Scientific program

Scientific_program.pdf

Objectives

The main objective of high energy physics is to unravel the nature of fundamental particles and their interactions. For this, precise comparisons of theoretical predictions to experimental results are necessary. The next energy frontier, the TeV scale is starting to being probed at the Tevatron collider. In a few years experiments at the CERN Large Hadron Collider (LHC) as well as at the planned future linear colliders will provide lots of new information about the physics at this energy scale. One will be able to test even further the standard model and in particular to probe the yet unknown scalar sector. One will get clues about the symmetry breaking mechanism and eventually find signals for new physics, in the form of supersymmetry, extra dimensions or any other unexpected signal.

Theoretical predictions for physical observables in the framework of the standard model are based on the computation of Feynman diagrams, a perturbative approach for calculations of high energy processes. Although the method is well standardized, the actual computation of processes involving many particles in the final states or higher order calculations of simple processes become rapidly cumbersome and lengthy. The task of computing the large number of processes that could constitute the signals for new physics or the standard model processes that appear as backgrounds to these processes require the use of advanced computational techniques. To this end, a vast research program was undertaken at many institutions around the world for automating as much as possible the computation of high energy processes [l]. The two leading teams in that field are the Japanese GRACE collaboration and the Russian CompHEP collaboration which have both developed independently a software for automatic calculations of Feynman diagrams at tree-level [2, 3].

As one reaches the TeV scale, the use of software packages for computation of high- energy processes become even more relevant. On the one hand, multiparticle processes, particularly those involving Quantum ChromoDynamics (QCD) , will play an important role. For example at the future LHC, the production of four, and even five or six jets will not be marginal. Beside providing a refined probe of the dynamics of color, such QCD processes constitute a background to the search for new particles. Indeed, the search for many of these new particles at hadronic colliders often relies on signatures based on cascade decays. The latter end up with final states involving a large jet multiplicity. On the other hand, the exploitation of precision measurements aimed at TeV hadronic colliders requires the account of higher-order, especially QCD, corrections in standard and beyond standard model predictions. Higher-order electroweak corrections become also relevant especially for the high luminosity electron-positron machines that are currently under discussion. The main physics objectives of the present proposal concern phenomenological studies within the Standard model and its extensions both at colliders (Tevatron, LHC and linear collider) and in astro-particle experiments, in particular :

• probing the symmetry breaking mechanism via the study of Higgs bosons in the standard model or its extensions, or studies of self-interactions of gauge bosons;

• phenomenology of new particles within supersymmetric models (minimal or non-minimal) or within models with extra-dimensions;

• calculation of non-leading corrections for precise comparison of theoretical results with experimental data, in particular higher order electroweak and QCD corrections;

• interplay between collider studies and astroparticle searches for dark matter as a probe of supersymmetric models.

In order to reach these physics objectives, progress in development of software for automatic calculation will be pursued, new methods and new programs will be created in particular concerning :

• The automatic calculations of Feynman diagrams within the standard model and its extensions ;
• The interface between the automatic calculation programs and standard software for high-energy physics (PYTHIA, HERWIG)
• The interface between the theoretical models, the matrix element automatic calculation and the simulation package ;
• The event generators for hadronic colliders and linear colliders ;
• The development of programs to evaluate automatically multi-loop integrals ;
• The inclusion in a systematic way of the dominant higher order corrections ;
• The development of specific software for astro-particle experiments.

Background and current status

To tackle the physics issues that are at the center of the physics program of the TeV scale colliders, that is understanding the symmetry breaking mechanism namely search for the Higgs and searches for the New Physics, one needs to be able to perform both accurate predictions of standard model contributions as well as precise predictions within the context of new theoretical models. To achieve this goal, the French, Japanese and Russian teams have been collaborating for many years towards the development of automatic computations of both tree-level and one-loop processes and their application for collider physics. This collaboration took part within the framework of a “Programme International de Cooperation Scientifique” (PICS) and has been extremely successful in performing physics studies and providing event generators for data analyses at the LEP and HERA colliders [4, 5, 6, 7, 8, 9 ,10] as well as studying physics prospects at future colliders [11, 12, 13]. The collaboration needs to be extended focusing mainly on pursuing physics studies for the large hadron colliders as well as for high luminosity linear colliders and astroparticle experiments.

