2014Fall QFT Final Examination—Hunting for the Higgs

Yao-Chieh Hu1, ∗ 1Department of Physics, National Taiwan University, Taipei 10617, Taiwan (Dated: January 18, 2015) There are many colliders and experiences now studying the Higgs bosons, like Large Electron- Positron Collider (LEP), the Tevatron, and the Large Hadron Collider (LHC). In this report, we will focus on the experiment at the LHC, where the Higgs was found on 4 July 2012 and be temporarily conﬁrmed on 14 March 2013 with the mass about 125GeV. The production and the detection of the Higgs will be mentioned, and also some future research for new physics at LHC.

I. INTRODUCTION Note that the coupling is proportional to the mass of the fermion. After Learning the electroweak interaction, we know The couplings of the Higgs boson to the gauge fields are µ † that the Higgs mechanism provides a general framework through the kinetic term, (D φ) (Dµφ). The covariant to explain the spontaneously symmetry breaking with derivative is ± SU(2) × U(1) to U(1)and give masses to the W and Z gauge bosons. The high energy U(1) symmetry is called a a 1 0 Dµφ = ∂µ − igAµτ − i g Bµ φ, (5) hypercharge, denoted as U(1)Y ; this U(1)Y should not 2 be confused with the EM gauge symmetry U(1)EM . (In a in which Aµ and Bµ are the gauge bosons of the SU(2) SM, the SU(2) × U(1)Y is broken by the VEV of a com- 0 plex doublet H with hypercharge 1/2 called the Higgs and U(1) groups, respectively, with g and g being the multiplet.) According to what we have learned, we can corresponding coupling constants. After evaluating in predict the behaviours of the Higgs boson, such as how the unitary gauge, one obtains it is produced and how to detect it by its decay mode. 1 1 h2 L = (∂µh)(∂ h) + m2 W +µW − + m2 ZµZ · 1 + , K 2 µ W µ 2 Z µ v II. WEINBERG-SALAM MODEL AND (6) COUPLING CONSTANTS where In the Glashow-Weinberg-Salam theory of electroweak ± 1 1 2 interactions [7,8,9], the mass terms of the fermions are W = √ A ∓ iA (7) µ 2 µ µ constructed by the spontaneous symmetry breaking of some scalar field coupled to the fermion fields. The scalar with mass, field couples to, say, the electrons and electron neutrinos, 1 through the Lagrangian (c = ~ = 1) m = gv, (8) W 2 ∆Le = −λeE¯L · φ eR + h.c. (1) and The coupling to the up and down quarks is similar, read- ing 1 3 0 Zµ = p gAµ − g Bµ (9) ¯ ab ¯ † g2 + g02 ∆Lq = −λdQL · φ dR − λu QLaφbuR + h.c. (2) Evaluating these Lagrangians in the unitarity gauge, in with mass, which the scalar field is parametrized by 1p m = g2 + g02 v, (10) 1 0 Z 2 φ(x) = √ , (3) v + h(x) 2 and one remaining massless gauge boson identified as the with v being the vacuum expectation value of the scalar electromagnetic vector potential. The SM Higgs boson field and the real-valued perturbation h(x) as the Higgs couplings to gauge bosons, Higgs bosons and fermions field, one obtains the general form of the coupling of the are summarized in the following Lagrangian: Higgs boson to any lepton or quark, gHHH 3 gHHHH 4 L = −g ¯ffH¯ + H + H ¯ h Hff 6 24 Lf = −mf ff 1 + . (4) 1 g (11) v + V V µ(g H + HHVV H2) 2 µ HVV 2 In standard model, it predict that the Higgs couplings ∗ [email protected] to fundamental fermions are proportional to the fermion 2 masses, and the coupling to the gauge bosons are pro- 2. Vector boson fusion production mechanism portional to the squares of the boson masses. That is, This mechanism has the second-largest cross-section at mf g ¯ = , LHC. The producing mode is by two reactions: Hff v 2m2 g = V , (12) qq −→ Hqq or qq¯ −→ Hqq¯ (14) HVV v 2m2 g = V . and the lowest order of the Feynman diagram is: HHVV v2 where V = W ± or Z is the gauge boson, f is any kind of fermion, and is the vacuum expectation value of the Higgs field. With these interactions in hand, one can predict the properties of the Higgs bosons, such as the cross sections and branching ratios of various processes, and compare them with the experiments.

