False Vacuum Decay in Kink Scattering JHEP10(2018)192 ]

Home , False vacuum decay

JHEP10(2018)192 Springer May 8, 2018 . The usual : October 19, 2018 October 30, 2018 : : September 24, 2018 : Received d,e,f Accepted Published Revised , 1 regime where the kink in the Published for SISSA by https://doi.org/10.1007/JHEP10(2018)192 and P.P. Avelino c [email protected] , K.Z. Nobrega b = 0. We investigate the [email protected] , . 3 F.C. Simas, a 1805.00991 The Authors. Solitons Monopoles and Instantons, Field Theories in Lower Dimensions, c

In this work we consider kink-antikink and antikink-kink collisions in a modi- , [email protected] model with a false vacuum characterized by a dimensionless parameter model. We show that the attractive interaction between the kink-antikink pair leads 4 4 φ φ model is recovered for [email protected] Centro de da Astrof´ısica Universidade doRua Porto, das Estrelas, PT4150-762 Porto,Departamento Portugal de e F´ısica Astronomia, FaculdadeRua de do Ciências,Universidade do Campo Alegre Porto, 687, PT4169-007E-mail: Porto, Portugal 65500-000, Chapadinha, Maranhão,Brazil Departamento de Eletro-Eletrônica, Instituto Federal Tecnologia de do Educa¸cão,Ciênciae Maranhão(IFMA), Campus Monte Castelo, 65030-005, SãoLu´ıs,Maranhão,Brazil Instituto de e do Astrof´ısica Ciências Espa¸co,Universidade doRua Porto, das CAUP, Estrelas, PT4150-762 Porto, Portugal Departamento de Universidade F´ısica, Federal doCampus Maranhão(UFMA), do Universitário Bacanga, 65085-580, SãoLu´ıs,Maranhão,Brazil Centro de CiênciasAgráriase Ambientais-CCAA, Universidade Federal do Maranhão(UFMA), 4 b c e d a f Open Access Article funded by SCOAP ArXiv ePrint: the to a rich scattering pattern, in some cases delayingKeywords: considerably the false vacuumNonperturbative decay. Effects Abstract: fied φ presence of false vacuum can be understood as a small deformation of the standard kink for Adalto R. Gomes, False vacuum decay in kink scattering JHEP10(2018)192 ]. ]. ], 1) , 69 23 76 , ] and 75 67 , ], bubble 8 ] and dark 66 – 4 18 – 16 3 ], kinks in models 58 – 6 56 ], quantum field theory [ 1) dimensional wave equation. 22 , ]. Further interesting directions ]. In this regime, collisions of two 55 ], boundary scattering [ 74 – 65 ], but also in potentials of higher self- 49 – ], optics [ ]. Domain wall collision with such high 40 63 – 21 77 31 ]. The simplest soliton solutions are the kink 30 – 1 – – 27 model [ ]. 4 φ 68 ], where planar symmetry is assumed and the dynamics is 73 – ], electroweak phase transition and baryogenesis [ 3 70 ], multi-kink collisions [ – 3 1 62 – ] and cosmology [ ]. Soliton solutions in nonlinear field theory describe localized energy 59 26 1) symmetry and are described by a (1 1)-dimensions. , – 20 , ] and non-polynomial potentials [ 1 , 10 is the Hubble expansion rate), one can neglect the spacial curvature of the 24 2 48 19 ], signals for the possible metastability of Higgs vacuum [ – H 1) dimensional. Solitons are also studied in the context of bubble collisions in 15 , 41 – 1) symmetry were considered in ref. [ 9 , (where 4 The mechanism of false vacuum decay in scalar field theories is well understood [ Embedded in higher dimensional spaces, kinks give rise to domain walls and branes [ Kink scattering processes in nonintegrable models have intrincate structures. This has 3.1 False vacuum3.2 in an unbounded False interval: vacuum kink-antikink in collisions a bounded interval: antikink-kink collisions H bubbles have SO(2 In particular, for anand asymmetric SO(2 double well potential,degree domain of wall symmetry collisions can with be planar described as collisions between a kink and an antikink in (1 In some cyclic universe scenarios,the domain walls Big were Bang considered conditions aseffectively [ a (1 possibility to generate the early universe. In theto limit of a high nucleation rateuniverse per and unit consider four-volume the in bubbles comparison as in flat spacetime [ interaction [ of investigation include the interactionof of two a scalar kink fields with an [ models impurity with [ generalized dynamics [ large applicability in condensed matternuclear physics physics [ [ and antikink in (1 been studied not only in the simple False vacua play anof important inflationary role models in [ collisions fundamental [ physics, in particularenergy models in [ the context concentrations which are able to propagate without modifying their shape. They have 1 Introduction 3 Numerical results 4 Conclusions Contents 1 Introduction 2 The model JHEP10(2018)192 ] ) 0 x 78 ≥ (2.1) (2.2) )), with . vt 4 ) = tanh( − model. The x 0 ( 4 x K φ φ − x ( ] and nonplanar [ γ = 2. In this case the kink 77 2 4 φ M = φ, λ 3 λ ) ) = tanh( φ √ M ( ] only provided some examples for = 0 (2.3) V 1 2 x, v, t 77 ( − − − K φ 2 1 limit, where the presence of the linear 3 φ µ kink that favors the expansion of the true φ , and we conclude in the section 2 4 φ∂ | λ φ 3 µ M + 2 | ∂ 1 2 – 2 – φ − = 0 and a global minimum (the true vacuum) 2 2 = 0, given by the usual φ φ − 00 ]. Applying a Lorentz boost, a travelling kink with dtdx φ 4 λ 1 the potential has a local minimum (the false vacuum) is obtained as − 81 Z , 0 ¨ φ ) = ). These solutions, of minimal energy, can also be obtained = x 80 