To reach our objectives, it is essential to bring together a group of theoreticians, experimentalists as well as specialists of software development for high-energy physics. Indeed, one of the strengths of this collaboration is that it includes the two teams that have developed independently a software package for automatic calculations of Feynman diagrams, CompHEP[3]and GRACE[2]. The two teams have followed a very different approach. CompHEP relies on the trace technique for evaluation of matrix elements and is basically a tree-level program while GRACE is based on the helicity method and aims at a systematic, automated computation of loop corrections [l4]. The complete independence of the two approaches is a desirable feature and this collaboration will pursue in that direction. Indeed one of the difficulties in performing these complex computations is to ensure the correctness of the numerical results obtained. Having completely independent checks of a given calculation certainly helps having confidence in the results.

While the development of specific tools for hadron colliders has already started [15] and event generators for given processes are available [16, 17], the collaboration will strive for a fully automatic approach to computation of processes starting from a given model (Standard model or beyond) all the way to the complete simulation of events in a detector. At the same time, the high precision that can be reached at colliders motivates taking into account higher order effects. GRACE has recently completed a full one-loop electroweak computation [18], and will continue to strive for automated higher order loop level calculations. The CompHEP approach to loop corrections is directed towards the incorporation of large effects in selected processes.

Beside the phenomenological studies of high energy physics at colliders which motivated their development initially, these computing tools start to be applied successfully in a new direction, namely astroparticle physics. In the last year, a French-Russian group (micrOMEGAs collaboration) has developed software based on CompHEP for the calculation of the relic density of dark matter in supersymmetric models [19]. Important constraints on supersymmetric models can be obtained from dark matter searches so these experiments are complementary to the ones performed at colliders searching for signals of supersymmetric extensions of the standard model. The development of this specific software for astroparticle experiments is underway.

Research programme

The physical issues to be tackled drive the planned developments of software and the progresses towards either goal are intimately interwoven in practice. For sake of synthesis, in this proposal the technical issues which the collaboration intends to address regarding the developments of automated calculations will be presented first. Then, a selection of physically relevant items, whose studies require or benefit from the use of automated calculations, and which the collaboration wishes to study, will be discussed.

1. Developing automated calculations further

The effort on development will be in two directions: the upgrade of tree-level calculations and their applications and the treatment of loop-corrections.

1.1. Tree-level computation in the standard model and its extensions.

The two codes for automatic calculation, GRACE and CompHEP, developed by this collaboration are in the public domain and have proven to be very powerful tools for computation of processes at high energies both for standard processes [20] as well as for study of new physics, particularly supersymmetry [21]. The system developed for tree-level processes in the standard model can in principle treat any number of external particles [22, 20]. In practice however, the calculations are very involved and results have been obtained for up to 6 fermions in the final state [23]. In the near future, the main developments for the tree-level automatic systems concern the standard model extensions as well as the construction of event generators for specific processes at colliders. There is also one feature that will be improved in the 1CompHEP package: the treatment of polarization [24].

1.1.1. Physics beyond the standard model.

To define the supersymmetric model, the LanHEP software has been developed for CompHEP. It allows extracting the Feynman rules necessary to the computation of physical processes starting from a given Lagrangian [25]. Similar software is currently under development by the GRACE collaboration. Within this framework, it is a rather simple task to introduce new models in the automatic programs, thus taking one more step towards the complete automation of the computation starting directly from the model parameters to a signal in a collider. The input parameters of the supersymmetric models are by default those relevant for the study of processes at the TeV scale. However it is often more interesting to start from a model defined at the unification scale. The fundamental parameters of the model at the high scale are related to the ones at the scale relevant for collider studies by the renormalization group equations. Sophisticated programs to do this evolution exist, including those developed by the Montpellier group Suspect[26]. These programs will be included within the packages, thus providing the tools for phenomenological studies of different supersymmetric models at colliders or in astroparticle physics. Among these we can mention supergravity models (SUGRA) [27], anomaly-mediated (AMSB) or gauge-mediated symmetry breaking (GMSB) models. The same approach can be applied to other extensions of the standard model as well. In the near future, the following issues will be tackled :

• parameter management in the MSSM: relating parameters at the electroweak scale to those at the high scale, facilities to switch from different sets of input parameters (from masses to soft parameters) [26, 28];
• development of symbolic system to derive Feynman rules automatically for a given model (GRACE) [29];
• implementing new models in GRACE and 1CompHEP (R-parity violation, extra-dimensions, non-minimal supersymmetry models) [30, 31, 32, 33];

1.1.2. Treatment of polarization

Full polarization information both in production and decays is desirable in automated calculations, as it can lead to many distinctive signals both for standard as well as non standard model processes. As mentioned above, GRACE is based on the helicity method which allows to keep all the information on the polarization. On the other hand, in the CompHEP package, it is only possible to account for the initial state polarization at the moment [24]. The procedure to do so needs to be simplified. In the longer term, full helicity amplitudes will be implemented.

