Enhancing Sensitivities to Long-lived Particles with High Granularity Calorimeters at the LHC

The search for long-lived particles (LLP) is an exciting physics opportunity in the upcoming runs of the Large Hadron Collider. In this paper, we focus on a new search strategy of using the High Granularity Calorimeter (HGCAL), part of the upgrade of the CMS detector, in such searches. In particular, we demonstrate that the high granularity of the calorimeter with this upgrade, which allows us to see"shower tracks"in the calorimeter, can play a crucial role in identifying the signal and suppressing the background. We study the potential reach of the HGCAL using a signal model in which the Standard Model Higgs boson decays into a pair of LLPs, $h \to XX$. After carefully estimating the Standard Model QCD and the misreconstructed fake-track backgrounds, we give the projected reach for both a more conservative vector boson fusion trigger and a novel displaced-track-based trigger. Our results show that the best reach for the Higgs decay branching ratio, BR$(h \to XX)$, in the vector boson fusion channel is about $\mathcal{O}(10^{-4})$ with lifetime $c\tau_X \sim 0.1$--$1$ meters, while for the gluon gluon fusion channel it is about $\mathcal{O}(10^{-5}\text{--}10^{-6})$ for similar lifetimes. Alternatively, for an LLP with $c\tau_X \sim 10^3$ meters, the HGCAL based search should be able to probe BR$(h\to XX)$ down to a few $\times 10^{-4}$($10^{-2}$) in the gluon gluon fusion (vector boson fusion) channels, respectively. In comparison with these previous searches, our new search shows enhanced sensitivity in complementary regions of the LLP parameter space.


I. Introduction
Models of new physics beyond the Standard Model (BSM) often predict the existence of long-lived particles (LLPs), giving rise to distinct signatures at colliders (see [1] for a recent review). There have been many searches for LLPs at the ATLAS, CMS, and LHCb experiments at the Large Hadron Collider (LHC). The signatures of the LLP depend on its charge, lifetime, and decay products. Accordingly, various search strategies and detection techniques can be used, including the non-prompt photon detection using the electromagnetic (EM) calorimeter [2, 3], the disappearing track search based on the tracking system [4][5][6], and the displaced leptons or lepton jets search based on the tracking system [7][8][9][10][11][12][13], the calorimeter [14,15], as well as the muon system [16][17][18]. Many new search targets and strategies for the LLPs based on the LHC experiment have also been proposed .
In this work, we focus on a new sub-detector HGCAL, a highly granular and silicon-based calorimeter, which is the Phase-2 upgrade of the CMS endcap calorimeter [66]. It consists of a sampling calorimeter with silicon and scintillators as active material, including both the electromagnetic and the hadronic sections with unprecedented fine segmentation. In particular, each section consists of silicon cells of size (0.5 -1 cm 2 ) and the remainder of the hadron calorimeter will use highly-segmented plastic scintillators of size (4 -30 cm 2 ) [66].
It has an intrinsic high-precision timing capability from silicon sensors with a resolution of ∼ 25 ps. Due to its fine transverse granularity, the HGCAL has an angular resolution of about 5 × 10 −3 radians for electromagnetic shower with p T > 20 GeV, after taking into account the broadening effect from the shower. The HGCAL can handle different LLPs signatures. It also serves as a semi-forward detector different from most LLP studies at LHC main detectors that are mainly based on central detectors.
We carefully simulated and estimated the SM background for generic LLP signals, which contains prompt and displaced QCD background and non-prompt misconnected fake-track background. Based on these, we design a set of cuts that take advantage of the unique features of the signal and the capabilities of the HGCAL detector. We use a signal model in which scalar LLPs (X) are produced from SM Higgs decay (h → XX). This simple model is quite representative [68], covering a broad range of new physics scenarios, such as the hidden valley models [69][70][71], and more recent proposals motivated by neutral naturalness [72][73][74][75][76][77]. Two production channels of SM Higgs are considered. One is the vector boson fusion searches based on prompt VH [67] (dotted), the muon spectrometer [18] (dashed), the calorimeter [14] (dot-dashed), and the CMS search based on displaced vertex in the tracker system [13]  about BR(h → XX) ∼ O(10 −5 -10 −6 ) for similar lifetime. Alternatively, for an LLP with cτ X ∼ 10 3 meters, the HGCAL based search should be able to probe BR(h → XX) down to a few ×10 −4 (10 −2 ) in the ggF (VBF) channels, respectively.
The paper is organized as follows. In Sec. II A, we discuss the signal model and the trigger considerations for the signal. In Sec. II C, we describe signal and background generation. In Sec. III, the distributions of kinematic variables are discussed, and the corresponding cuts are applied. Finally, we show our results in Sec. IV and conclude in Sec. V.