φ x ( S 1)-dimensions in Minkowski spacetime with a Lagrangian with V , tanh( − potential ]. For the sake of definiteness, we take ) = x 4 ( 79 φ , a local maximum at ) leads to a small force on the ¯ K λ φ . Here we are interested in the 2.2 √ λ and initial position √ M/ v is a dimensionless self-coupling parameter. From here on we will consider M/ Static solutions can be found for In the next section we review some of the main properties of the The present work intends to fill this gap, with the aim of investigating the kink scatter- ≈ − ≈ − + and antikink by first-order BPS equationsvelocity [ φ term in eq. ( vacuum region [ equation of motion is given by where without loosing generality. For φ and a modified 2 The model We consider the action in (1 standard dynamics factor affecting the structurethe of complete the decay scattering ofmass and, the of in false the some kink-antikink vacuum cases, pair. even delaying in considerably a restrictednumerical region results around are presented the in center the of section ing and the correspondingvacuum false occupying vacuum evolution, the considering unboundedpair; two situations: region i) i) outside the the the falsekink false pair. area vacuum We initially defined consider occupying symmetric byinitially kink-antikink the the at and restricted equal antikink-kink kink-antikink collisions, distances region withulus. from between the the We pair the show center antikink- how of the mass attractive and interaction initial between velocities the with kink same and mod- antikink is the main small fluctuations were investigated.the However, output ref. of [ backgroundinitial collisions, velocity or with with no thethe parameter description controlling two of the wells. their difference in dependence potential either energy between with dimensions. In this background the effects of small initial planar [ JHEP10(2018)192 . . 2 } k n ) = η (3.1) (3.2) (2.4) { model, x, t and we ]. Also, and the ( ˙ 6 φ 0 φ = 4 + 51 φ x 2 k − th order in ω and n ]. φ order symplectic 40 th = 0. We apply this , 1 ]; the presence of more − . ) we use a pseudospectral model [ 41 0) 0) ] as an exchange of energy 4 2.3 φ v, v, 33 : 09 and a 6 v − − . , , − 0 0 η. to the kink field in 2 x x = 0 ω n − − φ = δx x x ( ( η ) K K ˙ φ φ 2 K = 0 (the zero-mode or translational mode) φ 2 0 − − ω 0) 0) ] – 3 – 2 + 6 31 , v, , v, − 0 0 x x + ( 6= 0, as far as we know, there are no explicit solutions + + antikink with velocity 00 η x x 4 04. ( ( φ . = 200. A sympletic method with the Dirichlet condition − K K ˙ φ φ = 0 max x δt and a ], and are described in terms of the basis of eigenfunctions 0) = 0) = v was also applied to double check our numerical results. We used a 79 x, x, ) leads to a equation: Schrödinger-like ( ( ˙ φ φ max x, t x ( η . Linear stability analysis around the static kink solution with ) 2 . Note that the initial condition is only a solution for = 1 considering that the system will relax by emitting scalar radiation during 0 v ωt = 15 as the initial kink position, i.e., the kink solution centered at x x − 0 1 x = 3 (the vibrational mode), followed by a continuum of states with √ / 2 1 ) + cos( kink with velocity ω Now back to our problem for x order finite-difference method with spatial step 4 ( = 1 φ K th method on a gridset with 2048 the nodes grid with boundaryimposed periodic at at boundary conditions for 4 integrator with time step We fixed antikink at even for their free propagation toward the collision region. To solve eq. ( 3.1 False vacuum inFirst of an all unbounded let us interval: considera a kink-antikink symmetric collisions kink-antinkink collision. We take as initial conditions 3 Numerical results The kink scattering processes havefalse a vacuum strong is dependence finite or onantikink-kink not. whether collisions. the In initial the region following we with will consider separately kink-antikink and quasinormal modes can store energy during a collision inof the the equation ofwere motion. presented In in particular, ref. corrections [ second collision. This mechanismbetween was the described translational in andwe the vibrational remark ref. modes. [ that Despite theretwo-bounces applicable are occur in some even the in known presentthan the case, exceptions one vibrational absence to mode of this can a result mechanism: in vibrational the in mode suppression the of [ two-bounce windows [ The existence of vibrationalbehavior modes of is kink-antikinkis scattering. important characterized for by One the a suchthe comprehension collision effect vibrational of process is mode the where known ofthe complex the as the pair, initial kink-antikink two-bounces, after translational pair being and energy during scattered, it is an oscillates stored amount around in of the time. contact point As and a retrocedes result, for a φ This equation results in theand eigenvalues [ γ JHEP10(2018)192 26 . 0 = 1, (3.3) . This ∼ a, bion m 1 c. = 1 after a. crit 3 v 6= 0, that is 2 φ , the number t a — where the a, which shows m are not directly 2 1 b b we have N d show the number 1 6= 0. They show the growing with 2 c depict three profiles = 0. Scalar field at the 1 b– there are some velocity crit 17), b) two-bounce collision v a– 2 . , 0 50 100 150 200 1 0 -1 -2

