PTB: Dark Matter Colloquium

<div class="r-stack">
              <h1 class="fragment fade-out" data-fragment-index="0">Enlightening
                the search for Dark Matter
              </h1>
              <h1 class="fragment current-visible" data-fragment-index="0">En<i>light</i>ening
                the search for Dark Matter
              </h1>
            </div>
  
            <br>
            <br>
  
            ### Physikalisch-Technische Bundesanstalt (PTB) Colloquium
            #### Braunschweig, Germany
            #### 28 November 2024
  
            <div class="r-stretch"></div>
  
            ### Benjamin M. Roberts
  
            <br>
  
            School of Mathematics and Physics,
            University of Queensland, Australia
  
            <br><br>
  
            * Slides [broberts.io/talks](https://broberts.io/talks)
  
            <br>
            <br>
  
            <img src="img/uq-logo.svg" width="25%">
                            Supported by: ARC and
                           
            <img src="img/BQI.png" width="20%">
            <br><br>

# The Standard Model + General Relativity

<br>

<div style="text-align: center; float: left; width: 50%">
              <img
                src="https://upload.wikimedia.org/wikipedia/commons/2/2b/Standard_Model_of_Elementary_Particles_dark.svg"
                width="95%">
              <font size="3"> Credit: Cush [Wikimedia Commons]</font>
            </div>

<div style="text-align: left; float: right; width: 47%">
              <h2>Tested with extraordinary precision</h2>
              <br>
              <h3>   • e.g., electron magnetic moment, Higgs boson</h3>
              <h3>   • gravitational lensing, gravitational waves</h3>
              <br><br><br>
              <h2>However...</h2>
              <br><br><br>
              <div class="fragment">
                <h2>Several deep inconsistencies</h2>
                <h2>with the observed universe</h2>
              </div>
              
            </div>

# Unexplained mysteries (among others)

<br>
            <div style="text-align: center; float: left; width: 70%">
              <div class="fragment" data-fragment-index="0" style="text-align: left;" data-markdown>
  
                <h2>Matter anti-matter asymmetry</h2>
                <h3> • CP-violation in the Standard Model is too small</h3>
              </div>
  
  
              <br>
              <div class="fragment" data-fragment-index="1" style="text-align: left;" data-markdown>
  
                <h2>Nature of Dark Energy</h2>
                <h3> • Accelerated expansion of universe
                <h4>  • Cosmologists: Why is Λ so large?
                   • Particle theorists: Why is Λ so small?
                </h4>
  
              </div>
  
              <br>
              <div class="fragment" data-fragment-index="2" style="text-align: left;" data-markdown>
  
                <h2>Nature of Dark Matter</h2>
                <h3> • Missing mass from the universe
                  • Matter that interacts <em>only</em> gravitationally? </h3>
  
              </div>
  
              <br>
              <div class="fragment" data-fragment-index="3" style="text-align: left;" data-markdown>
                <h3> 95% of universe is "dark"; we can only use the 5% to learn about the rest! </h3>
              </div>
  
            </div>
  
            <div style="text-align: left; float: right; width: 25%">
              <br>
              <img class="fragment" data-fragment-index="0" src="img/antimatter.png" width="95%">
              <br><br><br><br>
              <img class="fragment" data-fragment-index="1" src="img/dm-pie.jpg" width="95%">
            </div>

# How to break physics?

## Want to find direct evidence for physics _beyond_ standard model

<div style="text-align: left; float: right; width: 45%">
            <br>
            <div class="fragment">
              <h2> Particle Accelerators</h2>
              <h3> • Directly search for new particles</h3>
              <h3> • High energy, very expensive</h3>
            </div>

<div class="fragment">
              <br>
              <h2> CERN/LHC</h2>
              <h3> • Hoped to find evidence for something beyond</h3>
              <h3> • So far, no luck!</h3>
            </div>

<div class="fragment">
              <br>
              <h2> Alternative approach</h2>
              <h3> • Low-energy, high precision</h3>
              <h3> • Look for any violations of laws of physics</h3>
            </div>