II. Analysis framework A. Signal model: long-lived particles from Higgs decay
To demonstrate the potential of our proposed search, we use a signal model in which the LLP couples to the SM through the Higgs portal. For m X < m h /2, the LLP will be produced through the Higgs boson decay h → XX. (1) We assume X is a neutral and meta-stable scalar which will further decay via X →bb. The free parameters in this simplified model are mass m X , lifetime cτ X , and the decay branching ratio BR(h → XX). We consider two Higgs production channels, namely, the VBF production and ggF production, shown in Fig. 2. The VBF channel is motivated by the possibility of using an existing VBF trigger that does not rely on the properties of the LLP. In the ggF channel, we will explore the physics potential of using displaced track triggers after LHC Phase-2 upgrades, e.g., Ref. [78].

B. Modeling the HGCAL detector
Our study focuses on the potential of the LLP search of the HGCAL detector [66]. Due to the novelty of the detector and the signature, we cannot perform a full-fledged detector simulation. Instead, we make assumptions based upon the HGCAL performance document.
We describe here the relevant detector parameters used in our study.
A schematic drawing for the decay products of the long-lived particle arriving the HGCAL.
The direction of the momentum of the decay products can be measured by the HGCAL with an angular resolution of σ θ , resulting in an error in reconstructing the displaced vertex.
The HGCAL detector locates at |z| = 3.2 m and extends to |z| = 5.2 m. The angular coverage of the detector is 1.5 < |η| < 3.0. Its stand-alone angular resolution on the shower direction is taken to be σ θ ∼ 5 × 10 −3 radians, with possible improvement when combining with the information from the inner detectors. 2 A schematic plot for the long-lived particle signal arriving the HGCAL is shown in Fig. 3. The particle will travel in a magnetic field of B = 3.8 Tesla along the z direction, therefore, it would follow a helical trajectory. We require the tracks to go through the first layer of HGCAL at |z| = 3.2 m. The tracks with 2 We note here in the text we will not distinguish tracks and shower when discussing HGCAL, since the shower can be viewed as a "fat track". A subtle difference is HGCAL will be able to see neutral particles shower as well, which traditionally do not correspond to tracks.
p T above 1 GeV can be reconstructed at L1 level [66]. Each point on the track trajectory has a 4D coordinate, (t, x, y, z). Once the momentum of a particle at a point on the track is known, the 4D trajectory of the full track can be calculated.
The directions of particles reaching HGCAL can be measured with an angular resolution of σ θ . The inaccuracy in measuring its direction is a main source of the error in the measurement of the track direction, which can fake our signal. We smear the direction of the momentum using a Gaussian function with a spread equal to the angular resolution σ θ .
With this new momentum for the particle at the first layer of HGCAL, we then recalculate its 4D spiral trajectory.

C. Signal and Background generation
The long-lived particle signal The signal events at parton level are generated using MadGraph5 aMC@NLO [79], and the parton shower is performed by Pythia8 [80,81]. The charged particles with p T > 1 GeV are kept as track candidates.
For the signal, the displaced tracks dominantly come from the displaced decay of the LLP X, which will give a displaced vertex (DV). The location and time of this DV results from a convolution of X momentum distribution and the lifetime of X. We also require X to decay within |z| < 1.5 m to ensure the tracks have five stubs in the tracker. Given the 4D vertex information and the 4-momentum of each charged particle at that vertex, one can reconstruct its 4D helical trajectory in the magnetic field. From this, we obtain the 3-momentum of the particle when it arrives at the HGCAL. We then smear the direction of its momentum and recalculate the 4D trajectory.
A further improvement of the HGCAL coverage can be achieved by considering LLPs decaying inside HGCAL. The LLP signal would appear as showers with an anomalous shape in the HGCAL. However, given the difficulty of modeling the showering pattern in this material-dense area and the lack of understanding of the background, we take the rather conservative class of signals in which X decay before entering HGCAL. In this case, we use HGCAL to only pick out the displaced tracks. These tracks are identified via the showering of the hadronic particles from the LLP decay. Hence, they have a degraded angular resolution than the HGCAL physical limitations due to the broadening caused by interaction with materials. 3 We also require these tracks to match hits in the outer part of the tracking system, which picks only the charged components of the signal. This is clearly a very conservative use of the HGCAL capability and leaves a large room for future improvement with a full understanding of the HGCAL performance.

