Charm-quark Yukawa Coupling in $h\rightarrow c\bar{c}\gamma$ at LHC

TL;DR

This paper explores the potential to measure the charm-quark Yukawa coupling at the LHC through the rare decay $h ightarrow car{c} ext{ } ext{ extgamma}$, using advanced triggering and machine learning techniques to overcome background challenges.

Contribution

It proposes a novel method to probe the charm Yukawa coupling via Higgs radiative decay, achieving a sensitivity of about 8 times the SM value at the HL-LHC.

Findings

Potential to set a coupling limit of ~8 times the SM value at HL-LHC.

Refined trigger strategy combined with machine learning improves signal detection.

No significant improvement expected from higher energy colliders without detector upgrades.

Abstract

It is extremely challenging to probe the charm-quark Yukawa coupling at hadron colliders primarily due to the large Standard Model (SM) background (including $h\to b\bar b$) and the lack of an effective trigger for the signal $h\to c\bar c$. We examine the feasibility of probing this coupling at the LHC via a Higgs radiative decay $h\rightarrow c\bar{c}\gamma$. The existence of an additional photon in the final state may help for the signal identification and background suppression. Adopting a refined triggering strategy and utilizing basic machine learning, we find that a coupling limit of about 8 times the SM value may be reached with $2\sigma$ sensitivity after the High Luminosity LHC (HL-LHC). Our result is comparable and complementary to other projections for direct and indirect probes of $h\to c\bar c$ at the HL-LHC. Without a significant change in detector capabilities, there would be no significant improvement for this search from higher energy hadron colliders.

Tables

Table 1. Table 1 : Representative operating points for the c 𝑐 c -tagging efficiency ( ϵ c subscript italic-ϵ 𝑐 \epsilon_{c} ), the b 𝑏 b -jet mis-tag rate ( ϵ b subscript italic-ϵ 𝑏 \epsilon_{b} ), and the light jet mist-tag rate ( ϵ j subscript italic-ϵ 𝑗 \epsilon_{j} ).

Operating Point	${ϵ}_c$	${ϵ}_b$	${ϵ}_j$
I	20%	33%	0.13%
II	30%	33%	1%
III	41%	50%	3.3%

Table 2. Table 2 : Expected numbers of events of the signal and background, and event rates, in the range of 100 < M j ​ j ​ γ < 140 ​ GeV 100 subscript 𝑀 𝑗 𝑗 𝛾 140 GeV 100<M_{jj\gamma}<140~{}{\rm GeV} at the HL-LHC with ℒ = 3 ​ ab − 1 ℒ 3 superscript ab 1 \mathcal{L}=3~{}{\rm ab}^{-1} . The first row gives the event rate at L1, with only the requirements in Sec.  2 applied. Systematic uncertainties are not accounted for in the significance calculation in the last column.

	Working	Signal	Background	Background	$S/\sqrt{S+B}$
	Point	(QED)	events	event rate [Hz]	$\left[{10}^{-2}\right]$
Level-1 (L1)	No Tag	-	-	$9.55\times {10}^3$	-
	I	$269$	$3.37\times {10}^8$	$5.62$	$1.47$
1 $c$-tag	II	$349$	$5.18\times {10}^8$	$8.63$	$1.54$
	III	$401$	$8.83\times {10}^8$	$14.7$	$1.35$
	I	$29$	$1.14\times {10}^7$	$0.191$	$0.878$
2 $c$-tags	II	$66$	$2.23\times {10}^7$	$0.371$	$1.42$
	III	$126$	$5.79\times {10}^7$	$0.966$	$1.66$

