Searches for Low Mass Strings and Unparticle Physics at the LHC with CMS

Andy Yen Mentor: Harvey Newman Co-Mentor: Marat Gataullin

I Introduction

In late summer 2009, the first physics runs at the Large Hadron Collider (LHC) at CERN will commence. With it comes the culmination of over fifteen years of hard work from thousands of theoretical and experimental physicists. The LHC, composed of 9300 superconducting magnets in a 26.7 kilometer tunnel at an operating temperature of 1.9°K, will achieve an unprecedented 14 TeV center of mass energy, opening up an entire new energy range for particle physicists to explore. The Caltech group, led by Professor Harvey Newman is participating in CMS (Compact Muon Solenoid), one of the two main experiments at the LHC. The CMS detector consists of an all–silicon tracker, a precision electromagnetic calorimeter (ECAL) composed of lead tungstate crystals, a hadron calorimeter (HCAL), a 4 Tesla superconducting solenoid, and an array of muon chambers. The superconducting solenoid deflects charged particles whose paths are then traced by the tracker and these data are then used to determine the particles’ momenta. The CMS ECAL, whose calibration the Caltech group specializes in, is used to reconstruct the energy of electrons and photons and aid in particle identification.

The ability of the ECAL to cleanly identify and reconstruct electrons and photons with 1% energy resolution or better at high energies is the source of much of CMS’s discovery potential. Signatures involving photons have been a main focus of the Caltech group’s preparations for the LHC physics program, including the decays of a relatively low mass Higgs or heavy graviton decays into photon pairs. In this proposed SURF project we will build upon the expertise of the group in photon reconstruction, including my work on diphoton production during my 2008 SURF, to search for signatures from low mass strings and unparticle physics.

II Background

The LHC is first and foremost, a discovery machine. By being the first accelerator to probe deep into the multi-TeV scale, it promises to revolutionize our current understanding of elementary particles. While extraordinarily accurate, the best current model, the Standard Model (SM) of Particle Physics, is far from complete as there are numerous observed physical phenomena which is it unable to explain. As many theoretical papers have hypothesized, there are plenty of reasons to believe in the existence of new physics beyond that of the current SM. One such 1

alternate model is superstring theory. Superstring theory attempts explain all the fundamental forces and particles of nature by modeling them as vibrations of tiny supersymmetric strings. By utilizing extra degrees of freedom in the form of extra spacetime dimensions, superstring theory also attempts to incorporate quantum gravity to create a grand unified theory. Superstring theory became connected to particle phenomenology with the development of the concept of the D-brane, a class of extended objects upon which open strings can end with Dirichlet boundary conditions. It has recently been demonstrated that signals for superstring theory may be detected at the LHC provided the fundamental mass scale is sufficiently low [1-2].

The mass scale (MS) of these fundamental strings may be as low as a couple TeV provided that spacetime extends into large extra dimensions [1]. Coincidentally, this extension into extra dimensions also provides a mechanism for solving the hierarchy problem, i.e. why the weak force is 1032 times stronger than gravity [3]. MS gives a lower bound on the collider center of mass energy (√s) above which Regge resonance can occur leading to the onset of string effects. As LHC is expected to have √s=14 TeV, the condition √s > Ms is clearly satisfied. Theorists have recently demonstrated that a consequence of TeV scale D-brane physics is that a “new physics” signal associated with low mass scale string theory can be detected at the LHC at 5 sigma significance for MS up to 2.3 TeV using only 100 fb-1 of integrated luminosity [2]. The “new physics” signal results from a scattering process that occurs on the (color) U(3) stack of D-branes. Of much more consequence is the fact that the amplitudes of this scattering are model independent. The calculations hold for arbitrary compactifications of superstring theory ranging from four to ten dimensions, including those that break symmetry [2]. Hence, the results that can be obtained will be very general and valid for a wide range of superstring scenarios.

As mentioned previously, the Standard Model has several crucial shortcomings which make alternate theories appealing. One of the problems with the SM is that it breaks scale invariance. Scale invariance is a powerful notion that results if physical laws do not change as energy scales are multiplied by a common factor. For instance, a particle such as an electron is not scale invariant because its mass remains the same regardless of how energy or momentum scales, i.e mass does not scale with the other quantities. A photon on the other hand has properties that scale equally. In particle physics under the SM, we observe a wide range of particles which have mass while in a scale invariant theory in four dimensions, there would be no particles with non-zero mass. Thus, while the SM may be accurate in the low energy regime, it is conceivable that at high energy there is a scale invariant sector and if scale invariance exists in nature, it is broken at an energy scale beyond the SM. Such an invariant sector could be described by a

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vector-like non-abelian gauge theory with a large number of massless fermions such as the Banks-Zaks (B-Z) sector [4]. Recent work done by Howard Georgi at Harvard has demonstrated that a nontrivial scale invariant section of dimensionality dU could lead to a low energy manifestation in the form of non-integer dU dimension invisible massless particles, dubbed unparticles [5-6]. Scale invariance in the B-Z sector emerges at energy scale ΛU so if ΛU is on the order of several TeV, the unparticle dynamics will be seen at the LHC through various high energy scattering processes. These processes can be detected through either a peculiar rise in missing energy distributions (as the unparticles cannot be detected) or an enhancement of SM diphoton production rate at high values of Mγγ.

