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the standard model ( sm ) is very successful in explaining almost all experimental data to date , culminating in the recent discovery of the long awaited higgs boson at the cern large hadron collider ( lhc )  @xcite . in the sm , all elementary particles acquire mass from a single higgs doublet that generates spontaneous electroweak symmetry breaking ( ewsb ) . all charged fermions have their masses and yukawa couplings to the higgs boson as correlated but free parameters . furthermore , there are no flavor changing neutral currents ( fcnc ) mediated by gauge interactions , nor by higgs interactions ( fcnh ) , at the tree level . the most important goals of the lhc , at run 2 and beyond , are the study of higgs properties and the search for signals , direct or indirect , of new physics beyond the sm . as the most massive particle ever discovered , the top quark might provide clues to better understand the mechanism of ewsb . a possible explanation for its heaviness could be provided by a special two higgs doublet model for the top quark ( t2hdm )  @xcite , where it is the only fermion that couples to a higgs doublet with a large vacuum expectation value ( vev ) . the second heaviest particle is the newly discovered higgs boson ( @xmath4 ) . with @xmath7 , it opens up the possibility of top quark decays into @xmath4 plus a charm quark . the branching fraction of @xmath8 in sm at one loop level is approximately @xmath9  @xcite for @xmath10 gev . if this decay is detected , it would indicate a large effective fcnh coupling of tree - level origins  @xcite , or very large enhancement from beyond sm loop effects  @xcite .    in flavor conserving two higgs doublet models , a discrete symmetry  @xcite is often imposed to distinguish the su(2 ) doublet fields @xmath11 from @xmath12 . without such a discrete symmetry , a general two higgs doublet model ( 2hdm ) should possess fcnh vertices . to study such interactions , we adopt the following lagrangian involving higgs bosons and fermions  @xcite , @xmath13 h^0 +   \left [ \kappa^fc_{\beta-\alpha}-\rho^fs_{\beta-\alpha } \right ] h^0 - i \ , { \rm sgn}(q_f)\rho^f a^0 \right\ } p_r f \nonumber \\   & & -\bar{u } \left [ v \rho^d p_r - \rho^{u\dagger } v p_l \right ] d h^+    -\bar{\nu } \left [ \rho^l p_r \right ] l h^+ + { \rm h.c . } \ , , \end{aligned}\ ] ] where @xmath14 , @xmath15 , @xmath16 , @xmath17 , and @xmath18 is the mixing angle between neutral higgs scalars in the type ii ( 2hdm - ii ) notation  @xcite . @xmath19  matrices are diagonal and fixed by fermion masses to @xmath20 with @xmath21  gev , while @xmath22 matrices are free and have both diagonal and off - diagonal elements . we adopt a cp conserving higgs model and choose @xmath22 matrices to be real but not necessarily hermitian . @xmath23 , @xmath24 , @xmath25 and @xmath26 are vectors in flavor space ( @xmath27 , etc . ) . @xmath4 and @xmath2 are cp - even scalars ( @xmath28 ) , while @xmath3 is a cp - odd pseudoscalar .    with the advent of the lhc , theoretical interest in search of fcnh top decays ( @xmath29 ) picked up  @xcite , and the atlas and cms experiments have already placed the branching fraction limit @xmath30  @xcite , implying @xmath31 . for lhc at @xmath32 tev and integrated luminosity of @xmath33 fb@xmath34 , the atlas experiment expects  @xcite to reach @xmath35 , i.e. probing down to @xmath36 . the flavor changing heavy higgs decay ( @xmath37 ) is complementary to fcnh top decay ( @xmath29 ) , since the coupling @xmath38 is proportional to @xmath5 while @xmath39 . higgs boson data from the lhc favor the decoupling limit  @xcite or the alignment limit  @xcite of a 2hdm . in this limit , fcnh couplings of @xmath4 are naturally suppressed by small @xmath5 , while off - diagonal couplings of @xmath2 , @xmath3 are sustained by @xmath40 .    