SM QCD background
The main SM prompt backgrounds are the QCD dijet events, including bottom quark pair bb. A main feature of the signals is the presence of tracks with large transverse impact parameters. There are two reasons for such a QCD background to also have displaced tracks.
The first one is the finite lifetime of mesons and baryons. The second one is from the finite angular resolution of HGCAL.
We use MadGraph5 aMC@NLO [79] and Pythia8 [80,81] to generate the SM background events, which properly include the finite lifetime effect of SM mesons and baryons. The displaced tracks come primarily from K 0 S meson (cτ ∼ 2.7 cm), with some addition contribution from heavy baryons like Λ 0 (cτ ∼ 7.8 cm).
After applying generator level cuts such as p T > 20 GeV at the parton level, the crosssections of bb and jj are 3.6 × 10 6 pb and 1.7 × 10 8 pb 4 , respectively. The jet matching has been applied with one extra jet added and the minimal k t is set to be 30 GeV. After hadronization, charged tracks with p T > 1 GeV are kept. Among the tracks arriving at HGCAL, we kept the five leading ones to be smeared 5 .

Fake-track background
We denote as fake-track background the events with mis-reconstructed tracks from the accidental connections of the hits in the tracker system. They can easily have very large d 0 , similar to those from the signal. There are O(30) such tracks per bunch crossing. This high combinatorics makes it possible for a selection of a few tracks to approximately form a 3 We take this into account by using a degraded angular resolution. 4 Here we use the 4-flavor PDF scheme. 5 This procedure tends to overestimate the suppression provided by our vertexing cuts. However, since our results essentially do not rely on the vertexing cuts for suppressing the SM QCD background, we keep only the five leading tracks for simplicity.

vertex.
We follow Ref. [82,83] to generate events with mis-reconstructed tracks. We also add the timing information to the tracks, which can potentially further reduce the background [84].
To generate a fake-track, we use a set of kinematical variables following a flat distribution within the ranges indicated below.
• φ 0 ∈ [0, 2π]: the azimuthal angle of a reference point from the beam spot in the x-y plane.
• η ∈ [−3, 3]: the pseudo-rapidity of the direction of the track at the reference point.
The reference point is defined at the location of the transverse impact parameter of a given track. The curvature of the track and the transverse momentum of the presumed particle responsible for it satisfy R = |p T /(q × B)| = (p T /GeV) × 0.88 m. q is the charge of the particle, assumed to be ±e with equal probability. From the range of the curvature, the tracks generated must have p T ≥ 2 GeV, with a flat probability in p −1 T . In the x-y plane, the trajectory of the track is a circle with a radius equals to R. However, the origin (the beam spot) can be either inside or outside the circle. The distance between the center of the circle and the origin can be either R − d 0 or R + d 0 . We assume the two cases occur with equal probability. With these parameters, the 4D trajectory of the fake tracks can be determined.

D. Triggering strategy
For the VBF channel, we require at least one forward jet p T > 110 GeV, and both of the forward jets p T > 35 GeV with an invariant mass m jj > 620 GeV [85].
For the ggF channel, we try two different trigger strategies. First, we use a proposed L1 displaced track trigger cuts with H T > 100 GeV, which has been demonstrated with two displaced tracks with p T > 2 GeV within an L1 jet [78]. This L1 trigger rate is about 10 kHz in the central region and about a factor of 2-3 higher in the endcap region [78]. We require our signals to have more than five displaced tracks and H T > 100 GeV, which is more stringent than Ref. [78]. Nevertheless, we still assume the same level of L1 trigger rate of 10 kHz. Because that displaced track selection and vertex reconstruction do provide suppression of the L1 rate, the average number of multiple track bundles passing all these trigger requirements should be around one per triggered event. Given that the HL-LHC will run for 10 8 seconds, the total number of such fake-track bundle events is about 1 × 10 12 .
The second trigger strategy for the ggF channel is a displace track trigger without the H T cut. It makes use of five displaced tracks with a vertex fitting, rather than the two displaced tracks [78]. This should reduce the low-level trigger rate and allow for the removal of the H T requirement. We also emphasize that these randomly connected tracks may not be corresponding calorimeter energy deposits in the HGCAL. Even if our estimate of the tracking alone suppression is not sufficient, consistency matching between different subdetectors of the experiment will provide sufficient suppression.