III Objectives/Approach

Low Mass Strings: Low mass strings will lead to the following scattering process (at the parton level): gg→gγ. This is a “new physics” signal which will show up as a non-SM contribution to the SM process pp→γ+jet. This SM background will primarily consist of the processes gq→γq and qq→γg. The string scattering process is illustrated in Figure 1.

Figure 1: Open string disk diagram for gg→gγ scattering. The dots represent vertex insertions of gauge bosons on the boundary of the world sheet [2].

Due to the high MS associated with this scattering process, the signal from this process will be a quite distinctive isolated hard photon. Theoretical predictions indicate a minimum Pt cut of 300 GeV can be used. This signal can be even better identified by searching for the energetic jet which is also produced. Figure 2 shows the deviation from the SM pp→γ+jet cross section predicted by the low mass strings model. It is immediately apparent that even for a low MS value of 1 TeV, a significant deviation is not expected until approximately Pt~300 GeV.

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Figure 2: The SM QCD pp→γ+jet cross section compared to the cross section with string effects taken into account for MS = 1 TeV.

There are two general approaches which can be used to verify the existence of these low mass string effects. One is to simply look for an excess of high Pt direct photon events that also contain a tagged jet. A significant excess over SM predictions would be indicative of a conclusive signal. Another method is the so called “bump-hunting” approach. In this approach, one would reconstruct the invariant mass of the high Pt photon and corresponding jet and plot the resulting distribution for the events which pass the selection. Then, one would try to spot resonant behavior (bumps) similar to the ones shown in Figure 3. If significant bumps are found, then a discovery can be claimed. Furthermore, due to the unique angular distributions inherent to the D-brane model, TeV-scale resonance associated with strings can be differentiated from other possible beyond the SM scenarios [2].

Figure 3: dσ/dM vs Mγ+jet plotted for SM QCD background and string signal + SM background [2]. 4

Unparticle Physics: To search for signs of unparticle physics, I will look for the effect of an invariant B-Z sector on prompt diphoton production. This will take advantage of work I completed last year on analyzing prompt diphoton events produced at the LHC. For ΛU on the TeV scale, both spin-0 and spin-2 unparticles are possible. Both types of unparticle operators will have anomalous couplings (λ) to the SM fields dependent on the value of dU. The impact of these couplings on prompt diphoton cross sections is show in Figure 4.

Figure 4: Impact of spin-0 and spin-2 unparticles on LHC diphoton production with ΛU = 1 TeV and λ =0.9 [7].

We can see that the net impact of unparticle physics at the LHC is an increase in diphoton production, especially at higher values of Mγγ. This impact will be experimentally manifested at the LHC through a large excess of high Mγγ diphoton events above SM predictions. The analysis techniques I developed last summer can be directly applied to perform this analysis. By measuring the excess and comparing to the theoretical cross sections, the validity of the unparticle theory can be tested.

The software and computational resources needed for this project are readily available on the Caltech CACR “Tier2” cluster. The ROOT [8] software framework will be used to perform the majority of the analysis. This project will enable the Caltech CMS group to explore two new beyond the SM theories which haven’t been investigated yet at CMS. It also ties in with work being done by Caltech theorists Hirosi Ooguri and Mark Wise.

IV Work Plan

The first step in this project will be producing the simulated datasets needed for the analysis. This will be challenging as both unparticle physics and low mass strings are relatively new models which have not yet been incorporated into 5

standard particle physics event generators such as PYTHIA or CompHEP. The second step will be to write a selection algorithm for low mass strings events using C++ and the ROOT program. This will also require a detailed study of photon fake rates and the systematics associated with high Pt jet reconstruction. The selection for unparticle physics signatures will be a slightly modified version of my diphoton analysis from the previous year. The final step will be developing the statistical data analysis tools needed to make an unambiguous discovery once real data becomes available. This step can be challenging because in the kinematic regions I am interested in for these analyses, the SM background is expected to be low so problems with limited statistics need to be taken under consideration.

Due to the work I have done in the past two years with the Caltech CMS group, I already have familiarity with the ROOT software framework and experience with developing selection algorithms. Additionally, I have experience with the CMSSW package which will allow me to start immediately on the analysis. Finally, my work for the past two years has given me exposure to many of the potential challenges which can arise in this project so I have background on how to confront these various issues.

V References

[1] L. Anchordoqui et al., Dijet Signals for Low Mass Strings at the Large Hadron Collider. Phys. Rev. Lett. 101, 241803 (2008). [2] L. Anchordoqui et al., Direct Photon as probes of low mass strings at the CERN LHC. Phys. Rev. D. 78, 016005 (2008). [3] L. Randall, R. Sundrum. Large Mass Hierarchy from a Small Extra Dimension. Phys. Rev. Lett. 83, 3370-3373 (1999). [4] T. Banks, A. Zaks, Nucl. Phys. B. 206, 23 (1982) [5] K Cheung et al., Collider Signals of Unparticle Physics. Phys. Rev. Lett. 99, 051803 (2007). [6] S. Chen, X. He., Interactions of Unparticles with Standard Model Particles. arXiv:0705.3946v4 [7] M.C. Kumar et al., Unparticle Physics in Diphoton Production at the LHC. Phys. Rev. Lett. B 657, 198-206 (2007). [8] http://root.cern.ch/

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