in this letter , we study the discovery potential of the lhc in the search for heavy higgs bosons @xmath2 or @xmath3 that decay into a top quark and a charm quark . the top quark then decays into a b quark , a charged lepton ( @xmath41 or @xmath42 ) , and a neutrino . taking lhc higgs data and @xmath43 physics constraints into account , we evaluate production rates with full tree - level matrix elements for both signal and background . we optimize the acceptance cuts to effectively reduce the latter with realistic @xmath44-tagging and mistag efficiencies . promising results are presented for the lhc with @xmath45 tev as well as @xmath46 tev . in this section , we apply the latest results from lhc higgs measurements , as well as from @xmath43 physics , to constrain the parameters @xmath47 , @xmath48 , @xmath49 , @xmath50 , and @xmath5 of a general 2hdm that are relevant for observing flavor changing decays of heavy higgs bosons at the lhc . run 1 of lhc at @xmath51 and 8 tev has provided us with information on the couplings of the higgs boson @xmath4 , by measuring the event rates relative to the sm signal strength . even with our general 2hdm , the light higgs boson @xmath4 constitutes a narrow resonance , and the signal strength for a production channel @xmath52 and final state @xmath53 can be written as @xmath54    atlas and cms often show the signal strength of measurements in two dimensions by grouping gluon fusion and @xmath55 production on one axis ( ggf ) , and vector boson fusion and associated production on the other axis ( vbf ) . these contours can be used to draw constraints on 2hdm s  @xcite . we follow a simpler approach and consider signal strengths for final states with the largest statistics , namely @xmath56 , @xmath57 , @xmath58 , and @xmath59 , where the dominant production mode is gluon fusion , as well as the signal strength for the @xmath60 final state from the associated production @xmath61 with @xmath62 or @xmath63 . table  [ tab : signalstrength ] shows the average signal strengths obtained by the experimental groups in run 1 . we combine the atlas and cms results and show both the combined values with their uncertainties in the last column . l3.4cm||c2.3cm|c2.3cm|c2.3 cm final state & @xmath42(atlas ) & @xmath42(cms ) & @xmath42(comb . ) + @xmath64 & @xmath65 @xcite & @xmath66 @xcite & @xmath67 + @xmath68 & @xmath69 @xcite & @xmath70 @xcite & @xmath71 + @xmath72 & @xmath73 @xcite & @xmath74 @xcite & @xmath75 + @xmath76 & @xmath77 @xcite & @xmath78 @xcite & @xmath79 + @xmath80 & @xmath81 @xcite & @xmath82 @xcite & @xmath83    to find the allowed regions of 2hdm parameter space compatible with atlas and cms data , we take the discovered higgs boson as the lightest cp even state ( @xmath4 ) of a general two higgs doublet model and scan over the following sets of parameters : @xmath84    in sm , the most important contributions to the higgs total width come from @xmath60 , @xmath58 , @xmath85 , @xmath59 , @xmath86 and @xmath57 . the same channels are expected to contribute in a general 2hdm . in our analysis , we include all the relevant parameters in eq . ( [ eq : scanpars ] ) that affect the total width , gluon fusion cross section , and the associated higgs production ( @xmath61 ) . we cover a wide range of values for each free parameter , and require that all yukawa couplings of the mass eigenstates ( @xmath4 , @xmath2 , @xmath3 , @xmath87 ) stay perturbative , and that the constraints given in table  [ tab : signalstrength ] are satisfied . the signal strength for each production and decay channel can be expressed in terms of scale factors which are couplings of the higgs boson to fermions and gauge bosons normalized to their standard model values  @xcite . these scale factors can then be expressed in terms of the parameters of a specific 2hdm . negative results from heavy higgs searches provide us further insights on the parameter space of an extended higgs sector . one of the strongest results comes from the search for a heavy higgs decaying into the @xmath88 and @xmath89 final states , excluding a heavy higgs boson with sm like couplings all the way up to 1 tev  @xcite . we use these results to further constraint the parameter space of 2hdm .    