</div>

# Focus: dark matter

<br>

<div style="text-align: center; float: left; width: 35%">
              <br><br><br>
              <h3>Coma Cluster</h3>
              <br>
              <img
                src="https://upload.wikimedia.org/wikipedia/commons/7/7d/Ssc2007-10a1.jpg"
                width="95%">
              <font size="3"> Sloan Digital Sky Survey + Spitzer Space
                Telescope
                [NASA / JPL-Caltech / L. Jenkins]</font>
            </div>

<div style="text-align: left; float: right; width: 47%">
              <h2>First major hints: galaxy clusters</h2>
              <br>
              <h3>Fritz Zwicky: clusters too fast. <br>
                • Termed phrase "dark matter"</h3><br>

<br>
              <div class="fragment">
                <h3>Then: Vera Rubin, along with Kent Ford and others</h3>
                <br>
                <img src="img/vera-rubin.jpg" width="60%"><br>
                <font size="3">
                  [AIP Emilio Segrè Visual Archives, Rubin Collection]
                </font>

</div>
            </div>

# Galactic Rotation Curves

<div style="text-align: center; float: left; width: 70%">
              <br><br>
              <img
                src="https://upload.wikimedia.org/wikipedia/commons/c/cd/Rotation_curve_of_spiral_galaxy_Messier_33_%28Triangulum%29.png"
                width="95%"><br>
              <font size="3">[Mario De Leo, Wikimedia Commons]</font>
            </div>

<div style="text-align: left; float: right; width: 30%">
              <br><br>
              <h2>Missing Matter?</h2>
              <br>
              <p data-markdown>• Not a small correction</p>
              
              <p data-markdown>• 80 - 95% of gravity is "missing"</p>
              
              <br>
              <div data-markdown class="fragment fade-in">
                <p data-markdown>• Implies <font color="orange">dark matter</font></p><br>
                \[a = \frac{G \, [M(r) + {\color{orange}\delta M(r)}]}{r^2} \]
                <br>
                <p data-markdown>  • Uniformly distributed (not all at core)</p>
                <p data-markdown>   • Simulations + observations: DM "halo"</p>
              </div>
              <br>
              <p data-markdown class="fragment fade-in">• ... or <font
                  color="green">modified
                  gravity</font><br><br>
                \[a = \frac{[G + {\color{green}\delta G(M,r)}] \, M(r)}{r^2} \]
              </p>
              <br>
              <p data-markdown class="fragment fade-in">
                Since then: the evidence grown
              </p>
            </div>

# Cosmic Microwave Background: ΛCDM model
    
                <div style="text-align: center; float: left; width: 70%">
                  <img src="img/CMB-PowerSpectrum-Planck.png" width="100%"><br>
                  <font size="3">[ESA/Planck Collaboration (2013)]</font>
                </div>
    
                <div style="text-align: center; float: right; width: 30%">

<br>
                  <br>
                  
                  $$\large
                  \Omega_{baryon} = 0.0486(10)
                  $$

$$\large\Omega_{\rm dark~matter} = 0.2589(57)
                  $$

$$\large\Omega_{\rm dark~energy} = 0.6911(1)
                  $$

<h3 class="fragment">• ΛCDM model works extremely well</h3>
                  <br>
                  <br>
                  <h3 class="fragment">• (Just need to work out the Λ and CDM parts)</h3>

</div>

# Dark Matter: What we know

<br>
            <h3> There's lots of it</h3>

<h3> It gravitationally clusters in halos around galaxies</h3>
            <h4> (really, galaxies gravitationally cluster around DM)</h4>

<div style="text-align: left; float: left; width: 50%"
              class="fragment">
              <br><br>
              <h2>Very strong evidence:</h2>
              <br>
              <h3>• Rotation curves, gravitational lensing, CMB </h3>
              <br>
              <h3>• Also: large scale structure, BAO etc. </h3>
              <br>
              <h3 class="fragment">• It's not strange for particles to not interact with
                light (e.g., neutrinos)</h3>
              <br>
              <br>
              