1.2. One-loop processes in the SM and its extensions

1.2.1. NLO calculations in QCD

For QCD processes, tree-level results alone are generally of little use because of their strong dependence on the renormalization scale. In order to provide quantitative estimates, the QCD processes have to be computed at least to the Next-to-Leading Order (NLO) accuracy, which involves the computation of one loop contributions. The ingredients to achieve a computation at NLO accuracy of a QCD process involving N external legs are:

1. the one loop correction to the N-leg partonic subprocesses,

2. the tree level N+1-leg partonic subprocesses,

3. an efficient method to merge the real and virtual contributions and cancel the infra-red singularities,

4. a parton shower generator at Next-to-Leading Logarithmic (NLL) accuracy

An extended effort has been devoted to deal with items 2 and 3 already, whereas a substantial progress would still be welcome regarding items 1 and 4. A new general algorithm for the recursive computation of one-loop tensor integrals has been recently developed by the LAPTH team [34] and applied to the calculation of the one-loop, six-leg scalar amplitude [35]. In order to tackle item 1 in the case of external leg with non-zero spins, the application of this algorithm has to be improved in order to circumvent the proliferation of terms coming from the tensor reduction. The Japanese team is addressing item 4 with the development of a NLL parton shower. Bringing together these expertises will allow to complete this program from 1) to 4) and apply it to the study of processes of particular physical interest.

Among the large numbers of relevant QCD processes, the associated production of a boson vector pair plus a jet (P+P→γ+γ+jet, Z+Z+jet, W++W-+jet) is of great importance for the Higgs boson search. Partial results are known already for photon pairs but not for massive vector boson pairs. An even more ambitious project would be the four-jet production at NLO accuracy. Phenomenological counterparts of these calculations are discussed in section 2.1.3.

1.2.2. Electroweak processes at one-loop

Because of the outstanding length and complexity of these calculations, one of the major difficulties that authors of these codes have to face is to make sure of the correctness of the results. Gauge invariance is a powerful tool to perform such tests. The LAPTH group had suggested a few years ago to use the non linear gauge fixing to perform further tests of gauge invariance [36]. Since, the non-linear gauge has been introduced in GRACE [37]. Recently, tests on the most complicated 2→2 processes in the standard model were completed and the independence on the choice of the non-linear gauge parameters has been numerically checked to a high level of accuracy. Results on e+e-→t that were obtained many years ago by the GRACE collaboration were confirmed only in the last year by two different groups [38]. More recently, the GRACE collaboration has succeeded in performing a full one-loop calculation of a 2→3 electroweak process (e+e-→vvh) [18, 39]. This is the first time such a calculation is performed. The non-linear gauge fixing has allowed to detect and to correct many bugs in the structure of the loop integration part of the package. The GRACE package can now be used for one-loop calculation of standard processes in particular those involving the Higgs boson or gauge bosons in e+e- colliders.

The GRACE collaboration has started as well to tackle the problem of one loop calculations for 2→4 processes. Although in principle the same formalism that has been used for 2→2 or 2→3 processes can be applied here, the complexity of the problem (thousands of loop diagrams) makes it necessary to improve the method used in order to greatly reduce the size of computations, so that they can be done on a realistic time scale. In the present version part of the loop calculation is done with symbolic manipulation programs such as REDUCE [40] and FORM [41]. The matrix elements thus computed are huge and one quickly reaches the limit of the computer as one tries to go beyond processes with three particles in the final state. The collaboration considers that a completely numerical approach to 3 and 4 points loop integrals will in the end be necessary to complete the program of computing 2→4 processes in the standard model.

Finally, the GRACE collaboration has also developed a program to calculate any one-loop processes in the MSSM, being thus the only program able to achieve this. However, before releasing the program on a wide scale, one needs to ensure the correctness of the results. The package for loop integrals has been extensively tested in the standard model case and the vertices of the supersymmetric models have also been tested in nearly half a million tree-level processes. Nevertheless, the French and Japanese teams consider it necessary to implement the non-linear gauge fixing in the MSSM, just as was done for the standard model.

