1.5 PANORAMA DEL SECTOR “INDUSTRIAS MANUFACTURERAS”
2.2.3 INDICADORES DE GESTIÓN EN EL SECTOR “D”, “INDUSTRIAS
Following the proposal of string theories as potentialUV-completions of theSM, there has been in- terest in exploring the region of high-scale parameter space which may lead to low-energy conditions consistent with the observed particles and gauge groups. Many such varieties of string phenomenol- ogy have been considered, in attempts to map the UV theory involving many extra space-time dimensions and large gauge groups to theMSSM at low energy. TheB−L MSSMis such a low- energy model arising from a compactification ofE8×E8heterotic M-theory [55–57]. This consists of the MSSMaugmented with chiral multiplets corresponding to right-handed neutrinos, with the
B−L symmetry gauged so that another vector multiplet is also produced. TheB−L symmetry is assumed to be broken at some intermediate scale when a right-handed sneutrino develops a non- zeroVEV; this leads to a mass for theB−Lgauge boson. After electroweak symmetry breaking is invoked this also leads toVEVs for the left-handed sneutrinos. This directly leads toRPV terms, specifically those that violate lepton number conservation.
The consequences of this model forLHC-accessible physics have been investigated in a series of results. Scans of model space have been conducted where the parameters of the theory are randomly scattered around an assumed SUSY breaking scale in the range of a few TeV, and RG evolution equations used to predict the resulting physical mass spectrum. Points in model-space that lead to the correct Higgs mass, achieve electroweak symmetry breaking, and satisfy all lower bounds
3. Supersymmetry 26
LSPs is specified in Table2. For example, out of the 67,576 valid black points, there are 4,858 that have a ˜±WWino chargino as their LSP. Similarly, out of all the valid black point initial conditions, 4,869 have a ˜0
W Wino neutralino as their LSP. And so on. Notice that the cases in which the chargino LSP is dominantly a charged Higgsino– that is, ˜±H –are rare. In fact, in Figure3there is precisely one such black point. As discussed above and shown in Section5, the lighter chargino state is dominantly Wino if|M2|<|µ|, and dominantly Higgsino if|µ|<|M2|. The little hierarchy
problem tells us thatµ is generally large, of the order of a few TeV. However, theM2 parameter
generally takes smaller values in our simulation. For this reason, the instances in which|µ|<|M2|–
required for the Higgsino chargino to be the LSP –are scarce.
˜0 B W˜0 ⌫˜0 c 3 ˜0 H W˜± H˜± ˜g adt˜ t˜c ˜uc b˜ b˜c d˜c 1,˜⌫ 2 ˜⌫ 3 1,˜⌫c 2 ˜⌧ ˜ec , ˜ µ c ˜⌧ c LSP 100 101 102 103 104 105 106 n um b er of valid p oin ts 0.01% 0.1% 1.0% 10.0% 100.0% p ercen t of valid p oin ts
Figure 3: A histogram of the LSPs associated with a random scan of 100 million initial data points, showing the percentage of valid black points with a given LSP. Sparticles which did not appear as LSPs are omitted. The y-axis has a log scale. The notation and discussion of the sparticle symbols on the x-axis is presented in Table 2.
For any given choice of LSP, we can plot the number of such points as a function of their masses in GeV. As an example, Figures 4 (a) and (b) present such a mass distribution for Wino chargino and Wino neutralino LSPs respectively. We obtain viable supersymmetric spectra with Wino chargino and Wino neutralino LSP masses ranging from about 200 GeV to 1700 GeV. A striking feature of the Wino chargino and Wino neutralino LSP mass distributions in Figure4is the peak towards the low mass values. Higher LSP masses are exponentially less probable. The reason is that we sample all soft mass terms log-uniformly in the interval[200GeV,10TeV]. This includes theM2gaugino mass term, which gives the dominant contribution for both the Wino chargino and
Wino neutralino masses, see (5.6) and (5.47) respectively. If we would plot all the Wino chargino or Wino neutralino masses for all the viable points in our simulation, we would obtain an almost uniform mass distribution. However, for the Wino charginos or Wino neutralinos to be the LSPs, their masses must be lower than all the other random soft masses in our simulation. Conversely, it demands that all the other random soft mass terms be larger than a Wino chargino or Wino
– 19 –
Figure 3.2: A histogram of the relative frequency of different LSPsobtained after a random scan
ofB−L MSSM SUSY parameters as described in Ref. [58]. A large fraction of simulated models
result in anLSPthat is a super-partner of one of the electroweak bosons.
on sparticle and Z0 masses have been analyzed to determine the distribution of possibleLSPs. A representative histogram is reproduced from from Ref. [58] in Figure 3.2, demonstrating the wide range of candidates. As theRPVcoupling predicted in theB−LMSSMare generally small, their most significant impact is in allowing the LSPto decay to SM particles, leading to novel collider signatures.
