typically) a pion. In the breaking, a quark and anti-quark pair form in a particular way.

Note that, when a speeding electron plows into a proton and hits a quark really hard. It would generate the jet but a single quark and the initial energy of the high- energy quark is now shared among the hadrons in the jet.

But for a quark with sufficiently high energy (roughly, 10 GeV or more) only a small amount of the quarks initial energy is used in forming the mass-energy of the new hadrons; most of it is in carried in their motion-energy.

As a result, the total energy and direction of the jet is quite similar to the initial energy and direction of the initial quark. By measuring the energy and direction of all the hadrons in the jet, and determining the energy and the direction of the jet as a whole, particle physi- cists obtain a pretty good estimate of the energy, and the direction of motion, of the original quark.

B. Luminosity

The performance of particle colliders is usually quan- tified by the beam energy and the luminosity. In scattering theory and accelerator physics, the quantity that measures the ability of a particle accelerator to produce

the required number of interactions is called the luminosity(L) and is the proportionality factor between the number of events per second ^dR_dt and the cross section σ:

dR

dt = L · σ

C. 5 sigma

5 sigma is a measure of how confident scientists feel their results are. If experiments show results to a 5 sigma confidence level, that means if the results were due to chance and the experiment was repeated 3.5 million times then it would be expected to see the strength of conclusion in the result no more than once.

In particle accelerators, scientists look at the particles produced by the collisions to work out what happened.

Lots of particles are produced at the collisions but only some come from important reactions that scientists are looking for, e.g. a Higgs Boson decaying into two photons at a specific energy. But there are many other processes that can produce two photons at the right energy. The LHC looks at millions of particle collisions and counts the number of times two photons at the right energy are produced and compares this to the number predicted by current. Similar to the dice when there was an excess number of 5s, the LHC looks for an excess number of times two photons are produced; with the excess number being produced by the Higgs Boson. Once the excess reaches a 5 sigma level, the Higgs is considered discov- ered.

D. Higgs bosons in the standard model The Standard Model Higgs boson is a CP-even scalar of spin 0. Its mass is given by mh=√

2λv, where λ is the Higgs self-coupling parameter in V(φ). The expectation value of the Higgs field, v = (√

2GF)^{( −1}₂ ) ≈ 246GeV , is fixed by the measurable Fermi coupling GF, which is determined with a precision of 0.6 ppm from muon decay measurements. The quadratic coupling λ, instead, is a free parameter in the SM, and this is one of the reasons why searching for the mass of Higgs is so important. Once the mass of Higgs is determined, the value of quadratic coupling λ would be known, making it possible to investigate its behaviour up to high energy scales.

Moreover, the Higgs boson couplings to the fundamental particles are set by their masses. In other words,

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2 the SM Higgs couplings to fundamental fermions are lin-

early proportional to the fermion masses, whereas the couplings to bosons are proportional to the square of the boson masses.

II. HAUNTING THE HIGGS

In the Standard Model the elementary particles ac- quire their mass through the Higgs mechanism. This mechanism foreseens the existence of the Higgs boson, a scalar particle which couples to massive particles. Its mass is the only yet un-known parameter of the Standard Model. Constraints on its value come from the theory and from the experimental results. The Large Hadron Collider (LHC) is the machine designed for its discovery. Thanks to its high center of mass energy (14 TeV, 7 Tev for each proton) the LHC will be able to explore the whole allowed mass range while its high instantaneous luminosity (10³⁴cm⁻²s¹) will allow to assess the small cross sections involved in the Higgs production.

FIG. 1. Generic Feynman diagrams contributing to the Higgs production in (a) gluon fusion, (b) weak-boson fusion, (c) Higgs-strahlung (or associated production with a gauge boson) and (d) associated production with top quarks.

Figure 1 shows the tree level diagrams of the four main Higgs production channels in p-p collisions and their cross sections, as a function of the Higgs mass, for a center of mass energy of 14 TeV. The gluon-gluon fusion is the dominant process over the whole mass spectrum. Its cross section suffers of high QCD corrections and large uncertainties due to the gluon structure functions. The Vector Boson Fusion (VBF) cross section is about one order of magnitude lower than the gg fusion one for a large range of the Higgs masses. The two processes become comparable for high values of the Higgs mass. This process has a well known next-to-leading-order cross section, small QCD corrections and a very clear experimental signature, due to the presence of the two spectator jets with high invariant mass in the forward region. The remain- ing production processes have very small cross sections, orders of magnitude lower than those of gg and VBF.

They will be used for the Higgs discovery in association with particular Higgs decay modes to exploit final states

with a clear signature.

