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Dark Matter Production at LHC from Black Hole Remnants

We study dark matter production at CERN LHC from black hole remnants (BHR). We find that the typical mass of these BHR at LHC is ~ 5-10 TeV which is heavier than other dark matter candidates such as: axion, axino, neutralino etc. We propose the detection of this dark matter via single jet production in the process pp ->jet +BHR(dark matter) at CERN LHC. We find that for zero impact parameter partonic collisions, the monojet cross section is not negligible in comparison to the standard model background and is much higher than the other dark matter scenarios studied so far. We also find that d\sigma/dp_T of jet production in this process increases as p_T increases, whereas in all other dark matter scenarios the d\sigma/dp_T decreases at CERN LHC. This may provide an useful signature for dark matter detection at LHC. However, we find that when the impact parameter dependent effect of inelasticity is included, the monojet cross section from the above process becomes much smaller than the standard model background and may not be detectable at LHC.

By now it is confirmed that dark matter exists and it consists of a large fraction of the energy density of the universe (∼ 25 percent) [1] while dark energy consists of ∼ 70 percent.
The energy density of the non-baryonic dark matter in the universe is known to be [2] Ω DM h 2 = 0.112 ± 0.009 (1) where Ω DM is the energy density in units of the critical density and h ∼ 0.71 is the normalized Hubble parameter. Since the visible matter consists of only ∼ 5 percent of the matter of the universe, the laws of physics or laws of gravity as we know today may not be sufficient to explain the dark matter and dark energy content of the universe.
One of the challenge we face today is to identify the non-baryonic weakly interacting massive particle (WIMP) or WIMP-like particle which consists of dark matter [3]. Identification of this WIMP or WIMP-like dark matter candidate is one of the outstanding questions in basic science today. At present the possible proposals include: axion, axino, neutralino, gravitino and black hole remnants etc. [4]. Black hole remnants as a source of dark matter is studied in various inflation models in [4,5,6]. These black hole remnants are from black holes which were produced due to the density perturbations in the early universe during inflation.
An exciting possibility is that black hole remnants (BHR) that make up some or all of dark matter may be produced at high energy colliders such as large hadron colliders (LHC) at CERN. Such prospects are particularly promising because both ATLAS and CMS detectors at LHC will search for black holes. In this paper we study dark matter production from black hole remnants at CERN LHC.
The Schwarzschild radius of d (= n + 4) dimensional black hole is given by where M BH is the black hole mass and M P is the Planck mass ∼ TeV at LHC [7]. The Hawking temperature of the black hole becomes Once black hole is produced at LHC it will emit particles due to Hawking radiation [8].
However, in the absence of a theory of quantum gravity it is not clear what happens to black hole radiation when its mass approaches Planck mass. It is commonly believed that quantum gravity implies the existence of a minimum length [9] which leads to a modification of the quantum mechanical uncertainty principle where L P is the Planck length and α ′ is a dimensionless constant ∼ 1 which depends on the details of the quantum gravity theory. The generalized uncertainty principle (GUP), equation (4), can be derived in the context of non-commutative quantum mechanics [10], string theory [11] or from minimum length considerations [12].
If we implement GUP and demand that the position uncertainty ∆x of the produced particle from the black hole is of the order of Schwarzschild radius, then the modified temperature of the black hole becomes [6,13] T The black hole temperature is undefined for M BH < M min where Black holes with mass less than M min do not exist, since their horizon radius would fall below the minimum allowed length. Hence Hawking evaporation must stop once the black hole mass reaches M min . This creates a black hole remnant of mass M min which is of ∼ TeV at LHC. Since this black hole remnant is weakly interacting and heavy, it is a possible candidate for dark matter at LHC [5,6].
Since the dark matter is weakly interacting it can not be directly detected at LHC. For this purpose we will study dark matter production from black hole remnants (BHR) at LHC in the process pp → jet + BHR(dark matter). We propose indirect detection of dark matter via single jet measurement in the above process pp → jet + BHR(dark matter) at LHC. The emission rate for jet production with momentum/energy E = | p| from a black hole, which becomes a black hole remnant of mass M min after time t f , is given by where σ s is the d−dimensional grey body factor [14], T BHR is the GUP implemented black hole temperature as given by eq. (5), t f is the decay time [13] and c s is the multiplicity factor. ± is for quark and gluon jets respectively.
This result in Eq. (7) is for jet production from a single black hole of temperature T BHR (with a black hole remnant of mass M min ). To obtain total jet cross section from this process we need to multiply the number of jets produced from a single black hole with the total black hole production cross section in pp collisions at LHC.
The black hole production cross section in pp collisions at √ s= 14 TeV at LHC is given by [8], In this expressionσ ab→BH (ŝ) = πR 2 BH is the black hole production cross section in partonic collisions at zero impact parameter, x i (x j ) is the longitudinal momentum fraction of the parton inside the proton at LHC and BH . We use Q = 1 R BH as the factorization scale at which the parton distribution functions are measured. ij represents the sum over all partonic contributions where i, j = q,q, g.