Equations

$$gg\to h\to c\bar{c}\gamma .$$

$$pp\to j\gamma \mathrm{and}pp\to jj.$$

$$r_c=\frac{\sum p_T^{\mathrm{track}}}{p_T^{\mathrm{jet}}},$$

$${ϵ}_{j\to \gamma }=2.5(0.7)\times 10^{-4},$$

$$E_T^{R<R_c}<6\mathrm{GeV}.$$

$$p_{Tj}>27\mathrm{GeV},p_{T\gamma }>20\mathrm{GeV},$$

$$|\eta |<2.5,\mathrm{and}\Delta R>\mathrm{0.4.}$$

$$r_c>\mathrm{0.2.}$$

$$90\mathrm{GeV}<M_{jj\gamma }<160\mathrm{GeV}.$$

$$L=5\times 10^{34}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}=5\times 10^{-5}{\mathrm{fb}}^{-1}{\mathrm{s}}^{-1}$$

$$p_{Tj}^{\max }>40\mathrm{GeV}.$$

$$\Delta R_{j\gamma }^{\min }<\mathrm{1.8.}$$

$$60\mathrm{GeV}<M_{jj\gamma }<160\mathrm{GeV},$$

$$\mu <106,88,86,$$

$$y_c^{\mathrm{BSM}}={\kappa }_c{y}_c^{\mathrm{SM}},$$

$$N_{\mathrm{sig}}\simeq {\kappa }_c^2{N}_{\mathrm{sig},\mathrm{QED}}^{\mathrm{SM}}.$$

$${\kappa }_c=\sqrt{\mu }<10.4,9.4,\mathrm{9.3.}$$

$$M_{j\gamma }^{\max },M_{j\gamma }^{\min },M_{jj},p_{T\gamma },p_{Tj}^{\max },p_{Tj}^{\min },{\eta }_{\gamma },{\eta }_j^{\max },{\eta }_j^{\min },\Delta R_{j\gamma }^{\max },\Delta R_{j\gamma }^{\min },\Delta R_{jj},p_{Tjj\gamma }.$$

$$\mu <91,77,75,\Rightarrow {\kappa }_c<9.6,8.8,\mathrm{8.6.}$$

$$p_{Tj}>40\mathrm{GeV},p_{T\gamma }>23\mathrm{GeV},$$

$$\mu <98,82,81,\Rightarrow {\kappa }_c<9.9,9.0,\mathrm{9.0.}$$

$$\mu <89,71,70,\Rightarrow {\kappa }_c<9.4,8.4,\mathrm{8.3.}$$

Full text

††preprint:

PITT-PACC-1819

1 Introduction

It is of fundamental importance to establish the pattern of the Higgs boson Yukawa couplings to fermions in order to verify the Standard Model (SM) and seek hints of physics beyond the SM (BSM). The couplings to third generation fermions have all been observed with over $5\sigma$ significance. For top quarks, there is a large indirect contribution to the gluon-gluon fusion production mode and the photon-photon decay mode. However, direct observation is important to ensure there are no BSM quantum corrections to Higgs boson production or decay. Both the ATLAS and CMS collaborations have recently observed the production of top quark pairs in association to the Higgs boson Aaboud:2018urx ; Sirunyan:2018hoz as well as Higgs boson decays to bottom quark pairs Aaboud:2018zhk ; Sirunyan:2018kst . For leptons, the challenging decay channel $h\to\tau^{+}\tau^{-}$ reached $5\sigma$ already from the LHC Run 1 data Khachatryan:2016vau and now ATLAS and CMS have both individually observed this decay mode Aaboud:2018pen ; Sirunyan:2017khh . With the upgrade of the LHC to its high-luminosity phase (HL-LHC), the Higgs coupling measurements to the heaviest generation of fermions will reach an accuracy of about or better than $20\%$ ATL-PHYS-PUB-2014-016 and will extend to kinematic regions with high transverse momenta of the Higgs boson ($p_{T}^{h}$) Sirunyan:2017dgc ; ATLAS-CONF-2018-052 .

