Boruah, K

Goswami, U D

IACS Institutional Repository

Indian J. Phys. 78 (11), 1253-1259 (2004)< U PSimulation for signature of Higgs boson in UHE cosmic ray interactions throughvacuum excitationIJ D Goswami ■ and K BoruahDepartment of Physics, Gauhati Univc|rMty, Guwahati-7S1 014, Assam. India E-mail udgoswaiiiC'^rediffmail com Received IJ Man h 200J. d(( cpted 6 September 2004Abstract ‘ We present here a new approach for signature ol Higgs Ixwon prcKiuclion in ultra high energy cosmic ray (UHE('R) interactions using ihc thermoficid theory The idea is the decay of Higgs bosons that are produced through bubble formation due to vacuum excitation in an UHE( R collision with air nuclei. We develop a model of hadronic interaction based on the GENC^ L code of the UA5 experiment of TERN and ('ORSIKA code (Karlsruhe report), incorporating a fraction of energy transfei to bubble formation by phase transition due to vacuum excitation and subsequent multiparticle prtxluction via conversion of Higgs boson to heavy fermion pairs Such events are expected to have high multiplicity and excess muons Wc compare the muon multiplicity distribution with and without this effect for different fractions of energy transfer to vacuum It has been found that ihc Higgs boson production mechanism has significant effect starting from -  lO’^ cVKeywords UHE cosmic ray interaction, Monte-Cailo simulation, Higgs boson production, hadronic interaction, vacuum excitation, bubble formation-PACS Nos. : 13 85 Tp, 14 80 Bn. 06.40 Dc1. IntroductionThe Higgs boson is the key missing ingredient of the Standard Model (SM) and is responsible for spontaneous breaking ot SU(2)  ^X U(1 )y symmetry of electroweak interactions. The quest tor its existence is one of the urgent endeavours ol the on­going and future particle physics experiment. So far, direct experimental searches for this scalar proved fruitless. The discovery of this particle is expected in the Large Hadron Collider (LHC) of CERN, v i^th experimental detection techniques guided by theoretical expectations. In this article, we explore the idea ot possible detection of Higgs signature in ultra high energy cosmic ray (UHECR) interactions with air nuclei. In IJHECR interactions, there is possibility that the vacuum becomes locally hot, bubbles are formed by phase transition, Higgs bosons are produced and decay very fast to heavy fermion pairs. This effect is manifested in a very rapid increase of the multiplicity ot charged hadrons with energy. The possibility of vacuum excitation depends on the fraction of the total energy of the collision (centre of mass energy) that goes to local vacuum excitation and bubble formation. This fraction of energy is not known.Corresponding AuthorBy considering a nonperlurbative mechanism of thermoHeld theory, Mishra e ta l\\\  have claimed that the Higgs particles are produced through vacuum excitations. This fact has been included in our present simulation model, which is based on the theoretical formalism of vacuum excitation using thermolield theory [2] followed by Higgs boson production and decay to high energy muons. The high energy muons produced at very first collision, bear signature of Higgs boson production. We therefore, incorporate this effect in the conventional hadronic cascade simulation program based on the GENCL code of UA5 experiment 13] of CERN and CORSIKA [4] code of Karlsruhe. This is our modified form of earlier mechanism [51 f(3r multiparticle production in the simulation of a cosmic ray cascade in the atmosphere due to UHE interactions. The theoretical basis of our model is described in Section 2. Section 3 is devoted to explain the structure of our model and Monte-Carlo algorithm to simulate the hadronic cascade. In the present analysis, we try to emphasize only on the concept of Higgs production by the new mechanism and for the sake of simplicity, we consider only first nuclear interaction. The interaction and decay processes in the atmosphere are simulated only for hadrons ( 7i, k, and N) and muons above 0.3 GeV, 1 GcV, 3 GeV, 10 GeV and 30 CieV. For the©20041ACS1254 V D Goswami and K Boruahproduction and decay processes of the hadrons and Higgs boson, subroutines are developed and are coupled to the cascade program in order to generate muons, to which most of the hadrons and Higgs particles finally decay. The results of the simulation are discussed in Section 4.2. Higgs boson production through vacuum excitation2,1. Temperature dependence of vacuum :Using the methodology of thermofield