            </div>

# Dark Matter: What we don't know

<br>
            <div class="fragment" data-fragment-index="0">
              <h2> ... everything else</h2>
            </div>

<br>

<div class="r-stack">
              <img class="fragment" data-fragment-index="1"
                src="img/DM_masses2.png" width="80%">
              <img class="fragment" data-fragment-index="3"
                src="img/DM_masses3.png" width="80%">
            </div>
            <div class="fragment" data-fragment-index="1">
              <font size="3">US "Cosmic Visions" report [arXiv:1707.04591]</font>
            </div>

<div class="fragment" data-fragment-index="1">
              <h3>• Possible mass range: 90 orders of magnitude!</h3>
            </div>
            <div class="fragment" data-fragment-index="2">
              <h3>• Fundamental particle: 50 orders (de Broglie to Planck)</h3>
            </div>

<br>

<div class="fragment">
              <h3> • Vast majority of focus on WIMPs, but field is very wide</h3>
            </div>

# WIMP miracle

<!-- <div class="r-stack">
              <img class="fragment fade-out" data-fragment-index="0"
                src="img/DM_masses2.png" width="80%">
              <img class="fragment current-visible" data-fragment-index="0"
                src="img/DM_masses3.png" width="80%">
            </div>

<div style="text-align: left; float: left; width: 30%">
              <br><br>
              <img src="img/Feynman.png" width="95%">
              <br><br>
              <h3> • Early universe: hot and dense</h3>
              <h3> DM + SM in thermal equilibrium</h3>
              <br>
              <h3 class="fragment fade-in" data-fragment-index="0">
                • Universe cools: <br>
                Boltzmann suppression
              </h3>
              <br>
              <h3 class="fragment fade-in" data-fragment-index="1">
                • Universe expands: <br>
                Shuts off annihilation
              </h3>
              
            </div>

<div style="text-align: center; float: right; width: 65%">
              <div class="r-stack">
                <img class="fragment fade-in" data-fragment-index="0"
                  src="img/YDM/Yeq.png" width="90%">
                <img class="fragment fade-in" data-fragment-index="1"
                  src="img/YDM/YDM1.png" width="90%">
                <img class="fragment fade-in" data-fragment-index="2"
                  src="img/YDM/YDM2.png" width="90%">
              </div>
              <h3 class="fragment fade-in" data-fragment-index="3">
                • Weak interaction ($G_F \simeq 10^{-5}\,{\rm
                GeV}^{-2}$): new physics scale<br>
                • $m_{\rm weak} \sim 100\,{\rm GeV}$ <br>
              </h3>
              <h3 class="fragment fade-in" data-fragment-index="4">
                • $\langle\sigma v\rangle_{\rm weak} \sim
                {\rm few}\times10^{-26}\,{\rm
                cm}^3/{\rm s}$ !!!
              </h3>
            </div>

# WIMP Searches: XENON

<div style="text-align: left; float: left; width: 60%">
              <div class="r-stack">
                <div class="fragment fade-out" data-fragment-index="1">
                  <br><br><br>
                  <img src="img/Feynman.png" width="65%">
                  <br><br>
                  <h3 class="fragment highlight-red" data-fragment-index="0">•
                    Direct detection
                    (scattering)</h3>
                  <h3>• Indirect detection (annihilation)</h3>
                  <h3>• Collider searches (production)</h3>
                </div>
                <div>
                  <div class="fragment fade-in" data-fragment-index="1">
                    <br>
                    <h3>Excluded cross-section for WIMPs:</h3>
                    <img
                      src="img/WIMP-constraints.png" width="90%">
                  </div>
                  <br>
                  <h3 class="fragment fade-in" data-fragment-index="2">
                     • Mass below nuclear mass: energy threshold
                  </h3>
                  <h3 class="fragment fade-in" data-fragment-index="2">
                     • High mass: fewer particles
                  </h3>
                  <h3 class="fragment fade-in" data-fragment-index="3">
                     • Challenge: extend to lower masses
                  </h3>
                </div>
              </div>
            </div>