Direct observations of the Higgs couplings to the second generation of fermions will be critically important to confirm the pattern of non-universal Yukawa couplings and search for deviations from the SM as predicted in theories with an extended Higgs sector Branco:2011iw . The channel $h\to\mu^{+}\mu^{-}$ is the cleanest Higgs signal of all decay modes Han:2002gp ; Plehn:2001qg . Even with a branching fraction as small as $2\times 10^{-4}$, ATLAS and CMS almost have the sensitivity to the SM rate Aaboud:2017ojs ; Sirunyan:2018hbu and a measurement with an accuracy of $13\%$ is expected at the HL-LHC ATL-PHYS-PUB-2018-006 . In contrast to $h\to\mu^{+}\mu^{-}$, the second generation hadronic decay modes of the Higgs boson are very difficult to distinguish from SM backgrounds, including other Higgs boson decays. While $b$-jet tagging is a powerful tool for rejecting backgrounds, $c$-jets are harder to distinguish from $b$ and light jets Sirunyan:2017ezt ; ATLAS:2015ctag ; Aaboud:2018fhh and strange-jets are nearly identical to up- and down-quark jets Duarte-Campderros:2018ouv ; dshih . The $h\to c\bar{c}$ branching ratio is expected to be about 3%, so the challenge is background rejection and triggering, not statistics.

So far, there have been two experimental studies to probe the Higgs-charm Yukawa coupling $(y_{c})$. One approach is to use the clean associated production of the Higgs boson with a vector boson and exploit charm tagging Aaboud:2018fhh . A key challenge with this method is that the $h\to b\bar{b}$ contribution is large compared to the $c\bar{c}$ signal. An optimistic projection111This projection does not account for systematic uncertainties, nor the degradation from the extreme pile-up at the HL-LHC, including the possible increases in lepton trigger thresholds. for the full HL-LHC dataset suggests that 6 times the SM rate at 95% confidence level may be achievable ATL-PHYS-PUB-2018-016 . A second approach used exclusive decays of the Higgs into a $J/\psi$ and a photon Bodwin:2013gca . While this final state can be well-separated from backgrounds in the $J/\psi\rightarrow\mu^{+}\mu^{-}$ channel  Aaboud:2018txb ; Aad:2015sda ; Khachatryan:2015lga , it suffers from a small branching ratio and modeling assumptions to extract the Higgs-charm Yukawa. In particular, the leading contribution to this process is via the vector meson dominance $\gamma^{*}\to J/\psi$, which is an order of magnitude larger than that involving the charm-quark Yukawa coupling Bodwin:2013gca ; Bodwin:2014bpa ; Koenig:2015pha , leading to a less sensitive upper bound on $y_{c}$ of about 50 times of the SM prediction at the HL-LHC ATL-PHYS-PUB-2015-043 .

Another recent proposal for probing the Higgs-charm Yukawa coupling is to study the associated production process $gc\to ch$ Brivio:2015fxa . This has the advantage that it is independent of the Higgs decay mode, but suffers from a low rate and significant background. Other proposals for direct or indirect probes of first- and second-generation quark-Higgs couplings Soreq:2016rae ; Yu:2016rvv ; Bishara:2016jga ; Cohen:2017rsk are challenging due to large SM backgrounds and contamination from other Higgs production and decay modes. A global analysis of Higgs decays can also constrain the charm-Higgs Yukawa coupling, with a projected sensitivity of about 6 times the SM expectation Perez:2015aoa ; Carpenter:2016mwd .

It has been recently pointed out that the radiative decay of the Higgs boson to a pair of charm quarks could be used to constrain the charm-quark Yukawa coupling with the final state $h\to c\bar{c}\gamma$ Han:2017yhy . The addition of the photon can be helpful for triggering as well as suppressing both non-Higgs and Higgs backgrounds. In particular, the electromagnetic coupling would disfavor the down-type quarks, especially the flavor-tagged $b\bar{b}\gamma$ mode. In this work, we examine the feasibility of a Higgs-charm Yukawa coupling measurement in the $h\rightarrow c\bar{c}\gamma$ channel at the HL-LHC. By proposing an optimal triggering strategy and simulating realistic detector effects, we show that a coupling of about 8 times the SM value may be reached at 95% confidence after the HL-LHC. This approach is complementary and competitive with other methods. We also explore the extent to which the energy upgrade of the LHC (HE-LHC) could improve the sensitivity.