in fig . [ fig : atlas_cms ] , we present the 68% ( 95% ) confidence level ( c.l . ) regions in dark ( light ) color that are compatible with lhc constraints from the light higgs boson ( @xmath4 ) alone as well as constraints from both the light higgs boson and the heavy higgs boson ( @xmath2 ) decaying into @xmath88 and @xmath89  @xcite for a general 2hdm and and a type - ii 2hdm . this figure shows that a large value of @xmath90 is still a possibility within a general model for @xmath91 . this is due to the lack of a strong constraint on the @xmath44-quark coupling of the higgs boson . to be consistent with the sm higgs cross section from gluon fusion , a small value of @xmath5 is favored for @xmath92 with @xmath93 . experimental data from run 2 with higher energy and higher luminosity will provide much better guidance for parameters such as @xmath47 and @xmath5 . @xmath47 plane at 68% ( 95% ) c.l . of lhc higgs data in a general 2hdm [ green , ( light cyan ) ] and type ii 2hdm [ red , ( light magenta ) ] , with constraints from ( a ) light higgs boson ( @xmath4 ) , ( b ) both light higgs boson ( @xmath4 ) and heavy higgs boson ( @xmath2 ) . [ fig : atlas_cms ] , title="fig:",width=272 ] @xmath47 plane at 68% ( 95% ) c.l . of lhc higgs data in a general 2hdm [ green , ( light cyan ) ] and type ii 2hdm [ red , ( light magenta ) ] , with constraints from ( a ) light higgs boson ( @xmath4 ) , ( b ) both light higgs boson ( @xmath4 ) and heavy higgs boson ( @xmath2 ) . [ fig : atlas_cms ] , title="fig:",width=272 ]      the fcnh coupling @xmath49 affects the @xmath94 couplings ( @xmath95 ) through @xmath96 . this effect contributes to fcnc processes in down - type quark sector via @xmath97 and @xmath98 loops . for simplicity , let us assume @xmath99 is negligible . recasting the 2hdm - ii expression @xcite , we estimate the modifications to the @xmath100-@xmath101 ( @xmath102 ) mixing amplitude ( @xmath103 ) from the box diagrams with internal @xmath104 and @xmath98 by @xmath105_{\rm sm } } & =   1 + \frac{i_{wh}(y^w , y^h , x ) + i_{hh}(y^h)}{i_{ww}(y^w ) } , \label{eq : b - mix}\end{aligned}\ ] ] where @xmath106 ( @xmath107 ) , @xmath108 , and @xmath109 , \\ & i_{hh } \simeq   \left(\frac{\rho_{tt}^*}{\kappa_t}+\frac{v_{cb}\rho_{ct}^*}{v_{tb}\kappa_t}\right)^2   \left(\frac{\rho_{tt}}{\kappa_t}+\frac{v_{cq}^*\rho_{ct}}{v_{tq}^*\kappa_t}\right)^2 y^h   \left [ \frac{1+y^h}{(1-y^h)^2}+\frac{2y^h\ln y^h}{(1-y^h)^3 } \right ] . \label{eq : b - mix - loop } \end{split}\end{aligned}\ ] ] we adopt the following intervals from the summer 2014 results by utfit @xcite , @xmath110 , \quad \phi_{b_d}\in [ -8.0^\circ,~4.4^\circ ] , \notag\\ c_{b_s}&\in [ 0.9,~1.23 ] , \quad \phi_{b_s}\in [ -3.0^\circ,~4.7^\circ ] , \label{eq : utfit}\end{aligned}\ ] ] at  95%  probability , where @xmath111_{\rm sm}$ ] . the constraints from @xmath112 mixing data are shown in fig . [ fig : b_physics](a ) on the @xmath113 plane with @xmath114 gev . shaded regions are excluded by the 95% probability ranges in eq . ( [ eq : utfit ] ) . the constraint from @xmath115 ( pink regions ) is slightly tighter than the @xmath116 exclusion ( blue - shaded regions ) . combining them with constraint from the @xmath117-violating phase @xmath118 ( light - green regions ) , we obtain the upper limit @xmath119 , regardless of @xmath49 . the parameter @xmath49 is strongly constrained since its effect in eq . ( [ eq : b - mix - loop ] ) is enhanced by the ckm factor @xmath120 ( @xmath102 ) . once @xmath47 is fixed within this range , we obtain a constraint on @xmath49 . for @xmath121 , we have @xmath122 . furthermore , the sizable phase in @xmath123 makes @xmath49 sensitive to the @xmath117-violating phase @xmath118 , even if @xmath49 is real . for @xmath124 gev , the constraints become : @xmath125 regardless of @xmath49 , and @xmath126 for @xmath127 . @xmath49 plane from @xmath112-mixing , with shaded regions excluded by eq . ( [ eq : utfit ] ) , i.e. blue ( pink ) regions by @xmath128 , light - green regions by @xmath118 ; ( b ) @xmath47@xmath48 plane from @xmath129 with @xmath130 and @xmath131 gev , with dark - green shaded regions excluded by @xmath132 in eq . ( [ eq : b2sgam - exp ] ) at @xmath133 , while pink regions by @xmath134 . blue - solid lines in ( b ) mark @xmath135 with @xmath136 . [ fig : b_physics ] , title="fig:",width=272 ] @xmath49 plane from @xmath112-mixing , with shaded regions excluded by eq . ( [ eq : utfit ] ) , i.e. blue ( pink ) regions by @xmath128 , light - green regions by @xmath118 ; ( b ) @xmath47@xmath48 plane from @xmath129 with @xmath130 and @xmath131 gev , with dark - green shaded regions excluded by @xmath132 in eq . ( [ eq : b2sgam - exp ] ) at @xmath133 , while pink regions by @xmath134 . blue - solid lines in ( b ) mark @xmath135 with @xmath136 . [ fig : b_physics ] , title="fig:",width=272 ]    we now turn to the @xmath137 constraint . the @xmath97-@xmath98 loop affects this process via the wilson coefficients @xmath138 at leading - order ( lo ) , which are , at the matching scale @xmath139 , given by @xmath140 here , the operator basis and the definition of @xmath141 follow ref . we follow the procedure in ref . @xcite and calculate first the ratio @xmath142 with world average of measurements @xmath143 @xcite and the next - to - next - to lo ( nnlo ) prediction in sm , @xmath144 @xcite . we then require the similar ratio based on our lo calculation , i.e. @xmath145 , to be within the range allowed by @xmath146 . choosing the matching scale and the low - energy scale as @xmath147 and @xmath148 , we reproduce the nnlo results of ref . @xcite , @xmath149 gev , with 95% c.l . in the type - ii 2hdm gev ) at 95% c.l . ] . [ fig : b_physics](b ) shows the allowed region in the @xmath150 plane from @xmath151 and @xmath43 mixing for @xmath114 gev and @xmath130 . the dark - green shaded regions are excluded by the @xmath133 experimental error of @xmath132 in eq . ( [ eq : b2sgam - exp ] ) , with the theoretical uncertainty linearly added . the constraint on @xmath47 by @xmath115 is also shown . for @xmath152 , @xmath48 is constrained to be within @xmath153 . note that this touches the region of @xmath154 . we set @xmath130 as it is already strongly constrained by @xmath112 mixing . for @xmath124 gev , the @xmath151 constraint on @xmath48 becomes : @xmath155 for @xmath156 . typically , @xmath157 constrains @xmath48 more strongly than @xmath47 , as the effect of @xmath48 is enhanced by the chiral factor @xmath158 in eq . ( [ eq : c7 ] ) . the contribution from charm loop has a mild dependence on @xmath50 through the @xmath97 couplings , @xmath159 ( @xmath160 ) . in general , @xmath50 may be very different from @xmath49 . since the charm quark in the loop is light and there is no ckm enhancement , the constraint on @xmath50 is expected to be much weaker . the constraint on @xmath50 has been analyzed in ref . @xcite . with @xmath161 , it is found from @xmath162 mixing that @xmath163 for @xmath131 gev and @xmath164 . this constraint implies that @xmath165 for @xmath131 gev . we note that a large @xmath50 can enhance @xmath166 rates via the @xmath97 coupling @xmath167 and can explain the 3.4@xmath168 discrepancy between the sm prediction and babar data  @xcite . for real valued @xmath50 and @xmath169 , the solution space shown in ref . @xcite reads @xmath170 . additional flavor constraints can be obtained from @xmath171 mixing ( @xmath172 )  @xcite and @xmath173 mixing ( @xmath174 )  @xcite for @xmath175 gev . the value of ( @xmath176 ) is expected to be very small , thus @xmath177 mixing provides a better limit for @xmath50 .    