For the understanding and interpretation of the experimental results, the computation of all relevant Higgs decay widths is essential. A Higgs mass of about 125GeV provides an excellent opportunity to explore the Higgs couplings to many SM particles. The Higgs decays into WW and ZZ effectively need to be studied considering the decays of the gauge bosons into four fermions, i.e., the leptonic, semi-leptonic and full hadronic final states, Figure 2. However, people then didn’t know the mass of the Higgs boson yet. So they separate the every possible mass into two kinds, low mass region(110 150GeV ) and high mass region(> 150GeV ) and focus on their corre- sponding decay channel.

FIG. 2.

A. Low mass region

The most promising discovery channels for 110 <

mh< 150(GeV ) are the decay modes into a pair of photons or τ leptons thanks to their clear signature. The first process suffers of a very high background coming from Drell-Yan e⁺e⁻, pp → γγ, pp → γ + jet, pp → jetss where one or more jets are misidentified as γ. The sup- pression of the last two contributions will require a good understanding of the performance of the electromagnetic calorimeter and a reliable modeling of the amount of ma- terial in front of it. The analysis on the H → τ τ decay mode focus on the VBF production channel because of its higher signal over background ratio. The most promising final state is the one with one τ decaying into leptons and the other into hadrons. The irreducible backgrounds to this process are the QCD and EW production of two τ leptons from Z or τ^∗ with associated jets. Contribu- tions also come from W + multi − jets production and tt events in which one of the jets can be misidentified as a τ jet. The signature is characterized by the hadroni- cally decaying τ (associated to a little (∆R = 0.4) isolated jet), the leptonically decaying τ (identified from the electron or the muon with highest transverse momentum pt> 15GeV ) and the two quarks emitting the bosons in the VBF process which have a high energy and rapidity gap.

The high branching ratio of the Higgs boson into a pair of b quarks can only be exploited in the study of the Higgs production via tt fusion. The most promising final states have at least one of the two t quark decaying leptonically thanks to the clear signature offered by the presence of at least one high pt lepton from one of the two W, missing

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3 energy and 4 b-tagged jets (of which two from the Higgs).

The 4 jets are the responsible of a very high background, mostly composed by ttbb, Zbb, tt + Njets and multi- jets QCD events and are the main sources of uncertainty.

A pioneer novel study has obtained good results on the signal over background ratio by reconstructing the H → b¯b decay (produced through VBF) asking the presence of a central high ptphoton in the final state.

B. High mass region

This region corresponds to values of mh > 150GeV , where the Higgs analysis are focused on the Higgs decays into a couple of vector bosons.

The main channels of interest are those where the two vector bosons decay leptonically. The clear experimental signature of these events compensates for their low branching ratio, which is about one order of magnitude lower than the hadronic ones.

In the H → W W → lνlν channel it is not possible to reconstruct the H invariant mass due to the presence of the two neutrinos. Since the signal selection can not exploit this variable other techniques must be used for the discrimination and a good control of the background shape is mandatory. The final state presents 2 isolated high ptleptons pointing to the primary vertex, high missing energy and no hadronic activity. The signal selection relies mainly on the request of a central jet veto, high missing energy and of a small angle between the two leptons due to the V-A structure of the weak interaction.

The H → ZZ → 4l (l = muons or electrons) channels are the ”golden channels” for the Higgs discovery. The main backgrounds are: t¯t, Zb¯b and the irreducible ZZ^∗/γ^∗. The trigger and the off-line cuts rely on the presence of isolated charged leptons coming from the primary vertex, with high transverse momentum. The instrumental backgrounds become negligible with the request of lepton isolation and using different cuts on the sorted lepton transverse momenta. The irreducible background can be suppressed applying cuts on angular variables. The main sources of systematic uncertainties come from the choice of the PDF and the QCD scale, the NLO versus the LO dynamics, the isolation cut and its efficiency, the electron reconstruction efficiency, the energy and the momentum scale and the charge identification.

As discussed above, the VBF production channel be- comes important in the very high mass region thanks to its clear experimental signature given by the two spectator jets and the Higgs decay products, which allows a good rejection of dominant background coming from V + njets, V V + njets and t¯t production. These jets are well separated in pseudo-rapidity and have a very high invariant mass.

Moreover, the Vector Boson Fusion cross section (with or without a production of an Higgs particle) is an extremely interesting process because the cross section σ(pp → V V jj) and the polarization of the VV pair de-

pend sensitively on the presence or absence of a light Higgs in the physical spectrum. If a massive Higgs boson exists, a resonance will be observed in the VV invariant mass spectrum in correspondence of the Higgs mass. In the absence of the Higgs particle the SM predicts that the scattering amplitude of longitudinally polarized vector bosons grows linearly with sad violates unitariety at about 1 ∼ 1.5T eV . This means that the measurement of the cross section at large M(VV) could provide information on the existence of the Higgs boson independently of its direct observation.

