Constraining Quirky Tracks with Conventional Searches
CConstraining Quirky Tracks with Conventional Searches
Marco Farina ∗ New High Energy Theory Center, Department of Physics, Rutgers University,136 Frelinghuisen Road, Piscataway, NJ 08854, USA
Matthew Low † School of Natural Sciences, Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540, USA
Quirks are particles that are both charged under the standard model and under a new confininggroup. The quirk setup assumes there are no light flavors of the new confining group so that whilethe theory is in a confining phase, the distance between quirk-antiquirk pairs can be macroscopic.In this work, we reinterpret existing collider limits, those from monojet and heavy stable chargedparticle searches, as limits on quirks. Additionally, we propose a new search in the magnetic-field-less CMS data for quirks and estimate the sensitivity. We focus on the region where the confinementscale is roughly between 1 eV and 100 eV and find mass constraints in the TeV-range, dependingon the quirk’s quantum numbers.
Introduction —
The Large Hadron Collider (LHC)has now been running for several years and continuesto be our most direct probe of electroweak-scale physics.The primary directions of phenomenological studies havebeen naturalness-driven and signature-driven. Along thesignature-driven direction, only relatively small develop-ments have been made in the study of unusual particletracks. Track reconstruction at colliders relies on thesimple assumption that all particles follow simple helicaltrajectories characteristic of the motion of charged parti-cles in a magnetic field. There are new physics scenarios,however, that transcend that assumption and give rise tomuch stranger types of tracks at the LHC. Some exam-ples of these track signatures include tracks that abruptlychange direction (kinked tracks), tracks that begin part-way through the detector (appearing tracks), tracks withanomalous deposits of energy, and tracks with unusualcurvature (see [1–8] for past and related theory studies).The latter case is typical of quirks, which will be thefocus of this work.Quirks are particles that are both charged underthe standard model (SM) and under a new confininggroup [9–11]. The quirk setup assumes there are no lightflavors of the new confining group so that while the the-ory is in a confining phase, the distance between quirk-antiquirk pairs can be macroscopic. This leads to an in-teresting array of collider signatures based on the length, (cid:96) , of the flux tube, or string, between the quirks.It is when (cid:96) becomes comparable to the length scalesrelevant for detectors that quirk tracks exhibit unusualcurvature. Due to the challenges in identifying suchtracks, there have been very few dedicated searches per-formed for quirks. A search from DZero sets the onlybound on quirks which is m Q (cid:38)
120 GeV when10 nm (cid:46) (cid:96) (cid:46) µ m (where the individual quirksare not resolved) [12].In this work, we will show for the first time that strongbounds can be set on quirks, at collider-relevant scales, using entirely standard LHC searches with no modifica-tions to tracking algorithms. These searches are sensitivefor macroscopic string lengths. In addition to reinter-preting existing searches, we propose a new search thatcan be performed in the magnetic-field-less “0T” data ofCMS (still using standard tracking algorithms). In the0T data all known charged particles are expected to leavestraight tracks making this dataset a nearly background-free sample for certain types of tracks with anomalouscurvature. While we propose a specific search for quirks,we are optimistic that the use of such a dataset can beextended to other scenarios beyond quirks.The remainder of the paper is organized as follows:first, we briefly describe quirk models and their colliderphenomenology. Then, we reinterpret monojet searchesand heavy stable charged particle (HSCP) searches inthe quirk parameter space, leveraging the fact thathadron colliders automatically scan a range of (cid:96) largelydue to the velocity distribution of particles produced.Next, we suggest a novel use of the 0T data from CMSto constrain quirks. Finally, we conclude with projectedresults and comments on the remaining quirk parameterspace. Quirks (at the LHC) —