), for diﬀerent values of the

1.5 0.5 crit λ

-0.5 -1.5 φ (x=0,t) v = 0 M , t = 1. For small velocities, the √ = 0 case, corresponding to the v . (0 φ − φ = 2) during the collision process, v ) b X , but with N ]. Figures − crit 40 x 0). Large values of 26). – . ( : the kink-antikink pair has not enought ∗ x, K 31 ( φ v > v = 0 t φ v − model, corresponding to v < v ) – 4 – 4 c. We could characterize this inelastic scattering 1. Velocities above a critical velocity X φ 1 − + x = 0 is at the vacuum = on kink scattering. Figures ( x φ K 0 50 100 150 200 1 0 φ -1 -2

1.5 0.5

-0.5 -1.5 φ (x=0,t) . One example of this is presented in the figure a. We observed an effect that appears only for ≈ b. Also, 2-bounce windows are still present, but are thinner 3 ) 3 x ( φ , but there one represent bion states as making frontier with the ) between the bounces. For instance, in figure 2 , t b. ), showing a) the formation of bion state (for (0 1 φ , t t (0 = 1 bounces. For smaller velocities with φ b N 1926) and c) one-bounce collision (for . Kink-antikink collisions for the . = 0 The behavior of the kink-antikink pair after the collision process can be understood Now we turn to the effect of The structure of such two-bounce windows is better visualized in figure We start our analysis by reviewing some aspects of the v theory, and well described in the literature [ 0 50 100 150 200 1 0 -1 -2

