Dalitz plot

<h2 id="square-dalitz-plot">Square Dalitz plot</h2>
<p>Modeling of the common representation of the Dalitz plot can be complicated due to its nontrivial shape. One can however introduce such kinematic variables so that Dalitz plot gets a rectangular (or squared) shape:<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a>
</p><p>
  
    
      
        
          m
          ′
        
        (
        1
        ,
        2
        )
        =
        
          
            1
            π
          
        
        arccos
        ⁡
        
          (
          
            2
            ∗
            
              
                
                  m
                  (
                  1
                  ,
                  2
                  )
                  −
                  m
                  (
                  1
                  ,
                  2
                  
                    )
                    
                      m
                      i
                      n
                    
                  
                
                
                  m
                  (
                  1
                  ,
                  2
                  
                    )
                    
                      m
                      a
                      x
                    
                  
                  −
                  m
                  (
                  1
                  ,
                  2
                  
                    )
                    
                      m
                      i
                      n
                    
                  
                
              
            
            −
            1
          
          )
        
      
    
    {\displaystyle m'(1,2)={\frac {1}{\pi }}\arccos \left(2*{\frac {m(1,2)-m(1,2)_{min}}{m(1,2)_{max}-m(1,2)_{min}}}-1\right)}
  
;
</p><p>
  
    
      
        
          θ
          ′
        
        (
        1
        ,
        2
        )
        =
        
          
            1
            π
          
        
        θ
        (
        1
        ,
        2
        )
      
    
    {\displaystyle \theta '(1,2)={\frac {1}{\pi }}\theta (1,2)}
  
;
</p><p>where 
  
    
      
        m
        (
        1
        ,
        2
        )
      
    
    {\displaystyle m(1,2)}
  
  is the invariant mass of particles 1 and 2 in a given decay event; 
  
    
      
        m
        (
        1
        ,
        2
        
          )
          
            m
            a
            x
          
        
      
    
    {\displaystyle m(1,2)_{max}}
  
 and 
  
    
      
        m
        (
        1
        ,
        2
        
          )
          
            m
            i
            n
          
        
      
    
    {\displaystyle m(1,2)_{min}}
  
  are its maximal and minimal kinematically allowed values, while 
  
    
      
        θ
        (
        1
        ,
        2
        )
      
    
    {\displaystyle \theta (1,2)}
  
  is the angle between particles 1 and 3 in the rest frame of particles 1 and 2. This technique is commonly called "Square Dalitz plot" (SDP). 
</p>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://www.slac.stanford.edu/slac/sass/talks/BrianL.pdf">Dalitz Plots: Past and Present (a presentation by Brian Lindquist at SLAC)</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>R. H. Dalitz (1953). "On the analysis of τ-meson data and the nature of the τ-meson". Philosophical Magazine. 44 (357): 1068–1080. doi:10.1080/14786441008520365. <a href="/wiki/Philosophical_Magazine" target="_blank">/wiki/Philosophical_Magazine</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>R. H. Dalitz (1954). "Decay of τ mesons of known charge". Physical Review. 94 (4): 1046–1051. Bibcode:1954PhRv...94.1046D. doi:10.1103/PhysRev.94.1046. <a href="/wiki/Physical_Review" target="_blank">/wiki/Physical_Review</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Close, Frank (24 January 2006). "Richard Dalitz: Physicist who mapped the behaviour of exotic particles and argued for the reality of quarks". The Guardian. <a href="https://www.theguardian.com/obituaries/story/0,3604,1693226,00.html" target="_blank">https://www.theguardian.com/obituaries/story/0,3604,1693226,00.html</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>P. Pakhlov and T. Uglov, Flavor physics at Super B-factories era, J. Phys.: Conf. Ser. 675, 022009 (2016). <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>R. H. Dalitz (1953). "On the analysis of τ-meson data and the nature of the τ-meson". Philosophical Magazine. 44 (357): 1068–1080. doi:10.1080/14786441008520365. <a href="/wiki/Philosophical_Magazine" target="_blank">/wiki/Philosophical_Magazine</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>R. H. Dalitz (1954). "Decay of τ mesons of known charge". Physical Review. 94 (4): 1046–1051. Bibcode:1954PhRv...94.1046D. doi:10.1103/PhysRev.94.1046. <a href="/wiki/Physical_Review" target="_blank">/wiki/Physical_Review</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>E. Fabri (1954). "A study of τ-meson decay". Nuovo Cimento. 11 (5): 479–491. Bibcode:1954NCim...11..479F. doi:10.1007/BF02781042. S2CID 120859580. <a href="/wiki/Nuovo_Cimento" target="_blank">/wiki/Nuovo_Cimento</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
<li id="fn:8"><p>M. Schulz; et al. (2007). "Four-particle Dalitz plots to visualize atomic break-up processes". Journal of Physics B. 40 (15): 3091–3099. Bibcode:2007JPhB...40.3091S. doi:10.1088/0953-4075/40/15/009. <a href="/wiki/Journal_of_Physics_B" target="_blank">/wiki/Journal_of_Physics_B</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li>
<li id="fn:9"><p>Aaij, R.; Adeva, B.; Adinolfi, M.; Affolder, A.; Ajaltouni, Z.; Akar, S.; Albrecht, J.; Alessio, F.; Alexander, M. (2014-10-14). "Dalitz plot analysis of B s 0 → D ¯ 0 K − π + decays". Physical Review D. Vol. 90, no. 7. p. 072003. doi:10.1103/PhysRevD.90.072003. ISSN 1550-7998. Retrieved 2021-02-19. <a href="https://link.aps.org/doi/10.1103/PhysRevD.90.072003" target="_blank">https://link.aps.org/doi/10.1103/PhysRevD.90.072003</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li>
</ol>

Dalitz plot open-in-new

Dalitz plot