We now introduce the min-imal ingredients for a quirk model. To the SM gaugegroup we add a new “infracolor” gauge group that is as-sumed to be asymptotically-free with a confinement scaleΛ and to the SM particle content we add a new species, Q , with mass m Q and infracolor representation size N c .The particle Q is called a quirk when it is much heavierthan the confinement scale ( m Q (cid:29) Λ). Since Q is as-sumed to be the lightest infracolored particle, there areno particles lighter than Λ that can form “hadrons” andthe only hadronic states are glueballs with masses a lit-tle above Λ. When quirks are pair produced, for instanceat the LHC, there are no light hadrons to break the in-fracolor flux tube between the quirks. This flux tube, a r X i v : . [ h e p - ph ] M a r or string, connecting the pair can be macroscopic in sizeand its tension results in an attractive force between thetwo particles.If the quirks are colored they hadronize, via QCD,forming color-neutral states with SM quarks or gluons,similar to the well-studied case of R -hadrons in super-symmetry (we will adopt the name R -hadron for thecolor-neutral quirk-parton state). The two R -hadronsare still connected by the infracolor flux tube and for allpractical purposes the effect of QCD hadronization onthe quirk dynamics can be neglected as m Q (cid:29) Λ QCD .On the other hand, the electric charge of the R -hadron,does affect its detection; we will return to this point inthe discussion of our results. Clearly, tracking methodscannot be used for neutral R -hadrons.We can now study the trajectory of quirks at the LHC.The equations of motion are given by the Nambu-Gotoaction with point masses on the ends of the string in anelectromagnetic background [11, 13]. The equations ofmotion for a single quirk are ∂∂t m Q (cid:126)v (cid:113) − (cid:126)v ⊥ − (cid:126)v (cid:107) = − T (cid:113) − (cid:126)v ⊥ ˆ s − T v (cid:107) (cid:126)v ⊥ (cid:112) − (cid:126)v ⊥ + q(cid:126)v × (cid:126)B. (1)Above ˆ s is a unit vector that points towards the otherquirk and is used to define v (cid:107) = ( (cid:126)v · ˆ s ), (cid:126)v (cid:107) = v (cid:107) ˆ s , and (cid:126)v ⊥ = (cid:126)v − (cid:126)v (cid:107) . The quirk charge is q and the magnetic fieldis (cid:126)B . For both the HSCP and monojet searches we usethe CMS magnetic field of (cid:126)B = (0 , , . (cid:126)B = (0 , , T which is proportional to Λ . There have been estimatesthat T (cid:39) . in QCD [14], but we take T = Λ forsimplicity (as the difference is simply a rescaling of theparameter space).In the absence of external forces and when the quirksare back-to-back the maximum distance between themcan be calculated to be (cid:96) eff = 2 m Q Λ ( γ −
1) = m Q Λ v + O ( v ) , (2)where γ is the boost factor. While the true string length, (cid:96) , can be different, we use (cid:96) eff as a simple approximation.The m Q / Λ factor follows from dimensional analysis andthe v factor plays a relevant role in collider searches.Numerically, one has (cid:96) eff ≈
10 m (cid:16) m Q (cid:17) (cid:18)
100 eVΛ (cid:19) (cid:16) v . (cid:17) . (3)From Eq. (3) one can map different types of searches tothe appropriate range of Λ. For 10 keV (cid:46) Λ (cid:46) ∼ µ m) so that the quirk pair is observed as a single highly-ionizing straighttrack [12]. For 1 eV (cid:46) Λ (cid:46)
10 keV one finds that (cid:96) eff is macroscopic and leads, in general, to oddly curvedtracks. Finally, for Λ (cid:46) xy -plane. Quirk tracks can exhibit a wide varietyof strange behaviors, for example, curving outside the xy -plane, reversing direction, or passing through thesame detector layer more than once. Crucially, however,they can also closely approximate a standard helixtrajectory (at least inside the detector volume). The v factor in Eq. (3) allows for a range of (cid:96) eff values for agiven Λ. Reinterpreting Existing Searches —