III. The kinematics of signal and backgrounds
There are two main characteristics of the signal. First, the signal tracks tend to have large impact parameter, d 0 . Hence, requiring a number of tracks (five in our case) to have large d 0 allows us to effectively separates the signal from the QCD background, which is mostly prompt. On the other hand, the fake-track background have a flat distribution in a large range of d 0 . This is where the second main characteristic comes into play. Namely, the signal tracks all originate from a single vertex. Since each fake-track is independent of each other, they have a small probability of reconstructing a common vertex. In the following, we will define a set of variables to quantify this feature. We note that if the tracks are generated via interaction with detector material, there would be a reconstructable displaced vertex. One could veto all the displaced vertices in the materiel-dense region, as has been done by many LLP searches [1, 8, 86].

A. The Displaced Vertex fitting variables
We fit the candidate tracks to a displaced vertex and define associated fitting variables as follows. We begin with five leading (in p T ) tracks and calculate their 4D trajectories. We perform a 2D vertex fit in the transverse plane by minimizing the following quantity, where {x cen i , y cen i } are the x-y coordinates of the center of the circle for the ith track and R i is the transverse radius of the track helix. The minimization gives the best-fit coordinates , x and y, for a presumed DV. Of course, this fit won't be perfect in reality and the tracks will miss the DV by some amount. To quantify this, we begin by identifying a point, with originating from a DV are perfectly reconstructed, all of the x i and y i will coincide with x and y. We can define the following variables associated with a fitted DV.
• The displacement of the vertex in the transverse plane r DV ≡ x 2 + y 2 that minimizes ∆D in Eq. 2.
• The imperfectness or the uncertainty of vertex fitting, ∆D min , based on the best-fit 2D vertex coordinates x and y that minimizes ∆D in Eq. 2.
• Based on the set of {z i , t i } for each track that form a DV, we can define the mean valuez andt, and their standard deviations σ z and σ t .
• For the ith track, we define the time delay as ∆t i ≡ t i − x 2 i + y 2 i + z 2 i /c. We define the time delay of the displaced vertex (∆t) as the average of the ∆t i of the five leading tracks (in p T ) and the standard deviation σ ∆t . For a slow moving LLP which decays at the DV, ∆t would be its time delay in comparison to the prompt particles propagating from the interaction point to the DV.
In summary, we can define the following kinematic variables using the above 2D-4D displaced vertex fitting procedure, r DV , ∆D min ,t,z, ∆t, σ t , σ z , σ ∆t .
(3) without ( Fig. 7) σ θ , we see that the angular resolution does lead to a broader shape.
However, turning off angular resolution does not lead to exact r DV = 0 m. Some charged tracks start from displaced vertexs from long lifetime mesons decay, e.g., K 0 S . There is no significant difference between QCD backgrounds jj and bb. The reason is that B-meson has a proper lifetime of ∼ 0.045 cm, which is too small to generate a difference between jj and bb.   point on the track to the beam spot. This feature can be seen in Fig. 4 (a) as well.
For the signal, r DV is approximately the position where X particle decays in the x-y plane. Its distribution has a very long tail, due to the lifetime of X particle.
• ∆D min : a measure of how well the set of candidate tracks fit in a common vertex.
Both QCD background and the signal should have a distribution of ∆D min peaks near zero. As shown in Fig. 5  Turning off the angular resolution in Fig. 7 (b), the signal events all have exactly ∆D min = 0 m, which also shows that our algorithm correctly finds the DV where X decays. For the QCD distributions, there are still a few percents of events with non-zero ∆D min , due to long-lived SM hadrons.
•t: the average of the time coordinate of the tracks at the fitted DV.
The QCD background peaks around zero as shown in Fig. 7 (c). The spread oft dominantly comes from the angular resolution, and it can be estimated to be ∆φR where v T is the transverse velocity of the particle responsible for the track and ∆φ is the azimuthal angle change when the track evolved from the fitted DV to the HGCAL.
The geometrical acceptance of the HGCAL selects forward tracks, leading to smaller v T ∼ 0.2 c, as shown in Fig. 8 in the Appendix. For ∆φ, its 1 σ spread is about 0.02 in Fig. 9 in the Appendix. Therefore, for a typical track radius of R = 3 m, the spread oft for QCD background is about 0.5 ns, agreeing with Fig. 5.
For the signal,t peaks around a few ns, due to the delayed decay of X. In both Fig. 5 and 7, we have chosen cτ X = 1 m which corresponds to 3 ns. Moreover, decay products from a lighter LLP (hence with a larger boost) has a largert than that of a heavier LLP.
For the fake tracks, the t i for each track should be determined mainly by the random seed time t 0 , ranging from {−6, 6} ns with a flat distribution. The distribution can be approximated by a Gaussian function peaking around zero, with a standard deviation of 3.5/ √ 5 = 1.6 ns, as shown in Fig. 5 (c). Here 3.5 is an ad hoc standard deviation of the flat distribution of each track. In the limit of a large number of tracks, Gaussian function can be used to estimate the spread of the fitted vertex. From Fig. 7 (c), we see that the distribution from the fake-track background is not affected by angular resolution, as expected.
• σ t : the standard deviation of the time-coordinates of the constituent tracks at the fitted DV.
For the signal and QCD background, the distribution is expected to be concentrated at small values, as shown in Fig. 7. The spread dominantly comes from the angular resolution, as shown in Fig. 5 (f). The spread can be estimated by ∆φR/v T . As explained fort, it is ∼ 1 ns for QCD background, which agrees with the broad distribution up to a few ns. In addition, some QCD events have large separation between the displaced tracks of the long-lived mesons and the prompt tracks. For the fake-track background, the spread is largely due to the uncorrelated large spread of the track seed time t 0 distributions.
•z: the averaged z-coordinate of the tracks at the fitted DV.
We first look at the distribution without σ θ in Fig. 7. The signals have a very flat distribution because of the long lifetime of X. There is a hard cut because X is required to decay in the region |z| < 1.5 m to ensure five stubs for the signal track. • σ z : the standard deviation of the z-coordinates of tracks from the fitted DV.
Starting with Fig. 7 without σ θ , it is exactly zero for the signal and almost zero for QCD background for the similar reason as σ t . σ θ broadens the distributions up to 0.15 m for the signal and QCD background, which is in agreement with the previous The QCD background has a larger spread than signal, for the same reason as σ t . For the fake-track background, the large spread in the seed z 0 of the constituent tracks leads to a large spread.
• ∆t: the average of the time delay for the tracks.
In Fig. 7, ∆t of the signal comes from the slow moving LLP X. Thus, the values of ∆t i are always positive. Moreover, a heavier X moves slower than a lighter X, thus the tail of heavier X is longer than that of the lighter X and the QCD background.
The QCD background has a peak around 0 since the track is prompt. The spread around 0 is due to smearing effects and the fact that some tracks come from long-lived meson. The fake-track background distribution is Gaussian-like with 1-σ spread of about 1.5 ns. It is almost symmetric around zero since its 4D parameters are random and independent from each other. The largest spread comes from random t i , thus ∆t is very similar to t.
• σ ∆t : the standard deviation of the time delay of the tracks.
Starting with Fig. 7 without σ θ , the signal has exactly σ ∆t = 0, while the QCD background peaks at zero with a spread from long-lived meson decay. The fake background is similar as in σ t because the dominant spread comes from random t 0 . After including σ θ , the distributions are broadened as expected but without qualitative change.
We see that the distribution of fake tracks are quite different from signal in general.
Based on this, we propose the six cuts according to the distributions and the cut flow table is given in Table V. Explicitly, the cuts for DV fitting variables are, r DV > 0.16 m, ∆D min < 0.02 m,t > 1 ns, σ t < 0.3 ns, |z| > 0.4 m, σ z < 0.05 m, (4) which we denoted them collectively as vertexing-cuts.