# En*light*ening the search for Dark Matter?
          ## Atomic Physics!

<br>

<h2> Mass drops below nuclear mass:</h2>
              <h3> • No nuclear recoils. Instead: electron recoils + ionisation
                 <font size="6">• e.g., Ashlee Caddell, Flambaum, BMR, <a href="https://journals.aps.org/prd/abstract/10.1103/PhysRevD.108.083030">Phys. Rev. D <b>108</b>, 083030 (2023)</a></font></h3>
            </div>

<h2> Mass drops below electron mass:</h2>
              <h3> • No electron recoils
                 • Instead: absorption (dark photoelectric effect)</h3>
            </div>
            <br>

<h2> Mass drops below eV:</h2>
              <h3> • Classical DM field
                 • Quantum sensing (atomic clocks)</h3>
            </div>
            <br>

</div>

<div style="text-align: center; float: right; width: 40%">
            <br>
            <img class="fragment" data-fragment-index="0" src="img/atom.png" width="40%">
            <br><br>
            <div class="r-stack">
              <div class="fragment" data-fragment-index="2">
                <img src="img/laser-JILA.jpg" width="90%"><br>
                <font size="3">[JILA]</font>
              </div>
              
            </div>
          </div>

# Ultralight Dark Matter

$$ \Huge
            {\rho_{\rm DM}\simeq 0.3 ~ \frac{\rm GeV}{{\rm cm}^3}}
            $$

<br>

## Mass decreases $\implies$ number density increases:
            ## Classical boson field (e.g., axions, scalars)

<br>

<div style="text-align: left; float: right; width: 70%">
              <div class="fragment fade-in">
                <h3>
                  1. No interaction: oscillation: $\phi = \phi_0 \cos(m_\phi
                  t)$
                </h3>
                \[\phi_0^2\propto \rho_{\rm DM}\]
              </div>

<h3 class="fragment fade-in">
                2. Interactions: clumps
              </h3>
              <br>
              <h3 class="fragment fade-in">
                3. Also: constant build-up (local over-densities)
              </h3>
            </div>

# "Listen" for DM field using atomic clocks

<br>

<div style="text-align: left; float: left; width: 50%">
              <br> <br>
              <img src="img/NHanacek_NIST.png" width="90%"><br>
              <font size="3">[N Hanacek/NIST]</font>
            </div>

<div style="text-align: left; float: right; width: 50%">
              <br>
              <div>
                <h3>
                   • Exotic field may have small interaction with matter<br>
                   • Shift atomic energy levels and frequencies
                </h3>
                <h3>
                      • Monitor with atomic clocks!
                </h3>
              </div>
              <br>
              <br>
              <div class="fragment fade-in">
                <h3>Observable shift:</h3>
                <br>
                \[{\large
                \frac{\delta f}{f} = \kappa \, \phi_{\rm DM}(\vec{r},t)}
                \]
              <br>
              <br>
                <h3>
                   • $\kappa$ - model dependent parameter
                </h3>
                <h3>
                   • Calculated: high-precision atomic theory
                </h3>
              </div>

<br>
              <div class="fragment fade-in">
                <h3>Example: variation of constants</h3>
                <br>
                \[{\large
                  {\mathcal{L} = \phi F_{\mu\nu}F^{\mu\nu}}
                  {\implies \alpha\to\alpha+\phi_{\rm DM}(\vec{r},t)}}
                \]
                $${\large
                  {\kappa = \frac{{\rm d} (f/f_0)}{{\rm d} (\alpha/\alpha_0)}}}
                $$
              </div>
              <br>
            </div>

# Variation of fundamental constants

<br>

<div>
          \[\large
            \omega^{A} = \underbrace{F_A(\alpha)}_{\text{Transition-specific}} 
            \times  \underbrace{m_e c^2\alpha^2}_{\text{Units}} 
          \]
          </div>