The rest of the paper is organized as follows. In Sec. 2, we consider the features for the signal and background processes and propose an optimal but realistic trigger. In Sec. 3, we perform detailed analyses, including some basic machine learning, to obtain the optimal signal sensitivity. We extend our analyses to the HE-LHC in Sec. 4. The paper ends with conclusions and outlook in Sec. 5.

2 Trigger Considerations at HL-LHC

We focus on the leading Higgs production channel, gluon fusion, followed by the radiative decay

[TABLE]

The signal is thus characterized by an isolated photon recoiling against two charm-tagged jets with a three-body invariant mass near the Higgs resonance. The energy of the two charm jets will be limited by the Higgs boson mass, and the photon tends to be soft and collinear with one of the charm quarks. Due to the large collision rate (40 MHz), enormous inelastic cross-section for $pp\rightarrow$ central activity, and limitations in hardware, most collisions at the LHC are discarded in real time. The trigger system is a key challenge for recording physics processes with relatively soft final states such as $h\rightarrow c\bar{c}\gamma$. The rest of this section explores the impact of triggering on the $h\to c\bar{c}\gamma$ analysis in the context of the HL-LHC.

2.1 Signal and background processes

Tagging jets originating from charm quarks ($c$-tagging) is challenging, but important for suppressing backgrounds originating from light Quantum Chromodynamic (QCD) jets and from $b$-quark jets. Encouragingly, a recent study from ATLAS Aaboud:2018fhh has shown very promising $c$-tagging results. Based on the ATLAS result, three $c$-tagging working points listed in Table 1 are studied for the $h\to c\bar{c}\gamma$ search.222We choose the $c$-tagging working points aiming at the rejection for the largest background of the QCD light-jets production for given $c$-tagging efficiencies.

One of the dominant backgrounds from the $h\to c\bar{c}\gamma$ search is QCD di-jet production associated with a photon, where both jets are (mis-)tagged as $c$-jets. Similarly, QCD 3-jet production also contributes to the background if one of the jets is mis-identified as a photon. In addition to these hard-scatter background processes, one or more of the tagged objects could come from an additional nearly simultaneous $pp$ collision (pile-up). Many sophisticated pile-up mitigation techniques have been proposed ATLAS:2017pfq ; Berta:2014eza ; Bertolini:2014bba ; Krohn:2013lba ; Cacciari:2014gra ; Cacciari:2007fd ; CMS:2013wea ; Aaboud:2017pou ; Aad:2015ina ; Martinez:2018fwc which can significantly reduce the contamination from pile-up both in the trigger and in offline analysis. However, no method can eliminate all of the pile-up and all methods perform worse (if even applicable) at the trigger level. Since pile-up conditions will be extreme at the HL-LHC (typically 200 pile-up collisions), their contribution to the event rate must be taken into account.

Current and future upgrades of the ATLAS and CMS trigger systems Collaboration:2285584 ; Collaboration:2283192 will allow for multi-object requirements using offline-like information. In order to have a high efficiency, (relatively) low rate trigger for $h\to c\bar{c}\gamma$, we propose a new approach which requires two jets and one photon in the central region with invariant mass near the Higgs resonance.

2.2 Simulation Setup

Since the cross section for Higgs bosons is much smaller than for multijet production, the trigger rate is dominated by background. In order to estimate the trigger rate, the following background processes are simulated using MG5aMCNLO Alwall:2014hca , including up to one additional jet matched using the MLM prescription Mangano:2002ea :

[TABLE]

The parton shower and hadronization are simulated with PYTHIA6.4.28 Sjostrand:2006za , and a fast detector simulation is implemented using DELPHES3 deFavereau:2013fsa with the detector card delphes_card_ATLAS_PilUp.tcl. Pile-up is modeled by mixing $\mu=200$ minimum bias events simulated using PYTHIA with the hard-scatter processes.