The above formula, eq. (8), is valid for zero impact parameter partonic collisions. To include the impact parameter dependent effect of inelasticity, we adopt the impact parameter b weighted average of the inelasticity used in [15] σ pp→BH where z = b/b max . The partonic level cross section is given by [16] σ where The inelasticity parameter y(z) and the cross section correction factor F (n) are taken from [17]. We use the factorization scale Q = 1 R S at which the parton distribution functions are measured. x min = M min BH M P , where M min BH is the smallest black hole mass for which we trust semi-classical calculation.
The total jet production cross section in the process pp → jet +BHR(dark matter) at LHC is then given by where σ BH is given by eq. (8). To obtain p T distribution we use d 3 p = 2π dp T p 2 T dy coshy in eq. (7). y is the rapidity.
In our calculation we use CTEQ6M parton distribution functions inside the proton [18].
The number of extra dimensions is chosen to be n = 6 so that we do not rule out the possibility of Planck mass M P = 1 TeV [19]. Since initial mass of the black hole must be greater than the Planck mass we choose M BH i = 5 M P in our calculation. It can be seen from eq. (6) that the black hole remnant mass M min does not depend on the black hole mass but depends on the Planck mass and number of extra dimensions. We find that the typical black hole remnant mass M min = 4.7 TeV for M P = 1 TeV and M min = 9.7 TeV for M P = 2 TeV at LHC.
In Fig. 1 we present the monojet cross section, in the process pp → jet +BHR(dark matter), as a function of initial black hole mass at CERN LHC. This result is for zero impact parameter partonic collisions. The solid line is for Planck mass 1 TeV and the dashed line is for Planck mass 2 TeV. It can be seen that for Planck mass 1 TeV and initial black hole mass 5 TeV the monojet cross section, in the process pp → jet +BHR(dark matter), is 38.5 (pb). This value is much higher than the cross section 18.6 (fb) obtained in other dark matter scenario with dark matter mass ∼ 100 GeV [20]. In our case the dark matter mass (BHR mass) is 4.7 TeV which is much heavier than 100 GeV dark matter mass used in [20]. This is very exciting because we have found a heavier dark matter candidate at LHC with larger cross section. This is due to the fact the temperature of a typical black hole formed at LHC ∼ TeV. Hence jets produced from black holes at such high temperature is large. On the other hand in other dark matter scenarios the jet plus dark matter production is via direct parton collisions and hence the cross section is small. Also unlike [20]  GeV. In our case the cross section is ∼ 40 pb whereas in case of [20] the cross section is 18.6 fb.
In Fig. 2 we present the p T distribution of the jet production cross section, in the process pp → jet +BHR(dark matter), at CERN LHC at √ s = 14 TeV. This result is for zero impact parameter partonic collisions. The solid line is for Planck mass equals to 1 TeV and the dashed line is for Planck mass equal to 2 TeV. It can be seen that dσ dp T of jet, from the process pp → jet +BHR(dark matter), increases as p T increases. This is in contrast to all other dark matter scenarios where dσ dp T decreases as p T increases. This is also in contrast to all standard model processes where dσ dp T decreases as p T increases. This may provide an unique signal for dark matter detection from black hole remnants at the CERN LHC.
In Fig. 3 we present the results which include the impact parameter dependent effect of inelasticity in the cross section (see eq. (9)). We present the monojet cross section, in the process pp → jet +BHR(dark matter), as a function of x min at CERN LHC. The solid line is for Planck mass 1 TeV and the dashed line is for Planck mass 1.5 TeV. The monojet cross section is very small for M P = 2 TeV and hence we do not report it. It can be seen that for Planck mass equal to 1 TeV and x min equals to 5, the monojet cross section, in the process pp → jet +BHR(dark matter), is 10 (fb) which is much smaller than the zero impact parameter case (see Fig. 1). Hence when the impact parameter weighted average of the inelasticity is included, the monojet cross section becomes much smaller than the standard model background and may not be detectable at LHC. In Fig. 4 we present the p T distribution of the cross section which include the impact parameter dependent effect of inelasticity (see eq. (9)). We use x min =5 in our calculation.
The solid line is for Planck mass equals to 1 TeV and the dashed line is for Planck mass equal to 1.5 TeV. The monojet cross section is very small for M P = 2 TeV and hence we do not report it. It can be seen that dσ dp T of jet, from the process pp → jet +BHR(dark matter), increases as p T increases. However, this cross section is much smaller than the standard model background and may not be detectable at LHC. Only for zero impact parameter partonic collisions, the cross section becomes comparable to the standard model predictions (see Fig.2).
To conclude, we have studied dark matter production at CERN LHC from black hole remnants (BHR). We have found that the typical mass of these BHR at LHC is ∼ 5-10 TeV which is heavier than other dark matter candidates such as: axion, axino, neutralino etc. We have proposed the detection of this dark matter via single jet production in the process pp → jet +BHR(dark matter) at CERN LHC. We have found that for zero impact parameter partonic collisions, the monojet cross section is not negligible in comparison to the standard model background and is much higher than the other dark matter scenarios studied so far. We have also found that dσ dp T of jet production in this process increases as p T increases, whereas in all other dark matter scenarios the dσ dp T decreases at CERN LHC. This may provide an useful signature for dark matter detection at LHC. However, we have also shown that when the impact parameter dependent effect of inelasticity is included, the monojet cross section from the above process becomes much smaller than the standard model background and may not be detectable at LHC.