III. PRODUCING HIGGS AT THE LHC And because of the coupling constant is proportional to the fermion masses, the main mode is with top-quarks. LHC is a proton-antiproton collider, like Tevatron but with higher center-of-mass energy (14T eV expected) and luminosity (10 ∼ 30 fb−1). They produce Higgs through 3. WH and ZH associated production mechanism four major processes : gluon fusion, weak-boson fusion, associated production with a gauge boson and associated This one is commonly called ”production in asso- production with top quarks. The ordering is for special ciate with a vector boson.” The producing mode is purpose, it is ordered with respect to the cross-section by the reaction: for the production of SM Higgs. qq¯ −→ HV (15)

where V = W ± or Z is the gauge boson, this is the 1. Gluon fusion production mechanism reason for its name (associate with a vector boson). And the lowest order of the Feynman diagram is At LHC, the Higgs boson production with largest cross-section is the gluon-fusion. This producing mode is by the reaction:

gg −→ H(+X) (13)

In this mechanism, the process is mediated by the ex- change of a virtual, heavy top quark. The detailed dis- cussion is in [2]. The lowest order of the Feynman diagram is : Considering the associated productions, we have the process:

pp −→ HV + X (16)

again where V = W ± or Z is the gauge boson. This process receive contributions at next-leading-order given by QCD corrections to the Drell-Yan cross-section and electroweak correction to next-leading-order. To see more de- tails of associated production of Higgs and weak bosons, one can check[4].

4. Higgs production in association with top quarks Moreover, the gluon-gluon fusion cross section of the Higgs particle in the SM in nexttoleading order QCD is For the ttH¯ production process, first, we note that discussed in first half of [3] this final state can arise form both qq¯ and gg initial 3 states. However, at LHC, only the gg contribution is In short, the above five channels are the major channels significant[5]. The process is give: for low mass SM Higgs boson searches at the LHC. We can see their mass resolution for each decay channel for pp −→ gg −→ Htt¯ (17) mH = 125Gev in below table: The corresponding Feyaman diagram is:

c. At even higher masses , for which mH > Short Conclusion 600GeV : H −→ ZZ. (23) We can summary above four processes in one diagram: So far, we have conﬁrmed that the mass of Higgs is about 125GeV. The all decay modes are shown in the picture below

This is for SM Higgs boson production cross√ sections as a function of the center of mass energy, s, for pp colli- sions.

V. NEW PHYSICS IMPLIED BY LHC IV. DETECTION OF HIGGS AT LHC Although the Higgs mechanism in Standard Model A variety of search channels are pursued by the LHC (SM) is very successful phenomenally, the electroweak collaborations, A Toroidal LHC Apparatus (ATLAS) symmetry breaking driven by a weakly-coupled elemen- and Compact Muon Solenoid (CMS), with the channels tary scalar sector still requires a mechanism to explain the relative importance changing due to the branching ratios smallness of the breaking scale compared with the Planck of the SM Higgs boson as functions of mH : scale. This problem lead to the extension as Minimal a. At low masses , for which mH < 120GeV : Supersymmetric Standard Model (MSSM). The diﬀerence between MSSM and SM Higgs mech- H −→ γγ, (18) anism is that MSSM contains the particle spectrum of a H −→ b¯b, (19) two-Higgs doublet model, Hu and Hd, which required to H −→ τ +τ −. (20) ensure an anomaly-free SUSY extension of the SM and to generate mass for both up-type and down-type quarks b. At higher masses , for which 120GeV < mH < and charged leptons. In this construction, ﬁve physical 150GeV : Higgs particles are left in the spectrum after the spontaneous breaking of the electroweak symmetry. They con- + − + − H −→ W W −→ l νl ν,¯ (21) tain one charged Higgs pair, H±, one CP-odd scalar, A, H −→ ZZ −→ l+l−l+l−. (22) and two CP-even states, H and h. 4

So far, LHC is working hard to find if there exits the implication from the different result from the prediction other neutron and charged Higgs which is predicted by of SM. And if we find them, it will indicate the new the MSSM. Although there are no yet any evidence for physics beyond the SM. the existence of these new particle, we can still find some

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