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Higgs Identity @ the LHC, Part I: Compositeness and Naturalness 1. 2. 3. R. Dermisek and I. L., hep-ph/0701235 I. L. and S. Shalgar: arXiv:0901.0266 I. L., R. Rattazzi, and A. Vichi: arXiv:0907.5413 Ian Low Argonne National Lab and Northwestern U. Outline • • • • • Mysteries at the TeV scale Higgs search @ the LHC Gluon fusion production Size of effects Summary and outlook Mysteries at the TeV Scale • Electroweak symmetry is broken, but we don’t know how. • W and Z bosons have masses, but we don’t know where they came from. • Electroweak scale (v=246 GeV) is much smaller than the next energy scale we know, Mp=1019 GeV. Why this big hierarchy? • Is there a stable neutral particle (dark matter)? There’s none in the SM… • etc. Understanding these mysteries requires new dynamics at the TeV scale, and possibly new physical principles associated with it. • • • • • • Supersymmetry? Extra dimensions? New (global or gauge) symmetries? Grand unification? All of the above? None of the above? The landsacpe of models is huge: Drawing by H. Murayama However, message from LEP is loud and clear: Precision electroweak measurements favor a weaklycoupled description at the TeV scale! If the dynamics responsible for EWSB were stronglycoupled at the TeV scale, the induced quantum effects at low energies would be large. Then we should have seen sizable deviations at the LEP!! QuickTime™ and a decompressor are needed to see this picture. • The only known way to construct a model of EWSB that is weakly-coupled at the TeV scale is through the Higgs mechanism: An electroweak doublet scalar receives a vacuum expectation value, v=246 GeV, and breaks SU(2)LxU(1)Y spontaneously. Searching for the Higgs at the LHC is among its top priorities! However, having a description based on the Higgs mechanism raises more questions: • We have never observed a fundamental scalar in nature so far. Is the Higgs fundamental? • A scalar mass is “fine-tuned” in quantum field theory, unless it is “cut off” by new physics. Is there new physics at the TeV scale in addition to the Higgs? • How do we know the new physics, if any, reduces the fine-tuning in the Higgs mass? • If we observe one or more scalars, how do we know it has a VEV that breaks the electroweak symmetry? All these questions are not necessarily “problems” if we could figure out easily that which one of the 10,000 models gives us the signals. eg, if we know it’s MSSM that gives us the multijet, multi-lepton, and missing ET, then we have answers to all the above problems immediately. There are discussions of discovering SUSY within a matter of weeks of turning on the LHC… Unfortunately, it’s not going to be that straightforward… Typical signatures for SUSY events are isolated leptons, missing ET, plus jets. They actually have nothing to do with SUSY!! A computer simulation of SUSY events. Any model with a new conserved parity at the TeV scale gives such signals: R-parity (SUSY), KK-parity (extra-dimension), T-parity (little Higgs) A computer simulation of UED events. Given the huge degeneracy, it is then important to ask global and structural questions first: • Is the Higgs fundamental or composite? • Is the new physics at the TeV scale, if any, follows from naturalness principle? • If we observe new particles, who ordered them? Does any of them reduce the fine-tuning in the Higgs mass? • If we observe one or more scalars, how do we know it has a VEV that breaks the electroweak symmetry? • Do the W and Z bosons get their masses from the Higgs mechanism? We need to answer them in order to navigate the infinite space of models!! I will try to provide answers to some of these questions, by looking into two particular processes: • Gluon-fusion production of the Higgs: could tell us whether the Higgs is a composite particle like the in low-energy QCD, and whether there exists new particle canceling the quadratic divergence in the Higgs mass. • Decay of a resonance into ZZ final states: could tell us whether it is a scalar with couplings following from the Higgs mechanism • Part I is mostly motivational: I want to convince you the wealth of information hidden behind (ggh). Thus it’s worth putting in resources to extract it with precision! • Part II is very specific: I will suggest smoking-gun signals in h ZZ that have not attracted enough attention until perhaps recently. Higgs search at the LHC The Higgs boson is the last particle in the standard model that hasn’t been observed directly! The History: Legacy of LEP -precision electroweak measurements LEPEWWG as of August 2009: Minimal chi-square at Higgs mass = 87 GeV with an uncertainty of +35 GeV and -26 GeV LEP did not see the SM Higgs before it was shut down in 2000. . combined four The LEP