B. The transverse impact parameter distribution
The d 0 distributions of the five tracks for the QCD background, fake-track background, and the signal are given in Fig. 6. In Fig. 6 (a), the magnetic field is set as zero, and the angular resolution effect is not included either. The fake tracks have a flat d 0 distribution from its definition. The signal has a broad distribution due to the delayed decay of X.
Moreover, the lighter X has a slightly narrower distribution since its decay products are more boosted. The QCD dijet background peaks at d 0 = 0 m, with a tail from the longlived hadron decay.
In Fig. 6 (b), the effect of the magnetic field is included. Comparing with Fig. 6 (a), the QCD background from long-lived hadron are broadened, while the signal is less affected since the displacement before the X decay is more important. The fake-track background is almost flat in d 0 by definition.
Both the magnetic field and the angular resolution effects are included in Fig. 6 (c). Comparing with Fig. 6 (b), the signal is almost unchanged. The QCD background is broadened with a spread of 0.015 m. The spread can be estimated by σ θ |z| ∼ 0.015 m, where |z| is taken to be 3.2 m, the distance to HGCAL. The fake-track background is still flat , with its edge smeared by the angular resolution.
In Fig. 6 (d), we have included both the magnetic field and angular resolution effect after applyingvertexing-cuts. Importantly, the distribution of the QCD background is trimmed to be a Gaussian shape. This is expected since the outliers with large d 0 come from the decay of long-lived hadron, which fails the DV fitting (and thus fail to pass the vertexing-cuts).

C. Correlations between the selection cuts
Due to the limited statistics of our simulation in some cases, we estimate cut efficiencies by the product of the efficiencies of different subsets of cuts. To validate this approach, we study the correlations between those cuts. To quantify the correlations among different cuts, we use the following function  We begin with the QCD jj and bb backgrounds. First of all, the correlations among vertexing-cuts variables are not needed, since we have enough simulated events to compute the efficiency without relying using the product of the efficiencies of the individual cuts.
However, the vertexing-cuts is not enough to suppress the background; we further require multiple tracks with large d 0 . Here, we are limited by the statistics. Hence, we need to check the the correlation between vertexing-cuts and d 0 cuts, and the correlation among different d 0 cuts.
The correlations between vertexing-cuts and the d 0 cut are given in Table I. With higher cut threshold of d 0 , the correlation between single d 0 cut and r DV ,t and |z| become stronger. This is expected. For jj and bb QCD backgrounds, the event with large transverse impact parameter is also likely to have large values for r DV ,t and |z|. Therefore, we will not use these cuts when calculating the final selection efficiencies. In this way, we avoid double counting and remain conservative because all the remaining columns have ρ > 1 . Next, we would estimate the cut efficiency on the QCD dijet background by the product of single track efficiency of d 0 > 0.03 m. We would like to show that the consecutive d 0 cuts are approximately independent. This is expected since the large d 0 tracks are mainly from detector resolution effects, which are independent between tracks. As shown in Fig. 10 in the Appendix, the d 0 distribution of the leading track is the same as the ensemble of the five tracks shown in Fig. 6. This indicates that we could apply the transverse impact parameter cut on multiple tracks independently. 6 To quantify this further, we define the 6 This independence of the tracks is true for both prompt QCD background from smearing effects and for the fake-track background. For the displaced tracks from long-lived hadrons, there is a certain level of correlations which is already removed by our vertexing-cuts. Hence, we ignore these minor correlations here.
following function to study the correlations between different d 0 cuts, where d 0 > 0.03 m is chosen as an example. Note the tracks in numerator are randomly chosen, while in the denominator they are the n hardest tracks. The correlation ρ dn for QCD jj and bb backgrounds after imposing vertexing-cuts are given in Table II.