1.5 0.5 4

-0.5 -1.5 φ (x=0,t) this effect is shown inin figure velocity for larger values of aproximating the static kink-antikink profile by of bounces as ainelastic function scattering of behavior with the 1-bounce initialis for velocity a for direct several effect valuescollision of of is the presented in tendency figure ofthe the lack false of bounces vacuum to orenergy decay. even to bion One encounter states at example for the of center 1-bounce of mass before the false vacuum decay. An example of represented in figure two-bounce windows. Eachof two-bounce oscillations window of is labeledmeaning by that this an collision integer belongs to the first two-bounce window from figure windows where the scalar fieldas presents shown two-bounces in ( figure the number of bouncesstates as have a a function large of number the of initial oscillations of velocity. As shown in figure pair radiates with thelong scalar run, field finishing oscillating at withoutshow the a an vacuum recognizable inelastic pattern scattering,one until, where bounce, in the as the in outputas the field example having retains of the figure initial value φ of scalar field at theinitial center velocity. of Initially mass the asoutput point a of function the of scattering time, process is a bion state — see an example in figure Figure 1 center of mass, (for JHEP10(2018)192 (d) (b) 01 with . = 0 d. Blue represents 01. . 2 = 0 v v 005 and (d) . = 0 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 3 2 1 0 3 2 1 0 0.54 0.55 0.56 0.57 0.58 0.59

2.5 1.5 0.5 2.5 1.5 0.5

Nb Nb = +1 is represented in green. φ 001, (c) . – 5 – (c) (a) = 0 558. Compare with diagram of ﬁgure . = 0 v = 0, (b) v v for (a) 1 and the true vacuum 54 and (c) . − v = = 0 φ v . False vacuum in an unbounded interval: kink-antikink collision for 59, (b) . False vacuum in an unbounded interval: kink-antikink collisions. Number of bounces . 0.18 0.2 0.22 0.24 0.26 = 0 v 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 3 2 1 0 3 2 1 0

2.5 1.5 0.5 2.5 1.5 0.5

Nb Nb Figure 3 (a) the false vacuum Figure 2 versus initial velocity JHEP10(2018)192 : ) ]. + v λ 66 − K (3 (3.4) (3.5) (3.6) / is the M 3 M ) between 2 = 2 , t √ ¯ KK = 0 = 2 E x K ( ] for kink-antikink φ , M 82 kink with velocity . 4 , meaning that soon af- φ 0) + 1 0) . where X λ v, v, M √ X, − − , in a net confining effect. ) , , ρ 0 0 and a X 008. An example of such effect is x x . ) + v 0 − − X 2(∆ & x x − − ( ( K x K K ( ˙ φ φ M K t φ is the energy density difference between the = 2 − 0) + 0) + ¯ ) K – 6 – /λ K 4 , v, , v, X 558. . 0 0 E x x + ] M = 0 x + + 82 ( v = x x K ( ( antikink with velocity ρ φ K K 4 ˙ φ φ = 0. The appearing of zero order two-bounce windows was φ ≈ ) − − m 01 with x . ( 0 50 100 150 200 φ 0 1 is given by [ -1 -2