Early searches were conducted for stopLSPsusing 8 TeV and 13 TeV data [59,60]. While not the most common LSPin random scans, the large cross section and novel decay signature to charged leptons and b quarks present an attractive experimental candidate. The likelier scenario however, according to Figure 3.2, is that the LSP is one of the neutralino or chargino states. These states may decay to electroweak bosons and leptons, leading to a variety of novel decay signatures not explicitly targeted by past SUSY searches. The phenomenology of such scenarios is presented in Refs. [61] and [11], exploring the case of a Wino-like and Bino-like LSP, respectively. The latter scenario is particularly interesting, as the Bino mass is completely unconstrained by collider searches and may be arbitrarily light. This is fundamentally different than the Wino and Higgsino cases, where limits on new charged particles below≈100 GeV have been established [62]. When the Bino mass is lighter than theW boson, each of the decays ˜B0→W±`∓, ˜B0→Z0ν, and ˜B0 →h0ν are suppressed, as the intermediate bosons are forced off-shell. While in other cases theLSP decays
proceed promptly, here the Bino can have a potentially long lifetime before its decay. This could result in a displaced vertex that may be directly reconstructed, a smoking-gun signature of new physics that is not produced by anySMprocess. AppendixA presents a more detailed analysis of the scenario with a BinoLSP. AppendixBexplores how traditional searches forSUSYwith stable
LSPsmay be recast to constrain models with R-parity violation, investigating the case of a Wino LSP in particular.
Chapter
4
Experimental Apparatus
4.1
The Large Hadron Collider
Protons which collide at the interaction point (IP) at the center of the ATLAS experiment are delivered by theLarge Hadron Collider(LHC) [63] and supporting injector complex. TheLHCwas designed with an ultimate energy of 8 TeV per colliding beam, leading to acenter-of-mass (CoM)
collision energy of√s = 14 TeV. Protons are grouped into discrete bunches in the injector path, so that ATLAS records events in which multiple proton-proton collisions take place, every 25 ns. Combined with the proton density and beam optics, this leads to a design luminosity for the machine of 1034cm−2s−1. As of 2018, collisions up to 13 TeV have been achieved and peak instantaneous luminosities greater than 2·1034cm−2s−1, corresponding to an average of 60 interactions per bunch crossing.
TheLHC injection chain makes extensive use of proton acceleration facilities designed for pre- vious, lower-energy experiments. The design is comprised of multiple sub-accelerator components each with a modest dynamic range, to achieve an ultimate acceleration of 8 TeV per beam. A hy- drogen source is first pulsed through an electric field to strip electrons from the nucleus, producing a jet of ions. TheLinear Accelerator 2 (LINAC 2)accelerates protons to 50 MeV through a series of
radio-frequency (RF)cavities over a length of 33 m. TheProton Synchrotron Booster (PSB)is the
first synchrotron in the complex, receiving injections fromLINAC 2 and accelerating protons up to 1.4 GeV. Pulsed bunches are added in the plane transverse to the beam propagation direction, so that thePSBstep limits the transverse emittance of the ultimate beam. The Proton Synchrotron has 4x the radius of thePSBat 628 m and accelerates protons to 26 GeV. A complex system ofRF
cavities allows the compression, merging, and splitting of the beam to mitigate beam-spread effects.