In Table II, from ρ 1 d to ρ 5 d , the correlations are mostly around 1, implying the d 0 cuts for different tracks are indeed independent 7 . After applying the vertexing-cuts and requiring  Next, we discuss the correlations of the cuts for the fake-track background. Firstly, among the vertexing-cuts variables, Table III shows that most of them are approximately independent. The correlation between |z|-σ z 1 , which is very conservative for an estimate of the background. The correlation between |z|-r DV is 0.16. This is not conservative but it can be compensated by using the |z|-σ z pair. Due to low statistics, we do not obtain reliable 7 ρ 1 d is not exactly 1, because the track in the numerator is randomly picked, while the track in the denominator is the leading track. Thus the fact that its value is close to 1 is a kind of proof that different tracks are independent.
estimates for the correlations between r DV -σ z , σ t -σ z , and σ t -∆D min . As a further check, we evaluated the correlations with a weaker set of cuts thus containing more statistics, shown in Table VII in the Appendix. For example, we relaxed the maximum σ t cut to 0.5 ns rather than 0.3 ns. In this case, we can conclude the most of the variables are approximately independent. In Table VII, the correlations between r DV -σ z , σ t -σ z and σ t -∆D min are 45.4, 0.7 and 2.7 respectively, which are either approximately independent or conservative. This is consistent with the results in Table III. From these results, we argue that the total cut efficiency for the vertexing-cuts variables estimated by using the product of the single cut efficiencies can be considered as conservative.  We note that there are enough statistics in the fake-track background to calculate the efficiency of the multiple (d 0 > 0.03m) cuts without approximation. Hence, there is no need to check the correlations among individual d 0 cuts here. We are left to check the independence between vertexing-cuts and d 0 cuts, which is given in Table. IV
For the signal, it is the combination of the geometric probability for X decay inside the |z| < 1.5 m region and the efficiency for tracks arriving HGCAL. The QCD backgrounds have a better efficiency for tracks arriving HGCAL, because their tracks are more forward than the signal (see the upper panel of Fig. 8). Furthermore, the background jets are usually more energetic thus containing more tracks than the signal, which makes it much easier to satisfy the requirement. The single-cut efficiencies for vertexing-cuts DV fitting variables are listed. The variables ∆t and σ ∆t are highly degenerate witht and σ t , and are not used here 8 . After multiplying N ini by the cut efficiencies in the "5 tracks" row, the " vtc " row and the "(d 0 > 0.03m) 5 " row, we obtain the final event number N fin .
For the QCD background, we apply a partial set of vertexing-cuts on ∆D min , σ t , and σ z . The cuts with ( * ) are correlated with transverse impact parameter d 0 cut. Hence, they are not included in " vtc " to avoid double counting 9 . Furthermore, we apply the single cut can suppress the background further by a factor of 0.34, leaving only 0.14 events. We note that, even though we did not include it in this analysis, the fake-track has to match the track information with the HGCAL calorimeter energy deposit [83], which can further suppress the fake-track background.
In summary, both the QCD background and the fake-track background can be suppressed to be smaller than one event during the lifetime of the HL-LHC. The suppression for the QCD background mainly comes from requiring large track displacement, while displaced vertex reconstruction is mainly responsible for suppressing the fake-track background.
For the signal, the full set of vertexing-cuts are applied with a total efficiency of vtc = 0.34 and 0.24 for m X = 20 GeV and 50 GeV, respectively. Applying d 0 cuts on all the tracks reduces the signal further. The remaining signal events as a function of branching ratio BR(h → XX) is given in the last row. Heavier X has higher efficiency for several reasons.
First, heavier X moves slower, leading to a larger probability of decaying before reaching HGCAL for a fixed proper lifetime. Second, lighter X has only a slightly better efficiency 8 For a general discussion on effectiveness of time-delay variable for a broad class of LLP signatures, see Ref. [87]. 9 One can apply them in an experimental search and it will help to further suppress the QCD background.
under the vtc cut. Last, lighter X has a lower d 0 cut efficiency, because the tracks tend to be collimated with the direction of X. Therefore, the search is more sensitive to heavier X.
For the VBF channel, the distributions of vertexing-cuts variables in Fig. 11 and transverse impact parameter d 0 in Fig. 12 are similar to those of the ggF signal. Comparing with the ggF signal, the sensitivity in the VBF channel is weaker by about two orders of magnitude due to the smaller cross-section and the stringent VBF trigger threshold.