= 0 0.5 1.5 0) = 0) =

the energy of the antikink-kink pair is given by -0.5 -1.5

φ (x=0,t) X x, x, ( ( . There one can see that there is no oscillations of X ˙ φ φ 4 . False vacuum in an unbounded interval: kink-antikink collision showing a zero order is the translational collective coordinate. The total energy of the kink-antikink sys- a–c. . This means that energy favors the reduction of 3 X X ) Another interesting aspect of kink-antikink collisions with the growing of ρ = 0) two-bounce for m scatering. The antikink-kink profile is aproximated by For large values of 2(∆ The numerical procedure wasattractive the antikink-kink interaction same and used the tendency forconfinement of of kink-antikink the the false collision. antikink-kink vacuum and to its In decaycollective subsequent favor this extinction. coordinates, the case, following This can the the be same explained procedure using described above [ 3.2 False vacuum inWe take a as bounded initial interval: condition antikink-kink a collisions appearing of a two-bounce windowpresented of in zero figure order for the bounces, meaning that reported before in models with degenerate vacua in the context of boundary scattering [ tem for large values of is the classical kinktwo mass vacua. and ∆ Theter energy the scattering is the reducedfigures kink-antikink for pair separate even at larger the values velocity of of light, as confirmed in Figure 4 ( where JHEP10(2018)192 (d) (b) 001. . = 0 001 and with . 6 (lower right). . d for 5 = 0 = 0 a– v a-b. There one can 5 6 4 (lower left), (d) . the low-frequency oscillation lasts even = 0 v v ), as shown in figures , t (0 – 7 – φ (a) (c) ) of the scalar field. Blue color represents the false vacuum x, t 25 (uper right), (c) . = +1 is represented in green. = 0 φ v b). 5 . False vacuum in a bounded interval: antikink-kink collision for 1 (upper left), (b) a– . 5 1 and the true vacuum = 0 The relation between high- and low-frequency oscillations is more evident in a plot The numerical simulations show that the complete process of vacuum decay has long − v = way that does not occurs forseveral the times degenerate and vacuum, and be thefigures even antikink-kink pair more can departed bounce during such low-frequency oscillations (compare of the scalar field at the center of mass, ing in the long runSurprisingly to larger the true initial vacuum velocities state.uum are This decay. not is On showed more the in contrary, effectivemore figures with in the before inducing growing starting of the the processvacuum, decaying larger of process initial vac- of velocities the excite false the vibrational vacuum. state It of seems the that, kink with and false antikink in a duration and that thea pattern two-step process: of oscillations firstlyThen the is the field antikink-kink intrincate. pair bounces radiates around The and the output the false field of oscillates vacuum mechanism in with a is low high-frequency, frequency. approach- Figure 5 (a) The figures show slices inφ the plane ( JHEP10(2018)192 d, a 5 c– ]. Also, . Larger ]. When 5 3 83 − 86 10 × 25, corresponding 5 . 1. As an example . = 15 considered in ∼ = 0 t 0 = 0 v x v a for 6 1 and (b) . = +1. As seen in figures = 0 φ v 0 50 100 150 200 250 300 350 400 2 1 0 b. There one can see three low-frequency -1 ]. The opposite process, that is, particle

1.5 0.5

-0.5 -1.5 6 φ (x=0,t) 85 1 before the field jumps and acquires the high- – 8 – ]. Then one expects that a breather-like profile 001 with (a) − . 84 -particles with a finite binding energy [ = = 0 φ φ 25 as in figure . = 0 theory for the creation kink-antikink pairs and radiation after v 4 φ t ) as a function of time for leads to a non-recognizable pattern, meaning that the nonlinear coupling for , t a-b. (0 . False vacuum in a bounded interval: antikink-kink collision. Scalar field at the center 5 φ 0 50 100 150 200 250 300 350 400 An important issue is the possibility of oscillon formation connected to particle pro- 0 1 2 -1