dynamics [2], we consider the basic idea of the temperature dependence of vacuum. In general, in the nonperturbati ve methodology of field theory, the coherent state of vacuum at zero temperature is defined as (1Jso so sowhereto is the value of = for zero temperatureThe expression for effective potential becomesA 4 A t 1 . , X 3A r , , i"’(0)whereIv«c') s: l J \v a c ) , (1)1 +2jt  ^ Jo tuU){exprv£w(x)l-l} ^where V  is a unitary operator. For complex field 0, the vacuum expectation value (VEV) is given as and{vac'\0(z)\vac') = ^ . (2)1^ 2;r^ Jo (u(af){exp [yty(jc)]-l} («)byThe expectation value of the Hamiltonian density is given(3)with co(x) = , The gap in energy density of thethermal vacuum with respect to the vacuum at zero temperature is given byA minimization of energy density with respect to ^ givesthe result ^ = -  J n r / a |  . This concept can be generalizedto finite temperature by using the methodology of thermofield dynamics [2\, The temperature dependent vacuum is given by(<))2.2. Vacuum excitation and bubble formation:I vac', )3) = L/(j8)| vac'). (4)where jS = l//t7 .I f  is effective Hamiltonian density, then energy density at temperature becomesV(^, p )  = f(/3) = (vac', j3 |r“  I vac', /?)= -(2 rer'*  f’  •' (i){k, p )  {exp [p(o(k, P ) ] - 1}23AThe possible local heating of vacuum with particle collision and dynamics of vacuum excitation and bubble formation is theoretically studied by Mishra et al [\] considering the nonperturbati ve mechanism for the production of Higgs boson  With vacuum as the medium in which collision takes place, a local destabilization of it can occur if enough energy is pumped into a microscopic volume which thermalizes locally and forms bubble having a nonzero temperature and local thermal equilibrium. The total energy of such a locally excited region or bubble can be given as(2;r)-^Jl2u){k, P) (exp [P(0(k, P)] - 1}. A c4 c24 ^  2 ^ ’,1/2dkEj, = j  [^(f)] d r , (10)(5)where [)3(r)] is the gap in energy density of the thermal vacuum with respect to the vacuum at zero temperature, given bywhere £u(A,/3) = + nj;/(/3)^j , with ntffiP) being theHiggs boson mass at temperature 1/ p .For numerical evaluation it is useful to rewrite eq. (5) in terms of the dimensionless quantities with substitutions:Ae[p(r)] = ^ t 1^1 (2min. ><'■))+ 74 (11)with e o = (w w /A ) being the field expectation value corresponding to the minimum potential V, (zmin •K '')) givenSimulation for signature o f Higgs boson in UHE cosmic ray interactions etc 1255in eq. (6). V^  and p  = l/kT  are now spatially dependent. The number of Higgs boson inside the bubble is given by'•h = J  ^[^('■)] (fr. (12)where N{p) is the number density of the Higgs particle at temperature p  and is given by(13)with co(k, p) being the Higgs boson mass.;The temperature distribution inside the bubble is taken as '= T {r)^  Tq t x p ( - a r ) , (14)where is the temperature at the centre of the bubble and the parameter a decides the region over which the vacuum is excited, with bubble volume approximately .3. The model,IJ. The structure:Considering the nonperturbative methodology of thermoficid theory, we develop a model of hadronic interaction in the light of possibility of Higgs boson production through vacuum excitation due to fraction of energy transfer to the vacuum during UHECR interactions. Fraction ol centre of mass energy (V^) that goes to bubble is unknown [ 1 J. For definiteness, we consider various fraction of ^  that goes tc» hi/bble formation a s = 0.0, 0.01,0.02,0.5.The gap in energy density of thermal vacuum with respect to the vacuum at zero temperature p  and number density of Higgs boson at different temperature is calculated using eqs.(11) and (13) for the simulated mass of Higgs boson for different central temperatures Assuming a given primary energy of proton (£^= 10^^- 10*^  eV) and a given fraction (/'^  = 0,0~0.5) of the energy transfer for vacuum excitation and bubble formation, first, bubble energy is calculated foreach event. Then the volume of the bubble or the excited region for each event is calculated /A s ) . Finally, the mean number of Higgs boson is evaluated for corresponding bubble volume. We parametrize approximately the relation between average number of Higgs bosons < with bubble energy E .