Abstract
          A search is presented for the pair production of new heavy resonances, each decaying into a top quark (t) or antiquark and a gluon (g). The analysis uses data recorded with the CMS detector from proton–proton collisions at a center-of-mass energy of 13
              
                $$\,\text {Te}\hspace{-.08em}\text {V}$$
                
                  
                    
                    Te
                    
                    V
                  
                
              
             at the LHC, corresponding to an integrated luminosity of 138
              
                $$\,\text {fb}^{-1}$$
                
                  
                    
                    
                      fb
                      
                        -
                        1
                      
                    
                  
                
              
            . Events with one muon or electron, multiple jets, and missing transverse momentum are selected. After using a deep neural network to enrich the data sample with signal-like events, distributions in the scalar sum of the transverse momenta of all reconstructed objects are analyzed in the search for a signal. No significant deviations from the standard model prediction are found. Upper limits at 95% confidence level are set on the product of cross section and branching fraction squared for the pair production of excited top quarks in the 
              
                $$\text {t}^{*} \rightarrow {\text {t}} {\text {g}} $$
                
                  
                    
                      t
                      
                      
                        
                        ∗
                      
                    
                    →
                    tg
                  
                
              
             decay channel. The upper limits range from 120 to 0.8
              
                $$\,\text {fb}$$
                
                  
                    
                    fb
                  
                
              
             for a 
              
                $$\text {t}^{*} $$
                
                  
                    t
                    
                    
                      
                      ∗
                    
                  
                
              
            with spin-1/2 and from 15 to 1.0
              
                $$\,\text {fb}$$
                
                  
                    
                    fb
                  
                
              
             for a 
              
                $$\text {t}^{*} $$
                
                  
                    t
                    
                    
                      
                      ∗
                    
                  
                
              
            with spin-3/2. These correspond to mass exclusion limits up to 1050 and 1700
              
                $$\,\text {Ge}\hspace{-.08em}\text {V}$$
                
                  
                    
                    Ge
                    
                    V
                  
                
              
             for spin-1/2 and spin-3/2 
              
                $$\text {t}^{*} $$
                
                  
                    t
                    
                    
                      
                      ∗
                    
                  
                
              
            particles, respectively. These are the most stringent limits to date on the existence of 
              
                $$\text {t}^{*} \rightarrow {\text {t}} {\text {g}} $$
                
                  
                    
                      t
                      
                      
                        
                        ∗
                      
                    
                    →
                    tg
                  
                
              
             resonances.