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| CMS-PAS-HIG-22-006 | ||
| Search for Higgs boson pair production with one associated vector boson in proton-proton collisions at $ \sqrt{s}=$ 13 TeV | ||
| CMS Collaboration | ||
| 24 March 2023 | ||
| Abstract: A search is presented for Higgs boson pair production (HH) associated with a vector boson V (W or Z boson) with 138 fb$ ^{-1} $ of proton-proton (pp) collisions at a center-of-mass energy of 13 TeV with the CMS detector at the LHC at CERN. The processes in this search include $ \text{pp}\to\text{ZHH} $ and $ \text{pp}\to\text{WHH} $ production. All hadronic decays and leptonic decays of W and Z bosons involving electrons, muons, and neutrinos are utilized. The decay channel of the Higgs bosons is restricted to $ \text{b}\bar{\text{b}}\text{b}\bar{\text{b}} $. An observed (expected) upper limit at 95% confidence level (CL) is set at 294 (124) times the cross section from the standard model prediction of the $ \text{pp}\to\text{VHH} $ process. Constraints are also set on the modifier of the Higgs boson trilinear self-coupling $ \kappa_{\lambda} $, and on the coupling of two Higgs bosons with two vector bosons $ \kappa_{\text{VV}} $. The observed (expected) allowed intervals of these coupling modifiers from this search at 95 $ % \text{CL} $ are $ -$37.7 $< \kappa_{\lambda} < $ 37.2 ($ -$30.1 $< \kappa_{\lambda} < $ 28.9) and $ -$12.2 $< \kappa_{\text{VV}} < $ 13.5 ($ -$7.64 $< \kappa_{\text{VV}} < $ 8.90). In addition, a 95% CL upper limit is set at 43 (22) times the cross section of the $ \text{pp}\to\text{VHH} $ process when $ \kappa_{\lambda}= $ 5.5 and other couplings are set to standard model predictions. | ||
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Links:
CDS record (PDF) ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, Submitted to JHEP. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
The three LO quark-initiated diagrams above result in a final state with two Higgs bosons and a W or Z boson. The first diagram requires one $ \kappa_{\mathrm{V}} $-coupling vertex and one $ \kappa_{\lambda} $-coupling vertex. The second diagram requires only one $ \kappa_{\mathrm{V}\mathrm{V}} $-coupling vertex, and the final diagram requires two $ \kappa_{\mathrm{V}} $-coupling vertices. |
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Figure 1-a:
The three LO quark-initiated diagrams above result in a final state with two Higgs bosons and a W or Z boson. The first diagram requires one $ \kappa_{\mathrm{V}} $-coupling vertex and one $ \kappa_{\lambda} $-coupling vertex. The second diagram requires only one $ \kappa_{\mathrm{V}\mathrm{V}} $-coupling vertex, and the final diagram requires two $ \kappa_{\mathrm{V}} $-coupling vertices. |
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Figure 1-b:
The three LO quark-initiated diagrams above result in a final state with two Higgs bosons and a W or Z boson. The first diagram requires one $ \kappa_{\mathrm{V}} $-coupling vertex and one $ \kappa_{\lambda} $-coupling vertex. The second diagram requires only one $ \kappa_{\mathrm{V}\mathrm{V}} $-coupling vertex, and the final diagram requires two $ \kappa_{\mathrm{V}} $-coupling vertices. |
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Figure 1-c:
The three LO quark-initiated diagrams above result in a final state with two Higgs bosons and a W or Z boson. The first diagram requires one $ \kappa_{\mathrm{V}} $-coupling vertex and one $ \kappa_{\lambda} $-coupling vertex. The second diagram requires only one $ \kappa_{\mathrm{V}\mathrm{V}} $-coupling vertex, and the final diagram requires two $ \kappa_{\mathrm{V}} $-coupling vertices. |
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Figure 2:
left: representative diagram for ZHH production initiated by gluon fusion via a quark loop, which represents approximately 14% of the total cross section for this process. right: distribution of $ p_{\mathrm{T}}^{\mathrm{Z}} $ with and without the gluon-fusion process. |
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Figure 2-a:
left: representative diagram for ZHH production initiated by gluon fusion via a quark loop, which represents approximately 14% of the total cross section for this process. right: distribution of $ p_{\mathrm{T}}^{\mathrm{Z}} $ with and without the gluon-fusion process. |
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Figure 2-b:
left: representative diagram for ZHH production initiated by gluon fusion via a quark loop, which represents approximately 14% of the total cross section for this process. right: distribution of $ p_{\mathrm{T}}^{\mathrm{Z}} $ with and without the gluon-fusion process. |
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Figure 3:
Efficiencies of trigger selections (dashed lines) and full SR selections (solid lines) are shown for all four analysis channels. The selection efficiency of the $ \text{FH} $ channel is scaled up by 10 for visibility. The SR selections include trigger selections. Both sets of efficiencies are absolute efficiencies. |
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Figure 4:
The kinematic distributions and primary phase spaces shift when coupling strengths are varied. Left: azimuthal angle between the two reconstructed Higgs boson candidates, $ \Delta\phi_{\mathrm{H}\mathrm{H}} $, in the 1L SR for two different coupling models, $ \kappa_{\lambda}= $ 20 and $ \kappa_{\lambda}= $ 0. Middle: the categorization BDT output for the same two models. The dashed vertical line shows where the categorization boundary was set. Right: the same two signal models on each side of categorization. All histograms are normalized to unity to highlight qualitative features. |
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Figure 4-a:
The kinematic distributions and primary phase spaces shift when coupling strengths are varied. Left: azimuthal angle between the two reconstructed Higgs boson candidates, $ \Delta\phi_{\mathrm{H}\mathrm{H}} $, in the 1L SR for two different coupling models, $ \kappa_{\lambda}= $ 20 and $ \kappa_{\lambda}= $ 0. Middle: the categorization BDT output for the same two models. The dashed vertical line shows where the categorization boundary was set. Right: the same two signal models on each side of categorization. All histograms are normalized to unity to highlight qualitative features. |
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Figure 4-b:
The kinematic distributions and primary phase spaces shift when coupling strengths are varied. Left: azimuthal angle between the two reconstructed Higgs boson candidates, $ \Delta\phi_{\mathrm{H}\mathrm{H}} $, in the 1L SR for two different coupling models, $ \kappa_{\lambda}= $ 20 and $ \kappa_{\lambda}= $ 0. Middle: the categorization BDT output for the same two models. The dashed vertical line shows where the categorization boundary was set. Right: the same two signal models on each side of categorization. All histograms are normalized to unity to highlight qualitative features. |
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Figure 4-c:
The kinematic distributions and primary phase spaces shift when coupling strengths are varied. Left: azimuthal angle between the two reconstructed Higgs boson candidates, $ \Delta\phi_{\mathrm{H}\mathrm{H}} $, in the 1L SR for two different coupling models, $ \kappa_{\lambda}= $ 20 and $ \kappa_{\lambda}= $ 0. Middle: the categorization BDT output for the same two models. The dashed vertical line shows where the categorization boundary was set. Right: the same two signal models on each side of categorization. All histograms are normalized to unity to highlight qualitative features. |
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Figure 5:
left: a reweighting BDT in the 1L LP region for the $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ process that is transformed such that all bins have approximately the same amount of the limited precision passing $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ sample shown in red. In blue is the same process where the b tagging cuts are inverted. right: the ratio is shown of passing $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ to inverted $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ (green points) as a function of the transformed reweighting BDT. The solid line is the second-order polynomial fit of the green points, which is used for the reweighting. In dashed blue and dashed red are the associated systematic uncertainties, which are obtained from the evaluation of the fit error on the weight and from shifting the BDT bin in evaluation of the model, respectively. |
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Figure 5-a:
left: a reweighting BDT in the 1L LP region for the $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ process that is transformed such that all bins have approximately the same amount of the limited precision passing $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ sample shown in red. In blue is the same process where the b tagging cuts are inverted. right: the ratio is shown of passing $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ to inverted $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ (green points) as a function of the transformed reweighting BDT. The solid line is the second-order polynomial fit of the green points, which is used for the reweighting. In dashed blue and dashed red are the associated systematic uncertainties, which are obtained from the evaluation of the fit error on the weight and from shifting the BDT bin in evaluation of the model, respectively. |
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Figure 5-b:
left: a reweighting BDT in the 1L LP region for the $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ process that is transformed such that all bins have approximately the same amount of the limited precision passing $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ sample shown in red. In blue is the same process where the b tagging cuts are inverted. right: the ratio is shown of passing $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ to inverted $ {\mathrm{t}\bar{\mathrm{t}}} \mathrm{b}\bar{\mathrm{b}} $ (green points) as a function of the transformed reweighting BDT. The solid line is the second-order polynomial fit of the green points, which is used for the reweighting. In dashed blue and dashed red are the associated systematic uncertainties, which are obtained from the evaluation of the fit error on the weight and from shifting the BDT bin in evaluation of the model, respectively. |
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Figure 6:
Machine learning distributions are transformed to $ \log_{10}\big( $ 100 (S}_\textSM/\text{B) $ \big) $ and summed for $ \kappa_{\lambda} $-enriched and $ \kappa_{\mathrm{V}\mathrm{V}} $-enriched SR samples separately. For the two enriched regions, data, simulated background, and three sensitive signal models are plotted. We observe that signal models with enhancement in a particular coupling appear enhanced also in the corresponding SR. |
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Figure 7:
The results of two maximum likelihood fits are summarized above. The top entry, labeled ``Inclusive'', is the result of a single signal strength fit of all channels. The other four entries are from a fit of the same regions but with independent signal strengths in each channel. The thinner, blue bands are one standard deviation from the full likelihood scan in that parameter, while the thicker, red bands are one standard deviation bands of the systematic uncertainties only. |
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Figure 8:
Upper 95% CL limits on signal cross section scanned over the $ \kappa $ parameter of interest while fixing the other two to their SM-predicted couplings. The independent axis is the scanned $ \kappa $ parameter, and the dependent axis is the 95% CL upper limit on signal cross section. The scans over $ \kappa_{\lambda} $, $ \kappa_{\mathrm{V}\mathrm{V}} $, and $ \kappa_{\mathrm{V}} $ are shown left, center, and right, respectively. |
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Figure 8-a:
Upper 95% CL limits on signal cross section scanned over the $ \kappa $ parameter of interest while fixing the other two to their SM-predicted couplings. The independent axis is the scanned $ \kappa $ parameter, and the dependent axis is the 95% CL upper limit on signal cross section. The scans over $ \kappa_{\lambda} $, $ \kappa_{\mathrm{V}\mathrm{V}} $, and $ \kappa_{\mathrm{V}} $ are shown left, center, and right, respectively. |
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Figure 8-b:
Upper 95% CL limits on signal cross section scanned over the $ \kappa $ parameter of interest while fixing the other two to their SM-predicted couplings. The independent axis is the scanned $ \kappa $ parameter, and the dependent axis is the 95% CL upper limit on signal cross section. The scans over $ \kappa_{\lambda} $, $ \kappa_{\mathrm{V}\mathrm{V}} $, and $ \kappa_{\mathrm{V}} $ are shown left, center, and right, respectively. |
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Figure 8-c:
Upper 95% CL limits on signal cross section scanned over the $ \kappa $ parameter of interest while fixing the other two to their SM-predicted couplings. The independent axis is the scanned $ \kappa $ parameter, and the dependent axis is the 95% CL upper limit on signal cross section. The scans over $ \kappa_{\lambda} $, $ \kappa_{\mathrm{V}\mathrm{V}} $, and $ \kappa_{\mathrm{V}} $ are shown left, center, and right, respectively. |
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Figure 9:
Expected (left) and observed (right) likelihood scans in $ \kappa_{\lambda} $ versus $ \kappa_{\mathrm{V}\mathrm{V}} $ are shown, with other SM couplings fixed to the SM predicted strength. The excess is most prominent in the $ \kappa_{\mathrm{V}\mathrm{V}} $-enriched region, and so the most likely point of the scan at $ \kappa_{\mathrm{V}\mathrm{V}}= $ 10.1 and $ \kappa_{\lambda}=- $ 2.6 is pulled than two standard deviations from the SM mostly in the $ \kappa_{\mathrm{V}\mathrm{V}} $ dimension. |
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Figure 9-a:
Expected (left) and observed (right) likelihood scans in $ \kappa_{\lambda} $ versus $ \kappa_{\mathrm{V}\mathrm{V}} $ are shown, with other SM couplings fixed to the SM predicted strength. The excess is most prominent in the $ \kappa_{\mathrm{V}\mathrm{V}} $-enriched region, and so the most likely point of the scan at $ \kappa_{\mathrm{V}\mathrm{V}}= $ 10.1 and $ \kappa_{\lambda}=- $ 2.6 is pulled than two standard deviations from the SM mostly in the $ \kappa_{\mathrm{V}\mathrm{V}} $ dimension. |
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Figure 9-b:
Expected (left) and observed (right) likelihood scans in $ \kappa_{\lambda} $ versus $ \kappa_{\mathrm{V}\mathrm{V}} $ are shown, with other SM couplings fixed to the SM predicted strength. The excess is most prominent in the $ \kappa_{\mathrm{V}\mathrm{V}} $-enriched region, and so the most likely point of the scan at $ \kappa_{\mathrm{V}\mathrm{V}}= $ 10.1 and $ \kappa_{\lambda}=- $ 2.6 is pulled than two standard deviations from the SM mostly in the $ \kappa_{\mathrm{V}\mathrm{V}} $ dimension. |
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Figure 10:
Expected (left) and observed (right) likelihood scans of $ \kappa_{\mathrm{W}\mathrm{W}} $ versus $ \kappa_{\mathrm{Z}\mathrm{Z}} $ are shown, with other SM couplings fixed to the SM predicted strength. The excess is most prominent in the $ \text{MET} $ channel, and so the most likely point of the scan at $ \kappa_{\mathrm{W}\mathrm{W}}= $ 7.1 and $ \kappa_{\mathrm{Z}\mathrm{Z}}= $ 12.3 is pulled than two standard deviations from the SM mostly in the $ \kappa_{\mathrm{Z}\mathrm{Z}} $ dimension, to which the signal in the $ \text{MET} $ channel is solely sensitive. |
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Figure 10-a:
Expected (left) and observed (right) likelihood scans of $ \kappa_{\mathrm{W}\mathrm{W}} $ versus $ \kappa_{\mathrm{Z}\mathrm{Z}} $ are shown, with other SM couplings fixed to the SM predicted strength. The excess is most prominent in the $ \text{MET} $ channel, and so the most likely point of the scan at $ \kappa_{\mathrm{W}\mathrm{W}}= $ 7.1 and $ \kappa_{\mathrm{Z}\mathrm{Z}}= $ 12.3 is pulled than two standard deviations from the SM mostly in the $ \kappa_{\mathrm{Z}\mathrm{Z}} $ dimension, to which the signal in the $ \text{MET} $ channel is solely sensitive. |
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Figure 10-b:
Expected (left) and observed (right) likelihood scans of $ \kappa_{\mathrm{W}\mathrm{W}} $ versus $ \kappa_{\mathrm{Z}\mathrm{Z}} $ are shown, with other SM couplings fixed to the SM predicted strength. The excess is most prominent in the $ \text{MET} $ channel, and so the most likely point of the scan at $ \kappa_{\mathrm{W}\mathrm{W}}= $ 7.1 and $ \kappa_{\mathrm{Z}\mathrm{Z}}= $ 12.3 is pulled than two standard deviations from the SM mostly in the $ \kappa_{\mathrm{Z}\mathrm{Z}} $ dimension, to which the signal in the $ \text{MET} $ channel is solely sensitive. |
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Figure 11:
The left plot shows the VHH cross section limits per channel and combined for SM-sized couplings, while results with $ \kappa_{\lambda}= $ 5.5 and $ \kappa_{\mathrm{V}\mathrm{V}}=\kappa_{\mathrm{V}}= $ 1.0 are shown on the right. The latter is a relatively sensitive region for VHH, where the primary HH production cross sections are near minimal because of destructive interference. |