4. Experimental Apparatus 29
2008 JINST 3 S08001
Proton kinetic energy [GeV] 25
Number of PS batches to fill SPS 3 or 4 Limited by SPS peak intensity
PS repetition time [s] 3.6 PS 2-batch filling from PSB
Number of bunches in PS 72 h=84, 12 empty buckets for
extraction kicker
Bunch spacing [ns] 24.97
Number of protons/bunchNb- ultimate 1.70⇥1011 100% transmission assumed
- nominal 1.15⇥1011 from PS to LHC
Transverse normalised rms emittance [µm] 3.0
Bunch area (longitudinal emittance) [eVs] 0.35
Bunch length (total) [ns] 4 Limited by SPS 200 MHz
buckets
Relative momentum spreadDp/ptotal
(4s)
0.004 Limited by TT2-TT10 accep-
tance
Figure 12.2: Proton bunches in the PS, SPS and one LHC ring. Note the partial filling of the SPS
(3/11 or 4/11) and the voids due to kicker rise-time. One LHC ring is filled in⇠3 min.
fundamental limitation are:
• filling the PS with two consecutive PSB pulses, thus significantly reducing the intensity per
pulse and thusDQat 50 MeV;
• raising the PS injection energy from 1 to 1.4 GeV, thus decreasingDQin the PS by a factor
1.5 from (1/bg2) rel.
– 141 –
Figure 4.1: The standard filling scheme is shown with notes on the origin of the bunch structure from upstream injector systems. Figure is reproduced from Ref. [63].
The 6.9 km circumferenceSuper Proton Synchrotron (SPS)further accelerates protons to 450 GeV before the 26.7 kmLHCring attains the final acceleration to an ultimate energy of 13 to 14 TeV.
The structure of the proton bunches delivered to the ATLASinteraction point (IP)is determined by the parameters of the upstream injectors. The LHC was designed to carry 2800 bunches per beam over the entire length of the LHC ring. These are nominally grouped into 72-bunch units corresponding to a single Proton Synchrotron fill. As four such fills populate the SPS, the LHC
is predominantly filled with 288-bunch such batches. Proton Synchrotron and SPS batches are separated by empty bunches corresponding to the time required to regenerate the ‘kicker’ magnetic fields used to deflect and extract the beam. These effects are illustrated in Figure 4.1. More recently alternative fill schemes have been tested and utilized to push the LHC beyond its initial design luminosity. The majority of 2018 data was taken with the ‘8b4e’ bunch scheme, where eight filled bunches are followed by four empty bunches, minimizing the splitting in the PSB to lead to lower emittance and higher luminosity.
Varying machine configurations lead to a significant change in performance over the LHCdata- taking periods to date. Run 1 of theLHCran from the inception of the machine to 2012, colliding beams up to 8 TeV and collecting a data set of nearly 25fb−1. Run 2 began in 2015 with an increased energy of 6.5 TeV per beam. After the first year of running where a 3.2fb−1 dataset was collected, the bunch spacing was decreased from 50 to 25 ns and higher-luminosity data-taking commenced.
4. Experimental Apparatus 30
0 10 20 30 40 50 60 70 80
Mean Number of Interactions per Crossing 0 100 200 300 400 500 600 /0.1] -1 Recorded Luminosity [pb Online, 13 TeV ATLAS -1 Ldt=146.9 fb
∫
> = 13.4 µ 2015: < > = 25.1 µ 2016: < > = 37.8 µ 2017: < > = 36.1 µ 2018: < > = 33.7 µ Total: < 2/19 calibration Month in YearJan Apr Jul Oct
] -1 Delivered Luminosity [fb 0 10 20 30 40 50 60 70 80
ATLAS Online Luminosity
= 7 TeV s 2011 pp = 8 TeV s 2012 pp = 13 TeV s 2015 pp = 13 TeV s 2016 pp = 13 TeV s 2017 pp = 13 TeV s 2018 pp 2/19 calibration
Figure 4.2: At left, the distribution of average number of interactions per bunch crossing is shown across the Run 2 data-taking period, with separate contributions shown for each year. At right, the recorded luminosity is shown as a function of time, with each year ofLHC running separately overlaid.
In 2016 a sample of 36.1fb−1 was collected in which the peak number of interactions per bunch crossing reached 40. In the following two years, a luminosity of over 2·1034cm−2s−1 was attained and a luminosity-leveling beam-separation strategy was used to maximize the size of the collected dataset while maintaining a peak collision rate near 60 interactions per crossing. This resulted in data sets of 47 and 61fb−1 in 2017 and 2018, respectively, leading to an ultimate Run 2 data set of nearly 150fb−1 collected. The distribution of the average number of interactions per bunch crossing for each year of Run 2 is shown in Figure4.2, alongside a comparison of the integrated luminosity collected throughout each year ofLHC running.