The ATLAS and CMS trigger systems consist of a hardware trigger (L1) and a software-based high-level trigger (HLT). While the HLT jet resolution is very similar to offline, at L1, the momentum resolution for jets is much worse than offline due to the coarser detector granularity and reduced information available for the reconstruction algorithms. The event rate will have a significant contribution from events with low transverse momenta that fluctuate high, since the $p_{T}$ spectrum is steeply falling. In order to model the L1 jet resolution, a normal random number is added to each jet energy with a mean of zero and a standard deviation of 13 GeV. This additional resolution is estimated from the trigger turn-on curves in Ref. Aaboud:2016leb as follows. Consider a jet trigger that requires a L1 $p_{T}^{\text{L1}}>X$ GeV. The distribution of L1 jet $p_{T}$ given the offline jet $p_{T}$ should be approximately Gaussian (ignoring effects from the prior) with a mean $\mu$ and standard deviation $\sigma$. Suppose that $\Pr(p_{T}^{\text{L1}}>X|p_{T}^{\text{offline}}=Y)=50\%$. Since the mean and median of a Gaussian are the same, it must be that for $p_{T}^{\text{offline}}=Y$, $\mu=X$. From Fig. 31a in Ref. Aaboud:2016leb , this procedure gives the relationship $p_{T}^{\text{offline}}\sim 2.5\times\mu$ that is nearly independent of $p_{T}$. Now, suppose that the same L1 trigger $p_{T}^{\text{L1}}>X$ GeV is $99\%$ efficient at $p_{T}^{\text{offline}}=Y$ GeV. This means that the $3\sigma$ tail of the Gaussian with $\mu\sim Y/2.5$ is at $X$. Therefore, $\sigma\sim(Y/2.5-X)/3$. Once again using Fig. 31a in Ref. Aaboud:2016leb , this procedure gives $\sigma\sim 5$ GeV, approximately independent of $p_{T}$. Translating this 5 GeV back to an offline-scale results in $5\times 2.5\sim 13$ GeV. Some degradation in this resolution will occur between the LHC and the HL-LHC, but a significant amount of the loss from pile-up will be compensated by gains in performance due to detector upgrades.

In addition to degrading the resolution of reconstructed jets, pile-up is also a source of jets from additional hard multijet events and random combinations of radiation from multiple soft collisions. Offline, the most effective method for tagging these pile-up jets is to identify the hard-scatter collision vertex and then record the contribution of momentum from tracks originating from other vertices. Full-scan tracking and vertexing is not currently available at L1, but both ATLAS and CMS will implement some form of tracking for the HL-LHC Collaboration:2285584 ; Collaboration:2272264 ; Collaboration:2283193 ; Collaboration:2296612 ; Collaboration:2290829 ; Collaboration:2257755 ; Collaboration:2285585 . Using Ref. Collaboration:2272264 as an example, we assume a L1 tracking system that has nearly 100% efficiency for central charged-particle tracks with $p_{T}>3$ GeV and a $z_{0}$ resolution of 0.2 cm. We further assume that some timing information will be available at L1 so that no pile-up tracks with $p_{T}>3$ GeV enter the analysis. All of these conditions are optimistic, but are useful when setting a bound on what is achievable with the HL-LHC dataset. Tracks that can be identified as originating from pile-up are removed before jet clustering so that in a particle-flow-like Sirunyan:2017ulk ; Aaboud:2017aca jet reconstruction algorithm, pile-up jets will be reconstructed with less energy than their true energy. To further suppress pile-up jets, a transverse momentum fraction of tracks within a jet is constructed per jet:

[TABLE]

where $p^{\rm track}_{T}$ is the transverse momenta of L1 reconstructable tracks and $p^{\rm jet}_{T}$ is the transverse momenta of the corresponding jet. Large values of $r_{c}$ correspond to more hard-scatter-like jets while low values of $r_{c}$ are indicative of pile-up jets. Since the sophisticated pile-up mitigation techniques mentioned earlier can be employed with nearly offline-level performance at the HLT and the pile-up challenge is most severe at L1, the impact of pile-up at the HLT and offline is ignored for the results presented in later sections.