^ We have used these equations in our simulation program to calculate average number of Higgs boson for a particular event and primary energy of proton. The actual number (Nf )^ for a particular event and primary energy is chosert from a Poisson distribution with this mean.In the energy range J s  ^ ^50 -  500 GeV, the linear Collider (LC) has provided that Higgs boson mass to be lies in the range= 2(X) GeV. The dominant production mechanism for such a light Higgs bo.son is e'*^ e“ hZ, with the largest decay channel being bb or WW* (6, 7j. Indirect evidence from precision measurements at eV'' colliders suggest the existence of a light Higgs boson in the mass range of 95 ~ 235 GeV at 95% confidence level with a statistical preference towards the lower end 18]. Direct experimental searches at the CHRN Large Electron Positron Collider (LEP) place the mass of a SM like Higgs state, with a significant decay branching ratio into bottom (b) quarks, approximately above 115 GeV. An alternative analysis based only on the assumption of Higgs boson, decay into hadronic jets, without b-tagging leads to a bound of about 113 GeV [7]. Following all these arguments for Higgs boson mass, we have used the following decay channels of the Higgs boson for our model to develop subroutines which are incorporated with the main cascade program to illustrate the idea of Higgs production through vacuum excitation 15,9):(i) < H  b b i-^  90%), t "t * (*^  10%),(ii) rwj,, < ni^ < m,, //   ^ />/?(- 85%), (~ 10%;),CT(- 4%),(iii) bb(-^ 80%~ 1% ),W W * i-0,0] % -  97%0, ZZ*(- 0% -  10%>),(IV) 2/n ,^ < niff < 2m ,, H WW(- 94% --100%;),(v) niff > 2m ,, H -> WW{- 75%>), ZZ(- 25%).The WW and ZZ channels further decay to electrons, muons and neutrinos according to W ev, pv or Z e^e“, bhchannel either directly decays to muons or electrons (10%;) orindirectly via intermediate states r ^ r ~ e t c .  e'e channel also either directly decay to muons or electrons (-  6%;) or indirectly via various intermediate states [lOJ. The decay modes arc decided by individual channels:18%), 17%), h^vv{^52%).We have calculated the muon multiplicity by considering only the various decay channels leading to muons. In the hadron-air interaction model, the particles arc produced in clusters according to recent theoretical f i l l  and experimental [31 considerations. In our present simulation for ultra high energy cosmic ray interactions, wc consider only non-diffracti ve (ND) events (actually non-single diffractive), where particle produced in a central region, flat in rapidity, and in two fragmentation regions. Here, an event is built up of two leading and a varying number of central clusters. Each cluster is given a transverse momentum and rapidity y. After transforming the rapidities to conserve energy and momentum, the clusters arc made to decay isotropically.1256 U D Goswami and K Boruah3,2, Monte-Carlo algorithm :The Montc-Carlo simulation program is written following the algorithm of the GENCL code developed at CERN» by the UA5 collaboration* including the effect of nuclear target mass, as follows:(i) The number of charged hadrons is chosen from a negative-binomial (NB) distribution:) -  777— 777with the following parameters := -7.0 + 7.25.?“ '^’ , andi r '  = -0 .104+  0.058 In (77), where j  is in GeV^.11 + («ca}A(15)(16)(17)(ii) Cluster formation and decay is the basic multiparticle production mechanism. Out of six different clusters, we consider only three, viz, pion, kaon and the leading cluster, excluding the less frequent nucleon, hyperon and Xi pairs. The nature of the leading particles (p or n) is chosen considering the charge exchange probability as given in [31.(iii) Number of kaons produced is grouped into pairs (cluster) of zero strangeness including neutral kaon and kaon resonances pairs [3, 12J. All pairs have same prcxluction probability and each kaon is a with 60% probability, according to CERN intersecting storage rings (ISR) measurements [13]. The actual number of kaon clusters is drawn from a Poisson distribution with a mean deduced from the k/n  ratio.A  = 0.024 + 0.0062 ln (i) . The decay into kn pairs as follows:it** 1-(18)(19)(20)it® 's (and it°'s) are considered to be )t® or it® with equal probability, All P s ,  and pions finally decay to muons and electrons and their decay are governed by standard branching ratio.(iv) Remaining charged particles are n* and n ~, which arc grouped into clusters including ^^o's. The algorithm is based on drawing the number of charged pions from a Poisson distributionwith an average of 1.8, repeatedly until there are no charged particle left and then drawing rr®'s from an independent Poisson di.stribution with the following parameter [3]= [0-5(2+ 1.03n,^)-0.4/t^]//i,., (21)where /(I + R* )]«^/,/,«,./,/ being the number of chargedparticles left to be simulated, and n^ , is the number of pion clusters.