B. The reach
The studies in the previous sections prepared us for estimating the reach of new physics with our proposed study. In this section, we present the results for both the ggF channel and the VBF channel. In Fig. 1 Alternatively, for an LLP with cτ X ∼ 10 3 meters, the HGCAL based search should be able to probe BR(h → XX) down to a few ×10 −4 (10 −2 ) in the ggF (VBF) channels, respectively.
For comparison, we show the limits from existing searches for our benchmark signal model in Fig. 1. For very small cτ X , the best limits come from the ATLAS search for the prompt h → XX → 4b, at 13 TeV with 36.1 fb −1 [67]. A short lifetime of X is allowed by the b-tagging algorithm, with maximal sensitivity for cτ X ∼ 0.5 mm. For cτ X between {10 −2 , 10 3 } m, there are several ATLAS searches using 13 TeV data. One is based on the muon spectrometer (MS) with 36.1 fb −1 [18]. The other uses the low-E T calorimeter energy ratio trigger, with 10.8 fb −1 [14]. In the gap for LLP lifetime around cm, the displaced jet searches can be sensitive. A recent CMS search based on displaced vertex in the tracker system with 139 fb −1 obtained limits at the level of 10 −1 -10 −2 [13]. In comparison with these previous searches, our new search shows enhanced sensitivity in the complementary region of the LLP parameter space.