1.2.3. Leading QCD and/or EW one-loop corrections

Present-day automated computations that perform calculations in the Born approximation are so conceived as to involve only tree-level parameters and vertices. However these lowest order ingredients are insufficient for quantitative estimates when the sought accuracy is sharper than the size of the contributions from higher orders in perturbation theory.

One such typical case happens when a quantity gets a contribution from a new mechanism appearing at a loop order. In this case, part of the higher order contributions which are known to be large can be accounted for in terms of effective parameters and vertices, thus allowing providing “improved tree-level calculations”. A notable example is the Higgs boson mass in supersymmetric models. Its tree-level contribution is bound to be much below the present direct experimental limit. Yet this mass receives large contributions from SUSY breaking loop effects in the top quark and squark sector, which are known at two- loops already [42]. Another typical example is the QCD corrections to the Higgs width or QCD corrections to Higgs production [43, 44]. Even in a tree-level calculation one then has to device ways to incorporate these higher order effects. In one specific case, an effective potential for the scalar sector of a two-Higgs model has been written [45]. The higher order corrections to the potential can be parameterized with just a handful of parameters thus taking into account higher order effects in tree-level calculations.

One of the main goals of the CompHEP collaboration in the near future is to incorporate the leading one-loop corrections by defining effective vertices for specific interactions. Note that this requires a major rewriting of the symbolic manipulation part of CompHEP. The association of the French experts of higher-order corrections with the Russian experts of automated calculations will be essential to the successful completion of this project.

2. Studying particle physics issues with automated calculations

2. 1. Collider physics

2.1.1. Event generators and simulations

For the specific physics studies that can be done at colliders the automatic programs that calculate the tree-level amplitude for some hard processs have to be linked to programs for parton showering, hadronization as well as detector simulations. In this way, the theoretical prediction for a process including the full simulation of events produced in the detector can be directly compared to actual data sets. Within GRACE and CompHEP efforts are being made to automate this procedure. The general framework is to use the automatic program to calculate all the processes leading to a given final state. All parton-level event information is then passed to general event generators such as PYTHIA[46] or HERWIG [47],all initial and final-state radiation, hadronization and decays are taken care of by the general event generators in order to make the generated events realistic [48, 49]. There has been intensive work along those lines from the CompHEP group in close collaboration with experimental teams at LHC and Tevatron. In the last year, an extended framework was developed by GRACE The framework (called GRQPPA) whose main function is to determine the initial-state partons using a parton distribution function (PDF) is not process specific and can be applied to any processes in hadron collisions [16]. So far an event generator for 4 botton quarks production in hadronic colliders has been developed. This is useful for studies of Higgs boson productions, especially within the context of supersymmetric models with enhanced scalar couplings to b-quarks.

In the next few years this collaboration will work on the following items:

• event data standardization following the Les Houches accord [50];
• event generators for hadronic colliders for simulation of gauge bosons, Higgs, super-symmetric particle production at Tevatron and LHC including both signal and back-ground;
• event generators for simulation of Higgs and/or new physics at the linear collider [11, 12];
• real simulations for LHC and Tevatron;
• creation of a database of processes at LHC and Fermilab.

2.1.2. Physics studies in the Standard Model and beyond

GRACE and CompHEP have been used intensively for physics studies and although improvements are currently being made along the lines describe above they are fully operational [3,2, 51]. At tree-level the list of processes that can be studied is very long, here we mention briefly some topics that are of interest to the members of this collaboration[52, 53, 54]. Those are relevant for collider studies either in the context of the standard model or as search of new physics especially pertaining to the Higgs sector and to supersymmetry and will be done including event generator analyses which takes into account the signals and the various backgrounds:

• electroweak processes with multi particle final states, e+e-→6 fermions, which are relevant for top or gauge bosons couplings studies;
• production and decays in supersymmetric models at LHC and linear colliders [55, 56];
• measurements of the Higgs self-couplings [45, 57];
• the intense Higgs coupling [58];
• phenomenology of extra dimension models [59, 32];
• phenomenological studies of non-minimal supersymmetry: non-universality in SUGRA models, R-parity violating models, next-to-minimal supersymmetric model [30, 60, 27].