0.5 1.5

-1.5 -0.5 φ (x=0,t) the scattering of smallproduction identical in wave pulses the [ wakeanalog of for the nonintegrable collidingstate theories, walls considered the needs as oscillon. a aquantized, better bound the The state extremely discussion oscillon stable of of classical is the oscillon an solution breather- has extremely its long-lived lifetime shortened due to coupling corresponds to a breatherin in the the quantized sine-Gordon breather model toresponds at lowest to order, small an the coupling integer energy [ numberis levels of a of particles, particle the leading in to quantizedcould the the breather be interpretation sine-Gordon cor- that model a the [ bridgereasoning breather was between used particle in and the soliton solutions in nonintegrable theories. This duction due to vacuumdisconnected: decay. that is, In the an kink-antikinkticle pair integrable production. scatter theory, with One the at knows most particleThirring that a and model. phase the shift kink integrable In with sine-Gordon sectors particular, no model the par- are is bound dual state to of the two massive massive Thirring fermions at strong too larger initial velocitythe would final require high-frequency a decay muchthe longer of simulations, running the the time false pattern of vacuum. ofvalues collisions simulations of For described to the here see values isantikink-kink valid collisions up to is already too large. see that, for afrequency too process already low takes initial place, velocity,for as the larger can velocities be field we see is take inoscillations not figure around even the able false to vacuum frequency bounce oscillations and that the approach the high- true vacuum Figure 6 of mass, to figures JHEP10(2018)192 ). (b) (d) B/E − ]. Once the exp( 66 ∼ = 0 (upper figures) dE/dt t t ] 89 1. . b. The emission of radiation is quanti- -3 -3 10 10 = 0 5 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000