combining experimental limits from lhc higgs data and @xmath43 physics , and assuming perturbativity , we consider @xmath178 , @xmath179 , and @xmath180 . we now discuss the prospects of discovering fcnh interactions at the lhc through @xmath2 and @xmath3 decays . the number of free parameters in a general 2hdm is too large for a comprehensive collider study of the fcnh signal , so we make some assumptions that are motivated by experiment . the latest experimental results point to a higgs sector with the light cp even state behaving like the sm higgs , indicating that @xmath5 should be small . we consider sample cases with @xmath181 and @xmath182 , which imply @xmath40 .    in our case study , we choose the heavier states ( @xmath2 , @xmath3 and @xmath183 ) to be degenerate for simplicity , which is also in accordance with the decoupling limit  @xcite , and we set @xmath184 in the higgs potential  @xcite . we also set @xmath185 and choose @xmath186 such that the scalar potential satisfies stability , tree - level unitarity , and perturbativity up to large masses . to fix the yukawa couplings , we assume that @xmath187 while @xmath188 . this is in good agreement with both @xmath43 physics constraints as well as lhc run 1 constraints . for the off - diagonal parts that generate the flavor changing signal , @xmath49 is constrained to small values by @xmath43  physics but we assume that @xmath50 can have larger values . in the massless limit for charm , the signal cross section is , to a very good approximation , only a function of a single effective coupling @xmath189 , but also very weakly depends on @xmath190 . the contribution to the cross section from terms with @xmath191 is at least 98% without cuts and more than 93% with all cuts for @xmath192 with @xmath193 tev , and it is even more dominating for a lower higgs mass .    with these experimentally motivated choices , gluon fusion is the dominant production mode for @xmath2 and @xmath3 states , and @xmath194 becomes the dominant final state at high mass ( @xmath195 tev ) . we display in fig . [ fig : br13 ] the branching fractions for ( a ) the heavier scalar @xmath2 , and ( b ) the pseudoscalar @xmath3 , as functions of higgs mass with @xmath181 and @xmath196 . the computer code 2hdmc  @xcite is employed to scan over @xmath197 tev and @xmath198 with sets of parameters that satisfy potential stability , tree - level unitarity , and perturbativity . this gives rise to the `` bands '' in fig . we also display the branching fraction @xmath199 for the aforementioned choice of @xmath200 and @xmath186 in our lhc case study with a dashed curve in fig . we note that with large branching fraction in most of the parameter space , @xmath201 might offer great promise to discover higgs pairs at the lhc .     and ( b ) higgs pseudoscalar @xmath3 versus @xmath202 , with @xmath181 , @xmath196 , and @xmath203 for diagonal couplings . we show the allowed regions when @xmath200 and @xmath186 are varied . branching fraction @xmath199 for the lhc case study is shown as a dashed curve . [ fig : br13 ] , title="fig:",width=283 ]   and ( b ) higgs pseudoscalar @xmath3 versus @xmath202 , with @xmath181 , @xmath196 , and @xmath203 for diagonal couplings . we show the allowed regions when @xmath200 and @xmath186 are varied . branching fraction @xmath199 for the lhc case study is shown as a dashed curve . [ fig : br13 ] , title="fig:",width=283 ]      our signal is the production of a heavy higgs boson from gluon fusion , with subsequent flavor changing decays into a charm quark and a top quark , and the top decays semileptonically . more explicitly , we consider @xmath204 ( @xmath205 or @xmath3 ) , followed by @xmath206 with @xmath207 or @xmath42 . unless explicitly specified , @xmath208 generally denotes a quark ( @xmath208 ) or