(v) All clusters made up of more than one particle are given some excitation energy in terms of an additional mass. For the kaon clusters, the excitation energy follows the distributiondnexp~2£(22)where is a free parameter having the value 0,75 GeV for kaon clusters. The pion clusters are given masses ni from the following distributiond m= 1.1 [l + A?o(0.0-2)]exp (23)where n„ is the number of pions in the cluster and (0,0.2) is a number drawn from a Gaussian distribution with mean 0 and standard deviation 0.2 GeV.(vi) Transverse momenta and longitudinal momenta are given to the clusters in two steps. The transverse momenta are randomized from either an exponential distributiondNdPn7 ° ' exp {-bPr), (24)or from an inverse power-law distribution d NdPr (Pr + PoT(25)where b=60eVlc, Ro=3GeV/c, a  = 3+  l/l0.01 + 0.0111n(5)l. For thesingle pions (-10% of all clusters), is always sampledfrom the exponential distribution. In other cases, the relative amount of the two distributions is made to depend on the multiplicity of the event. For proton-air interactions, these distributions are multiplied by the parameterR (P^) = 0.0363 Pj.-  ^0.057 for Pr < 4.52 GeV/c. (26)The azimuthal angles of the leading nucleons and of the mesons clusters are chosen randomly between 0 and 2n- To conserve momenta in the XK-plane perpendicular to the beam axis (Z-direction), we make two independent linear translations in the components of^  paid / = ;c,y. (27)Simulation for signature o f Higgs boson in UHE cosmic ray interactions etc 1257where the summEtion is over the N clusters in the event. Here is generated independent of rapidity. Longitudinal momentum IS given to a cluster by assigning to it rapidity v,= m-r sinh (y), (28)where m-j- = + P f ) is the transverse mass. Rapiditydistribution has a central plateau and a fall-off at higher values of |y |, and can be described analytically by two Gaussian peaks114], with the following parameters [15]:and.V, =0.146 In (£  )-!-0.164,CT, =0.120 In (£ ,,) +0.255.(29)(30)Box-Muller method is used to generate the rapidities and the two leading clusters are given the highest and lowest rapidities. They are converted to longitudinal momenta P^  and so adjusted as to conserve total momentum and energy, after assigning a fraction <k> (inelasticity parameter- 0.5) of available energy to leading nucleons.(vii) Each cluster with given energy is made to decay via the available channels with a probability proportional to theirrespective branching ratios. The numbers of muons above threshold energy 0.3 GeV, I GeV, 3 GeV, 10 GcV and 30 GeV arc counted for each event.4. Results and discussionWe have presented a simple model tor Higgs boson production in UHECR interactions and the Monie-Carlo simulation program based on this model following the algorithm of the GRNCL code developed at CFiRN, by UA5 collaboration |3J and using some features ot the CORSIKA code of Karlsruhe 14]. Here, we have basically tried to manifest the idea of new mechanism of Higgs particle production in UHECR interactions due to vacuum excitation. For the sake ot simplicity, we have prepared our simulation program for first interaction only. We run this program for primary energies = 10*^  ^-  1O**" cV and different fractions of energy transfer to bubble formation^ (0.0-~ 0.5). The resulting muon multiplicity distribution for 1000 showers for different E  ^andy^ are compared with corresponding simulations with = 0. In order to derive signature of Higgs boson production, muon multiplicity distribution for muon energy thresholds of 0.3 GeV,1 GcV, 3 GcV, 10 GcV and 30 GeV are selected as the probe. Results are summarized in Figures 1-7. It is seen that the HiggsFigure 1, Muon multiplicity di.stribulion al first interaction level for 1000 showers with primary energy of 10** eV for different fraction of energy transfer. 'A' represents 0.3 GeV and 'B' represents 30 GeV muon threshold energies.Figure 2. Muon multiplicity distribution at first interaction level for 1000 showers with primary energy of 10*’ eV for different fraction of energy transfer. ’A' represents 0.3 GcV and ’B’ represents 30 GeV muon threshold energies.

Simulation for Signature of Higgs Boson in UHE Cosmic Ray Interactions Through Vacuum Excitation

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Simulation for Signature of Higgs Boson in UHE Cosmic Ray Interactions Through Vacuum Excitation

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