<div class="fragment" style="text-align: center; float: left; width: 50%">
            <br><br>
            <img src="img/Bohr.png" width="30%"><br>
            <font size="3">[JabberWok/Wikipedia]</font>
            <br><br><br>
            \[
            \frac{\Delta\omega}{\omega} = \kappa\frac{\Delta\alpha}{\alpha}
            \qquad\qquad\qquad
            \left(
                {\color{red}\kappa \equiv \frac{\partial \omega}{\partial \alpha}\frac{\alpha_0}{\omega}}
            \right)
            \]

<br>

* In general, $\kappa$ calculated from atomic theory
            
            <br>

* Dzuba, Flambaum, Webb [Phys Rev Lett 82, 888 (1999)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.82.888)
          </div>

<div class="fragment" style="text-align: center; float: right; width: 50%">
            <br> <br>
            <img src="img/AlphaSensitivity.png" width="90%"><br>
            <font size="3">[M. Murphy 2012]</font>
            <br>
            <br>
             • Difference transitions: different $\kappa$ sensitivity
          </div>

# Oscillating signals

<div style="text-align: left; float: left; width: 50%">
              <br>
              <h3>Case: oscillating field:</h3>
              \[{\large
              \phi_{\rm DM} = \phi_0 \cos({m_\phi t})}
              \]
              <br>
              \[\large
              \frac{\delta f}{f} = \kappa \phi_0 \cos({m_\phi t})
              \]
              <br>
              <br>
              <div class="fragment fade-in">
                <h2>Constraints from clock-clock comparisons</h2><br>
                <h3>• Different systems: probe different couplings</h3>
                <br>
                <h4>• Optical-Optical: $d_e$ ($\delta\alpha)$</h4>
                <br>
                <h4>• Optical-Microwave: $d_{m_e}-d_{m_p}$ ($\delta(m_e/m_p)$)</h4>
                <br>
              </div>
              <div class="fragment fade-in">
                <h3>• Dimensionful couplings always cancel in these ratios</h3>
              </div>
            </div>

<div style="text-align: center; float: right; width: 50%">
              <br> <br>
              <div class="fragment fade-in" data-fragment-index="3">
                <h3>Typical: Compare two local clocks, different $\kappa$</h3>
                <img src="img/scalarphoton2.png" width="100%"><br>
                <p>[O'Hare - GitHub/AxionLimits]</p><br>
              </div>
            </div>

# Space-time separated sensors
      
                * Filzinger, Caddell, Jani, Steinel, Giani, Huntemann, BMR, [arXiv:2312.13723](https://arxiv.org/abs/2312.13723)
      
                <br>
                <br>
                <br>
      
                <div style="text-align: left; float: left; width: 50%">
      
                  ### Typical local experiment:
      
                  <br>
      
                  $$\large
                    \frac{\delta(\nu_a/\nu_b)}{(\nu_a/\nu_b)} = \phi_0 \\, ( d_{a} - d_b) \\, \cos(\omega t)
                  $$
      
                  <br>

<div class="fragment fade-in">
                  
                  * Non-zero effect from two _different_ transitions only
                  * Certain couplings always cancel 
                  * e.g., Universal couplings

</div>

<br><br>
      
                  <img src="img/Local.png" width="75%"><br>
                </div>
                
                <div style="text-align: left; float: right; width: 50%" class="fragment fade-in">
      
                  ### Separated (identical) sensors:
      
                  <br>
      
                  <div>
                  \[\large
                    \frac{\delta(\nu_a/\nu_b)}{(\nu_a/\nu_b)} = \phi_0 \, d_{\rm eff} \left(\cos(\omega t) -\cos(\omega t-\delta)\right) \\
                      \delta = \omega\Delta t - k_z D 
                  \]
                  </div>
                  <br>
                  <div class="fragment fade-in">
                  
                  * Now: _field_ is different between clocks
                  * Spatial and temporal component (depends on experiment)
                  * Allows access to unconstrained couplings
  
                  </div>
      
                  <img src="img/Separated.png" width="80%"><br>
                </div>

# Space-time separated sensors: initial results

* Filzinger, Caddell, Jani, Steinel, Giani, Huntemann, BMR, [arXiv:2312.13723](https://arxiv.org/abs/2312.13723)
        <br>