an anti - quark ( @xmath209 ) and @xmath210 represents a lepton ( @xmath211 ) or anti - lepton ( @xmath212 ) . we calculate the matrix elements analytically , and compute the signal cross section with the parton distribution functions of mstw2008  @xcite . the factorization and renormalization scales are chosen to be @xmath213 . in addition , to estimate the nlo cross section for @xmath214 , we use the computer code higlu  @xcite to calculate @xmath215 ( @xmath216 ) , including both top and bottom quark loops to find a @xmath217-factor . the dominant physics background to the final state of @xmath218 comes from @xmath219 , as well as @xmath220- and @xmath98-channel single top ( @xmath221 ) . another important background is @xmath194 production where either one of the two leptons is missed for both top quarks decaying semileptonically , or two of the four jets are missed when only one of top quarks decays semileptonically . we employ the programs madgraph  @xcite and helas  @xcite to evaluate the exact matrix elements for the background processes . the factorization and the renormalization scales are chosen to be @xmath222 for @xmath223 and @xmath224 , @xmath225 for @xmath220- and @xmath98-channel single top , and @xmath226 for @xmath194 . we use mcfm  @xcite to calculate the nlo @xmath217-factors for our background processes . let us present our strategy for full reconstruction of each event with the help of intermediate on - shell particles . for each event , we require one @xmath44 jet and one non-@xmath44 jet , identified through @xmath44-tagging . in addition , we require a single isolated lepton and missing transverse energy from the neutrino in the semileptonic decay of the top quark in our fcnh signal . for lepton momentum @xmath227 and neutrino momentum @xmath228 , the invariant mass constraint for an on - shell @xmath229 , @xmath230 , can be solved for the longitudinal component of the neutrino momentum ( @xmath231 ) , which is the only unknown in the event . we obtain two solutions @xmath232 if @xmath233 hence @xmath234 complex , the event is vetoed . for @xmath235 with @xmath234 real , we choose the solution that minimizes the reconstructed top mass @xmath236 or @xmath237 . systematics can be the limiting factor for new physics searches at high luminosities . precise determination of the background needs to include systematics in experiments . since our signal is a sharp peak over a smoothly falling background , the precise knowledge of background cross section at percent level is not required for a @xmath238 discovery . an uncertainty of 30% in the background estimation might shift the limit on @xmath239 by 10% without affecting our results .      to study the discovery potential , we employ three sets of realistic cuts and tagging efficiencies . for low luminosity ( ll ) : ( a ) lhc run  1 ( @xmath240 tev ) with @xmath24125 fb@xmath34  @xcite ; and ( b ) full cm energy ( @xmath45 or 14 tev ) with @xmath242 fb@xmath34 . for high luminosity ( hl ) : ( c ) full cm energy ( @xmath32 tev ) with @xmath243 fb@xmath34 or @xmath244 fb@xmath34@xcite . we require that in every event there should be ( a ) exactly 2 jets that have @xmath245 gev ( 30 gev for hl ) and @xmath246 , and one of them must be tagged as a @xmath44-jet ; ( b ) exactly one isolated lepton that has @xmath245 gev and @xmath246 ; ( c ) at least 20 gev ( 40 gev for hl ) of missing transverse energy ( @xmath247 ) . after reconstructing the longitudinal component of the neutrino momentum , we further require that ( d ) the reconstructed invariant mass of the top satisfies @xmath248 ; ( e ) the reconstructed invariant mass of the higgs boson satisfies @xmath249 . we consider a further powerful acceptance cut on non-@xmath44-tagged jet momentum . in the higgs boson decay frame , the charm quark momentum from @xmath250 is approximately given by @xmath251}.