As concerns the full one-loop electroweak processes, as was already mentioned, the first results of a full one-loop electroweak 2→2 process were obtained by this collaboration. After this success, we can now pursue the study of many other processes relevant for linear colliders. The high precision of the measurements that will be performed at these high-luminosity machines makes it necessary to make higher-order theoretical predictions. Among various processes we mention, e+e→t h, a process that is sensitive to the Higgs-top quark coupling or e+e-→WWγ which is a sensitive probe of the self-couplings of gauge bosons (couplings of vector bosons). The probing of these couplings is relevant for our understanding of the symmetry breaking mechanism.

2.1.3. Multi-particle QCD processes and Higgs background

The associated production of two photons plus jets is an example of a physical process where the QCD background to an electroweak signal plays a crucial role. If the Higgs boson mass is less than 140 GeV, the H→γγ channel is promising to search for the Higgs boson. Unfortunately, in this channel, the QCD background is severe. As shown by the Russian team [61], the ratio of signal S over background B turns out to be higher in the associated production of two photons plus a high pT jet, than in the inclusive case, with the same significance . This comes from the fact that, for the signal, the angular distance between the two photons tends to be small (the two photons are the products of the decay of the transversally boosted Higgs boson) whereas for the background the configurations of photon pairs are nearly spread in the whole phase space. Up to now the study of two photons plus jet production of [61] relies on a Lowest Order (LO) calculation. Beyond this, the NLO contribution coming from the one-loop corrections to gg→gγγ, which are supposed to be dominant, has been computed. Yet a complete calculation at NLO is desirable in order to get estimates of signal and background with the same accuracy and to confirm at the NLO accuracy the conclusions drawn from the LO study. This would allow t o optimize the selection cuts t o be applied to Higgs candidates and hopefully make the eventual discovery of the Higgs boson easier in the channel considered. The French team has a long time expertise in the physics of photon pair production, and developped a NLO computer code dedicated to diphoton production, DIPHOX [62]. The CompHEP collaboration has already computed the two photons plus jet process at LO and studied the experimental implication. A collaboration of these teams using the program presented in the previous section could successfully tackle this question. '

2.2. Astro-particle physics and micrOMEGAs

Supersymmetric theories with R-parity conservation have a cold dark matter (CDM) can didate, the lightest supersymmetric particle (LSP), generally assumed to be the lightest neutralino. As the predictions for relic density vary by many orders of magnitude over the allowed MSSM parameter space the relic density measurements impose strong constraints on the models. To be able to make precise predictions, one needs to be able to treat the case of coannihilation and annihilation through s-channel poles very carefully. Coannihilation occurs when the LSP interacts with slightly heavier SUSY particles and can reduce significantly the prediction of the relic density from the main annihilation channels [64]. It is then necessary to include all processes involving a pair of supersymmetric particles annihilating into two standard model particles. It is obviously interesting to use an automatic program such as CompHEP for this purpose. The program micrOMEGAs based on CompHEP for the calculation of all cross-sections was developed to calculate the relic density in the MSSM [19]. The relic density however is not the only relevant quantity and an intense effort is being made to search directly or indirectly for this dark matter candidate, with roughly a dozen experiments running or being planned. The direct searches involve looking for a signal coming from the interaction of the LSP with the quarks in the nucleis of the detector. The indirect searches involve measuring the positron spectrum, the photon spectrum or the proton spectrum coming from the annihilation of the LSP in the galactic halos. In order to study the potential of indirect searches experiments, such as AMS [63], to probe the parameter space of supersymmetric models, micrOMEGAs needs to be upgraded. The parton-level cross-sections relevant for the indirect searches are already included with the exception of the loop-process involving two photons. Adding this new process and inter- facing micrOMEGAs to standard programs of parton showering, such as PYTHIA, in order to predict the spectrum of photons, positrons or antiprotons caracteristic of a given super-symmetric model are among the goals of this collaboration. To study the physics potential of dark matter searches to probe supersymmetric models, micrOMEGAs will be developed to include :

• routines relevant for direct and indirect detection of dark matter;
• interface to codes to calculate the parameters at the weak scale from the unification scale (studies of mSUGRA, AMSB, string models) [26, 65];
• models other than the MSSM [30];
• dominant higher-order corrections [43, 66, 67].

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-- DenisPerretGallix - 15 Apr 2005