<div style="text-align: center; float: left; width: 50%">
          <br>
          
          <div class="r-stack">
          <img class="fragment fade-out" data-fragment-index="1" src="img/deff.png" width="90%"><br>
          <img src="img/dme2.png" width="90%"><br>
          </div>
          <font size="4"><a href="http://arxiv.org/abs/2312.13723">[arXiv:2312.13723]</a></font>
        </div>

* Existing data: [Schioppo _et al._, Nat.Comms 13 (2022)](https://www.nature.com/articles/s41467-021-27884-3)
          * Comparison of ultra-stable cavity lasers
          * 750 km apart (2220 km Fibre cable: PTB to NPL via SYRTE)
          * Sensitive to _spatial_ phase shift

<br>
          
          * Also: Data from GPS satellites (Rb clocks)
          * Clocks less accurate, but setup sensitive to _temporal_ term

<br>

* First Constraints on $d_{m_e}$ along at low-frequency<br>
          * Sensitivity to _spatial_ fluctions of DM, daily oscillation<br>
          
          <br>
          <div class="fragment fade-in" data-fragment-index="2">
          <img src="img/dailymod.png" width="90%"><br>
          </div>

</div>

# GPS.DM

<div style="text-align: left; float: left; width: 35%">
              <br>
              <h3>• 30 Cs, Rb atomic clocks</h3>
              <br>
              <h3>• Over 20 years of high-quality data</h3>
              <br>
              <h3>• Publicly available (JPL)</h3>
              <br>
              <h3>• 50,000 km Dark Matter observatory</h3>
              <br>
              <div class="fragment fade-in">
                <video width="75%" data-autoplay muted>
                  <source src="img/GPSDM.mp4"></video><br>
                <font size="3">[Video: Conner Dailey]</font>
              </div>
            </div>

<div style="text-align: center; float: right; width: 65%">
              <img div class="fragment fade-in" src="img/gps-data.png"
                width="45%">
              <br>
              <br>
              <br>
              <div class="fragment fade-in">
                <img src="img/GPSDM-results.png" width="98%">
                <b>BMR</b>, Blewitt, Dailey, Murphy, Pospelov, Rollings,
                Sherman,
                Williams, Derevianko, <br>
                <a
                  href="http://www.nature.com/articles/s41467-017-01440-4">
                  Nature Comms.
                  (2017)</a>

</div>

# Super-massive black hole at the Galactic Centre

<div style="text-align: left; float: left; width: 50%">
            <h3>• with UCLA Galactic Centre Group</h3>
            <h4>   • Observations led by Tuan Do</h4>
            <h4>   • Andrea Ghez: 2020 Nobel
              prize for discovery of black hole</h4>
            <h4>   • Analysis led by Aurelien Hees</h4>
            <br>
            <h3>• Keck telescope in Hawaii</h3>
            <br>
            <h3>• Motion of ∼1000 stars tracked</h3>
            <h4>   • Precise spectroscopy for many stars</h4>
            <br>
            <br>
            <div class="fragment fade-in">
              <h3>• High gravitational potential</h3>
              <h3>• Possibly large concentration of dark
                matter </h3>
              <h3>• (also other "exotic" physics)</h3>
            </div>
          </div>

<div style="text-align: center; float: right; width: 50%">
            <img src="img/keck-ao.jpg" width="95%">
            <font size="3">[Keck Observatory | Ethan Tweedie Photography]</font>
            <br>
            <br>
            
            <br>
          </div>

# Conclusion

### Standard Model + General Relativity

* Extremely successful, but incomplete
  
            
            <br>
            <br>

### Dark Matter: Strong evidence, no detection
  
            * Low-energy, high-precision atomic physics
            * Allows search for very low-mass dark matter
  
          </div>  
            <br>

### PTB Colloquium, Braunschweig, November 2024

<br>
  
            ### Benjamin M. Roberts
    
            _School of Mathematics and Physics,_

_University of Queensland, Australia_
  
            <br>
  
            * Slides [broberts.io/talks](https://broberts.io/talks)

