In an experiment like CMS, it is important to know where all the detector material is. For example, in order to properly simulate the detector response, you need to know not only where the sensors are, but also the locations of the inactive material. Suppose you are searching for a long-lived particle that decays inside your detector. A significant background to your search would come from particles interacting with the material that they pass through, resulting in electron bremsstrahlung, photon conversions, or nuclear interactions (NIs) that could create a pattern of tracks that resembles your particle’s decay signature. Material also affects your ability to precisely reconstruct particle trajectories because of multiple scattering and energy loss and it is important to model this properly.

Precise survey measurements are made of the positions of detector components at the time of installation, but these positions might change with time. Gravity can cause structures to sag. Variations in temperature, air pressure, and the magnetic field can cause components to move. So it is important to re-measure the positions of detector components during operation. Sensor positions can be determined using various alignment procedures, but these procedures don’t work for inactive elements such as the beam pipe or support structures. 

The CMS Collaboration’s 800th paper describes a technique for measuring the positions of inactive elements using NIs (“Measurement of the structure of the inner tracking detector of the CMS experiment using nuclear interactions,” arXiv:1807.03289 [physics.ins-det]). Photon conversions can also be used to track the positions of inactive material, but because the opening angle between the electron and positron produced in the conversion is so narrow, the location of the point where the conversion occurred cannot be precisely determined along the direction of the original photon. (It is well determined perpendicular to the photon direction.) When a hadron undergoes a nuclear interaction with material in the detector several particles can emerge with larger scattering angles. The location where the interaction occurred is referred to as the NI vertex. The position resolution for reconstructed NI vertices is typically less than a millimeter. By reconstructing a large number of NI vertices in a detector element, the element’s position can be determined with a precision on the order of 100 microns. This equals or exceeds the precision of the original survey measurements. 

The measurements described in the paper focused on the inner detector where the density of reconstructed NI vertices is the highest. The innermost of the CMS subdetectors is the pixel tracker. The barrel portion of the pixel detector (BPIX) and its inner shield are composed of two semi-circular halves. Figure 1 shows a photograph of one of the halves of the BPIX detector prior to installation. The BPIX detector support rails are located on the outer edge of the BPIX detector, and hold its layers in place. The pixel detector support tube encloses the BPIX detector and the support rails. The pixel detectors are installed around the beam pipe, and an accurate measurement of the beam pipe position is also important. 

Figure 1: (left) Photograph of one half of the BPIX detector showing longitudinal support, three layers, and inner shield. (right) Photograph showing an end of the BPIX detector while standing on the installation cassette. Optical targets, indicated by the numbers 2001, 2002, and 2003, are used to locate the BPIX detector within the CMS cavern. Photographs by Antje Behrens, CERN.

The data reported in the paper were recorded from proton-proton collisions at a center-of-mass energy of 13 TeV in 2015. The data set used in this analysis yielded 5.40 million events with at least one NI vertex. These NI’s produced an image of the inner CMS detector that is shown in Fig. 2. If a “photograph” is an image made from photons, then we can call our image made from hadrons a “hadrograph.” The ``hadrograph" shows the density of NI vertices projected onto the x-y plane (the plane perpendicular to the proton beam direction) in the barrel region (|z| < 25 cm). The beam pipe, the BPIX detector with its support, and the first layer of the barrel strip tracking detector can be seen in the image.

Figure 2: Hadrography of the tracker detector in the x-y plane in the barrel region (|z| < 25 cm). The density of NI vertices is indicated by the color scale. The signatures of the beam pipe, the BPIX detector with its support, and the first layer of the TIB detector can be observed above the background of misreconstructed NIs.

To determine the positions of the inactive detector elements, we modeled the elements using geometrical shapes, and fit those shapes to a background-subtracted NI vertex position distribution. All the inactive elements we considered, except for the support rails, have a cylindrical geometry with their axes being collinear to the beam axis. We could thus perform our position fits in the x-y plane using shapes such as a circle (for the beam pipe), a half-circle (for the BPIX detector inner shield), or an ellipse (for the pixel detector support tube). Background came from tracks forming fake vertices due to randomly occurring spatial overlaps. 

Figure 3: The beam pipe region at the barrel part (|z| < 25 cm) for the x-y plane (left) and the r-φ coordinates (right) are shown. The density of NI vertices is indicated by the color scale. The red line shows the fitted circle in the r-φ coordinates. The blue point in the center of the r-φ plane corresponds to the average beam spot position of xbs = 0.8 mm and ybs = 0.9 mm in 2015.

In Fig. 3, we show the data used to measure the position of the beam pipe along with the fit (red curve). In Fig. 4, we show the data and fit for the BPIX inner shield. These figures show the density of NI vertices in the relevant regions. In the left plot the data are projected onto the x-y plane, while the right plot shows the r-φ coordinates with the fit. If the beam pipe or BPIX inner shield were centered at (0, 0) in the CMS coordinate system, the fit in the r-φ plane would look like a simple horizontal line. The sinusoidal distributions in the right-hand plots indicate that the centers are shifted away from the origin by about a millimeter.

Figure 4: The BPIX detector inner shield at the barrel part (|z| < 25 cm) for the x-y plane (left) and the r-φ coordinates (right) are shown. The density of NI vertices is indicated by the color scale. The red and black lines at around r = 3.8 cm show the fitted half-circles on the far and near sides, respectively for r-φ coordinates. Modules in the first BPIX detector layer are visible at larger radius. The small bumps that can be seen around the shield correspond to cables connected to the first BPIX detector layer.

Table 1 summarizes the results from the fits. The values of the parameters are tabulated for the fits to the beam pipe with a circle, the BPIX detector inner shield with two half-circles, and the pixel detector support tube with an ellipse.

Only systematic uncertainties are provided, since the statistical uncertainties are negligible (below 10 μm). Not listed in the table is the fit to the BPIX detector support rails, which were observed to be 3 mm below the CMS center.

CMS has been using NI hadrography for some time. It was used in 2010 to "weigh" the CMS tracker by relating the density of NI vertices to the flux of particles and the local density of the material. By comparing this density in data with the detector simulation it was shown that the tracker material was well modeled. (http://cds.cern.ch/record/1279138?ln=en). Hadrography was again used in 2011 to determine whether the magnetic field caused deformations of the beam pipe. A special run with the field set to 2 Tesla was compared with normal runs at 4 Tesla. No deformation above 300 microns was observed. 

Table 1: Results of the fit to the beam pipe with a circle, the BPIX detector inner shield with two half-circles, and the pixel detector support tube with an ellipse. Only systematic uncertainties are provided, since the statistical uncertainties are negligible.

In Spring 2017, an upgraded pixel detector was installed. Since the innermost layer of the 2017 upgraded pixel detector is closer to the beam pipe than the original detector was, we needed to have precise measurements of the mechanical clearances. To prepare for this upgrade, a special narrow section of the beam pipe was inserted in 2013-2014. The radius of this beam pipe was 2.2 cm and the position of the first layer of the pixel detector as was close as 2.6 cm. In 2015, hadrography was used to conclude that the sagging due to gravity of the beam pipe was negligible compared to the allowed clearances. 

Nuclear interactions have a bad reputation because they can degrade the quality of the reconstruction of charged and neutral hadrons. But we have seen that they can be useful too. NI vertices can be used to produce a high-precision map of the material inside the tracker. Our NI material mapping provided important information for the design of the new pixel detector’s support system and helped to establish reliable installation procedures. We were able to map structures with a precision that is better than the typical installation tolerances and compatible with previous survey measurements.