V. Conclusion
High granularity calorimeters offer new opportunities for the search of the long-lived particle. In this work, we study the potential reach for the long-lived particle signal based upon a new search mainly relying on the HGCAL upgrade of the CMS detector. We present results based on both the more conservative traditional VBF trigger and a pair of novel displaced track triggers. Based on a simplified modeling of the signal and background of this new approach, we carefully devised kinematical cuts and estimated the size of the leading backgrounds. HGCAL can obtain the shower direction and timing information with unprecedented precision, enabling us to view them as "tracks". We find that the QCD background is mostly prompt, which can be suppressed effectively by requiring a large transverse impact parameter for multiple tracks. The second-largest source of background is the fake-track background, which comes from mis-connected hits. The resulting tracks have a random distribution, typically with a large transverse impact parameter. However, it is hard for those tracks to fit in a common vertex. Taking advantage of this feature, we design a set of corresponding vertexing-cuts to suppress such backgrounds. The excellent precision of HGCAL in shower direction measurement plays a central role in the effectiveness of these cuts.
Finally, we note here our study is rather conservative in many aspects. For the QCD background and the signal, the most relevant parameter of the HGCAL detector is its angular resolution. In this study, we use the standalone angular resolution from HGCAL.
In reality, the track trajectory can be detected by both the tracking system and the tracker inside the HGCAL. Combining the two can further improve the angular resolution. This will result in a better DV fitting and enhance the suppression of the QCD background. Thus, we expect the reach can be further improved. We also require the LLP to decay before reaching the HGCAL detector. With a detailed understanding of the showering behavior of the background, novel searches for LLP decaying within the HGCAL can also be sensitive.
This will enable an HGCAL standalone trigger, and enlarge the decay volume for the LLP (hence the reach in cτ X ) by a factor of a few.

Acknowledgement
We thank Jared Evans, Yuri Gershtein, Simon Knapen for helpful discussion. JL acknowledges support by an Oehme Fellowship. ZL is supported in part by the NSF under

VI. Appendix
We put the supportive figures and tables in the Appendix to avoid redundancy in the main text while keeping helpful information to the readers.
In Fig. 7, kinetic variable distributions for the QCD background, fake-track background and the signal are shown without the angular resolution effect included. This is a sanity check for Fig. 5 which has included the angular resolution effect. For the distribution of ∆D min , σ t , σ z and σ ∆t , the signals are exactly at 0 while the QCD background are peaked at 0. It shows that the DV fitting algorithm has worked well and found the expected true vertex.
In Fig. 8  Once requiring arriving at HGCAL, we can see that the v T for signal and backgrounds are dominated by small values, e.g., 0.1 ∼ 0.4. The reason is that HGCAL is a forward detector, which picks the forward tracks. Therefore, the v T is forced to be small.
In Fig. 9, we show the distribution of ∆φ for the tracks in the DV fitting procedure. The QCD background and the signal have a similar distribution, peaked with ∆φ = 0 because they both have a common vertex. ∆φ comes from the angular resolution effect of HGCAL, which has a spread of about 0.02, which is a few times the angular resolution σ θ . For fake-track background, the distribution of ∆φ has a reason smaller than order 1. From the definition of ∆φ, its starting point (the reference point) is the closest point to the origin.
Hence, the fitted DV should be enclosed within these reference points, as going far from the origin will lead to a bad fit. As a result, the movement in φ angle is not large from the starting point to DV.
In Table VI, we show the independence correlation table for  . dijet backgrounds without applying vertexing-cuts. This is an auxiliary check for Table II. It has higher statistics and also shows the d 0 of different tracks are nicely independent under this condition.
The Table VII shows the independence correlation table for vertexing-cuts variables for fake-track backgrounds, but with a weaker set of cuts comparing with Table III. We can see that most of the correlations are around 1 (approximate independent), with some results are 4.8 and 20 which are conservative. With the Table III and Table VII, it indicates that the estimate of fake-track background by multiplying each of these efficiency should be considered as conservative.
In Fig. 10, we show the transverse impact parameter d 0 distribution of the leading track for QCD background, fake-track background, and the signal. This figure is similar to Fig. 6, but with only the leading track included.
In Fig. 11 and Fig. 12, the kinetic variables and d 0 distributions for VBF channel are given. One can see that the distributions of the VBF channel are similar to the ggF channel.