experiments put a lower bound on the Higgs mass at 114.4 GeV at the 95% confidence Level. (hep-ex/0306033) The latest -- Legacy of Tevatron ?? Combined CDF and D0 in January of 2010: A SM Higgs in the mass range of 162-166 GeV is now ruled out at 95% C.L. All eyes on the LHC now for the discovery of the Higgs. Main production mechanisms of the Higgs at hadron colliders: Ref: A. Djouadi, hep-ph/0503172 Among them gluon fusion is the dominant mechanism! At Tevatron: Ref: A. Djouadi, hep-ph/0503172 At the LHC: Decay channels depend on the Higgs mass: Ref: A. Djouadi, hep-ph/0503172 • For low Higgs mass mh 150 GeV, the Higgs mostly decays to two b-quarks, two tau leptons, two gluons and etc. • In hadron colliders these modes are difficult to extract because of the large QCD jet background. • The silver detection mode in this mass range is the two photons mode: h , which like the gluon fusion is a loop-induced process. Higgs mass can be measured very precisely by, for example, looking at the invariant mass of the di-photon. Ref: CMS physics TDR Furthermore, it is possible to extract individual partial widths of the Higgs boson. LHC at 200 fb-1 D. Zeppenfeld, hep-ph/0203123 Gluon Fusion Production • gg h is the dominant production mechanism at the LHC. • gg h is a loop-induced process, and hence very sensitive to new physics running in the loop. Thus, this particular channel provides a unique window into new physics at higher energy scales. We will analyze ways new physics could enter into this production channel. In the SM the dominant contribution comes from the top loop. Since the top is “heavy”, the loop can be shrunk to a point and approximated by a dim-5 operator: QuickTime™ and a decompressor are needed to see this picture. In this diagram alone, there are two ways new physics could enter: 1. The Higgs-fermion-fermion coupling could be modified by new physics: (roughly) scale of new physics QuickTime™ and a decompressor are needed to see this picture. In this diagram alone, there are two ways new physics could enter: 2. The definition of the Higgs field may be modified: QuickTime™ and a decompressor are needed to see this picture. Finally, there could a new loop diagram in addition to the SM top loop: 1. For non-supersymmetric theories, it could be a new top-like fermion, the top partner . 2. For supersymmetric theories, it could be a new top-like scalar, the stop . QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. When the new particle in the loop is heavy, the new contribution is encoded in the parameter cg: QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. Summarizing these three effects, we have QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. Quite amazingly, the sign of all three parameters are correlated with the identity of the Higgs boson, whether it is a fundamental or composite particle like the pion in QCD. In addition, the sign of cg is correlated with whether the Higgs mass is “natural” or not. First let’s consider the sign of cH, cy, and cH+2cy. (The latter controls the Higgs-fermion-fermion coupling.) We have the following “robust” positivity constraints: • cH>0 except when there exists electroweak triplet scalars, regardless of whether the Higgs is a fundamental or composite scalar. • cH+2cy >0 when the Higgs is fundamental, even in the presence of a triplet. On the other hand, the following positivity constraint is “almost robust,” and holds for all known models: cH+2cy >0 in models where the Higgs is a composite scalar (Goldstone boson) like the pion in QCD. There are several contributions to this coefficient in composite Higgs models. We proved rigorously the positivity of all but one of them. The remaining one turns out to be positive as well in known models. Next we consider the sign of cg, which is the relative sign between the SM top loop and the new loop diagram. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. We first consider the sign of cg for a new top-like fermion, the top partner. We will establish that If the Higgs quadratic divergence in the top sector is cancelled, the interference between the SM top and the top partner is destructive. cg > 0 in our sign convention Conversely, if the quadratic divergence is enhanced, the interference is constructive. cg < 0 • There’s a simple diagrammatic argument: The interaction of the Higgs with the top quark induces a quadratically divergent contribution in the Higgs mass: Q: How do we use another fermion to cancel the above divergence? • There’s a simple diagrammatic argument: The interaction of the Higgs with the top quark induces a quadratically divergent contribution in the Higgs mass: Q: How do we use another fermion to cancel the above divergence? Wrong answer: another fermion T with only Yukawa coupling to the