Displaced vertex reconstruction at L1 is likely not possible with high efficiency and so we assume that no explicit $c$-tagging will be possible at L1. At the HLT, we assume offline-like $c$-tagging. Flavor tagging does degrade with pile-up, but detector upgrades are expected to compensate for pile-up (Fig. 6 in Ref. ATL-PHYS-PUB-2016-026 and Fig. 19a in Ref. ATL-PHYS-PUB-2017-013 ).

The probability for jets faking photons depends on how well-isolated photon candidates are required to be. Very stringent isolation requirements result in a purer sample of prompt photons at a cost of signal efficiency while loose requirements result in many fragmentation photons originating from jets. In our study, we follow the performance evaluation by ATLAS ATL-PHYS-PUB-2016-026 , and assume that the fake photon rate would be

[TABLE]

for a hard-scatter (pile-up) jet.333In our simulation, we define hard-scatter jets as jets close to a truth level jet with $\Delta R<0.3$. This false positive rate corresponds to an isolation criterion that requires the sum of the transverse energy from the calorimeter within a cone of size $R_{c}=0.2$ centered around the photon candidate $E^{R<R_{c}}_{T}$ to be

[TABLE]

We further assume the misidentified photons carries 75% of the jet transverse momenta.

2.3 Trigger Design

Currently, the L1 trigger has a maximum rate of 100 kHz, while HLT has a maximum rate of 1 kHz. After the HL-LHC upgrades Butler:2055167 ; CERN-LHCC-2015-020 , the trigger rates at L1 and HLT are expected to be about 1 MHz and 10 kHz, respectively. Therefore, it is vital to make sure the event rates of the processes are within the capacities of both the L1 trigger and the HLT.

For the L1 trigger, we required the two jets and a photon with transverse momenta

[TABLE]

and well-separated in the central region

[TABLE]

Pile-up jets are rejected by requiring

[TABLE]

To suppress the QCD background and put the L1 trigger rate under control, we make use of the fact that the three final state objects come from the Higgs resonance decay. Therefore, we also require the invariant mass of the three trigger objects at L1 to be

[TABLE]

As the two jets come from the Higgs decay and do not tend to have rather high transverse momenta, they are often not the two leading jets at L1. Therefore, we require the two candidate jets must be among the 5 hardest jets in each event.

The the corresponding trigger rate is listed in the first row of Table 2. The trigger rate is calculated using the instantaneous luminosity

[TABLE]

at the HL-LHC Apollinari:2017cqg . We note that the most dominant contribution at L1 comes from the QCD multi-light-jet production with a jet-faked photon. As shown in Table 2, the trigger proposed above would occupy less than 1% of the total bandwidth, and thus is plausible to implement as part of the HL-LHC trigger menus of ATLAS and CMS.

3 Analyses

3.1 Cut-based Analysis

To gain physical intuition, we start with a simple analysis that uses only thresholds on various kinematic quantities (“cut-based”). In addition to the trigger requirements as before, we select the signal events with a basic threshold on the leading jet

[TABLE]

Figure 1(a) shows the normalized distribution of the smaller value of the separations between photon and jets. As the photon in the signal process comes from final-state radiation, it tends to be close in angle to one of the jets.

Therefore, to optimize the signal significance, we further require the smaller one of the separations between the candidate jets and photon to be

[TABLE]

We quantify the sensitivity using a profile likelihood fit to the three-body invariant mass in the range

[TABLE]

as shown in Fig. 1(b), with bin widths of 5 GeV, in two event categories. The two categories are defined as having either 1 or 2 of the Higgs candidate jets $c$-tagged.

The expected 95% ${\rm CL_{s}}$ Read:2002hq upper limit (approximately at a $2\sigma$-level) on the signal strength in the absence of systematic uncertainties is found to be444In principle, one-loop electroweak processes also contribute to $h\rightarrow c\bar{c}\gamma$, as discussed in Han:2017yhy . However, it can be safely neglected given the hypothetically large Yukawa coupling $y_{c}$ accessible here and the absence of interference between the QED radiation and EW contributions.