\ ] ] since the higgs boson from gluon fusion has little transverse momentum , the @xmath252 distribution has both a kinematic cut - off and a peak at the above @xmath253 value . we require that the transverse momentum of the non-@xmath44-tagged jet satisfies @xmath254 . to simulate detector effects based on atlas  @xcite and cms  @xcite specifications , we apply gaussian smearing of momenta : @xmath255 with individual terms added in quadrature ( @xmath256 ) . in lhc run  1 at @xmath240 tev , the @xmath44-tagging efficiency ( @xmath257 ) is taken to be @xmath258 , the probability that a @xmath259-jet is mistagged as a @xmath44-jet ( @xmath260 ) is @xmath261 and the probability that any other jet is mistagged as a @xmath44-jet ( @xmath262 ) is taken to be @xmath263 . at the full cm energy ( @xmath45 or 14 tev ) with @xmath264 30 fb@xmath34 , we follow the tagging and mistag efficiencies in the atlas technical design report  @xcite : @xmath265 , @xmath266 and @xmath267 . for the full cm energy ( @xmath45 or 14 tev ) with hl of 300 fb@xmath34 or 3000 fb@xmath34 , the tagging and mistag efficiencies are taken to be @xmath268 , @xmath266 and @xmath267 . ( solid ) @xmath269 at the lhc versus @xmath270 for ( a ) @xmath240 tev and ( b ) @xmath32 tev , with @xmath271 and @xmath272 . also shown are the background cross sections ( dashed ) from single top ( @xmath273 and @xmath274 ) , @xmath229+jets ( @xmath223 and @xmath275 ) and @xmath194 with @xmath217-factors , acceptance cuts , and tagging efficiencies . [ fig : sigma ] , title="fig:",width=272 ]   ( solid ) @xmath269 at the lhc versus @xmath270 for ( a ) @xmath240 tev and ( b ) @xmath32 tev , with @xmath271 and @xmath272 . also shown are the background cross sections ( dashed ) from single top ( @xmath273 and @xmath274 ) , @xmath229+jets ( @xmath223 and @xmath275 ) and @xmath194 with @xmath217-factors , acceptance cuts , and tagging efficiencies . [ fig : sigma ] , title="fig:",width=272 ] we present the signal and background cross sections at the lhc for @xmath240 tev and @xmath46 tev in fig . [ fig : sigma ] . all tagging efficiencies and @xmath217-factors discussed above are included . we observe that the largest contributions to the sm background come from single - top and @xmath229+jets processes , which is to be expected , since they can both produce very similar kinematics to our signal process . in contrast , the @xmath194 background is substantially lower because of the requirement on the number of jets and leptons passing our cuts .    [ cols="^,^ " , ]     to estimate the discovery potential , we obtain the lower limit on @xmath276 by requiring that the 99.4%-confidence - level ( cl ) upper limit on the background is smaller than the 99.4%-cl lower limit on the signal plus background  @xcite with statistical fluctuations . this leads to the condition , @xmath277,\ ] ] where @xmath278 is the signal ( background ) cross section and @xmath25 the integrated luminosity . choosing the parameter @xmath279 corresponds to 5@xmath168 significance . for a large number of events ( @xmath280 ) , this requirement is equivalent to the statistical significance @xmath281 where @xmath282 is the number of signal ( background ) events . we show in fig . [ fig : reach ] the discovery reach in the @xmath202@xmath191 plane for the fcnh signal @xmath283 at the lhc with @xmath45 ( 14 ) tev , for dashed ( solid ) contours and for @xmath181 and @xmath182 . fig . [ fig : reach](a , c ) are for the heavier scalar @xmath2 alone , whereas fig .  [ fig : reach](b , d ) are for the degenerate case , for which the scalar @xmath2 and pseudoscalar @xmath3 signals are added together . the fcnh decay of the heavy higgs will be observable for @xmath272 and @xmath284 up to @xmath285 gev with 3000 fb@xmath34 data . a larger value of @xmath50 will enhance the cross section , hence statistical significance , of this fcnh signal . in a general two higgs doublet model , there could be flavor changing neutral higgs interactions with fermions . strong limits exist for these fcnh interactions , except those involving the third generation quarks . it is of great interest to study the relation between the most massive elementary particle ( the top quark ) and the higgs bosons . the lhc has discovered a higgs boson lighter than the top , which makes the rare decay @xmath8 kinematically possible . in a general 2hdm , the decay width of @xmath8 is proportional to @xmath286 , while that of @xmath287 is proportional to @xmath288 . therefore , they are complementary to each other in the search for new physics beyond the standard model . we investigated the prospects for discovering @xmath289 at the lhc , where the heavy scalar @xmath2 and pseudoscalar @xmath3 are produced via gluon fusion , which are facilitated by the extra @xmath290 couplings . the primary physics background comes from @xmath223 , @xmath274 , @xmath275 , @xmath273 , and @xmath194 . both signal and background processes are studied with realistic acceptance cuts as well as tagging and mistag efficiencies . promising results have been found for the lhc with a center of mass energy of 13 tev and 14 tev . the fcnh decay of the heavy higgs will be observable for @xmath272 and @xmath284 up to @xmath291 gev with 3000 fb@xmath34 of integrated luminosity . this result is robust against a small @xmath286 , independent of the @xmath29 search , which becomes diminished . if c - tagging efficiency can be improved  @xcite , the discovery potential of this fcnh signal will be greatly enhanced . if @xmath292 , @xmath293 can become comparable to @xmath294 or surpass it . recently , it was suggested that next - to - leading order qcd and electroweak corrections might swamp the signal of higgs decays into top quark pairs  @xcite . a recent analysis shows that @xmath295 with sm couplings can be very difficult to observe at the lhc  @xcite . in that case the fcnh decay of @xmath296 might offer a promising opportunity to observe the heavier higgs bosons . we have not emphasized the @xmath297 lepton sector . recently , the cms collaboration reported unexpected @xmath298 events  @xcite that might be explained by neutral higgs boson decay  @xcite . if this can be confirmed by the atlas collaboration in the near future , or at lhc run 2 , it will be exciting new physics for fcnh interactions , and @xmath299 , unsuppressed by decoupling ( i.e. small @xmath286 ) , could help discover the exotic scalars . ck thanks the academia sinica , national taiwan university , and national center for theoretical sciences for excellent hospitality . ba thanks kyu jung bae for discussions . the computing for this project was performed at the ou supercomputing center for education & research ( oscer ) at the university of oklahoma ( ou ) . this research was supported in part by the u.s . department of energy under grant no . de - fg02 - 13er41979 ( ck , ba , and bm ) ; 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a general two higgs doublet model ( 2hdm ) is adopted to study the signature of flavor changing neutral higgs ( fcnh ) decay @xmath0 , where @xmath1 could be a cp - even scalar ( @xmath2 ) or a cp - odd pseudoscalar ( @xmath3 ) . 
 measurement of the light 125 gev neutral higgs boson ( @xmath4 ) couplings at the large hadron collider ( lhc ) favor the decoupling limit or the alignment limit of a 2hdm , in which gauge boson and diagonal fermion couplings of @xmath4 approach standard model values . in such limit , fcnh couplings of @xmath4 are naturally suppressed by a small mixing parameter @xmath5 , while the off - diagonal couplings of heavier neutral scalars @xmath1 are sustained by @xmath6 . 
 we study physics background from dominant processes with realistic acceptance cuts and tagging efficiencies . 
 promising results are found for the lhc running at 13 or 14 tev collision energies .