As mentionedabove, for a wide range of Λ there is a non-zero proba-bility that a quirk track would be reconstructed at theLHC. When this happens the quirk will appear simply asa heavy stable (or long-lived) charged particle. In a col-lider, such particles are found by looking for tracks withlarge deposits of energy and/or a long time of flight (ascompared to muons). When both tracks fail to be recon-structed monojet searches will have sensitivity, providedthat the quirks have been produced in association witha sufficiently energetic jet (through either initial or finalstate radiation). Monojet searches look for large missingtransverse energy that results from a jet recoiling againstundetected particles.The probability to reconstruct a track is characterizedby the track efficiency and is shown in Fig. 1 for HSCPsearches (red) and for monojet searches (blue). The trackefficiency is computed by applying a series of track selec-tion cuts (as used by CMS in their HSCP analysis [15])listed in Table I and described below.First, the quirk propagation is found by solving Eq. (1).We use the straight string approximation throughout.Each time a quirk passes through a tracker layer it reg-isters as a hit with an efficiency that we assume to be100%. To account for the fact that in practice the hitefficiency is less than 100% we increase the n hits require-ment to ≥ ≥
8. The n hits requirementspecifies the minimum number of layers a track must hit.We model the tracker geometry following the specifi-cations of the CMS tracker, which consists of a combi- Note that the range 1 eV (cid:46) Λ (cid:46)
10 keV roughly corresponds tothe length range 1 mm (cid:46) (cid:96) eff (cid:46)
100 km. The distance ∼
100 kmis still relevant for the LHC because the sagitta of an LHC track isroughly d /R where d max ∼ µ m, one finds that there is sensitivity up to R ∼
100 km. We use the CMS tracker to maximize the accuracy of our resultsfor the HSCP and 0T searches. � �� � �� � �� - � �� - � �� - � ��� � �� � Λ ( �� ) � � �� � � �� � � � � � � � � - � � �� � � �� � � � � � � � ��� ������ ������� �������������� χ � / ��� < � FIG. 1: Track efficiency as a function of confinementscale, Λ, for various quirk masses with a magnetic fieldof (cid:126)B = (0 , , . − . < η < . ≈ −
16 layers depending on its trajectory [16]. Detailsof our tracker model are given in the appendix.The tracks are then fit to a helix, which correspondsto the trajectory of a charged particle in the longitudinalmagnetic field of the detector. A helix is given by h x ( t ; R, φ, λ ) = R cos( φ ± ( t/R ) cos λ ) − cos φ, (4a) h y ( t ; R, φ, λ ) = R sin( φ ± ( t/R ) cos λ ) − sin φ, (4b) h z ( t ; R, φ, λ ) = t sin λ, (4c)where t is the parameter along the curve, R is the radius, φ is the initial azimuthal direction, and λ is the dip angle.For a completely general helix there are 3 additional pa-rameters specifying the initial position of the helix, butwe set this to the origin for simplicity. The ± dependson the charge of the particle.Next, we perform a χ / NDF fit to Eq. (4) and assumethat quirks with χ / NDF < µ m for eachhit [16]. The p eff T cut is applied to the measured p T of thetrack (computed from the best fit R value) rather thanthe true p T of the particle.The first search that we reinterpret is the HSCP search.The most sensitive HSCP searches have been performedat 13 TeV by CMS with 12.9 fb − [15] and by ATLASwith 3.2 fb − [17] and are presented as mass limits onstable particles of different charges and SU(3) represen-tations. We follow the event selection of the former anal-ysis which primarily consists of a χ / NDF cut on thetrack and a cut of p eff T >
65 GeV. We only consider thesample that would be selected by the muon trigger whichadds the additional requirement that v > . ≈ cut HSCP monojet 0T | η | < . < . < . n hits ≥ ≥ ≥ v > . − − p eff T >
65 GeV >
10 GeV >
65 GeV χ / NDF < < < R − − < TABLE I: Cut flow for identifying a track.pair events using Madgraph 5 v2.3.3 [18]. The trackingefficiency is shown in Fig. 1 (red). We define the trackefficiency as the number of tracks passing all track re-quirements divided by the number of tracks passing the | η | cut. As expected, the efficiency drops as the stringlength becomes comparable to the detector scale, whileit approaches 100% when the string tension is small com-pared to the Lorentz force. The asymptotic value at lowΛ is determined by primarily by the v > . − [19] and from ATLAS it is at 13 TeV using3.2 fb − [20]. While the CMS search has better reach,we use the ATLAS limits because they are presented aslimits on compressed stop squarks which is kinematicallymore similar to quirk events than the setups in the CMSsearch. We also show limits scaling the ATLAS resultup to 12.9 fb − . We generate quirk pair events alongwith a radiated jet of p T >