* Caddell, Flambaum, BMR, [Phys. Rev. D **108**, 083030 (2023)](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.108.083030)
            <br>
            * Savalle _et al._, [Phys. Rev. Lett. **126**, 051301 (2021)](https://link.aps.org/doi/10.1103/PhysRevLett.126.051301)
            <br>
            * BMR _et al._, [Nature Comms. **8**, 1195 (2017)](http://www.nature.com/articles/s41467-017-01440-4)
            <br>
            * BMR _et al._, [N. J. Phys. **22**, 093010 (2020)](https://iopscience.iop.org/article/10.1088/1367-2630/abaace)
            <br>
            * Hees, Do, BMR, Ghez _et al._, [Phys. Rev. Lett. **124** 081101
            (2020)](https://link.aps.org/doi/10.1103/PhysRevLett.124.081101)
            <br>
            * Filzinger, Caddell _et al._, [arXiv:2312.13723](http://arxiv.org/abs/2312.13723)

<br><br>
            <br><br>
            Supported by: ARC and       <img src="img/BQI.png" width="55%">
          </div>

</div>

# Light "WIMPs": electron ionisation

<div>
              <br>
              <div style="text-align: center; float: left; width: 40%">
                <img src="img/ionisation.svg" width="65%"><br>
                <font size="2">[nagwa.com/]</font>
              </div>

<div style="text-align: center; float: right; width: 60%">
                <br>
                <h2>Mass drops below nucleus: no nuclear recoils</h2>
                <br>
                <h2>Instead: electron recoils - ionisation $R\propto K$</h2>
                <br>
                <img class="fragment fade-in" src="img/K-approx2.png"
                  width="65%">
              </div>
            </div>

* A. R. Caddell, **BMR**,
            [Phys. Rev. D **108**, 083030 (2023)](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.108.083030) -- _Led by PhD student: Ashlee Caddell_
            * **BMR**, V. V. Flambaum, [Phys. Rev. D **100** 063017
            (2019)](https://link.aps.org/doi/10.1103/PhysRevD.100.063017)
            * **BMR**, Flambaum, Gribakin, [Phys. Rev. Lett **116** 023201
            (2016)](http://link.aps.org/doi/10.1103/PhysRevLett.116.023201)

# Scalar-SM?

* Overview: Hees _et al._, [PhysRevD.98.064051 (2018)](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.064051)
        <br>

<div>

</div>

<div class="r-stack">
              \[\huge
              \mathcal{L}_{\rm int.} = \phi \left[ {d_e \, F_{\mu\nu}F^{\mu\nu}} + {d_{m_f} \, \bar\psi\psi}  + {d_g \, G^a_{\mu\nu}G^{a\mu\nu}}\right]
              \]
            <div class="fragment fade-in-then-out" data-fragment-index="1">
              \[\huge
              \mathcal{L}_{\rm int.} = \phi \left[ {\color{yellow}d_e \, F_{\mu\nu}F^{\mu\nu}} + {d_{m_f} \, \bar\psi\psi}  + {d_g \, G^a_{\mu\nu}G^{a\mu\nu}}\right]
              \]
            </div>
            <div class="fragment fade-in-then-out" data-fragment-index="2">
              \[\huge
              \mathcal{L}_{\rm int.} = \phi \left[ {\color{yellow}d_e \, F_{\mu\nu}F^{\mu\nu}} + {\color{orange}d_{m_f} \, \bar\psi\psi}  + {d_g \, G^a_{\mu\nu}G^{a\mu\nu}}\right]
              \]
            </div>
            <div class="fragment fade-in" data-fragment-index="3">
              \[\huge
              \mathcal{L}_{\rm int.} = \phi \left[ {\color{yellow}d_e \, F_{\mu\nu}F^{\mu\nu}} + {\color{orange}d_{m_f} \, \bar\psi\psi}  + {\color{red}d_g \, G^a_{\mu\nu}G^{a\mu\nu}}\right]
              \]
            </div>
          </div>