[TABLE]

for operating points I, II, III with a luminosity of $3~{}{\rm ab^{-1}}$. If the BSM physics significantly modifies the charm-Yukawa coupling, which can be parametrized using the $\kappa$-scheme,

[TABLE]

then the number of signal events would approximately scale as

[TABLE]

Then the above upper limit can be translated into

[TABLE]

The expected numbers of events and event rates, in the range of $100<M_{jj\gamma}<140~{}{\rm GeV}$, are summarized in Table 2, for different event categories and $c$-tag working points described in Table 1. The third column shows the numbers of events for $h\rightarrow c\bar{c}\gamma$ through QED radiation. The signal-to-background ratio $S/B$ is between $10^{-5}$ to $10^{-6}$. As the background is dominated by QCD multi-jet processes, it is likely that the background would be estimated using data-driven techniques. The resulting systematic uncertainties may not be small, but would likely be comparable to or smaller than the large relative statistical uncertainty on the signal. We also note that, although we aimed to optimize the light-jet rejection, the yields of the background process $h\rightarrow b\bar{b}\gamma$ due to mis-tagging is about $1.5-3$ times larger than those of $h\rightarrow c\bar{c}\gamma$ for different $c$-tagging working points, comparable to the previous studies.555For reference, the background rates for $h\rightarrow b\bar{b}$ in the $Vh(\to c\bar{c})$ searches presented in Ref. Aaboud:2018fhh and Ref. ATL-PHYS-PUB-2018-016 are $5-10$ and $1-5$ times higher than the signal $h\rightarrow c\bar{c}$, respectively, where different $c$-tagging working points are used.

3.2 Machine Learning Analysis

In order to study the benefit from a more complex analysis approach, a boosted decision tree (BDT) is trained to distinguish the Higgs signal from the multi-jet background. The BDT is trained using XGBoost Chen_2016 with 5-fold cross-validation. The following 13 input features are used for training:

[TABLE]

Even though $M_{jj\gamma}$ is the most important feature, it is not explicitly provided to the BDT in order to minimize the bias to the distribution used for the profile likelihood fit in the range of Eq. (13) for extracting the expected upper limit.666There are many methods for performing this decorrelation using more explicit and even automated methods Louppe:2016ylz ; Shimmin:2017mfk ; Aguilar-Saavedra:2017rzt ; Stevens:2013dya ; Dolen:2016kst ; Moult:2017okx ; ATL-PHYS-PUB-2018-014 . The distribution of the BDT output on signal and background along with a receiver operator characteristic (ROC) curve are shown in Fig. 2. The two most important features used by the BDT are $p_{Tj}^{\rm max}$ and $\Delta R_{j\gamma}^{\rm min}$, which are also the features used to form the simple event selection in the previous section.

Using a selection based on the BDT, the expected 95% ${\rm CL_{s}}$ upper limit on the signal strength in the absence of systematic uncertainties is found to be

[TABLE]

for operating points I, II, III with a luminosity of $3~{}{\rm ab^{-1}}$. This is a modest improvement over the cut-based result by about 10%. Further gains using multivariate approaches may be possible, but will likely require advances in photon, pile-up, and $c$-tagging using low-level information. The distribution of $M_{jj\gamma}$ already captures most of the information available for separating signal and background given that the correct objects are identified.

4 HE-LHC Projection

Given the recent proposal of an energy upgrade (HE-LHC) operating at $\sqrt{s}=27$ TeV 1742-6596-1067-2-022009 after the high-luminosity phase (HL-LHC), it would be informative to estimate the potential reach for the radiative decay $h\to c\bar{c}\gamma$. However, it would be a non-trivial job to do so without knowing the high pile-up and the detector performance under the new conditions. As such, for the purpose of illustration, we can only give a crude projection by assuming a similar environment as in the above studies for HL-LHC. We consider the option with luminosity $\mathcal{L}=3~{}{\rm ab}^{-1}$ and the same pile-up $\mu=200$. We also assume the same L1 trigger rate.