200 GeV and follow themonojet event selection in [20]. The track selection in thiscase still identifies when a good track would be selected,however, opposite to the HSCP case, this means the eventwould be rejected. For this reason we plot the quantity(1 − track efficiency) in Fig. 1 (blue). Note that even forsmall Λ the efficiency does not go to zero because sometracks still fail the selection criteria.Using both HSCP and monojet searches providesa very complementary approach so that while oursimplified tracker parametrization could differ from afull simulation it still captures the crucial features. Inparticular, the complementarity ensures that our resultsreliably cover the full range of Λ we study. When oneefficiency degrades, the other reaches its maximum (andat the maximum the tracking reconstruction details areless important). Another important feature capturedin Fig. 1 is the weak dependence on the quirk mass(since (cid:96) eff is approximately linear in mass). In a similarmanner, the quirk’s electric charge has a minor impacton the efficiencies. Indeed, while we use a fermionic colortriplet quirk with quantum numbers ( , ) / under theSM gauge group as a case study, we will provide limitsfor a few other cases. The results are shown in Fig. 3which will be further explained in the following section. � �� � �� � �� - � �� - � �� - � �� - � ��� � Λ ( �� ) � � �� � � �� � � � � � � � �� ������ ������ ������� ����� ������ χ � / ��� < �� < ���� � FIG. 2: Track efficiency as a function of confinementscale, Λ, for various quirk masses with a magnetic fieldof (cid:126)B = (0 , ,
0) at 13 TeV.
Using the 0T Data —
In addition to the reinter-preted searches, we propose an entirely new search whosesensitivity is maximal in the challenging region nearΛ ∼
10 eV. This search makes use of the 0.6 fb − of 13 TeV data with a 0T magnetic field [21]. With-out a magnetic field, all SM particles, both neutral andcharged, travel in straight lines. Quirks, on the otherhand, still curve due to the string tension. This meansone can simply count the number of curved tracks in the0T data and accordingly set a limit or make an observa-tion of quirks. Operationally, this would entail runningthe tracking algorithm on the 0T data while pretendingthere is a magnetic field and should not require any mod-ifications to the tracking algorithm itself.The efficiency for identifying a track in the 0T datais shown in Fig. 2. For the 0T search we use themonojet trigger [22] which uses an analysis-level cut of p T >
100 GeV for the leading jet and /E T >
200 GeVwhere /E T excludes muons (and would also exclude thequirk tracks). While in principle one could use the muontrigger as in done in the HSCP searches, in practice themonojet trigger is more effective. The reason is thatwithout sizable initial radiation for the quirk system torecoil against, the quirks will be almost back-to-back inthe transverse plane. This means there is no curvaturein the xy -plane so that the quirk trajectories cannot bereconstructed as non-straight helices. Therefore, at leastsome initial state radiation is required for a non-zero ef-ficiency.We generate events with a single jet with p T >
200 GeV and apply the track cuts in Ta-ble I. These closely follow the selection from the HSCPsearch with the exception that we add a requirementthat the fitted radius must be
R < R value from the sagitta s of a track s ≈ d R , (5) where d max is the chord length, corresponding to the ra-dius of the tracker. We take d max ≈ s ≈ µ m [16] andrequire a 3 σ single hit fluctuation to find R ≈ ≥ σ requirement. The R cut is responsible for the decrease in track efficiency atΛ <
20 eV.We assume that the fake rate is sufficiently low andthat multiple scattering effects faking a curved track aresufficiently rare to treat the analysis as zero-background.In principle, if a track with non-zero curvature is discov-ered the event could be inspected and checked for thepresence of a second curved track, providing a smokinggun of the signal. A limit is projected corresponding toobserving ≤ Discussion of Results —