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Figure 11-a:
The left plot shows the VHH cross section limits per channel and combined for SM-sized couplings, while results with $ \kappa_{\lambda}= $ 5.5 and $ \kappa_{\mathrm{V}\mathrm{V}}=\kappa_{\mathrm{V}}= $ 1.0 are shown on the right. The latter is a relatively sensitive region for VHH, where the primary HH production cross sections are near minimal because of destructive interference. |
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Figure 11-b:
The left plot shows the VHH cross section limits per channel and combined for SM-sized couplings, while results with $ \kappa_{\lambda}= $ 5.5 and $ \kappa_{\mathrm{V}\mathrm{V}}=\kappa_{\mathrm{V}}= $ 1.0 are shown on the right. The latter is a relatively sensitive region for VHH, where the primary HH production cross sections are near minimal because of destructive interference. |
| Tables | |
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Table 1:
Kinematic thresholds for L1 and HLT triggers are listed below for each analysis channel with variations per year as needed. HLT reconstruction is very similiar to offline reconstruction. L1 reconstruction does not include any information from tracking. Transverse energy from ECAL plus HCAL systems is referred to as $ E_{\mathrm{T}}_{,\text{L1}} $. The scalar sum of $ E_{\mathrm{T}}_{,\text{L1}} $ from all energy deposits over a threshold of 30 GeV is $ H_{\text{T}} $. |
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Table 2:
Thresholds on kinematic variables for all selected objects are listed for each channel. Objects are always required to be within the acceptance of the CMS subdetectors, which is $ |\eta| < $ 2.4 or 2.5 depending on the object and channel, as well as outside of barrel-endcap transition regions near $ |\eta|\sim $ 1.5. |
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Table 3:
Kinematic variables used in the categorization BDTs for separation of the $ \kappa_{\lambda} $-enriched and $ \kappa_{\mathrm{V}\mathrm{V}} $-enriched regions. While there are some minor difference in importance of each variable per channel, the table is constructed such that variables at the top tend to be the most important, which is universally true for $ m_{\mathrm{H}\mathrm{H}} $, and the least important are at the bottom. |
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Table 4:
A summary of categorization in all channels. |
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Table 5:
The contribution of each group of uncertainties is quantified relative to the total absolute uncertainty in signal strength, which is listed in the final line. To compute these relative contributes, the group of nuisance parameters are fixed to the best fit value while the likelihood is scanned again profiling all other nuisance parameters. The reduction in the up and down bands are shown in each line. The likelihood shape is asymmetric, and so up and down are quantified separately. |
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Table 6:
Observed and expected 95% CL upper limits on the coupling modifiers. |
| Summary |
| A search for Higgs boson pair production in association with a vector boson (VHH) using a data set comprising 138 fb$^{-1}$ of proton-proton collisions at $ \sqrt{s}= $ 13 TeV is presented. Final states including Higgs boson decay to bottom quarks are analyzed in events where the W or Z boson decay to electrons, muons, or hadrons. Coupling modifiers, defined relative to the SM coupling strength, are scanned and constrained for Higgs boson trilinear self-interaction coupling, $ \kappa_{\lambda} $, and two W or two Z with two Higgs bosons, $ \kappa_{\mathrm{V}\mathrm{V}} $. The observed (expected) 95% CL limits constrain $ \kappa_{\lambda} $ and $ \kappa_{\mathrm{V}\mathrm{V}} $ to be $ -$37.7 $< \kappa_{\lambda} < $ 37.2 ($ -$30.1 $< \kappa_{\lambda} < $ 28.9) and $ -$12.2 $< \kappa_{\lambda} < $ 13.5 ($ -$7.2 $< \kappa_{\lambda} < $ 8.9). In the range of 4 $ < \kappa_{\lambda} < $ 7 where matrix-element level interference is destructive for leading production mechanisms, VHH has constructive interference and the sensitivity of the VHH search is similar to $ \mathrm{b}\bar{\mathrm{b}}\tau\tau $ search on the equivalent data set. |
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