8 7 6 5 4 3 2 1 0 8 7 6 5 4 3 2 1 0 v

-1 -1

t t

a and . The parameters chosed are t – 9 – 5 (c) (a) < dE/dt > 01 in figures ]. This means that the production of particles is connected in . , meaning an amplitude of the vibrational mode decaying as 2 87 − = 0 t ∼ c. There one can see the long-lived oscillations after the scattering . ) showing long-lived oscillations after the scattering. (Right) Corresponding 7 x, t ( -particles [ = 0), the rate of energy loss by the discrete mode, averaged over a period, φ dE/dt φ a and ] 7 . If the vibrational mode has low energy such that the second harmonic is (lower figures). In both cases we fixed 88 2 2 / 1 − − . (Left) t model ( = 10 ∼ 4 The fact that the existence of false vacuum in a limited region induces energy dissi- φ ) t ( the is given by [ A bellow the continuum threshold,oscillon radiation is is formed, emitted the by decay higher rate harmonics is [ considerably smaller, with [ pation is evident from thewith reduction time, as of shown the for maximumtatively distance explained by between the antikink coupling andcontinuum. of kink As the a vibrational result (normal)radiation of mode this with with coupling twice the in the states nonlinear of frequency theories, the of an the oscillating vibrational kink produces state. For example, for the kink of our classical setup byvacuum the in production a of bounded interval oscillons. suggestsduring the Our the tendency numerical of high-frequency simulations oscillon oscillations production forin in of the the the the false long-term figures scalar fieldfor at several the values of center of mass, as showed time-averaged energy-emission rate and the emission of Figure 7 JHEP10(2018)192 ¯ & . For 7 . For crit v = 1, we have the we have inelastic for several values t λ . For the complete 6 crit v > v 0) can show bion or two- (not present for degenerate ∗ x, < dE/dt > ( v φ = 0, energy is conserved better than 1 d present 7 = 25 mean more time for the false vacuum 0 . x 4 b and – 10 – 7 . We also verified that the radiated power grows for 01, this means better 1 part in 10 . ). Integrating the former expression in a box close to ˙ = 0, energy is conserved better than 1 part in 10 we have inelastic scattering of the pair without contact. φ 0 ∗ is acompanied with energy conservation with less precision. φ = 0 ( x . The figures t ∂ = < v < v 6= 0, energy conservation results in the following expression for the 0) presents one-bounce around the true vacuum. Larger choices of the scalar field at the center of mass dρ/dt x, ( < dE/dt > . After a transition, the decay rate is reduced considerably, but it is not : crit φ . For 0 ρ λ crit v . . The increasing of 9 crit < v < v v 01, this means better than 1 part in 10 ∗ . v It is relatively easier for a finite region in a true vacuum to expand through the false We remark that we have confirmed with very good precision, for all cases considered, . There one sees that radiation is emitted in bursts connected with the bouncings, and and = 0 ∗ to the true vacuum.kink-antikink interaction We showed favors this thevacuum formation for decay. of antikink-kink a collisions. The long-lived antikink-kinklow-frequency That bion oscillation collisions is, state around were the that the described attractive false inhibitstending in vacuum the to followed a the by true two-step a vacuum process high-frequency in oscillation with the long a run. This two-step process resembles the behavior to decay during the freev propagation of the kink-antikink pair, leading to anvacuum increasing region, of as described herevelocities, in where kink-antikink collisions. the This kink-antikinkdemands is pair considerably evident scatters more for low time at initial for non-null a distance. finite In region in comparison, false it vacuum to decay completely bounce around the true vacuum.bion In states a and diagram a inthere sequence velocities is of we the have two-bounce appearance the windowsscattering, of usual accumulating zero-order and structure around two-bounce of windows.initial For position of the kink-antikink pair up to In this work we haveantikink studied collisions the are effect characterized by of two kinkvacua) critical scattering velocities, and in the falseFor vacuum decay. Kink- For the worst case analyzed, scattering process, for the case 4 Conclusions the conservation of total energy inis the in simulation a box. limited For instance, regionfollowing when (antikink-kink results the collisions before false in vacuum the ourpart bounces: setup), in for and 10 the fixing case lower values of suppressed, being very smallfor with an an oscillon. almostfrequency constant (which Despite rate characterize the for an lowpower long-run oscillon and energies, in oscillations long as a described lifetime strictly expected oflow here way), the amplitude, the still formed suggests behavior the oscillatory have of existence state not of low approaching a the a radiated true mechanism single of vacuum with oscillon formation. energy density the scattered region and(radiated averaging power) in timeof results in the averagethat emitted the rate radiated power of grows energy with In general, even for JHEP10(2018)192 16, / ] in a 90 14, APCINTER- is the reduction of / 17, Universal-01191 / . For kink-antikink collisions we 2015-8 for financial support. This / 14, PRONEM 01852 . / crit 17, Universal-01332 v / – 11 – and ∗ v 2013. / 04434 / 17, Universal-01061 / FIS / theory with an additional potential that vanishes asymptotically. In the present 4 φ 14, COOPI-07838 / For antikink-kink collisions the center of mass belongs to the false vacuum region by the FCT grant UID study was financed inSuperior part — by Brasil (CAPES) the de — Aperfei¸coamento Coordena¸cãode — Finance Pessoal Fundo Code de Europeu 001. N´ıvel de P.P.A. workOperational Desenvolvimento was Programme Regional supported for Competitiveness by funds and FEDER through Internationalisationtuguese (POCI), the funds and through COMPETE by FCT a Por- 2020 — Ciênciae a Funda¸cãopara the Tecnologia — in project the POCI-01-0145-FEDER-031938. framework P.P.A. of also acknowledges the support provided The authors thank FAPEMAdo — Amparo Funda¸cãode Maranhão àPesquisa through e ao grants00256 Desenvolvimento PRONEX 01452 and CNPq (brazilian agency) through grant 309842 Depending on the initial velocity,step the process, route where to the sharp oscillonfield emission formation is of is folowed radiation preceded by sincronized by a to a bion the two- solution bouncings with of an theAcknowledgments almost scalar constant emission rate. We interpret that the radiation ratefrom suffered the a vibrational changing state connected of totransformation a the from transition antikink-kink of oscillational pair energy normal tomodified an modes oscillon to configuration. oscillons A waswork smooth verified such recently transformation is [ induced by the false vacuum decay and occurs nonadiabatically. decaying bouncing state,radiates followed by continuously, suggesting another a long-livedantikink-kink transition collisions, high the in frequency more the bionthe notable long maximum state effect separation run that of of to theThis the shows an increasing the antikink-kink of stronger oscillon pair tendency state.with of during the the the false field For low-frequency vacuum oscillating to fastly oscillations. decay. around The the final true state vacuum is and the radiating same, energy in a low rate. windows must be falseinvestigated since the the effect scalar of fieldhave increasing the will the increasing not gap of remain both parameter in velocities the initial state.and we We have also a complex mechanism for decay of the false vacuum: a low-frequency fast of what is known in the literature as false n-bounce-windows. 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