The results are shown, fora ( , ) / fermion with N c = 2, in Fig. 3. The shadedred region shows the limits from HSCP searches whichdrive the limits for Λ (cid:46)
200 eV. The shaded greenregion shows the limits from the ATLAS monojet searchthat used 3.2 fb − and the unshaded green limit scalesup the limit to a dataset of 12.9 fb − (the amount usedin the CMS monojet search). Our projection for the0T search is given by the shaded blue region which uses0.6 fb − . The unshaded blue line shows a hypotheticaldataset of 20 fb − with no magnetic field and is the min-imum amount of data required to probe parameter spacebeyond what is covered by HSCP and monojet searches.The HSCP and 0T bounds are cut off at Λ = 300 eVbecause our statistics there are insufficient for a reliableestimate.Regarding QCD hadronization, the HSCP searches atthe LHC use two different models [15, 17]. The firstmodel [24, 25] assumes that the heavy hadrons can becharged or neutral when exiting the calorimeter whilethe second model [26] assumes the all heavy hadrons areneutral when exiting the calorimeter. The 0T search onlyuses information from the tracker and therefore does notdepend on this assumption. We take the fraction of R -hadrons that are charged to be 0 .
55 from Pythia 8 [27].For the 0T and HSCP searches we allow for 1 or 2identified tracks while for the monojet search we require0 identified tracks. The overall efficiency includes an ac-ceptance factor ( ≈ −
95% in the relevant region) thatwas not used in Figs. 1 and 2. We find that HSCP canconstrain higher masses than monojet searches or the 0Tsearch. This is not surprising as both the monojet and0T searches require an additional radiated jet and havea larger background or smaller dataset.In Table II we report the limits for various other quan-tum numbers using Λ = 1 eV, Λ = 100 eV, andΛ = 10 eV as benchmark points.The gray lines in Fig. 3 show contours of constant (cid:96) eff . ������� ��� ������������ � � � ( ��� ) Λ ( � � ) ( ��� ) � / � ������� � � = � ������������� �� � � � � - � � � � � � - � � � � � - � � � � � � - � �� � � � � - � �� �� � � �� ���� �� ���� ����� �� �� � � � � � - � � � � � - � FIG. 3: The 95% C.L. limits on a color triplet fermionicquirk with N c = 2. The red/green bound comes fromHSCP/monojet searches and the blue bound is ourprojection for the 0T data. The grey dashed lines showcontours of (cid:96) eff .The v used to compute (cid:96) eff is the mean of the velocitydistribution at 13 TeV. The (cid:96) eff contours give an idea ofthe length scales where each search is most effective andconversely, show where in parameter space other types ofquirk searches would lie.For Λ (cid:46) (cid:96) eff simply gets larger. On theother end, for Λ (cid:38)
200 eV, the monojet limit stays con-stant until (cid:96) eff ∼ µ m where the quirk system will appearas a single straight track. Here, HSCP searches mighthave some sensitivity again. For large enough Λ even-tually quirk-antiquirk annihilation can become promptand searches for various resonances, like γγ or jγ can berelevant [11].Before concluding we note that when a quirk paircrosses, soft radiation could be emitted as hadrons orglueballs, leading to a loss of energy and modification ofthe quirk trajectories, as well as extra activity in the de-tector. In most of the parameter space shown, however,we study (cid:96) eff (cid:38) (cid:38)
200 eV. For quirks, however, onelimitation at the LHC is that the string length should belarger than the average distance traveled by the quirk be-tween two layers of the tracker, which is ≈
10 cm. If not, spin charge N c m Q m Q m Q (Λ = 1 eV) (Λ = 100 eV) (Λ = 10 eV)fermion ( , ) / , ) / , ) − − scalar ( , ) − − fermion ( , ) / , ) / , ) − , ) − − TABLE II: Quirk mass limits for various quantumnumbers at the benchmark points of Λ = 1 eV,Λ = 100 eV, and Λ = 10 eV.then the sampling of the track would lose information onthe peculiar “periodic” structure of the trajectory. It istherefore in the region 10 cm (cid:46) (cid:96) eff (cid:46)
10 m wheresubstantial improvements are possible. This correspondsto an order of magnitude in Λ and we believe that amore detailed study is warranted, not only at ATLASand CMS, but also at more specialized detector such asMoEDAL [28].