To compensate the larger and harder background at 27 TeV, we raise the trigger threshold to

[TABLE]

in order to maintain the same L1 event rate. As future experiments would come with significant improvements, we relax the isolation cut in Eq. (5) and conservatively assume that the same fake photon rate can be achieved while the photon isolation efficiency remains unchanged for photon with $p_{T}>20$ GeV.

The expected 95% ${\rm CL_{s}}$ upper limit on the signal strength via cut-based analysis is found to be

[TABLE]

for operating points I, II, III with a luminosity of $3~{}{\rm ab^{-1}}$, in comparison with the expected 95% ${\rm CL_{s}}$ upper limit on the signal strength via BDT-based analysis to be

[TABLE]

We thus do not find significant improvement for probing the charm-quark Yukawa coupling at the high energy upgrade of the LHC, since the sensitivity is mostly limited by the L1 rate which in this work is assumed to stay the same at the HE-LHC. We would like to reiterate that the estimated projection here should be considered in the context of our assumptions since the results sensitively depend on the unknown pile-up and the detector performance. Given our assumptions, there is room for potential improvements should the HE-LHC experiments be constructed.

5 Conclusion

While it is of fundamental importance to probe the charm-quark Yukawa coupling, it is extremely challenging at hadron colliders primarily due to the SM background and the lack of an effective trigger for the signal $h\to c\bar{c}$. We pointed out that the branching fraction for the Higgs radiative decay $h\rightarrow c\bar{c}\gamma$ is about $4\times 10^{-4}$ and thus would yield a large number of events at the HL-LHC. The existence of an additional photon in the final state may help for the signal identification and background suppression. For instance, the electromagnetic coupling would disfavor the down-type quarks, especially the flavor-tagged $b\bar{b}\gamma$ mode. We thus proposed to take advantage of the radiative decay and examine the feasibility of probing the charm-quark Yukawa coupling. We proposed a refined triggering strategy that also included many event features combined with a boosted decision tree. Our results can be summarized as follows.

• •

A traditional cut-based analysis for identifying the signal $h\to c\bar{c}\gamma$ yields the sensitivity for a coupling of about 9 times of the SM value at $2\sigma$ level at the HL-LHC.

• •

A boosted decision tree improves the sensitivity by about 10%, reaching a coupling limit of about 8 times the SM value at $2\sigma$.

• •

As a crude estimate for the sensitivity reach at the HE-LHC, assuming the same pile-up and L1 trigger rate, we found no significant improvement over the results of HL-LHC. There is room for improvement given the assumptions about the HE-LHC experiments and running conditions.

Our results with semi-realistic simulations are comparable to the other related studies Brivio:2015fxa ; Perez:2015aoa ; Carpenter:2016mwd ; Soreq:2016rae ; Yu:2016rvv ; Bishara:2016jga ; Cohen:2017rsk and better than the $h\to J/\psi+\gamma$ channel ATL-PHYS-PUB-2015-043 in constraining the charm-Yukawa coupling. Although slightly weaker than the sensitivity from the ATLAS direct search of about 3 times of the SM value ATL-PHYS-PUB-2018-016 , there are uncertainties in both analyses due to missing effects in one or the other and so more detailed experimental studies would be required to know which method will achieve the best precision. Multiple complementary approaches are needed to improve the sensitivity to test the SM prediction.

We close by making a few remarks on the possible future improvement. Since one of the limiting factors is the huge L1 event rate from QCD multi-jets background, a better photon identification would significantly improve the results. Furthermore, improved $c$-tagging would also enhance the sensitivity and the machine learning techniques would be more beneficial there. Finally, extending the analysis to other Higgs production modes and different kinematic regimes may help with the trigger challenge.

Acknowledgments

TH and XW were supported in part by the U.S. Department of Energy under contract DE-FG02-95ER40896 and in part by the PITT PACC. BN was supported by the U.S. Department of Energy under contract DE-AC02-05CH11231. XW was also supported by an Andrew Mellon Fellowship from the Dietrich School of Arts and Sciences, the University of Pittsburgh. TH also would like to acknowledge the hospitality for the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.