Higgs wouldn’t work. The divergences always add up! • There’s a simple diagrammatic argument: The interaction of the Higgs with the top quark induces a quadratically divergent contribution in the Higgs mass: Q: How do we use another fermion to cancel the above divergence? Correct answer: always need a dimension-five coupling with the Higgs! • If the following two diagrams have a relative minus sign, then Higgs quadratic divergence is cancelled. Otherwise, the divergences add up. Now let’s massage the diagrams a little bit: Now let’s massage the diagrams a little bit: -- First putting one of the Higgs field in its VEV. Now let’s massage the diagrams a little bit: -- First putting one of the Higgs field in its VEV. -- Next let’s insert two gluons into the fermion line. These are exactly the two diagrams contributing to gluon fusion from the top quark and the new state! Because we have the same number of insertions along the fermion line, the relative sign between the diagrams is preserved! In other words, if the Higgs divergence is cancelled, the new state would interfere destructively with the top quark. But if the divergence is NOT canceled, the new state would interfere constructively with the top quark. The only assumption here is there is a new degree of freedom that is colored and has a significant coupling to the Higgs. Otherwise, our statement is completely general, model independent, and applies to any non-supersymmetric theories. The diagrammatic arguments can be formalized using the low-energy Higgs theorem, where the coefficient cg is related to the one-loop QCD beta function. Taking into account all the effects discussed so far QuickTime™ and a decompressor are needed to see this picture. We conclude the gluon fusion production rate is reduced in composite Higgs models! • The same diagrammatic argument can be extended to the case of MSSM. The difference is the pattern of interference is reversed because of the opposite spin of stop to the top. Size of Effects • cH and cy, roughly speaking, is a measure of the compositeness of the Higgs (in the sense of the pion in QCD.) If the Higgs is fundamental, we expect their effects to be small. • cg is suppressed by the mass of the new particles, relative the SM contribution. Examples: In SUSY or flat extra-dimensional theories, where the Higgs is a fundamental scalar, the partial width is then dominated by the cg term, which is in the order So the effects could be sizable if the top partner or the stop is light, and/or when there’s more than one new particles contributing coherently. The ratio of the gluon fusion rate in the MSSM over the SM: The right panel is the region where the Higgs mass in the MSSM is least fine-tuned, and the rate is reduced! QuickTime™ and a decompressor are needed to see this picture. Gluon Fusion Rate in the Universal Extra-Dimension (UED): The Higgs scalar is fundamental and its mass unnatural (finetuned). The rate is enhanced over the SM! QuickTime™ and a decompressor are needed to see this picture. F. Petriello, hep-ph/0204067 In composite Higgs models, such as the little Higgs or the holographic Higgs, all three terms, cH, cy, and cg, contribute (somewhat!) equally. The generic size varies: However, in this case all three terms go in the same direction of reducing the rate! So the pile-up effect could be important. Gluon Fusion Rate in the littlest Higgs with T-parity (LHT): The Higgs is a composite scalar like the pion and the rate is reduced! QuickTime™ and a decompressor are needed to see this picture. Chuan-Ren Chen et al, hep-ph/0602211 Gluon Fusion Rate in the littlest Higgs (without T-parity): The Higgs is a composite scalar like the pion and the rate is reduced! QuickTime™ and a decompressor are needed to see this picture. T. Han et al, hep-ph/0302188 Summary and Outlook • We found the gluon fusion production rate is a unique handle into the compositeness of the Higgs boson as well as the naturalness of the mass. • Composite Higgs models generally have a reduced gluon fusion rate. • Unnatural models tend to have an enhanced production rate. • The size of effects depends on the underlying models, ranging from modest, in the order of 10-30 %, to as small as SM one-loop effect. • Given the wealth of information that could be revealed, there’s strong motivation to improve on measurements at the LHC both theoretically and experimentally. For example, some advocate that the theoretical uncertainties should be smaller than it is often quoted: QuickTime™ and a decompressor are needed to see this picture. C. Anastasiou, et al, hep-ph/0509014 Last but not the least: If the LHC sees the Higgs and nothing else, in my mind there is still a strong scientific case for building a precision machine such as the linear (or muon) collider!