Outlook —
In this paper, we demonstrated that whilequirk dynamics can result in very exotic tracks, they canalso result in very standard looking tracks allowing forstandard searches to constrain a substantial region of pa-rameter space. In particular, reinterpreting HSCP andmonojet searches allows one to set limits in the regionsΛ (cid:46)
100 eV and Λ (cid:38) (cid:96) eff (cid:38) (cid:96) (cid:46)
100 km.For colored quirks the limits range from 1.0 TeV to 1.6TeV with N c = 2. The limits get correspondingly higheras N c is increased. Limits on uncolored quirks were foundto range from 150 GeV to 650 GeV.We then proposed a novel use of the 0T data from CMSwhich involved looking for curved tracks in the dataset.Given the small size of the dataset, 0.6 fb − , we predictthat no curved tracks (at least due to quirks) should beobserved in the data as HSCP searches already rule outthe parameter space. Amusingly, the 0T search couldoutdo the current HSCP limits if it had only (cid:38)
20 fb − of data.We chose a few sample quantum numbers, in Table II,but it would be interesting to see limits for a larger va-riety of quantum numbers. On the experimental side, itwould interesting to see if dedicated quirk searches canbe done and would they compare to the monojet andHSCP searches.Finally, we argued that in the region10 cm (cid:46) (cid:96) eff (cid:46)
10 m there is an opportunityto go well beyond the sensitivity of current searchesby developing novel tracking techniques. Such tech-niques could then be applied to other physics cases,for instance, kinked or appearing tracks. Given thesimplicity of our 0T analysis, we hope that this work canserve as motivation for moving towards more involvedtracking modifications in order to fully exploit the LHC’spotential for unusual tracks.The authors would like to thank Raffaele TitoD’Agnolo, Markus Luty, Duccio Pappadopulo, JoshuaRuderman, Andreas Salzburg, and Kris Sigurdson foruseful discussions and Yuri Gershtein, Philip Harris, Si-mon Knapen, Scott Thomas, and Nhan Tran for helpfuldiscussions and reading the manuscript. M.F. is sup-ported in part by the DOE Grant DE-SC0010008. M.L.is supported by a Frank and Peggy Taplin membershipat the Institute for Advanced Study. This work waspartly completed at KITP, which is supported in partby the National Science Foundation under Grant No.NSF PHY11-25915 and at the Aspen Center for Physics,which is supported by National Science Foundation grantPHY-1066293.
Appendix A: Tracker Model Details
We model the tracker following the specificationsin [16]. The tracker is comprised of a cylindrical barrelthat surrounds the beam pipe and two disks (end caps)on each side of the barrel. We consider each layer tobe of negligible thickness. In cylindrical coordinates wespecify barrel layers by their r position and z extent anddisk layers by their | z | position and r extent.The tracker consists of the pixel detector: • Pixel barrel (3 layers) r = 4 . , . , . | z | = 0 cm − . • Pixel end cap (2 layers) | z | = 34 . , . r = 6 cm −
15 cmand the strip tracker: • Tracker inner barrel (4 layers) r = 25 . , . , .
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