In 2012, two independent group in LHC, ATLAS and CMS, announced highly consistent value of Higgs mass, by observing different kinds of channel.

FIG. 3. Results

III. PHYSICS BEYOND STANDARD MODEL A. Neutrino got mass

In standard model, there is no right-handed neutrino, which implies that it should be massless. However many experiment, including those in LHC, had suggested that neutrino have mass, < 2eV . In this sense, the standard model would be incomplete. One might guess there would be right-handed neutrino that can couple to Higgs field with the left-handed neutrino to get mass.

B. Neutrino oscillation

A neutrino, is an electrically neutral, weakly interact- ing elementary subatomic particle with half-integer spin.

There are three types, or ”flavors”, of neutrinos: electron neutrinos, muon neutrinos and tau neutrinos. In a standard model, it is believed that neutrinos is created with a well-defined flavour, and the transition between fermions in different flavour are highly suppressed. For example,

W⁻→ e⁻+ ντ

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4 W⁻→ e⁻+ νe

the former one is highly suppressed, while the later one is what we measure in usual case. However, in a phe- nomenon known as neutrino flavor oscillation, neutrinos are able to oscillate among the three available flavors while they propagate through space. This is due to the mismatch between the neutrino mass eigenstates and the neutrino flavour eigenstates. This allows for a neutrino that was produced as an electron neutrino at a given location to have a calculable probability to be detected as either a muon or tau neutrino after it has traveled to another location. This quantum mechanical effect was first hinted by the discrepancy between the number of electron neutrinos detected from the Sun’s core failing to match the expected numbers, dubbed as the ”solar neutrino problem”. In the Standard Model the existence of flavor oscillations implies nonzero differences between the neutrino masses, because the amount of mixing between neutrino flavors at a given time depends on the differences between their squared masses.

C. CKM matrix

The masses and mixings of quarks have a common ori- gin in the Standard Model (SM). They arise from the Yukawa interactions with the Higgs condensate,

£Y = −Y_ij^dQ¯Î_ijφdÎ_ij− Y_ijûQ¯Î_ijφ^∗uÎ_ij+ h.c

where Yû,d are 3 × 3 complex matrices, φ is the Higgs field, i, j are generation labels, and is the 2 × 2 anti- symmetric tensor. QÎ_L are left-handed quark doublets, and dÎ_R and uÎ_R are right-handed down- and up-type quark singlets, respectively, in the weak-eigenstate ba- sis. The non-zero vev of φ, ^√^v

2, yields the mass terms for the quarks. The physical states are obtained by diagonalizing Y^u,d by four unitary matrices, V_L,R^u,d, as M_diag^f = V_L^fY^fV_R^{f †}(^√^v

2), f = u, d. As a result, the charged-current W^± interactions couple to the physical

uLj and dLk quarks with couplings given by

√−g

2( ¯uL, ¯cL, ¯tL)γ^µW_µ⁺VCKM



 dL

cL

tL





VCKM ≡ V_L^uV_L^d†=





V_ud V_us V_ub Vcd Vcs Vcb

Vtd Vts Vtb





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The rotation unitary matrix VCKM was introduced by Kobayashi and Maskawa as a generalization of the 2 × 2 Cabbibo matrix. This matrix is called the CKM matrix after the name of the people who introduce it. It describes the probability of a transition of one type of quark to another type of quark. From the view that there should be no FCNC, it is idealized to have VCKM

diagonal. Unfortunately, by the experiments, we found out that it ins’t. This is called the the mismatch between the quark mass eigenstates and the weak eigenstates in the Standard Model. Note that VCKM must be unitary, we have constraints

X

i

VijV_ik^∗ = δjk

By independent measurement for CKM elements made by LHC, we obatin

VCKM ≈





0.9742 0.2253 0.0041 0.225 0.986 0.0411 0.0084 0.040 1.021





The diagonal element value |Mii| are very close to 1 as expected, while the farther we go from the diagonal the smaller these probabilities get. We therefore realize that, in weak doublet, the up quark coulpes not only to the down quark, but it has a probability to transform to a strange an bottom quarks. This probability is coded in the CKM matrix. Note that the definition of the CKM matrix using the down-type quarks is arbitrary. One could have used the up-type quarks and the CKM matrix would be identical.Another view of CKM matrix is that, due to the non-diagonal nature of the CKM matrix, one might geuss that there are other types of quarks that we don’t know yet. Once we have every kind of quarks, the extended CKM matrix might therefore be perfectly diagonal.

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C, 38, 090001 (2014)

[2] J. Beringer et al. (Particle Data Group), Phys. Rev.

D86, 010001 (2012)