<div style="text-align: left; float: left; width: 50%">
          <br>
          <div class="fragment fade-in" data-fragment-index="1">
            \[\large
              {\color{yellow}\alpha \to \alpha(1 + d_e \phi(r,t))}
            \]
            <h3>
               • nb: $d_e = d_\gamma = d_\alpha = 1/\Lambda_\gamma$
            </h3>
          </div>
          <br>
          <div class="fragment fade-in" data-fragment-index="2">
            \[\large
              {\color{orange}m_e \to m_e(1 + d_{m_e} \phi(r,t))}
            \]
            <h3>
               • electron and quark masses
            </h3>
          </div>
          <br>
          <div class="fragment fade-in" data-fragment-index="3">
            \[\large
              {\color{red}m_p \to m_p(1 + d_{g} \phi(r,t))}
            \]
            <h3>
               • Proton mass: binding energy: QCD scale $\Lambda_{\rm QCD}$<br>
               • Nuclear moments (+ radius): depend on $\Lambda_{\rm QCD}$, $m_q$
            </h3>
          </div>
        </div>

<div class="fragment fade-in" data-fragment-index="4">
            <h3>
               • Optical clock
            </h3>
            \[
            \begin{align*}\large
             \omega &\propto R_y \, F_{\rm rel}(Z\alpha) \sim \alpha^{(2+K_{\rm rel})}m_e \\
              \frac{\delta\omega}{\omega} &= (2+K_{\rm rel}){\color{yellow}d_e} +{\color{orange}d_{m_e}}
            \end{align*}
            \]
          </div>
          <br>
          <div class="fragment fade-in" data-fragment-index="4">
            <h3>
               • Microwave (hyperfine) clock
            </h3>
            \[
            \begin{align*}\large
              \omega &\propto R_y \, [\alpha^2 F_{\rm rel}(Z\alpha)] \, (\mu \, m_e/m_p) \\
              \frac{\delta\omega}{\omega} &= (4+K_{\rm rel}'){\color{yellow}d_e} + {\color{orange}d_{m_e}} + ({\color{orange}d_{m_e}} - {\color{red}d_g}) + \kappa\,  ({\color{orange}d_{m_q}} - {\color{red}d_g})
            \end{align*}
            \]
          </div>
          <br>
          <div class="fragment fade-in" data-fragment-index="4">
            <h3>
               • Cavity-stabilised laser
            </h3>
            \[
            \begin{align*}\large
              \omega &\propto 1/a_0 \\
              \frac{\delta\omega}{\omega} &= {\color{yellow}d_e} + {\color{orange}d_{m_e}}
            \end{align*}
            \]
          </div>
          </div>

# Bullet Cluster

<div class="r-stack">
                <div class="fragment fade-out" data-fragment-index="0">
                  <img
                    src="https://upload.wikimedia.org/wikipedia/commons/e/ea/Bullet_cluster.jpg"
                    width="100%"><br>
                  <font size="3">Chandra X-ray Observatory [NASA]</font>
                </div>

<div class="fragment fade-in" data-fragment-index="0">
                  <img
                    src="https://upload.wikimedia.org/wikipedia/commons/a/a8/1e0657_scale.jpg"
                    width="90%">
                  <font size="3">NASA/CXC/M. Weiss - Chandra X-Ray Observatory</font>
                </div>
              </div>

</div>

<div style="text-align: left; float: right; width: 35%">
              <br>
              <h3>Colliding galaxy clusters ~ 4 Gyr</h3>
              <br>
              <h3>• X-ray emission image:<br> distribution of gas (baryons)</h3>
              <br>
              <br>
              <div class="fragment fade-in" data-fragment-index="0">
                <h3>Composite image: X-ray + lensing</h3>
                <br>
                <h3><font color="pink">• Pink = gas (X-ray)</font></h3>
                <h3><font color="skyblue">• blue = mass (lensing)</font></h3>
                <br>
                <h3 class="fragment fade-in" data-fragment-index="1">
                  • Frictionless dark matter: <br>
                  passes straight through
                </h3>
              </div>
            </div>